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 | 1.19 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 35.2875 | 1.55950 | 0.779752 | − | 0.626089i | \(-0.215345\pi\) | ||||
0.779752 | + | 0.626089i | \(0.215345\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 733.210 | 1.43205 | ||||||||
\(5\) | 388.913 | 0.278283 | 0.139142 | − | 0.990272i | \(-0.455566\pi\) | ||||
0.139142 | + | 0.990272i | \(0.455566\pi\) | |||||||
\(6\) | 2858.29 | 0.900380 | ||||||||
\(7\) | −2376.48 | −0.374104 | −0.187052 | − | 0.982350i | \(-0.559893\pi\) | ||||
−0.187052 | + | 0.982350i | \(0.559893\pi\) | |||||||
\(8\) | 7805.95 | 0.673784 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 13723.8 | 0.433984 | ||||||||
\(11\) | −88771.9 | −1.82814 | −0.914068 | − | 0.405561i | \(-0.867076\pi\) | ||||
−0.914068 | + | 0.405561i | \(0.867076\pi\) | |||||||
\(12\) | 59390.0 | 0.826795 | ||||||||
\(13\) | −95019.6 | −0.922716 | −0.461358 | − | 0.887214i | \(-0.652638\pi\) | ||||
−0.461358 | + | 0.887214i | \(0.652638\pi\) | |||||||
\(14\) | −83860.1 | −0.583417 | ||||||||
\(15\) | 31501.9 | 0.160667 | ||||||||
\(16\) | −99950.7 | −0.381282 | ||||||||
\(17\) | 444928. | 1.29202 | 0.646011 | − | 0.763328i | \(-0.276436\pi\) | ||||
0.646011 | + | 0.763328i | \(0.276436\pi\) | |||||||
\(18\) | 231521. | 0.519834 | ||||||||
\(19\) | −770917. | −1.35711 | −0.678557 | − | 0.734547i | \(-0.737395\pi\) | ||||
−0.678557 | + | 0.734547i | \(0.737395\pi\) | |||||||
\(20\) | 285155. | 0.398516 | ||||||||
\(21\) | −192495. | −0.215989 | ||||||||
\(22\) | −3.13254e6 | −2.85098 | ||||||||
\(23\) | −766183. | −0.570897 | −0.285448 | − | 0.958394i | \(-0.592142\pi\) | ||||
−0.285448 | + | 0.958394i | \(0.592142\pi\) | |||||||
\(24\) | 632282. | 0.389010 | ||||||||
\(25\) | −1.80187e6 | −0.922558 | ||||||||
\(26\) | −3.35301e6 | −1.43898 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −1.74246e6 | −0.535736 | ||||||||
\(29\) | 3.07733e6 | 0.807947 | 0.403974 | − | 0.914771i | \(-0.367629\pi\) | ||||
0.403974 | + | 0.914771i | \(0.367629\pi\) | |||||||
\(30\) | 1.11163e6 | 0.250561 | ||||||||
\(31\) | −4.59754e6 | −0.894124 | −0.447062 | − | 0.894503i | \(-0.647530\pi\) | ||||
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(32\) | −7.52366e6 | −1.26839 | ||||||||
\(33\) | −7.19053e6 | −1.05548 | ||||||||
\(34\) | 1.57004e7 | 2.01491 | ||||||||
\(35\) | −924243. | −0.104107 | ||||||||
\(36\) | 4.81059e6 | 0.477350 | ||||||||
\(37\) | 8.69434e6 | 0.762657 | 0.381328 | − | 0.924440i | \(-0.375467\pi\) | ||||
0.381328 | + | 0.924440i | \(0.375467\pi\) | |||||||
\(38\) | −2.72038e7 | −2.11643 | ||||||||
\(39\) | −7.69659e6 | −0.532731 | ||||||||
\(40\) | 3.03583e6 | 0.187503 | ||||||||
\(41\) | 3.69424e6 | 0.204173 | 0.102086 | − | 0.994776i | \(-0.467448\pi\) | ||||
0.102086 | + | 0.994776i | \(0.467448\pi\) | |||||||
\(42\) | −6.79267e6 | −0.336836 | ||||||||
\(43\) | −1.75003e7 | −0.780618 | −0.390309 | − | 0.920684i | \(-0.627632\pi\) | ||||
−0.390309 | + | 0.920684i | \(0.627632\pi\) | |||||||
\(44\) | −6.50885e7 | −2.61798 | ||||||||
\(45\) | 2.55166e6 | 0.0927611 | ||||||||
\(46\) | −2.70367e7 | −0.890315 | ||||||||
\(47\) | 3.58402e7 | 1.07135 | 0.535674 | − | 0.844425i | \(-0.320058\pi\) | ||||
0.535674 | + | 0.844425i | \(0.320058\pi\) | |||||||
\(48\) | −8.09601e6 | −0.220133 | ||||||||
\(49\) | −3.47060e7 | −0.860046 | ||||||||
\(50\) | −6.35836e7 | −1.43873 | ||||||||
\(51\) | 3.60392e7 | 0.745949 | ||||||||
\(52\) | −6.96693e7 | −1.32138 | ||||||||
\(53\) | 7.15070e7 | 1.24482 | 0.622411 | − | 0.782690i | \(-0.286153\pi\) | ||||
0.622411 | + | 0.782690i | \(0.286153\pi\) | |||||||
\(54\) | 1.87532e7 | 0.300127 | ||||||||
\(55\) | −3.45245e7 | −0.508740 | ||||||||
\(56\) | −1.85507e7 | −0.252066 | ||||||||
\(57\) | −6.24443e7 | −0.783531 | ||||||||
\(58\) | 1.08591e8 | 1.26000 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 2.30975e7 | 0.230083 | ||||||||
\(61\) | 1.49133e8 | 1.37908 | 0.689542 | − | 0.724246i | \(-0.257812\pi\) | ||||
0.689542 | + | 0.724246i | \(0.257812\pi\) | |||||||
\(62\) | −1.62236e8 | −1.39439 | ||||||||
\(63\) | −1.55921e7 | −0.124701 | ||||||||
\(64\) | −2.14317e8 | −1.59678 | ||||||||
\(65\) | −3.69543e7 | −0.256777 | ||||||||
\(66\) | −2.53736e8 | −1.64602 | ||||||||
\(67\) | −1.05475e8 | −0.639459 | −0.319730 | − | 0.947509i | \(-0.603592\pi\) | ||||
−0.319730 | + | 0.947509i | \(0.603592\pi\) | |||||||
\(68\) | 3.26226e8 | 1.85024 | ||||||||
\(69\) | −6.20608e7 | −0.329607 | ||||||||
\(70\) | −3.26143e7 | −0.162355 | ||||||||
\(71\) | −4.67229e7 | −0.218206 | −0.109103 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109103 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(72\) | 5.12148e7 | 0.224595 | ||||||||
\(73\) | −4.65823e7 | −0.191985 | −0.0959927 | − | 0.995382i | \(-0.530603\pi\) | ||||
−0.0959927 | + | 0.995382i | \(0.530603\pi\) | |||||||
\(74\) | 3.06802e8 | 1.18937 | ||||||||
\(75\) | −1.45952e8 | −0.532639 | ||||||||
\(76\) | −5.65244e8 | −1.94346 | ||||||||
\(77\) | 2.10965e8 | 0.683914 | ||||||||
\(78\) | −2.71594e8 | −0.830795 | ||||||||
\(79\) | 2.64195e8 | 0.763137 | 0.381568 | − | 0.924341i | \(-0.375384\pi\) | ||||
0.381568 | + | 0.924341i | \(0.375384\pi\) | |||||||
\(80\) | −3.88721e7 | −0.106104 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.30361e8 | 0.318408 | ||||||||
\(83\) | −8.34051e8 | −1.92904 | −0.964520 | − | 0.264011i | \(-0.914954\pi\) | ||||
−0.964520 | + | 0.264011i | \(0.914954\pi\) | |||||||
\(84\) | −1.41139e8 | −0.309308 | ||||||||
\(85\) | 1.73038e8 | 0.359548 | ||||||||
\(86\) | −6.17544e8 | −1.21738 | ||||||||
\(87\) | 2.49264e8 | 0.466469 | ||||||||
\(88\) | −6.92949e8 | −1.23177 | ||||||||
\(89\) | 2.19514e8 | 0.370858 | 0.185429 | − | 0.982658i | \(-0.440633\pi\) | ||||
0.185429 | + | 0.982658i | \(0.440633\pi\) | |||||||
\(90\) | 9.00417e7 | 0.144661 | ||||||||
\(91\) | 2.25812e8 | 0.345192 | ||||||||
\(92\) | −5.61773e8 | −0.817553 | ||||||||
\(93\) | −3.72401e8 | −0.516223 | ||||||||
\(94\) | 1.26471e9 | 1.67077 | ||||||||
\(95\) | −2.99820e8 | −0.377662 | ||||||||
\(96\) | −6.09417e8 | −0.732308 | ||||||||
\(97\) | −6.96003e8 | −0.798249 | −0.399124 | − | 0.916897i | \(-0.630686\pi\) | ||||
−0.399124 | + | 0.916897i | \(0.630686\pi\) | |||||||
\(98\) | −1.22469e9 | −1.34124 | ||||||||
\(99\) | −5.82433e8 | −0.609379 | ||||||||
\(100\) | −1.32115e9 | −1.32115 | ||||||||
\(101\) | 1.26703e9 | 1.21155 | 0.605776 | − | 0.795635i | \(-0.292863\pi\) | ||||
0.605776 | + | 0.795635i | \(0.292863\pi\) | |||||||
\(102\) | 1.27173e9 | 1.16331 | ||||||||
\(103\) | −3.05984e8 | −0.267875 | −0.133937 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133937 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(104\) | −7.41718e8 | −0.621712 | ||||||||
\(105\) | −7.48637e7 | −0.0601062 | ||||||||
\(106\) | 2.52331e9 | 1.94130 | ||||||||
\(107\) | −1.88673e9 | −1.39150 | −0.695748 | − | 0.718286i | \(-0.744927\pi\) | ||||
−0.695748 | + | 0.718286i | \(0.744927\pi\) | |||||||
\(108\) | 3.89658e8 | 0.275598 | ||||||||
\(109\) | −4.53422e8 | −0.307669 | −0.153834 | − | 0.988097i | \(-0.549162\pi\) | ||||
−0.153834 | + | 0.988097i | \(0.549162\pi\) | |||||||
\(110\) | −1.21829e9 | −0.793382 | ||||||||
\(111\) | 7.04242e8 | 0.440320 | ||||||||
\(112\) | 2.37531e8 | 0.142639 | ||||||||
\(113\) | −1.03901e9 | −0.599470 | −0.299735 | − | 0.954022i | \(-0.596898\pi\) | ||||
−0.299735 | + | 0.954022i | \(0.596898\pi\) | |||||||
\(114\) | −2.20351e9 | −1.22192 | ||||||||
\(115\) | −2.97978e8 | −0.158871 | ||||||||
\(116\) | 2.25633e9 | 1.15702 | ||||||||
\(117\) | −6.23424e8 | −0.307572 | ||||||||
\(118\) | 4.27592e8 | 0.203030 | ||||||||
\(119\) | −1.05736e9 | −0.483351 | ||||||||
\(120\) | 2.45903e8 | 0.108255 | ||||||||
\(121\) | 5.52251e9 | 2.34208 | ||||||||
\(122\) | 5.26255e9 | 2.15068 | ||||||||
\(123\) | 2.99234e8 | 0.117879 | ||||||||
\(124\) | −3.37096e9 | −1.28043 | ||||||||
\(125\) | −1.46037e9 | −0.535016 | ||||||||
\(126\) | −5.50206e8 | −0.194472 | ||||||||
\(127\) | −1.27717e9 | −0.435644 | −0.217822 | − | 0.975989i | \(-0.569895\pi\) | ||||
−0.217822 | + | 0.975989i | \(0.569895\pi\) | |||||||
\(128\) | −3.71059e9 | −1.22179 | ||||||||
\(129\) | −1.41753e9 | −0.450690 | ||||||||
\(130\) | −1.30403e9 | −0.400444 | ||||||||
\(131\) | 4.28850e9 | 1.27229 | 0.636143 | − | 0.771571i | \(-0.280529\pi\) | ||||
0.636143 | + | 0.771571i | \(0.280529\pi\) | |||||||
\(132\) | −5.27217e9 | −1.51149 | ||||||||
\(133\) | 1.83207e9 | 0.507703 | ||||||||
\(134\) | −3.72195e9 | −0.997238 | ||||||||
\(135\) | 2.06684e8 | 0.0535557 | ||||||||
\(136\) | 3.47309e9 | 0.870544 | ||||||||
\(137\) | −2.80697e9 | −0.680763 | −0.340381 | − | 0.940287i | \(-0.610556\pi\) | ||||
−0.340381 | + | 0.940287i | \(0.610556\pi\) | |||||||
\(138\) | −2.18997e9 | −0.514024 | ||||||||
\(139\) | −5.88780e9 | −1.33778 | −0.668892 | − | 0.743359i | \(-0.733231\pi\) | ||||
−0.668892 | + | 0.743359i | \(0.733231\pi\) | |||||||
\(140\) | −6.77664e8 | −0.149086 | ||||||||
\(141\) | 2.90306e9 | 0.618543 | ||||||||
\(142\) | −1.64873e9 | −0.340293 | ||||||||
\(143\) | 8.43508e9 | 1.68685 | ||||||||
\(144\) | −6.55777e8 | −0.127094 | ||||||||
\(145\) | 1.19681e9 | 0.224838 | ||||||||
\(146\) | −1.64377e9 | −0.299402 | ||||||||
\(147\) | −2.81118e9 | −0.496548 | ||||||||
\(148\) | 6.37478e9 | 1.09216 | ||||||||
\(149\) | 7.38986e9 | 1.22828 | 0.614141 | − | 0.789196i | \(-0.289503\pi\) | ||||
0.614141 | + | 0.789196i | \(0.289503\pi\) | |||||||
\(150\) | −5.15027e9 | −0.830653 | ||||||||
\(151\) | −3.01188e8 | −0.0471456 | −0.0235728 | − | 0.999722i | \(-0.507504\pi\) | ||||
−0.0235728 | + | 0.999722i | \(0.507504\pi\) | |||||||
\(152\) | −6.01774e9 | −0.914403 | ||||||||
\(153\) | 2.91918e9 | 0.430674 | ||||||||
\(154\) | 7.44442e9 | 1.06657 | ||||||||
\(155\) | −1.78804e9 | −0.248820 | ||||||||
\(156\) | −5.64322e9 | −0.762897 | ||||||||
\(157\) | 5.43841e9 | 0.714370 | 0.357185 | − | 0.934034i | \(-0.383737\pi\) | ||||
0.357185 | + | 0.934034i | \(0.383737\pi\) | |||||||
\(158\) | 9.32278e9 | 1.19011 | ||||||||
\(159\) | 5.79207e9 | 0.718699 | ||||||||
\(160\) | −2.92605e9 | −0.352973 | ||||||||
\(161\) | 1.82082e9 | 0.213575 | ||||||||
\(162\) | 1.51901e9 | 0.173278 | ||||||||
\(163\) | −1.08869e10 | −1.20798 | −0.603988 | − | 0.796993i | \(-0.706423\pi\) | ||||
−0.603988 | + | 0.796993i | \(0.706423\pi\) | |||||||
\(164\) | 2.70865e9 | 0.292386 | ||||||||
\(165\) | −2.79649e9 | −0.293721 | ||||||||
\(166\) | −2.94316e10 | −3.00834 | ||||||||
\(167\) | 1.30636e10 | 1.29969 | 0.649845 | − | 0.760066i | \(-0.274834\pi\) | ||||
0.649845 | + | 0.760066i | \(0.274834\pi\) | |||||||
\(168\) | −1.50260e9 | −0.145530 | ||||||||
\(169\) | −1.57577e9 | −0.148595 | ||||||||
\(170\) | 6.10610e9 | 0.560717 | ||||||||
\(171\) | −5.05799e9 | −0.452372 | ||||||||
\(172\) | −1.28314e10 | −1.11788 | ||||||||
\(173\) | 1.81666e10 | 1.54193 | 0.770967 | − | 0.636875i | \(-0.219773\pi\) | ||||
0.770967 | + | 0.636875i | \(0.219773\pi\) | |||||||
\(174\) | 8.79590e9 | 0.727459 | ||||||||
\(175\) | 4.28211e9 | 0.345133 | ||||||||
\(176\) | 8.87282e9 | 0.697035 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 7.74612e9 | 0.578354 | ||||||||
\(179\) | −2.07402e10 | −1.50999 | −0.754995 | − | 0.655731i | \(-0.772361\pi\) | ||||
−0.754995 | + | 0.655731i | \(0.772361\pi\) | |||||||
\(180\) | 1.87090e9 | 0.132839 | ||||||||
\(181\) | −5.49313e9 | −0.380422 | −0.190211 | − | 0.981743i | \(-0.560917\pi\) | ||||
−0.190211 | + | 0.981743i | \(0.560917\pi\) | |||||||
\(182\) | 7.96835e9 | 0.538328 | ||||||||
\(183\) | 1.20798e10 | 0.796214 | ||||||||
\(184\) | −5.98079e9 | −0.384661 | ||||||||
\(185\) | 3.38134e9 | 0.212235 | ||||||||
\(186\) | −1.31411e10 | −0.805051 | ||||||||
\(187\) | −3.94972e10 | −2.36199 | ||||||||
\(188\) | 2.62784e10 | 1.53422 | ||||||||
\(189\) | −1.26296e9 | −0.0719964 | ||||||||
\(190\) | −1.05799e10 | −0.588966 | ||||||||
\(191\) | −2.67154e10 | −1.45248 | −0.726242 | − | 0.687439i | \(-0.758735\pi\) | ||||
−0.726242 | + | 0.687439i | \(0.758735\pi\) | |||||||
\(192\) | −1.73596e10 | −0.921903 | ||||||||
\(193\) | −2.33288e10 | −1.21027 | −0.605137 | − | 0.796121i | \(-0.706882\pi\) | ||||
−0.605137 | + | 0.796121i | \(0.706882\pi\) | |||||||
\(194\) | −2.45602e10 | −1.24487 | ||||||||
\(195\) | −2.99330e9 | −0.148250 | ||||||||
\(196\) | −2.54468e10 | −1.23163 | ||||||||
\(197\) | −3.67488e10 | −1.73838 | −0.869190 | − | 0.494478i | \(-0.835359\pi\) | ||||
−0.869190 | + | 0.494478i | \(0.835359\pi\) | |||||||
\(198\) | −2.05526e10 | −0.950328 | ||||||||
\(199\) | −1.48780e10 | −0.672522 | −0.336261 | − | 0.941769i | \(-0.609162\pi\) | ||||
−0.336261 | + | 0.941769i | \(0.609162\pi\) | |||||||
\(200\) | −1.40653e10 | −0.621605 | ||||||||
\(201\) | −8.54347e9 | −0.369192 | ||||||||
\(202\) | 4.47105e10 | 1.88942 | ||||||||
\(203\) | −7.31321e9 | −0.302257 | ||||||||
\(204\) | 2.64243e10 | 1.06824 | ||||||||
\(205\) | 1.43674e9 | 0.0568179 | ||||||||
\(206\) | −1.07974e10 | −0.417751 | ||||||||
\(207\) | −5.02693e9 | −0.190299 | ||||||||
\(208\) | 9.49728e9 | 0.351815 | ||||||||
\(209\) | 6.84358e10 | 2.48099 | ||||||||
\(210\) | −2.64175e9 | −0.0937358 | ||||||||
\(211\) | 4.69174e10 | 1.62953 | 0.814766 | − | 0.579790i | \(-0.196865\pi\) | ||||
0.814766 | + | 0.579790i | \(0.196865\pi\) | |||||||
\(212\) | 5.24297e10 | 1.78265 | ||||||||
\(213\) | −3.78455e9 | −0.125981 | ||||||||
\(214\) | −6.65779e10 | −2.17004 | ||||||||
\(215\) | −6.80610e9 | −0.217233 | ||||||||
\(216\) | 4.14840e9 | 0.129670 | ||||||||
\(217\) | 1.09259e10 | 0.334496 | ||||||||
\(218\) | −1.60001e10 | −0.479810 | ||||||||
\(219\) | −3.77317e9 | −0.110843 | ||||||||
\(220\) | −2.53137e10 | −0.728541 | ||||||||
\(221\) | −4.22769e10 | −1.19217 | ||||||||
\(222\) | 2.48510e10 | 0.686681 | ||||||||
\(223\) | 1.08667e10 | 0.294256 | 0.147128 | − | 0.989117i | \(-0.452997\pi\) | ||||
0.147128 | + | 0.989117i | \(0.452997\pi\) | |||||||
\(224\) | 1.78798e10 | 0.474512 | ||||||||
\(225\) | −1.18221e10 | −0.307519 | ||||||||
\(226\) | −3.66642e10 | −0.934876 | ||||||||
\(227\) | −1.18817e10 | −0.297005 | −0.148502 | − | 0.988912i | \(-0.547445\pi\) | ||||
−0.148502 | + | 0.988912i | \(0.547445\pi\) | |||||||
\(228\) | −4.57848e10 | −1.12206 | ||||||||
\(229\) | −3.31356e10 | −0.796223 | −0.398111 | − | 0.917337i | \(-0.630334\pi\) | ||||
−0.398111 | + | 0.917337i | \(0.630334\pi\) | |||||||
\(230\) | −1.05149e10 | −0.247760 | ||||||||
\(231\) | 1.70881e10 | 0.394858 | ||||||||
\(232\) | 2.40215e10 | 0.544382 | ||||||||
\(233\) | 7.33018e10 | 1.62934 | 0.814672 | − | 0.579922i | \(-0.196917\pi\) | ||||
0.814672 | + | 0.579922i | \(0.196917\pi\) | |||||||
\(234\) | −2.19991e10 | −0.479660 | ||||||||
\(235\) | 1.39387e10 | 0.298138 | ||||||||
\(236\) | 8.88457e9 | 0.186437 | ||||||||
\(237\) | 2.13998e10 | 0.440597 | ||||||||
\(238\) | −3.73117e10 | −0.753788 | ||||||||
\(239\) | −4.41464e10 | −0.875195 | −0.437597 | − | 0.899171i | \(-0.644170\pi\) | ||||
−0.437597 | + | 0.899171i | \(0.644170\pi\) | |||||||
\(240\) | −3.14864e9 | −0.0612594 | ||||||||
\(241\) | −2.28274e10 | −0.435893 | −0.217946 | − | 0.975961i | \(-0.569936\pi\) | ||||
−0.217946 | + | 0.975961i | \(0.569936\pi\) | |||||||
\(242\) | 1.94876e11 | 3.65249 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 1.09346e11 | 1.97492 | ||||||||
\(245\) | −1.34976e10 | −0.239336 | ||||||||
\(246\) | 1.05592e10 | 0.183833 | ||||||||
\(247\) | 7.32523e10 | 1.25223 | ||||||||
\(248\) | −3.58882e10 | −0.602447 | ||||||||
\(249\) | −6.75581e10 | −1.11373 | ||||||||
\(250\) | −5.15327e10 | −0.834359 | ||||||||
\(251\) | 9.73729e9 | 0.154848 | 0.0774242 | − | 0.996998i | \(-0.475330\pi\) | ||||
0.0774242 | + | 0.996998i | \(0.475330\pi\) | |||||||
\(252\) | −1.14323e10 | −0.178579 | ||||||||
\(253\) | 6.80156e10 | 1.04368 | ||||||||
\(254\) | −4.50681e10 | −0.679388 | ||||||||
\(255\) | 1.40161e10 | 0.207585 | ||||||||
\(256\) | −2.12075e10 | −0.308609 | ||||||||
\(257\) | 1.33586e11 | 1.91012 | 0.955061 | − | 0.296410i | \(-0.0957896\pi\) | ||||
0.955061 | + | 0.296410i | \(0.0957896\pi\) | |||||||
\(258\) | −5.00210e10 | −0.702852 | ||||||||
\(259\) | −2.06619e10 | −0.285313 | ||||||||
\(260\) | −2.70953e10 | −0.367717 | ||||||||
\(261\) | 2.01904e10 | 0.269316 | ||||||||
\(262\) | 1.51331e11 | 1.98413 | ||||||||
\(263\) | 1.31485e11 | 1.69463 | 0.847314 | − | 0.531092i | \(-0.178218\pi\) | ||||
0.847314 | + | 0.531092i | \(0.178218\pi\) | |||||||
\(264\) | −5.61289e10 | −0.711162 | ||||||||
\(265\) | 2.78100e10 | 0.346413 | ||||||||
\(266\) | 6.46492e10 | 0.791764 | ||||||||
\(267\) | 1.77807e10 | 0.214115 | ||||||||
\(268\) | −7.73353e10 | −0.915738 | ||||||||
\(269\) | 1.01003e11 | 1.17612 | 0.588058 | − | 0.808819i | \(-0.299893\pi\) | ||||
0.588058 | + | 0.808819i | \(0.299893\pi\) | |||||||
\(270\) | 7.29338e9 | 0.0835202 | ||||||||
\(271\) | 7.61574e10 | 0.857730 | 0.428865 | − | 0.903369i | \(-0.358914\pi\) | ||||
0.428865 | + | 0.903369i | \(0.358914\pi\) | |||||||
\(272\) | −4.44709e10 | −0.492625 | ||||||||
\(273\) | 1.82908e10 | 0.199297 | ||||||||
\(274\) | −9.90512e10 | −1.06165 | ||||||||
\(275\) | 1.59956e11 | 1.68656 | ||||||||
\(276\) | −4.55036e10 | −0.472014 | ||||||||
\(277\) | 3.71033e10 | 0.378664 | 0.189332 | − | 0.981913i | \(-0.439368\pi\) | ||||
0.189332 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(278\) | −2.07766e11 | −2.08628 | ||||||||
\(279\) | −3.01644e10 | −0.298041 | ||||||||
\(280\) | −7.21459e9 | −0.0701457 | ||||||||
\(281\) | −8.14367e10 | −0.779187 | −0.389593 | − | 0.920987i | \(-0.627384\pi\) | ||||
−0.389593 | + | 0.920987i | \(0.627384\pi\) | |||||||
\(282\) | 1.02442e11 | 0.964619 | ||||||||
\(283\) | −3.03484e9 | −0.0281253 | −0.0140627 | − | 0.999901i | \(-0.504476\pi\) | ||||
−0.0140627 | + | 0.999901i | \(0.504476\pi\) | |||||||
\(284\) | −3.42577e10 | −0.312482 | ||||||||
\(285\) | −2.42854e10 | −0.218044 | ||||||||
\(286\) | 2.97653e11 | 2.63065 | ||||||||
\(287\) | −8.77929e9 | −0.0763819 | ||||||||
\(288\) | −4.93627e10 | −0.422798 | ||||||||
\(289\) | 7.93734e10 | 0.669321 | ||||||||
\(290\) | 4.22326e10 | 0.350636 | ||||||||
\(291\) | −5.63762e10 | −0.460869 | ||||||||
\(292\) | −3.41546e10 | −0.274933 | ||||||||
\(293\) | 1.24746e11 | 0.988835 | 0.494417 | − | 0.869225i | \(-0.335381\pi\) | ||||
0.494417 | + | 0.869225i | \(0.335381\pi\) | |||||||
\(294\) | −9.91997e10 | −0.774368 | ||||||||
\(295\) | 4.71260e9 | 0.0362294 | ||||||||
\(296\) | 6.78676e10 | 0.513866 | ||||||||
\(297\) | −4.71770e10 | −0.351825 | ||||||||
\(298\) | 2.60770e11 | 1.91551 | ||||||||
\(299\) | 7.28024e10 | 0.526776 | ||||||||
\(300\) | −1.07013e11 | −0.762766 | ||||||||
\(301\) | 4.15892e10 | 0.292032 | ||||||||
\(302\) | −1.06282e10 | −0.0735237 | ||||||||
\(303\) | 1.02630e11 | 0.699490 | ||||||||
\(304\) | 7.70538e10 | 0.517443 | ||||||||
\(305\) | 5.79999e10 | 0.383776 | ||||||||
\(306\) | 1.03010e11 | 0.671638 | ||||||||
\(307\) | −2.13327e11 | −1.37064 | −0.685318 | − | 0.728244i | \(-0.740337\pi\) | ||||
−0.685318 | + | 0.728244i | \(0.740337\pi\) | |||||||
\(308\) | 1.54681e11 | 0.979399 | ||||||||
\(309\) | −2.47847e10 | −0.154658 | ||||||||
\(310\) | −6.30956e10 | −0.388035 | ||||||||
\(311\) | −3.12533e10 | −0.189441 | −0.0947205 | − | 0.995504i | \(-0.530196\pi\) | ||||
−0.0947205 | + | 0.995504i | \(0.530196\pi\) | |||||||
\(312\) | −6.00792e10 | −0.358945 | ||||||||
\(313\) | −1.74897e11 | −1.02999 | −0.514995 | − | 0.857193i | \(-0.672206\pi\) | ||||
−0.514995 | + | 0.857193i | \(0.672206\pi\) | |||||||
\(314\) | 1.91908e11 | 1.11406 | ||||||||
\(315\) | −6.06396e9 | −0.0347023 | ||||||||
\(316\) | 1.93710e11 | 1.09285 | ||||||||
\(317\) | 1.30476e11 | 0.725709 | 0.362855 | − | 0.931846i | \(-0.381802\pi\) | ||||
0.362855 | + | 0.931846i | \(0.381802\pi\) | |||||||
\(318\) | 2.04388e11 | 1.12081 | ||||||||
\(319\) | −2.73181e11 | −1.47704 | ||||||||
\(320\) | −8.33505e10 | −0.444358 | ||||||||
\(321\) | −1.52825e11 | −0.803380 | ||||||||
\(322\) | 6.42522e10 | 0.333071 | ||||||||
\(323\) | −3.43003e11 | −1.75342 | ||||||||
\(324\) | 3.15623e10 | 0.159117 | ||||||||
\(325\) | 1.71213e11 | 0.851260 | ||||||||
\(326\) | −3.84171e11 | −1.88384 | ||||||||
\(327\) | −3.67272e10 | −0.177632 | ||||||||
\(328\) | 2.88371e10 | 0.137568 | ||||||||
\(329\) | −8.51735e10 | −0.400796 | ||||||||
\(330\) | −9.86811e10 | −0.458059 | ||||||||
\(331\) | 3.15453e11 | 1.44447 | 0.722236 | − | 0.691647i | \(-0.243114\pi\) | ||||
0.722236 | + | 0.691647i | \(0.243114\pi\) | |||||||
\(332\) | −6.11534e11 | −2.76248 | ||||||||
\(333\) | 5.70436e10 | 0.254219 | ||||||||
\(334\) | 4.60984e11 | 2.02687 | ||||||||
\(335\) | −4.10206e10 | −0.177951 | ||||||||
\(336\) | 1.92400e10 | 0.0823528 | ||||||||
\(337\) | 3.13163e11 | 1.32262 | 0.661311 | − | 0.750112i | \(-0.270000\pi\) | ||||
0.661311 | + | 0.750112i | \(0.270000\pi\) | |||||||
\(338\) | −5.56051e10 | −0.231734 | ||||||||
\(339\) | −8.41600e10 | −0.346104 | ||||||||
\(340\) | 1.26873e11 | 0.514891 | ||||||||
\(341\) | 4.08132e11 | 1.63458 | ||||||||
\(342\) | −1.78484e11 | −0.705475 | ||||||||
\(343\) | 1.78377e11 | 0.695851 | ||||||||
\(344\) | −1.36607e11 | −0.525968 | ||||||||
\(345\) | −2.41363e10 | −0.0917242 | ||||||||
\(346\) | 6.41054e11 | 2.40465 | ||||||||
\(347\) | −1.66053e11 | −0.614844 | −0.307422 | − | 0.951573i | \(-0.599466\pi\) | ||||
−0.307422 | + | 0.951573i | \(0.599466\pi\) | |||||||
\(348\) | 1.82763e11 | 0.668007 | ||||||||
\(349\) | −2.49063e11 | −0.898659 | −0.449329 | − | 0.893366i | \(-0.648337\pi\) | ||||
−0.449329 | + | 0.893366i | \(0.648337\pi\) | |||||||
\(350\) | 1.51105e11 | 0.538236 | ||||||||
\(351\) | −5.04973e10 | −0.177577 | ||||||||
\(352\) | 6.67890e11 | 2.31880 | ||||||||
\(353\) | 2.16105e11 | 0.740762 | 0.370381 | − | 0.928880i | \(-0.379227\pi\) | ||||
0.370381 | + | 0.928880i | \(0.379227\pi\) | |||||||
\(354\) | 3.46349e10 | 0.117219 | ||||||||
\(355\) | −1.81711e10 | −0.0607231 | ||||||||
\(356\) | 1.60950e11 | 0.531087 | ||||||||
\(357\) | −8.56464e10 | −0.279063 | ||||||||
\(358\) | −7.31870e11 | −2.35483 | ||||||||
\(359\) | −3.36268e11 | −1.06846 | −0.534232 | − | 0.845338i | \(-0.679399\pi\) | ||||
−0.534232 | + | 0.845338i | \(0.679399\pi\) | |||||||
\(360\) | 1.99181e10 | 0.0625010 | ||||||||
\(361\) | 2.71626e11 | 0.841761 | ||||||||
\(362\) | −1.93839e11 | −0.593270 | ||||||||
\(363\) | 4.47323e11 | 1.35220 | ||||||||
\(364\) | 1.65568e11 | 0.494333 | ||||||||
\(365\) | −1.81165e10 | −0.0534263 | ||||||||
\(366\) | 4.26266e11 | 1.24170 | ||||||||
\(367\) | 4.49802e11 | 1.29427 | 0.647134 | − | 0.762377i | \(-0.275968\pi\) | ||||
0.647134 | + | 0.762377i | \(0.275968\pi\) | |||||||
\(368\) | 7.65806e10 | 0.217672 | ||||||||
\(369\) | 2.42379e10 | 0.0680576 | ||||||||
\(370\) | 1.19319e11 | 0.330981 | ||||||||
\(371\) | −1.69935e11 | −0.465693 | ||||||||
\(372\) | −2.73048e11 | −0.739257 | ||||||||
\(373\) | −1.71165e11 | −0.457852 | −0.228926 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228926 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(374\) | −1.39376e12 | −3.68354 | ||||||||
\(375\) | −1.18290e11 | −0.308892 | ||||||||
\(376\) | 2.79767e11 | 0.721857 | ||||||||
\(377\) | −2.92407e11 | −0.745506 | ||||||||
\(378\) | −4.45667e10 | −0.112279 | ||||||||
\(379\) | 2.37121e11 | 0.590329 | 0.295164 | − | 0.955447i | \(-0.404626\pi\) | ||||
0.295164 | + | 0.955447i | \(0.404626\pi\) | |||||||
\(380\) | −2.19831e11 | −0.540832 | ||||||||
\(381\) | −1.03451e11 | −0.251519 | ||||||||
\(382\) | −9.42720e11 | −2.26515 | ||||||||
\(383\) | −4.26137e11 | −1.01194 | −0.505970 | − | 0.862551i | \(-0.668865\pi\) | ||||
−0.505970 | + | 0.862551i | \(0.668865\pi\) | |||||||
\(384\) | −3.00558e11 | −0.705404 | ||||||||
\(385\) | 8.20468e10 | 0.190322 | ||||||||
\(386\) | −8.23214e11 | −1.88743 | ||||||||
\(387\) | −1.14820e11 | −0.260206 | ||||||||
\(388\) | −5.10316e11 | −1.14313 | ||||||||
\(389\) | −4.49580e11 | −0.995484 | −0.497742 | − | 0.867325i | \(-0.665837\pi\) | ||||
−0.497742 | + | 0.867325i | \(0.665837\pi\) | |||||||
\(390\) | −1.05626e11 | −0.231196 | ||||||||
\(391\) | −3.40897e11 | −0.737611 | ||||||||
\(392\) | −2.70913e11 | −0.579485 | ||||||||
\(393\) | 3.47368e11 | 0.734554 | ||||||||
\(394\) | −1.29677e12 | −2.71101 | ||||||||
\(395\) | 1.02749e11 | 0.212368 | ||||||||
\(396\) | −4.27045e11 | −0.872661 | ||||||||
\(397\) | −4.70283e11 | −0.950172 | −0.475086 | − | 0.879939i | \(-0.657583\pi\) | ||||
−0.475086 | + | 0.879939i | \(0.657583\pi\) | |||||||
\(398\) | −5.25009e11 | −1.04880 | ||||||||
\(399\) | 1.48398e11 | 0.293122 | ||||||||
\(400\) | 1.80098e11 | 0.351755 | ||||||||
\(401\) | −2.57893e10 | −0.0498070 | −0.0249035 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249035 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(402\) | −3.01478e11 | −0.575756 | ||||||||
\(403\) | 4.36856e11 | 0.825023 | ||||||||
\(404\) | 9.29002e11 | 1.73500 | ||||||||
\(405\) | 1.67414e10 | 0.0309204 | ||||||||
\(406\) | −2.58065e11 | −0.471370 | ||||||||
\(407\) | −7.71814e11 | −1.39424 | ||||||||
\(408\) | 2.81320e11 | 0.502609 | ||||||||
\(409\) | −6.37794e11 | −1.12700 | −0.563502 | − | 0.826115i | \(-0.690546\pi\) | ||||
−0.563502 | + | 0.826115i | \(0.690546\pi\) | |||||||
\(410\) | 5.06989e10 | 0.0886077 | ||||||||
\(411\) | −2.27365e11 | −0.393039 | ||||||||
\(412\) | −2.24351e11 | −0.383610 | ||||||||
\(413\) | −2.87966e10 | −0.0487042 | ||||||||
\(414\) | −1.77388e11 | −0.296772 | ||||||||
\(415\) | −3.24373e11 | −0.536819 | ||||||||
\(416\) | 7.14895e11 | 1.17037 | ||||||||
\(417\) | −4.76912e11 | −0.772370 | ||||||||
\(418\) | 2.41493e12 | 3.86911 | ||||||||
\(419\) | 4.40211e11 | 0.697746 | 0.348873 | − | 0.937170i | \(-0.386564\pi\) | ||||
0.348873 | + | 0.937170i | \(0.386564\pi\) | |||||||
\(420\) | −5.48908e10 | −0.0860751 | ||||||||
\(421\) | −8.51162e11 | −1.32051 | −0.660257 | − | 0.751040i | \(-0.729553\pi\) | ||||
−0.660257 | + | 0.751040i | \(0.729553\pi\) | |||||||
\(422\) | 1.65560e12 | 2.54126 | ||||||||
\(423\) | 2.35148e11 | 0.357116 | ||||||||
\(424\) | 5.58180e11 | 0.838742 | ||||||||
\(425\) | −8.01704e11 | −1.19197 | ||||||||
\(426\) | −1.33547e11 | −0.196468 | ||||||||
\(427\) | −3.54412e11 | −0.515921 | ||||||||
\(428\) | −1.38337e12 | −1.99269 | ||||||||
\(429\) | 6.83241e11 | 0.973904 | ||||||||
\(430\) | −2.40171e11 | −0.338775 | ||||||||
\(431\) | −6.20060e11 | −0.865538 | −0.432769 | − | 0.901505i | \(-0.642463\pi\) | ||||
−0.432769 | + | 0.901505i | \(0.642463\pi\) | |||||||
\(432\) | −5.31179e10 | −0.0733777 | ||||||||
\(433\) | 8.37180e11 | 1.14452 | 0.572260 | − | 0.820072i | \(-0.306067\pi\) | ||||
0.572260 | + | 0.820072i | \(0.306067\pi\) | |||||||
\(434\) | 3.85550e11 | 0.521647 | ||||||||
\(435\) | 9.69419e10 | 0.129810 | ||||||||
\(436\) | −3.32453e11 | −0.440597 | ||||||||
\(437\) | 5.90664e11 | 0.774772 | ||||||||
\(438\) | −1.33146e11 | −0.172860 | ||||||||
\(439\) | 7.66484e11 | 0.984947 | 0.492474 | − | 0.870327i | \(-0.336093\pi\) | ||||
0.492474 | + | 0.870327i | \(0.336093\pi\) | |||||||
\(440\) | −2.69497e11 | −0.342781 | ||||||||
\(441\) | −2.27706e11 | −0.286682 | ||||||||
\(442\) | −1.49185e12 | −1.85919 | ||||||||
\(443\) | −1.30219e12 | −1.60642 | −0.803209 | − | 0.595698i | \(-0.796876\pi\) | ||||
−0.803209 | + | 0.595698i | \(0.796876\pi\) | |||||||
\(444\) | 5.16357e11 | 0.630561 | ||||||||
\(445\) | 8.53719e10 | 0.103204 | ||||||||
\(446\) | 3.83459e11 | 0.458894 | ||||||||
\(447\) | 5.98579e11 | 0.709149 | ||||||||
\(448\) | 5.09319e11 | 0.597364 | ||||||||
\(449\) | −1.53372e12 | −1.78089 | −0.890446 | − | 0.455089i | \(-0.849608\pi\) | ||||
−0.890446 | + | 0.455089i | \(0.849608\pi\) | |||||||
\(450\) | −4.17172e11 | −0.479578 | ||||||||
\(451\) | −3.27945e11 | −0.373256 | ||||||||
\(452\) | −7.61814e11 | −0.858471 | ||||||||
\(453\) | −2.43962e10 | −0.0272195 | ||||||||
\(454\) | −4.19277e11 | −0.463180 | ||||||||
\(455\) | 8.78212e10 | 0.0960612 | ||||||||
\(456\) | −4.87437e11 | −0.527931 | ||||||||
\(457\) | −4.73372e11 | −0.507668 | −0.253834 | − | 0.967248i | \(-0.581692\pi\) | ||||
−0.253834 | + | 0.967248i | \(0.581692\pi\) | |||||||
\(458\) | −1.16927e12 | −1.24171 | ||||||||
\(459\) | 2.36453e11 | 0.248650 | ||||||||
\(460\) | −2.18481e11 | −0.227511 | ||||||||
\(461\) | −5.55441e11 | −0.572774 | −0.286387 | − | 0.958114i | \(-0.592454\pi\) | ||||
−0.286387 | + | 0.958114i | \(0.592454\pi\) | |||||||
\(462\) | 6.02998e11 | 0.615782 | ||||||||
\(463\) | 1.00553e12 | 1.01690 | 0.508452 | − | 0.861090i | \(-0.330218\pi\) | ||||
0.508452 | + | 0.861090i | \(0.330218\pi\) | |||||||
\(464\) | −3.07581e11 | −0.308056 | ||||||||
\(465\) | −1.44831e11 | −0.143656 | ||||||||
\(466\) | 2.58664e12 | 2.54097 | ||||||||
\(467\) | 9.53952e11 | 0.928112 | 0.464056 | − | 0.885806i | \(-0.346394\pi\) | ||||
0.464056 | + | 0.885806i | \(0.346394\pi\) | |||||||
\(468\) | −4.57100e11 | −0.440459 | ||||||||
\(469\) | 2.50659e11 | 0.239224 | ||||||||
\(470\) | 4.91863e11 | 0.464947 | ||||||||
\(471\) | 4.40511e11 | 0.412442 | ||||||||
\(472\) | 9.45875e10 | 0.0877192 | ||||||||
\(473\) | 1.55354e12 | 1.42708 | ||||||||
\(474\) | 7.55145e11 | 0.687113 | ||||||||
\(475\) | 1.38909e12 | 1.25202 | ||||||||
\(476\) | −7.75269e11 | −0.692183 | ||||||||
\(477\) | 4.69158e11 | 0.414941 | ||||||||
\(478\) | −1.55782e12 | −1.36487 | ||||||||
\(479\) | −1.56392e12 | −1.35739 | −0.678696 | − | 0.734419i | \(-0.737455\pi\) | ||||
−0.678696 | + | 0.734419i | \(0.737455\pi\) | |||||||
\(480\) | −2.37010e11 | −0.203789 | ||||||||
\(481\) | −8.26133e11 | −0.703716 | ||||||||
\(482\) | −8.05522e11 | −0.679776 | ||||||||
\(483\) | 1.47486e11 | 0.123308 | ||||||||
\(484\) | 4.04916e12 | 3.35398 | ||||||||
\(485\) | −2.70684e11 | −0.222139 | ||||||||
\(486\) | 1.23040e11 | 0.100042 | ||||||||
\(487\) | −1.90185e12 | −1.53213 | −0.766065 | − | 0.642763i | \(-0.777788\pi\) | ||||
−0.766065 | + | 0.642763i | \(0.777788\pi\) | |||||||
\(488\) | 1.16413e12 | 0.929205 | ||||||||
\(489\) | −8.81836e11 | −0.697426 | ||||||||
\(490\) | −4.76297e11 | −0.373246 | ||||||||
\(491\) | −1.22015e12 | −0.947428 | −0.473714 | − | 0.880679i | \(-0.657087\pi\) | ||||
−0.473714 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(492\) | 2.19401e11 | 0.168809 | ||||||||
\(493\) | 1.36919e12 | 1.04389 | ||||||||
\(494\) | 2.58489e12 | 1.95286 | ||||||||
\(495\) | −2.26516e11 | −0.169580 | ||||||||
\(496\) | 4.59527e11 | 0.340913 | ||||||||
\(497\) | 1.11036e11 | 0.0816318 | ||||||||
\(498\) | −2.38396e12 | −1.73687 | ||||||||
\(499\) | 6.90463e11 | 0.498526 | 0.249263 | − | 0.968436i | \(-0.419812\pi\) | ||||
0.249263 | + | 0.968436i | \(0.419812\pi\) | |||||||
\(500\) | −1.07076e12 | −0.766170 | ||||||||
\(501\) | 1.05815e12 | 0.750377 | ||||||||
\(502\) | 3.43605e11 | 0.241486 | ||||||||
\(503\) | 2.00172e12 | 1.39427 | 0.697135 | − | 0.716940i | \(-0.254458\pi\) | ||||
0.697135 | + | 0.716940i | \(0.254458\pi\) | |||||||
\(504\) | −1.21711e11 | −0.0840219 | ||||||||
\(505\) | 4.92766e11 | 0.337155 | ||||||||
\(506\) | 2.40010e12 | 1.62762 | ||||||||
\(507\) | −1.27637e11 | −0.0857911 | ||||||||
\(508\) | −9.36433e11 | −0.623864 | ||||||||
\(509\) | −4.83312e11 | −0.319152 | −0.159576 | − | 0.987186i | \(-0.551013\pi\) | ||||
−0.159576 | + | 0.987186i | \(0.551013\pi\) | |||||||
\(510\) | 4.94594e11 | 0.323730 | ||||||||
\(511\) | 1.10702e11 | 0.0718225 | ||||||||
\(512\) | 1.15146e12 | 0.740517 | ||||||||
\(513\) | −4.09697e11 | −0.261177 | ||||||||
\(514\) | 4.71391e12 | 2.97884 | ||||||||
\(515\) | −1.19001e11 | −0.0745451 | ||||||||
\(516\) | −1.03935e12 | −0.645411 | ||||||||
\(517\) | −3.18161e12 | −1.95857 | ||||||||
\(518\) | −7.29108e11 | −0.444947 | ||||||||
\(519\) | 1.47149e12 | 0.890236 | ||||||||
\(520\) | −2.88464e11 | −0.173012 | ||||||||
\(521\) | −1.07336e12 | −0.638230 | −0.319115 | − | 0.947716i | \(-0.603386\pi\) | ||||
−0.319115 | + | 0.947716i | \(0.603386\pi\) | |||||||
\(522\) | 7.12468e11 | 0.419999 | ||||||||
\(523\) | 2.32758e12 | 1.36034 | 0.680169 | − | 0.733056i | \(-0.261907\pi\) | ||||
0.680169 | + | 0.733056i | \(0.261907\pi\) | |||||||
\(524\) | 3.14437e12 | 1.82198 | ||||||||
\(525\) | 3.46851e11 | 0.199263 | ||||||||
\(526\) | 4.63977e12 | 2.64278 | ||||||||
\(527\) | −2.04558e12 | −1.15523 | ||||||||
\(528\) | 7.18698e11 | 0.402433 | ||||||||
\(529\) | −1.21412e12 | −0.674077 | ||||||||
\(530\) | 9.81346e11 | 0.540233 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 1.34329e12 | 0.727056 | ||||||||
\(533\) | −3.51025e11 | −0.188394 | ||||||||
\(534\) | 6.27435e11 | 0.333913 | ||||||||
\(535\) | −7.33772e11 | −0.387230 | ||||||||
\(536\) | −8.23332e11 | −0.430857 | ||||||||
\(537\) | −1.67995e12 | −0.871793 | ||||||||
\(538\) | 3.56416e12 | 1.83416 | ||||||||
\(539\) | 3.08091e12 | 1.57228 | ||||||||
\(540\) | 1.51543e11 | 0.0766944 | ||||||||
\(541\) | −2.13813e11 | −0.107312 | −0.0536558 | − | 0.998559i | \(-0.517087\pi\) | ||||
−0.0536558 | + | 0.998559i | \(0.517087\pi\) | |||||||
\(542\) | 2.68741e12 | 1.33763 | ||||||||
\(543\) | −4.44943e11 | −0.219637 | ||||||||
\(544\) | −3.34749e12 | −1.63879 | ||||||||
\(545\) | −1.76341e11 | −0.0856190 | ||||||||
\(546\) | 6.45436e11 | 0.310804 | ||||||||
\(547\) | −2.35000e12 | −1.12234 | −0.561170 | − | 0.827701i | \(-0.689649\pi\) | ||||
−0.561170 | + | 0.827701i | \(0.689649\pi\) | |||||||
\(548\) | −2.05810e12 | −0.974887 | ||||||||
\(549\) | 9.78464e11 | 0.459694 | ||||||||
\(550\) | 5.64444e12 | 2.63020 | ||||||||
\(551\) | −2.37237e12 | −1.09648 | ||||||||
\(552\) | −4.84444e11 | −0.222084 | ||||||||
\(553\) | −6.27853e11 | −0.285493 | ||||||||
\(554\) | 1.30928e12 | 0.590528 | ||||||||
\(555\) | 2.73889e11 | 0.122534 | ||||||||
\(556\) | −4.31699e12 | −1.91578 | ||||||||
\(557\) | −3.02608e12 | −1.33209 | −0.666044 | − | 0.745913i | \(-0.732014\pi\) | ||||
−0.666044 | + | 0.745913i | \(0.732014\pi\) | |||||||
\(558\) | −1.06443e12 | −0.464796 | ||||||||
\(559\) | 1.66288e12 | 0.720289 | ||||||||
\(560\) | 9.23788e10 | 0.0396941 | ||||||||
\(561\) | −3.19927e12 | −1.36370 | ||||||||
\(562\) | −2.87370e12 | −1.21514 | ||||||||
\(563\) | −1.05199e12 | −0.441291 | −0.220645 | − | 0.975354i | \(-0.570816\pi\) | ||||
−0.220645 | + | 0.975354i | \(0.570816\pi\) | |||||||
\(564\) | 2.12855e12 | 0.885785 | ||||||||
\(565\) | −4.04085e11 | −0.166823 | ||||||||
\(566\) | −1.07092e11 | −0.0438615 | ||||||||
\(567\) | −1.02300e11 | −0.0415671 | ||||||||
\(568\) | −3.64716e11 | −0.147024 | ||||||||
\(569\) | −2.24721e12 | −0.898751 | −0.449375 | − | 0.893343i | \(-0.648353\pi\) | ||||
−0.449375 | + | 0.893343i | \(0.648353\pi\) | |||||||
\(570\) | −8.56971e11 | −0.340040 | ||||||||
\(571\) | 3.88739e12 | 1.53037 | 0.765183 | − | 0.643813i | \(-0.222649\pi\) | ||||
0.765183 | + | 0.643813i | \(0.222649\pi\) | |||||||
\(572\) | 6.18468e12 | 2.41566 | ||||||||
\(573\) | −2.16395e12 | −0.838592 | ||||||||
\(574\) | −3.09799e11 | −0.119118 | ||||||||
\(575\) | 1.38056e12 | 0.526685 | ||||||||
\(576\) | −1.40613e12 | −0.532261 | ||||||||
\(577\) | −5.00381e12 | −1.87936 | −0.939679 | − | 0.342057i | \(-0.888876\pi\) | ||||
−0.939679 | + | 0.342057i | \(0.888876\pi\) | |||||||
\(578\) | 2.80089e12 | 1.04381 | ||||||||
\(579\) | −1.88963e12 | −0.698752 | ||||||||
\(580\) | 8.77515e11 | 0.321980 | ||||||||
\(581\) | 1.98210e12 | 0.721662 | ||||||||
\(582\) | −1.98938e12 | −0.718727 | ||||||||
\(583\) | −6.34782e12 | −2.27570 | ||||||||
\(584\) | −3.63619e11 | −0.129357 | ||||||||
\(585\) | −2.42457e11 | −0.0855922 | ||||||||
\(586\) | 4.40199e12 | 1.54209 | ||||||||
\(587\) | −1.72176e12 | −0.598552 | −0.299276 | − | 0.954167i | \(-0.596745\pi\) | ||||
−0.299276 | + | 0.954167i | \(0.596745\pi\) | |||||||
\(588\) | −2.06119e12 | −0.711081 | ||||||||
\(589\) | 3.54432e12 | 1.21343 | ||||||||
\(590\) | 1.66296e11 | 0.0564999 | ||||||||
\(591\) | −2.97665e12 | −1.00365 | ||||||||
\(592\) | −8.69006e11 | −0.290787 | ||||||||
\(593\) | −3.09332e12 | −1.02726 | −0.513628 | − | 0.858013i | \(-0.671699\pi\) | ||||
−0.513628 | + | 0.858013i | \(0.671699\pi\) | |||||||
\(594\) | −1.66476e12 | −0.548672 | ||||||||
\(595\) | −4.11222e11 | −0.134509 | ||||||||
\(596\) | 5.41832e12 | 1.75896 | ||||||||
\(597\) | −1.20512e12 | −0.388281 | ||||||||
\(598\) | 2.56902e12 | 0.821508 | ||||||||
\(599\) | −5.51356e12 | −1.74989 | −0.874947 | − | 0.484219i | \(-0.839104\pi\) | ||||
−0.874947 | + | 0.484219i | \(0.839104\pi\) | |||||||
\(600\) | −1.13929e12 | −0.358884 | ||||||||
\(601\) | −2.07713e12 | −0.649424 | −0.324712 | − | 0.945813i | \(-0.605267\pi\) | ||||
−0.324712 | + | 0.945813i | \(0.605267\pi\) | |||||||
\(602\) | 1.46758e12 | 0.455426 | ||||||||
\(603\) | −6.92021e11 | −0.213153 | ||||||||
\(604\) | −2.20834e11 | −0.0675149 | ||||||||
\(605\) | 2.14777e12 | 0.651763 | ||||||||
\(606\) | 3.62155e12 | 1.09086 | ||||||||
\(607\) | −3.23861e12 | −0.968299 | −0.484149 | − | 0.874985i | \(-0.660871\pi\) | ||||
−0.484149 | + | 0.874985i | \(0.660871\pi\) | |||||||
\(608\) | 5.80012e12 | 1.72136 | ||||||||
\(609\) | −5.92370e11 | −0.174508 | ||||||||
\(610\) | 2.04667e12 | 0.598500 | ||||||||
\(611\) | −3.40552e12 | −0.988550 | ||||||||
\(612\) | 2.14037e12 | 0.616747 | ||||||||
\(613\) | −4.38376e11 | −0.125393 | −0.0626967 | − | 0.998033i | \(-0.519970\pi\) | ||||
−0.0626967 | + | 0.998033i | \(0.519970\pi\) | |||||||
\(614\) | −7.52777e12 | −2.13751 | ||||||||
\(615\) | 1.16376e11 | 0.0328038 | ||||||||
\(616\) | 1.64678e12 | 0.460810 | ||||||||
\(617\) | −1.81189e12 | −0.503324 | −0.251662 | − | 0.967815i | \(-0.580977\pi\) | ||||
−0.251662 | + | 0.967815i | \(0.580977\pi\) | |||||||
\(618\) | −8.74592e11 | −0.241189 | ||||||||
\(619\) | −1.52091e12 | −0.416386 | −0.208193 | − | 0.978088i | \(-0.566758\pi\) | ||||
−0.208193 | + | 0.978088i | \(0.566758\pi\) | |||||||
\(620\) | −1.31101e12 | −0.356322 | ||||||||
\(621\) | −4.07181e11 | −0.109869 | ||||||||
\(622\) | −1.10285e12 | −0.295434 | ||||||||
\(623\) | −5.21671e11 | −0.138740 | ||||||||
\(624\) | 7.69280e11 | 0.203120 | ||||||||
\(625\) | 2.95133e12 | 0.773672 | ||||||||
\(626\) | −6.17169e12 | −1.60627 | ||||||||
\(627\) | 5.54330e12 | 1.43240 | ||||||||
\(628\) | 3.98749e12 | 1.02301 | ||||||||
\(629\) | 3.86836e12 | 0.985369 | ||||||||
\(630\) | −2.13982e11 | −0.0541184 | ||||||||
\(631\) | −1.89271e12 | −0.475283 | −0.237641 | − | 0.971353i | \(-0.576374\pi\) | ||||
−0.237641 | + | 0.971353i | \(0.576374\pi\) | |||||||
\(632\) | 2.06229e12 | 0.514189 | ||||||||
\(633\) | 3.80031e12 | 0.940811 | ||||||||
\(634\) | 4.60416e12 | 1.13175 | ||||||||
\(635\) | −4.96707e11 | −0.121232 | ||||||||
\(636\) | 4.24680e12 | 1.02921 | ||||||||
\(637\) | 3.29775e12 | 0.793578 | ||||||||
\(638\) | −9.63987e12 | −2.30345 | ||||||||
\(639\) | −3.06549e11 | −0.0727354 | ||||||||
\(640\) | −1.44310e12 | −0.340005 | ||||||||
\(641\) | −1.16060e12 | −0.271533 | −0.135767 | − | 0.990741i | \(-0.543350\pi\) | ||||
−0.135767 | + | 0.990741i | \(0.543350\pi\) | |||||||
\(642\) | −5.39281e12 | −1.25287 | ||||||||
\(643\) | 6.78316e12 | 1.56488 | 0.782442 | − | 0.622723i | \(-0.213974\pi\) | ||||
0.782442 | + | 0.622723i | \(0.213974\pi\) | |||||||
\(644\) | 1.33504e12 | 0.305850 | ||||||||
\(645\) | −5.51294e11 | −0.125419 | ||||||||
\(646\) | −1.21037e13 | −2.73447 | ||||||||
\(647\) | −1.40949e12 | −0.316223 | −0.158112 | − | 0.987421i | \(-0.550541\pi\) | ||||
−0.158112 | + | 0.987421i | \(0.550541\pi\) | |||||||
\(648\) | 3.36021e11 | 0.0748649 | ||||||||
\(649\) | −1.07568e12 | −0.238003 | ||||||||
\(650\) | 6.04169e12 | 1.32754 | ||||||||
\(651\) | 8.85002e11 | 0.193121 | ||||||||
\(652\) | −7.98236e12 | −1.72988 | ||||||||
\(653\) | 4.47782e12 | 0.963735 | 0.481868 | − | 0.876244i | \(-0.339959\pi\) | ||||
0.481868 | + | 0.876244i | \(0.339959\pi\) | |||||||
\(654\) | −1.29601e12 | −0.277018 | ||||||||
\(655\) | 1.66785e12 | 0.354056 | ||||||||
\(656\) | −3.69242e11 | −0.0778474 | ||||||||
\(657\) | −3.05626e11 | −0.0639951 | ||||||||
\(658\) | −3.00556e12 | −0.625042 | ||||||||
\(659\) | 3.08721e12 | 0.637650 | 0.318825 | − | 0.947814i | \(-0.396712\pi\) | ||||
0.318825 | + | 0.947814i | \(0.396712\pi\) | |||||||
\(660\) | −2.05041e12 | −0.420623 | ||||||||
\(661\) | 4.08659e12 | 0.832636 | 0.416318 | − | 0.909219i | \(-0.363320\pi\) | ||||
0.416318 | + | 0.909219i | \(0.363320\pi\) | |||||||
\(662\) | 1.11316e13 | 2.25266 | ||||||||
\(663\) | −3.42443e12 | −0.688300 | ||||||||
\(664\) | −6.51056e12 | −1.29976 | ||||||||
\(665\) | 7.12515e11 | 0.141285 | ||||||||
\(666\) | 2.01293e12 | 0.396455 | ||||||||
\(667\) | −2.35780e12 | −0.461254 | ||||||||
\(668\) | 9.57839e12 | 1.86122 | ||||||||
\(669\) | 8.80203e11 | 0.169889 | ||||||||
\(670\) | −1.44751e12 | −0.277515 | ||||||||
\(671\) | −1.32389e13 | −2.52115 | ||||||||
\(672\) | 1.44827e12 | 0.273960 | ||||||||
\(673\) | −7.17605e12 | −1.34840 | −0.674198 | − | 0.738550i | \(-0.735511\pi\) | ||||
−0.674198 | + | 0.738550i | \(0.735511\pi\) | |||||||
\(674\) | 1.10507e13 | 2.06263 | ||||||||
\(675\) | −9.57589e11 | −0.177546 | ||||||||
\(676\) | −1.15537e12 | −0.212795 | ||||||||
\(677\) | 4.40269e12 | 0.805507 | 0.402753 | − | 0.915309i | \(-0.368053\pi\) | ||||
0.402753 | + | 0.915309i | \(0.368053\pi\) | |||||||
\(678\) | −2.96980e12 | −0.539751 | ||||||||
\(679\) | 1.65404e12 | 0.298628 | ||||||||
\(680\) | 1.35073e12 | 0.242258 | ||||||||
\(681\) | −9.62421e11 | −0.171476 | ||||||||
\(682\) | 1.44020e13 | 2.54913 | ||||||||
\(683\) | 8.67012e12 | 1.52452 | 0.762258 | − | 0.647274i | \(-0.224091\pi\) | ||||
0.762258 | + | 0.647274i | \(0.224091\pi\) | |||||||
\(684\) | −3.70857e12 | −0.647819 | ||||||||
\(685\) | −1.09167e12 | −0.189445 | ||||||||
\(686\) | 6.29450e12 | 1.08518 | ||||||||
\(687\) | −2.68398e12 | −0.459700 | ||||||||
\(688\) | 1.74917e12 | 0.297635 | ||||||||
\(689\) | −6.79457e12 | −1.14862 | ||||||||
\(690\) | −8.51709e11 | −0.143044 | ||||||||
\(691\) | 1.93668e11 | 0.0323151 | 0.0161576 | − | 0.999869i | \(-0.494857\pi\) | ||||
0.0161576 | + | 0.999869i | \(0.494857\pi\) | |||||||
\(692\) | 1.33199e13 | 2.20813 | ||||||||
\(693\) | 1.38414e12 | 0.227971 | ||||||||
\(694\) | −5.85961e12 | −0.958852 | ||||||||
\(695\) | −2.28984e12 | −0.372283 | ||||||||
\(696\) | 1.94574e12 | 0.314299 | ||||||||
\(697\) | 1.64367e12 | 0.263796 | ||||||||
\(698\) | −8.78882e12 | −1.40146 | ||||||||
\(699\) | 5.93744e12 | 0.940702 | ||||||||
\(700\) | 3.13969e12 | 0.494248 | ||||||||
\(701\) | 1.12033e13 | 1.75232 | 0.876162 | − | 0.482017i | \(-0.160096\pi\) | ||||
0.876162 | + | 0.482017i | \(0.160096\pi\) | |||||||
\(702\) | −1.78193e12 | −0.276932 | ||||||||
\(703\) | −6.70262e12 | −1.03501 | ||||||||
\(704\) | 1.90253e13 | 2.91914 | ||||||||
\(705\) | 1.12904e12 | 0.172130 | ||||||||
\(706\) | 7.62582e12 | 1.15522 | ||||||||
\(707\) | −3.01108e12 | −0.453247 | ||||||||
\(708\) | 7.19650e11 | 0.107640 | ||||||||
\(709\) | 3.44393e12 | 0.511854 | 0.255927 | − | 0.966696i | \(-0.417619\pi\) | ||||
0.255927 | + | 0.966696i | \(0.417619\pi\) | |||||||
\(710\) | −6.41214e11 | −0.0946979 | ||||||||
\(711\) | 1.73338e12 | 0.254379 | ||||||||
\(712\) | 1.71352e12 | 0.249878 | ||||||||
\(713\) | 3.52256e12 | 0.510452 | ||||||||
\(714\) | −3.02225e12 | −0.435200 | ||||||||
\(715\) | 3.28051e12 | 0.469423 | ||||||||
\(716\) | −1.52069e13 | −2.16238 | ||||||||
\(717\) | −3.57586e12 | −0.505294 | ||||||||
\(718\) | −1.18661e13 | −1.66627 | ||||||||
\(719\) | −1.08645e13 | −1.51610 | −0.758050 | − | 0.652197i | \(-0.773848\pi\) | ||||
−0.758050 | + | 0.652197i | \(0.773848\pi\) | |||||||
\(720\) | −2.55040e11 | −0.0353681 | ||||||||
\(721\) | 7.27165e11 | 0.100213 | ||||||||
\(722\) | 9.58501e12 | 1.31273 | ||||||||
\(723\) | −1.84902e12 | −0.251663 | ||||||||
\(724\) | −4.02761e12 | −0.544784 | ||||||||
\(725\) | −5.54495e12 | −0.745379 | ||||||||
\(726\) | 1.57849e13 | 2.10876 | ||||||||
\(727\) | 3.05328e12 | 0.405380 | 0.202690 | − | 0.979243i | \(-0.435032\pi\) | ||||
0.202690 | + | 0.979243i | \(0.435032\pi\) | |||||||
\(728\) | 1.76268e12 | 0.232585 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −6.39285e11 | −0.0833185 | ||||||||
\(731\) | −7.78640e12 | −1.00858 | ||||||||
\(732\) | 8.85703e12 | 1.14022 | ||||||||
\(733\) | −6.43109e12 | −0.822842 | −0.411421 | − | 0.911445i | \(-0.634967\pi\) | ||||
−0.411421 | + | 0.911445i | \(0.634967\pi\) | |||||||
\(734\) | 1.58724e13 | 2.01841 | ||||||||
\(735\) | −1.09330e12 | −0.138181 | ||||||||
\(736\) | 5.76450e12 | 0.724122 | ||||||||
\(737\) | 9.36322e12 | 1.16902 | ||||||||
\(738\) | 8.55296e11 | 0.106136 | ||||||||
\(739\) | −4.53850e12 | −0.559774 | −0.279887 | − | 0.960033i | \(-0.590297\pi\) | ||||
−0.279887 | + | 0.960033i | \(0.590297\pi\) | |||||||
\(740\) | 2.47923e12 | 0.303931 | ||||||||
\(741\) | 5.93343e12 | 0.722977 | ||||||||
\(742\) | −5.99658e12 | −0.726250 | ||||||||
\(743\) | 1.04874e13 | 1.26247 | 0.631234 | − | 0.775593i | \(-0.282549\pi\) | ||||
0.631234 | + | 0.775593i | \(0.282549\pi\) | |||||||
\(744\) | −2.90694e12 | −0.347823 | ||||||||
\(745\) | 2.87401e12 | 0.341810 | ||||||||
\(746\) | −6.03999e12 | −0.714021 | ||||||||
\(747\) | −5.47221e12 | −0.643013 | ||||||||
\(748\) | −2.89597e13 | −3.38249 | ||||||||
\(749\) | 4.48376e12 | 0.520564 | ||||||||
\(750\) | −4.17415e12 | −0.481717 | ||||||||
\(751\) | 5.78172e12 | 0.663250 | 0.331625 | − | 0.943411i | \(-0.392403\pi\) | ||||
0.331625 | + | 0.943411i | \(0.392403\pi\) | |||||||
\(752\) | −3.58226e12 | −0.408485 | ||||||||
\(753\) | 7.88721e11 | 0.0894017 | ||||||||
\(754\) | −1.03183e13 | −1.16262 | ||||||||
\(755\) | −1.17136e11 | −0.0131198 | ||||||||
\(756\) | −9.26013e11 | −0.103103 | ||||||||
\(757\) | −1.49716e13 | −1.65706 | −0.828528 | − | 0.559948i | \(-0.810821\pi\) | ||||
−0.828528 | + | 0.559948i | \(0.810821\pi\) | |||||||
\(758\) | 8.36742e12 | 0.920619 | ||||||||
\(759\) | 5.50926e12 | 0.602567 | ||||||||
\(760\) | −2.34038e12 | −0.254463 | ||||||||
\(761\) | −4.47071e12 | −0.483221 | −0.241611 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241611 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(762\) | −3.65052e12 | −0.392245 | ||||||||
\(763\) | 1.07755e12 | 0.115100 | ||||||||
\(764\) | −1.95880e13 | −2.08003 | ||||||||
\(765\) | 1.13530e12 | 0.119849 | ||||||||
\(766\) | −1.50373e13 | −1.57812 | ||||||||
\(767\) | −1.15139e12 | −0.120127 | ||||||||
\(768\) | −1.71781e12 | −0.178176 | ||||||||
\(769\) | −1.16212e13 | −1.19835 | −0.599175 | − | 0.800618i | \(-0.704505\pi\) | ||||
−0.599175 | + | 0.800618i | \(0.704505\pi\) | |||||||
\(770\) | 2.89523e12 | 0.296807 | ||||||||
\(771\) | 1.08204e13 | 1.10281 | ||||||||
\(772\) | −1.71049e13 | −1.73317 | ||||||||
\(773\) | 3.55448e12 | 0.358070 | 0.179035 | − | 0.983843i | \(-0.442702\pi\) | ||||
0.179035 | + | 0.983843i | \(0.442702\pi\) | |||||||
\(774\) | −4.05170e12 | −0.405792 | ||||||||
\(775\) | 8.28417e12 | 0.824881 | ||||||||
\(776\) | −5.43297e12 | −0.537848 | ||||||||
\(777\) | −1.67362e12 | −0.164726 | ||||||||
\(778\) | −1.58646e13 | −1.55246 | ||||||||
\(779\) | −2.84796e12 | −0.277086 | ||||||||
\(780\) | −2.19472e12 | −0.212302 | ||||||||
\(781\) | 4.14768e12 | 0.398910 | ||||||||
\(782\) | −1.20294e13 | −1.15031 | ||||||||
\(783\) | 1.63542e12 | 0.155490 | ||||||||
\(784\) | 3.46889e12 | 0.327920 | ||||||||
\(785\) | 2.11507e12 | 0.198797 | ||||||||
\(786\) | 1.22578e13 | 1.14554 | ||||||||
\(787\) | 3.33602e12 | 0.309986 | 0.154993 | − | 0.987916i | \(-0.450464\pi\) | ||||
0.154993 | + | 0.987916i | \(0.450464\pi\) | |||||||
\(788\) | −2.69446e13 | −2.48945 | ||||||||
\(789\) | 1.06503e13 | 0.978394 | ||||||||
\(790\) | 3.62575e12 | 0.331189 | ||||||||
\(791\) | 2.46919e12 | 0.224264 | ||||||||
\(792\) | −4.54644e12 | −0.410590 | ||||||||
\(793\) | −1.41706e13 | −1.27250 | ||||||||
\(794\) | −1.65951e13 | −1.48180 | ||||||||
\(795\) | 2.25261e12 | 0.200002 | ||||||||
\(796\) | −1.09087e13 | −0.963086 | ||||||||
\(797\) | −1.81568e13 | −1.59396 | −0.796979 | − | 0.604007i | \(-0.793570\pi\) | ||||
−0.796979 | + | 0.604007i | \(0.793570\pi\) | |||||||
\(798\) | 5.23658e12 | 0.457125 | ||||||||
\(799\) | 1.59463e13 | 1.38420 | ||||||||
\(800\) | 1.35567e13 | 1.17017 | ||||||||
\(801\) | 1.44023e12 | 0.123619 | ||||||||
\(802\) | −9.10042e11 | −0.0776742 | ||||||||
\(803\) | 4.13520e12 | 0.350975 | ||||||||
\(804\) | −6.26416e12 | −0.528701 | ||||||||
\(805\) | 7.08140e11 | 0.0594343 | ||||||||
\(806\) | 1.54156e13 | 1.28663 | ||||||||
\(807\) | 8.18126e12 | 0.679031 | ||||||||
\(808\) | 9.89041e12 | 0.816325 | ||||||||
\(809\) | −6.19366e12 | −0.508369 | −0.254184 | − | 0.967156i | \(-0.581807\pi\) | ||||
−0.254184 | + | 0.967156i | \(0.581807\pi\) | |||||||
\(810\) | 5.90763e11 | 0.0482204 | ||||||||
\(811\) | 1.44878e13 | 1.17600 | 0.588000 | − | 0.808861i | \(-0.299915\pi\) | ||||
0.588000 | + | 0.808861i | \(0.299915\pi\) | |||||||
\(812\) | −5.36212e12 | −0.432847 | ||||||||
\(813\) | 6.16875e12 | 0.495211 | ||||||||
\(814\) | −2.72354e13 | −2.17432 | ||||||||
\(815\) | −4.23404e12 | −0.336160 | ||||||||
\(816\) | −3.60214e12 | −0.284417 | ||||||||
\(817\) | 1.34913e13 | 1.05939 | ||||||||
\(818\) | −2.25062e13 | −1.75757 | ||||||||
\(819\) | 1.48155e12 | 0.115064 | ||||||||
\(820\) | 1.05343e12 | 0.0813661 | ||||||||
\(821\) | −5.08820e12 | −0.390859 | −0.195429 | − | 0.980718i | \(-0.562610\pi\) | ||||
−0.195429 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(822\) | −8.02314e12 | −0.612945 | ||||||||
\(823\) | 1.62319e13 | 1.23330 | 0.616650 | − | 0.787237i | \(-0.288489\pi\) | ||||
0.616650 | + | 0.787237i | \(0.288489\pi\) | |||||||
\(824\) | −2.38850e12 | −0.180490 | ||||||||
\(825\) | 1.29564e13 | 0.973737 | ||||||||
\(826\) | −1.01616e12 | −0.0759544 | ||||||||
\(827\) | 1.70769e12 | 0.126950 | 0.0634752 | − | 0.997983i | \(-0.479782\pi\) | ||||
0.0634752 | + | 0.997983i | \(0.479782\pi\) | |||||||
\(828\) | −3.68579e12 | −0.272518 | ||||||||
\(829\) | −7.13685e12 | −0.524821 | −0.262411 | − | 0.964956i | \(-0.584517\pi\) | ||||
−0.262411 | + | 0.964956i | \(0.584517\pi\) | |||||||
\(830\) | −1.14463e13 | −0.837172 | ||||||||
\(831\) | 3.00537e12 | 0.218622 | ||||||||
\(832\) | 2.03643e13 | 1.47338 | ||||||||
\(833\) | −1.54417e13 | −1.11120 | ||||||||
\(834\) | −1.68290e13 | −1.20451 | ||||||||
\(835\) | 5.08062e12 | 0.361682 | ||||||||
\(836\) | 5.01778e13 | 3.55290 | ||||||||
\(837\) | −2.44332e12 | −0.172074 | ||||||||
\(838\) | 1.55340e13 | 1.08814 | ||||||||
\(839\) | 2.19459e13 | 1.52906 | 0.764529 | − | 0.644590i | \(-0.222972\pi\) | ||||
0.764529 | + | 0.644590i | \(0.222972\pi\) | |||||||
\(840\) | −5.84382e11 | −0.0404986 | ||||||||
\(841\) | −5.03719e12 | −0.347221 | ||||||||
\(842\) | −3.00354e13 | −2.05935 | ||||||||
\(843\) | −6.59637e12 | −0.449864 | ||||||||
\(844\) | 3.44003e13 | 2.33357 | ||||||||
\(845\) | −6.12838e11 | −0.0413514 | ||||||||
\(846\) | 8.29778e12 | 0.556923 | ||||||||
\(847\) | −1.31241e13 | −0.876183 | ||||||||
\(848\) | −7.14718e12 | −0.474628 | ||||||||
\(849\) | −2.45822e11 | −0.0162382 | ||||||||
\(850\) | −2.82902e13 | −1.85887 | ||||||||
\(851\) | −6.66146e12 | −0.435398 | ||||||||
\(852\) | −2.77487e12 | −0.180412 | ||||||||
\(853\) | −1.48939e13 | −0.963249 | −0.481624 | − | 0.876378i | \(-0.659953\pi\) | ||||
−0.481624 | + | 0.876378i | \(0.659953\pi\) | |||||||
\(854\) | −1.25063e13 | −0.804580 | ||||||||
\(855\) | −1.96712e12 | −0.125887 | ||||||||
\(856\) | −1.47277e13 | −0.937568 | ||||||||
\(857\) | −1.35869e13 | −0.860415 | −0.430208 | − | 0.902730i | \(-0.641560\pi\) | ||||
−0.430208 | + | 0.902730i | \(0.641560\pi\) | |||||||
\(858\) | 2.41099e13 | 1.51881 | ||||||||
\(859\) | 7.93178e12 | 0.497052 | 0.248526 | − | 0.968625i | \(-0.420054\pi\) | ||||
0.248526 | + | 0.968625i | \(0.420054\pi\) | |||||||
\(860\) | −4.99030e12 | −0.311088 | ||||||||
\(861\) | −7.11122e11 | −0.0440991 | ||||||||
\(862\) | −2.18804e13 | −1.34981 | ||||||||
\(863\) | 2.41151e13 | 1.47993 | 0.739963 | − | 0.672648i | \(-0.234843\pi\) | ||||
0.739963 | + | 0.672648i | \(0.234843\pi\) | |||||||
\(864\) | −3.99838e12 | −0.244103 | ||||||||
\(865\) | 7.06521e12 | 0.429094 | ||||||||
\(866\) | 2.95420e13 | 1.78488 | ||||||||
\(867\) | 6.42925e12 | 0.386433 | ||||||||
\(868\) | 8.01101e12 | 0.479015 | ||||||||
\(869\) | −2.34531e13 | −1.39512 | ||||||||
\(870\) | 3.42084e12 | 0.202440 | ||||||||
\(871\) | 1.00222e13 | 0.590039 | ||||||||
\(872\) | −3.53939e12 | −0.207302 | ||||||||
\(873\) | −4.56648e12 | −0.266083 | ||||||||
\(874\) | 2.08431e13 | 1.20826 | ||||||||
\(875\) | 3.47053e12 | 0.200152 | ||||||||
\(876\) | −2.76652e12 | −0.158732 | ||||||||
\(877\) | 1.78340e13 | 1.01801 | 0.509005 | − | 0.860764i | \(-0.330014\pi\) | ||||
0.509005 | + | 0.860764i | \(0.330014\pi\) | |||||||
\(878\) | 2.70473e13 | 1.53603 | ||||||||
\(879\) | 1.01045e13 | 0.570904 | ||||||||
\(880\) | 3.45075e12 | 0.193973 | ||||||||
\(881\) | 1.07118e13 | 0.599059 | 0.299529 | − | 0.954087i | \(-0.403170\pi\) | ||||
0.299529 | + | 0.954087i | \(0.403170\pi\) | |||||||
\(882\) | −8.03517e12 | −0.447082 | ||||||||
\(883\) | −6.53602e12 | −0.361818 | −0.180909 | − | 0.983500i | \(-0.557904\pi\) | ||||
−0.180909 | + | 0.983500i | \(0.557904\pi\) | |||||||
\(884\) | −3.09979e13 | −1.70725 | ||||||||
\(885\) | 3.81720e11 | 0.0209171 | ||||||||
\(886\) | −4.59512e13 | −2.50521 | ||||||||
\(887\) | −2.36595e13 | −1.28336 | −0.641681 | − | 0.766972i | \(-0.721763\pi\) | ||||
−0.641681 | + | 0.766972i | \(0.721763\pi\) | |||||||
\(888\) | 5.49728e12 | 0.296681 | ||||||||
\(889\) | 3.03516e12 | 0.162976 | ||||||||
\(890\) | 3.01256e12 | 0.160946 | ||||||||
\(891\) | −3.82134e12 | −0.203126 | ||||||||
\(892\) | 7.96757e12 | 0.421390 | ||||||||
\(893\) | −2.76299e13 | −1.45394 | ||||||||
\(894\) | 2.11224e13 | 1.10592 | ||||||||
\(895\) | −8.06612e12 | −0.420205 | ||||||||
\(896\) | 8.81814e12 | 0.457079 | ||||||||
\(897\) | 5.89700e12 | 0.304134 | ||||||||
\(898\) | −5.41212e13 | −2.77731 | ||||||||
\(899\) | −1.41481e13 | −0.722405 | ||||||||
\(900\) | −8.66807e12 | −0.440383 | ||||||||
\(901\) | 3.18155e13 | 1.60834 | ||||||||
\(902\) | −1.15724e13 | −0.582094 | ||||||||
\(903\) | 3.36872e12 | 0.168605 | ||||||||
\(904\) | −8.11048e12 | −0.403913 | ||||||||
\(905\) | −2.13635e12 | −0.105865 | ||||||||
\(906\) | −8.60882e11 | −0.0424489 | ||||||||
\(907\) | 2.65879e12 | 0.130452 | 0.0652261 | − | 0.997871i | \(-0.479223\pi\) | ||||
0.0652261 | + | 0.997871i | \(0.479223\pi\) | |||||||
\(908\) | −8.71181e12 | −0.425326 | ||||||||
\(909\) | 8.31301e12 | 0.403851 | ||||||||
\(910\) | 3.09899e12 | 0.149808 | ||||||||
\(911\) | −1.64923e13 | −0.793322 | −0.396661 | − | 0.917965i | \(-0.629831\pi\) | ||||
−0.396661 | + | 0.917965i | \(0.629831\pi\) | |||||||
\(912\) | 6.24135e12 | 0.298746 | ||||||||
\(913\) | 7.40403e13 | 3.52655 | ||||||||
\(914\) | −1.67041e13 | −0.791710 | ||||||||
\(915\) | 4.69799e12 | 0.221573 | ||||||||
\(916\) | −2.42953e13 | −1.14023 | ||||||||
\(917\) | −1.01915e13 | −0.475968 | ||||||||
\(918\) | 8.34385e12 | 0.387770 | ||||||||
\(919\) | 3.80293e12 | 0.175873 | 0.0879365 | − | 0.996126i | \(-0.471973\pi\) | ||||
0.0879365 | + | 0.996126i | \(0.471973\pi\) | |||||||
\(920\) | −2.32601e12 | −0.107045 | ||||||||
\(921\) | −1.72795e13 | −0.791338 | ||||||||
\(922\) | −1.96001e13 | −0.893243 | ||||||||
\(923\) | 4.43959e12 | 0.201342 | ||||||||
\(924\) | 1.25292e13 | 0.565456 | ||||||||
\(925\) | −1.56661e13 | −0.703595 | ||||||||
\(926\) | 3.54826e13 | 1.58586 | ||||||||
\(927\) | −2.00756e12 | −0.0892916 | ||||||||
\(928\) | −2.31528e13 | −1.02480 | ||||||||
\(929\) | −6.89689e12 | −0.303796 | −0.151898 | − | 0.988396i | \(-0.548539\pi\) | ||||
−0.151898 | + | 0.988396i | \(0.548539\pi\) | |||||||
\(930\) | −5.11074e12 | −0.224032 | ||||||||
\(931\) | 2.67554e13 | 1.16718 | ||||||||
\(932\) | 5.37456e13 | 2.33330 | ||||||||
\(933\) | −2.53152e12 | −0.109374 | ||||||||
\(934\) | 3.36626e13 | 1.44739 | ||||||||
\(935\) | −1.53609e13 | −0.657303 | ||||||||
\(936\) | −4.86641e12 | −0.207237 | ||||||||
\(937\) | 2.21460e13 | 0.938571 | 0.469286 | − | 0.883046i | \(-0.344511\pi\) | ||||
0.469286 | + | 0.883046i | \(0.344511\pi\) | |||||||
\(938\) | 8.84514e12 | 0.373071 | ||||||||
\(939\) | −1.41667e13 | −0.594665 | ||||||||
\(940\) | 1.02200e13 | 0.426949 | ||||||||
\(941\) | 1.85240e13 | 0.770159 | 0.385080 | − | 0.922883i | \(-0.374174\pi\) | ||||
0.385080 | + | 0.922883i | \(0.374174\pi\) | |||||||
\(942\) | 1.55445e13 | 0.643204 | ||||||||
\(943\) | −2.83047e12 | −0.116562 | ||||||||
\(944\) | −1.21114e12 | −0.0496387 | ||||||||
\(945\) | −4.91181e11 | −0.0200354 | ||||||||
\(946\) | 5.48205e13 | 2.22553 | ||||||||
\(947\) | 4.78860e13 | 1.93479 | 0.967394 | − | 0.253277i | \(-0.0815083\pi\) | ||||
0.967394 | + | 0.253277i | \(0.0815083\pi\) | |||||||
\(948\) | 1.56905e13 | 0.630957 | ||||||||
\(949\) | 4.42623e12 | 0.177148 | ||||||||
\(950\) | 4.90177e13 | 1.95253 | ||||||||
\(951\) | 1.05685e13 | 0.418988 | ||||||||
\(952\) | −8.25372e12 | −0.325674 | ||||||||
\(953\) | −1.27910e13 | −0.502327 | −0.251163 | − | 0.967945i | \(-0.580813\pi\) | ||||
−0.251163 | + | 0.967945i | \(0.580813\pi\) | |||||||
\(954\) | 1.65554e13 | 0.647102 | ||||||||
\(955\) | −1.03900e13 | −0.404202 | ||||||||
\(956\) | −3.23686e13 | −1.25332 | ||||||||
\(957\) | −2.21276e13 | −0.852768 | ||||||||
\(958\) | −5.51869e13 | −2.11686 | ||||||||
\(959\) | 6.67071e12 | 0.254676 | ||||||||
\(960\) | −6.75139e12 | −0.256550 | ||||||||
\(961\) | −5.30227e12 | −0.200543 | ||||||||
\(962\) | −2.91522e13 | −1.09745 | ||||||||
\(963\) | −1.23788e13 | −0.463832 | ||||||||
\(964\) | −1.67373e13 | −0.624220 | ||||||||
\(965\) | −9.07285e12 | −0.336799 | ||||||||
\(966\) | 5.20443e12 | 0.192298 | ||||||||
\(967\) | 3.54914e13 | 1.30528 | 0.652640 | − | 0.757668i | \(-0.273661\pi\) | ||||
0.652640 | + | 0.757668i | \(0.273661\pi\) | |||||||
\(968\) | 4.31084e13 | 1.57806 | ||||||||
\(969\) | −2.77832e13 | −1.01234 | ||||||||
\(970\) | −9.55179e12 | −0.346427 | ||||||||
\(971\) | −1.76220e13 | −0.636163 | −0.318081 | − | 0.948063i | \(-0.603039\pi\) | ||||
−0.318081 | + | 0.948063i | \(0.603039\pi\) | |||||||
\(972\) | 2.55654e12 | 0.0918661 | ||||||||
\(973\) | 1.39922e13 | 0.500471 | ||||||||
\(974\) | −6.71116e13 | −2.38936 | ||||||||
\(975\) | 1.38683e13 | 0.491475 | ||||||||
\(976\) | −1.49060e13 | −0.525819 | ||||||||
\(977\) | −3.75917e13 | −1.31998 | −0.659988 | − | 0.751276i | \(-0.729439\pi\) | ||||
−0.659988 | + | 0.751276i | \(0.729439\pi\) | |||||||
\(978\) | −3.11178e13 | −1.08764 | ||||||||
\(979\) | −1.94867e13 | −0.677979 | ||||||||
\(980\) | −9.89657e12 | −0.342742 | ||||||||
\(981\) | −2.97490e12 | −0.102556 | ||||||||
\(982\) | −4.30560e13 | −1.47752 | ||||||||
\(983\) | 4.15795e13 | 1.42033 | 0.710164 | − | 0.704037i | \(-0.248621\pi\) | ||||
0.710164 | + | 0.704037i | \(0.248621\pi\) | |||||||
\(984\) | 2.33580e12 | 0.0794252 | ||||||||
\(985\) | −1.42921e13 | −0.483762 | ||||||||
\(986\) | 4.83154e13 | 1.62794 | ||||||||
\(987\) | −6.89906e12 | −0.231400 | ||||||||
\(988\) | 5.37093e13 | 1.79326 | ||||||||
\(989\) | 1.34085e13 | 0.445652 | ||||||||
\(990\) | −7.99317e12 | −0.264461 | ||||||||
\(991\) | 4.43558e11 | 0.0146089 | 0.00730447 | − | 0.999973i | \(-0.497675\pi\) | ||||
0.00730447 | + | 0.999973i | \(0.497675\pi\) | |||||||
\(992\) | 3.45903e13 | 1.13410 | ||||||||
\(993\) | 2.55517e13 | 0.833967 | ||||||||
\(994\) | 3.91818e12 | 0.127305 | ||||||||
\(995\) | −5.78626e12 | −0.187152 | ||||||||
\(996\) | −4.95343e13 | −1.59492 | ||||||||
\(997\) | 4.97398e13 | 1.59432 | 0.797161 | − | 0.603767i | \(-0.206334\pi\) | ||||
0.797161 | + | 0.603767i | \(0.206334\pi\) | |||||||
\(998\) | 2.43647e13 | 0.777454 | ||||||||
\(999\) | 4.62053e12 | 0.146773 |
(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.a.1.19 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.19 | ✓ | 21 | 1.1 | even | 1 | trivial |