Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −166.716 | −1.84197 | −0.920985 | − | 0.389597i | \(-0.872614\pi\) | ||||
−0.920985 | + | 0.389597i | \(0.872614\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 19602.3 | 2.39286 | ||||||||
\(5\) | 43558.7 | 1.24672 | 0.623361 | − | 0.781934i | \(-0.285767\pi\) | ||||
0.623361 | + | 0.781934i | \(0.285767\pi\) | |||||||
\(6\) | −121536. | −1.06346 | ||||||||
\(7\) | −395203. | −1.26965 | −0.634823 | − | 0.772658i | \(-0.718927\pi\) | ||||
−0.634823 | + | 0.772658i | \(0.718927\pi\) | |||||||
\(8\) | −1.90228e6 | −2.56560 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −7.26193e6 | −2.29642 | ||||||||
\(11\) | 2.80600e6 | 0.477568 | 0.238784 | − | 0.971073i | \(-0.423251\pi\) | ||||
0.238784 | + | 0.971073i | \(0.423251\pi\) | |||||||
\(12\) | 1.42901e7 | 1.38152 | ||||||||
\(13\) | 2.66316e7 | 1.53026 | 0.765131 | − | 0.643875i | \(-0.222674\pi\) | ||||
0.765131 | + | 0.643875i | \(0.222674\pi\) | |||||||
\(14\) | 6.58867e7 | 2.33865 | ||||||||
\(15\) | 3.17543e7 | 0.719795 | ||||||||
\(16\) | 1.56559e8 | 2.33290 | ||||||||
\(17\) | 1.05903e8 | 1.06412 | 0.532061 | − | 0.846706i | \(-0.321418\pi\) | ||||
0.532061 | + | 0.846706i | \(0.321418\pi\) | |||||||
\(18\) | −8.85998e7 | −0.613990 | ||||||||
\(19\) | 1.56853e8 | 0.764880 | 0.382440 | − | 0.923980i | \(-0.375084\pi\) | ||||
0.382440 | + | 0.923980i | \(0.375084\pi\) | |||||||
\(20\) | 8.53849e8 | 2.98323 | ||||||||
\(21\) | −2.88103e8 | −0.733030 | ||||||||
\(22\) | −4.67805e8 | −0.879666 | ||||||||
\(23\) | −2.25613e8 | −0.317785 | −0.158892 | − | 0.987296i | \(-0.550792\pi\) | ||||
−0.158892 | + | 0.987296i | \(0.550792\pi\) | |||||||
\(24\) | −1.38676e9 | −1.48125 | ||||||||
\(25\) | 6.76654e8 | 0.554315 | ||||||||
\(26\) | −4.43992e9 | −2.81870 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −7.74687e9 | −3.03808 | ||||||||
\(29\) | 4.55422e8 | 0.142176 | 0.0710881 | − | 0.997470i | \(-0.477353\pi\) | ||||
0.0710881 | + | 0.997470i | \(0.477353\pi\) | |||||||
\(30\) | −5.29395e9 | −1.32584 | ||||||||
\(31\) | 3.56282e9 | 0.721012 | 0.360506 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360506 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(32\) | −1.05174e10 | −1.73154 | ||||||||
\(33\) | 2.04557e9 | 0.275724 | ||||||||
\(34\) | −1.76558e10 | −1.96008 | ||||||||
\(35\) | −1.72145e10 | −1.58289 | ||||||||
\(36\) | 1.04175e10 | 0.797619 | ||||||||
\(37\) | 2.68695e10 | 1.72166 | 0.860831 | − | 0.508890i | \(-0.169944\pi\) | ||||
0.860831 | + | 0.508890i | \(0.169944\pi\) | |||||||
\(38\) | −2.61499e10 | −1.40889 | ||||||||
\(39\) | 1.94144e10 | 0.883497 | ||||||||
\(40\) | −8.28607e10 | −3.19859 | ||||||||
\(41\) | −1.72189e10 | −0.566121 | −0.283061 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283061 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(42\) | 4.80314e10 | 1.35022 | ||||||||
\(43\) | 2.91163e10 | 0.702411 | 0.351206 | − | 0.936298i | \(-0.385772\pi\) | ||||
0.351206 | + | 0.936298i | \(0.385772\pi\) | |||||||
\(44\) | 5.50040e10 | 1.14275 | ||||||||
\(45\) | 2.31489e10 | 0.415574 | ||||||||
\(46\) | 3.76133e10 | 0.585350 | ||||||||
\(47\) | 1.44877e8 | 0.00196048 | 0.000980241 | − | 1.00000i | \(-0.499688\pi\) | ||||
0.000980241 | 1.00000i | \(0.499688\pi\) | ||||||||
\(48\) | 1.14131e11 | 1.34690 | ||||||||
\(49\) | 5.92961e10 | 0.612000 | ||||||||
\(50\) | −1.12809e11 | −1.02103 | ||||||||
\(51\) | 7.72036e10 | 0.614372 | ||||||||
\(52\) | 5.22040e11 | 3.66170 | ||||||||
\(53\) | 4.30140e10 | 0.266574 | 0.133287 | − | 0.991078i | \(-0.457447\pi\) | ||||
0.133287 | + | 0.991078i | \(0.457447\pi\) | |||||||
\(54\) | −6.45893e10 | −0.354487 | ||||||||
\(55\) | 1.22226e11 | 0.595394 | ||||||||
\(56\) | 7.51785e11 | 3.25740 | ||||||||
\(57\) | 1.14346e11 | 0.441604 | ||||||||
\(58\) | −7.59262e10 | −0.261884 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 6.22456e11 | 1.72237 | ||||||||
\(61\) | −2.11973e11 | −0.526789 | −0.263394 | − | 0.964688i | \(-0.584842\pi\) | ||||
−0.263394 | + | 0.964688i | \(0.584842\pi\) | |||||||
\(62\) | −5.93979e11 | −1.32808 | ||||||||
\(63\) | −2.10027e11 | −0.423215 | ||||||||
\(64\) | 4.70889e11 | 0.856543 | ||||||||
\(65\) | 1.16004e12 | 1.90781 | ||||||||
\(66\) | −3.41030e11 | −0.507875 | ||||||||
\(67\) | −9.17316e11 | −1.23889 | −0.619445 | − | 0.785040i | \(-0.712642\pi\) | ||||
−0.619445 | + | 0.785040i | \(0.712642\pi\) | |||||||
\(68\) | 2.07595e12 | 2.54629 | ||||||||
\(69\) | −1.64472e11 | −0.183473 | ||||||||
\(70\) | 2.86993e12 | 2.91565 | ||||||||
\(71\) | 1.33109e12 | 1.23318 | 0.616592 | − | 0.787283i | \(-0.288513\pi\) | ||||
0.616592 | + | 0.787283i | \(0.288513\pi\) | |||||||
\(72\) | −1.01095e12 | −0.855200 | ||||||||
\(73\) | −1.30644e12 | −1.01039 | −0.505196 | − | 0.863005i | \(-0.668580\pi\) | ||||
−0.505196 | + | 0.863005i | \(0.668580\pi\) | |||||||
\(74\) | −4.47958e12 | −3.17125 | ||||||||
\(75\) | 4.93281e11 | 0.320034 | ||||||||
\(76\) | 3.07467e12 | 1.83025 | ||||||||
\(77\) | −1.10894e12 | −0.606342 | ||||||||
\(78\) | −3.23670e12 | −1.62738 | ||||||||
\(79\) | 3.47198e12 | 1.60694 | 0.803472 | − | 0.595343i | \(-0.202984\pi\) | ||||
0.803472 | + | 0.595343i | \(0.202984\pi\) | |||||||
\(80\) | 6.81948e12 | 2.90848 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 2.87066e12 | 1.04278 | ||||||||
\(83\) | 3.63991e12 | 1.22203 | 0.611017 | − | 0.791618i | \(-0.290761\pi\) | ||||
0.611017 | + | 0.791618i | \(0.290761\pi\) | |||||||
\(84\) | −5.64747e12 | −1.75404 | ||||||||
\(85\) | 4.61301e12 | 1.32667 | ||||||||
\(86\) | −4.85416e12 | −1.29382 | ||||||||
\(87\) | 3.32003e11 | 0.0820855 | ||||||||
\(88\) | −5.33779e12 | −1.22525 | ||||||||
\(89\) | −1.84291e12 | −0.393070 | −0.196535 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196535 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(90\) | −3.85929e12 | −0.765475 | ||||||||
\(91\) | −1.05249e13 | −1.94289 | ||||||||
\(92\) | −4.42253e12 | −0.760413 | ||||||||
\(93\) | 2.59729e12 | 0.416276 | ||||||||
\(94\) | −2.41533e10 | −0.00361115 | ||||||||
\(95\) | 6.83229e12 | 0.953592 | ||||||||
\(96\) | −7.66717e12 | −0.999705 | ||||||||
\(97\) | −1.21303e13 | −1.47862 | −0.739310 | − | 0.673365i | \(-0.764848\pi\) | ||||
−0.739310 | + | 0.673365i | \(0.764848\pi\) | |||||||
\(98\) | −9.88561e12 | −1.12729 | ||||||||
\(99\) | 1.49122e12 | 0.159189 | ||||||||
\(100\) | 1.32640e13 | 1.32640 | ||||||||
\(101\) | 9.46306e12 | 0.887038 | 0.443519 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443519 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(102\) | −1.28711e13 | −1.13165 | ||||||||
\(103\) | 3.13670e11 | 0.0258840 | 0.0129420 | − | 0.999916i | \(-0.495880\pi\) | ||||
0.0129420 | + | 0.999916i | \(0.495880\pi\) | |||||||
\(104\) | −5.06607e13 | −3.92604 | ||||||||
\(105\) | −1.25494e13 | −0.913885 | ||||||||
\(106\) | −7.17114e12 | −0.491021 | ||||||||
\(107\) | 1.29230e13 | 0.832470 | 0.416235 | − | 0.909257i | \(-0.363349\pi\) | ||||
0.416235 | + | 0.909257i | \(0.363349\pi\) | |||||||
\(108\) | 7.59432e12 | 0.460505 | ||||||||
\(109\) | 6.73016e12 | 0.384373 | 0.192187 | − | 0.981358i | \(-0.438442\pi\) | ||||
0.192187 | + | 0.981358i | \(0.438442\pi\) | |||||||
\(110\) | −2.03770e13 | −1.09670 | ||||||||
\(111\) | 1.95879e13 | 0.994003 | ||||||||
\(112\) | −6.18723e13 | −2.96196 | ||||||||
\(113\) | 9.15347e12 | 0.413596 | 0.206798 | − | 0.978384i | \(-0.433696\pi\) | ||||
0.206798 | + | 0.978384i | \(0.433696\pi\) | |||||||
\(114\) | −1.90632e13 | −0.813421 | ||||||||
\(115\) | −9.82740e12 | −0.396189 | ||||||||
\(116\) | 8.92731e12 | 0.340207 | ||||||||
\(117\) | 1.41531e13 | 0.510087 | ||||||||
\(118\) | 7.03218e12 | 0.239804 | ||||||||
\(119\) | −4.18533e13 | −1.35106 | ||||||||
\(120\) | −6.04054e13 | −1.84671 | ||||||||
\(121\) | −2.66491e13 | −0.771929 | ||||||||
\(122\) | 3.53393e13 | 0.970330 | ||||||||
\(123\) | −1.25526e13 | −0.326850 | ||||||||
\(124\) | 6.98393e13 | 1.72528 | ||||||||
\(125\) | −2.36980e13 | −0.555645 | ||||||||
\(126\) | 3.50149e13 | 0.779550 | ||||||||
\(127\) | 1.74328e13 | 0.368674 | 0.184337 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184337 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(128\) | 7.65350e12 | 0.153814 | ||||||||
\(129\) | 2.12258e13 | 0.405537 | ||||||||
\(130\) | −1.93397e14 | −3.51413 | ||||||||
\(131\) | −2.37102e13 | −0.409894 | −0.204947 | − | 0.978773i | \(-0.565702\pi\) | ||||
−0.204947 | + | 0.978773i | \(0.565702\pi\) | |||||||
\(132\) | 4.00979e13 | 0.659767 | ||||||||
\(133\) | −6.19885e13 | −0.971126 | ||||||||
\(134\) | 1.52931e14 | 2.28200 | ||||||||
\(135\) | 1.68755e13 | 0.239932 | ||||||||
\(136\) | −2.01458e14 | −2.73011 | ||||||||
\(137\) | 9.22184e13 | 1.19161 | 0.595805 | − | 0.803129i | \(-0.296833\pi\) | ||||
0.595805 | + | 0.803129i | \(0.296833\pi\) | |||||||
\(138\) | 2.74201e13 | 0.337952 | ||||||||
\(139\) | −4.30398e13 | −0.506144 | −0.253072 | − | 0.967447i | \(-0.581441\pi\) | ||||
−0.253072 | + | 0.967447i | \(0.581441\pi\) | |||||||
\(140\) | −3.37443e14 | −3.78764 | ||||||||
\(141\) | 1.05615e11 | 0.00113189 | ||||||||
\(142\) | −2.21914e14 | −2.27149 | ||||||||
\(143\) | 7.47283e13 | 0.730803 | ||||||||
\(144\) | 8.32016e13 | 0.777635 | ||||||||
\(145\) | 1.98376e13 | 0.177254 | ||||||||
\(146\) | 2.17804e14 | 1.86111 | ||||||||
\(147\) | 4.32268e13 | 0.353338 | ||||||||
\(148\) | 5.26703e14 | 4.11969 | ||||||||
\(149\) | −8.82130e13 | −0.660423 | −0.330211 | − | 0.943907i | \(-0.607120\pi\) | ||||
−0.330211 | + | 0.943907i | \(0.607120\pi\) | |||||||
\(150\) | −8.22379e13 | −0.589493 | ||||||||
\(151\) | −2.27439e13 | −0.156140 | −0.0780701 | − | 0.996948i | \(-0.524876\pi\) | ||||
−0.0780701 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(152\) | −2.98377e14 | −1.96238 | ||||||||
\(153\) | 5.62814e13 | 0.354708 | ||||||||
\(154\) | 1.84878e14 | 1.11686 | ||||||||
\(155\) | 1.55192e14 | 0.898901 | ||||||||
\(156\) | 3.80567e14 | 2.11408 | ||||||||
\(157\) | −3.12906e14 | −1.66750 | −0.833750 | − | 0.552143i | \(-0.813810\pi\) | ||||
−0.833750 | + | 0.552143i | \(0.813810\pi\) | |||||||
\(158\) | −5.78835e14 | −2.95994 | ||||||||
\(159\) | 3.13572e13 | 0.153906 | ||||||||
\(160\) | −4.58123e14 | −2.15875 | ||||||||
\(161\) | 8.91628e13 | 0.403474 | ||||||||
\(162\) | −4.70856e13 | −0.204663 | ||||||||
\(163\) | 3.26303e14 | 1.36270 | 0.681352 | − | 0.731955i | \(-0.261392\pi\) | ||||
0.681352 | + | 0.731955i | \(0.261392\pi\) | |||||||
\(164\) | −3.37529e14 | −1.35465 | ||||||||
\(165\) | 8.91024e13 | 0.343751 | ||||||||
\(166\) | −6.06832e14 | −2.25095 | ||||||||
\(167\) | −4.85092e14 | −1.73048 | −0.865241 | − | 0.501356i | \(-0.832835\pi\) | ||||
−0.865241 | + | 0.501356i | \(0.832835\pi\) | |||||||
\(168\) | 5.48051e14 | 1.88066 | ||||||||
\(169\) | 4.06368e14 | 1.34170 | ||||||||
\(170\) | −7.69063e14 | −2.44368 | ||||||||
\(171\) | 8.33579e13 | 0.254960 | ||||||||
\(172\) | 5.70746e14 | 1.68077 | ||||||||
\(173\) | −3.13899e14 | −0.890206 | −0.445103 | − | 0.895479i | \(-0.646833\pi\) | ||||
−0.445103 | + | 0.895479i | \(0.646833\pi\) | |||||||
\(174\) | −5.53502e13 | −0.151199 | ||||||||
\(175\) | −2.67416e14 | −0.703784 | ||||||||
\(176\) | 4.39303e14 | 1.11412 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | 3.07243e14 | 0.724023 | ||||||||
\(179\) | 5.26309e14 | 1.19590 | 0.597952 | − | 0.801532i | \(-0.295981\pi\) | ||||
0.597952 | + | 0.801532i | \(0.295981\pi\) | |||||||
\(180\) | 4.53770e14 | 0.994409 | ||||||||
\(181\) | −1.41686e14 | −0.299513 | −0.149757 | − | 0.988723i | \(-0.547849\pi\) | ||||
−0.149757 | + | 0.988723i | \(0.547849\pi\) | |||||||
\(182\) | 1.75467e15 | 3.57875 | ||||||||
\(183\) | −1.54528e14 | −0.304142 | ||||||||
\(184\) | 4.29178e14 | 0.815309 | ||||||||
\(185\) | 1.17040e15 | 2.14643 | ||||||||
\(186\) | −4.33011e14 | −0.766769 | ||||||||
\(187\) | 2.97165e14 | 0.508191 | ||||||||
\(188\) | 2.83992e12 | 0.00469115 | ||||||||
\(189\) | −1.53110e14 | −0.244343 | ||||||||
\(190\) | −1.13905e15 | −1.75649 | ||||||||
\(191\) | −1.13302e14 | −0.168857 | −0.0844285 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844285 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(192\) | 3.43278e14 | 0.494525 | ||||||||
\(193\) | −5.04772e14 | −0.703028 | −0.351514 | − | 0.936183i | \(-0.614333\pi\) | ||||
−0.351514 | + | 0.936183i | \(0.614333\pi\) | |||||||
\(194\) | 2.02232e15 | 2.72358 | ||||||||
\(195\) | 8.45667e14 | 1.10147 | ||||||||
\(196\) | 1.16234e15 | 1.46443 | ||||||||
\(197\) | −1.14653e15 | −1.39751 | −0.698756 | − | 0.715360i | \(-0.746263\pi\) | ||||
−0.698756 | + | 0.715360i | \(0.746263\pi\) | |||||||
\(198\) | −2.48611e14 | −0.293222 | ||||||||
\(199\) | −1.38430e15 | −1.58010 | −0.790049 | − | 0.613044i | \(-0.789945\pi\) | ||||
−0.790049 | + | 0.613044i | \(0.789945\pi\) | |||||||
\(200\) | −1.28718e15 | −1.42215 | ||||||||
\(201\) | −6.68723e14 | −0.715273 | ||||||||
\(202\) | −1.57764e15 | −1.63390 | ||||||||
\(203\) | −1.79984e14 | −0.180513 | ||||||||
\(204\) | 1.51337e15 | 1.47010 | ||||||||
\(205\) | −7.50031e14 | −0.705796 | ||||||||
\(206\) | −5.22939e13 | −0.0476775 | ||||||||
\(207\) | −1.19900e14 | −0.105928 | ||||||||
\(208\) | 4.16940e15 | 3.56995 | ||||||||
\(209\) | 4.40128e14 | 0.365282 | ||||||||
\(210\) | 2.09218e15 | 1.68335 | ||||||||
\(211\) | −2.36304e15 | −1.84347 | −0.921734 | − | 0.387823i | \(-0.873227\pi\) | ||||
−0.921734 | + | 0.387823i | \(0.873227\pi\) | |||||||
\(212\) | 8.43173e14 | 0.637872 | ||||||||
\(213\) | 9.70364e14 | 0.711979 | ||||||||
\(214\) | −2.15447e15 | −1.53339 | ||||||||
\(215\) | 1.26827e15 | 0.875711 | ||||||||
\(216\) | −7.36981e14 | −0.493750 | ||||||||
\(217\) | −1.40803e15 | −0.915430 | ||||||||
\(218\) | −1.12203e15 | −0.708004 | ||||||||
\(219\) | −9.52393e14 | −0.583350 | ||||||||
\(220\) | 2.39590e15 | 1.42469 | ||||||||
\(221\) | 2.82038e15 | 1.62839 | ||||||||
\(222\) | −3.26561e15 | −1.83092 | ||||||||
\(223\) | −1.11944e15 | −0.609563 | −0.304782 | − | 0.952422i | \(-0.598583\pi\) | ||||
−0.304782 | + | 0.952422i | \(0.598583\pi\) | |||||||
\(224\) | 4.15649e15 | 2.19844 | ||||||||
\(225\) | 3.59602e14 | 0.184772 | ||||||||
\(226\) | −1.52603e15 | −0.761831 | ||||||||
\(227\) | 3.69508e15 | 1.79249 | 0.896244 | − | 0.443562i | \(-0.146286\pi\) | ||||
0.896244 | + | 0.443562i | \(0.146286\pi\) | |||||||
\(228\) | 2.24143e15 | 1.05669 | ||||||||
\(229\) | 1.30647e15 | 0.598646 | 0.299323 | − | 0.954152i | \(-0.403239\pi\) | ||||
0.299323 | + | 0.954152i | \(0.403239\pi\) | |||||||
\(230\) | 1.63839e15 | 0.729769 | ||||||||
\(231\) | −8.08416e14 | −0.350072 | ||||||||
\(232\) | −8.66339e14 | −0.364767 | ||||||||
\(233\) | 2.77607e15 | 1.13662 | 0.568312 | − | 0.822813i | \(-0.307597\pi\) | ||||
0.568312 | + | 0.822813i | \(0.307597\pi\) | |||||||
\(234\) | −2.35956e15 | −0.939566 | ||||||||
\(235\) | 6.31064e12 | 0.00244418 | ||||||||
\(236\) | −8.26834e14 | −0.311523 | ||||||||
\(237\) | 2.53107e15 | 0.927770 | ||||||||
\(238\) | 6.97762e15 | 2.48861 | ||||||||
\(239\) | 2.48628e15 | 0.862908 | 0.431454 | − | 0.902135i | \(-0.358001\pi\) | ||||
0.431454 | + | 0.902135i | \(0.358001\pi\) | |||||||
\(240\) | 4.97140e15 | 1.67921 | ||||||||
\(241\) | 4.45058e15 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238772\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238772\pi\) | |||||||
\(242\) | 4.44283e15 | 1.42187 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −4.15515e15 | −1.26053 | ||||||||
\(245\) | 2.58286e15 | 0.762994 | ||||||||
\(246\) | 2.09271e15 | 0.602049 | ||||||||
\(247\) | 4.17724e15 | 1.17047 | ||||||||
\(248\) | −6.77746e15 | −1.84983 | ||||||||
\(249\) | 2.65349e15 | 0.705541 | ||||||||
\(250\) | 3.95085e15 | 1.02348 | ||||||||
\(251\) | 2.69542e15 | 0.680374 | 0.340187 | − | 0.940358i | \(-0.389510\pi\) | ||||
0.340187 | + | 0.940358i | \(0.389510\pi\) | |||||||
\(252\) | −4.11700e15 | −1.01269 | ||||||||
\(253\) | −6.33070e14 | −0.151764 | ||||||||
\(254\) | −2.90632e15 | −0.679086 | ||||||||
\(255\) | 3.36288e15 | 0.765951 | ||||||||
\(256\) | −5.13349e15 | −1.13986 | ||||||||
\(257\) | 1.37462e15 | 0.297589 | 0.148794 | − | 0.988868i | \(-0.452461\pi\) | ||||
0.148794 | + | 0.988868i | \(0.452461\pi\) | |||||||
\(258\) | −3.53868e15 | −0.746988 | ||||||||
\(259\) | −1.06189e16 | −2.18590 | ||||||||
\(260\) | 2.27394e16 | 4.56511 | ||||||||
\(261\) | 2.42030e14 | 0.0473921 | ||||||||
\(262\) | 3.95287e15 | 0.755013 | ||||||||
\(263\) | 1.00126e16 | 1.86567 | 0.932835 | − | 0.360303i | \(-0.117327\pi\) | ||||
0.932835 | + | 0.360303i | \(0.117327\pi\) | |||||||
\(264\) | −3.89125e15 | −0.707397 | ||||||||
\(265\) | 1.87363e15 | 0.332343 | ||||||||
\(266\) | 1.03345e16 | 1.78879 | ||||||||
\(267\) | −1.34348e15 | −0.226939 | ||||||||
\(268\) | −1.79815e16 | −2.96449 | ||||||||
\(269\) | −5.49516e15 | −0.884281 | −0.442141 | − | 0.896946i | \(-0.645781\pi\) | ||||
−0.442141 | + | 0.896946i | \(0.645781\pi\) | |||||||
\(270\) | −2.81342e15 | −0.441947 | ||||||||
\(271\) | 8.53635e15 | 1.30910 | 0.654549 | − | 0.756020i | \(-0.272859\pi\) | ||||
0.654549 | + | 0.756020i | \(0.272859\pi\) | |||||||
\(272\) | 1.65801e16 | 2.48250 | ||||||||
\(273\) | −7.67264e15 | −1.12173 | ||||||||
\(274\) | −1.53743e16 | −2.19491 | ||||||||
\(275\) | 1.89869e15 | 0.264723 | ||||||||
\(276\) | −3.22402e15 | −0.439025 | ||||||||
\(277\) | −1.03907e16 | −1.38205 | −0.691027 | − | 0.722829i | \(-0.742842\pi\) | ||||
−0.691027 | + | 0.722829i | \(0.742842\pi\) | |||||||
\(278\) | 7.17544e15 | 0.932303 | ||||||||
\(279\) | 1.89343e15 | 0.240337 | ||||||||
\(280\) | 3.27467e16 | 4.06107 | ||||||||
\(281\) | 3.02542e14 | 0.0366601 | 0.0183301 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183301 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(282\) | −1.76078e13 | −0.00208490 | ||||||||
\(283\) | 1.43459e16 | 1.66003 | 0.830017 | − | 0.557739i | \(-0.188331\pi\) | ||||
0.830017 | + | 0.557739i | \(0.188331\pi\) | |||||||
\(284\) | 2.60924e16 | 2.95083 | ||||||||
\(285\) | 4.98074e15 | 0.550557 | ||||||||
\(286\) | −1.24584e16 | −1.34612 | ||||||||
\(287\) | 6.80494e15 | 0.718774 | ||||||||
\(288\) | −5.58937e15 | −0.577180 | ||||||||
\(289\) | 1.31095e15 | 0.132358 | ||||||||
\(290\) | −3.30724e15 | −0.326497 | ||||||||
\(291\) | −8.84302e15 | −0.853682 | ||||||||
\(292\) | −2.56091e16 | −2.41772 | ||||||||
\(293\) | −1.07037e16 | −0.988316 | −0.494158 | − | 0.869372i | \(-0.664524\pi\) | ||||
−0.494158 | + | 0.869372i | \(0.664524\pi\) | |||||||
\(294\) | −7.20661e15 | −0.650839 | ||||||||
\(295\) | −1.83733e15 | −0.162309 | ||||||||
\(296\) | −5.11132e16 | −4.41710 | ||||||||
\(297\) | 1.08710e15 | 0.0919079 | ||||||||
\(298\) | 1.47065e16 | 1.21648 | ||||||||
\(299\) | −6.00844e15 | −0.486294 | ||||||||
\(300\) | 9.66943e15 | 0.765795 | ||||||||
\(301\) | −1.15068e16 | −0.891813 | ||||||||
\(302\) | 3.79178e15 | 0.287606 | ||||||||
\(303\) | 6.89857e15 | 0.512132 | ||||||||
\(304\) | 2.45566e16 | 1.78439 | ||||||||
\(305\) | −9.23326e15 | −0.656759 | ||||||||
\(306\) | −9.38302e15 | −0.653361 | ||||||||
\(307\) | 5.22880e15 | 0.356453 | 0.178227 | − | 0.983989i | \(-0.442964\pi\) | ||||
0.178227 | + | 0.983989i | \(0.442964\pi\) | |||||||
\(308\) | −2.17377e16 | −1.45089 | ||||||||
\(309\) | 2.28665e14 | 0.0149441 | ||||||||
\(310\) | −2.58729e16 | −1.65575 | ||||||||
\(311\) | −2.44661e15 | −0.153328 | −0.0766641 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766641 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(312\) | −3.69317e16 | −2.26670 | ||||||||
\(313\) | −1.71237e15 | −0.102934 | −0.0514670 | − | 0.998675i | \(-0.516390\pi\) | ||||
−0.0514670 | + | 0.998675i | \(0.516390\pi\) | |||||||
\(314\) | 5.21664e16 | 3.07148 | ||||||||
\(315\) | −9.14849e15 | −0.527632 | ||||||||
\(316\) | 6.80587e16 | 3.84519 | ||||||||
\(317\) | −2.84323e16 | −1.57372 | −0.786859 | − | 0.617133i | \(-0.788294\pi\) | ||||
−0.786859 | + | 0.617133i | \(0.788294\pi\) | |||||||
\(318\) | −5.22776e15 | −0.283491 | ||||||||
\(319\) | 1.27791e15 | 0.0678988 | ||||||||
\(320\) | 2.05113e16 | 1.06787 | ||||||||
\(321\) | 9.42086e15 | 0.480627 | ||||||||
\(322\) | −1.48649e16 | −0.743187 | ||||||||
\(323\) | 1.66112e16 | 0.813926 | ||||||||
\(324\) | 5.53626e15 | 0.265873 | ||||||||
\(325\) | 1.80204e16 | 0.848247 | ||||||||
\(326\) | −5.44000e16 | −2.51006 | ||||||||
\(327\) | 4.90629e15 | 0.221918 | ||||||||
\(328\) | 3.27551e16 | 1.45244 | ||||||||
\(329\) | −5.72557e13 | −0.00248912 | ||||||||
\(330\) | −1.48548e16 | −0.633179 | ||||||||
\(331\) | −3.78376e16 | −1.58140 | −0.790700 | − | 0.612204i | \(-0.790283\pi\) | ||||
−0.790700 | + | 0.612204i | \(0.790283\pi\) | |||||||
\(332\) | 7.13505e16 | 2.92415 | ||||||||
\(333\) | 1.42795e16 | 0.573888 | ||||||||
\(334\) | 8.08727e16 | 3.18750 | ||||||||
\(335\) | −3.99571e16 | −1.54455 | ||||||||
\(336\) | −4.51049e16 | −1.71009 | ||||||||
\(337\) | −5.01871e16 | −1.86637 | −0.933185 | − | 0.359396i | \(-0.882983\pi\) | ||||
−0.933185 | + | 0.359396i | \(0.882983\pi\) | |||||||
\(338\) | −6.77480e16 | −2.47137 | ||||||||
\(339\) | 6.67288e15 | 0.238790 | ||||||||
\(340\) | 9.04255e16 | 3.17452 | ||||||||
\(341\) | 9.99726e15 | 0.344332 | ||||||||
\(342\) | −1.38971e16 | −0.469629 | ||||||||
\(343\) | 1.48568e16 | 0.492622 | ||||||||
\(344\) | −5.53873e16 | −1.80211 | ||||||||
\(345\) | −7.16417e15 | −0.228740 | ||||||||
\(346\) | 5.23321e16 | 1.63973 | ||||||||
\(347\) | −9.80701e15 | −0.301575 | −0.150787 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150787 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(348\) | 6.50801e15 | 0.196419 | ||||||||
\(349\) | −1.70944e16 | −0.506395 | −0.253197 | − | 0.967415i | \(-0.581482\pi\) | ||||
−0.253197 | + | 0.967415i | \(0.581482\pi\) | |||||||
\(350\) | 4.45825e16 | 1.29635 | ||||||||
\(351\) | 1.03176e16 | 0.294499 | ||||||||
\(352\) | −2.95117e16 | −0.826928 | ||||||||
\(353\) | 6.53098e16 | 1.79656 | 0.898282 | − | 0.439419i | \(-0.144816\pi\) | ||||
0.898282 | + | 0.439419i | \(0.144816\pi\) | |||||||
\(354\) | 5.12646e15 | 0.138451 | ||||||||
\(355\) | 5.79805e16 | 1.53744 | ||||||||
\(356\) | −3.61253e16 | −0.940560 | ||||||||
\(357\) | −3.05110e16 | −0.780034 | ||||||||
\(358\) | −8.77442e16 | −2.20282 | ||||||||
\(359\) | −6.09707e16 | −1.50317 | −0.751583 | − | 0.659638i | \(-0.770710\pi\) | ||||
−0.751583 | + | 0.659638i | \(0.770710\pi\) | |||||||
\(360\) | −4.40356e16 | −1.06620 | ||||||||
\(361\) | −1.74503e16 | −0.414959 | ||||||||
\(362\) | 2.36213e16 | 0.551695 | ||||||||
\(363\) | −1.94272e16 | −0.445673 | ||||||||
\(364\) | −2.06312e17 | −4.64906 | ||||||||
\(365\) | −5.69067e16 | −1.25968 | ||||||||
\(366\) | 2.57624e16 | 0.560220 | ||||||||
\(367\) | 2.21422e16 | 0.473033 | 0.236516 | − | 0.971627i | \(-0.423994\pi\) | ||||
0.236516 | + | 0.971627i | \(0.423994\pi\) | |||||||
\(368\) | −3.53216e16 | −0.741361 | ||||||||
\(369\) | −9.15081e15 | −0.188707 | ||||||||
\(370\) | −1.95124e17 | −3.95367 | ||||||||
\(371\) | −1.69993e16 | −0.338454 | ||||||||
\(372\) | 5.09129e16 | 0.996089 | ||||||||
\(373\) | 5.12228e16 | 0.984818 | 0.492409 | − | 0.870364i | \(-0.336117\pi\) | ||||
0.492409 | + | 0.870364i | \(0.336117\pi\) | |||||||
\(374\) | −4.95422e16 | −0.936072 | ||||||||
\(375\) | −1.72759e16 | −0.320802 | ||||||||
\(376\) | −2.75596e14 | −0.00502981 | ||||||||
\(377\) | 1.21286e16 | 0.217567 | ||||||||
\(378\) | 2.55258e16 | 0.450073 | ||||||||
\(379\) | −2.65278e16 | −0.459775 | −0.229888 | − | 0.973217i | \(-0.573836\pi\) | ||||
−0.229888 | + | 0.973217i | \(0.573836\pi\) | |||||||
\(380\) | 1.33928e17 | 2.28181 | ||||||||
\(381\) | 1.27085e16 | 0.212854 | ||||||||
\(382\) | 1.88892e16 | 0.311030 | ||||||||
\(383\) | 6.59095e16 | 1.06698 | 0.533490 | − | 0.845806i | \(-0.320880\pi\) | ||||
0.533490 | + | 0.845806i | \(0.320880\pi\) | |||||||
\(384\) | 5.57940e15 | 0.0888045 | ||||||||
\(385\) | −4.83039e16 | −0.755939 | ||||||||
\(386\) | 8.41536e16 | 1.29496 | ||||||||
\(387\) | 1.54736e16 | 0.234137 | ||||||||
\(388\) | −2.37782e17 | −3.53813 | ||||||||
\(389\) | 9.18217e15 | 0.134361 | 0.0671804 | − | 0.997741i | \(-0.478600\pi\) | ||||
0.0671804 | + | 0.997741i | \(0.478600\pi\) | |||||||
\(390\) | −1.40986e17 | −2.02888 | ||||||||
\(391\) | −2.38932e16 | −0.338162 | ||||||||
\(392\) | −1.12798e17 | −1.57015 | ||||||||
\(393\) | −1.72847e16 | −0.236652 | ||||||||
\(394\) | 1.91145e17 | 2.57418 | ||||||||
\(395\) | 1.51235e17 | 2.00341 | ||||||||
\(396\) | 2.92314e16 | 0.380917 | ||||||||
\(397\) | 7.78847e16 | 0.998421 | 0.499210 | − | 0.866481i | \(-0.333623\pi\) | ||||
0.499210 | + | 0.866481i | \(0.333623\pi\) | |||||||
\(398\) | 2.30784e17 | 2.91049 | ||||||||
\(399\) | −4.51896e16 | −0.560680 | ||||||||
\(400\) | 1.05936e17 | 1.29316 | ||||||||
\(401\) | −1.77085e16 | −0.212688 | −0.106344 | − | 0.994329i | \(-0.533914\pi\) | ||||
−0.106344 | + | 0.994329i | \(0.533914\pi\) | |||||||
\(402\) | 1.11487e17 | 1.31751 | ||||||||
\(403\) | 9.48835e16 | 1.10334 | ||||||||
\(404\) | 1.85497e17 | 2.12256 | ||||||||
\(405\) | 1.23023e16 | 0.138525 | ||||||||
\(406\) | 3.00062e16 | 0.332500 | ||||||||
\(407\) | 7.53957e16 | 0.822211 | ||||||||
\(408\) | −1.46863e17 | −1.57623 | ||||||||
\(409\) | 5.64265e16 | 0.596048 | 0.298024 | − | 0.954558i | \(-0.403672\pi\) | ||||
0.298024 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(410\) | 1.25042e17 | 1.30006 | ||||||||
\(411\) | 6.72272e16 | 0.687976 | ||||||||
\(412\) | 6.14865e15 | 0.0619366 | ||||||||
\(413\) | 1.66699e16 | 0.165294 | ||||||||
\(414\) | 1.99893e16 | 0.195117 | ||||||||
\(415\) | 1.58550e17 | 1.52354 | ||||||||
\(416\) | −2.80095e17 | −2.64971 | ||||||||
\(417\) | −3.13760e16 | −0.292223 | ||||||||
\(418\) | −7.33765e16 | −0.672839 | ||||||||
\(419\) | 9.61919e16 | 0.868455 | 0.434228 | − | 0.900803i | \(-0.357021\pi\) | ||||
0.434228 | + | 0.900803i | \(0.357021\pi\) | |||||||
\(420\) | −2.45996e17 | −2.18679 | ||||||||
\(421\) | −5.22604e16 | −0.457445 | −0.228722 | − | 0.973492i | \(-0.573455\pi\) | ||||
−0.228722 | + | 0.973492i | \(0.573455\pi\) | |||||||
\(422\) | 3.93957e17 | 3.39561 | ||||||||
\(423\) | 7.69935e13 | 0.000653494 0 | ||||||||
\(424\) | −8.18246e16 | −0.683921 | ||||||||
\(425\) | 7.16600e16 | 0.589860 | ||||||||
\(426\) | −1.61775e17 | −1.31145 | ||||||||
\(427\) | 8.37723e16 | 0.668835 | ||||||||
\(428\) | 2.53320e17 | 1.99198 | ||||||||
\(429\) | 5.44769e16 | 0.421930 | ||||||||
\(430\) | −2.11441e17 | −1.61303 | ||||||||
\(431\) | 1.12144e17 | 0.842702 | 0.421351 | − | 0.906898i | \(-0.361556\pi\) | ||||
0.421351 | + | 0.906898i | \(0.361556\pi\) | |||||||
\(432\) | 6.06540e16 | 0.448967 | ||||||||
\(433\) | 3.70819e16 | 0.270390 | 0.135195 | − | 0.990819i | \(-0.456834\pi\) | ||||
0.135195 | + | 0.990819i | \(0.456834\pi\) | |||||||
\(434\) | 2.34742e17 | 1.68619 | ||||||||
\(435\) | 1.44616e16 | 0.102338 | ||||||||
\(436\) | 1.31926e17 | 0.919750 | ||||||||
\(437\) | −3.53880e16 | −0.243067 | ||||||||
\(438\) | 1.58779e17 | 1.07451 | ||||||||
\(439\) | −1.76562e17 | −1.17728 | −0.588638 | − | 0.808396i | \(-0.700336\pi\) | ||||
−0.588638 | + | 0.808396i | \(0.700336\pi\) | |||||||
\(440\) | −2.32507e17 | −1.52754 | ||||||||
\(441\) | 3.15124e16 | 0.204000 | ||||||||
\(442\) | −4.70202e17 | −2.99944 | ||||||||
\(443\) | 1.96195e17 | 1.23329 | 0.616644 | − | 0.787242i | \(-0.288492\pi\) | ||||
0.616644 | + | 0.787242i | \(0.288492\pi\) | |||||||
\(444\) | 3.83967e17 | 2.37850 | ||||||||
\(445\) | −8.02748e16 | −0.490049 | ||||||||
\(446\) | 1.86629e17 | 1.12280 | ||||||||
\(447\) | −6.43073e16 | −0.381295 | ||||||||
\(448\) | −1.86097e17 | −1.08751 | ||||||||
\(449\) | −1.36970e17 | −0.788905 | −0.394452 | − | 0.918916i | \(-0.629066\pi\) | ||||
−0.394452 | + | 0.918916i | \(0.629066\pi\) | |||||||
\(450\) | −5.99514e16 | −0.340344 | ||||||||
\(451\) | −4.83161e16 | −0.270361 | ||||||||
\(452\) | 1.79429e17 | 0.989675 | ||||||||
\(453\) | −1.65803e16 | −0.0901476 | ||||||||
\(454\) | −6.16030e17 | −3.30171 | ||||||||
\(455\) | −4.58450e17 | −2.42224 | ||||||||
\(456\) | −2.17517e17 | −1.13298 | ||||||||
\(457\) | 1.20278e17 | 0.617636 | 0.308818 | − | 0.951121i | \(-0.400067\pi\) | ||||
0.308818 | + | 0.951121i | \(0.400067\pi\) | |||||||
\(458\) | −2.17810e17 | −1.10269 | ||||||||
\(459\) | 4.10291e16 | 0.204791 | ||||||||
\(460\) | −1.92639e17 | −0.948024 | ||||||||
\(461\) | 2.94491e17 | 1.42895 | 0.714474 | − | 0.699662i | \(-0.246666\pi\) | ||||
0.714474 | + | 0.699662i | \(0.246666\pi\) | |||||||
\(462\) | 1.34776e17 | 0.644822 | ||||||||
\(463\) | 3.10512e17 | 1.46488 | 0.732439 | − | 0.680833i | \(-0.238382\pi\) | ||||
0.732439 | + | 0.680833i | \(0.238382\pi\) | |||||||
\(464\) | 7.13002e16 | 0.331683 | ||||||||
\(465\) | 1.13135e17 | 0.518981 | ||||||||
\(466\) | −4.62815e17 | −2.09363 | ||||||||
\(467\) | 3.66019e17 | 1.63284 | 0.816421 | − | 0.577458i | \(-0.195955\pi\) | ||||
0.816421 | + | 0.577458i | \(0.195955\pi\) | |||||||
\(468\) | 2.77434e17 | 1.22057 | ||||||||
\(469\) | 3.62526e17 | 1.57295 | ||||||||
\(470\) | −1.05209e15 | −0.00450210 | ||||||||
\(471\) | −2.28108e17 | −0.962731 | ||||||||
\(472\) | 8.02391e16 | 0.334013 | ||||||||
\(473\) | 8.17003e16 | 0.335449 | ||||||||
\(474\) | −4.21970e17 | −1.70892 | ||||||||
\(475\) | 1.06135e17 | 0.423985 | ||||||||
\(476\) | −8.20420e17 | −3.23289 | ||||||||
\(477\) | 2.28594e16 | 0.0888579 | ||||||||
\(478\) | −4.14504e17 | −1.58945 | ||||||||
\(479\) | −1.92869e17 | −0.729596 | −0.364798 | − | 0.931087i | \(-0.618862\pi\) | ||||
−0.364798 | + | 0.931087i | \(0.618862\pi\) | |||||||
\(480\) | −3.33972e17 | −1.24635 | ||||||||
\(481\) | 7.15578e17 | 2.63459 | ||||||||
\(482\) | −7.41983e17 | −2.69518 | ||||||||
\(483\) | 6.49997e16 | 0.232946 | ||||||||
\(484\) | −5.22383e17 | −1.84712 | ||||||||
\(485\) | −5.28381e17 | −1.84343 | ||||||||
\(486\) | −3.43254e16 | −0.118162 | ||||||||
\(487\) | 9.24807e16 | 0.314133 | 0.157066 | − | 0.987588i | \(-0.449796\pi\) | ||||
0.157066 | + | 0.987588i | \(0.449796\pi\) | |||||||
\(488\) | 4.03231e17 | 1.35153 | ||||||||
\(489\) | 2.37875e17 | 0.786758 | ||||||||
\(490\) | −4.30604e17 | −1.40541 | ||||||||
\(491\) | 5.83125e16 | 0.187816 | 0.0939079 | − | 0.995581i | \(-0.470064\pi\) | ||||
0.0939079 | + | 0.995581i | \(0.470064\pi\) | |||||||
\(492\) | −2.46059e17 | −0.782106 | ||||||||
\(493\) | 4.82307e16 | 0.151293 | ||||||||
\(494\) | −6.96413e17 | −2.15596 | ||||||||
\(495\) | 6.49557e16 | 0.198465 | ||||||||
\(496\) | 5.57789e17 | 1.68205 | ||||||||
\(497\) | −5.26050e17 | −1.56571 | ||||||||
\(498\) | −4.42380e17 | −1.29959 | ||||||||
\(499\) | 4.12178e17 | 1.19517 | 0.597587 | − | 0.801804i | \(-0.296126\pi\) | ||||
0.597587 | + | 0.801804i | \(0.296126\pi\) | |||||||
\(500\) | −4.64536e17 | −1.32958 | ||||||||
\(501\) | −3.53632e17 | −0.999094 | ||||||||
\(502\) | −4.49371e17 | −1.25323 | ||||||||
\(503\) | 5.29139e17 | 1.45673 | 0.728363 | − | 0.685192i | \(-0.240282\pi\) | ||||
0.728363 | + | 0.685192i | \(0.240282\pi\) | |||||||
\(504\) | 3.99529e17 | 1.08580 | ||||||||
\(505\) | 4.12198e17 | 1.10589 | ||||||||
\(506\) | 1.05543e17 | 0.279544 | ||||||||
\(507\) | 2.96242e17 | 0.774631 | ||||||||
\(508\) | 3.41722e17 | 0.882183 | ||||||||
\(509\) | −3.99011e17 | −1.01700 | −0.508498 | − | 0.861063i | \(-0.669799\pi\) | ||||
−0.508498 | + | 0.861063i | \(0.669799\pi\) | |||||||
\(510\) | −5.60647e17 | −1.41086 | ||||||||
\(511\) | 5.16307e17 | 1.28284 | ||||||||
\(512\) | 7.93138e17 | 1.94578 | ||||||||
\(513\) | 6.07679e16 | 0.147201 | ||||||||
\(514\) | −2.29171e17 | −0.548150 | ||||||||
\(515\) | 1.36630e16 | 0.0322701 | ||||||||
\(516\) | 4.16074e17 | 0.970392 | ||||||||
\(517\) | 4.06524e14 | 0.000936263 0 | ||||||||
\(518\) | 1.77034e18 | 4.02637 | ||||||||
\(519\) | −2.28833e17 | −0.513961 | ||||||||
\(520\) | −2.20671e18 | −4.89468 | ||||||||
\(521\) | 2.52542e17 | 0.553208 | 0.276604 | − | 0.960984i | \(-0.410791\pi\) | ||||
0.276604 | + | 0.960984i | \(0.410791\pi\) | |||||||
\(522\) | −4.03503e16 | −0.0872948 | ||||||||
\(523\) | −4.88553e17 | −1.04388 | −0.521940 | − | 0.852982i | \(-0.674791\pi\) | ||||
−0.521940 | + | 0.852982i | \(0.674791\pi\) | |||||||
\(524\) | −4.64774e17 | −0.980818 | ||||||||
\(525\) | −1.94946e17 | −0.406330 | ||||||||
\(526\) | −1.66926e18 | −3.43651 | ||||||||
\(527\) | 3.77314e17 | 0.767245 | ||||||||
\(528\) | 3.20252e17 | 0.643237 | ||||||||
\(529\) | −4.53135e17 | −0.899013 | ||||||||
\(530\) | −3.12365e17 | −0.612166 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −1.21512e18 | −2.32377 | ||||||||
\(533\) | −4.58566e17 | −0.866314 | ||||||||
\(534\) | 2.23980e17 | 0.418015 | ||||||||
\(535\) | 5.62908e17 | 1.03786 | ||||||||
\(536\) | 1.74499e18 | 3.17850 | ||||||||
\(537\) | 3.83679e17 | 0.690455 | ||||||||
\(538\) | 9.16132e17 | 1.62882 | ||||||||
\(539\) | 1.66385e17 | 0.292271 | ||||||||
\(540\) | 3.30799e17 | 0.574122 | ||||||||
\(541\) | 1.11207e17 | 0.190700 | 0.0953499 | − | 0.995444i | \(-0.469603\pi\) | ||||
0.0953499 | + | 0.995444i | \(0.469603\pi\) | |||||||
\(542\) | −1.42315e18 | −2.41132 | ||||||||
\(543\) | −1.03289e17 | −0.172924 | ||||||||
\(544\) | −1.11383e18 | −1.84257 | ||||||||
\(545\) | 2.93157e17 | 0.479206 | ||||||||
\(546\) | 1.27915e18 | 2.06619 | ||||||||
\(547\) | 7.63636e16 | 0.121890 | 0.0609451 | − | 0.998141i | \(-0.480589\pi\) | ||||
0.0609451 | + | 0.998141i | \(0.480589\pi\) | |||||||
\(548\) | 1.80769e18 | 2.85135 | ||||||||
\(549\) | −1.12651e17 | −0.175596 | ||||||||
\(550\) | −3.16542e17 | −0.487612 | ||||||||
\(551\) | 7.14341e16 | 0.108748 | ||||||||
\(552\) | 3.12871e17 | 0.470719 | ||||||||
\(553\) | −1.37213e18 | −2.04025 | ||||||||
\(554\) | 1.73229e18 | 2.54570 | ||||||||
\(555\) | 8.53221e17 | 1.23924 | ||||||||
\(556\) | −8.43679e17 | −1.21113 | ||||||||
\(557\) | 4.01835e17 | 0.570150 | 0.285075 | − | 0.958505i | \(-0.407981\pi\) | ||||
0.285075 | + | 0.958505i | \(0.407981\pi\) | |||||||
\(558\) | −3.15665e17 | −0.442694 | ||||||||
\(559\) | 7.75414e17 | 1.07487 | ||||||||
\(560\) | −2.69508e18 | −3.69274 | ||||||||
\(561\) | 2.16633e17 | 0.293404 | ||||||||
\(562\) | −5.04386e16 | −0.0675269 | ||||||||
\(563\) | 8.18065e17 | 1.08264 | 0.541319 | − | 0.840817i | \(-0.317925\pi\) | ||||
0.541319 | + | 0.840817i | \(0.317925\pi\) | |||||||
\(564\) | 2.07030e15 | 0.00270844 | ||||||||
\(565\) | 3.98713e17 | 0.515639 | ||||||||
\(566\) | −2.39170e18 | −3.05773 | ||||||||
\(567\) | −1.11617e17 | −0.141072 | ||||||||
\(568\) | −2.53210e18 | −3.16386 | ||||||||
\(569\) | 1.02365e18 | 1.26451 | 0.632253 | − | 0.774762i | \(-0.282130\pi\) | ||||
0.632253 | + | 0.774762i | \(0.282130\pi\) | |||||||
\(570\) | −8.30370e17 | −1.01411 | ||||||||
\(571\) | 8.02040e16 | 0.0968415 | 0.0484207 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484207 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(572\) | 1.46484e18 | 1.74871 | ||||||||
\(573\) | −8.25969e16 | −0.0974896 | ||||||||
\(574\) | −1.13449e18 | −1.32396 | ||||||||
\(575\) | −1.52662e17 | −0.176153 | ||||||||
\(576\) | 2.50250e17 | 0.285514 | ||||||||
\(577\) | −6.55279e16 | −0.0739236 | −0.0369618 | − | 0.999317i | \(-0.511768\pi\) | ||||
−0.0369618 | + | 0.999317i | \(0.511768\pi\) | |||||||
\(578\) | −2.18556e17 | −0.243799 | ||||||||
\(579\) | −3.67979e17 | −0.405893 | ||||||||
\(580\) | 3.88862e17 | 0.424144 | ||||||||
\(581\) | −1.43850e18 | −1.55155 | ||||||||
\(582\) | 1.47427e18 | 1.57246 | ||||||||
\(583\) | 1.20697e17 | 0.127307 | ||||||||
\(584\) | 2.48521e18 | 2.59226 | ||||||||
\(585\) | 6.16491e17 | 0.635937 | ||||||||
\(586\) | 1.78449e18 | 1.82045 | ||||||||
\(587\) | −1.41001e18 | −1.42257 | −0.711284 | − | 0.702905i | \(-0.751886\pi\) | ||||
−0.711284 | + | 0.702905i | \(0.751886\pi\) | |||||||
\(588\) | 8.47344e17 | 0.845488 | ||||||||
\(589\) | 5.58837e17 | 0.551487 | ||||||||
\(590\) | 3.06312e17 | 0.298969 | ||||||||
\(591\) | −8.35821e17 | −0.806854 | ||||||||
\(592\) | 4.20665e18 | 4.01647 | ||||||||
\(593\) | 1.76703e18 | 1.66874 | 0.834368 | − | 0.551208i | \(-0.185833\pi\) | ||||
0.834368 | + | 0.551208i | \(0.185833\pi\) | |||||||
\(594\) | −1.81237e17 | −0.169292 | ||||||||
\(595\) | −1.82307e18 | −1.68439 | ||||||||
\(596\) | −1.72918e18 | −1.58030 | ||||||||
\(597\) | −1.00915e18 | −0.912269 | ||||||||
\(598\) | 1.00170e18 | 0.895739 | ||||||||
\(599\) | 7.43189e17 | 0.657393 | 0.328696 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328696 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(600\) | −9.38357e17 | −0.821079 | ||||||||
\(601\) | 5.45093e15 | 0.00471831 | 0.00235916 | − | 0.999997i | \(-0.499249\pi\) | ||||
0.00235916 | + | 0.999997i | \(0.499249\pi\) | |||||||
\(602\) | 1.91838e18 | 1.64269 | ||||||||
\(603\) | −4.87499e17 | −0.412963 | ||||||||
\(604\) | −4.45832e17 | −0.373621 | ||||||||
\(605\) | −1.16080e18 | −0.962381 | ||||||||
\(606\) | −1.15010e18 | −0.943332 | ||||||||
\(607\) | 1.82401e18 | 1.48013 | 0.740067 | − | 0.672534i | \(-0.234794\pi\) | ||||
0.740067 | + | 0.672534i | \(0.234794\pi\) | |||||||
\(608\) | −1.64968e18 | −1.32442 | ||||||||
\(609\) | −1.31208e17 | −0.104219 | ||||||||
\(610\) | 1.53933e18 | 1.20973 | ||||||||
\(611\) | 3.85830e15 | 0.00300005 | ||||||||
\(612\) | 1.10324e18 | 0.848764 | ||||||||
\(613\) | 2.14261e18 | 1.63098 | 0.815492 | − | 0.578769i | \(-0.196467\pi\) | ||||
0.815492 | + | 0.578769i | \(0.196467\pi\) | |||||||
\(614\) | −8.71726e17 | −0.656577 | ||||||||
\(615\) | −5.46773e17 | −0.407491 | ||||||||
\(616\) | 2.10951e18 | 1.55563 | ||||||||
\(617\) | −1.47169e18 | −1.07390 | −0.536949 | − | 0.843615i | \(-0.680423\pi\) | ||||
−0.536949 | + | 0.843615i | \(0.680423\pi\) | |||||||
\(618\) | −3.81222e16 | −0.0275266 | ||||||||
\(619\) | −2.34920e18 | −1.67854 | −0.839268 | − | 0.543718i | \(-0.817016\pi\) | ||||
−0.839268 | + | 0.543718i | \(0.817016\pi\) | |||||||
\(620\) | 3.04211e18 | 2.15094 | ||||||||
\(621\) | −8.74071e16 | −0.0611577 | ||||||||
\(622\) | 4.07889e17 | 0.282426 | ||||||||
\(623\) | 7.28324e17 | 0.499060 | ||||||||
\(624\) | 3.03950e18 | 2.06111 | ||||||||
\(625\) | −1.85825e18 | −1.24705 | ||||||||
\(626\) | 2.85480e17 | 0.189602 | ||||||||
\(627\) | 3.20853e17 | 0.210896 | ||||||||
\(628\) | −6.13366e18 | −3.99009 | ||||||||
\(629\) | 2.84557e18 | 1.83206 | ||||||||
\(630\) | 1.52520e18 | 0.971882 | ||||||||
\(631\) | −3.37780e17 | −0.213031 | −0.106516 | − | 0.994311i | \(-0.533969\pi\) | ||||
−0.106516 | + | 0.994311i | \(0.533969\pi\) | |||||||
\(632\) | −6.60466e18 | −4.12278 | ||||||||
\(633\) | −1.72266e18 | −1.06433 | ||||||||
\(634\) | 4.74012e18 | 2.89874 | ||||||||
\(635\) | 7.59348e17 | 0.459633 | ||||||||
\(636\) | 6.14673e17 | 0.368276 | ||||||||
\(637\) | 1.57915e18 | 0.936520 | ||||||||
\(638\) | −2.13049e17 | −0.125068 | ||||||||
\(639\) | 7.07396e17 | 0.411061 | ||||||||
\(640\) | 3.33376e17 | 0.191763 | ||||||||
\(641\) | −1.95698e17 | −0.111432 | −0.0557160 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557160 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(642\) | −1.57061e18 | −0.885300 | ||||||||
\(643\) | 2.67575e18 | 1.49305 | 0.746526 | − | 0.665357i | \(-0.231720\pi\) | ||||
0.746526 | + | 0.665357i | \(0.231720\pi\) | |||||||
\(644\) | 1.74779e18 | 0.965455 | ||||||||
\(645\) | 9.24567e17 | 0.505592 | ||||||||
\(646\) | −2.76936e18 | −1.49923 | ||||||||
\(647\) | −1.32947e18 | −0.712526 | −0.356263 | − | 0.934386i | \(-0.615949\pi\) | ||||
−0.356263 | + | 0.934386i | \(0.615949\pi\) | |||||||
\(648\) | −5.37259e17 | −0.285067 | ||||||||
\(649\) | −1.18359e17 | −0.0621740 | ||||||||
\(650\) | −3.00429e18 | −1.56245 | ||||||||
\(651\) | −1.02646e18 | −0.528523 | ||||||||
\(652\) | 6.39628e18 | 3.26076 | ||||||||
\(653\) | −1.93417e17 | −0.0976243 | −0.0488122 | − | 0.998808i | \(-0.515544\pi\) | ||||
−0.0488122 | + | 0.998808i | \(0.515544\pi\) | |||||||
\(654\) | −8.17957e17 | −0.408766 | ||||||||
\(655\) | −1.03278e18 | −0.511024 | ||||||||
\(656\) | −2.69576e18 | −1.32071 | ||||||||
\(657\) | −6.94294e17 | −0.336797 | ||||||||
\(658\) | 9.54545e15 | 0.00458488 | ||||||||
\(659\) | 2.20254e18 | 1.04753 | 0.523766 | − | 0.851862i | \(-0.324526\pi\) | ||||
0.523766 | + | 0.851862i | \(0.324526\pi\) | |||||||
\(660\) | 1.74661e18 | 0.822546 | ||||||||
\(661\) | −3.58539e18 | −1.67196 | −0.835982 | − | 0.548756i | \(-0.815101\pi\) | ||||
−0.835982 | + | 0.548756i | \(0.815101\pi\) | |||||||
\(662\) | 6.30814e18 | 2.91289 | ||||||||
\(663\) | 2.05606e18 | 0.940149 | ||||||||
\(664\) | −6.92412e18 | −3.13525 | ||||||||
\(665\) | −2.70014e18 | −1.21072 | ||||||||
\(666\) | −2.38063e18 | −1.05708 | ||||||||
\(667\) | −1.02749e17 | −0.0451814 | ||||||||
\(668\) | −9.50891e18 | −4.14080 | ||||||||
\(669\) | −8.16071e17 | −0.351931 | ||||||||
\(670\) | 6.66149e18 | 2.84502 | ||||||||
\(671\) | −5.94796e17 | −0.251577 | ||||||||
\(672\) | 3.03008e18 | 1.26927 | ||||||||
\(673\) | 2.03328e18 | 0.843529 | 0.421765 | − | 0.906705i | \(-0.361411\pi\) | ||||
0.421765 | + | 0.906705i | \(0.361411\pi\) | |||||||
\(674\) | 8.36700e18 | 3.43780 | ||||||||
\(675\) | 2.62150e17 | 0.106678 | ||||||||
\(676\) | 7.96573e18 | 3.21049 | ||||||||
\(677\) | −4.31426e18 | −1.72219 | −0.861093 | − | 0.508447i | \(-0.830220\pi\) | ||||
−0.861093 | + | 0.508447i | \(0.830220\pi\) | |||||||
\(678\) | −1.11248e18 | −0.439843 | ||||||||
\(679\) | 4.79394e18 | 1.87732 | ||||||||
\(680\) | −8.77522e18 | −3.40369 | ||||||||
\(681\) | 2.69371e18 | 1.03489 | ||||||||
\(682\) | −1.66670e18 | −0.634249 | ||||||||
\(683\) | −3.28300e18 | −1.23748 | −0.618738 | − | 0.785597i | \(-0.712356\pi\) | ||||
−0.618738 | + | 0.785597i | \(0.712356\pi\) | |||||||
\(684\) | 1.63400e18 | 0.610082 | ||||||||
\(685\) | 4.01691e18 | 1.48561 | ||||||||
\(686\) | −2.47687e18 | −0.907396 | ||||||||
\(687\) | 9.52420e17 | 0.345629 | ||||||||
\(688\) | 4.55841e18 | 1.63866 | ||||||||
\(689\) | 1.14553e18 | 0.407927 | ||||||||
\(690\) | 1.19438e18 | 0.421332 | ||||||||
\(691\) | 2.85949e18 | 0.999267 | 0.499633 | − | 0.866237i | \(-0.333468\pi\) | ||||
0.499633 | + | 0.866237i | \(0.333468\pi\) | |||||||
\(692\) | −6.15314e18 | −2.13014 | ||||||||
\(693\) | −5.89335e17 | −0.202114 | ||||||||
\(694\) | 1.63499e18 | 0.555492 | ||||||||
\(695\) | −1.87476e18 | −0.631021 | ||||||||
\(696\) | −6.31561e17 | −0.210598 | ||||||||
\(697\) | −1.82354e18 | −0.602423 | ||||||||
\(698\) | 2.84992e18 | 0.932764 | ||||||||
\(699\) | 2.02375e18 | 0.656230 | ||||||||
\(700\) | −5.24195e18 | −1.68405 | ||||||||
\(701\) | −3.12642e18 | −0.995131 | −0.497566 | − | 0.867426i | \(-0.665773\pi\) | ||||
−0.497566 | + | 0.867426i | \(0.665773\pi\) | |||||||
\(702\) | −1.72012e18 | −0.542458 | ||||||||
\(703\) | 4.21455e18 | 1.31687 | ||||||||
\(704\) | 1.32131e18 | 0.409057 | ||||||||
\(705\) | 4.60046e15 | 0.00141115 | ||||||||
\(706\) | −1.08882e19 | −3.30922 | ||||||||
\(707\) | −3.73982e18 | −1.12622 | ||||||||
\(708\) | −6.02762e17 | −0.179858 | ||||||||
\(709\) | −6.61539e18 | −1.95594 | −0.977969 | − | 0.208750i | \(-0.933060\pi\) | ||||
−0.977969 | + | 0.208750i | \(0.933060\pi\) | |||||||
\(710\) | −9.66628e18 | −2.83192 | ||||||||
\(711\) | 1.84515e18 | 0.535648 | ||||||||
\(712\) | 3.50573e18 | 1.00846 | ||||||||
\(713\) | −8.03818e17 | −0.229127 | ||||||||
\(714\) | 5.08668e18 | 1.43680 | ||||||||
\(715\) | 3.25506e18 | 0.911109 | ||||||||
\(716\) | 1.03169e19 | 2.86162 | ||||||||
\(717\) | 1.81250e18 | 0.498200 | ||||||||
\(718\) | 1.01648e19 | 2.76879 | ||||||||
\(719\) | 7.26986e18 | 1.96240 | 0.981202 | − | 0.192984i | \(-0.0618166\pi\) | ||||
0.981202 | + | 0.192984i | \(0.0618166\pi\) | |||||||
\(720\) | 3.62415e18 | 0.969494 | ||||||||
\(721\) | −1.23963e17 | −0.0328635 | ||||||||
\(722\) | 2.90924e18 | 0.764342 | ||||||||
\(723\) | 3.24447e18 | 0.844783 | ||||||||
\(724\) | −2.77737e18 | −0.716692 | ||||||||
\(725\) | 3.08163e17 | 0.0788104 | ||||||||
\(726\) | 3.23883e18 | 0.820917 | ||||||||
\(727\) | 7.25236e18 | 1.82182 | 0.910910 | − | 0.412604i | \(-0.135381\pi\) | ||||
0.910910 | + | 0.412604i | \(0.135381\pi\) | |||||||
\(728\) | 2.00212e19 | 4.98468 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 9.48726e18 | 2.32029 | ||||||||
\(731\) | 3.08352e18 | 0.747452 | ||||||||
\(732\) | −3.02911e18 | −0.727767 | ||||||||
\(733\) | 3.90928e18 | 0.930938 | 0.465469 | − | 0.885064i | \(-0.345886\pi\) | ||||
0.465469 | + | 0.885064i | \(0.345886\pi\) | |||||||
\(734\) | −3.69146e18 | −0.871313 | ||||||||
\(735\) | 1.88290e18 | 0.440515 | ||||||||
\(736\) | 2.37286e18 | 0.550257 | ||||||||
\(737\) | −2.57399e18 | −0.591654 | ||||||||
\(738\) | 1.52559e18 | 0.347593 | ||||||||
\(739\) | −1.18734e17 | −0.0268156 | −0.0134078 | − | 0.999910i | \(-0.504268\pi\) | ||||
−0.0134078 | + | 0.999910i | \(0.504268\pi\) | |||||||
\(740\) | 2.29425e19 | 5.13611 | ||||||||
\(741\) | 3.04521e18 | 0.675769 | ||||||||
\(742\) | 2.83405e18 | 0.623422 | ||||||||
\(743\) | 5.62331e18 | 1.22621 | 0.613105 | − | 0.790002i | \(-0.289920\pi\) | ||||
0.613105 | + | 0.790002i | \(0.289920\pi\) | |||||||
\(744\) | −4.94077e18 | −1.06800 | ||||||||
\(745\) | −3.84244e18 | −0.823363 | ||||||||
\(746\) | −8.53967e18 | −1.81401 | ||||||||
\(747\) | 1.93440e18 | 0.407344 | ||||||||
\(748\) | 5.82510e18 | 1.21603 | ||||||||
\(749\) | −5.10720e18 | −1.05694 | ||||||||
\(750\) | 2.88017e18 | 0.590907 | ||||||||
\(751\) | −7.12638e17 | −0.144947 | −0.0724736 | − | 0.997370i | \(-0.523089\pi\) | ||||
−0.0724736 | + | 0.997370i | \(0.523089\pi\) | |||||||
\(752\) | 2.26817e16 | 0.00457362 | ||||||||
\(753\) | 1.96496e18 | 0.392814 | ||||||||
\(754\) | −2.02204e18 | −0.400752 | ||||||||
\(755\) | −9.90694e17 | −0.194663 | ||||||||
\(756\) | −3.00130e18 | −0.584679 | ||||||||
\(757\) | −6.26409e18 | −1.20986 | −0.604929 | − | 0.796279i | \(-0.706799\pi\) | ||||
−0.604929 | + | 0.796279i | \(0.706799\pi\) | |||||||
\(758\) | 4.42261e18 | 0.846893 | ||||||||
\(759\) | −4.61508e17 | −0.0876208 | ||||||||
\(760\) | −1.29969e19 | −2.44654 | ||||||||
\(761\) | 1.33282e18 | 0.248755 | 0.124377 | − | 0.992235i | \(-0.460307\pi\) | ||||
0.124377 | + | 0.992235i | \(0.460307\pi\) | |||||||
\(762\) | −2.11871e18 | −0.392070 | ||||||||
\(763\) | −2.65978e18 | −0.488018 | ||||||||
\(764\) | −2.22097e18 | −0.404051 | ||||||||
\(765\) | 2.45154e18 | 0.442222 | ||||||||
\(766\) | −1.09882e19 | −1.96535 | ||||||||
\(767\) | −1.12334e18 | −0.199223 | ||||||||
\(768\) | −3.74231e18 | −0.658100 | ||||||||
\(769\) | −1.52159e17 | −0.0265324 | −0.0132662 | − | 0.999912i | \(-0.504223\pi\) | ||||
−0.0132662 | + | 0.999912i | \(0.504223\pi\) | |||||||
\(770\) | 8.05303e18 | 1.39242 | ||||||||
\(771\) | 1.00210e18 | 0.171813 | ||||||||
\(772\) | −9.89468e18 | −1.68224 | ||||||||
\(773\) | −9.30354e18 | −1.56849 | −0.784244 | − | 0.620452i | \(-0.786949\pi\) | ||||
−0.784244 | + | 0.620452i | \(0.786949\pi\) | |||||||
\(774\) | −2.57970e18 | −0.431274 | ||||||||
\(775\) | 2.41079e18 | 0.399668 | ||||||||
\(776\) | 2.30753e19 | 3.79355 | ||||||||
\(777\) | −7.74117e18 | −1.26203 | ||||||||
\(778\) | −1.53082e18 | −0.247489 | ||||||||
\(779\) | −2.70082e18 | −0.433015 | ||||||||
\(780\) | 1.65770e19 | 2.63567 | ||||||||
\(781\) | 3.73504e18 | 0.588929 | ||||||||
\(782\) | 3.98338e18 | 0.622885 | ||||||||
\(783\) | 1.76440e17 | 0.0273618 | ||||||||
\(784\) | 9.28331e18 | 1.42774 | ||||||||
\(785\) | −1.36298e19 | −2.07891 | ||||||||
\(786\) | 2.88164e18 | 0.435907 | ||||||||
\(787\) | −7.83821e18 | −1.17593 | −0.587965 | − | 0.808887i | \(-0.700071\pi\) | ||||
−0.587965 | + | 0.808887i | \(0.700071\pi\) | |||||||
\(788\) | −2.24746e19 | −3.34404 | ||||||||
\(789\) | 7.29919e18 | 1.07715 | ||||||||
\(790\) | −2.52133e19 | −3.69023 | ||||||||
\(791\) | −3.61748e18 | −0.525120 | ||||||||
\(792\) | −2.83672e18 | −0.408416 | ||||||||
\(793\) | −5.64518e18 | −0.806125 | ||||||||
\(794\) | −1.29846e19 | −1.83906 | ||||||||
\(795\) | 1.36588e18 | 0.191878 | ||||||||
\(796\) | −2.71353e19 | −3.78094 | ||||||||
\(797\) | 4.87347e18 | 0.673533 | 0.336767 | − | 0.941588i | \(-0.390667\pi\) | ||||
0.336767 | + | 0.941588i | \(0.390667\pi\) | |||||||
\(798\) | 7.53384e18 | 1.03276 | ||||||||
\(799\) | 1.53430e16 | 0.00208619 | ||||||||
\(800\) | −7.11663e18 | −0.959819 | ||||||||
\(801\) | −9.79400e17 | −0.131023 | ||||||||
\(802\) | 2.95229e18 | 0.391765 | ||||||||
\(803\) | −3.66586e18 | −0.482531 | ||||||||
\(804\) | −1.31085e19 | −1.71155 | ||||||||
\(805\) | 3.88381e18 | 0.503020 | ||||||||
\(806\) | −1.58186e19 | −2.03231 | ||||||||
\(807\) | −4.00597e18 | −0.510540 | ||||||||
\(808\) | −1.80014e19 | −2.27579 | ||||||||
\(809\) | −1.56659e18 | −0.196467 | −0.0982333 | − | 0.995163i | \(-0.531319\pi\) | ||||
−0.0982333 | + | 0.995163i | \(0.531319\pi\) | |||||||
\(810\) | −2.05098e18 | −0.255158 | ||||||||
\(811\) | 1.55373e19 | 1.91752 | 0.958762 | − | 0.284211i | \(-0.0917316\pi\) | ||||
0.958762 | + | 0.284211i | \(0.0917316\pi\) | |||||||
\(812\) | −3.52809e18 | −0.431943 | ||||||||
\(813\) | 6.22300e18 | 0.755808 | ||||||||
\(814\) | −1.25697e19 | −1.51449 | ||||||||
\(815\) | 1.42133e19 | 1.69891 | ||||||||
\(816\) | 1.20869e19 | 1.43327 | ||||||||
\(817\) | 4.56697e18 | 0.537260 | ||||||||
\(818\) | −9.40720e18 | −1.09790 | ||||||||
\(819\) | −5.59335e18 | −0.647630 | ||||||||
\(820\) | −1.47023e19 | −1.68887 | ||||||||
\(821\) | 6.52725e18 | 0.743874 | 0.371937 | − | 0.928258i | \(-0.378694\pi\) | ||||
0.371937 | + | 0.928258i | \(0.378694\pi\) | |||||||
\(822\) | −1.12079e19 | −1.26723 | ||||||||
\(823\) | −1.64640e18 | −0.184687 | −0.0923435 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923435 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(824\) | −5.96687e17 | −0.0664079 | ||||||||
\(825\) | 1.38415e18 | 0.152838 | ||||||||
\(826\) | −2.77913e18 | −0.304466 | ||||||||
\(827\) | −7.15086e18 | −0.777271 | −0.388635 | − | 0.921392i | \(-0.627053\pi\) | ||||
−0.388635 | + | 0.921392i | \(0.627053\pi\) | |||||||
\(828\) | −2.35031e18 | −0.253471 | ||||||||
\(829\) | −8.31028e18 | −0.889224 | −0.444612 | − | 0.895723i | \(-0.646659\pi\) | ||||
−0.444612 | + | 0.895723i | \(0.646659\pi\) | |||||||
\(830\) | −2.64328e19 | −2.80631 | ||||||||
\(831\) | −7.57480e18 | −0.797930 | ||||||||
\(832\) | 1.25405e19 | 1.31073 | ||||||||
\(833\) | 6.27966e18 | 0.651243 | ||||||||
\(834\) | 5.23089e18 | 0.538265 | ||||||||
\(835\) | −2.11300e19 | −2.15743 | ||||||||
\(836\) | 8.62751e18 | 0.874067 | ||||||||
\(837\) | 1.38031e18 | 0.138759 | ||||||||
\(838\) | −1.60367e19 | −1.59967 | ||||||||
\(839\) | 1.80617e18 | 0.178775 | 0.0893874 | − | 0.995997i | \(-0.471509\pi\) | ||||
0.0893874 | + | 0.995997i | \(0.471509\pi\) | |||||||
\(840\) | 2.38724e19 | 2.34466 | ||||||||
\(841\) | −1.00532e19 | −0.979786 | ||||||||
\(842\) | 8.71265e18 | 0.842600 | ||||||||
\(843\) | 2.20553e17 | 0.0211657 | ||||||||
\(844\) | −4.63210e19 | −4.41115 | ||||||||
\(845\) | 1.77008e19 | 1.67273 | ||||||||
\(846\) | −1.28361e16 | −0.00120372 | ||||||||
\(847\) | 1.05318e19 | 0.980076 | ||||||||
\(848\) | 6.73421e18 | 0.621890 | ||||||||
\(849\) | 1.04582e19 | 0.958421 | ||||||||
\(850\) | −1.19469e19 | −1.08650 | ||||||||
\(851\) | −6.06210e18 | −0.547118 | ||||||||
\(852\) | 1.90213e19 | 1.70366 | ||||||||
\(853\) | −6.78932e18 | −0.603472 | −0.301736 | − | 0.953391i | \(-0.597566\pi\) | ||||
−0.301736 | + | 0.953391i | \(0.597566\pi\) | |||||||
\(854\) | −1.39662e19 | −1.23197 | ||||||||
\(855\) | 3.63096e18 | 0.317864 | ||||||||
\(856\) | −2.45831e19 | −2.13578 | ||||||||
\(857\) | 1.28230e19 | 1.10564 | 0.552820 | − | 0.833301i | \(-0.313552\pi\) | ||||
0.552820 | + | 0.833301i | \(0.313552\pi\) | |||||||
\(858\) | −9.08218e18 | −0.777182 | ||||||||
\(859\) | −4.19378e18 | −0.356164 | −0.178082 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178082 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(860\) | 2.48609e19 | 2.09545 | ||||||||
\(861\) | 4.96080e18 | 0.414984 | ||||||||
\(862\) | −1.86962e19 | −1.55223 | ||||||||
\(863\) | 1.77382e18 | 0.146163 | 0.0730817 | − | 0.997326i | \(-0.476717\pi\) | ||||
0.0730817 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(864\) | −4.07465e18 | −0.333235 | ||||||||
\(865\) | −1.36730e19 | −1.10984 | ||||||||
\(866\) | −6.18215e18 | −0.498051 | ||||||||
\(867\) | 9.55681e17 | 0.0764168 | ||||||||
\(868\) | −2.76007e19 | −2.19049 | ||||||||
\(869\) | 9.74236e18 | 0.767425 | ||||||||
\(870\) | −2.41098e18 | −0.188503 | ||||||||
\(871\) | −2.44296e19 | −1.89583 | ||||||||
\(872\) | −1.28026e19 | −0.986148 | ||||||||
\(873\) | −6.44656e18 | −0.492873 | ||||||||
\(874\) | 5.89975e18 | 0.447723 | ||||||||
\(875\) | 9.36553e18 | 0.705472 | ||||||||
\(876\) | −1.86691e19 | −1.39587 | ||||||||
\(877\) | 1.29299e19 | 0.959616 | 0.479808 | − | 0.877373i | \(-0.340706\pi\) | ||||
0.479808 | + | 0.877373i | \(0.340706\pi\) | |||||||
\(878\) | 2.94358e19 | 2.16851 | ||||||||
\(879\) | −7.80303e18 | −0.570605 | ||||||||
\(880\) | 1.91354e19 | 1.38900 | ||||||||
\(881\) | −2.59331e19 | −1.86858 | −0.934289 | − | 0.356516i | \(-0.883964\pi\) | ||||
−0.934289 | + | 0.356516i | \(0.883964\pi\) | |||||||
\(882\) | −5.25362e18 | −0.375762 | ||||||||
\(883\) | 1.38109e19 | 0.980566 | 0.490283 | − | 0.871563i | \(-0.336893\pi\) | ||||
0.490283 | + | 0.871563i | \(0.336893\pi\) | |||||||
\(884\) | 5.52858e19 | 3.89649 | ||||||||
\(885\) | −1.33941e18 | −0.0937093 | ||||||||
\(886\) | −3.27089e19 | −2.27168 | ||||||||
\(887\) | 5.85589e18 | 0.403729 | 0.201864 | − | 0.979413i | \(-0.435300\pi\) | ||||
0.201864 | + | 0.979413i | \(0.435300\pi\) | |||||||
\(888\) | −3.72615e19 | −2.55021 | ||||||||
\(889\) | −6.88947e18 | −0.468085 | ||||||||
\(890\) | 1.33831e19 | 0.902656 | ||||||||
\(891\) | 7.92497e17 | 0.0530631 | ||||||||
\(892\) | −2.19435e19 | −1.45860 | ||||||||
\(893\) | 2.27243e16 | 0.00149953 | ||||||||
\(894\) | 1.07211e19 | 0.702335 | ||||||||
\(895\) | 2.29253e19 | 1.49096 | ||||||||
\(896\) | −3.02468e18 | −0.195289 | ||||||||
\(897\) | −4.38015e18 | −0.280762 | ||||||||
\(898\) | 2.28351e19 | 1.45314 | ||||||||
\(899\) | 1.62258e18 | 0.102511 | ||||||||
\(900\) | 7.04901e18 | 0.442132 | ||||||||
\(901\) | 4.55533e18 | 0.283667 | ||||||||
\(902\) | 8.05508e18 | 0.497998 | ||||||||
\(903\) | −8.38849e18 | −0.514889 | ||||||||
\(904\) | −1.74124e19 | −1.06112 | ||||||||
\(905\) | −6.17165e18 | −0.373410 | ||||||||
\(906\) | 2.76421e18 | 0.166049 | ||||||||
\(907\) | −2.59316e18 | −0.154661 | −0.0773307 | − | 0.997005i | \(-0.524640\pi\) | ||||
−0.0773307 | + | 0.997005i | \(0.524640\pi\) | |||||||
\(908\) | 7.24320e19 | 4.28916 | ||||||||
\(909\) | 5.02906e18 | 0.295679 | ||||||||
\(910\) | 7.64310e19 | 4.46170 | ||||||||
\(911\) | −1.64343e19 | −0.952537 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(912\) | 1.79018e19 | 1.03022 | ||||||||
\(913\) | 1.02136e19 | 0.583604 | ||||||||
\(914\) | −2.00524e19 | −1.13767 | ||||||||
\(915\) | −6.73105e18 | −0.379180 | ||||||||
\(916\) | 2.56099e19 | 1.43247 | ||||||||
\(917\) | 9.37033e18 | 0.520420 | ||||||||
\(918\) | −6.84022e18 | −0.377218 | ||||||||
\(919\) | −8.26113e18 | −0.452365 | −0.226182 | − | 0.974085i | \(-0.572625\pi\) | ||||
−0.226182 | + | 0.974085i | \(0.572625\pi\) | |||||||
\(920\) | 1.86944e19 | 1.01646 | ||||||||
\(921\) | 3.81180e18 | 0.205798 | ||||||||
\(922\) | −4.90964e19 | −2.63208 | ||||||||
\(923\) | 3.54491e19 | 1.88709 | ||||||||
\(924\) | −1.58468e19 | −0.837671 | ||||||||
\(925\) | 1.81814e19 | 0.954344 | ||||||||
\(926\) | −5.17673e19 | −2.69826 | ||||||||
\(927\) | 1.66697e17 | 0.00862799 | ||||||||
\(928\) | −4.78984e18 | −0.246184 | ||||||||
\(929\) | 6.48641e17 | 0.0331057 | 0.0165528 | − | 0.999863i | \(-0.494731\pi\) | ||||
0.0165528 | + | 0.999863i | \(0.494731\pi\) | |||||||
\(930\) | −1.88614e19 | −0.955947 | ||||||||
\(931\) | 9.30074e18 | 0.468107 | ||||||||
\(932\) | 5.44172e19 | 2.71978 | ||||||||
\(933\) | −1.78358e18 | −0.0885240 | ||||||||
\(934\) | −6.10213e19 | −3.00765 | ||||||||
\(935\) | 1.29441e19 | 0.633573 | ||||||||
\(936\) | −2.69232e19 | −1.30868 | ||||||||
\(937\) | 3.08366e19 | 1.48854 | 0.744268 | − | 0.667881i | \(-0.232799\pi\) | ||||
0.744268 | + | 0.667881i | \(0.232799\pi\) | |||||||
\(938\) | −6.04389e19 | −2.89733 | ||||||||
\(939\) | −1.24832e18 | −0.0594290 | ||||||||
\(940\) | 1.23703e17 | 0.00584856 | ||||||||
\(941\) | 1.48854e19 | 0.698919 | 0.349460 | − | 0.936951i | \(-0.386365\pi\) | ||||
0.349460 | + | 0.936951i | \(0.386365\pi\) | |||||||
\(942\) | 3.80293e19 | 1.77332 | ||||||||
\(943\) | 3.88480e18 | 0.179905 | ||||||||
\(944\) | −6.60372e18 | −0.303718 | ||||||||
\(945\) | −6.66925e18 | −0.304628 | ||||||||
\(946\) | −1.36208e19 | −0.617887 | ||||||||
\(947\) | 1.95065e19 | 0.878829 | 0.439415 | − | 0.898284i | \(-0.355186\pi\) | ||||
0.439415 | + | 0.898284i | \(0.355186\pi\) | |||||||
\(948\) | 4.96148e19 | 2.22002 | ||||||||
\(949\) | −3.47925e19 | −1.54616 | ||||||||
\(950\) | −1.76944e19 | −0.780967 | ||||||||
\(951\) | −2.07271e19 | −0.908586 | ||||||||
\(952\) | 7.96166e19 | 3.46628 | ||||||||
\(953\) | 3.67148e19 | 1.58759 | 0.793794 | − | 0.608187i | \(-0.208103\pi\) | ||||
0.793794 | + | 0.608187i | \(0.208103\pi\) | |||||||
\(954\) | −3.81104e18 | −0.163674 | ||||||||
\(955\) | −4.93527e18 | −0.210518 | ||||||||
\(956\) | 4.87368e19 | 2.06481 | ||||||||
\(957\) | 9.31599e17 | 0.0392014 | ||||||||
\(958\) | 3.21545e19 | 1.34389 | ||||||||
\(959\) | −3.64449e19 | −1.51292 | ||||||||
\(960\) | 1.49527e19 | 0.616535 | ||||||||
\(961\) | −1.17239e19 | −0.480142 | ||||||||
\(962\) | −1.19298e20 | −4.85285 | ||||||||
\(963\) | 6.86781e18 | 0.277490 | ||||||||
\(964\) | 8.72415e19 | 3.50124 | ||||||||
\(965\) | −2.19872e19 | −0.876480 | ||||||||
\(966\) | −1.08365e19 | −0.429079 | ||||||||
\(967\) | 2.37395e19 | 0.933683 | 0.466841 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466841 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(968\) | 5.06939e19 | 1.98046 | ||||||||
\(969\) | 1.21096e19 | 0.469921 | ||||||||
\(970\) | 8.80897e19 | 3.39554 | ||||||||
\(971\) | −4.75630e19 | −1.82114 | −0.910572 | − | 0.413350i | \(-0.864359\pi\) | ||||
−0.910572 | + | 0.413350i | \(0.864359\pi\) | |||||||
\(972\) | 4.03593e18 | 0.153502 | ||||||||
\(973\) | 1.70095e19 | 0.642624 | ||||||||
\(974\) | −1.54180e19 | −0.578623 | ||||||||
\(975\) | 1.31369e19 | 0.489736 | ||||||||
\(976\) | −3.31862e19 | −1.22895 | ||||||||
\(977\) | 1.03472e19 | 0.380635 | 0.190317 | − | 0.981723i | \(-0.439048\pi\) | ||||
0.190317 | + | 0.981723i | \(0.439048\pi\) | |||||||
\(978\) | −3.96576e19 | −1.44919 | ||||||||
\(979\) | −5.17121e18 | −0.187718 | ||||||||
\(980\) | 5.06299e19 | 1.82573 | ||||||||
\(981\) | 3.57668e18 | 0.128124 | ||||||||
\(982\) | −9.72164e18 | −0.345951 | ||||||||
\(983\) | 4.52073e19 | 1.59813 | 0.799063 | − | 0.601247i | \(-0.205329\pi\) | ||||
0.799063 | + | 0.601247i | \(0.205329\pi\) | |||||||
\(984\) | 2.38784e19 | 0.838567 | ||||||||
\(985\) | −4.99414e19 | −1.74231 | ||||||||
\(986\) | −8.04084e18 | −0.278677 | ||||||||
\(987\) | −4.17394e16 | −0.00143709 | ||||||||
\(988\) | 8.18833e19 | 2.80076 | ||||||||
\(989\) | −6.56902e18 | −0.223216 | ||||||||
\(990\) | −1.08292e19 | −0.365566 | ||||||||
\(991\) | 3.34899e19 | 1.12314 | 0.561571 | − | 0.827428i | \(-0.310197\pi\) | ||||
0.561571 | + | 0.827428i | \(0.310197\pi\) | |||||||
\(992\) | −3.74715e19 | −1.24846 | ||||||||
\(993\) | −2.75836e19 | −0.913021 | ||||||||
\(994\) | 8.77010e19 | 2.88399 | ||||||||
\(995\) | −6.02981e19 | −1.96994 | ||||||||
\(996\) | 5.20145e19 | 1.68826 | ||||||||
\(997\) | 3.31750e17 | 0.0106977 | 0.00534887 | − | 0.999986i | \(-0.498297\pi\) | ||||
0.00534887 | + | 0.999986i | \(0.498297\pi\) | |||||||
\(998\) | −6.87167e19 | −2.20148 | ||||||||
\(999\) | 1.04098e19 | 0.331334 |
(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 | 177.14.a.c.1.2 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.2 | ✓ | 31 | 1.1 | even | 1 | trivial |