Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-22.4329\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 20.4329 | 0.903014 | 0.451507 | − | 0.892268i | \(-0.350887\pi\) | ||||
0.451507 | + | 0.892268i | \(0.350887\pi\) | |||||||
\(3\) | 231.971 | 1.65344 | 0.826719 | − | 0.562615i | \(-0.190205\pi\) | ||||
0.826719 | + | 0.562615i | \(0.190205\pi\) | |||||||
\(4\) | −94.4979 | −0.184566 | ||||||||
\(5\) | −2583.58 | −1.84866 | −0.924331 | − | 0.381592i | \(-0.875376\pi\) | ||||
−0.924331 | + | 0.381592i | \(0.875376\pi\) | |||||||
\(6\) | 4739.83 | 1.49308 | ||||||||
\(7\) | −1769.99 | −0.278631 | −0.139315 | − | 0.990248i | \(-0.544490\pi\) | ||||
−0.139315 | + | 0.990248i | \(0.544490\pi\) | |||||||
\(8\) | −12392.5 | −1.06968 | ||||||||
\(9\) | 34127.5 | 1.73386 | ||||||||
\(10\) | −52790.0 | −1.66937 | ||||||||
\(11\) | −74570.0 | −1.53567 | −0.767833 | − | 0.640650i | \(-0.778665\pi\) | ||||
−0.767833 | + | 0.640650i | \(0.778665\pi\) | |||||||
\(12\) | −21920.8 | −0.305169 | ||||||||
\(13\) | 7100.10 | 0.0689476 | 0.0344738 | − | 0.999406i | \(-0.489024\pi\) | ||||
0.0344738 | + | 0.999406i | \(0.489024\pi\) | |||||||
\(14\) | −36165.9 | −0.251608 | ||||||||
\(15\) | −599316. | −3.05665 | ||||||||
\(16\) | −204831. | −0.781369 | ||||||||
\(17\) | −268650. | −0.780131 | −0.390065 | − | 0.920787i | \(-0.627548\pi\) | ||||
−0.390065 | + | 0.920787i | \(0.627548\pi\) | |||||||
\(18\) | 697323. | 1.56570 | ||||||||
\(19\) | 572153. | 1.00721 | 0.503606 | − | 0.863933i | \(-0.332006\pi\) | ||||
0.503606 | + | 0.863933i | \(0.332006\pi\) | |||||||
\(20\) | 244143. | 0.341201 | ||||||||
\(21\) | −410586. | −0.460699 | ||||||||
\(22\) | −1.52368e6 | −1.38673 | ||||||||
\(23\) | 1.28932e6 | 0.960694 | 0.480347 | − | 0.877079i | \(-0.340511\pi\) | ||||
0.480347 | + | 0.877079i | \(0.340511\pi\) | |||||||
\(24\) | −2.87470e6 | −1.76865 | ||||||||
\(25\) | 4.72177e6 | 2.41755 | ||||||||
\(26\) | 145075. | 0.0622606 | ||||||||
\(27\) | 3.35071e6 | 1.21339 | ||||||||
\(28\) | 167260. | 0.0514259 | ||||||||
\(29\) | −6.39915e6 | −1.68009 | −0.840043 | − | 0.542520i | \(-0.817470\pi\) | ||||
−0.840043 | + | 0.542520i | \(0.817470\pi\) | |||||||
\(30\) | −1.22457e7 | −2.76019 | ||||||||
\(31\) | −2.00450e6 | −0.389833 | −0.194916 | − | 0.980820i | \(-0.562444\pi\) | ||||
−0.194916 | + | 0.980820i | \(0.562444\pi\) | |||||||
\(32\) | 2.15967e6 | 0.364093 | ||||||||
\(33\) | −1.72981e7 | −2.53913 | ||||||||
\(34\) | −5.48930e6 | −0.704469 | ||||||||
\(35\) | 4.57291e6 | 0.515094 | ||||||||
\(36\) | −3.22498e6 | −0.320012 | ||||||||
\(37\) | 1.49299e7 | 1.30963 | 0.654815 | − | 0.755789i | \(-0.272746\pi\) | ||||
0.654815 | + | 0.755789i | \(0.272746\pi\) | |||||||
\(38\) | 1.16907e7 | 0.909527 | ||||||||
\(39\) | 1.64702e6 | 0.114001 | ||||||||
\(40\) | 3.20170e7 | 1.97748 | ||||||||
\(41\) | −1.77326e7 | −0.980042 | −0.490021 | − | 0.871711i | \(-0.663011\pi\) | ||||
−0.490021 | + | 0.871711i | \(0.663011\pi\) | |||||||
\(42\) | −8.38945e6 | −0.416017 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | 7.04671e6 | 0.283432 | ||||||||
\(45\) | −8.81712e7 | −3.20531 | ||||||||
\(46\) | 2.63445e7 | 0.867520 | ||||||||
\(47\) | 1.13138e7 | 0.338196 | 0.169098 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169098 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(48\) | −4.75149e7 | −1.29195 | ||||||||
\(49\) | −3.72207e7 | −0.922365 | ||||||||
\(50\) | 9.64794e7 | 2.18308 | ||||||||
\(51\) | −6.23191e7 | −1.28990 | ||||||||
\(52\) | −670945. | −0.0127254 | ||||||||
\(53\) | −1.02987e8 | −1.79283 | −0.896417 | − | 0.443211i | \(-0.853839\pi\) | ||||
−0.896417 | + | 0.443211i | \(0.853839\pi\) | |||||||
\(54\) | 6.84645e7 | 1.09570 | ||||||||
\(55\) | 1.92658e8 | 2.83893 | ||||||||
\(56\) | 2.19346e7 | 0.298046 | ||||||||
\(57\) | 1.32723e8 | 1.66536 | ||||||||
\(58\) | −1.30753e8 | −1.51714 | ||||||||
\(59\) | −8.07005e7 | −0.867046 | −0.433523 | − | 0.901143i | \(-0.642730\pi\) | ||||
−0.433523 | + | 0.901143i | \(0.642730\pi\) | |||||||
\(60\) | 5.66341e7 | 0.564154 | ||||||||
\(61\) | 6.21644e7 | 0.574854 | 0.287427 | − | 0.957803i | \(-0.407200\pi\) | ||||
0.287427 | + | 0.957803i | \(0.407200\pi\) | |||||||
\(62\) | −4.09577e7 | −0.352024 | ||||||||
\(63\) | −6.04053e7 | −0.483106 | ||||||||
\(64\) | 1.49002e8 | 1.11015 | ||||||||
\(65\) | −1.83437e7 | −0.127461 | ||||||||
\(66\) | −3.53449e8 | −2.29287 | ||||||||
\(67\) | 1.55110e8 | 0.940381 | 0.470191 | − | 0.882565i | \(-0.344185\pi\) | ||||
0.470191 | + | 0.882565i | \(0.344185\pi\) | |||||||
\(68\) | 2.53869e7 | 0.143986 | ||||||||
\(69\) | 2.99084e8 | 1.58845 | ||||||||
\(70\) | 9.34377e7 | 0.465137 | ||||||||
\(71\) | −1.87869e8 | −0.877390 | −0.438695 | − | 0.898636i | \(-0.644559\pi\) | ||||
−0.438695 | + | 0.898636i | \(0.644559\pi\) | |||||||
\(72\) | −4.22925e8 | −1.85467 | ||||||||
\(73\) | 4.82049e7 | 0.198673 | 0.0993363 | − | 0.995054i | \(-0.468328\pi\) | ||||
0.0993363 | + | 0.995054i | \(0.468328\pi\) | |||||||
\(74\) | 3.05060e8 | 1.18261 | ||||||||
\(75\) | 1.09531e9 | 3.99727 | ||||||||
\(76\) | −5.40673e7 | −0.185898 | ||||||||
\(77\) | 1.31988e8 | 0.427884 | ||||||||
\(78\) | 3.36533e7 | 0.102944 | ||||||||
\(79\) | −4.54354e8 | −1.31242 | −0.656210 | − | 0.754579i | \(-0.727841\pi\) | ||||
−0.656210 | + | 0.754579i | \(0.727841\pi\) | |||||||
\(80\) | 5.29198e8 | 1.44449 | ||||||||
\(81\) | 1.05534e8 | 0.272403 | ||||||||
\(82\) | −3.62328e8 | −0.884991 | ||||||||
\(83\) | 1.00047e8 | 0.231394 | 0.115697 | − | 0.993285i | \(-0.463090\pi\) | ||||
0.115697 | + | 0.993285i | \(0.463090\pi\) | |||||||
\(84\) | 3.87995e7 | 0.0850295 | ||||||||
\(85\) | 6.94081e8 | 1.44220 | ||||||||
\(86\) | −6.98559e7 | −0.137708 | ||||||||
\(87\) | −1.48442e9 | −2.77792 | ||||||||
\(88\) | 9.24108e8 | 1.64267 | ||||||||
\(89\) | 1.13769e9 | 1.92207 | 0.961034 | − | 0.276431i | \(-0.0891518\pi\) | ||||
0.961034 | + | 0.276431i | \(0.0891518\pi\) | |||||||
\(90\) | −1.80159e9 | −2.89444 | ||||||||
\(91\) | −1.25671e7 | −0.0192109 | ||||||||
\(92\) | −1.21838e8 | −0.177312 | ||||||||
\(93\) | −4.64985e8 | −0.644564 | ||||||||
\(94\) | 2.31174e8 | 0.305396 | ||||||||
\(95\) | −1.47821e9 | −1.86200 | ||||||||
\(96\) | 5.00980e8 | 0.602005 | ||||||||
\(97\) | −2.37271e8 | −0.272127 | −0.136064 | − | 0.990700i | \(-0.543445\pi\) | ||||
−0.136064 | + | 0.990700i | \(0.543445\pi\) | |||||||
\(98\) | −7.60527e8 | −0.832908 | ||||||||
\(99\) | −2.54489e9 | −2.66263 | ||||||||
\(100\) | −4.46198e8 | −0.446198 | ||||||||
\(101\) | −7.88795e8 | −0.754254 | −0.377127 | − | 0.926162i | \(-0.623088\pi\) | ||||
−0.377127 | + | 0.926162i | \(0.623088\pi\) | |||||||
\(102\) | −1.27336e9 | −1.16480 | ||||||||
\(103\) | −1.40500e9 | −1.23001 | −0.615004 | − | 0.788524i | \(-0.710845\pi\) | ||||
−0.615004 | + | 0.788524i | \(0.710845\pi\) | |||||||
\(104\) | −8.79879e7 | −0.0737518 | ||||||||
\(105\) | 1.06078e9 | 0.851676 | ||||||||
\(106\) | −2.10432e9 | −1.61895 | ||||||||
\(107\) | 1.23319e9 | 0.909499 | 0.454749 | − | 0.890619i | \(-0.349729\pi\) | ||||
0.454749 | + | 0.890619i | \(0.349729\pi\) | |||||||
\(108\) | −3.16635e8 | −0.223950 | ||||||||
\(109\) | 5.28937e8 | 0.358909 | 0.179455 | − | 0.983766i | \(-0.442567\pi\) | ||||
0.179455 | + | 0.983766i | \(0.442567\pi\) | |||||||
\(110\) | 3.93655e9 | 2.56359 | ||||||||
\(111\) | 3.46330e9 | 2.16539 | ||||||||
\(112\) | 3.62549e8 | 0.217714 | ||||||||
\(113\) | 6.54283e8 | 0.377496 | 0.188748 | − | 0.982026i | \(-0.439557\pi\) | ||||
0.188748 | + | 0.982026i | \(0.439557\pi\) | |||||||
\(114\) | 2.71191e9 | 1.50385 | ||||||||
\(115\) | −3.33106e9 | −1.77600 | ||||||||
\(116\) | 6.04706e8 | 0.310087 | ||||||||
\(117\) | 2.42309e8 | 0.119545 | ||||||||
\(118\) | −1.64894e9 | −0.782954 | ||||||||
\(119\) | 4.75508e8 | 0.217369 | ||||||||
\(120\) | 7.42702e9 | 3.26963 | ||||||||
\(121\) | 3.20273e9 | 1.35827 | ||||||||
\(122\) | 1.27020e9 | 0.519101 | ||||||||
\(123\) | −4.11344e9 | −1.62044 | ||||||||
\(124\) | 1.89421e8 | 0.0719500 | ||||||||
\(125\) | −7.15304e9 | −2.62057 | ||||||||
\(126\) | −1.23425e9 | −0.436251 | ||||||||
\(127\) | −3.42183e9 | −1.16719 | −0.583595 | − | 0.812045i | \(-0.698354\pi\) | ||||
−0.583595 | + | 0.812045i | \(0.698354\pi\) | |||||||
\(128\) | 1.93878e9 | 0.638388 | ||||||||
\(129\) | −7.93062e8 | −0.252147 | ||||||||
\(130\) | −3.74814e8 | −0.115099 | ||||||||
\(131\) | 2.65085e9 | 0.786439 | 0.393220 | − | 0.919445i | \(-0.371361\pi\) | ||||
0.393220 | + | 0.919445i | \(0.371361\pi\) | |||||||
\(132\) | 1.63463e9 | 0.468638 | ||||||||
\(133\) | −1.01270e9 | −0.280641 | ||||||||
\(134\) | 3.16935e9 | 0.849177 | ||||||||
\(135\) | −8.65682e9 | −2.24314 | ||||||||
\(136\) | 3.32925e9 | 0.834490 | ||||||||
\(137\) | −9.18404e7 | −0.0222736 | −0.0111368 | − | 0.999938i | \(-0.503545\pi\) | ||||
−0.0111368 | + | 0.999938i | \(0.503545\pi\) | |||||||
\(138\) | 6.11115e9 | 1.43439 | ||||||||
\(139\) | 7.61102e7 | 0.0172932 | 0.00864662 | − | 0.999963i | \(-0.497248\pi\) | ||||
0.00864662 | + | 0.999963i | \(0.497248\pi\) | |||||||
\(140\) | −4.32131e8 | −0.0950690 | ||||||||
\(141\) | 2.62448e9 | 0.559187 | ||||||||
\(142\) | −3.83870e9 | −0.792295 | ||||||||
\(143\) | −5.29454e8 | −0.105881 | ||||||||
\(144\) | −6.99038e9 | −1.35478 | ||||||||
\(145\) | 1.65327e10 | 3.10591 | ||||||||
\(146\) | 9.84964e8 | 0.179404 | ||||||||
\(147\) | −8.63413e9 | −1.52507 | ||||||||
\(148\) | −1.41084e9 | −0.241714 | ||||||||
\(149\) | 4.91840e9 | 0.817495 | 0.408748 | − | 0.912647i | \(-0.365966\pi\) | ||||
0.408748 | + | 0.912647i | \(0.365966\pi\) | |||||||
\(150\) | 2.23804e10 | 3.60959 | ||||||||
\(151\) | −6.55107e9 | −1.02545 | −0.512727 | − | 0.858552i | \(-0.671365\pi\) | ||||
−0.512727 | + | 0.858552i | \(0.671365\pi\) | |||||||
\(152\) | −7.09041e9 | −1.07739 | ||||||||
\(153\) | −9.16837e9 | −1.35264 | ||||||||
\(154\) | 2.69689e9 | 0.386385 | ||||||||
\(155\) | 5.17879e9 | 0.720668 | ||||||||
\(156\) | −1.55640e8 | −0.0210407 | ||||||||
\(157\) | −2.66784e9 | −0.350438 | −0.175219 | − | 0.984530i | \(-0.556063\pi\) | ||||
−0.175219 | + | 0.984530i | \(0.556063\pi\) | |||||||
\(158\) | −9.28376e9 | −1.18513 | ||||||||
\(159\) | −2.38899e10 | −2.96434 | ||||||||
\(160\) | −5.57968e9 | −0.673084 | ||||||||
\(161\) | −2.28208e9 | −0.267679 | ||||||||
\(162\) | 2.15637e9 | 0.245983 | ||||||||
\(163\) | −9.83535e8 | −0.109130 | −0.0545652 | − | 0.998510i | \(-0.517377\pi\) | ||||
−0.0545652 | + | 0.998510i | \(0.517377\pi\) | |||||||
\(164\) | 1.67569e9 | 0.180883 | ||||||||
\(165\) | 4.46910e10 | 4.69399 | ||||||||
\(166\) | 2.04425e9 | 0.208952 | ||||||||
\(167\) | 9.80315e9 | 0.975307 | 0.487654 | − | 0.873037i | \(-0.337853\pi\) | ||||
0.487654 | + | 0.873037i | \(0.337853\pi\) | |||||||
\(168\) | 5.08818e9 | 0.492800 | ||||||||
\(169\) | −1.05541e10 | −0.995246 | ||||||||
\(170\) | 1.41821e10 | 1.30232 | ||||||||
\(171\) | 1.95262e10 | 1.74636 | ||||||||
\(172\) | 3.23070e8 | 0.0281461 | ||||||||
\(173\) | −3.11130e9 | −0.264079 | −0.132040 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132040 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(174\) | −3.03309e10 | −2.50850 | ||||||||
\(175\) | −8.35749e9 | −0.673604 | ||||||||
\(176\) | 1.52743e10 | 1.19992 | ||||||||
\(177\) | −1.87202e10 | −1.43361 | ||||||||
\(178\) | 2.32463e10 | 1.73565 | ||||||||
\(179\) | −1.52460e10 | −1.10999 | −0.554993 | − | 0.831855i | \(-0.687279\pi\) | ||||
−0.554993 | + | 0.831855i | \(0.687279\pi\) | |||||||
\(180\) | 8.33200e9 | 0.591593 | ||||||||
\(181\) | −2.42388e10 | −1.67864 | −0.839319 | − | 0.543640i | \(-0.817046\pi\) | ||||
−0.839319 | + | 0.543640i | \(0.817046\pi\) | |||||||
\(182\) | −2.56782e8 | −0.0173477 | ||||||||
\(183\) | 1.44203e10 | 0.950485 | ||||||||
\(184\) | −1.59779e10 | −1.02763 | ||||||||
\(185\) | −3.85726e10 | −2.42106 | ||||||||
\(186\) | −9.50098e9 | −0.582050 | ||||||||
\(187\) | 2.00333e10 | 1.19802 | ||||||||
\(188\) | −1.06913e9 | −0.0624197 | ||||||||
\(189\) | −5.93071e9 | −0.338087 | ||||||||
\(190\) | −3.02040e10 | −1.68141 | ||||||||
\(191\) | 8.62554e9 | 0.468960 | 0.234480 | − | 0.972121i | \(-0.424661\pi\) | ||||
0.234480 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(192\) | 3.45641e10 | 1.83556 | ||||||||
\(193\) | 3.46237e10 | 1.79624 | 0.898122 | − | 0.439747i | \(-0.144932\pi\) | ||||
0.898122 | + | 0.439747i | \(0.144932\pi\) | |||||||
\(194\) | −4.84813e9 | −0.245735 | ||||||||
\(195\) | −4.25520e9 | −0.210748 | ||||||||
\(196\) | 3.51728e9 | 0.170237 | ||||||||
\(197\) | −2.05360e10 | −0.971444 | −0.485722 | − | 0.874113i | \(-0.661443\pi\) | ||||
−0.485722 | + | 0.874113i | \(0.661443\pi\) | |||||||
\(198\) | −5.19993e10 | −2.40439 | ||||||||
\(199\) | −1.56130e10 | −0.705745 | −0.352873 | − | 0.935671i | \(-0.614795\pi\) | ||||
−0.352873 | + | 0.935671i | \(0.614795\pi\) | |||||||
\(200\) | −5.85146e10 | −2.58600 | ||||||||
\(201\) | 3.59811e10 | 1.55486 | ||||||||
\(202\) | −1.61173e10 | −0.681102 | ||||||||
\(203\) | 1.13264e10 | 0.468124 | ||||||||
\(204\) | 5.88903e9 | 0.238072 | ||||||||
\(205\) | 4.58136e10 | 1.81177 | ||||||||
\(206\) | −2.87081e10 | −1.11071 | ||||||||
\(207\) | 4.40012e10 | 1.66571 | ||||||||
\(208\) | −1.45432e9 | −0.0538735 | ||||||||
\(209\) | −4.26655e10 | −1.54674 | ||||||||
\(210\) | 2.16748e10 | 0.769075 | ||||||||
\(211\) | −3.30552e10 | −1.14807 | −0.574036 | − | 0.818830i | \(-0.694623\pi\) | ||||
−0.574036 | + | 0.818830i | \(0.694623\pi\) | |||||||
\(212\) | 9.73204e9 | 0.330897 | ||||||||
\(213\) | −4.35801e10 | −1.45071 | ||||||||
\(214\) | 2.51976e10 | 0.821290 | ||||||||
\(215\) | 8.83276e9 | 0.281918 | ||||||||
\(216\) | −4.15236e10 | −1.29794 | ||||||||
\(217\) | 3.54794e9 | 0.108619 | ||||||||
\(218\) | 1.08077e10 | 0.324100 | ||||||||
\(219\) | 1.11821e10 | 0.328493 | ||||||||
\(220\) | −1.82058e10 | −0.523970 | ||||||||
\(221\) | −1.90744e9 | −0.0537882 | ||||||||
\(222\) | 7.07652e10 | 1.95538 | ||||||||
\(223\) | 2.45049e10 | 0.663560 | 0.331780 | − | 0.943357i | \(-0.392351\pi\) | ||||
0.331780 | + | 0.943357i | \(0.392351\pi\) | |||||||
\(224\) | −3.82259e9 | −0.101447 | ||||||||
\(225\) | 1.61142e11 | 4.19168 | ||||||||
\(226\) | 1.33689e10 | 0.340884 | ||||||||
\(227\) | −2.42024e10 | −0.604981 | −0.302490 | − | 0.953152i | \(-0.597818\pi\) | ||||
−0.302490 | + | 0.953152i | \(0.597818\pi\) | |||||||
\(228\) | −1.25420e10 | −0.307370 | ||||||||
\(229\) | −3.44206e10 | −0.827102 | −0.413551 | − | 0.910481i | \(-0.635712\pi\) | ||||
−0.413551 | + | 0.910481i | \(0.635712\pi\) | |||||||
\(230\) | −6.80631e10 | −1.60375 | ||||||||
\(231\) | 3.06174e10 | 0.707480 | ||||||||
\(232\) | 7.93014e10 | 1.79715 | ||||||||
\(233\) | 4.12963e10 | 0.917929 | 0.458964 | − | 0.888455i | \(-0.348221\pi\) | ||||
0.458964 | + | 0.888455i | \(0.348221\pi\) | |||||||
\(234\) | 4.95106e9 | 0.107951 | ||||||||
\(235\) | −2.92302e10 | −0.625211 | ||||||||
\(236\) | 7.62603e9 | 0.160027 | ||||||||
\(237\) | −1.05397e11 | −2.17000 | ||||||||
\(238\) | 9.71600e9 | 0.196287 | ||||||||
\(239\) | −2.39540e10 | −0.474883 | −0.237442 | − | 0.971402i | \(-0.576309\pi\) | ||||
−0.237442 | + | 0.971402i | \(0.576309\pi\) | |||||||
\(240\) | 1.22759e11 | 2.38837 | ||||||||
\(241\) | 3.26986e10 | 0.624385 | 0.312192 | − | 0.950019i | \(-0.398937\pi\) | ||||
0.312192 | + | 0.950019i | \(0.398937\pi\) | |||||||
\(242\) | 6.54410e10 | 1.22654 | ||||||||
\(243\) | −4.14710e10 | −0.762986 | ||||||||
\(244\) | −5.87441e9 | −0.106099 | ||||||||
\(245\) | 9.61629e10 | 1.70514 | ||||||||
\(246\) | −8.40495e10 | −1.46328 | ||||||||
\(247\) | 4.06234e9 | 0.0694449 | ||||||||
\(248\) | 2.48407e10 | 0.416996 | ||||||||
\(249\) | 2.32080e10 | 0.382596 | ||||||||
\(250\) | −1.46157e11 | −2.36641 | ||||||||
\(251\) | −4.46019e10 | −0.709286 | −0.354643 | − | 0.935002i | \(-0.615398\pi\) | ||||
−0.354643 | + | 0.935002i | \(0.615398\pi\) | |||||||
\(252\) | 5.70818e9 | 0.0891651 | ||||||||
\(253\) | −9.61445e10 | −1.47531 | ||||||||
\(254\) | −6.99178e10 | −1.05399 | ||||||||
\(255\) | 1.61007e11 | 2.38458 | ||||||||
\(256\) | −3.66740e10 | −0.533677 | ||||||||
\(257\) | 4.55935e10 | 0.651935 | 0.325967 | − | 0.945381i | \(-0.394310\pi\) | ||||
0.325967 | + | 0.945381i | \(0.394310\pi\) | |||||||
\(258\) | −1.62045e10 | −0.227692 | ||||||||
\(259\) | −2.64257e10 | −0.364904 | ||||||||
\(260\) | 1.73344e9 | 0.0235250 | ||||||||
\(261\) | −2.18387e11 | −2.91303 | ||||||||
\(262\) | 5.41646e10 | 0.710165 | ||||||||
\(263\) | −8.02154e10 | −1.03385 | −0.516924 | − | 0.856031i | \(-0.672923\pi\) | ||||
−0.516924 | + | 0.856031i | \(0.672923\pi\) | |||||||
\(264\) | 2.14366e11 | 2.71605 | ||||||||
\(265\) | 2.66075e11 | 3.31434 | ||||||||
\(266\) | −2.06925e10 | −0.253422 | ||||||||
\(267\) | 2.63911e11 | 3.17802 | ||||||||
\(268\) | −1.46576e10 | −0.173563 | ||||||||
\(269\) | 1.79789e10 | 0.209352 | 0.104676 | − | 0.994506i | \(-0.466619\pi\) | ||||
0.104676 | + | 0.994506i | \(0.466619\pi\) | |||||||
\(270\) | −1.76884e11 | −2.02559 | ||||||||
\(271\) | −5.80992e10 | −0.654347 | −0.327173 | − | 0.944964i | \(-0.606096\pi\) | ||||
−0.327173 | + | 0.944964i | \(0.606096\pi\) | |||||||
\(272\) | 5.50280e10 | 0.609570 | ||||||||
\(273\) | −2.91520e9 | −0.0317641 | ||||||||
\(274\) | −1.87656e9 | −0.0201134 | ||||||||
\(275\) | −3.52103e11 | −3.71255 | ||||||||
\(276\) | −2.82629e10 | −0.293174 | ||||||||
\(277\) | 7.56051e10 | 0.771600 | 0.385800 | − | 0.922582i | \(-0.373925\pi\) | ||||
0.385800 | + | 0.922582i | \(0.373925\pi\) | |||||||
\(278\) | 1.55515e9 | 0.0156160 | ||||||||
\(279\) | −6.84085e10 | −0.675914 | ||||||||
\(280\) | −5.66698e10 | −0.550986 | ||||||||
\(281\) | 7.81929e10 | 0.748151 | 0.374075 | − | 0.927398i | \(-0.377960\pi\) | ||||
0.374075 | + | 0.927398i | \(0.377960\pi\) | |||||||
\(282\) | 5.36256e10 | 0.504953 | ||||||||
\(283\) | 1.17607e11 | 1.08992 | 0.544961 | − | 0.838462i | \(-0.316545\pi\) | ||||
0.544961 | + | 0.838462i | \(0.316545\pi\) | |||||||
\(284\) | 1.77532e10 | 0.161937 | ||||||||
\(285\) | −3.42901e11 | −3.07869 | ||||||||
\(286\) | −1.08183e10 | −0.0956116 | ||||||||
\(287\) | 3.13865e10 | 0.273070 | ||||||||
\(288\) | 7.37041e10 | 0.631285 | ||||||||
\(289\) | −4.64148e10 | −0.391396 | ||||||||
\(290\) | 3.37811e11 | 2.80468 | ||||||||
\(291\) | −5.50400e10 | −0.449946 | ||||||||
\(292\) | −4.55526e9 | −0.0366683 | ||||||||
\(293\) | 1.39474e11 | 1.10557 | 0.552787 | − | 0.833323i | \(-0.313564\pi\) | ||||
0.552787 | + | 0.833323i | \(0.313564\pi\) | |||||||
\(294\) | −1.76420e11 | −1.37716 | ||||||||
\(295\) | 2.08496e11 | 1.60287 | ||||||||
\(296\) | −1.85019e11 | −1.40089 | ||||||||
\(297\) | −2.49862e11 | −1.86336 | ||||||||
\(298\) | 1.00497e11 | 0.738209 | ||||||||
\(299\) | 9.15429e9 | 0.0662375 | ||||||||
\(300\) | −1.03505e11 | −0.737761 | ||||||||
\(301\) | 6.05124e9 | 0.0424908 | ||||||||
\(302\) | −1.33857e11 | −0.925999 | ||||||||
\(303\) | −1.82977e11 | −1.24711 | ||||||||
\(304\) | −1.17195e11 | −0.787005 | ||||||||
\(305\) | −1.60607e11 | −1.06271 | ||||||||
\(306\) | −1.87336e11 | −1.22145 | ||||||||
\(307\) | 3.89983e10 | 0.250567 | 0.125283 | − | 0.992121i | \(-0.460016\pi\) | ||||
0.125283 | + | 0.992121i | \(0.460016\pi\) | |||||||
\(308\) | −1.24726e10 | −0.0789730 | ||||||||
\(309\) | −3.25918e11 | −2.03374 | ||||||||
\(310\) | 1.05817e11 | 0.650773 | ||||||||
\(311\) | 2.46919e11 | 1.49669 | 0.748347 | − | 0.663308i | \(-0.230848\pi\) | ||||
0.748347 | + | 0.663308i | \(0.230848\pi\) | |||||||
\(312\) | −2.04106e10 | −0.121944 | ||||||||
\(313\) | 1.43556e11 | 0.845416 | 0.422708 | − | 0.906266i | \(-0.361080\pi\) | ||||
0.422708 | + | 0.906266i | \(0.361080\pi\) | |||||||
\(314\) | −5.45115e10 | −0.316450 | ||||||||
\(315\) | 1.56062e11 | 0.893100 | ||||||||
\(316\) | 4.29355e10 | 0.242228 | ||||||||
\(317\) | −2.92123e11 | −1.62480 | −0.812399 | − | 0.583102i | \(-0.801839\pi\) | ||||
−0.812399 | + | 0.583102i | \(0.801839\pi\) | |||||||
\(318\) | −4.88140e11 | −2.67684 | ||||||||
\(319\) | 4.77184e11 | 2.58005 | ||||||||
\(320\) | −3.84958e11 | −2.05229 | ||||||||
\(321\) | 2.86064e11 | 1.50380 | ||||||||
\(322\) | −4.66294e10 | −0.241718 | ||||||||
\(323\) | −1.53709e11 | −0.785758 | ||||||||
\(324\) | −9.97279e9 | −0.0502764 | ||||||||
\(325\) | 3.35251e10 | 0.166684 | ||||||||
\(326\) | −2.00964e10 | −0.0985462 | ||||||||
\(327\) | 1.22698e11 | 0.593434 | ||||||||
\(328\) | 2.19751e11 | 1.04833 | ||||||||
\(329\) | −2.00253e10 | −0.0942320 | ||||||||
\(330\) | 9.13165e11 | 4.23874 | ||||||||
\(331\) | −3.59742e10 | −0.164727 | −0.0823636 | − | 0.996602i | \(-0.526247\pi\) | ||||
−0.0823636 | + | 0.996602i | \(0.526247\pi\) | |||||||
\(332\) | −9.45423e9 | −0.0427076 | ||||||||
\(333\) | 5.09520e11 | 2.27071 | ||||||||
\(334\) | 2.00306e11 | 0.880716 | ||||||||
\(335\) | −4.00740e11 | −1.73845 | ||||||||
\(336\) | 8.41008e10 | 0.359976 | ||||||||
\(337\) | 4.12227e11 | 1.74101 | 0.870506 | − | 0.492157i | \(-0.163791\pi\) | ||||
0.870506 | + | 0.492157i | \(0.163791\pi\) | |||||||
\(338\) | −2.15650e11 | −0.898721 | ||||||||
\(339\) | 1.51775e11 | 0.624167 | ||||||||
\(340\) | −6.55892e10 | −0.266181 | ||||||||
\(341\) | 1.49475e11 | 0.598653 | ||||||||
\(342\) | 3.98976e11 | 1.57699 | ||||||||
\(343\) | 1.37306e11 | 0.535630 | ||||||||
\(344\) | 4.23675e10 | 0.163125 | ||||||||
\(345\) | −7.72709e11 | −2.93650 | ||||||||
\(346\) | −6.35728e10 | −0.238467 | ||||||||
\(347\) | −7.23809e10 | −0.268004 | −0.134002 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134002 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(348\) | 1.40274e11 | 0.512710 | ||||||||
\(349\) | 2.59445e11 | 0.936119 | 0.468060 | − | 0.883697i | \(-0.344953\pi\) | ||||
0.468060 | + | 0.883697i | \(0.344953\pi\) | |||||||
\(350\) | −1.70767e11 | −0.608273 | ||||||||
\(351\) | 2.37903e10 | 0.0836601 | ||||||||
\(352\) | −1.61046e11 | −0.559125 | ||||||||
\(353\) | 8.53217e10 | 0.292465 | 0.146232 | − | 0.989250i | \(-0.453285\pi\) | ||||
0.146232 | + | 0.989250i | \(0.453285\pi\) | |||||||
\(354\) | −3.82507e11 | −1.29457 | ||||||||
\(355\) | 4.85375e11 | 1.62200 | ||||||||
\(356\) | −1.07509e11 | −0.354749 | ||||||||
\(357\) | 1.10304e11 | 0.359405 | ||||||||
\(358\) | −3.11520e11 | −1.00233 | ||||||||
\(359\) | −2.92377e11 | −0.929005 | −0.464503 | − | 0.885572i | \(-0.653767\pi\) | ||||
−0.464503 | + | 0.885572i | \(0.653767\pi\) | |||||||
\(360\) | 1.09266e12 | 3.42866 | ||||||||
\(361\) | 4.67171e9 | 0.0144775 | ||||||||
\(362\) | −4.95267e11 | −1.51583 | ||||||||
\(363\) | 7.42941e11 | 2.24582 | ||||||||
\(364\) | 1.18756e9 | 0.00354569 | ||||||||
\(365\) | −1.24541e11 | −0.367278 | ||||||||
\(366\) | 2.94649e11 | 0.858301 | ||||||||
\(367\) | 5.23535e11 | 1.50643 | 0.753214 | − | 0.657775i | \(-0.228502\pi\) | ||||
0.753214 | + | 0.657775i | \(0.228502\pi\) | |||||||
\(368\) | −2.64093e11 | −0.750656 | ||||||||
\(369\) | −6.05169e11 | −1.69925 | ||||||||
\(370\) | −7.88149e11 | −2.18625 | ||||||||
\(371\) | 1.82285e11 | 0.499539 | ||||||||
\(372\) | 4.39402e10 | 0.118965 | ||||||||
\(373\) | 2.22087e11 | 0.594063 | 0.297032 | − | 0.954868i | \(-0.404003\pi\) | ||||
0.297032 | + | 0.954868i | \(0.404003\pi\) | |||||||
\(374\) | 4.09337e11 | 1.08183 | ||||||||
\(375\) | −1.65930e12 | −4.33295 | ||||||||
\(376\) | −1.40206e11 | −0.361762 | ||||||||
\(377\) | −4.54346e10 | −0.115838 | ||||||||
\(378\) | −1.21181e11 | −0.305297 | ||||||||
\(379\) | 5.93299e10 | 0.147706 | 0.0738528 | − | 0.997269i | \(-0.476470\pi\) | ||||
0.0738528 | + | 0.997269i | \(0.476470\pi\) | |||||||
\(380\) | 1.39687e11 | 0.343662 | ||||||||
\(381\) | −7.93765e11 | −1.92988 | ||||||||
\(382\) | 1.76244e11 | 0.423478 | ||||||||
\(383\) | 3.66860e11 | 0.871175 | 0.435587 | − | 0.900146i | \(-0.356541\pi\) | ||||
0.435587 | + | 0.900146i | \(0.356541\pi\) | |||||||
\(384\) | 4.49741e11 | 1.05553 | ||||||||
\(385\) | −3.41002e11 | −0.791013 | ||||||||
\(386\) | 7.07461e11 | 1.62203 | ||||||||
\(387\) | −1.16675e11 | −0.264411 | ||||||||
\(388\) | 2.24216e10 | 0.0502255 | ||||||||
\(389\) | −8.75015e11 | −1.93750 | −0.968751 | − | 0.248035i | \(-0.920215\pi\) | ||||
−0.968751 | + | 0.248035i | \(0.920215\pi\) | |||||||
\(390\) | −8.69460e10 | −0.190309 | ||||||||
\(391\) | −3.46376e11 | −0.749467 | ||||||||
\(392\) | 4.61258e11 | 0.986635 | ||||||||
\(393\) | 6.14921e11 | 1.30033 | ||||||||
\(394\) | −4.19609e11 | −0.877227 | ||||||||
\(395\) | 1.17386e12 | 2.42622 | ||||||||
\(396\) | 2.40487e11 | 0.491431 | ||||||||
\(397\) | −5.04810e11 | −1.01993 | −0.509965 | − | 0.860195i | \(-0.670342\pi\) | ||||
−0.509965 | + | 0.860195i | \(0.670342\pi\) | |||||||
\(398\) | −3.19019e11 | −0.637298 | ||||||||
\(399\) | −2.34918e11 | −0.464022 | ||||||||
\(400\) | −9.67167e11 | −1.88900 | ||||||||
\(401\) | 7.68568e11 | 1.48434 | 0.742169 | − | 0.670213i | \(-0.233797\pi\) | ||||
0.742169 | + | 0.670213i | \(0.233797\pi\) | |||||||
\(402\) | 7.35197e11 | 1.40406 | ||||||||
\(403\) | −1.42321e10 | −0.0268780 | ||||||||
\(404\) | 7.45395e10 | 0.139210 | ||||||||
\(405\) | −2.72657e11 | −0.503581 | ||||||||
\(406\) | 2.31431e11 | 0.422722 | ||||||||
\(407\) | −1.11332e12 | −2.01116 | ||||||||
\(408\) | 7.72289e11 | 1.37978 | ||||||||
\(409\) | −6.22133e11 | −1.09933 | −0.549665 | − | 0.835385i | \(-0.685245\pi\) | ||||
−0.549665 | + | 0.835385i | \(0.685245\pi\) | |||||||
\(410\) | 9.36103e11 | 1.63605 | ||||||||
\(411\) | −2.13043e10 | −0.0368281 | ||||||||
\(412\) | 1.32769e11 | 0.227018 | ||||||||
\(413\) | 1.42839e11 | 0.241586 | ||||||||
\(414\) | 8.99071e11 | 1.50416 | ||||||||
\(415\) | −2.58479e11 | −0.427769 | ||||||||
\(416\) | 1.53338e10 | 0.0251033 | ||||||||
\(417\) | 1.76554e10 | 0.0285933 | ||||||||
\(418\) | −8.71778e11 | −1.39673 | ||||||||
\(419\) | −1.15967e12 | −1.83812 | −0.919058 | − | 0.394122i | \(-0.871049\pi\) | ||||
−0.919058 | + | 0.394122i | \(0.871049\pi\) | |||||||
\(420\) | −1.00242e11 | −0.157191 | ||||||||
\(421\) | 8.01209e10 | 0.124302 | 0.0621508 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621508 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(422\) | −6.75413e11 | −1.03672 | ||||||||
\(423\) | 3.86113e11 | 0.586384 | ||||||||
\(424\) | 1.27626e12 | 1.91776 | ||||||||
\(425\) | −1.26851e12 | −1.88600 | ||||||||
\(426\) | −8.90467e11 | −1.31001 | ||||||||
\(427\) | −1.10030e11 | −0.160172 | ||||||||
\(428\) | −1.16534e11 | −0.167863 | ||||||||
\(429\) | −1.22818e11 | −0.175067 | ||||||||
\(430\) | 1.80479e11 | 0.254576 | ||||||||
\(431\) | 3.08981e11 | 0.431304 | 0.215652 | − | 0.976470i | \(-0.430812\pi\) | ||||
0.215652 | + | 0.976470i | \(0.430812\pi\) | |||||||
\(432\) | −6.86329e11 | −0.948103 | ||||||||
\(433\) | 7.06997e11 | 0.966544 | 0.483272 | − | 0.875470i | \(-0.339448\pi\) | ||||
0.483272 | + | 0.875470i | \(0.339448\pi\) | |||||||
\(434\) | 7.24946e10 | 0.0980848 | ||||||||
\(435\) | 3.83511e12 | 5.13543 | ||||||||
\(436\) | −4.99834e10 | −0.0662425 | ||||||||
\(437\) | 7.37688e11 | 0.967623 | ||||||||
\(438\) | 2.28483e11 | 0.296634 | ||||||||
\(439\) | −1.15067e12 | −1.47864 | −0.739318 | − | 0.673356i | \(-0.764852\pi\) | ||||
−0.739318 | + | 0.673356i | \(0.764852\pi\) | |||||||
\(440\) | −2.38751e12 | −3.03674 | ||||||||
\(441\) | −1.27025e12 | −1.59925 | ||||||||
\(442\) | −3.89746e10 | −0.0485714 | ||||||||
\(443\) | 1.45765e12 | 1.79819 | 0.899095 | − | 0.437754i | \(-0.144226\pi\) | ||||
0.899095 | + | 0.437754i | \(0.144226\pi\) | |||||||
\(444\) | −3.27275e11 | −0.399659 | ||||||||
\(445\) | −2.93931e12 | −3.55325 | ||||||||
\(446\) | 5.00705e11 | 0.599204 | ||||||||
\(447\) | 1.14092e12 | 1.35168 | ||||||||
\(448\) | −2.63731e11 | −0.309322 | ||||||||
\(449\) | 1.51686e12 | 1.76132 | 0.880658 | − | 0.473753i | \(-0.157101\pi\) | ||||
0.880658 | + | 0.473753i | \(0.157101\pi\) | |||||||
\(450\) | 3.29260e12 | 3.78515 | ||||||||
\(451\) | 1.32232e12 | 1.50502 | ||||||||
\(452\) | −6.18284e10 | −0.0696731 | ||||||||
\(453\) | −1.51966e12 | −1.69552 | ||||||||
\(454\) | −4.94524e11 | −0.546306 | ||||||||
\(455\) | 3.24681e10 | 0.0355145 | ||||||||
\(456\) | −1.64477e12 | −1.78141 | ||||||||
\(457\) | −1.58795e12 | −1.70300 | −0.851501 | − | 0.524354i | \(-0.824307\pi\) | ||||
−0.851501 | + | 0.524354i | \(0.824307\pi\) | |||||||
\(458\) | −7.03312e11 | −0.746884 | ||||||||
\(459\) | −9.00169e11 | −0.946601 | ||||||||
\(460\) | 3.14778e11 | 0.327789 | ||||||||
\(461\) | −5.06836e11 | −0.522653 | −0.261326 | − | 0.965251i | \(-0.584160\pi\) | ||||
−0.261326 | + | 0.965251i | \(0.584160\pi\) | |||||||
\(462\) | 6.25601e11 | 0.638864 | ||||||||
\(463\) | −1.40219e12 | −1.41806 | −0.709028 | − | 0.705180i | \(-0.750866\pi\) | ||||
−0.709028 | + | 0.705180i | \(0.750866\pi\) | |||||||
\(464\) | 1.31075e12 | 1.31277 | ||||||||
\(465\) | 1.20133e12 | 1.19158 | ||||||||
\(466\) | 8.43801e11 | 0.828902 | ||||||||
\(467\) | −9.39462e11 | −0.914015 | −0.457008 | − | 0.889463i | \(-0.651079\pi\) | ||||
−0.457008 | + | 0.889463i | \(0.651079\pi\) | |||||||
\(468\) | −2.28977e10 | −0.0220640 | ||||||||
\(469\) | −2.74543e11 | −0.262019 | ||||||||
\(470\) | −5.97257e11 | −0.564574 | ||||||||
\(471\) | −6.18860e11 | −0.579427 | ||||||||
\(472\) | 1.00008e12 | 0.927461 | ||||||||
\(473\) | 2.54940e11 | 0.234187 | ||||||||
\(474\) | −2.15356e12 | −1.95954 | ||||||||
\(475\) | 2.70158e12 | 2.43499 | ||||||||
\(476\) | −4.49346e10 | −0.0401189 | ||||||||
\(477\) | −3.51468e12 | −3.10852 | ||||||||
\(478\) | −4.89448e11 | −0.428826 | ||||||||
\(479\) | −9.05240e11 | −0.785695 | −0.392847 | − | 0.919604i | \(-0.628510\pi\) | ||||
−0.392847 | + | 0.919604i | \(0.628510\pi\) | |||||||
\(480\) | −1.29432e12 | −1.11290 | ||||||||
\(481\) | 1.06004e11 | 0.0902959 | ||||||||
\(482\) | 6.68126e11 | 0.563828 | ||||||||
\(483\) | −5.29376e11 | −0.442591 | ||||||||
\(484\) | −3.02652e11 | −0.250691 | ||||||||
\(485\) | 6.13010e11 | 0.503071 | ||||||||
\(486\) | −8.47372e11 | −0.688986 | ||||||||
\(487\) | −6.82703e11 | −0.549986 | −0.274993 | − | 0.961446i | \(-0.588675\pi\) | ||||
−0.274993 | + | 0.961446i | \(0.588675\pi\) | |||||||
\(488\) | −7.70372e11 | −0.614909 | ||||||||
\(489\) | −2.28151e11 | −0.180440 | ||||||||
\(490\) | 1.96488e12 | 1.53976 | ||||||||
\(491\) | 2.15045e11 | 0.166979 | 0.0834897 | − | 0.996509i | \(-0.473393\pi\) | ||||
0.0834897 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(492\) | 3.88712e11 | 0.299078 | ||||||||
\(493\) | 1.71913e12 | 1.31069 | ||||||||
\(494\) | 8.30053e10 | 0.0627097 | ||||||||
\(495\) | 6.57493e12 | 4.92229 | ||||||||
\(496\) | 4.10584e11 | 0.304603 | ||||||||
\(497\) | 3.32526e11 | 0.244468 | ||||||||
\(498\) | 4.74205e11 | 0.345489 | ||||||||
\(499\) | −5.06026e10 | −0.0365359 | −0.0182680 | − | 0.999833i | \(-0.505815\pi\) | ||||
−0.0182680 | + | 0.999833i | \(0.505815\pi\) | |||||||
\(500\) | 6.75947e11 | 0.483668 | ||||||||
\(501\) | 2.27404e12 | 1.61261 | ||||||||
\(502\) | −9.11345e11 | −0.640495 | ||||||||
\(503\) | 2.64497e12 | 1.84232 | 0.921161 | − | 0.389183i | \(-0.127242\pi\) | ||||
0.921161 | + | 0.389183i | \(0.127242\pi\) | |||||||
\(504\) | 7.48572e11 | 0.516769 | ||||||||
\(505\) | 2.03792e12 | 1.39436 | ||||||||
\(506\) | −1.96451e12 | −1.33222 | ||||||||
\(507\) | −2.44824e12 | −1.64558 | ||||||||
\(508\) | 3.23356e11 | 0.215424 | ||||||||
\(509\) | 1.81937e12 | 1.20141 | 0.600703 | − | 0.799472i | \(-0.294887\pi\) | ||||
0.600703 | + | 0.799472i | \(0.294887\pi\) | |||||||
\(510\) | 3.28983e12 | 2.15331 | ||||||||
\(511\) | −8.53221e10 | −0.0553563 | ||||||||
\(512\) | −1.74201e12 | −1.12031 | ||||||||
\(513\) | 1.91712e12 | 1.22214 | ||||||||
\(514\) | 9.31607e11 | 0.588706 | ||||||||
\(515\) | 3.62992e12 | 2.27387 | ||||||||
\(516\) | 7.49428e10 | 0.0465378 | ||||||||
\(517\) | −8.43671e11 | −0.519357 | ||||||||
\(518\) | −5.39954e11 | −0.329513 | ||||||||
\(519\) | −7.21731e11 | −0.436639 | ||||||||
\(520\) | 2.27324e11 | 0.136342 | ||||||||
\(521\) | −6.58651e11 | −0.391639 | −0.195819 | − | 0.980640i | \(-0.562737\pi\) | ||||
−0.195819 | + | 0.980640i | \(0.562737\pi\) | |||||||
\(522\) | −4.46227e12 | −2.63050 | ||||||||
\(523\) | −2.09316e12 | −1.22333 | −0.611666 | − | 0.791116i | \(-0.709500\pi\) | ||||
−0.611666 | + | 0.791116i | \(0.709500\pi\) | |||||||
\(524\) | −2.50500e11 | −0.145150 | ||||||||
\(525\) | −1.93869e12 | −1.11376 | ||||||||
\(526\) | −1.63903e12 | −0.933579 | ||||||||
\(527\) | 5.38510e11 | 0.304120 | ||||||||
\(528\) | 3.54318e12 | 1.98400 | ||||||||
\(529\) | −1.38810e11 | −0.0770672 | ||||||||
\(530\) | 5.43667e12 | 2.99290 | ||||||||
\(531\) | −2.75411e12 | −1.50333 | ||||||||
\(532\) | 9.56985e10 | 0.0517968 | ||||||||
\(533\) | −1.25903e11 | −0.0675716 | ||||||||
\(534\) | 5.39245e12 | 2.86979 | ||||||||
\(535\) | −3.18604e12 | −1.68135 | ||||||||
\(536\) | −1.92220e12 | −1.00591 | ||||||||
\(537\) | −3.53663e12 | −1.83529 | ||||||||
\(538\) | 3.67360e11 | 0.189048 | ||||||||
\(539\) | 2.77555e12 | 1.41644 | ||||||||
\(540\) | 8.18052e11 | 0.414008 | ||||||||
\(541\) | 2.75220e12 | 1.38131 | 0.690656 | − | 0.723184i | \(-0.257322\pi\) | ||||
0.690656 | + | 0.723184i | \(0.257322\pi\) | |||||||
\(542\) | −1.18713e12 | −0.590884 | ||||||||
\(543\) | −5.62269e12 | −2.77552 | ||||||||
\(544\) | −5.80196e11 | −0.284040 | ||||||||
\(545\) | −1.36655e12 | −0.663502 | ||||||||
\(546\) | −5.95659e10 | −0.0286834 | ||||||||
\(547\) | −1.67438e12 | −0.799669 | −0.399835 | − | 0.916587i | \(-0.630932\pi\) | ||||
−0.399835 | + | 0.916587i | \(0.630932\pi\) | |||||||
\(548\) | 8.67873e9 | 0.00411096 | ||||||||
\(549\) | 2.12152e12 | 0.996714 | ||||||||
\(550\) | −7.19447e12 | −3.35248 | ||||||||
\(551\) | −3.66129e12 | −1.69220 | ||||||||
\(552\) | −3.70640e12 | −1.69913 | ||||||||
\(553\) | 8.04202e11 | 0.365681 | ||||||||
\(554\) | 1.54483e12 | 0.696765 | ||||||||
\(555\) | −8.94772e12 | −4.00308 | ||||||||
\(556\) | −7.19226e9 | −0.00319175 | ||||||||
\(557\) | 2.66058e12 | 1.17119 | 0.585596 | − | 0.810603i | \(-0.300860\pi\) | ||||
0.585596 | + | 0.810603i | \(0.300860\pi\) | |||||||
\(558\) | −1.39778e12 | −0.610360 | ||||||||
\(559\) | −2.42738e10 | −0.0105144 | ||||||||
\(560\) | −9.36675e11 | −0.402479 | ||||||||
\(561\) | 4.64713e12 | 1.98085 | ||||||||
\(562\) | 1.59771e12 | 0.675590 | ||||||||
\(563\) | −1.80763e12 | −0.758268 | −0.379134 | − | 0.925342i | \(-0.623778\pi\) | ||||
−0.379134 | + | 0.925342i | \(0.623778\pi\) | |||||||
\(564\) | −2.48008e11 | −0.103207 | ||||||||
\(565\) | −1.69040e12 | −0.697863 | ||||||||
\(566\) | 2.40305e12 | 0.984214 | ||||||||
\(567\) | −1.86795e11 | −0.0758999 | ||||||||
\(568\) | 2.32817e12 | 0.938526 | ||||||||
\(569\) | −3.50663e12 | −1.40244 | −0.701220 | − | 0.712944i | \(-0.747361\pi\) | ||||
−0.701220 | + | 0.712944i | \(0.747361\pi\) | |||||||
\(570\) | −7.00644e12 | −2.78010 | ||||||||
\(571\) | 2.95802e12 | 1.16450 | 0.582248 | − | 0.813011i | \(-0.302173\pi\) | ||||
0.582248 | + | 0.813011i | \(0.302173\pi\) | |||||||
\(572\) | 5.00323e10 | 0.0195420 | ||||||||
\(573\) | 2.00087e12 | 0.775397 | ||||||||
\(574\) | 6.41316e11 | 0.246586 | ||||||||
\(575\) | 6.08787e12 | 2.32252 | ||||||||
\(576\) | 5.08506e12 | 1.92484 | ||||||||
\(577\) | −9.05526e11 | −0.340103 | −0.170051 | − | 0.985435i | \(-0.554393\pi\) | ||||
−0.170051 | + | 0.985435i | \(0.554393\pi\) | |||||||
\(578\) | −9.48387e11 | −0.353436 | ||||||||
\(579\) | 8.03168e12 | 2.96998 | ||||||||
\(580\) | −1.56231e12 | −0.573246 | ||||||||
\(581\) | −1.77082e11 | −0.0644735 | ||||||||
\(582\) | −1.12463e12 | −0.406307 | ||||||||
\(583\) | 7.67972e12 | 2.75320 | ||||||||
\(584\) | −5.97378e11 | −0.212516 | ||||||||
\(585\) | −6.26024e11 | −0.220999 | ||||||||
\(586\) | 2.84985e12 | 0.998348 | ||||||||
\(587\) | −6.85640e11 | −0.238355 | −0.119178 | − | 0.992873i | \(-0.538026\pi\) | ||||
−0.119178 | + | 0.992873i | \(0.538026\pi\) | |||||||
\(588\) | 8.15908e11 | 0.281477 | ||||||||
\(589\) | −1.14688e12 | −0.392644 | ||||||||
\(590\) | 4.26018e12 | 1.44742 | ||||||||
\(591\) | −4.76376e12 | −1.60622 | ||||||||
\(592\) | −3.05811e12 | −1.02330 | ||||||||
\(593\) | −6.58143e11 | −0.218562 | −0.109281 | − | 0.994011i | \(-0.534855\pi\) | ||||
−0.109281 | + | 0.994011i | \(0.534855\pi\) | |||||||
\(594\) | −5.10540e12 | −1.68264 | ||||||||
\(595\) | −1.22852e12 | −0.401841 | ||||||||
\(596\) | −4.64778e11 | −0.150882 | ||||||||
\(597\) | −3.62177e12 | −1.16691 | ||||||||
\(598\) | 1.87048e11 | 0.0598134 | ||||||||
\(599\) | −1.58033e12 | −0.501564 | −0.250782 | − | 0.968044i | \(-0.580688\pi\) | ||||
−0.250782 | + | 0.968044i | \(0.580688\pi\) | |||||||
\(600\) | −1.35737e13 | −4.27579 | ||||||||
\(601\) | −1.50248e12 | −0.469756 | −0.234878 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234878 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(602\) | 1.23644e11 | 0.0383698 | ||||||||
\(603\) | 5.29353e12 | 1.63049 | ||||||||
\(604\) | 6.19063e11 | 0.189264 | ||||||||
\(605\) | −8.27452e12 | −2.51098 | ||||||||
\(606\) | −3.73875e12 | −1.12616 | ||||||||
\(607\) | 5.26894e12 | 1.57534 | 0.787670 | − | 0.616097i | \(-0.211287\pi\) | ||||
0.787670 | + | 0.616097i | \(0.211287\pi\) | |||||||
\(608\) | 1.23566e12 | 0.366719 | ||||||||
\(609\) | 2.62740e12 | 0.774013 | ||||||||
\(610\) | −3.28166e12 | −0.959642 | ||||||||
\(611\) | 8.03292e10 | 0.0233178 | ||||||||
\(612\) | 8.66392e11 | 0.249651 | ||||||||
\(613\) | 2.66173e12 | 0.761364 | 0.380682 | − | 0.924706i | \(-0.375689\pi\) | ||||
0.380682 | + | 0.924706i | \(0.375689\pi\) | |||||||
\(614\) | 7.96848e11 | 0.226265 | ||||||||
\(615\) | 1.06274e13 | 2.99564 | ||||||||
\(616\) | −1.63566e12 | −0.457699 | ||||||||
\(617\) | 3.08426e12 | 0.856777 | 0.428388 | − | 0.903595i | \(-0.359082\pi\) | ||||
0.428388 | + | 0.903595i | \(0.359082\pi\) | |||||||
\(618\) | −6.65944e12 | −1.83650 | ||||||||
\(619\) | 1.96063e12 | 0.536769 | 0.268384 | − | 0.963312i | \(-0.413510\pi\) | ||||
0.268384 | + | 0.963312i | \(0.413510\pi\) | |||||||
\(620\) | −4.89385e11 | −0.133011 | ||||||||
\(621\) | 4.32013e12 | 1.16569 | ||||||||
\(622\) | 5.04526e12 | 1.35153 | ||||||||
\(623\) | −2.01370e12 | −0.535547 | ||||||||
\(624\) | −3.37360e11 | −0.0890765 | ||||||||
\(625\) | 9.25824e12 | 2.42699 | ||||||||
\(626\) | 2.93325e12 | 0.763423 | ||||||||
\(627\) | −9.89714e12 | −2.55744 | ||||||||
\(628\) | 2.52105e11 | 0.0646790 | ||||||||
\(629\) | −4.01092e12 | −1.02168 | ||||||||
\(630\) | 3.18880e12 | 0.806481 | ||||||||
\(631\) | 1.03708e12 | 0.260424 | 0.130212 | − | 0.991486i | \(-0.458434\pi\) | ||||
0.130212 | + | 0.991486i | \(0.458434\pi\) | |||||||
\(632\) | 5.63058e12 | 1.40387 | ||||||||
\(633\) | −7.66785e12 | −1.89827 | ||||||||
\(634\) | −5.96892e12 | −1.46722 | ||||||||
\(635\) | 8.84058e12 | 2.15774 | ||||||||
\(636\) | 2.25755e12 | 0.547117 | ||||||||
\(637\) | −2.64271e11 | −0.0635948 | ||||||||
\(638\) | 9.75025e12 | 2.32982 | ||||||||
\(639\) | −6.41150e12 | −1.52127 | ||||||||
\(640\) | −5.00901e12 | −1.18016 | ||||||||
\(641\) | 5.27910e12 | 1.23509 | 0.617545 | − | 0.786535i | \(-0.288127\pi\) | ||||
0.617545 | + | 0.786535i | \(0.288127\pi\) | |||||||
\(642\) | 5.84510e12 | 1.35795 | ||||||||
\(643\) | 3.47722e11 | 0.0802201 | 0.0401100 | − | 0.999195i | \(-0.487229\pi\) | ||||
0.0401100 | + | 0.999195i | \(0.487229\pi\) | |||||||
\(644\) | 2.15652e11 | 0.0494045 | ||||||||
\(645\) | 2.04894e12 | 0.466134 | ||||||||
\(646\) | −3.14072e12 | −0.709550 | ||||||||
\(647\) | 7.11791e11 | 0.159692 | 0.0798460 | − | 0.996807i | \(-0.474557\pi\) | ||||
0.0798460 | + | 0.996807i | \(0.474557\pi\) | |||||||
\(648\) | −1.30783e12 | −0.291384 | ||||||||
\(649\) | 6.01783e12 | 1.33149 | ||||||||
\(650\) | 6.85013e11 | 0.150518 | ||||||||
\(651\) | 8.23019e11 | 0.179595 | ||||||||
\(652\) | 9.29420e10 | 0.0201418 | ||||||||
\(653\) | −1.71011e12 | −0.368056 | −0.184028 | − | 0.982921i | \(-0.558914\pi\) | ||||
−0.184028 | + | 0.982921i | \(0.558914\pi\) | |||||||
\(654\) | 2.50707e12 | 0.535879 | ||||||||
\(655\) | −6.84870e12 | −1.45386 | ||||||||
\(656\) | 3.63219e12 | 0.765775 | ||||||||
\(657\) | 1.64511e12 | 0.344470 | ||||||||
\(658\) | −4.09175e11 | −0.0850928 | ||||||||
\(659\) | −3.21878e12 | −0.664825 | −0.332412 | − | 0.943134i | \(-0.607863\pi\) | ||||
−0.332412 | + | 0.943134i | \(0.607863\pi\) | |||||||
\(660\) | −4.22321e12 | −0.866352 | ||||||||
\(661\) | −1.29023e12 | −0.262882 | −0.131441 | − | 0.991324i | \(-0.541960\pi\) | ||||
−0.131441 | + | 0.991324i | \(0.541960\pi\) | |||||||
\(662\) | −7.35056e11 | −0.148751 | ||||||||
\(663\) | −4.42472e11 | −0.0889354 | ||||||||
\(664\) | −1.23983e12 | −0.247518 | ||||||||
\(665\) | 2.61641e12 | 0.518809 | ||||||||
\(666\) | 1.04110e13 | 2.05048 | ||||||||
\(667\) | −8.25054e12 | −1.61405 | ||||||||
\(668\) | −9.26377e11 | −0.180009 | ||||||||
\(669\) | 5.68442e12 | 1.09716 | ||||||||
\(670\) | −8.18827e12 | −1.56984 | ||||||||
\(671\) | −4.63560e12 | −0.882784 | ||||||||
\(672\) | −8.86729e11 | −0.167737 | ||||||||
\(673\) | −2.68951e12 | −0.505365 | −0.252682 | − | 0.967549i | \(-0.581313\pi\) | ||||
−0.252682 | + | 0.967549i | \(0.581313\pi\) | |||||||
\(674\) | 8.42298e12 | 1.57216 | ||||||||
\(675\) | 1.58213e13 | 2.93342 | ||||||||
\(676\) | 9.97340e11 | 0.183689 | ||||||||
\(677\) | 3.07951e12 | 0.563421 | 0.281710 | − | 0.959500i | \(-0.409098\pi\) | ||||
0.281710 | + | 0.959500i | \(0.409098\pi\) | |||||||
\(678\) | 3.10119e12 | 0.563631 | ||||||||
\(679\) | 4.19967e11 | 0.0758231 | ||||||||
\(680\) | −8.60139e12 | −1.54269 | ||||||||
\(681\) | −5.61425e12 | −1.00030 | ||||||||
\(682\) | 3.05421e12 | 0.540592 | ||||||||
\(683\) | −1.87777e12 | −0.330178 | −0.165089 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165089 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(684\) | −1.84518e12 | −0.322320 | ||||||||
\(685\) | 2.37277e11 | 0.0411764 | ||||||||
\(686\) | 2.80555e12 | 0.483681 | ||||||||
\(687\) | −7.98458e12 | −1.36756 | ||||||||
\(688\) | 7.00277e11 | 0.119158 | ||||||||
\(689\) | −7.31216e11 | −0.123612 | ||||||||
\(690\) | −1.57887e13 | −2.65170 | ||||||||
\(691\) | −1.40579e12 | −0.234568 | −0.117284 | − | 0.993098i | \(-0.537419\pi\) | ||||
−0.117284 | + | 0.993098i | \(0.537419\pi\) | |||||||
\(692\) | 2.94012e11 | 0.0487402 | ||||||||
\(693\) | 4.50442e12 | 0.741890 | ||||||||
\(694\) | −1.47895e12 | −0.242011 | ||||||||
\(695\) | −1.96637e11 | −0.0319693 | ||||||||
\(696\) | 1.83956e13 | 2.97148 | ||||||||
\(697\) | 4.76387e12 | 0.764561 | ||||||||
\(698\) | 5.30121e12 | 0.845328 | ||||||||
\(699\) | 9.57953e12 | 1.51774 | ||||||||
\(700\) | 7.89765e11 | 0.124325 | ||||||||
\(701\) | −1.02642e13 | −1.60544 | −0.802720 | − | 0.596356i | \(-0.796615\pi\) | ||||
−0.802720 | + | 0.596356i | \(0.796615\pi\) | |||||||
\(702\) | 4.86105e11 | 0.0755462 | ||||||||
\(703\) | 8.54219e12 | 1.31908 | ||||||||
\(704\) | −1.11111e13 | −1.70482 | ||||||||
\(705\) | −6.78056e12 | −1.03375 | ||||||||
\(706\) | 1.74337e12 | 0.264100 | ||||||||
\(707\) | 1.39616e12 | 0.210159 | ||||||||
\(708\) | 1.76902e12 | 0.264595 | ||||||||
\(709\) | −6.07076e12 | −0.902267 | −0.451133 | − | 0.892457i | \(-0.648980\pi\) | ||||
−0.451133 | + | 0.892457i | \(0.648980\pi\) | |||||||
\(710\) | 9.91761e12 | 1.46469 | ||||||||
\(711\) | −1.55060e13 | −2.27555 | ||||||||
\(712\) | −1.40988e13 | −2.05600 | ||||||||
\(713\) | −2.58444e12 | −0.374510 | ||||||||
\(714\) | 2.25383e12 | 0.324548 | ||||||||
\(715\) | 1.36789e12 | 0.195737 | ||||||||
\(716\) | 1.44072e12 | 0.204866 | ||||||||
\(717\) | −5.55662e12 | −0.785190 | ||||||||
\(718\) | −5.97410e12 | −0.838905 | ||||||||
\(719\) | −4.59470e12 | −0.641175 | −0.320588 | − | 0.947219i | \(-0.603880\pi\) | ||||
−0.320588 | + | 0.947219i | \(0.603880\pi\) | |||||||
\(720\) | 1.80602e13 | 2.50453 | ||||||||
\(721\) | 2.48683e12 | 0.342718 | ||||||||
\(722\) | 9.54564e10 | 0.0130734 | ||||||||
\(723\) | 7.58512e12 | 1.03238 | ||||||||
\(724\) | 2.29051e12 | 0.309820 | ||||||||
\(725\) | −3.02153e13 | −4.06169 | ||||||||
\(726\) | 1.51804e13 | 2.02800 | ||||||||
\(727\) | 3.53648e12 | 0.469533 | 0.234767 | − | 0.972052i | \(-0.424567\pi\) | ||||
0.234767 | + | 0.972052i | \(0.424567\pi\) | |||||||
\(728\) | 1.55738e11 | 0.0205495 | ||||||||
\(729\) | −1.16973e13 | −1.53395 | ||||||||
\(730\) | −2.54474e12 | −0.331657 | ||||||||
\(731\) | 9.18463e11 | 0.118969 | ||||||||
\(732\) | −1.36269e12 | −0.175427 | ||||||||
\(733\) | −5.36402e12 | −0.686314 | −0.343157 | − | 0.939278i | \(-0.611496\pi\) | ||||
−0.343157 | + | 0.939278i | \(0.611496\pi\) | |||||||
\(734\) | 1.06973e13 | 1.36033 | ||||||||
\(735\) | 2.23070e13 | 2.81934 | ||||||||
\(736\) | 2.78450e12 | 0.349782 | ||||||||
\(737\) | −1.15666e13 | −1.44411 | ||||||||
\(738\) | −1.23653e13 | −1.53445 | ||||||||
\(739\) | 1.14197e12 | 0.140850 | 0.0704249 | − | 0.997517i | \(-0.477564\pi\) | ||||
0.0704249 | + | 0.997517i | \(0.477564\pi\) | |||||||
\(740\) | 3.64503e12 | 0.446847 | ||||||||
\(741\) | 9.42346e11 | 0.114823 | ||||||||
\(742\) | 3.72462e12 | 0.451091 | ||||||||
\(743\) | −6.88545e11 | −0.0828863 | −0.0414431 | − | 0.999141i | \(-0.513196\pi\) | ||||
−0.0414431 | + | 0.999141i | \(0.513196\pi\) | |||||||
\(744\) | 5.76233e12 | 0.689477 | ||||||||
\(745\) | −1.27071e13 | −1.51127 | ||||||||
\(746\) | 4.53787e12 | 0.536447 | ||||||||
\(747\) | 3.41435e12 | 0.401204 | ||||||||
\(748\) | −1.89310e12 | −0.221114 | ||||||||
\(749\) | −2.18273e12 | −0.253414 | ||||||||
\(750\) | −3.39042e13 | −3.91271 | ||||||||
\(751\) | 4.45256e12 | 0.510776 | 0.255388 | − | 0.966839i | \(-0.417797\pi\) | ||||
0.255388 | + | 0.966839i | \(0.417797\pi\) | |||||||
\(752\) | −2.31742e12 | −0.264256 | ||||||||
\(753\) | −1.03463e13 | −1.17276 | ||||||||
\(754\) | −9.28359e11 | −0.104603 | ||||||||
\(755\) | 1.69252e13 | 1.89572 | ||||||||
\(756\) | 5.60440e11 | 0.0623995 | ||||||||
\(757\) | 8.14319e12 | 0.901287 | 0.450643 | − | 0.892704i | \(-0.351195\pi\) | ||||
0.450643 | + | 0.892704i | \(0.351195\pi\) | |||||||
\(758\) | 1.21228e12 | 0.133380 | ||||||||
\(759\) | −2.23027e13 | −2.43933 | ||||||||
\(760\) | 1.83186e13 | 1.99174 | ||||||||
\(761\) | −7.09695e12 | −0.767080 | −0.383540 | − | 0.923524i | \(-0.625295\pi\) | ||||
−0.383540 | + | 0.923524i | \(0.625295\pi\) | |||||||
\(762\) | −1.62189e13 | −1.74270 | ||||||||
\(763\) | −9.36212e11 | −0.100003 | ||||||||
\(764\) | −8.15096e11 | −0.0865543 | ||||||||
\(765\) | 2.36872e13 | 2.50056 | ||||||||
\(766\) | 7.49599e12 | 0.786683 | ||||||||
\(767\) | −5.72981e11 | −0.0597807 | ||||||||
\(768\) | −8.50730e12 | −0.882402 | ||||||||
\(769\) | −1.45984e13 | −1.50535 | −0.752673 | − | 0.658395i | \(-0.771236\pi\) | ||||
−0.752673 | + | 0.658395i | \(0.771236\pi\) | |||||||
\(770\) | −6.96765e12 | −0.714295 | ||||||||
\(771\) | 1.05764e13 | 1.07793 | ||||||||
\(772\) | −3.27187e12 | −0.331526 | ||||||||
\(773\) | 4.52458e11 | 0.0455796 | 0.0227898 | − | 0.999740i | \(-0.492745\pi\) | ||||
0.0227898 | + | 0.999740i | \(0.492745\pi\) | |||||||
\(774\) | −2.38401e12 | −0.238766 | ||||||||
\(775\) | −9.46479e12 | −0.942439 | ||||||||
\(776\) | 2.94038e12 | 0.291089 | ||||||||
\(777\) | −6.13000e12 | −0.603346 | ||||||||
\(778\) | −1.78791e13 | −1.74959 | ||||||||
\(779\) | −1.01458e13 | −0.987111 | ||||||||
\(780\) | 4.02108e11 | 0.0388971 | ||||||||
\(781\) | 1.40094e13 | 1.34738 | ||||||||
\(782\) | −7.07746e12 | −0.676779 | ||||||||
\(783\) | −2.14417e13 | −2.03859 | ||||||||
\(784\) | 7.62397e12 | 0.720707 | ||||||||
\(785\) | 6.89257e12 | 0.647840 | ||||||||
\(786\) | 1.25646e13 | 1.17421 | ||||||||
\(787\) | 1.47638e13 | 1.37187 | 0.685935 | − | 0.727663i | \(-0.259394\pi\) | ||||
0.685935 | + | 0.727663i | \(0.259394\pi\) | |||||||
\(788\) | 1.94061e12 | 0.179296 | ||||||||
\(789\) | −1.86076e13 | −1.70940 | ||||||||
\(790\) | 2.39854e13 | 2.19091 | ||||||||
\(791\) | −1.15807e12 | −0.105182 | ||||||||
\(792\) | 3.15375e13 | 2.84816 | ||||||||
\(793\) | 4.41373e11 | 0.0396348 | ||||||||
\(794\) | −1.03147e13 | −0.921011 | ||||||||
\(795\) | 6.17217e13 | 5.48006 | ||||||||
\(796\) | 1.47540e12 | 0.130257 | ||||||||
\(797\) | −1.34285e13 | −1.17887 | −0.589435 | − | 0.807816i | \(-0.700649\pi\) | ||||
−0.589435 | + | 0.807816i | \(0.700649\pi\) | |||||||
\(798\) | −4.80005e12 | −0.419018 | ||||||||
\(799\) | −3.03946e12 | −0.263837 | ||||||||
\(800\) | 1.01975e13 | 0.880212 | ||||||||
\(801\) | 3.88265e13 | 3.33259 | ||||||||
\(802\) | 1.57041e13 | 1.34038 | ||||||||
\(803\) | −3.59464e12 | −0.305095 | ||||||||
\(804\) | −3.40014e12 | −0.286975 | ||||||||
\(805\) | 5.89594e12 | 0.494848 | ||||||||
\(806\) | −2.90803e11 | −0.0242712 | ||||||||
\(807\) | 4.17057e12 | 0.346150 | ||||||||
\(808\) | 9.77513e12 | 0.806810 | ||||||||
\(809\) | 6.69281e12 | 0.549338 | 0.274669 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274669 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(810\) | −5.57116e12 | −0.454740 | ||||||||
\(811\) | −3.84593e11 | −0.0312182 | −0.0156091 | − | 0.999878i | \(-0.504969\pi\) | ||||
−0.0156091 | + | 0.999878i | \(0.504969\pi\) | |||||||
\(812\) | −1.07032e12 | −0.0863998 | ||||||||
\(813\) | −1.34773e13 | −1.08192 | ||||||||
\(814\) | −2.27484e13 | −1.81610 | ||||||||
\(815\) | 2.54104e12 | 0.201745 | ||||||||
\(816\) | 1.27649e13 | 1.00789 | ||||||||
\(817\) | −1.95608e12 | −0.153599 | ||||||||
\(818\) | −1.27120e13 | −0.992711 | ||||||||
\(819\) | −4.28883e11 | −0.0333090 | ||||||||
\(820\) | −4.32929e12 | −0.334391 | ||||||||
\(821\) | −2.49941e13 | −1.91997 | −0.959983 | − | 0.280057i | \(-0.909647\pi\) | ||||
−0.959983 | + | 0.280057i | \(0.909647\pi\) | |||||||
\(822\) | −4.35308e11 | −0.0332563 | ||||||||
\(823\) | 6.40992e12 | 0.487027 | 0.243514 | − | 0.969897i | \(-0.421700\pi\) | ||||
0.243514 | + | 0.969897i | \(0.421700\pi\) | |||||||
\(824\) | 1.74114e13 | 1.31571 | ||||||||
\(825\) | −8.16776e13 | −6.13847 | ||||||||
\(826\) | 2.91861e12 | 0.218155 | ||||||||
\(827\) | 1.16763e13 | 0.868019 | 0.434010 | − | 0.900908i | \(-0.357098\pi\) | ||||
0.434010 | + | 0.900908i | \(0.357098\pi\) | |||||||
\(828\) | −4.15803e12 | −0.307433 | ||||||||
\(829\) | −1.45512e13 | −1.07005 | −0.535024 | − | 0.844837i | \(-0.679698\pi\) | ||||
−0.535024 | + | 0.844837i | \(0.679698\pi\) | |||||||
\(830\) | −5.28148e12 | −0.386282 | ||||||||
\(831\) | 1.75382e13 | 1.27579 | ||||||||
\(832\) | 1.05793e12 | 0.0765422 | ||||||||
\(833\) | 9.99937e12 | 0.719565 | ||||||||
\(834\) | 3.60750e11 | 0.0258201 | ||||||||
\(835\) | −2.53272e13 | −1.80301 | ||||||||
\(836\) | 4.03180e12 | 0.285477 | ||||||||
\(837\) | −6.71648e12 | −0.473018 | ||||||||
\(838\) | −2.36955e13 | −1.65984 | ||||||||
\(839\) | −1.63671e13 | −1.14036 | −0.570180 | − | 0.821519i | \(-0.693127\pi\) | ||||
−0.570180 | + | 0.821519i | \(0.693127\pi\) | |||||||
\(840\) | −1.31457e13 | −0.911021 | ||||||||
\(841\) | 2.64420e13 | 1.82269 | ||||||||
\(842\) | 1.63710e12 | 0.112246 | ||||||||
\(843\) | 1.81385e13 | 1.23702 | ||||||||
\(844\) | 3.12365e12 | 0.211895 | ||||||||
\(845\) | 2.72674e13 | 1.83987 | ||||||||
\(846\) | 7.88939e12 | 0.529513 | ||||||||
\(847\) | −5.66880e12 | −0.378456 | ||||||||
\(848\) | 2.10949e13 | 1.40087 | ||||||||
\(849\) | 2.72815e13 | 1.80212 | ||||||||
\(850\) | −2.59192e13 | −1.70309 | ||||||||
\(851\) | 1.92494e13 | 1.25815 | ||||||||
\(852\) | 4.11823e12 | 0.267752 | ||||||||
\(853\) | 5.19459e12 | 0.335954 | 0.167977 | − | 0.985791i | \(-0.446276\pi\) | ||||
0.167977 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(854\) | −2.24823e12 | −0.144638 | ||||||||
\(855\) | −5.04475e13 | −3.22843 | ||||||||
\(856\) | −1.52823e13 | −0.972872 | ||||||||
\(857\) | −2.66688e12 | −0.168885 | −0.0844423 | − | 0.996428i | \(-0.526911\pi\) | ||||
−0.0844423 | + | 0.996428i | \(0.526911\pi\) | |||||||
\(858\) | −2.50952e12 | −0.158088 | ||||||||
\(859\) | −1.08042e13 | −0.677054 | −0.338527 | − | 0.940957i | \(-0.609929\pi\) | ||||
−0.338527 | + | 0.940957i | \(0.609929\pi\) | |||||||
\(860\) | −8.34677e11 | −0.0520326 | ||||||||
\(861\) | 7.28075e12 | 0.451504 | ||||||||
\(862\) | 6.31336e12 | 0.389474 | ||||||||
\(863\) | −1.34009e13 | −0.822407 | −0.411204 | − | 0.911544i | \(-0.634891\pi\) | ||||
−0.411204 | + | 0.911544i | \(0.634891\pi\) | |||||||
\(864\) | 7.23641e12 | 0.441785 | ||||||||
\(865\) | 8.03830e12 | 0.488193 | ||||||||
\(866\) | 1.44460e13 | 0.872803 | ||||||||
\(867\) | −1.07669e13 | −0.647149 | ||||||||
\(868\) | −3.35273e11 | −0.0200475 | ||||||||
\(869\) | 3.38812e13 | 2.01544 | ||||||||
\(870\) | 7.83624e13 | 4.63736 | ||||||||
\(871\) | 1.10130e12 | 0.0648370 | ||||||||
\(872\) | −6.55485e12 | −0.383918 | ||||||||
\(873\) | −8.09748e12 | −0.471830 | ||||||||
\(874\) | 1.50731e13 | 0.873777 | ||||||||
\(875\) | 1.26608e13 | 0.730171 | ||||||||
\(876\) | −1.05669e12 | −0.0606287 | ||||||||
\(877\) | 7.67119e12 | 0.437890 | 0.218945 | − | 0.975737i | \(-0.429739\pi\) | ||||
0.218945 | + | 0.975737i | \(0.429739\pi\) | |||||||
\(878\) | −2.35115e13 | −1.33523 | ||||||||
\(879\) | 3.23538e13 | 1.82800 | ||||||||
\(880\) | −3.94623e13 | −2.21825 | ||||||||
\(881\) | −2.06346e13 | −1.15400 | −0.576998 | − | 0.816746i | \(-0.695776\pi\) | ||||
−0.576998 | + | 0.816746i | \(0.695776\pi\) | |||||||
\(882\) | −2.59549e13 | −1.44414 | ||||||||
\(883\) | −2.76514e13 | −1.53071 | −0.765357 | − | 0.643606i | \(-0.777438\pi\) | ||||
−0.765357 | + | 0.643606i | \(0.777438\pi\) | |||||||
\(884\) | 1.80250e11 | 0.00992748 | ||||||||
\(885\) | 4.83651e13 | 2.65025 | ||||||||
\(886\) | 2.97839e13 | 1.62379 | ||||||||
\(887\) | −8.21082e12 | −0.445379 | −0.222690 | − | 0.974889i | \(-0.571484\pi\) | ||||
−0.222690 | + | 0.974889i | \(0.571484\pi\) | |||||||
\(888\) | −4.29189e13 | −2.31628 | ||||||||
\(889\) | 6.05660e12 | 0.325215 | ||||||||
\(890\) | −6.00586e13 | −3.20863 | ||||||||
\(891\) | −7.86970e12 | −0.418320 | ||||||||
\(892\) | −2.31566e12 | −0.122471 | ||||||||
\(893\) | 6.47324e12 | 0.340636 | ||||||||
\(894\) | 2.33124e13 | 1.22058 | ||||||||
\(895\) | 3.93893e13 | 2.05199 | ||||||||
\(896\) | −3.43162e12 | −0.177875 | ||||||||
\(897\) | 2.12353e12 | 0.109520 | ||||||||
\(898\) | 3.09938e13 | 1.59049 | ||||||||
\(899\) | 1.28271e13 | 0.654952 | ||||||||
\(900\) | −1.52276e13 | −0.773643 | ||||||||
\(901\) | 2.76675e13 | 1.39865 | ||||||||
\(902\) | 2.70188e13 | 1.35905 | ||||||||
\(903\) | 1.40371e12 | 0.0702559 | ||||||||
\(904\) | −8.10820e12 | −0.403800 | ||||||||
\(905\) | 6.26229e13 | 3.10323 | ||||||||
\(906\) | −3.10510e13 | −1.53108 | ||||||||
\(907\) | 2.10695e13 | 1.03376 | 0.516881 | − | 0.856057i | \(-0.327093\pi\) | ||||
0.516881 | + | 0.856057i | \(0.327093\pi\) | |||||||
\(908\) | 2.28707e12 | 0.111659 | ||||||||
\(909\) | −2.69196e13 | −1.30777 | ||||||||
\(910\) | 6.63417e11 | 0.0320701 | ||||||||
\(911\) | 2.33428e13 | 1.12285 | 0.561423 | − | 0.827529i | \(-0.310254\pi\) | ||||
0.561423 | + | 0.827529i | \(0.310254\pi\) | |||||||
\(912\) | −2.71858e13 | −1.30126 | ||||||||
\(913\) | −7.46050e12 | −0.355344 | ||||||||
\(914\) | −3.24464e13 | −1.53783 | ||||||||
\(915\) | −3.72561e13 | −1.75712 | ||||||||
\(916\) | 3.25268e12 | 0.152655 | ||||||||
\(917\) | −4.69198e12 | −0.219126 | ||||||||
\(918\) | −1.83930e13 | −0.854793 | ||||||||
\(919\) | −2.76026e13 | −1.27653 | −0.638264 | − | 0.769818i | \(-0.720347\pi\) | ||||
−0.638264 | + | 0.769818i | \(0.720347\pi\) | |||||||
\(920\) | 4.12802e13 | 1.89975 | ||||||||
\(921\) | 9.04648e12 | 0.414296 | ||||||||
\(922\) | −1.03561e13 | −0.471962 | ||||||||
\(923\) | −1.33389e12 | −0.0604939 | ||||||||
\(924\) | −2.89328e12 | −0.130577 | ||||||||
\(925\) | 7.04956e13 | 3.16610 | ||||||||
\(926\) | −2.86508e13 | −1.28052 | ||||||||
\(927\) | −4.79490e13 | −2.13266 | ||||||||
\(928\) | −1.38200e13 | −0.611707 | ||||||||
\(929\) | −1.82656e13 | −0.804570 | −0.402285 | − | 0.915514i | \(-0.631784\pi\) | ||||
−0.402285 | + | 0.915514i | \(0.631784\pi\) | |||||||
\(930\) | 2.45466e13 | 1.07601 | ||||||||
\(931\) | −2.12960e13 | −0.929018 | ||||||||
\(932\) | −3.90241e12 | −0.169419 | ||||||||
\(933\) | 5.72780e13 | 2.47469 | ||||||||
\(934\) | −1.91959e13 | −0.825368 | ||||||||
\(935\) | −5.17576e13 | −2.21473 | ||||||||
\(936\) | −3.00281e12 | −0.127875 | ||||||||
\(937\) | 1.64822e12 | 0.0698534 | 0.0349267 | − | 0.999390i | \(-0.488880\pi\) | ||||
0.0349267 | + | 0.999390i | \(0.488880\pi\) | |||||||
\(938\) | −5.60971e12 | −0.236607 | ||||||||
\(939\) | 3.33007e13 | 1.39784 | ||||||||
\(940\) | 2.76219e12 | 0.115393 | ||||||||
\(941\) | −1.96652e13 | −0.817608 | −0.408804 | − | 0.912622i | \(-0.634054\pi\) | ||||
−0.408804 | + | 0.912622i | \(0.634054\pi\) | |||||||
\(942\) | −1.26451e13 | −0.523230 | ||||||||
\(943\) | −2.28630e13 | −0.941521 | ||||||||
\(944\) | 1.65300e13 | 0.677483 | ||||||||
\(945\) | 1.53225e13 | 0.625008 | ||||||||
\(946\) | 5.20915e12 | 0.211474 | ||||||||
\(947\) | −2.10340e13 | −0.849860 | −0.424930 | − | 0.905226i | \(-0.639701\pi\) | ||||
−0.424930 | + | 0.905226i | \(0.639701\pi\) | |||||||
\(948\) | 9.95979e12 | 0.400510 | ||||||||
\(949\) | 3.42259e11 | 0.0136980 | ||||||||
\(950\) | 5.52010e13 | 2.19883 | ||||||||
\(951\) | −6.77641e13 | −2.68650 | ||||||||
\(952\) | −5.89273e12 | −0.232515 | ||||||||
\(953\) | 1.36899e13 | 0.537629 | 0.268814 | − | 0.963192i | \(-0.413368\pi\) | ||||
0.268814 | + | 0.963192i | \(0.413368\pi\) | |||||||
\(954\) | −7.18151e13 | −2.80703 | ||||||||
\(955\) | −2.22848e13 | −0.866949 | ||||||||
\(956\) | 2.26360e12 | 0.0876474 | ||||||||
\(957\) | 1.10693e14 | 4.26595 | ||||||||
\(958\) | −1.84966e13 | −0.709493 | ||||||||
\(959\) | 1.62556e11 | 0.00620612 | ||||||||
\(960\) | −8.92991e13 | −3.39334 | ||||||||
\(961\) | −2.24216e13 | −0.848031 | ||||||||
\(962\) | 2.16596e12 | 0.0815384 | ||||||||
\(963\) | 4.20856e13 | 1.57694 | ||||||||
\(964\) | −3.08995e12 | −0.115240 | ||||||||
\(965\) | −8.94531e13 | −3.32065 | ||||||||
\(966\) | −1.08167e13 | −0.399665 | ||||||||
\(967\) | 1.15243e12 | 0.0423835 | 0.0211917 | − | 0.999775i | \(-0.493254\pi\) | ||||
0.0211917 | + | 0.999775i | \(0.493254\pi\) | |||||||
\(968\) | −3.96898e13 | −1.45291 | ||||||||
\(969\) | −3.56561e13 | −1.29920 | ||||||||
\(970\) | 1.25255e13 | 0.454280 | ||||||||
\(971\) | −3.56388e13 | −1.28658 | −0.643290 | − | 0.765623i | \(-0.722431\pi\) | ||||
−0.643290 | + | 0.765623i | \(0.722431\pi\) | |||||||
\(972\) | 3.91892e12 | 0.140821 | ||||||||
\(973\) | −1.34714e11 | −0.00481843 | ||||||||
\(974\) | −1.39496e13 | −0.496645 | ||||||||
\(975\) | 7.77684e12 | 0.275602 | ||||||||
\(976\) | −1.27332e13 | −0.449173 | ||||||||
\(977\) | −2.68281e13 | −0.942029 | −0.471014 | − | 0.882126i | \(-0.656112\pi\) | ||||
−0.471014 | + | 0.882126i | \(0.656112\pi\) | |||||||
\(978\) | −4.66179e12 | −0.162940 | ||||||||
\(979\) | −8.48374e13 | −2.95165 | ||||||||
\(980\) | −9.08719e12 | −0.314711 | ||||||||
\(981\) | 1.80513e13 | 0.622297 | ||||||||
\(982\) | 4.39399e12 | 0.150785 | ||||||||
\(983\) | −3.23922e12 | −0.110649 | −0.0553247 | − | 0.998468i | \(-0.517619\pi\) | ||||
−0.0553247 | + | 0.998468i | \(0.517619\pi\) | |||||||
\(984\) | 5.09758e13 | 1.73335 | ||||||||
\(985\) | 5.30565e13 | 1.79587 | ||||||||
\(986\) | 3.51269e13 | 1.18357 | ||||||||
\(987\) | −4.64530e12 | −0.155807 | ||||||||
\(988\) | −3.83883e11 | −0.0128172 | ||||||||
\(989\) | −4.40792e12 | −0.146504 | ||||||||
\(990\) | 1.34345e14 | 4.44490 | ||||||||
\(991\) | −1.57632e13 | −0.519174 | −0.259587 | − | 0.965720i | \(-0.583586\pi\) | ||||
−0.259587 | + | 0.965720i | \(0.583586\pi\) | |||||||
\(992\) | −4.32905e12 | −0.141935 | ||||||||
\(993\) | −8.34497e12 | −0.272366 | ||||||||
\(994\) | 6.79446e12 | 0.220758 | ||||||||
\(995\) | 4.03375e13 | 1.30468 | ||||||||
\(996\) | −2.19311e12 | −0.0706143 | ||||||||
\(997\) | −6.52488e12 | −0.209144 | −0.104572 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104572 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(998\) | −1.03396e12 | −0.0329924 | ||||||||
\(999\) | 5.00257e13 | 1.58909 |
(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 | 43.10.a.a.1.11 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.5 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.11 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.5 | 15 | 3.2 | odd | 2 |