Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,10,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(19.5713617742\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(219.264\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −66.6053 | −0.474748 | −0.237374 | − | 0.971418i | \(-0.576287\pi\) | ||||
−0.237374 | + | 0.971418i | \(0.576287\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | −2418.56 | −1.73058 | −0.865289 | − | 0.501273i | \(-0.832865\pi\) | ||||
−0.865289 | + | 0.501273i | \(0.832865\pi\) | |||||||
\(6\) | 1065.68 | 0.335697 | ||||||||
\(7\) | −1533.95 | −0.241474 | −0.120737 | − | 0.992685i | \(-0.538526\pi\) | ||||
−0.120737 | + | 0.992685i | \(0.538526\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −15246.7 | −0.774615 | ||||||||
\(10\) | 38696.9 | 1.22370 | ||||||||
\(11\) | −5815.50 | −0.119762 | −0.0598812 | − | 0.998206i | \(-0.519072\pi\) | ||||
−0.0598812 | + | 0.998206i | \(0.519072\pi\) | |||||||
\(12\) | −17051.0 | −0.237374 | ||||||||
\(13\) | −135546. | −1.31626 | −0.658130 | − | 0.752904i | \(-0.728652\pi\) | ||||
−0.658130 | + | 0.752904i | \(0.728652\pi\) | |||||||
\(14\) | 24543.2 | 0.170748 | ||||||||
\(15\) | 161089. | 0.821588 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −448133. | −1.30133 | −0.650663 | − | 0.759366i | \(-0.725509\pi\) | ||||
−0.650663 | + | 0.759366i | \(0.725509\pi\) | |||||||
\(18\) | 243948. | 0.547735 | ||||||||
\(19\) | 130321. | 0.229416 | ||||||||
\(20\) | −619151. | −0.865289 | ||||||||
\(21\) | 102169. | 0.114639 | ||||||||
\(22\) | 93048.1 | 0.0846848 | ||||||||
\(23\) | 2.07551e6 | 1.54650 | 0.773249 | − | 0.634102i | \(-0.218630\pi\) | ||||
0.773249 | + | 0.634102i | \(0.218630\pi\) | |||||||
\(24\) | 272815. | 0.167849 | ||||||||
\(25\) | 3.89629e6 | 1.99490 | ||||||||
\(26\) | 2.16874e6 | 0.930737 | ||||||||
\(27\) | 2.32650e6 | 0.842494 | ||||||||
\(28\) | −392691. | −0.120737 | ||||||||
\(29\) | −643630. | −0.168984 | −0.0844920 | − | 0.996424i | \(-0.526927\pi\) | ||||
−0.0844920 | + | 0.996424i | \(0.526927\pi\) | |||||||
\(30\) | −2.57742e6 | −0.580951 | ||||||||
\(31\) | −194155. | −0.0377591 | −0.0188796 | − | 0.999822i | \(-0.506010\pi\) | ||||
−0.0188796 | + | 0.999822i | \(0.506010\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | 387343. | 0.0568569 | ||||||||
\(34\) | 7.17012e6 | 0.920177 | ||||||||
\(35\) | 3.70994e6 | 0.417889 | ||||||||
\(36\) | −3.90316e6 | −0.387307 | ||||||||
\(37\) | 9.46515e6 | 0.830271 | 0.415135 | − | 0.909760i | \(-0.363734\pi\) | ||||
0.415135 | + | 0.909760i | \(0.363734\pi\) | |||||||
\(38\) | −2.08514e6 | −0.162221 | ||||||||
\(39\) | 9.02808e6 | 0.624892 | ||||||||
\(40\) | 9.90641e6 | 0.611852 | ||||||||
\(41\) | −2.34337e7 | −1.29513 | −0.647565 | − | 0.762010i | \(-0.724213\pi\) | ||||
−0.647565 | + | 0.762010i | \(0.724213\pi\) | |||||||
\(42\) | −1.63471e6 | −0.0810621 | ||||||||
\(43\) | 3.80295e7 | 1.69634 | 0.848170 | − | 0.529724i | \(-0.177704\pi\) | ||||
0.848170 | + | 0.529724i | \(0.177704\pi\) | |||||||
\(44\) | −1.48877e6 | −0.0598812 | ||||||||
\(45\) | 3.68751e7 | 1.34053 | ||||||||
\(46\) | −3.32081e7 | −1.09354 | ||||||||
\(47\) | −2.28118e7 | −0.681897 | −0.340948 | − | 0.940082i | \(-0.610748\pi\) | ||||
−0.340948 | + | 0.940082i | \(0.610748\pi\) | |||||||
\(48\) | −4.36504e6 | −0.118687 | ||||||||
\(49\) | −3.80006e7 | −0.941690 | ||||||||
\(50\) | −6.23407e7 | −1.41061 | ||||||||
\(51\) | 2.98480e7 | 0.617802 | ||||||||
\(52\) | −3.46998e7 | −0.658130 | ||||||||
\(53\) | −6.65359e7 | −1.15828 | −0.579141 | − | 0.815227i | \(-0.696612\pi\) | ||||
−0.579141 | + | 0.815227i | \(0.696612\pi\) | |||||||
\(54\) | −3.72241e7 | −0.595733 | ||||||||
\(55\) | 1.40651e7 | 0.207258 | ||||||||
\(56\) | 6.28306e6 | 0.0853739 | ||||||||
\(57\) | −8.68007e6 | −0.108915 | ||||||||
\(58\) | 1.02981e7 | 0.119490 | ||||||||
\(59\) | −9.14212e7 | −0.982230 | −0.491115 | − | 0.871095i | \(-0.663410\pi\) | ||||
−0.491115 | + | 0.871095i | \(0.663410\pi\) | |||||||
\(60\) | 4.12387e7 | 0.410794 | ||||||||
\(61\) | −4.02765e7 | −0.372450 | −0.186225 | − | 0.982507i | \(-0.559625\pi\) | ||||
−0.186225 | + | 0.982507i | \(0.559625\pi\) | |||||||
\(62\) | 3.10649e6 | 0.0266997 | ||||||||
\(63\) | 2.33877e7 | 0.187049 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 3.27826e8 | 2.27789 | ||||||||
\(66\) | −6.19749e6 | −0.0402039 | ||||||||
\(67\) | 2.42739e8 | 1.47164 | 0.735822 | − | 0.677175i | \(-0.236796\pi\) | ||||
0.735822 | + | 0.677175i | \(0.236796\pi\) | |||||||
\(68\) | −1.14722e8 | −0.650663 | ||||||||
\(69\) | −1.38240e8 | −0.734197 | ||||||||
\(70\) | −5.93591e7 | −0.295492 | ||||||||
\(71\) | −1.83180e8 | −0.855491 | −0.427745 | − | 0.903899i | \(-0.640692\pi\) | ||||
−0.427745 | + | 0.903899i | \(0.640692\pi\) | |||||||
\(72\) | 6.24506e7 | 0.273868 | ||||||||
\(73\) | −1.39336e8 | −0.574264 | −0.287132 | − | 0.957891i | \(-0.592702\pi\) | ||||
−0.287132 | + | 0.957891i | \(0.592702\pi\) | |||||||
\(74\) | −1.51442e8 | −0.587090 | ||||||||
\(75\) | −2.59514e8 | −0.947075 | ||||||||
\(76\) | 3.33622e7 | 0.114708 | ||||||||
\(77\) | 8.92069e6 | 0.0289195 | ||||||||
\(78\) | −1.44449e8 | −0.441865 | ||||||||
\(79\) | 2.51527e8 | 0.726546 | 0.363273 | − | 0.931683i | \(-0.381659\pi\) | ||||
0.363273 | + | 0.931683i | \(0.381659\pi\) | |||||||
\(80\) | −1.58503e8 | −0.432645 | ||||||||
\(81\) | 1.45144e8 | 0.374642 | ||||||||
\(82\) | 3.74939e8 | 0.915795 | ||||||||
\(83\) | −1.30417e8 | −0.301636 | −0.150818 | − | 0.988562i | \(-0.548191\pi\) | ||||
−0.150818 | + | 0.988562i | \(0.548191\pi\) | |||||||
\(84\) | 2.61553e7 | 0.0573196 | ||||||||
\(85\) | 1.08383e9 | 2.25205 | ||||||||
\(86\) | −6.08473e8 | −1.19949 | ||||||||
\(87\) | 4.28692e7 | 0.0802247 | ||||||||
\(88\) | 2.38203e7 | 0.0423424 | ||||||||
\(89\) | 7.10883e8 | 1.20100 | 0.600500 | − | 0.799625i | \(-0.294968\pi\) | ||||
0.600500 | + | 0.799625i | \(0.294968\pi\) | |||||||
\(90\) | −5.90002e8 | −0.947899 | ||||||||
\(91\) | 2.07921e8 | 0.317842 | ||||||||
\(92\) | 5.31330e8 | 0.773249 | ||||||||
\(93\) | 1.29318e7 | 0.0179261 | ||||||||
\(94\) | 3.64988e8 | 0.482174 | ||||||||
\(95\) | −3.15189e8 | −0.397022 | ||||||||
\(96\) | 6.98407e7 | 0.0839244 | ||||||||
\(97\) | −1.31644e9 | −1.50983 | −0.754916 | − | 0.655822i | \(-0.772322\pi\) | ||||
−0.754916 | + | 0.655822i | \(0.772322\pi\) | |||||||
\(98\) | 6.08010e8 | 0.665876 | ||||||||
\(99\) | 8.86675e7 | 0.0927696 | ||||||||
\(100\) | 9.97451e8 | 0.997451 | ||||||||
\(101\) | 1.38054e9 | 1.32009 | 0.660044 | − | 0.751227i | \(-0.270538\pi\) | ||||
0.660044 | + | 0.751227i | \(0.270538\pi\) | |||||||
\(102\) | −4.77568e8 | −0.436852 | ||||||||
\(103\) | −9.35066e8 | −0.818606 | −0.409303 | − | 0.912399i | \(-0.634228\pi\) | ||||
−0.409303 | + | 0.912399i | \(0.634228\pi\) | |||||||
\(104\) | 5.55197e8 | 0.465368 | ||||||||
\(105\) | −2.47102e8 | −0.198392 | ||||||||
\(106\) | 1.06457e9 | 0.819030 | ||||||||
\(107\) | −4.27772e8 | −0.315490 | −0.157745 | − | 0.987480i | \(-0.550422\pi\) | ||||
−0.157745 | + | 0.987480i | \(0.550422\pi\) | |||||||
\(108\) | 5.95585e8 | 0.421247 | ||||||||
\(109\) | −1.13801e8 | −0.0772197 | −0.0386098 | − | 0.999254i | \(-0.512293\pi\) | ||||
−0.0386098 | + | 0.999254i | \(0.512293\pi\) | |||||||
\(110\) | −2.25042e8 | −0.146554 | ||||||||
\(111\) | −6.30429e8 | −0.394169 | ||||||||
\(112\) | −1.00529e8 | −0.0603684 | ||||||||
\(113\) | 1.37096e9 | 0.790990 | 0.395495 | − | 0.918468i | \(-0.370573\pi\) | ||||
0.395495 | + | 0.918468i | \(0.370573\pi\) | |||||||
\(114\) | 1.38881e8 | 0.0770143 | ||||||||
\(115\) | −5.01974e9 | −2.67634 | ||||||||
\(116\) | −1.64769e8 | −0.0844920 | ||||||||
\(117\) | 2.06663e9 | 1.01959 | ||||||||
\(118\) | 1.46274e9 | 0.694541 | ||||||||
\(119\) | 6.87413e8 | 0.314236 | ||||||||
\(120\) | −6.59819e8 | −0.290475 | ||||||||
\(121\) | −2.32413e9 | −0.985657 | ||||||||
\(122\) | 6.44424e8 | 0.263362 | ||||||||
\(123\) | 1.56081e9 | 0.614860 | ||||||||
\(124\) | −4.97038e7 | −0.0188796 | ||||||||
\(125\) | −4.69966e9 | −1.72176 | ||||||||
\(126\) | −3.74204e8 | −0.132264 | ||||||||
\(127\) | 1.64706e9 | 0.561813 | 0.280906 | − | 0.959735i | \(-0.409365\pi\) | ||||
0.280906 | + | 0.959735i | \(0.409365\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −2.53297e9 | −0.805334 | ||||||||
\(130\) | −5.24521e9 | −1.61071 | ||||||||
\(131\) | −3.65669e9 | −1.08485 | −0.542423 | − | 0.840106i | \(-0.682493\pi\) | ||||
−0.542423 | + | 0.840106i | \(0.682493\pi\) | |||||||
\(132\) | 9.91599e7 | 0.0284285 | ||||||||
\(133\) | −1.99906e8 | −0.0553979 | ||||||||
\(134\) | −3.88382e9 | −1.04061 | ||||||||
\(135\) | −5.62678e9 | −1.45800 | ||||||||
\(136\) | 1.83555e9 | 0.460088 | ||||||||
\(137\) | −3.24163e9 | −0.786179 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(138\) | 2.21184e9 | 0.519155 | ||||||||
\(139\) | 8.69038e9 | 1.97457 | 0.987285 | − | 0.158963i | \(-0.0508151\pi\) | ||||
0.987285 | + | 0.158963i | \(0.0508151\pi\) | |||||||
\(140\) | 9.49746e8 | 0.208945 | ||||||||
\(141\) | 1.51938e9 | 0.323729 | ||||||||
\(142\) | 2.93088e9 | 0.604923 | ||||||||
\(143\) | 7.88269e8 | 0.157638 | ||||||||
\(144\) | −9.99210e8 | −0.193654 | ||||||||
\(145\) | 1.55666e9 | 0.292440 | ||||||||
\(146\) | 2.22938e9 | 0.406066 | ||||||||
\(147\) | 2.53104e9 | 0.447065 | ||||||||
\(148\) | 2.42308e9 | 0.415135 | ||||||||
\(149\) | −7.11665e9 | −1.18287 | −0.591435 | − | 0.806353i | \(-0.701438\pi\) | ||||
−0.591435 | + | 0.806353i | \(0.701438\pi\) | |||||||
\(150\) | 4.15222e9 | 0.669683 | ||||||||
\(151\) | 1.87879e9 | 0.294091 | 0.147046 | − | 0.989130i | \(-0.453024\pi\) | ||||
0.147046 | + | 0.989130i | \(0.453024\pi\) | |||||||
\(152\) | −5.33795e8 | −0.0811107 | ||||||||
\(153\) | 6.83256e9 | 1.00803 | ||||||||
\(154\) | −1.42731e8 | −0.0204491 | ||||||||
\(155\) | 4.69576e8 | 0.0653451 | ||||||||
\(156\) | 2.31119e9 | 0.312446 | ||||||||
\(157\) | 4.95963e9 | 0.651480 | 0.325740 | − | 0.945459i | \(-0.394387\pi\) | ||||
0.325740 | + | 0.945459i | \(0.394387\pi\) | |||||||
\(158\) | −4.02444e9 | −0.513746 | ||||||||
\(159\) | 4.43164e9 | 0.549892 | ||||||||
\(160\) | 2.53604e9 | 0.305926 | ||||||||
\(161\) | −3.18373e9 | −0.373439 | ||||||||
\(162\) | −2.32230e9 | −0.264912 | ||||||||
\(163\) | 2.87539e9 | 0.319046 | 0.159523 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159523 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(164\) | −5.99902e9 | −0.647565 | ||||||||
\(165\) | −9.36812e8 | −0.0983953 | ||||||||
\(166\) | 2.08668e9 | 0.213289 | ||||||||
\(167\) | 1.47841e10 | 1.47085 | 0.735427 | − | 0.677604i | \(-0.236982\pi\) | ||||
0.735427 | + | 0.677604i | \(0.236982\pi\) | |||||||
\(168\) | −4.18485e8 | −0.0405310 | ||||||||
\(169\) | 7.76823e9 | 0.732541 | ||||||||
\(170\) | −1.73413e10 | −1.59244 | ||||||||
\(171\) | −1.98697e9 | −0.177709 | ||||||||
\(172\) | 9.73556e9 | 0.848170 | ||||||||
\(173\) | 1.45582e10 | 1.23566 | 0.617832 | − | 0.786310i | \(-0.288011\pi\) | ||||
0.617832 | + | 0.786310i | \(0.288011\pi\) | |||||||
\(174\) | −6.85907e8 | −0.0567275 | ||||||||
\(175\) | −5.97672e9 | −0.481716 | ||||||||
\(176\) | −3.81125e8 | −0.0299406 | ||||||||
\(177\) | 6.08914e9 | 0.466311 | ||||||||
\(178\) | −1.13741e10 | −0.849235 | ||||||||
\(179\) | −1.82403e10 | −1.32799 | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(180\) | 9.44003e9 | 0.670266 | ||||||||
\(181\) | 2.81167e10 | 1.94720 | 0.973602 | − | 0.228252i | \(-0.0733011\pi\) | ||||
0.973602 | + | 0.228252i | \(0.0733011\pi\) | |||||||
\(182\) | −3.32673e9 | −0.224748 | ||||||||
\(183\) | 2.68263e9 | 0.176820 | ||||||||
\(184\) | −8.50129e9 | −0.546770 | ||||||||
\(185\) | −2.28920e10 | −1.43685 | ||||||||
\(186\) | −2.06908e8 | −0.0126756 | ||||||||
\(187\) | 2.60612e9 | 0.155850 | ||||||||
\(188\) | −5.83981e9 | −0.340948 | ||||||||
\(189\) | −3.56874e9 | −0.203440 | ||||||||
\(190\) | 5.04302e9 | 0.280737 | ||||||||
\(191\) | 2.82317e8 | 0.0153492 | 0.00767462 | − | 0.999971i | \(-0.497557\pi\) | ||||
0.00767462 | + | 0.999971i | \(0.497557\pi\) | |||||||
\(192\) | −1.11745e9 | −0.0593435 | ||||||||
\(193\) | 1.43117e10 | 0.742477 | 0.371239 | − | 0.928538i | \(-0.378933\pi\) | ||||
0.371239 | + | 0.928538i | \(0.378933\pi\) | |||||||
\(194\) | 2.10630e10 | 1.06761 | ||||||||
\(195\) | −2.18349e10 | −1.08142 | ||||||||
\(196\) | −9.72816e9 | −0.470845 | ||||||||
\(197\) | 2.02116e10 | 0.956100 | 0.478050 | − | 0.878333i | \(-0.341344\pi\) | ||||
0.478050 | + | 0.878333i | \(0.341344\pi\) | |||||||
\(198\) | −1.41868e9 | −0.0655980 | ||||||||
\(199\) | −3.95924e10 | −1.78967 | −0.894835 | − | 0.446398i | \(-0.852707\pi\) | ||||
−0.894835 | + | 0.446398i | \(0.852707\pi\) | |||||||
\(200\) | −1.59592e10 | −0.705304 | ||||||||
\(201\) | −1.61677e10 | −0.698660 | ||||||||
\(202\) | −2.20886e10 | −0.933443 | ||||||||
\(203\) | 9.87296e8 | 0.0408052 | ||||||||
\(204\) | 7.64109e9 | 0.308901 | ||||||||
\(205\) | 5.66757e10 | 2.24132 | ||||||||
\(206\) | 1.49611e10 | 0.578842 | ||||||||
\(207\) | −3.16447e10 | −1.19794 | ||||||||
\(208\) | −8.88315e9 | −0.329065 | ||||||||
\(209\) | −7.57882e8 | −0.0274754 | ||||||||
\(210\) | 3.95363e9 | 0.140284 | ||||||||
\(211\) | −1.31017e10 | −0.455047 | −0.227523 | − | 0.973773i | \(-0.573063\pi\) | ||||
−0.227523 | + | 0.973773i | \(0.573063\pi\) | |||||||
\(212\) | −1.70332e10 | −0.579141 | ||||||||
\(213\) | 1.22008e10 | 0.406142 | ||||||||
\(214\) | 6.84436e9 | 0.223085 | ||||||||
\(215\) | −9.19766e10 | −2.93565 | ||||||||
\(216\) | −9.52936e9 | −0.297867 | ||||||||
\(217\) | 2.97825e8 | 0.00911784 | ||||||||
\(218\) | 1.82082e9 | 0.0546026 | ||||||||
\(219\) | 9.28054e9 | 0.272631 | ||||||||
\(220\) | 3.60067e9 | 0.103629 | ||||||||
\(221\) | 6.07426e10 | 1.71288 | ||||||||
\(222\) | 1.00869e10 | 0.278720 | ||||||||
\(223\) | 6.50346e10 | 1.76105 | 0.880526 | − | 0.473997i | \(-0.157189\pi\) | ||||
0.880526 | + | 0.473997i | \(0.157189\pi\) | |||||||
\(224\) | 1.60846e9 | 0.0426869 | ||||||||
\(225\) | −5.94058e10 | −1.54528 | ||||||||
\(226\) | −2.19353e10 | −0.559315 | ||||||||
\(227\) | 1.02990e10 | 0.257442 | 0.128721 | − | 0.991681i | \(-0.458913\pi\) | ||||
0.128721 | + | 0.991681i | \(0.458913\pi\) | |||||||
\(228\) | −2.22210e9 | −0.0544573 | ||||||||
\(229\) | 1.71789e10 | 0.412797 | 0.206398 | − | 0.978468i | \(-0.433826\pi\) | ||||
0.206398 | + | 0.978468i | \(0.433826\pi\) | |||||||
\(230\) | 8.03158e10 | 1.89246 | ||||||||
\(231\) | −5.94165e8 | −0.0137294 | ||||||||
\(232\) | 2.63631e9 | 0.0597448 | ||||||||
\(233\) | −6.52465e10 | −1.45029 | −0.725146 | − | 0.688595i | \(-0.758228\pi\) | ||||
−0.725146 | + | 0.688595i | \(0.758228\pi\) | |||||||
\(234\) | −3.30662e10 | −0.720962 | ||||||||
\(235\) | 5.51716e10 | 1.18008 | ||||||||
\(236\) | −2.34038e10 | −0.491115 | ||||||||
\(237\) | −1.67530e10 | −0.344926 | ||||||||
\(238\) | −1.09986e10 | −0.222199 | ||||||||
\(239\) | −1.43024e10 | −0.283543 | −0.141771 | − | 0.989899i | \(-0.545280\pi\) | ||||
−0.141771 | + | 0.989899i | \(0.545280\pi\) | |||||||
\(240\) | 1.05571e10 | 0.205397 | ||||||||
\(241\) | −4.79560e10 | −0.915727 | −0.457864 | − | 0.889022i | \(-0.651385\pi\) | ||||
−0.457864 | + | 0.889022i | \(0.651385\pi\) | |||||||
\(242\) | 3.71860e10 | 0.696965 | ||||||||
\(243\) | −5.54600e10 | −1.02035 | ||||||||
\(244\) | −1.03108e10 | −0.186225 | ||||||||
\(245\) | 9.19066e10 | 1.62967 | ||||||||
\(246\) | −2.49729e10 | −0.434772 | ||||||||
\(247\) | −1.76645e10 | −0.301971 | ||||||||
\(248\) | 7.95261e8 | 0.0133499 | ||||||||
\(249\) | 8.68647e9 | 0.143201 | ||||||||
\(250\) | 7.51946e10 | 1.21747 | ||||||||
\(251\) | −1.25023e10 | −0.198819 | −0.0994096 | − | 0.995047i | \(-0.531695\pi\) | ||||
−0.0994096 | + | 0.995047i | \(0.531695\pi\) | |||||||
\(252\) | 5.98726e9 | 0.0935245 | ||||||||
\(253\) | −1.20701e10 | −0.185212 | ||||||||
\(254\) | −2.63529e10 | −0.397261 | ||||||||
\(255\) | −7.21891e10 | −1.06915 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 1.83653e10 | 0.262602 | 0.131301 | − | 0.991343i | \(-0.458085\pi\) | ||||
0.131301 | + | 0.991343i | \(0.458085\pi\) | |||||||
\(258\) | 4.05275e10 | 0.569457 | ||||||||
\(259\) | −1.45191e10 | −0.200489 | ||||||||
\(260\) | 8.39234e10 | 1.13895 | ||||||||
\(261\) | 9.81326e9 | 0.130897 | ||||||||
\(262\) | 5.85071e10 | 0.767101 | ||||||||
\(263\) | 8.39157e10 | 1.08154 | 0.540770 | − | 0.841171i | \(-0.318133\pi\) | ||||
0.540770 | + | 0.841171i | \(0.318133\pi\) | |||||||
\(264\) | −1.58656e9 | −0.0201020 | ||||||||
\(265\) | 1.60921e11 | 2.00450 | ||||||||
\(266\) | 3.19849e9 | 0.0391722 | ||||||||
\(267\) | −4.73485e10 | −0.570172 | ||||||||
\(268\) | 6.21412e10 | 0.735822 | ||||||||
\(269\) | 9.33233e9 | 0.108669 | 0.0543344 | − | 0.998523i | \(-0.482696\pi\) | ||||
0.0543344 | + | 0.998523i | \(0.482696\pi\) | |||||||
\(270\) | 9.00286e10 | 1.03096 | ||||||||
\(271\) | −1.57854e11 | −1.77785 | −0.888924 | − | 0.458055i | \(-0.848546\pi\) | ||||
−0.888924 | + | 0.458055i | \(0.848546\pi\) | |||||||
\(272\) | −2.93688e10 | −0.325332 | ||||||||
\(273\) | −1.38486e10 | −0.150895 | ||||||||
\(274\) | 5.18661e10 | 0.555912 | ||||||||
\(275\) | −2.26589e10 | −0.238914 | ||||||||
\(276\) | −3.53894e10 | −0.367098 | ||||||||
\(277\) | −1.12981e11 | −1.15305 | −0.576525 | − | 0.817080i | \(-0.695592\pi\) | ||||
−0.576525 | + | 0.817080i | \(0.695592\pi\) | |||||||
\(278\) | −1.39046e11 | −1.39623 | ||||||||
\(279\) | 2.96024e9 | 0.0292488 | ||||||||
\(280\) | −1.51959e10 | −0.147746 | ||||||||
\(281\) | 7.83548e10 | 0.749699 | 0.374849 | − | 0.927086i | \(-0.377694\pi\) | ||||
0.374849 | + | 0.927086i | \(0.377694\pi\) | |||||||
\(282\) | −2.43102e10 | −0.228911 | ||||||||
\(283\) | 8.46004e10 | 0.784032 | 0.392016 | − | 0.919958i | \(-0.371778\pi\) | ||||
0.392016 | + | 0.919958i | \(0.371778\pi\) | |||||||
\(284\) | −4.68941e10 | −0.427745 | ||||||||
\(285\) | 2.09932e10 | 0.188485 | ||||||||
\(286\) | −1.26123e10 | −0.111467 | ||||||||
\(287\) | 3.59461e10 | 0.312740 | ||||||||
\(288\) | 1.59874e10 | 0.136934 | ||||||||
\(289\) | 8.22349e10 | 0.693451 | ||||||||
\(290\) | −2.49065e10 | −0.206786 | ||||||||
\(291\) | 8.76819e10 | 0.716789 | ||||||||
\(292\) | −3.56701e10 | −0.287132 | ||||||||
\(293\) | −1.06621e11 | −0.845157 | −0.422579 | − | 0.906326i | \(-0.638875\pi\) | ||||
−0.422579 | + | 0.906326i | \(0.638875\pi\) | |||||||
\(294\) | −4.04967e10 | −0.316123 | ||||||||
\(295\) | 2.21107e11 | 1.69983 | ||||||||
\(296\) | −3.87693e10 | −0.293545 | ||||||||
\(297\) | −1.35298e10 | −0.100899 | ||||||||
\(298\) | 1.13866e11 | 0.836416 | ||||||||
\(299\) | −2.81327e11 | −2.03559 | ||||||||
\(300\) | −6.64355e10 | −0.473538 | ||||||||
\(301\) | −5.83354e10 | −0.409622 | ||||||||
\(302\) | −3.00606e10 | −0.207954 | ||||||||
\(303\) | −9.19513e10 | −0.626709 | ||||||||
\(304\) | 8.54072e9 | 0.0573539 | ||||||||
\(305\) | 9.74110e10 | 0.644553 | ||||||||
\(306\) | −1.09321e11 | −0.712782 | ||||||||
\(307\) | 1.65292e11 | 1.06201 | 0.531006 | − | 0.847368i | \(-0.321814\pi\) | ||||
0.531006 | + | 0.847368i | \(0.321814\pi\) | |||||||
\(308\) | 2.28370e9 | 0.0144597 | ||||||||
\(309\) | 6.22803e10 | 0.388631 | ||||||||
\(310\) | −7.51322e9 | −0.0462060 | ||||||||
\(311\) | −1.08969e11 | −0.660515 | −0.330257 | − | 0.943891i | \(-0.607136\pi\) | ||||
−0.330257 | + | 0.943891i | \(0.607136\pi\) | |||||||
\(312\) | −3.69790e10 | −0.220933 | ||||||||
\(313\) | 9.48622e10 | 0.558655 | 0.279328 | − | 0.960196i | \(-0.409888\pi\) | ||||
0.279328 | + | 0.960196i | \(0.409888\pi\) | |||||||
\(314\) | −7.93541e10 | −0.460666 | ||||||||
\(315\) | −5.65645e10 | −0.323703 | ||||||||
\(316\) | 6.43910e10 | 0.363273 | ||||||||
\(317\) | 2.75000e11 | 1.52956 | 0.764780 | − | 0.644291i | \(-0.222848\pi\) | ||||
0.764780 | + | 0.644291i | \(0.222848\pi\) | |||||||
\(318\) | −7.09063e10 | −0.388833 | ||||||||
\(319\) | 3.74303e9 | 0.0202379 | ||||||||
\(320\) | −4.05767e10 | −0.216322 | ||||||||
\(321\) | 2.84919e10 | 0.149778 | ||||||||
\(322\) | 5.09396e10 | 0.264061 | ||||||||
\(323\) | −5.84011e10 | −0.298545 | ||||||||
\(324\) | 3.71569e10 | 0.187321 | ||||||||
\(325\) | −5.28127e11 | −2.62581 | ||||||||
\(326\) | −4.60063e10 | −0.225599 | ||||||||
\(327\) | 7.57977e9 | 0.0366599 | ||||||||
\(328\) | 9.59844e10 | 0.457898 | ||||||||
\(329\) | 3.49921e10 | 0.164660 | ||||||||
\(330\) | 1.49890e10 | 0.0695760 | ||||||||
\(331\) | −1.28057e11 | −0.586378 | −0.293189 | − | 0.956055i | \(-0.594716\pi\) | ||||
−0.293189 | + | 0.956055i | \(0.594716\pi\) | |||||||
\(332\) | −3.33868e10 | −0.150818 | ||||||||
\(333\) | −1.44313e11 | −0.643140 | ||||||||
\(334\) | −2.36545e11 | −1.04005 | ||||||||
\(335\) | −5.87078e11 | −2.54680 | ||||||||
\(336\) | 6.69576e9 | 0.0286598 | ||||||||
\(337\) | −3.03698e10 | −0.128265 | −0.0641324 | − | 0.997941i | \(-0.520428\pi\) | ||||
−0.0641324 | + | 0.997941i | \(0.520428\pi\) | |||||||
\(338\) | −1.24292e11 | −0.517985 | ||||||||
\(339\) | −9.13130e10 | −0.375521 | ||||||||
\(340\) | 2.77462e11 | 1.12602 | ||||||||
\(341\) | 1.12911e9 | 0.00452212 | ||||||||
\(342\) | 3.17915e10 | 0.125659 | ||||||||
\(343\) | 1.20191e11 | 0.468867 | ||||||||
\(344\) | −1.55769e11 | −0.599747 | ||||||||
\(345\) | 3.34341e11 | 1.27059 | ||||||||
\(346\) | −2.32931e11 | −0.873747 | ||||||||
\(347\) | 4.03811e11 | 1.49519 | 0.747594 | − | 0.664156i | \(-0.231209\pi\) | ||||
0.747594 | + | 0.664156i | \(0.231209\pi\) | |||||||
\(348\) | 1.09745e10 | 0.0401124 | ||||||||
\(349\) | 6.29420e10 | 0.227105 | 0.113552 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(350\) | 9.56275e10 | 0.340625 | ||||||||
\(351\) | −3.15349e11 | −1.10894 | ||||||||
\(352\) | 6.09800e9 | 0.0211712 | ||||||||
\(353\) | 9.36033e10 | 0.320852 | 0.160426 | − | 0.987048i | \(-0.448713\pi\) | ||||
0.160426 | + | 0.987048i | \(0.448713\pi\) | |||||||
\(354\) | −9.74262e10 | −0.329732 | ||||||||
\(355\) | 4.43031e11 | 1.48049 | ||||||||
\(356\) | 1.81986e11 | 0.600500 | ||||||||
\(357\) | −4.57853e10 | −0.149183 | ||||||||
\(358\) | 2.91846e11 | 0.939030 | ||||||||
\(359\) | 3.18605e11 | 1.01234 | 0.506171 | − | 0.862433i | \(-0.331060\pi\) | ||||
0.506171 | + | 0.862433i | \(0.331060\pi\) | |||||||
\(360\) | −1.51040e11 | −0.473949 | ||||||||
\(361\) | 1.69836e10 | 0.0526316 | ||||||||
\(362\) | −4.49868e11 | −1.37688 | ||||||||
\(363\) | 1.54799e11 | 0.467939 | ||||||||
\(364\) | 5.32277e10 | 0.158921 | ||||||||
\(365\) | 3.36993e11 | 0.993810 | ||||||||
\(366\) | −4.29220e10 | −0.125030 | ||||||||
\(367\) | 9.81213e10 | 0.282336 | 0.141168 | − | 0.989986i | \(-0.454914\pi\) | ||||
0.141168 | + | 0.989986i | \(0.454914\pi\) | |||||||
\(368\) | 1.36021e11 | 0.386625 | ||||||||
\(369\) | 3.57287e11 | 1.00323 | ||||||||
\(370\) | 3.66272e11 | 1.01601 | ||||||||
\(371\) | 1.02063e11 | 0.279695 | ||||||||
\(372\) | 3.31054e9 | 0.00896303 | ||||||||
\(373\) | 2.24989e11 | 0.601827 | 0.300913 | − | 0.953652i | \(-0.402709\pi\) | ||||
0.300913 | + | 0.953652i | \(0.402709\pi\) | |||||||
\(374\) | −4.16979e10 | −0.110203 | ||||||||
\(375\) | 3.13022e11 | 0.817400 | ||||||||
\(376\) | 9.34370e10 | 0.241087 | ||||||||
\(377\) | 8.72415e10 | 0.222427 | ||||||||
\(378\) | 5.70999e10 | 0.143854 | ||||||||
\(379\) | 6.24000e11 | 1.55349 | 0.776744 | − | 0.629817i | \(-0.216870\pi\) | ||||
0.776744 | + | 0.629817i | \(0.216870\pi\) | |||||||
\(380\) | −8.06883e10 | −0.198511 | ||||||||
\(381\) | −1.09703e11 | −0.266719 | ||||||||
\(382\) | −4.51707e9 | −0.0108536 | ||||||||
\(383\) | 5.36899e11 | 1.27497 | 0.637483 | − | 0.770465i | \(-0.279976\pi\) | ||||
0.637483 | + | 0.770465i | \(0.279976\pi\) | |||||||
\(384\) | 1.78792e10 | 0.0419622 | ||||||||
\(385\) | −2.15752e10 | −0.0500474 | ||||||||
\(386\) | −2.28987e11 | −0.525011 | ||||||||
\(387\) | −5.79826e11 | −1.31401 | ||||||||
\(388\) | −3.37009e11 | −0.754916 | ||||||||
\(389\) | −1.30155e11 | −0.288195 | −0.144097 | − | 0.989564i | \(-0.546028\pi\) | ||||
−0.144097 | + | 0.989564i | \(0.546028\pi\) | |||||||
\(390\) | 3.49359e11 | 0.764682 | ||||||||
\(391\) | −9.30103e11 | −2.01250 | ||||||||
\(392\) | 1.55650e11 | 0.332938 | ||||||||
\(393\) | 2.43555e11 | 0.515028 | ||||||||
\(394\) | −3.23386e11 | −0.676064 | ||||||||
\(395\) | −6.08333e11 | −1.25735 | ||||||||
\(396\) | 2.26989e10 | 0.0463848 | ||||||||
\(397\) | −7.36706e11 | −1.48846 | −0.744230 | − | 0.667924i | \(-0.767183\pi\) | ||||
−0.744230 | + | 0.667924i | \(0.767183\pi\) | |||||||
\(398\) | 6.33478e11 | 1.26549 | ||||||||
\(399\) | 1.33148e10 | 0.0263000 | ||||||||
\(400\) | 2.55347e11 | 0.498726 | ||||||||
\(401\) | −5.90469e11 | −1.14037 | −0.570187 | − | 0.821515i | \(-0.693129\pi\) | ||||
−0.570187 | + | 0.821515i | \(0.693129\pi\) | |||||||
\(402\) | 2.58683e11 | 0.494027 | ||||||||
\(403\) | 2.63170e10 | 0.0497008 | ||||||||
\(404\) | 3.53418e11 | 0.660044 | ||||||||
\(405\) | −3.51039e11 | −0.648348 | ||||||||
\(406\) | −1.57967e10 | −0.0288536 | ||||||||
\(407\) | −5.50446e10 | −0.0994352 | ||||||||
\(408\) | −1.22257e11 | −0.218426 | ||||||||
\(409\) | −4.27579e11 | −0.755547 | −0.377773 | − | 0.925898i | \(-0.623310\pi\) | ||||
−0.377773 | + | 0.925898i | \(0.623310\pi\) | |||||||
\(410\) | −9.06811e11 | −1.58486 | ||||||||
\(411\) | 2.15910e11 | 0.373237 | ||||||||
\(412\) | −2.39377e11 | −0.409303 | ||||||||
\(413\) | 1.40236e11 | 0.237183 | ||||||||
\(414\) | 5.06316e11 | 0.847071 | ||||||||
\(415\) | 3.15421e11 | 0.522005 | ||||||||
\(416\) | 1.42130e11 | 0.232684 | ||||||||
\(417\) | −5.78825e11 | −0.937422 | ||||||||
\(418\) | 1.21261e10 | 0.0194280 | ||||||||
\(419\) | 9.75902e11 | 1.54683 | 0.773416 | − | 0.633899i | \(-0.218546\pi\) | ||||
0.773416 | + | 0.633899i | \(0.218546\pi\) | |||||||
\(420\) | −6.32581e10 | −0.0991960 | ||||||||
\(421\) | −6.82920e10 | −0.105950 | −0.0529750 | − | 0.998596i | \(-0.516870\pi\) | ||||
−0.0529750 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(422\) | 2.09627e11 | 0.321766 | ||||||||
\(423\) | 3.47805e11 | 0.528207 | ||||||||
\(424\) | 2.72531e11 | 0.409515 | ||||||||
\(425\) | −1.74606e12 | −2.59602 | ||||||||
\(426\) | −1.95212e11 | −0.287186 | ||||||||
\(427\) | 6.17821e10 | 0.0899368 | ||||||||
\(428\) | −1.09510e11 | −0.157745 | ||||||||
\(429\) | −5.25028e10 | −0.0748385 | ||||||||
\(430\) | 1.47163e12 | 2.07582 | ||||||||
\(431\) | −2.97113e11 | −0.414738 | −0.207369 | − | 0.978263i | \(-0.566490\pi\) | ||||
−0.207369 | + | 0.978263i | \(0.566490\pi\) | |||||||
\(432\) | 1.52470e11 | 0.210624 | ||||||||
\(433\) | −4.51168e11 | −0.616798 | −0.308399 | − | 0.951257i | \(-0.599793\pi\) | ||||
−0.308399 | + | 0.951257i | \(0.599793\pi\) | |||||||
\(434\) | −4.76520e9 | −0.00644729 | ||||||||
\(435\) | −1.03682e11 | −0.138835 | ||||||||
\(436\) | −2.91331e10 | −0.0386098 | ||||||||
\(437\) | 2.70482e11 | 0.354791 | ||||||||
\(438\) | −1.48489e11 | −0.192779 | ||||||||
\(439\) | 5.55482e11 | 0.713805 | 0.356903 | − | 0.934142i | \(-0.383833\pi\) | ||||
0.356903 | + | 0.934142i | \(0.383833\pi\) | |||||||
\(440\) | −5.76108e10 | −0.0732768 | ||||||||
\(441\) | 5.79385e11 | 0.729447 | ||||||||
\(442\) | −9.71881e11 | −1.21119 | ||||||||
\(443\) | −1.61691e12 | −1.99466 | −0.997329 | − | 0.0730386i | \(-0.976730\pi\) | ||||
−0.997329 | + | 0.0730386i | \(0.976730\pi\) | |||||||
\(444\) | −1.61390e11 | −0.197085 | ||||||||
\(445\) | −1.71931e12 | −2.07842 | ||||||||
\(446\) | −1.04055e12 | −1.24525 | ||||||||
\(447\) | 4.74006e11 | 0.561565 | ||||||||
\(448\) | −2.57354e10 | −0.0301842 | ||||||||
\(449\) | 4.52893e11 | 0.525880 | 0.262940 | − | 0.964812i | \(-0.415308\pi\) | ||||
0.262940 | + | 0.964812i | \(0.415308\pi\) | |||||||
\(450\) | 9.50492e11 | 1.09268 | ||||||||
\(451\) | 1.36279e11 | 0.155108 | ||||||||
\(452\) | 3.50965e11 | 0.395495 | ||||||||
\(453\) | −1.25137e11 | −0.139619 | ||||||||
\(454\) | −1.64784e11 | −0.182039 | ||||||||
\(455\) | −5.02868e11 | −0.550051 | ||||||||
\(456\) | 3.55536e10 | 0.0385071 | ||||||||
\(457\) | 1.10310e12 | 1.18302 | 0.591511 | − | 0.806297i | \(-0.298532\pi\) | ||||
0.591511 | + | 0.806297i | \(0.298532\pi\) | |||||||
\(458\) | −2.74863e11 | −0.291891 | ||||||||
\(459\) | −1.04258e12 | −1.09636 | ||||||||
\(460\) | −1.28505e12 | −1.33817 | ||||||||
\(461\) | 2.22092e11 | 0.229023 | 0.114511 | − | 0.993422i | \(-0.463470\pi\) | ||||
0.114511 | + | 0.993422i | \(0.463470\pi\) | |||||||
\(462\) | 9.50664e9 | 0.00970819 | ||||||||
\(463\) | 9.97229e11 | 1.00851 | 0.504255 | − | 0.863555i | \(-0.331767\pi\) | ||||
0.504255 | + | 0.863555i | \(0.331767\pi\) | |||||||
\(464\) | −4.21809e10 | −0.0422460 | ||||||||
\(465\) | −3.12762e10 | −0.0310225 | ||||||||
\(466\) | 1.04394e12 | 1.02551 | ||||||||
\(467\) | 8.73582e11 | 0.849919 | 0.424959 | − | 0.905212i | \(-0.360288\pi\) | ||||
0.424959 | + | 0.905212i | \(0.360288\pi\) | |||||||
\(468\) | 5.29059e11 | 0.509797 | ||||||||
\(469\) | −3.72349e11 | −0.355363 | ||||||||
\(470\) | −8.82745e11 | −0.834440 | ||||||||
\(471\) | −3.30338e11 | −0.309289 | ||||||||
\(472\) | 3.74461e11 | 0.347271 | ||||||||
\(473\) | −2.21161e11 | −0.203158 | ||||||||
\(474\) | 2.68049e11 | 0.243900 | ||||||||
\(475\) | 5.07769e11 | 0.457662 | ||||||||
\(476\) | 1.75978e11 | 0.157118 | ||||||||
\(477\) | 1.01446e12 | 0.897223 | ||||||||
\(478\) | 2.28838e11 | 0.200495 | ||||||||
\(479\) | 1.60658e12 | 1.39442 | 0.697209 | − | 0.716868i | \(-0.254425\pi\) | ||||
0.697209 | + | 0.716868i | \(0.254425\pi\) | |||||||
\(480\) | −1.68914e11 | −0.145238 | ||||||||
\(481\) | −1.28296e12 | −1.09285 | ||||||||
\(482\) | 7.67296e11 | 0.647517 | ||||||||
\(483\) | 2.12053e11 | 0.177289 | ||||||||
\(484\) | −5.94977e11 | −0.492828 | ||||||||
\(485\) | 3.18389e12 | 2.61288 | ||||||||
\(486\) | 8.87359e11 | 0.721500 | ||||||||
\(487\) | −9.25381e11 | −0.745487 | −0.372744 | − | 0.927934i | \(-0.621583\pi\) | ||||
−0.372744 | + | 0.927934i | \(0.621583\pi\) | |||||||
\(488\) | 1.64973e11 | 0.131681 | ||||||||
\(489\) | −1.91516e11 | −0.151466 | ||||||||
\(490\) | −1.47051e12 | −1.15235 | ||||||||
\(491\) | −9.28628e11 | −0.721066 | −0.360533 | − | 0.932746i | \(-0.617405\pi\) | ||||
−0.360533 | + | 0.932746i | \(0.617405\pi\) | |||||||
\(492\) | 3.99567e11 | 0.307430 | ||||||||
\(493\) | 2.88432e11 | 0.219903 | ||||||||
\(494\) | 2.82632e11 | 0.213526 | ||||||||
\(495\) | −2.14447e11 | −0.160545 | ||||||||
\(496\) | −1.27242e10 | −0.00943978 | ||||||||
\(497\) | 2.80989e11 | 0.206579 | ||||||||
\(498\) | −1.38984e11 | −0.101259 | ||||||||
\(499\) | 1.19609e12 | 0.863601 | 0.431800 | − | 0.901969i | \(-0.357878\pi\) | ||||
0.431800 | + | 0.901969i | \(0.357878\pi\) | |||||||
\(500\) | −1.20311e12 | −0.860878 | ||||||||
\(501\) | −9.84696e11 | −0.698285 | ||||||||
\(502\) | 2.00037e11 | 0.140586 | ||||||||
\(503\) | 1.02039e12 | 0.710741 | 0.355370 | − | 0.934726i | \(-0.384355\pi\) | ||||
0.355370 | + | 0.934726i | \(0.384355\pi\) | |||||||
\(504\) | −9.57961e10 | −0.0661318 | ||||||||
\(505\) | −3.33892e12 | −2.28452 | ||||||||
\(506\) | 1.93122e11 | 0.130965 | ||||||||
\(507\) | −5.17405e11 | −0.347772 | ||||||||
\(508\) | 4.21646e11 | 0.280906 | ||||||||
\(509\) | −5.49549e11 | −0.362891 | −0.181446 | − | 0.983401i | \(-0.558078\pi\) | ||||
−0.181446 | + | 0.983401i | \(0.558078\pi\) | |||||||
\(510\) | 1.15503e12 | 0.756007 | ||||||||
\(511\) | 2.13735e11 | 0.138670 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 3.03192e11 | 0.193281 | ||||||||
\(514\) | −2.93844e11 | −0.185688 | ||||||||
\(515\) | 2.26151e12 | 1.41666 | ||||||||
\(516\) | −6.48440e11 | −0.402667 | ||||||||
\(517\) | 1.32662e11 | 0.0816656 | ||||||||
\(518\) | 2.32305e11 | 0.141767 | ||||||||
\(519\) | −9.69654e11 | −0.586629 | ||||||||
\(520\) | −1.34277e12 | −0.805356 | ||||||||
\(521\) | 1.28517e12 | 0.764172 | 0.382086 | − | 0.924127i | \(-0.375206\pi\) | ||||
0.382086 | + | 0.924127i | \(0.375206\pi\) | |||||||
\(522\) | −1.57012e11 | −0.0925584 | ||||||||
\(523\) | 1.65568e12 | 0.967654 | 0.483827 | − | 0.875164i | \(-0.339246\pi\) | ||||
0.483827 | + | 0.875164i | \(0.339246\pi\) | |||||||
\(524\) | −9.36114e11 | −0.542423 | ||||||||
\(525\) | 3.98081e11 | 0.228694 | ||||||||
\(526\) | −1.34265e12 | −0.764764 | ||||||||
\(527\) | 8.70074e10 | 0.0491370 | ||||||||
\(528\) | 2.53849e10 | 0.0142142 | ||||||||
\(529\) | 2.50659e12 | 1.39166 | ||||||||
\(530\) | −2.57473e12 | −1.41740 | ||||||||
\(531\) | 1.39388e12 | 0.760849 | ||||||||
\(532\) | −5.11759e10 | −0.0276989 | ||||||||
\(533\) | 3.17634e12 | 1.70473 | ||||||||
\(534\) | 7.57577e11 | 0.403172 | ||||||||
\(535\) | 1.03459e12 | 0.545980 | ||||||||
\(536\) | −9.94259e11 | −0.520305 | ||||||||
\(537\) | 1.21490e12 | 0.630460 | ||||||||
\(538\) | −1.49317e11 | −0.0768404 | ||||||||
\(539\) | 2.20993e11 | 0.112779 | ||||||||
\(540\) | −1.44046e12 | −0.729001 | ||||||||
\(541\) | −1.91314e12 | −0.960192 | −0.480096 | − | 0.877216i | \(-0.659398\pi\) | ||||
−0.480096 | + | 0.877216i | \(0.659398\pi\) | |||||||
\(542\) | 2.52567e12 | 1.25713 | ||||||||
\(543\) | −1.87272e12 | −0.924431 | ||||||||
\(544\) | 4.69901e11 | 0.230044 | ||||||||
\(545\) | 2.75235e11 | 0.133635 | ||||||||
\(546\) | 2.21578e11 | 0.106699 | ||||||||
\(547\) | −8.87680e11 | −0.423949 | −0.211974 | − | 0.977275i | \(-0.567989\pi\) | ||||
−0.211974 | + | 0.977275i | \(0.567989\pi\) | |||||||
\(548\) | −8.29858e11 | −0.393089 | ||||||||
\(549\) | 6.14085e11 | 0.288505 | ||||||||
\(550\) | 3.62543e11 | 0.168938 | ||||||||
\(551\) | −8.38785e10 | −0.0387676 | ||||||||
\(552\) | 5.66231e11 | 0.259578 | ||||||||
\(553\) | −3.85830e11 | −0.175442 | ||||||||
\(554\) | 1.80770e12 | 0.815329 | ||||||||
\(555\) | 1.52473e12 | 0.682141 | ||||||||
\(556\) | 2.22474e12 | 0.987285 | ||||||||
\(557\) | −1.28351e12 | −0.565001 | −0.282501 | − | 0.959267i | \(-0.591164\pi\) | ||||
−0.282501 | + | 0.959267i | \(0.591164\pi\) | |||||||
\(558\) | −4.73638e10 | −0.0206820 | ||||||||
\(559\) | −5.15475e12 | −2.23283 | ||||||||
\(560\) | 2.43135e11 | 0.104472 | ||||||||
\(561\) | −1.73581e11 | −0.0739894 | ||||||||
\(562\) | −1.25368e12 | −0.530117 | ||||||||
\(563\) | 4.00016e12 | 1.67799 | 0.838995 | − | 0.544139i | \(-0.183144\pi\) | ||||
0.838995 | + | 0.544139i | \(0.183144\pi\) | |||||||
\(564\) | 3.88962e11 | 0.161865 | ||||||||
\(565\) | −3.31574e12 | −1.36887 | ||||||||
\(566\) | −1.35361e12 | −0.554394 | ||||||||
\(567\) | −2.22644e11 | −0.0904662 | ||||||||
\(568\) | 7.50305e11 | 0.302462 | ||||||||
\(569\) | −1.23909e12 | −0.495563 | −0.247782 | − | 0.968816i | \(-0.579702\pi\) | ||||
−0.247782 | + | 0.968816i | \(0.579702\pi\) | |||||||
\(570\) | −3.35892e11 | −0.133279 | ||||||||
\(571\) | −5.04024e12 | −1.98421 | −0.992107 | − | 0.125395i | \(-0.959980\pi\) | ||||
−0.992107 | + | 0.125395i | \(0.959980\pi\) | |||||||
\(572\) | 2.01797e11 | 0.0788192 | ||||||||
\(573\) | −1.88038e10 | −0.00728702 | ||||||||
\(574\) | −5.75137e11 | −0.221140 | ||||||||
\(575\) | 8.08679e12 | 3.08511 | ||||||||
\(576\) | −2.55798e11 | −0.0968268 | ||||||||
\(577\) | −4.83898e12 | −1.81745 | −0.908725 | − | 0.417395i | \(-0.862943\pi\) | ||||
−0.908725 | + | 0.417395i | \(0.862943\pi\) | |||||||
\(578\) | −1.31576e12 | −0.490344 | ||||||||
\(579\) | −9.53234e11 | −0.352489 | ||||||||
\(580\) | 3.98504e11 | 0.146220 | ||||||||
\(581\) | 2.00053e11 | 0.0728372 | ||||||||
\(582\) | −1.40291e12 | −0.506846 | ||||||||
\(583\) | 3.86940e11 | 0.138719 | ||||||||
\(584\) | 5.70722e11 | 0.203033 | ||||||||
\(585\) | −4.99827e12 | −1.76449 | ||||||||
\(586\) | 1.70593e12 | 0.597617 | ||||||||
\(587\) | −1.95960e12 | −0.681233 | −0.340617 | − | 0.940202i | \(-0.610636\pi\) | ||||
−0.340617 | + | 0.940202i | \(0.610636\pi\) | |||||||
\(588\) | 6.47946e11 | 0.223533 | ||||||||
\(589\) | −2.53025e10 | −0.00866254 | ||||||||
\(590\) | −3.53772e12 | −1.20196 | ||||||||
\(591\) | −1.34620e12 | −0.453906 | ||||||||
\(592\) | 6.20308e11 | 0.207568 | ||||||||
\(593\) | −4.89414e12 | −1.62529 | −0.812643 | − | 0.582762i | \(-0.801972\pi\) | ||||
−0.812643 | + | 0.582762i | \(0.801972\pi\) | |||||||
\(594\) | 2.16477e11 | 0.0713464 | ||||||||
\(595\) | −1.66255e12 | −0.543810 | ||||||||
\(596\) | −1.82186e12 | −0.591435 | ||||||||
\(597\) | 2.63706e12 | 0.849642 | ||||||||
\(598\) | 4.50123e12 | 1.43938 | ||||||||
\(599\) | 4.50082e12 | 1.42847 | 0.714235 | − | 0.699906i | \(-0.246775\pi\) | ||||
0.714235 | + | 0.699906i | \(0.246775\pi\) | |||||||
\(600\) | 1.06297e12 | 0.334842 | ||||||||
\(601\) | −5.43075e12 | −1.69795 | −0.848974 | − | 0.528435i | \(-0.822779\pi\) | ||||
−0.848974 | + | 0.528435i | \(0.822779\pi\) | |||||||
\(602\) | 9.33366e11 | 0.289646 | ||||||||
\(603\) | −3.70098e12 | −1.13996 | ||||||||
\(604\) | 4.80970e11 | 0.147046 | ||||||||
\(605\) | 5.62104e12 | 1.70576 | ||||||||
\(606\) | 1.47122e12 | 0.443150 | ||||||||
\(607\) | 5.89921e12 | 1.76378 | 0.881891 | − | 0.471454i | \(-0.156271\pi\) | ||||
0.881891 | + | 0.471454i | \(0.156271\pi\) | |||||||
\(608\) | −1.36651e11 | −0.0405554 | ||||||||
\(609\) | −6.57591e10 | −0.0193722 | ||||||||
\(610\) | −1.55858e12 | −0.455768 | ||||||||
\(611\) | 3.09205e12 | 0.897554 | ||||||||
\(612\) | 1.74914e12 | 0.504013 | ||||||||
\(613\) | −2.44465e11 | −0.0699268 | −0.0349634 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349634 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(614\) | −2.64467e12 | −0.750955 | ||||||||
\(615\) | −3.77490e12 | −1.06406 | ||||||||
\(616\) | −3.65391e10 | −0.0102246 | ||||||||
\(617\) | −6.79288e11 | −0.188699 | −0.0943497 | − | 0.995539i | \(-0.530077\pi\) | ||||
−0.0943497 | + | 0.995539i | \(0.530077\pi\) | |||||||
\(618\) | −9.96485e11 | −0.274804 | ||||||||
\(619\) | 1.31874e12 | 0.361037 | 0.180519 | − | 0.983572i | \(-0.442222\pi\) | ||||
0.180519 | + | 0.983572i | \(0.442222\pi\) | |||||||
\(620\) | 1.20211e11 | 0.0326726 | ||||||||
\(621\) | 4.82868e12 | 1.30292 | ||||||||
\(622\) | 1.74351e12 | 0.467054 | ||||||||
\(623\) | −1.09046e12 | −0.290010 | ||||||||
\(624\) | 5.91664e11 | 0.156223 | ||||||||
\(625\) | 3.75646e12 | 0.984732 | ||||||||
\(626\) | −1.51780e12 | −0.395029 | ||||||||
\(627\) | 5.04790e10 | 0.0130439 | ||||||||
\(628\) | 1.26967e12 | 0.325740 | ||||||||
\(629\) | −4.24164e12 | −1.08045 | ||||||||
\(630\) | 9.05033e11 | 0.228893 | ||||||||
\(631\) | −6.44908e12 | −1.61944 | −0.809721 | − | 0.586815i | \(-0.800382\pi\) | ||||
−0.809721 | + | 0.586815i | \(0.800382\pi\) | |||||||
\(632\) | −1.03026e12 | −0.256873 | ||||||||
\(633\) | 8.72641e11 | 0.216032 | ||||||||
\(634\) | −4.40001e12 | −1.08156 | ||||||||
\(635\) | −3.98350e12 | −0.972261 | ||||||||
\(636\) | 1.13450e12 | 0.274946 | ||||||||
\(637\) | 5.15083e12 | 1.23951 | ||||||||
\(638\) | −5.98885e10 | −0.0143104 | ||||||||
\(639\) | 2.79290e12 | 0.662676 | ||||||||
\(640\) | 6.49226e11 | 0.152963 | ||||||||
\(641\) | −5.38181e12 | −1.25912 | −0.629561 | − | 0.776951i | \(-0.716765\pi\) | ||||
−0.629561 | + | 0.776951i | \(0.716765\pi\) | |||||||
\(642\) | −4.55870e11 | −0.105909 | ||||||||
\(643\) | −7.16838e12 | −1.65376 | −0.826878 | − | 0.562381i | \(-0.809885\pi\) | ||||
−0.826878 | + | 0.562381i | \(0.809885\pi\) | |||||||
\(644\) | −8.15034e11 | −0.186719 | ||||||||
\(645\) | 6.12613e12 | 1.39369 | ||||||||
\(646\) | 9.34417e11 | 0.211103 | ||||||||
\(647\) | −1.24135e12 | −0.278501 | −0.139250 | − | 0.990257i | \(-0.544469\pi\) | ||||
−0.139250 | + | 0.990257i | \(0.544469\pi\) | |||||||
\(648\) | −5.94510e11 | −0.132456 | ||||||||
\(649\) | 5.31661e11 | 0.117634 | ||||||||
\(650\) | 8.45003e12 | 1.85673 | ||||||||
\(651\) | −1.98367e10 | −0.00432867 | ||||||||
\(652\) | 7.36100e11 | 0.159523 | ||||||||
\(653\) | 6.46167e12 | 1.39071 | 0.695353 | − | 0.718669i | \(-0.255248\pi\) | ||||
0.695353 | + | 0.718669i | \(0.255248\pi\) | |||||||
\(654\) | −1.21276e11 | −0.0259224 | ||||||||
\(655\) | 8.84392e12 | 1.87741 | ||||||||
\(656\) | −1.53575e12 | −0.323782 | ||||||||
\(657\) | 2.12443e12 | 0.444834 | ||||||||
\(658\) | −5.59874e11 | −0.116432 | ||||||||
\(659\) | 3.48331e12 | 0.719462 | 0.359731 | − | 0.933056i | \(-0.382869\pi\) | ||||
0.359731 | + | 0.933056i | \(0.382869\pi\) | |||||||
\(660\) | −2.39824e11 | −0.0491977 | ||||||||
\(661\) | −2.69783e12 | −0.549678 | −0.274839 | − | 0.961490i | \(-0.588625\pi\) | ||||
−0.274839 | + | 0.961490i | \(0.588625\pi\) | |||||||
\(662\) | 2.04891e12 | 0.414632 | ||||||||
\(663\) | −4.04578e12 | −0.813188 | ||||||||
\(664\) | 5.34189e11 | 0.106645 | ||||||||
\(665\) | 4.83484e11 | 0.0958704 | ||||||||
\(666\) | 2.30900e12 | 0.454769 | ||||||||
\(667\) | −1.33586e12 | −0.261333 | ||||||||
\(668\) | 3.78472e12 | 0.735427 | ||||||||
\(669\) | −4.33165e12 | −0.836056 | ||||||||
\(670\) | 9.39325e12 | 1.80086 | ||||||||
\(671\) | 2.34228e11 | 0.0446054 | ||||||||
\(672\) | −1.07132e11 | −0.0202655 | ||||||||
\(673\) | −7.15485e12 | −1.34441 | −0.672207 | − | 0.740364i | \(-0.734653\pi\) | ||||
−0.672207 | + | 0.740364i | \(0.734653\pi\) | |||||||
\(674\) | 4.85917e11 | 0.0906970 | ||||||||
\(675\) | 9.06474e12 | 1.68069 | ||||||||
\(676\) | 1.98867e12 | 0.366271 | ||||||||
\(677\) | 3.99069e12 | 0.730127 | 0.365064 | − | 0.930983i | \(-0.381047\pi\) | ||||
0.365064 | + | 0.930983i | \(0.381047\pi\) | |||||||
\(678\) | 1.46101e12 | 0.265533 | ||||||||
\(679\) | 2.01935e12 | 0.364585 | ||||||||
\(680\) | −4.43938e12 | −0.796219 | ||||||||
\(681\) | −6.85969e11 | −0.122220 | ||||||||
\(682\) | −1.80658e10 | −0.00319762 | ||||||||
\(683\) | −7.70306e12 | −1.35447 | −0.677236 | − | 0.735766i | \(-0.736823\pi\) | ||||
−0.677236 | + | 0.735766i | \(0.736823\pi\) | |||||||
\(684\) | −5.08664e11 | −0.0888544 | ||||||||
\(685\) | 7.84008e12 | 1.36054 | ||||||||
\(686\) | −1.92306e12 | −0.331539 | ||||||||
\(687\) | −1.14421e12 | −0.195974 | ||||||||
\(688\) | 2.49230e12 | 0.424085 | ||||||||
\(689\) | 9.01868e12 | 1.52460 | ||||||||
\(690\) | −5.34946e12 | −0.898439 | ||||||||
\(691\) | −6.94842e12 | −1.15940 | −0.579702 | − | 0.814828i | \(-0.696831\pi\) | ||||
−0.579702 | + | 0.814828i | \(0.696831\pi\) | |||||||
\(692\) | 3.72690e12 | 0.617832 | ||||||||
\(693\) | −1.36011e11 | −0.0224014 | ||||||||
\(694\) | −6.46098e12 | −1.05726 | ||||||||
\(695\) | −2.10182e13 | −3.41715 | ||||||||
\(696\) | −1.75592e11 | −0.0283637 | ||||||||
\(697\) | 1.05014e13 | 1.68539 | ||||||||
\(698\) | −1.00707e12 | −0.160587 | ||||||||
\(699\) | 4.34576e12 | 0.688523 | ||||||||
\(700\) | −1.53004e12 | −0.240858 | ||||||||
\(701\) | 8.89057e12 | 1.39059 | 0.695294 | − | 0.718725i | \(-0.255274\pi\) | ||||
0.695294 | + | 0.718725i | \(0.255274\pi\) | |||||||
\(702\) | 5.04558e12 | 0.784140 | ||||||||
\(703\) | 1.23351e12 | 0.190477 | ||||||||
\(704\) | −9.75680e10 | −0.0149703 | ||||||||
\(705\) | −3.67472e12 | −0.560239 | ||||||||
\(706\) | −1.49765e12 | −0.226877 | ||||||||
\(707\) | −2.11768e12 | −0.318767 | ||||||||
\(708\) | 1.55882e12 | 0.233156 | ||||||||
\(709\) | 5.07939e12 | 0.754924 | 0.377462 | − | 0.926025i | \(-0.376797\pi\) | ||||
0.377462 | + | 0.926025i | \(0.376797\pi\) | |||||||
\(710\) | −7.08850e12 | −1.04687 | ||||||||
\(711\) | −3.83497e12 | −0.562793 | ||||||||
\(712\) | −2.91178e12 | −0.424617 | ||||||||
\(713\) | −4.02972e11 | −0.0583944 | ||||||||
\(714\) | 7.32565e11 | 0.105488 | ||||||||
\(715\) | −1.90647e12 | −0.272806 | ||||||||
\(716\) | −4.66953e12 | −0.663994 | ||||||||
\(717\) | 9.52615e11 | 0.134611 | ||||||||
\(718\) | −5.09768e12 | −0.715834 | ||||||||
\(719\) | −2.62697e11 | −0.0366585 | −0.0183293 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183293 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(720\) | 2.41665e12 | 0.335133 | ||||||||
\(721\) | 1.43434e12 | 0.197672 | ||||||||
\(722\) | −2.71737e11 | −0.0372161 | ||||||||
\(723\) | 3.19412e12 | 0.434739 | ||||||||
\(724\) | 7.19789e12 | 0.973602 | ||||||||
\(725\) | −2.50777e12 | −0.337106 | ||||||||
\(726\) | −2.47679e12 | −0.330882 | ||||||||
\(727\) | −5.69375e12 | −0.755951 | −0.377976 | − | 0.925816i | \(-0.623380\pi\) | ||||
−0.377976 | + | 0.925816i | \(0.623380\pi\) | |||||||
\(728\) | −8.51644e11 | −0.112374 | ||||||||
\(729\) | 8.37055e11 | 0.109769 | ||||||||
\(730\) | −5.39189e12 | −0.702730 | ||||||||
\(731\) | −1.70423e13 | −2.20749 | ||||||||
\(732\) | 6.86753e11 | 0.0884098 | ||||||||
\(733\) | −1.28415e13 | −1.64304 | −0.821521 | − | 0.570178i | \(-0.806874\pi\) | ||||
−0.821521 | + | 0.570178i | \(0.806874\pi\) | |||||||
\(734\) | −1.56994e12 | −0.199642 | ||||||||
\(735\) | −6.12147e12 | −0.773682 | ||||||||
\(736\) | −2.17633e12 | −0.273385 | ||||||||
\(737\) | −1.41165e12 | −0.176248 | ||||||||
\(738\) | −5.71660e12 | −0.709388 | ||||||||
\(739\) | 2.66001e12 | 0.328083 | 0.164042 | − | 0.986453i | \(-0.447547\pi\) | ||||
0.164042 | + | 0.986453i | \(0.447547\pi\) | |||||||
\(740\) | −5.86035e12 | −0.718425 | ||||||||
\(741\) | 1.17655e12 | 0.143360 | ||||||||
\(742\) | −1.63300e12 | −0.197774 | ||||||||
\(743\) | 1.02254e13 | 1.23092 | 0.615462 | − | 0.788166i | \(-0.288969\pi\) | ||||
0.615462 | + | 0.788166i | \(0.288969\pi\) | |||||||
\(744\) | −5.29686e10 | −0.00633782 | ||||||||
\(745\) | 1.72120e13 | 2.04705 | ||||||||
\(746\) | −3.59982e12 | −0.425556 | ||||||||
\(747\) | 1.98844e12 | 0.233652 | ||||||||
\(748\) | 6.67166e11 | 0.0779250 | ||||||||
\(749\) | 6.56181e11 | 0.0761826 | ||||||||
\(750\) | −5.00836e12 | −0.577989 | ||||||||
\(751\) | 7.08317e12 | 0.812546 | 0.406273 | − | 0.913752i | \(-0.366828\pi\) | ||||
0.406273 | + | 0.913752i | \(0.366828\pi\) | |||||||
\(752\) | −1.49499e12 | −0.170474 | ||||||||
\(753\) | 8.32720e11 | 0.0943890 | ||||||||
\(754\) | −1.39586e12 | −0.157280 | ||||||||
\(755\) | −4.54396e12 | −0.508948 | ||||||||
\(756\) | −9.13598e11 | −0.101720 | ||||||||
\(757\) | 1.55185e13 | 1.71758 | 0.858792 | − | 0.512325i | \(-0.171216\pi\) | ||||
0.858792 | + | 0.512325i | \(0.171216\pi\) | |||||||
\(758\) | −9.98399e12 | −1.09848 | ||||||||
\(759\) | 8.03934e11 | 0.0879291 | ||||||||
\(760\) | 1.29101e12 | 0.140368 | ||||||||
\(761\) | 3.36663e12 | 0.363885 | 0.181943 | − | 0.983309i | \(-0.441761\pi\) | ||||
0.181943 | + | 0.983309i | \(0.441761\pi\) | |||||||
\(762\) | 1.75524e12 | 0.188599 | ||||||||
\(763\) | 1.74565e11 | 0.0186465 | ||||||||
\(764\) | 7.22732e10 | 0.00767462 | ||||||||
\(765\) | −1.65249e13 | −1.74447 | ||||||||
\(766\) | −8.59039e12 | −0.901537 | ||||||||
\(767\) | 1.23918e13 | 1.29287 | ||||||||
\(768\) | −2.86067e11 | −0.0296717 | ||||||||
\(769\) | −9.31790e12 | −0.960836 | −0.480418 | − | 0.877040i | \(-0.659515\pi\) | ||||
−0.480418 | + | 0.877040i | \(0.659515\pi\) | |||||||
\(770\) | 3.45203e11 | 0.0353888 | ||||||||
\(771\) | −1.22322e12 | −0.124670 | ||||||||
\(772\) | 3.66379e12 | 0.371239 | ||||||||
\(773\) | −7.33840e12 | −0.739254 | −0.369627 | − | 0.929180i | \(-0.620514\pi\) | ||||
−0.369627 | + | 0.929180i | \(0.620514\pi\) | |||||||
\(774\) | 9.27722e12 | 0.929145 | ||||||||
\(775\) | −7.56487e11 | −0.0753258 | ||||||||
\(776\) | 5.39214e12 | 0.533806 | ||||||||
\(777\) | 9.67046e11 | 0.0951815 | ||||||||
\(778\) | 2.08247e12 | 0.203784 | ||||||||
\(779\) | −3.05390e12 | −0.297123 | ||||||||
\(780\) | −5.58974e12 | −0.540712 | ||||||||
\(781\) | 1.06528e12 | 0.102456 | ||||||||
\(782\) | 1.48817e13 | 1.42305 | ||||||||
\(783\) | −1.49741e12 | −0.142368 | ||||||||
\(784\) | −2.49041e12 | −0.235423 | ||||||||
\(785\) | −1.19951e13 | −1.12744 | ||||||||
\(786\) | −3.89688e12 | −0.364180 | ||||||||
\(787\) | 1.81540e13 | 1.68689 | 0.843443 | − | 0.537219i | \(-0.180525\pi\) | ||||
0.843443 | + | 0.537219i | \(0.180525\pi\) | |||||||
\(788\) | 5.17417e12 | 0.478050 | ||||||||
\(789\) | −5.58923e12 | −0.513459 | ||||||||
\(790\) | 9.73333e12 | 0.889077 | ||||||||
\(791\) | −2.10298e12 | −0.191003 | ||||||||
\(792\) | −3.63182e11 | −0.0327990 | ||||||||
\(793\) | 5.45932e12 | 0.490241 | ||||||||
\(794\) | 1.17873e13 | 1.05250 | ||||||||
\(795\) | −1.07182e13 | −0.951632 | ||||||||
\(796\) | −1.01356e13 | −0.894835 | ||||||||
\(797\) | 5.44638e12 | 0.478129 | 0.239065 | − | 0.971004i | \(-0.423159\pi\) | ||||
0.239065 | + | 0.971004i | \(0.423159\pi\) | |||||||
\(798\) | −2.13037e11 | −0.0185969 | ||||||||
\(799\) | 1.02227e13 | 0.887371 | ||||||||
\(800\) | −4.08556e12 | −0.352652 | ||||||||
\(801\) | −1.08386e13 | −0.930312 | ||||||||
\(802\) | 9.44751e12 | 0.806367 | ||||||||
\(803\) | 8.10312e11 | 0.0687753 | ||||||||
\(804\) | −4.13893e12 | −0.349330 | ||||||||
\(805\) | 7.70002e12 | 0.646265 | ||||||||
\(806\) | −4.21072e11 | −0.0351438 | ||||||||
\(807\) | −6.21582e11 | −0.0515903 | ||||||||
\(808\) | −5.65469e12 | −0.466722 | ||||||||
\(809\) | 2.44611e11 | 0.0200774 | 0.0100387 | − | 0.999950i | \(-0.496805\pi\) | ||||
0.0100387 | + | 0.999950i | \(0.496805\pi\) | |||||||
\(810\) | 5.61663e12 | 0.458451 | ||||||||
\(811\) | 1.86901e13 | 1.51711 | 0.758555 | − | 0.651609i | \(-0.225906\pi\) | ||||
0.758555 | + | 0.651609i | \(0.225906\pi\) | |||||||
\(812\) | 2.52748e11 | 0.0204026 | ||||||||
\(813\) | 1.05139e13 | 0.844030 | ||||||||
\(814\) | 8.80714e11 | 0.0703113 | ||||||||
\(815\) | −6.95430e12 | −0.552134 | ||||||||
\(816\) | 1.95612e12 | 0.154450 | ||||||||
\(817\) | 4.95605e12 | 0.389167 | ||||||||
\(818\) | 6.84126e12 | 0.534252 | ||||||||
\(819\) | −3.17011e12 | −0.246205 | ||||||||
\(820\) | 1.45090e13 | 1.12066 | ||||||||
\(821\) | 2.98096e12 | 0.228987 | 0.114494 | − | 0.993424i | \(-0.463475\pi\) | ||||
0.114494 | + | 0.993424i | \(0.463475\pi\) | |||||||
\(822\) | −3.45456e12 | −0.263918 | ||||||||
\(823\) | −1.01707e13 | −0.772774 | −0.386387 | − | 0.922337i | \(-0.626277\pi\) | ||||
−0.386387 | + | 0.922337i | \(0.626277\pi\) | |||||||
\(824\) | 3.83003e12 | 0.289421 | ||||||||
\(825\) | 1.50920e12 | 0.113424 | ||||||||
\(826\) | −2.24377e12 | −0.167713 | ||||||||
\(827\) | 1.99682e13 | 1.48445 | 0.742223 | − | 0.670153i | \(-0.233771\pi\) | ||||
0.742223 | + | 0.670153i | \(0.233771\pi\) | |||||||
\(828\) | −8.10105e12 | −0.598970 | ||||||||
\(829\) | 2.35288e13 | 1.73023 | 0.865115 | − | 0.501574i | \(-0.167245\pi\) | ||||
0.865115 | + | 0.501574i | \(0.167245\pi\) | |||||||
\(830\) | −5.04674e12 | −0.369113 | ||||||||
\(831\) | 7.52516e12 | 0.547408 | ||||||||
\(832\) | −2.27409e12 | −0.164533 | ||||||||
\(833\) | 1.70293e13 | 1.22545 | ||||||||
\(834\) | 9.26121e12 | 0.662858 | ||||||||
\(835\) | −3.57561e13 | −2.54543 | ||||||||
\(836\) | −1.94018e11 | −0.0137377 | ||||||||
\(837\) | −4.51704e11 | −0.0318119 | ||||||||
\(838\) | −1.56144e13 | −1.09378 | ||||||||
\(839\) | 9.16607e12 | 0.638637 | 0.319319 | − | 0.947647i | \(-0.396546\pi\) | ||||
0.319319 | + | 0.947647i | \(0.396546\pi\) | |||||||
\(840\) | 1.01213e12 | 0.0701422 | ||||||||
\(841\) | −1.40929e13 | −0.971444 | ||||||||
\(842\) | 1.09267e12 | 0.0749179 | ||||||||
\(843\) | −5.21884e12 | −0.355918 | ||||||||
\(844\) | −3.35403e12 | −0.227523 | ||||||||
\(845\) | −1.87879e13 | −1.26772 | ||||||||
\(846\) | −5.56488e12 | −0.373499 | ||||||||
\(847\) | 3.56509e12 | 0.238010 | ||||||||
\(848\) | −4.36050e12 | −0.289571 | ||||||||
\(849\) | −5.63484e12 | −0.372217 | ||||||||
\(850\) | 2.79369e13 | 1.83566 | ||||||||
\(851\) | 1.96450e13 | 1.28401 | ||||||||
\(852\) | 3.12339e12 | 0.203071 | ||||||||
\(853\) | 9.94411e12 | 0.643125 | 0.321562 | − | 0.946888i | \(-0.395792\pi\) | ||||
0.321562 | + | 0.946888i | \(0.395792\pi\) | |||||||
\(854\) | −9.88514e11 | −0.0635949 | ||||||||
\(855\) | 4.80560e12 | 0.307539 | ||||||||
\(856\) | 1.75216e12 | 0.111543 | ||||||||
\(857\) | −1.90800e13 | −1.20827 | −0.604137 | − | 0.796880i | \(-0.706482\pi\) | ||||
−0.604137 | + | 0.796880i | \(0.706482\pi\) | |||||||
\(858\) | 8.40045e11 | 0.0529188 | ||||||||
\(859\) | 3.10124e12 | 0.194342 | 0.0971710 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971710 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(860\) | −2.35460e13 | −1.46782 | ||||||||
\(861\) | −2.39420e12 | −0.148473 | ||||||||
\(862\) | 4.75381e12 | 0.293264 | ||||||||
\(863\) | −2.40338e13 | −1.47494 | −0.737470 | − | 0.675380i | \(-0.763980\pi\) | ||||
−0.737470 | + | 0.675380i | \(0.763980\pi\) | |||||||
\(864\) | −2.43952e12 | −0.148933 | ||||||||
\(865\) | −3.52099e13 | −2.13842 | ||||||||
\(866\) | 7.21869e12 | 0.436142 | ||||||||
\(867\) | −5.47728e12 | −0.329214 | ||||||||
\(868\) | 7.62431e10 | 0.00455892 | ||||||||
\(869\) | −1.46276e12 | −0.0870129 | ||||||||
\(870\) | 1.65890e12 | 0.0981713 | ||||||||
\(871\) | −3.29023e13 | −1.93707 | ||||||||
\(872\) | 4.66130e11 | 0.0273013 | ||||||||
\(873\) | 2.00714e13 | 1.16954 | ||||||||
\(874\) | −4.32772e12 | −0.250875 | ||||||||
\(875\) | 7.20905e12 | 0.415759 | ||||||||
\(876\) | 2.37582e12 | 0.136315 | ||||||||
\(877\) | −5.20893e12 | −0.297338 | −0.148669 | − | 0.988887i | \(-0.547499\pi\) | ||||
−0.148669 | + | 0.988887i | \(0.547499\pi\) | |||||||
\(878\) | −8.88771e12 | −0.504736 | ||||||||
\(879\) | 7.10151e12 | 0.401237 | ||||||||
\(880\) | 9.21772e11 | 0.0518145 | ||||||||
\(881\) | −7.36387e12 | −0.411826 | −0.205913 | − | 0.978570i | \(-0.566016\pi\) | ||||
−0.205913 | + | 0.978570i | \(0.566016\pi\) | |||||||
\(882\) | −9.27016e12 | −0.515797 | ||||||||
\(883\) | 2.98715e13 | 1.65362 | 0.826808 | − | 0.562485i | \(-0.190155\pi\) | ||||
0.826808 | + | 0.562485i | \(0.190155\pi\) | |||||||
\(884\) | 1.55501e13 | 0.856442 | ||||||||
\(885\) | −1.47269e13 | −0.806988 | ||||||||
\(886\) | 2.58705e13 | 1.41044 | ||||||||
\(887\) | −1.43208e13 | −0.776802 | −0.388401 | − | 0.921490i | \(-0.626973\pi\) | ||||
−0.388401 | + | 0.921490i | \(0.626973\pi\) | |||||||
\(888\) | 2.58224e12 | 0.139360 | ||||||||
\(889\) | −2.52650e12 | −0.135663 | ||||||||
\(890\) | 2.75090e13 | 1.46967 | ||||||||
\(891\) | −8.44086e11 | −0.0448680 | ||||||||
\(892\) | 1.66489e13 | 0.880526 | ||||||||
\(893\) | −2.97285e12 | −0.156438 | ||||||||
\(894\) | −7.58410e12 | −0.397086 | ||||||||
\(895\) | 4.41153e13 | 2.29819 | ||||||||
\(896\) | 4.11766e11 | 0.0213435 | ||||||||
\(897\) | 1.87379e13 | 0.966394 | ||||||||
\(898\) | −7.24628e12 | −0.371853 | ||||||||
\(899\) | 1.24964e11 | 0.00638069 | ||||||||
\(900\) | −1.52079e13 | −0.772640 | ||||||||
\(901\) | 2.98169e13 | 1.50730 | ||||||||
\(902\) | −2.18046e12 | −0.109678 | ||||||||
\(903\) | 3.88544e12 | 0.194467 | ||||||||
\(904\) | −5.61544e12 | −0.279657 | ||||||||
\(905\) | −6.80020e13 | −3.36979 | ||||||||
\(906\) | 2.00220e12 | 0.0987257 | ||||||||
\(907\) | −3.98348e13 | −1.95448 | −0.977238 | − | 0.212146i | \(-0.931955\pi\) | ||||
−0.977238 | + | 0.212146i | \(0.931955\pi\) | |||||||
\(908\) | 2.63655e12 | 0.128721 | ||||||||
\(909\) | −2.10487e13 | −1.02256 | ||||||||
\(910\) | 8.04589e12 | 0.388945 | ||||||||
\(911\) | −8.77892e12 | −0.422288 | −0.211144 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211144 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(912\) | −5.68857e11 | −0.0272287 | ||||||||
\(913\) | 7.58442e11 | 0.0361247 | ||||||||
\(914\) | −1.76496e13 | −0.836522 | ||||||||
\(915\) | −6.48809e12 | −0.306000 | ||||||||
\(916\) | 4.39780e12 | 0.206398 | ||||||||
\(917\) | 5.60918e12 | 0.261962 | ||||||||
\(918\) | 1.66813e13 | 0.775244 | ||||||||
\(919\) | 2.89837e12 | 0.134040 | 0.0670200 | − | 0.997752i | \(-0.478651\pi\) | ||||
0.0670200 | + | 0.997752i | \(0.478651\pi\) | |||||||
\(920\) | 2.05608e13 | 0.946228 | ||||||||
\(921\) | −1.10093e13 | −0.504188 | ||||||||
\(922\) | −3.55347e12 | −0.161943 | ||||||||
\(923\) | 2.48293e13 | 1.12605 | ||||||||
\(924\) | −1.52106e11 | −0.00686472 | ||||||||
\(925\) | 3.68790e13 | 1.65631 | ||||||||
\(926\) | −1.59557e13 | −0.713125 | ||||||||
\(927\) | 1.42567e13 | 0.634104 | ||||||||
\(928\) | 6.74895e11 | 0.0298724 | ||||||||
\(929\) | 1.09141e13 | 0.480749 | 0.240375 | − | 0.970680i | \(-0.422730\pi\) | ||||
0.240375 | + | 0.970680i | \(0.422730\pi\) | |||||||
\(930\) | 5.00420e11 | 0.0219362 | ||||||||
\(931\) | −4.95228e12 | −0.216039 | ||||||||
\(932\) | −1.67031e13 | −0.725146 | ||||||||
\(933\) | 7.25793e12 | 0.313578 | ||||||||
\(934\) | −1.39773e13 | −0.600983 | ||||||||
\(935\) | −6.30304e12 | −0.269711 | ||||||||
\(936\) | −8.46494e12 | −0.360481 | ||||||||
\(937\) | 3.31892e13 | 1.40659 | 0.703296 | − | 0.710897i | \(-0.251711\pi\) | ||||
0.703296 | + | 0.710897i | \(0.251711\pi\) | |||||||
\(938\) | 5.95759e12 | 0.251280 | ||||||||
\(939\) | −6.31832e12 | −0.265220 | ||||||||
\(940\) | 1.41239e13 | 0.590038 | ||||||||
\(941\) | −4.06875e13 | −1.69164 | −0.845819 | − | 0.533471i | \(-0.820888\pi\) | ||||
−0.845819 | + | 0.533471i | \(0.820888\pi\) | |||||||
\(942\) | 5.28540e12 | 0.218700 | ||||||||
\(943\) | −4.86368e13 | −2.00292 | ||||||||
\(944\) | −5.99138e12 | −0.245557 | ||||||||
\(945\) | 8.63120e12 | 0.352069 | ||||||||
\(946\) | 3.53857e12 | 0.143654 | ||||||||
\(947\) | −1.90875e13 | −0.771211 | −0.385606 | − | 0.922664i | \(-0.626007\pi\) | ||||
−0.385606 | + | 0.922664i | \(0.626007\pi\) | |||||||
\(948\) | −4.28878e12 | −0.172463 | ||||||||
\(949\) | 1.88865e13 | 0.755882 | ||||||||
\(950\) | −8.12430e12 | −0.323616 | ||||||||
\(951\) | −1.83165e13 | −0.726155 | ||||||||
\(952\) | −2.81564e12 | −0.111099 | ||||||||
\(953\) | −2.79671e12 | −0.109832 | −0.0549161 | − | 0.998491i | \(-0.517489\pi\) | ||||
−0.0549161 | + | 0.998491i | \(0.517489\pi\) | |||||||
\(954\) | −1.62313e13 | −0.634432 | ||||||||
\(955\) | −6.82800e11 | −0.0265631 | ||||||||
\(956\) | −3.66141e12 | −0.141771 | ||||||||
\(957\) | −2.49306e11 | −0.00960790 | ||||||||
\(958\) | −2.57053e13 | −0.986002 | ||||||||
\(959\) | 4.97250e12 | 0.189842 | ||||||||
\(960\) | 2.70262e12 | 0.102699 | ||||||||
\(961\) | −2.64019e13 | −0.998574 | ||||||||
\(962\) | 2.05274e13 | 0.772764 | ||||||||
\(963\) | 6.52213e12 | 0.244383 | ||||||||
\(964\) | −1.22767e13 | −0.457864 | ||||||||
\(965\) | −3.46136e13 | −1.28492 | ||||||||
\(966\) | −3.39285e12 | −0.125362 | ||||||||
\(967\) | −1.90809e10 | −0.000701745 0 | −0.000350873 | − | 1.00000i | \(-0.500112\pi\) | ||||
−0.000350873 | 1.00000i | \(0.500112\pi\) | ||||||||
\(968\) | 9.51963e12 | 0.348482 | ||||||||
\(969\) | 3.88982e12 | 0.141733 | ||||||||
\(970\) | −5.09422e13 | −1.84759 | ||||||||
\(971\) | −4.13526e12 | −0.149285 | −0.0746426 | − | 0.997210i | \(-0.523782\pi\) | ||||
−0.0746426 | + | 0.997210i | \(0.523782\pi\) | |||||||
\(972\) | −1.41977e13 | −0.510177 | ||||||||
\(973\) | −1.33306e13 | −0.476807 | ||||||||
\(974\) | 1.48061e13 | 0.527139 | ||||||||
\(975\) | 3.51761e13 | 1.24660 | ||||||||
\(976\) | −2.63956e12 | −0.0931124 | ||||||||
\(977\) | 3.74336e13 | 1.31443 | 0.657213 | − | 0.753705i | \(-0.271735\pi\) | ||||
0.657213 | + | 0.753705i | \(0.271735\pi\) | |||||||
\(978\) | 3.06426e12 | 0.107103 | ||||||||
\(979\) | −4.13414e12 | −0.143835 | ||||||||
\(980\) | 2.35281e13 | 0.814835 | ||||||||
\(981\) | 1.73510e12 | 0.0598155 | ||||||||
\(982\) | 1.48581e13 | 0.509871 | ||||||||
\(983\) | 1.37412e13 | 0.469390 | 0.234695 | − | 0.972069i | \(-0.424591\pi\) | ||||
0.234695 | + | 0.972069i | \(0.424591\pi\) | |||||||
\(984\) | −6.39307e12 | −0.217386 | ||||||||
\(985\) | −4.88830e13 | −1.65461 | ||||||||
\(986\) | −4.61491e12 | −0.155495 | ||||||||
\(987\) | −2.33066e12 | −0.0781721 | ||||||||
\(988\) | −4.52211e12 | −0.150985 | ||||||||
\(989\) | 7.89307e13 | 2.62339 | ||||||||
\(990\) | 3.43116e12 | 0.113523 | ||||||||
\(991\) | −2.92261e13 | −0.962584 | −0.481292 | − | 0.876560i | \(-0.659832\pi\) | ||||
−0.481292 | + | 0.876560i | \(0.659832\pi\) | |||||||
\(992\) | 2.03587e11 | 0.00667494 | ||||||||
\(993\) | 8.52927e12 | 0.278381 | ||||||||
\(994\) | −4.49582e12 | −0.146073 | ||||||||
\(995\) | 9.57564e13 | 3.09716 | ||||||||
\(996\) | 2.22374e12 | 0.0716006 | ||||||||
\(997\) | 1.27081e13 | 0.407335 | 0.203668 | − | 0.979040i | \(-0.434714\pi\) | ||||
0.203668 | + | 0.979040i | \(0.434714\pi\) | |||||||
\(998\) | −1.91375e13 | −0.610658 | ||||||||
\(999\) | 2.20207e13 | 0.699499 |
(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 | 38.10.a.d.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 342.10.a.l.1.4 | 4 | |||
4.3 | odd | 2 | 304.10.a.e.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.10.a.d.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
304.10.a.e.1.3 | 4 | 4.3 | odd | 2 | |||
342.10.a.l.1.4 | 4 | 3.2 | odd | 2 |