Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,26,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.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: | \(194.038422177\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 1893235651143 x^{10} + \cdots + 18\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | multiple of \( 2^{48}\cdot 3^{20}\cdot 5^{5}\cdot 7^{15} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(765345.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 300.357 | 0.0518516 | 0.0259258 | − | 0.999664i | \(-0.491747\pi\) | ||||
0.0259258 | + | 0.999664i | \(0.491747\pi\) | |||||||
\(3\) | −1.52968e6 | −1.66183 | −0.830913 | − | 0.556402i | \(-0.812182\pi\) | ||||
−0.830913 | + | 0.556402i | \(0.812182\pi\) | |||||||
\(4\) | −3.34642e7 | −0.997311 | ||||||||
\(5\) | −9.44412e8 | −1.72996 | −0.864981 | − | 0.501805i | \(-0.832670\pi\) | ||||
−0.864981 | + | 0.501805i | \(0.832670\pi\) | |||||||
\(6\) | −4.59451e8 | −0.0861685 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.01295e10 | −0.103564 | ||||||||
\(9\) | 1.49264e12 | 1.76167 | ||||||||
\(10\) | −2.83661e11 | −0.0897014 | ||||||||
\(11\) | −2.47255e12 | −0.237540 | −0.118770 | − | 0.992922i | \(-0.537895\pi\) | ||||
−0.118770 | + | 0.992922i | \(0.537895\pi\) | |||||||
\(12\) | 5.11896e13 | 1.65736 | ||||||||
\(13\) | 6.66288e13 | 0.793177 | 0.396588 | − | 0.917997i | \(-0.370194\pi\) | ||||
0.396588 | + | 0.917997i | \(0.370194\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.44465e15 | 2.87490 | ||||||||
\(16\) | 1.11683e15 | 0.991941 | ||||||||
\(17\) | 2.96239e15 | 1.23319 | 0.616596 | − | 0.787280i | \(-0.288511\pi\) | ||||
0.616596 | + | 0.787280i | \(0.288511\pi\) | |||||||
\(18\) | 4.48325e14 | 0.0913454 | ||||||||
\(19\) | −5.82342e15 | −0.603612 | −0.301806 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301806 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(20\) | 3.16040e16 | 1.72531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.42646e14 | −0.0123168 | ||||||||
\(23\) | −1.71029e17 | −1.62732 | −0.813659 | − | 0.581342i | \(-0.802528\pi\) | ||||
−0.813659 | + | 0.581342i | \(0.802528\pi\) | |||||||
\(24\) | 3.07918e16 | 0.172105 | ||||||||
\(25\) | 5.93891e17 | 1.99277 | ||||||||
\(26\) | 2.00124e16 | 0.0411275 | ||||||||
\(27\) | −9.87186e17 | −1.26576 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51070e18 | 1.84255 | 0.921273 | − | 0.388916i | \(-0.127150\pi\) | ||||
0.921273 | + | 0.388916i | \(0.127150\pi\) | |||||||
\(30\) | 4.33911e17 | 0.149068 | ||||||||
\(31\) | −5.01950e18 | −1.14456 | −0.572281 | − | 0.820057i | \(-0.693941\pi\) | ||||
−0.572281 | + | 0.820057i | \(0.693941\pi\) | |||||||
\(32\) | 1.01088e18 | 0.154998 | ||||||||
\(33\) | 3.78221e18 | 0.394750 | ||||||||
\(34\) | 8.89773e17 | 0.0639430 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.99501e19 | −1.75693 | ||||||||
\(37\) | −1.07367e19 | −0.268133 | −0.134067 | − | 0.990972i | \(-0.542804\pi\) | ||||
−0.134067 | + | 0.990972i | \(0.542804\pi\) | |||||||
\(38\) | −1.74910e18 | −0.0312983 | ||||||||
\(39\) | −1.01921e20 | −1.31812 | ||||||||
\(40\) | 1.90106e19 | 0.179162 | ||||||||
\(41\) | −2.09028e20 | −1.44680 | −0.723398 | − | 0.690432i | \(-0.757421\pi\) | ||||
−0.723398 | + | 0.690432i | \(0.757421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.88141e20 | 1.09964 | 0.549818 | − | 0.835284i | \(-0.314697\pi\) | ||||
0.549818 | + | 0.835284i | \(0.314697\pi\) | |||||||
\(44\) | 8.27418e19 | 0.236901 | ||||||||
\(45\) | −1.40967e21 | −3.04762 | ||||||||
\(46\) | −5.13698e19 | −0.0843791 | ||||||||
\(47\) | 6.92528e20 | 0.869388 | 0.434694 | − | 0.900578i | \(-0.356856\pi\) | ||||
0.434694 | + | 0.900578i | \(0.356856\pi\) | |||||||
\(48\) | −1.70839e21 | −1.64844 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.78379e20 | 0.103328 | ||||||||
\(51\) | −4.53151e21 | −2.04935 | ||||||||
\(52\) | −2.22968e21 | −0.791044 | ||||||||
\(53\) | 1.61704e21 | 0.452139 | 0.226070 | − | 0.974111i | \(-0.427412\pi\) | ||||
0.226070 | + | 0.974111i | \(0.427412\pi\) | |||||||
\(54\) | −2.96508e20 | −0.0656318 | ||||||||
\(55\) | 2.33510e21 | 0.410934 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.90799e21 | 1.00310 | ||||||||
\(58\) | 1.05446e21 | 0.0955391 | ||||||||
\(59\) | −1.36756e22 | −1.00068 | −0.500340 | − | 0.865829i | \(-0.666792\pi\) | ||||
−0.500340 | + | 0.865829i | \(0.666792\pi\) | |||||||
\(60\) | −4.83441e22 | −2.86717 | ||||||||
\(61\) | −2.85683e22 | −1.37804 | −0.689020 | − | 0.724742i | \(-0.741959\pi\) | ||||
−0.689020 | + | 0.724742i | \(0.741959\pi\) | |||||||
\(62\) | −1.50764e21 | −0.0593475 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.71709e22 | −0.983905 | ||||||||
\(65\) | −6.29250e22 | −1.37217 | ||||||||
\(66\) | 1.13601e21 | 0.0204684 | ||||||||
\(67\) | 5.59142e22 | 0.834809 | 0.417404 | − | 0.908721i | \(-0.362940\pi\) | ||||
0.417404 | + | 0.908721i | \(0.362940\pi\) | |||||||
\(68\) | −9.91340e22 | −1.22988 | ||||||||
\(69\) | 2.61621e23 | 2.70432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.07670e23 | 1.50191 | 0.750957 | − | 0.660351i | \(-0.229593\pi\) | ||||
0.750957 | + | 0.660351i | \(0.229593\pi\) | |||||||
\(72\) | −3.00461e22 | −0.182445 | ||||||||
\(73\) | 3.73651e22 | 0.190955 | 0.0954775 | − | 0.995432i | \(-0.469562\pi\) | ||||
0.0954775 | + | 0.995432i | \(0.469562\pi\) | |||||||
\(74\) | −3.22485e21 | −0.0139031 | ||||||||
\(75\) | −9.08465e23 | −3.31164 | ||||||||
\(76\) | 1.94876e23 | 0.601989 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.06126e22 | −0.0683468 | ||||||||
\(79\) | 4.44457e23 | 0.846235 | 0.423117 | − | 0.906075i | \(-0.360936\pi\) | ||||
0.423117 | + | 0.906075i | \(0.360936\pi\) | |||||||
\(80\) | −1.05474e24 | −1.71602 | ||||||||
\(81\) | 2.45383e23 | 0.341808 | ||||||||
\(82\) | −6.27831e22 | −0.0750187 | ||||||||
\(83\) | 1.41422e22 | 0.0145225 | 0.00726125 | − | 0.999974i | \(-0.497689\pi\) | ||||
0.00726125 | + | 0.999974i | \(0.497689\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.79771e24 | −2.13337 | ||||||||
\(86\) | 8.65451e22 | 0.0570180 | ||||||||
\(87\) | −5.37026e24 | −3.06199 | ||||||||
\(88\) | 4.97712e22 | 0.0246005 | ||||||||
\(89\) | −2.95320e24 | −1.26741 | −0.633705 | − | 0.773575i | \(-0.718467\pi\) | ||||
−0.633705 | + | 0.773575i | \(0.718467\pi\) | |||||||
\(90\) | −4.23404e23 | −0.158024 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.72336e24 | 1.62294 | ||||||||
\(93\) | 7.67825e24 | 1.90206 | ||||||||
\(94\) | 2.08005e23 | 0.0450792 | ||||||||
\(95\) | 5.49971e24 | 1.04423 | ||||||||
\(96\) | −1.54633e24 | −0.257579 | ||||||||
\(97\) | −1.91879e23 | −0.0280790 | −0.0140395 | − | 0.999901i | \(-0.504469\pi\) | ||||
−0.0140395 | + | 0.999901i | \(0.504469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.69063e24 | −0.418466 | ||||||||
\(100\) | −1.98741e25 | −1.98741 | ||||||||
\(101\) | 3.36187e24 | 0.296868 | 0.148434 | − | 0.988922i | \(-0.452577\pi\) | ||||
0.148434 | + | 0.988922i | \(0.452577\pi\) | |||||||
\(102\) | −1.36107e24 | −0.106262 | ||||||||
\(103\) | 1.48667e25 | 1.02742 | 0.513712 | − | 0.857962i | \(-0.328270\pi\) | ||||
0.513712 | + | 0.857962i | \(0.328270\pi\) | |||||||
\(104\) | −1.34120e24 | −0.0821445 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.85689e23 | 0.0234442 | ||||||||
\(107\) | 4.59102e24 | 0.197066 | 0.0985330 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985330 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(108\) | 3.30354e25 | 1.26236 | ||||||||
\(109\) | −2.07503e25 | −0.706633 | −0.353317 | − | 0.935504i | \(-0.614946\pi\) | ||||
−0.353317 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(110\) | 7.01364e23 | 0.0213076 | ||||||||
\(111\) | 1.64238e25 | 0.445591 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.42749e25 | 0.526838 | 0.263419 | − | 0.964682i | \(-0.415150\pi\) | ||||
0.263419 | + | 0.964682i | \(0.415150\pi\) | |||||||
\(114\) | 2.67557e24 | 0.0520123 | ||||||||
\(115\) | 1.61522e26 | 2.81520 | ||||||||
\(116\) | −1.17483e26 | −1.83759 | ||||||||
\(117\) | 9.94529e25 | 1.39731 | ||||||||
\(118\) | −4.10755e24 | −0.0518869 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.90801e25 | −0.297736 | ||||||||
\(121\) | −1.02234e26 | −0.943575 | ||||||||
\(122\) | −8.58069e24 | −0.0714536 | ||||||||
\(123\) | 3.19747e26 | 2.40432 | ||||||||
\(124\) | 1.67974e26 | 1.14149 | ||||||||
\(125\) | −2.79421e26 | −1.71745 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57593e26 | 0.794311 | 0.397156 | − | 0.917751i | \(-0.369997\pi\) | ||||
0.397156 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(128\) | −4.50841e25 | −0.206015 | ||||||||
\(129\) | −4.40764e26 | −1.82741 | ||||||||
\(130\) | −1.89000e25 | −0.0711490 | ||||||||
\(131\) | 8.74455e25 | 0.299121 | 0.149560 | − | 0.988753i | \(-0.452214\pi\) | ||||
0.149560 | + | 0.988753i | \(0.452214\pi\) | |||||||
\(132\) | −1.26569e26 | −0.393688 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.67942e25 | 0.0432862 | ||||||||
\(135\) | 9.32310e26 | 2.18972 | ||||||||
\(136\) | −5.96314e25 | −0.127714 | ||||||||
\(137\) | −6.03372e26 | −1.17917 | −0.589587 | − | 0.807705i | \(-0.700710\pi\) | ||||
−0.589587 | + | 0.807705i | \(0.700710\pi\) | |||||||
\(138\) | 7.85795e25 | 0.140224 | ||||||||
\(139\) | 5.46912e26 | 0.891729 | 0.445864 | − | 0.895101i | \(-0.352896\pi\) | ||||
0.445864 | + | 0.895101i | \(0.352896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.05935e27 | −1.44477 | ||||||||
\(142\) | 6.23752e25 | 0.0778767 | ||||||||
\(143\) | −1.64743e26 | −0.188411 | ||||||||
\(144\) | 1.66702e27 | 1.74747 | ||||||||
\(145\) | −3.31555e27 | −3.18754 | ||||||||
\(146\) | 1.12229e25 | 0.00990133 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.59296e26 | 0.267412 | ||||||||
\(149\) | −1.57289e27 | −1.07615 | −0.538073 | − | 0.842898i | \(-0.680848\pi\) | ||||
−0.538073 | + | 0.842898i | \(0.680848\pi\) | |||||||
\(150\) | −2.72864e26 | −0.171714 | ||||||||
\(151\) | −1.68207e27 | −0.974165 | −0.487082 | − | 0.873356i | \(-0.661939\pi\) | ||||
−0.487082 | + | 0.873356i | \(0.661939\pi\) | |||||||
\(152\) | 1.17223e26 | 0.0625124 | ||||||||
\(153\) | 4.42178e27 | 2.17247 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.74048e27 | 1.98005 | ||||||||
\(156\) | 3.41070e27 | 1.31458 | ||||||||
\(157\) | −2.58732e27 | −0.920672 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(158\) | 1.33496e26 | 0.0438787 | ||||||||
\(159\) | −2.47356e27 | −0.751377 | ||||||||
\(160\) | −9.54688e26 | −0.268140 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.37025e25 | 0.0177233 | ||||||||
\(163\) | −6.00179e27 | −1.33640 | −0.668199 | − | 0.743983i | \(-0.732935\pi\) | ||||
−0.668199 | + | 0.743983i | \(0.732935\pi\) | |||||||
\(164\) | 6.99497e27 | 1.44291 | ||||||||
\(165\) | −3.57197e27 | −0.682902 | ||||||||
\(166\) | 4.24771e24 | 0.000753016 0 | ||||||||
\(167\) | −4.11051e27 | −0.675989 | −0.337995 | − | 0.941148i | \(-0.609749\pi\) | ||||
−0.337995 | + | 0.941148i | \(0.609749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.61702e27 | −0.370871 | ||||||||
\(170\) | −8.40313e26 | −0.110619 | ||||||||
\(171\) | −8.69228e27 | −1.06336 | ||||||||
\(172\) | −9.64241e27 | −1.09668 | ||||||||
\(173\) | 5.87547e27 | 0.621536 | 0.310768 | − | 0.950486i | \(-0.399414\pi\) | ||||
0.310768 | + | 0.950486i | \(0.399414\pi\) | |||||||
\(174\) | −1.61299e27 | −0.158769 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.76141e27 | −0.235625 | ||||||||
\(177\) | 2.09193e28 | 1.66296 | ||||||||
\(178\) | −8.87013e26 | −0.0657173 | ||||||||
\(179\) | 2.78322e27 | 0.192258 | 0.0961292 | − | 0.995369i | \(-0.469354\pi\) | ||||
0.0961292 | + | 0.995369i | \(0.469354\pi\) | |||||||
\(180\) | 4.71735e28 | 3.03943 | ||||||||
\(181\) | −2.86445e28 | −1.72210 | −0.861051 | − | 0.508519i | \(-0.830193\pi\) | ||||
−0.861051 | + | 0.508519i | \(0.830193\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.37005e28 | 2.29006 | ||||||||
\(184\) | 3.44274e27 | 0.168531 | ||||||||
\(185\) | 1.01399e28 | 0.463860 | ||||||||
\(186\) | 2.30621e27 | 0.0986252 | ||||||||
\(187\) | −7.32464e27 | −0.292932 | ||||||||
\(188\) | −2.31749e28 | −0.867051 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.65187e27 | 0.0541449 | ||||||||
\(191\) | 3.65037e28 | 1.12052 | 0.560261 | − | 0.828316i | \(-0.310701\pi\) | ||||
0.560261 | + | 0.828316i | \(0.310701\pi\) | |||||||
\(192\) | 5.68596e28 | 1.63508 | ||||||||
\(193\) | 4.22298e28 | 1.13803 | 0.569014 | − | 0.822328i | \(-0.307325\pi\) | ||||
0.569014 | + | 0.822328i | \(0.307325\pi\) | |||||||
\(194\) | −5.76322e25 | −0.00145594 | ||||||||
\(195\) | 9.62553e28 | 2.28030 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.69294e28 | −0.770096 | −0.385048 | − | 0.922896i | \(-0.625815\pi\) | ||||
−0.385048 | + | 0.922896i | \(0.625815\pi\) | |||||||
\(198\) | −1.10850e27 | −0.0216982 | ||||||||
\(199\) | 4.31066e28 | 0.792283 | 0.396142 | − | 0.918189i | \(-0.370349\pi\) | ||||
0.396142 | + | 0.918189i | \(0.370349\pi\) | |||||||
\(200\) | −1.19547e28 | −0.206379 | ||||||||
\(201\) | −8.55310e28 | −1.38731 | ||||||||
\(202\) | 1.00976e27 | 0.0153931 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.51644e29 | 2.04384 | ||||||||
\(205\) | 1.97409e29 | 2.50290 | ||||||||
\(206\) | 4.46532e27 | 0.0532737 | ||||||||
\(207\) | −2.55285e29 | −2.86680 | ||||||||
\(208\) | 7.44128e28 | 0.786785 | ||||||||
\(209\) | 1.43987e28 | 0.143382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.08925e29 | 0.962934 | 0.481467 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481467 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(212\) | −5.41129e28 | −0.450923 | ||||||||
\(213\) | −3.17670e29 | −2.49592 | ||||||||
\(214\) | 1.37894e27 | 0.0102182 | ||||||||
\(215\) | −2.72124e29 | −1.90233 | ||||||||
\(216\) | 1.98716e28 | 0.131087 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.23251e27 | −0.0366401 | ||||||||
\(219\) | −5.71568e28 | −0.317334 | ||||||||
\(220\) | −7.81424e28 | −0.409830 | ||||||||
\(221\) | 1.97380e29 | 0.978138 | ||||||||
\(222\) | 4.93300e27 | 0.0231046 | ||||||||
\(223\) | −3.47042e28 | −0.153663 | −0.0768317 | − | 0.997044i | \(-0.524480\pi\) | ||||
−0.0768317 | + | 0.997044i | \(0.524480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.86467e29 | 3.51060 | ||||||||
\(226\) | 7.29113e27 | 0.0273174 | ||||||||
\(227\) | −2.93853e29 | −1.04185 | −0.520927 | − | 0.853601i | \(-0.674414\pi\) | ||||
−0.520927 | + | 0.853601i | \(0.674414\pi\) | |||||||
\(228\) | −2.98099e29 | −1.00040 | ||||||||
\(229\) | −2.73707e29 | −0.869646 | −0.434823 | − | 0.900516i | \(-0.643189\pi\) | ||||
−0.434823 | + | 0.900516i | \(0.643189\pi\) | |||||||
\(230\) | 4.85143e28 | 0.145973 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.06686e28 | −0.190821 | ||||||||
\(233\) | 5.86808e29 | 1.50157 | 0.750787 | − | 0.660544i | \(-0.229674\pi\) | ||||
0.750787 | + | 0.660544i | \(0.229674\pi\) | |||||||
\(234\) | 2.98714e28 | 0.0724531 | ||||||||
\(235\) | −6.54031e29 | −1.50401 | ||||||||
\(236\) | 4.57642e29 | 0.997989 | ||||||||
\(237\) | −6.79878e29 | −1.40630 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.68799e29 | 1.24544 | 0.622719 | − | 0.782446i | \(-0.286028\pi\) | ||||
0.622719 | + | 0.782446i | \(0.286028\pi\) | |||||||
\(240\) | 1.61343e30 | 2.85173 | ||||||||
\(241\) | 4.01605e29 | 0.673885 | 0.336943 | − | 0.941525i | \(-0.390607\pi\) | ||||
0.336943 | + | 0.941525i | \(0.390607\pi\) | |||||||
\(242\) | −3.07066e28 | −0.0489259 | ||||||||
\(243\) | 4.61073e29 | 0.697736 | ||||||||
\(244\) | 9.56017e29 | 1.37433 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.60382e28 | 0.124668 | ||||||||
\(247\) | −3.88007e29 | −0.478771 | ||||||||
\(248\) | 1.01040e29 | 0.118535 | ||||||||
\(249\) | −2.16331e28 | −0.0241339 | ||||||||
\(250\) | −8.39261e28 | −0.0890526 | ||||||||
\(251\) | −1.15661e29 | −0.116752 | −0.0583762 | − | 0.998295i | \(-0.518592\pi\) | ||||
−0.0583762 | + | 0.998295i | \(0.518592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.22878e29 | 0.386553 | ||||||||
\(254\) | 4.73342e28 | 0.0411863 | ||||||||
\(255\) | 4.27962e30 | 3.54530 | ||||||||
\(256\) | 1.23371e30 | 0.973222 | ||||||||
\(257\) | 1.30924e30 | 0.983682 | 0.491841 | − | 0.870685i | \(-0.336324\pi\) | ||||
0.491841 | + | 0.870685i | \(0.336324\pi\) | |||||||
\(258\) | −1.32387e29 | −0.0947540 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.10574e30 | 1.36848 | ||||||||
\(261\) | 5.24021e30 | 3.24596 | ||||||||
\(262\) | 2.62649e28 | 0.0155099 | ||||||||
\(263\) | −2.36399e30 | −1.33107 | −0.665533 | − | 0.746369i | \(-0.731796\pi\) | ||||
−0.665533 | + | 0.746369i | \(0.731796\pi\) | |||||||
\(264\) | −7.61341e28 | −0.0408818 | ||||||||
\(265\) | −1.52715e30 | −0.782183 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.51746e30 | 2.10622 | ||||||||
\(268\) | −1.87112e30 | −0.832564 | ||||||||
\(269\) | −9.03280e29 | −0.383636 | −0.191818 | − | 0.981431i | \(-0.561438\pi\) | ||||
−0.191818 | + | 0.981431i | \(0.561438\pi\) | |||||||
\(270\) | 2.80026e29 | 0.113541 | ||||||||
\(271\) | 2.30713e30 | 0.893215 | 0.446608 | − | 0.894730i | \(-0.352632\pi\) | ||||
0.446608 | + | 0.894730i | \(0.352632\pi\) | |||||||
\(272\) | 3.30847e30 | 1.22325 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.81227e29 | −0.0611422 | ||||||||
\(275\) | −1.46842e30 | −0.473361 | ||||||||
\(276\) | −8.75493e30 | −2.69705 | ||||||||
\(277\) | −2.38991e30 | −0.703694 | −0.351847 | − | 0.936057i | \(-0.614446\pi\) | ||||
−0.351847 | + | 0.936057i | \(0.614446\pi\) | |||||||
\(278\) | 1.64269e29 | 0.0462376 | ||||||||
\(279\) | −7.49232e30 | −2.01634 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.32085e30 | −1.06351 | −0.531753 | − | 0.846899i | \(-0.678467\pi\) | ||||
−0.531753 | + | 0.846899i | \(0.678467\pi\) | |||||||
\(282\) | −3.18182e29 | −0.0749139 | ||||||||
\(283\) | −1.53040e30 | −0.344725 | −0.172363 | − | 0.985034i | \(-0.555140\pi\) | ||||
−0.172363 | + | 0.985034i | \(0.555140\pi\) | |||||||
\(284\) | −6.94952e30 | −1.49788 | ||||||||
\(285\) | −8.41281e30 | −1.73532 | ||||||||
\(286\) | −4.94816e28 | −0.00976941 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.50888e30 | 0.273055 | ||||||||
\(289\) | 3.00511e30 | 0.520760 | ||||||||
\(290\) | −9.95847e29 | −0.165279 | ||||||||
\(291\) | 2.93514e29 | 0.0466624 | ||||||||
\(292\) | −1.25040e30 | −0.190442 | ||||||||
\(293\) | 2.06559e30 | 0.301438 | 0.150719 | − | 0.988577i | \(-0.451841\pi\) | ||||
0.150719 | + | 0.988577i | \(0.451841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.29154e31 | 1.73114 | ||||||||
\(296\) | 2.16125e29 | 0.0277689 | ||||||||
\(297\) | 2.44086e30 | 0.300668 | ||||||||
\(298\) | −4.72430e29 | −0.0558000 | ||||||||
\(299\) | −1.13955e31 | −1.29075 | ||||||||
\(300\) | 3.04011e31 | 3.30273 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.05221e29 | −0.0505120 | ||||||||
\(303\) | −5.14260e30 | −0.493344 | ||||||||
\(304\) | −6.50375e30 | −0.598748 | ||||||||
\(305\) | 2.69803e31 | 2.38396 | ||||||||
\(306\) | 1.32811e30 | 0.112646 | ||||||||
\(307\) | −1.61945e31 | −1.31867 | −0.659337 | − | 0.751848i | \(-0.729163\pi\) | ||||
−0.659337 | + | 0.751848i | \(0.729163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.27414e31 | −1.70740 | ||||||||
\(310\) | 1.42384e30 | 0.102669 | ||||||||
\(311\) | 1.32005e31 | 0.914294 | 0.457147 | − | 0.889391i | \(-0.348871\pi\) | ||||
0.457147 | + | 0.889391i | \(0.348871\pi\) | |||||||
\(312\) | 2.05162e30 | 0.136510 | ||||||||
\(313\) | −1.51942e31 | −0.971344 | −0.485672 | − | 0.874141i | \(-0.661425\pi\) | ||||
−0.485672 | + | 0.874141i | \(0.661425\pi\) | |||||||
\(314\) | −7.77120e29 | −0.0477383 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.48734e31 | −0.843960 | ||||||||
\(317\) | −1.02409e29 | −0.00558593 | −0.00279297 | − | 0.999996i | \(-0.500889\pi\) | ||||
−0.00279297 | + | 0.999996i | \(0.500889\pi\) | |||||||
\(318\) | −7.42950e29 | −0.0389601 | ||||||||
\(319\) | −8.68036e30 | −0.437678 | ||||||||
\(320\) | 3.51046e31 | 1.70212 | ||||||||
\(321\) | −7.02280e30 | −0.327490 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.72512e31 | −0.744369 | ||||||||
\(324\) | −8.21156e30 | −0.340889 | ||||||||
\(325\) | 3.95702e31 | 1.58062 | ||||||||
\(326\) | −1.80268e30 | −0.0692944 | ||||||||
\(327\) | 3.17414e31 | 1.17430 | ||||||||
\(328\) | 4.20764e30 | 0.149836 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.07286e30 | −0.0354096 | ||||||||
\(331\) | 5.49413e30 | 0.174602 | 0.0873009 | − | 0.996182i | \(-0.472176\pi\) | ||||
0.0873009 | + | 0.996182i | \(0.472176\pi\) | |||||||
\(332\) | −4.73258e29 | −0.0144835 | ||||||||
\(333\) | −1.60261e31 | −0.472362 | ||||||||
\(334\) | −1.23462e30 | −0.0350512 | ||||||||
\(335\) | −5.28060e31 | −1.44419 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.63930e31 | −1.17782 | −0.588910 | − | 0.808198i | \(-0.700443\pi\) | ||||
−0.588910 | + | 0.808198i | \(0.700443\pi\) | |||||||
\(338\) | −7.86039e29 | −0.0192303 | ||||||||
\(339\) | −3.71329e31 | −0.875513 | ||||||||
\(340\) | 9.36233e31 | 2.12764 | ||||||||
\(341\) | 1.24110e31 | 0.271879 | ||||||||
\(342\) | −2.61079e30 | −0.0551372 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.80014e30 | −0.113883 | ||||||||
\(345\) | −2.47078e32 | −4.67837 | ||||||||
\(346\) | 1.76474e30 | 0.0322276 | ||||||||
\(347\) | 4.66143e30 | 0.0821110 | 0.0410555 | − | 0.999157i | \(-0.486928\pi\) | ||||
0.0410555 | + | 0.999157i | \(0.486928\pi\) | |||||||
\(348\) | 1.79711e32 | 3.05376 | ||||||||
\(349\) | −1.05203e32 | −1.72469 | −0.862344 | − | 0.506322i | \(-0.831005\pi\) | ||||
−0.862344 | + | 0.506322i | \(0.831005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.57750e31 | −1.00397 | ||||||||
\(352\) | −2.49945e30 | −0.0368181 | ||||||||
\(353\) | −3.18266e31 | −0.452487 | −0.226244 | − | 0.974071i | \(-0.572645\pi\) | ||||
−0.226244 | + | 0.974071i | \(0.572645\pi\) | |||||||
\(354\) | 6.28325e30 | 0.0862270 | ||||||||
\(355\) | −1.96126e32 | −2.59825 | ||||||||
\(356\) | 9.88264e31 | 1.26400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.35960e29 | 0.00996891 | ||||||||
\(359\) | 8.23739e31 | 0.948656 | 0.474328 | − | 0.880348i | \(-0.342691\pi\) | ||||
0.474328 | + | 0.880348i | \(0.342691\pi\) | |||||||
\(360\) | 2.83759e31 | 0.315623 | ||||||||
\(361\) | −5.91643e31 | −0.635652 | ||||||||
\(362\) | −8.60357e30 | −0.0892938 | ||||||||
\(363\) | 1.56385e32 | 1.56806 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.52881e31 | −0.330345 | ||||||||
\(366\) | 1.31257e31 | 0.118744 | ||||||||
\(367\) | 9.43154e31 | 0.824625 | 0.412313 | − | 0.911042i | \(-0.364721\pi\) | ||||
0.412313 | + | 0.911042i | \(0.364721\pi\) | |||||||
\(368\) | −1.91010e32 | −1.61420 | ||||||||
\(369\) | −3.12004e32 | −2.54877 | ||||||||
\(370\) | 3.04559e30 | 0.0240519 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.56947e32 | −1.89695 | ||||||||
\(373\) | −1.43554e32 | −1.02484 | −0.512420 | − | 0.858735i | \(-0.671251\pi\) | ||||
−0.512420 | + | 0.858735i | \(0.671251\pi\) | |||||||
\(374\) | −2.20001e30 | −0.0151890 | ||||||||
\(375\) | 4.27426e32 | 2.85410 | ||||||||
\(376\) | −1.39402e31 | −0.0900372 | ||||||||
\(377\) | 2.33913e32 | 1.46146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.58402e31 | −0.501996 | −0.250998 | − | 0.967988i | \(-0.580759\pi\) | ||||
−0.250998 | + | 0.967988i | \(0.580759\pi\) | |||||||
\(380\) | −1.84043e32 | −1.04142 | ||||||||
\(381\) | −2.41067e32 | −1.32001 | ||||||||
\(382\) | 1.09641e31 | 0.0581009 | ||||||||
\(383\) | 1.23830e31 | 0.0635098 | 0.0317549 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317549 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(384\) | 6.89643e31 | 0.342361 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.26840e31 | 0.0590086 | ||||||||
\(387\) | 4.30091e32 | 1.93720 | ||||||||
\(388\) | 6.42108e30 | 0.0280035 | ||||||||
\(389\) | 1.04615e32 | 0.441798 | 0.220899 | − | 0.975297i | \(-0.429101\pi\) | ||||
0.220899 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(390\) | 2.89110e31 | 0.118237 | ||||||||
\(391\) | −5.06655e32 | −2.00679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.33764e32 | −0.497087 | ||||||||
\(394\) | −1.10920e31 | −0.0399308 | ||||||||
\(395\) | −4.19750e32 | −1.46395 | ||||||||
\(396\) | 1.23504e32 | 0.417341 | ||||||||
\(397\) | 6.93650e31 | 0.227122 | 0.113561 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113561 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(398\) | 1.29474e31 | 0.0410812 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.63273e32 | 1.97671 | ||||||||
\(401\) | −1.05318e32 | −0.304226 | −0.152113 | − | 0.988363i | \(-0.548608\pi\) | ||||
−0.152113 | + | 0.988363i | \(0.548608\pi\) | |||||||
\(402\) | −2.56898e31 | −0.0719342 | ||||||||
\(403\) | −3.34443e32 | −0.907840 | ||||||||
\(404\) | −1.12502e32 | −0.296070 | ||||||||
\(405\) | −2.31743e32 | −0.591315 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.65471e31 | 0.0636922 | ||||||||
\(408\) | 9.12172e31 | 0.212239 | ||||||||
\(409\) | 5.60357e32 | 1.26451 | 0.632257 | − | 0.774759i | \(-0.282129\pi\) | ||||
0.632257 | + | 0.774759i | \(0.282129\pi\) | |||||||
\(410\) | 5.92931e31 | 0.129780 | ||||||||
\(411\) | 9.22968e32 | 1.95958 | ||||||||
\(412\) | −4.97503e32 | −1.02466 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.66767e31 | −0.148648 | ||||||||
\(415\) | −1.33561e31 | −0.0251234 | ||||||||
\(416\) | 6.73537e31 | 0.122941 | ||||||||
\(417\) | −8.36603e32 | −1.48190 | ||||||||
\(418\) | 4.32474e30 | 0.00743458 | ||||||||
\(419\) | 8.52671e32 | 1.42268 | 0.711339 | − | 0.702849i | \(-0.248089\pi\) | ||||
0.711339 | + | 0.702849i | \(0.248089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.69154e32 | −0.737546 | −0.368773 | − | 0.929519i | \(-0.620222\pi\) | ||||
−0.368773 | + | 0.929519i | \(0.620222\pi\) | |||||||
\(422\) | 3.27163e31 | 0.0499297 | ||||||||
\(423\) | 1.03370e33 | 1.53157 | ||||||||
\(424\) | −3.25502e31 | −0.0468253 | ||||||||
\(425\) | 1.75934e33 | 2.45746 | ||||||||
\(426\) | −9.54143e31 | −0.129418 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.53635e32 | −0.196536 | ||||||||
\(429\) | 2.52004e32 | 0.313106 | ||||||||
\(430\) | −8.17343e31 | −0.0986389 | ||||||||
\(431\) | −1.15764e33 | −1.35708 | −0.678542 | − | 0.734562i | \(-0.737388\pi\) | ||||
−0.678542 | + | 0.734562i | \(0.737388\pi\) | |||||||
\(432\) | −1.10252e33 | −1.25556 | ||||||||
\(433\) | −7.58667e32 | −0.839368 | −0.419684 | − | 0.907670i | \(-0.637859\pi\) | ||||
−0.419684 | + | 0.907670i | \(0.637859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.07173e33 | 5.29713 | ||||||||
\(436\) | 6.94394e32 | 0.704733 | ||||||||
\(437\) | 9.95975e32 | 0.982269 | ||||||||
\(438\) | −1.71674e31 | −0.0164543 | ||||||||
\(439\) | −1.86519e33 | −1.73746 | −0.868732 | − | 0.495283i | \(-0.835064\pi\) | ||||
−0.868732 | + | 0.495283i | \(0.835064\pi\) | |||||||
\(440\) | −4.70045e31 | −0.0425580 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.92845e31 | 0.0507181 | ||||||||
\(443\) | 8.79334e32 | 0.731320 | 0.365660 | − | 0.930749i | \(-0.380843\pi\) | ||||
0.365660 | + | 0.930749i | \(0.380843\pi\) | |||||||
\(444\) | −5.49609e32 | −0.444393 | ||||||||
\(445\) | 2.78903e33 | 2.19257 | ||||||||
\(446\) | −1.04236e31 | −0.00796771 | ||||||||
\(447\) | 2.40603e33 | 1.78837 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.64616e33 | −1.15716 | −0.578578 | − | 0.815627i | \(-0.696392\pi\) | ||||
−0.578578 | + | 0.815627i | \(0.696392\pi\) | |||||||
\(450\) | 2.66256e32 | 0.182030 | ||||||||
\(451\) | 5.16832e32 | 0.343671 | ||||||||
\(452\) | −8.12340e32 | −0.525421 | ||||||||
\(453\) | 2.57303e33 | 1.61889 | ||||||||
\(454\) | −8.82607e31 | −0.0540218 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.79313e32 | −0.103885 | ||||||||
\(457\) | 1.49461e32 | 0.0842509 | 0.0421255 | − | 0.999112i | \(-0.486587\pi\) | ||||
0.0421255 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(458\) | −8.22098e31 | −0.0450926 | ||||||||
\(459\) | −2.92443e33 | −1.56093 | ||||||||
\(460\) | −5.40521e33 | −2.80763 | ||||||||
\(461\) | 1.53425e33 | 0.775594 | 0.387797 | − | 0.921745i | \(-0.373236\pi\) | ||||
0.387797 | + | 0.921745i | \(0.373236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.72850e33 | 0.827765 | 0.413883 | − | 0.910330i | \(-0.364172\pi\) | ||||
0.413883 | + | 0.910330i | \(0.364172\pi\) | |||||||
\(464\) | 3.92084e33 | 1.82770 | ||||||||
\(465\) | −7.25143e33 | −3.29050 | ||||||||
\(466\) | 1.76252e32 | 0.0778591 | ||||||||
\(467\) | 5.52669e32 | 0.237686 | 0.118843 | − | 0.992913i | \(-0.462081\pi\) | ||||
0.118843 | + | 0.992913i | \(0.462081\pi\) | |||||||
\(468\) | −3.32811e33 | −1.39356 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.96443e32 | −0.0779853 | ||||||||
\(471\) | 3.95778e33 | 1.53000 | ||||||||
\(472\) | 2.75282e32 | 0.103634 | ||||||||
\(473\) | −7.12442e32 | −0.261207 | ||||||||
\(474\) | −2.04206e32 | −0.0729188 | ||||||||
\(475\) | −3.45848e33 | −1.20286 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41366e33 | 0.796519 | ||||||||
\(478\) | 2.00878e32 | 0.0645780 | ||||||||
\(479\) | −5.94920e33 | −1.86322 | −0.931611 | − | 0.363456i | \(-0.881597\pi\) | ||||
−0.931611 | + | 0.363456i | \(0.881597\pi\) | |||||||
\(480\) | 1.46037e33 | 0.445602 | ||||||||
\(481\) | −7.15375e32 | −0.212677 | ||||||||
\(482\) | 1.20625e32 | 0.0349421 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.42117e33 | 0.941038 | ||||||||
\(485\) | 1.81213e32 | 0.0485755 | ||||||||
\(486\) | 1.38486e32 | 0.0361788 | ||||||||
\(487\) | −1.29730e33 | −0.330316 | −0.165158 | − | 0.986267i | \(-0.552813\pi\) | ||||
−0.165158 | + | 0.986267i | \(0.552813\pi\) | |||||||
\(488\) | 5.75066e32 | 0.142715 | ||||||||
\(489\) | 9.18084e33 | 2.22086 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.96688e33 | −0.452125 | −0.226062 | − | 0.974113i | \(-0.572585\pi\) | ||||
−0.226062 | + | 0.974113i | \(0.572585\pi\) | |||||||
\(492\) | −1.07001e34 | −2.39786 | ||||||||
\(493\) | 1.04000e34 | 2.27221 | ||||||||
\(494\) | −1.16541e32 | −0.0248251 | ||||||||
\(495\) | 3.48547e33 | 0.723930 | ||||||||
\(496\) | −5.60591e33 | −1.13534 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.49765e30 | −0.00125138 | ||||||||
\(499\) | −3.31607e33 | −0.622827 | −0.311413 | − | 0.950275i | \(-0.600802\pi\) | ||||
−0.311413 | + | 0.950275i | \(0.600802\pi\) | |||||||
\(500\) | 9.35061e33 | 1.71283 | ||||||||
\(501\) | 6.28778e33 | 1.12338 | ||||||||
\(502\) | −3.47396e31 | −0.00605380 | ||||||||
\(503\) | 3.38649e33 | 0.575640 | 0.287820 | − | 0.957685i | \(-0.407070\pi\) | ||||
0.287820 | + | 0.957685i | \(0.407070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.17499e33 | −0.513571 | ||||||||
\(506\) | 1.27014e32 | 0.0200434 | ||||||||
\(507\) | 4.00321e33 | 0.616323 | ||||||||
\(508\) | −5.27373e33 | −0.792175 | ||||||||
\(509\) | −4.03391e33 | −0.591227 | −0.295613 | − | 0.955308i | \(-0.595524\pi\) | ||||
−0.295613 | + | 0.955308i | \(0.595524\pi\) | |||||||
\(510\) | 1.28541e33 | 0.183830 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.88332e33 | 0.256478 | ||||||||
\(513\) | 5.74880e33 | 0.764029 | ||||||||
\(514\) | 3.93239e32 | 0.0510055 | ||||||||
\(515\) | −1.40403e34 | −1.77741 | ||||||||
\(516\) | 1.47498e34 | 1.82249 | ||||||||
\(517\) | −1.71231e33 | −0.206514 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.98760e33 | −1.03288 | ||||||||
\(520\) | 1.26665e33 | 0.142107 | ||||||||
\(521\) | 7.20328e32 | 0.0788967 | 0.0394483 | − | 0.999222i | \(-0.487440\pi\) | ||||
0.0394483 | + | 0.999222i | \(0.487440\pi\) | |||||||
\(522\) | 1.57393e33 | 0.168308 | ||||||||
\(523\) | 7.40980e33 | 0.773634 | 0.386817 | − | 0.922156i | \(-0.373574\pi\) | ||||
0.386817 | + | 0.922156i | \(0.373574\pi\) | |||||||
\(524\) | −2.92630e33 | −0.298316 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.10041e32 | −0.0690179 | ||||||||
\(527\) | −1.48697e34 | −1.41146 | ||||||||
\(528\) | 4.22408e33 | 0.391569 | ||||||||
\(529\) | 1.82053e34 | 1.64817 | ||||||||
\(530\) | −4.58690e32 | −0.0405575 | ||||||||
\(531\) | −2.04127e34 | −1.76287 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.39273e34 | −1.14756 | ||||||||
\(534\) | 1.35685e33 | 0.109211 | ||||||||
\(535\) | −4.33581e33 | −0.340917 | ||||||||
\(536\) | −1.12552e33 | −0.0864560 | ||||||||
\(537\) | −4.25745e33 | −0.319500 | ||||||||
\(538\) | −2.71306e32 | −0.0198921 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.11990e34 | −2.18383 | ||||||||
\(541\) | −2.28059e34 | −1.55985 | −0.779923 | − | 0.625876i | \(-0.784742\pi\) | ||||
−0.779923 | + | 0.625876i | \(0.784742\pi\) | |||||||
\(542\) | 6.92963e32 | 0.0463147 | ||||||||
\(543\) | 4.38170e34 | 2.86184 | ||||||||
\(544\) | 2.99462e33 | 0.191142 | ||||||||
\(545\) | 1.95969e34 | 1.22245 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.07649e33 | 0.421674 | 0.210837 | − | 0.977521i | \(-0.432381\pi\) | ||||
0.210837 | + | 0.977521i | \(0.432381\pi\) | |||||||
\(548\) | 2.01914e34 | 1.17600 | ||||||||
\(549\) | −4.26423e34 | −2.42765 | ||||||||
\(550\) | −4.41051e32 | −0.0245446 | ||||||||
\(551\) | −2.04443e34 | −1.11218 | ||||||||
\(552\) | −5.26630e33 | −0.280070 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.17825e32 | −0.0364877 | ||||||||
\(555\) | −1.55108e34 | −0.770855 | ||||||||
\(556\) | −1.83020e34 | −0.889331 | ||||||||
\(557\) | −3.52550e34 | −1.67506 | −0.837530 | − | 0.546391i | \(-0.816001\pi\) | ||||
−0.837530 | + | 0.546391i | \(0.816001\pi\) | |||||||
\(558\) | −2.25037e33 | −0.104551 | ||||||||
\(559\) | 1.91985e34 | 0.872206 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.12044e34 | 0.486802 | ||||||||
\(562\) | −1.29780e33 | −0.0551446 | ||||||||
\(563\) | 5.41988e33 | 0.225234 | 0.112617 | − | 0.993638i | \(-0.464077\pi\) | ||||
0.112617 | + | 0.993638i | \(0.464077\pi\) | |||||||
\(564\) | 3.54502e34 | 1.44089 | ||||||||
\(565\) | −2.29255e34 | −0.911409 | ||||||||
\(566\) | −4.59665e32 | −0.0178746 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.18030e33 | −0.155544 | ||||||||
\(569\) | 3.14649e33 | 0.114531 | 0.0572655 | − | 0.998359i | \(-0.481762\pi\) | ||||
0.0572655 | + | 0.998359i | \(0.481762\pi\) | |||||||
\(570\) | −2.52685e33 | −0.0899794 | ||||||||
\(571\) | 1.08463e34 | 0.377860 | 0.188930 | − | 0.981991i | \(-0.439498\pi\) | ||||
0.188930 | + | 0.981991i | \(0.439498\pi\) | |||||||
\(572\) | 5.51299e33 | 0.187904 | ||||||||
\(573\) | −5.58391e34 | −1.86211 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.01573e35 | −3.24287 | ||||||||
\(576\) | −5.54828e34 | −1.73331 | ||||||||
\(577\) | 2.14266e34 | 0.655023 | 0.327512 | − | 0.944847i | \(-0.393790\pi\) | ||||
0.327512 | + | 0.944847i | \(0.393790\pi\) | |||||||
\(578\) | 9.02606e32 | 0.0270023 | ||||||||
\(579\) | −6.45982e34 | −1.89120 | ||||||||
\(580\) | 1.10952e35 | 3.17897 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.81590e31 | 0.00241952 | ||||||||
\(583\) | −3.99820e33 | −0.107401 | ||||||||
\(584\) | −7.52142e32 | −0.0197760 | ||||||||
\(585\) | −9.39245e34 | −2.41730 | ||||||||
\(586\) | 6.20413e32 | 0.0156301 | ||||||||
\(587\) | −1.24448e34 | −0.306911 | −0.153455 | − | 0.988156i | \(-0.549040\pi\) | ||||
−0.153455 | + | 0.988156i | \(0.549040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.92307e34 | 0.690872 | ||||||||
\(590\) | 3.87922e33 | 0.0897623 | ||||||||
\(591\) | 5.64904e34 | 1.27977 | ||||||||
\(592\) | −1.19911e34 | −0.265972 | ||||||||
\(593\) | 3.18871e34 | 0.692519 | 0.346260 | − | 0.938139i | \(-0.387452\pi\) | ||||
0.346260 | + | 0.938139i | \(0.387452\pi\) | |||||||
\(594\) | 7.33130e32 | 0.0155902 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.26357e34 | 1.07325 | ||||||||
\(597\) | −6.59395e34 | −1.31664 | ||||||||
\(598\) | −3.42271e33 | −0.0669276 | ||||||||
\(599\) | 8.22623e34 | 1.57531 | 0.787655 | − | 0.616117i | \(-0.211295\pi\) | ||||
0.787655 | + | 0.616117i | \(0.211295\pi\) | |||||||
\(600\) | 1.82870e34 | 0.342966 | ||||||||
\(601\) | 4.72278e34 | 0.867495 | 0.433747 | − | 0.901034i | \(-0.357191\pi\) | ||||
0.433747 | + | 0.901034i | \(0.357191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.34598e34 | 1.47066 | ||||||||
\(604\) | 5.62892e34 | 0.971545 | ||||||||
\(605\) | 9.65506e34 | 1.63235 | ||||||||
\(606\) | −1.54461e33 | −0.0255807 | ||||||||
\(607\) | 8.65747e34 | 1.40453 | 0.702267 | − | 0.711913i | \(-0.252171\pi\) | ||||
0.702267 | + | 0.711913i | \(0.252171\pi\) | |||||||
\(608\) | −5.88678e33 | −0.0935585 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.10371e33 | 0.123612 | ||||||||
\(611\) | 4.61423e34 | 0.689579 | ||||||||
\(612\) | −1.47972e35 | −2.16663 | ||||||||
\(613\) | 1.01940e35 | 1.46247 | 0.731235 | − | 0.682125i | \(-0.238944\pi\) | ||||
0.731235 | + | 0.682125i | \(0.238944\pi\) | |||||||
\(614\) | −4.86412e33 | −0.0683754 | ||||||||
\(615\) | −3.01973e35 | −4.15939 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.76112e34 | 0.365192 | 0.182596 | − | 0.983188i | \(-0.441550\pi\) | ||||
0.182596 | + | 0.983188i | \(0.441550\pi\) | |||||||
\(618\) | −6.83053e33 | −0.0885316 | ||||||||
\(619\) | 8.47803e34 | 1.07687 | 0.538433 | − | 0.842668i | \(-0.319016\pi\) | ||||
0.538433 | + | 0.842668i | \(0.319016\pi\) | |||||||
\(620\) | −1.58636e35 | −1.97473 | ||||||||
\(621\) | 1.68838e35 | 2.05980 | ||||||||
\(622\) | 3.96486e33 | 0.0474077 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.13828e35 | −1.30750 | ||||||||
\(625\) | 8.68954e34 | 0.978355 | ||||||||
\(626\) | −4.56368e33 | −0.0503658 | ||||||||
\(627\) | −2.20254e34 | −0.238276 | ||||||||
\(628\) | 8.65827e34 | 0.918196 | ||||||||
\(629\) | −3.18063e34 | −0.330659 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.38341e34 | −0.837633 | −0.418817 | − | 0.908071i | \(-0.637555\pi\) | ||||
−0.418817 | + | 0.908071i | \(0.637555\pi\) | |||||||
\(632\) | −8.94670e33 | −0.0876394 | ||||||||
\(633\) | −1.66621e35 | −1.60023 | ||||||||
\(634\) | −3.07591e31 | −0.000289640 0 | ||||||||
\(635\) | −1.48833e35 | −1.37413 | ||||||||
\(636\) | 8.27756e34 | 0.749357 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.60721e33 | −0.0226943 | ||||||||
\(639\) | 3.09977e35 | 2.64587 | ||||||||
\(640\) | 4.25779e34 | 0.356398 | ||||||||
\(641\) | −2.39743e34 | −0.196798 | −0.0983990 | − | 0.995147i | \(-0.531372\pi\) | ||||
−0.0983990 | + | 0.995147i | \(0.531372\pi\) | |||||||
\(642\) | −2.10935e33 | −0.0169809 | ||||||||
\(643\) | 1.85782e35 | 1.46678 | 0.733391 | − | 0.679807i | \(-0.237937\pi\) | ||||
0.733391 | + | 0.679807i | \(0.237937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.16263e35 | 3.16134 | ||||||||
\(646\) | −5.18152e33 | −0.0385968 | ||||||||
\(647\) | 2.25609e35 | 1.64836 | 0.824181 | − | 0.566326i | \(-0.191636\pi\) | ||||
0.824181 | + | 0.566326i | \(0.191636\pi\) | |||||||
\(648\) | −4.93944e33 | −0.0353990 | ||||||||
\(649\) | 3.38135e34 | 0.237701 | ||||||||
\(650\) | 1.18852e34 | 0.0819576 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00845e35 | 1.33280 | ||||||||
\(653\) | 1.67096e35 | 1.08780 | 0.543902 | − | 0.839149i | \(-0.316946\pi\) | ||||
0.543902 | + | 0.839149i | \(0.316946\pi\) | |||||||
\(654\) | 9.53376e33 | 0.0608895 | ||||||||
\(655\) | −8.25846e34 | −0.517467 | ||||||||
\(656\) | −2.33448e35 | −1.43514 | ||||||||
\(657\) | 5.57728e34 | 0.336399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.08497e34 | 0.121069 | 0.0605344 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605344 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(660\) | 1.19533e35 | 0.681066 | ||||||||
\(661\) | −1.06866e35 | −0.597475 | −0.298738 | − | 0.954335i | \(-0.596566\pi\) | ||||
−0.298738 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(662\) | 1.65020e33 | 0.00905339 | ||||||||
\(663\) | −3.01929e35 | −1.62550 | ||||||||
\(664\) | −2.84676e32 | −0.00150401 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.81354e33 | −0.0244927 | ||||||||
\(667\) | −6.00432e35 | −2.99841 | ||||||||
\(668\) | 1.37555e35 | 0.674172 | ||||||||
\(669\) | 5.30864e34 | 0.255362 | ||||||||
\(670\) | −1.58607e34 | −0.0748835 | ||||||||
\(671\) | 7.06365e34 | 0.327339 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.13809e34 | −0.0954635 | −0.0477317 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477317 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(674\) | −1.39345e34 | −0.0610719 | ||||||||
\(675\) | −5.86281e35 | −2.52237 | ||||||||
\(676\) | 8.75764e34 | 0.369874 | ||||||||
\(677\) | −2.21336e35 | −0.917684 | −0.458842 | − | 0.888518i | \(-0.651736\pi\) | ||||
−0.458842 | + | 0.888518i | \(0.651736\pi\) | |||||||
\(678\) | −1.11531e34 | −0.0453968 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.63166e34 | 0.220940 | ||||||||
\(681\) | 4.49502e35 | 1.73138 | ||||||||
\(682\) | 3.72772e33 | 0.0140974 | ||||||||
\(683\) | −3.91218e35 | −1.45265 | −0.726323 | − | 0.687354i | \(-0.758772\pi\) | ||||
−0.726323 | + | 0.687354i | \(0.758772\pi\) | |||||||
\(684\) | 2.90880e35 | 1.06051 | ||||||||
\(685\) | 5.69832e35 | 2.03993 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.18685e35 | 1.44520 | ||||||||
\(688\) | 3.21804e35 | 1.09078 | ||||||||
\(689\) | 1.07741e35 | 0.358626 | ||||||||
\(690\) | −7.42115e34 | −0.242581 | ||||||||
\(691\) | −3.80918e35 | −1.22280 | −0.611400 | − | 0.791322i | \(-0.709393\pi\) | ||||
−0.611400 | + | 0.791322i | \(0.709393\pi\) | |||||||
\(692\) | −1.96618e35 | −0.619865 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.40009e33 | 0.00425759 | ||||||||
\(695\) | −5.16511e35 | −1.54266 | ||||||||
\(696\) | 1.08101e35 | 0.317112 | ||||||||
\(697\) | −6.19223e35 | −1.78417 | ||||||||
\(698\) | −3.15985e34 | −0.0894280 | ||||||||
\(699\) | −8.97630e35 | −2.49536 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.68030e34 | 0.232841 | 0.116421 | − | 0.993200i | \(-0.462858\pi\) | ||||
0.116421 | + | 0.993200i | \(0.462858\pi\) | |||||||
\(702\) | −1.97560e34 | −0.0520576 | ||||||||
\(703\) | 6.25245e34 | 0.161848 | ||||||||
\(704\) | 9.19067e34 | 0.233716 | ||||||||
\(705\) | 1.00046e36 | 2.49940 | ||||||||
\(706\) | −9.55934e33 | −0.0234622 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.00047e35 | −1.65848 | ||||||||
\(709\) | 4.90839e35 | 1.14251 | 0.571256 | − | 0.820772i | \(-0.306456\pi\) | ||||
0.571256 | + | 0.820772i | \(0.306456\pi\) | |||||||
\(710\) | −5.89079e34 | −0.134724 | ||||||||
\(711\) | 6.63415e35 | 1.49079 | ||||||||
\(712\) | 5.94464e34 | 0.131258 | ||||||||
\(713\) | 8.58482e35 | 1.86257 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.55585e35 | 0.325944 | ||||||||
\(716\) | −9.31384e34 | −0.191741 | ||||||||
\(717\) | −1.02305e36 | −2.06970 | ||||||||
\(718\) | 2.47416e34 | 0.0491894 | ||||||||
\(719\) | 5.04396e35 | 0.985509 | 0.492755 | − | 0.870168i | \(-0.335990\pi\) | ||||
0.492755 | + | 0.870168i | \(0.335990\pi\) | |||||||
\(720\) | −1.57436e36 | −3.02306 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.77704e34 | −0.0329596 | ||||||||
\(723\) | −6.14328e35 | −1.11988 | ||||||||
\(724\) | 9.58565e35 | 1.71747 | ||||||||
\(725\) | 2.08497e36 | 3.67177 | ||||||||
\(726\) | 4.69713e34 | 0.0813064 | ||||||||
\(727\) | −2.86199e34 | −0.0486954 | −0.0243477 | − | 0.999704i | \(-0.507751\pi\) | ||||
−0.0243477 | + | 0.999704i | \(0.507751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.13206e35 | −1.50132 | ||||||||
\(730\) | −1.05990e34 | −0.0171289 | ||||||||
\(731\) | 8.53585e35 | 1.35606 | ||||||||
\(732\) | −1.46240e36 | −2.28391 | ||||||||
\(733\) | 3.05062e35 | 0.468370 | 0.234185 | − | 0.972192i | \(-0.424758\pi\) | ||||
0.234185 | + | 0.972192i | \(0.424758\pi\) | |||||||
\(734\) | 2.83283e34 | 0.0427582 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.72890e35 | −0.252231 | ||||||||
\(737\) | −1.38250e35 | −0.198300 | ||||||||
\(738\) | −9.37127e34 | −0.132158 | ||||||||
\(739\) | 5.77113e35 | 0.800212 | 0.400106 | − | 0.916469i | \(-0.368973\pi\) | ||||
0.400106 | + | 0.916469i | \(0.368973\pi\) | |||||||
\(740\) | −3.39324e35 | −0.462613 | ||||||||
\(741\) | 5.93528e35 | 0.795635 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.31674e35 | 0.559494 | 0.279747 | − | 0.960074i | \(-0.409749\pi\) | ||||
0.279747 | + | 0.960074i | \(0.409749\pi\) | |||||||
\(744\) | −1.54559e35 | −0.196985 | ||||||||
\(745\) | 1.48546e36 | 1.86169 | ||||||||
\(746\) | −4.31175e34 | −0.0531396 | ||||||||
\(747\) | 2.11093e34 | 0.0255838 | ||||||||
\(748\) | 2.45113e35 | 0.292144 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.28380e35 | 0.147990 | ||||||||
\(751\) | 1.13779e36 | 1.28992 | 0.644959 | − | 0.764217i | \(-0.276874\pi\) | ||||
0.644959 | + | 0.764217i | \(0.276874\pi\) | |||||||
\(752\) | 7.73433e35 | 0.862382 | ||||||||
\(753\) | 1.76925e35 | 0.194022 | ||||||||
\(754\) | 7.02575e34 | 0.0757794 | ||||||||
\(755\) | 1.58857e36 | 1.68527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.93410e36 | −1.98509 | −0.992546 | − | 0.121872i | \(-0.961110\pi\) | ||||
−0.992546 | + | 0.121872i | \(0.961110\pi\) | |||||||
\(758\) | −2.57827e34 | −0.0260293 | ||||||||
\(759\) | −6.46869e35 | −0.642383 | ||||||||
\(760\) | −1.10706e35 | −0.108144 | ||||||||
\(761\) | 5.50323e35 | 0.528822 | 0.264411 | − | 0.964410i | \(-0.414822\pi\) | ||||
0.264411 | + | 0.964410i | \(0.414822\pi\) | |||||||
\(762\) | −7.24063e34 | −0.0684446 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.22157e36 | −1.11751 | ||||||||
\(765\) | −4.17599e36 | −3.75830 | ||||||||
\(766\) | 3.71931e33 | 0.00329309 | ||||||||
\(767\) | −9.11186e35 | −0.793715 | ||||||||
\(768\) | −1.88718e36 | −1.61733 | ||||||||
\(769\) | 3.37946e35 | 0.284949 | 0.142475 | − | 0.989798i | \(-0.454494\pi\) | ||||
0.142475 | + | 0.989798i | \(0.454494\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.00272e36 | −1.63471 | ||||||||
\(772\) | −1.41319e36 | −1.13497 | ||||||||
\(773\) | −1.97789e36 | −1.56300 | −0.781499 | − | 0.623907i | \(-0.785544\pi\) | ||||
−0.781499 | + | 0.623907i | \(0.785544\pi\) | |||||||
\(774\) | 1.29181e35 | 0.100447 | ||||||||
\(775\) | −2.98104e36 | −2.28085 | ||||||||
\(776\) | 3.86243e33 | 0.00290797 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.14218e34 | 0.0229080 | ||||||||
\(779\) | 1.21726e36 | 0.873303 | ||||||||
\(780\) | −3.22111e36 | −2.27417 | ||||||||
\(781\) | −5.13474e35 | −0.356764 | ||||||||
\(782\) | −1.52177e35 | −0.104056 | ||||||||
\(783\) | −3.46571e36 | −2.33222 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.44350e36 | 1.59273 | ||||||||
\(786\) | −4.01769e34 | −0.0257748 | ||||||||
\(787\) | 3.56804e35 | 0.225292 | 0.112646 | − | 0.993635i | \(-0.464067\pi\) | ||||
0.112646 | + | 0.993635i | \(0.464067\pi\) | |||||||
\(788\) | 1.23582e36 | 0.768026 | ||||||||
\(789\) | 3.61616e36 | 2.21200 | ||||||||
\(790\) | −1.26075e35 | −0.0759084 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.42905e34 | 0.0433380 | ||||||||
\(793\) | −1.90347e36 | −1.09303 | ||||||||
\(794\) | 2.08343e34 | 0.0117767 | ||||||||
\(795\) | 2.33606e36 | 1.29985 | ||||||||
\(796\) | −1.44253e36 | −0.790153 | ||||||||
\(797\) | 2.08564e36 | 1.12463 | 0.562317 | − | 0.826922i | \(-0.309910\pi\) | ||||
0.562317 | + | 0.826922i | \(0.309910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.05154e36 | 1.07212 | ||||||||
\(800\) | 6.00353e35 | 0.308874 | ||||||||
\(801\) | −4.40806e36 | −2.23276 | ||||||||
\(802\) | −3.16328e34 | −0.0157746 | ||||||||
\(803\) | −9.23871e34 | −0.0453594 | ||||||||
\(804\) | 2.86223e36 | 1.38358 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.00452e35 | −0.0470730 | ||||||||
\(807\) | 1.38173e36 | 0.637536 | ||||||||
\(808\) | −6.76728e34 | −0.0307448 | ||||||||
\(809\) | 1.27866e36 | 0.572003 | 0.286001 | − | 0.958229i | \(-0.407674\pi\) | ||||
0.286001 | + | 0.958229i | \(0.407674\pi\) | |||||||
\(810\) | −6.96056e34 | −0.0306606 | ||||||||
\(811\) | −3.41904e36 | −1.48301 | −0.741505 | − | 0.670947i | \(-0.765888\pi\) | ||||
−0.741505 | + | 0.670947i | \(0.765888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.52918e36 | −1.48437 | ||||||||
\(814\) | 7.97359e33 | 0.00330255 | ||||||||
\(815\) | 5.66816e36 | 2.31192 | ||||||||
\(816\) | −5.06092e36 | −2.03284 | ||||||||
\(817\) | −1.67797e36 | −0.663754 | ||||||||
\(818\) | 1.68307e35 | 0.0655671 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.60614e36 | −2.49617 | ||||||||
\(821\) | −5.12217e36 | −1.90618 | −0.953092 | − | 0.302681i | \(-0.902118\pi\) | ||||
−0.953092 | + | 0.302681i | \(0.902118\pi\) | |||||||
\(822\) | 2.77220e35 | 0.101608 | ||||||||
\(823\) | 5.26462e35 | 0.190050 | 0.0950252 | − | 0.995475i | \(-0.469707\pi\) | ||||
0.0950252 | + | 0.995475i | \(0.469707\pi\) | |||||||
\(824\) | −2.99260e35 | −0.106404 | ||||||||
\(825\) | 2.24622e36 | 0.786644 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.25397e36 | 0.765825 | 0.382913 | − | 0.923785i | \(-0.374921\pi\) | ||||
0.382913 | + | 0.923785i | \(0.374921\pi\) | |||||||
\(828\) | 8.54293e36 | 2.85909 | ||||||||
\(829\) | 3.48267e36 | 1.14810 | 0.574052 | − | 0.818819i | \(-0.305371\pi\) | ||||
0.574052 | + | 0.818819i | \(0.305371\pi\) | |||||||
\(830\) | −4.01159e33 | −0.00130269 | ||||||||
\(831\) | 3.65580e36 | 1.16942 | ||||||||
\(832\) | −2.47665e36 | −0.780410 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.51279e35 | −0.0768389 | ||||||||
\(835\) | 3.88202e36 | 1.16944 | ||||||||
\(836\) | −4.81840e35 | −0.142996 | ||||||||
\(837\) | 4.95518e36 | 1.44874 | ||||||||
\(838\) | 2.56106e35 | 0.0737682 | ||||||||
\(839\) | −1.38679e36 | −0.393536 | −0.196768 | − | 0.980450i | \(-0.563045\pi\) | ||||
−0.196768 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.69464e36 | 2.39498 | ||||||||
\(842\) | −1.40914e35 | −0.0382430 | ||||||||
\(843\) | 6.60953e36 | 1.76736 | ||||||||
\(844\) | −3.64509e36 | −0.960345 | ||||||||
\(845\) | 2.47154e36 | 0.641592 | ||||||||
\(846\) | 3.10478e35 | 0.0794147 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.80595e36 | 0.448496 | ||||||||
\(849\) | 2.34102e36 | 0.572874 | ||||||||
\(850\) | 5.28428e35 | 0.127424 | ||||||||
\(851\) | 1.83629e36 | 0.436338 | ||||||||
\(852\) | 1.06306e37 | 2.48921 | ||||||||
\(853\) | −1.28825e36 | −0.297261 | −0.148631 | − | 0.988893i | \(-0.547487\pi\) | ||||
−0.148631 | + | 0.988893i | \(0.547487\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.20909e36 | 1.83958 | ||||||||
\(856\) | −9.24149e34 | −0.0204089 | ||||||||
\(857\) | 1.05441e36 | 0.229482 | 0.114741 | − | 0.993395i | \(-0.463396\pi\) | ||||
0.114741 | + | 0.993395i | \(0.463396\pi\) | |||||||
\(858\) | 7.56912e34 | 0.0162351 | ||||||||
\(859\) | −7.57439e36 | −1.60115 | −0.800576 | − | 0.599231i | \(-0.795473\pi\) | ||||
−0.800576 | + | 0.599231i | \(0.795473\pi\) | |||||||
\(860\) | 9.10641e36 | 1.89722 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.47704e35 | −0.0703670 | ||||||||
\(863\) | −3.22715e36 | −0.643701 | −0.321850 | − | 0.946791i | \(-0.604305\pi\) | ||||
−0.321850 | + | 0.946791i | \(0.604305\pi\) | |||||||
\(864\) | −9.97927e35 | −0.196190 | ||||||||
\(865\) | −5.54886e36 | −1.07523 | ||||||||
\(866\) | −2.27871e35 | −0.0435226 | ||||||||
\(867\) | −4.59687e36 | −0.865413 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.09894e36 | −0.201014 | ||||||||
\(870\) | 1.52333e36 | 0.274665 | ||||||||
\(871\) | 3.72549e36 | 0.662151 | ||||||||
\(872\) | 4.17694e35 | 0.0731817 | ||||||||
\(873\) | −2.86407e35 | −0.0494658 | ||||||||
\(874\) | 2.99148e35 | 0.0509323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.91271e36 | 0.316481 | ||||||||
\(877\) | 5.54904e36 | 0.905154 | 0.452577 | − | 0.891725i | \(-0.350505\pi\) | ||||
0.452577 | + | 0.891725i | \(0.350505\pi\) | |||||||
\(878\) | −5.60221e35 | −0.0900903 | ||||||||
\(879\) | −3.15969e36 | −0.500938 | ||||||||
\(880\) | 2.60791e36 | 0.407623 | ||||||||
\(881\) | −9.25222e36 | −1.42576 | −0.712881 | − | 0.701285i | \(-0.752610\pi\) | ||||
−0.712881 | + | 0.701285i | \(0.752610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.33411e36 | 0.349633 | 0.174817 | − | 0.984601i | \(-0.444067\pi\) | ||||
0.174817 | + | 0.984601i | \(0.444067\pi\) | |||||||
\(884\) | −6.60518e36 | −0.975508 | ||||||||
\(885\) | −1.97564e37 | −2.87685 | ||||||||
\(886\) | 2.64114e35 | 0.0379201 | ||||||||
\(887\) | −1.00103e37 | −1.41710 | −0.708550 | − | 0.705661i | \(-0.750650\pi\) | ||||
−0.708550 | + | 0.705661i | \(0.750650\pi\) | |||||||
\(888\) | −3.30603e35 | −0.0461471 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.37706e35 | 0.113688 | ||||||||
\(891\) | −6.06722e35 | −0.0811929 | ||||||||
\(892\) | 1.16135e36 | 0.153250 | ||||||||
\(893\) | −4.03288e36 | −0.524774 | ||||||||
\(894\) | 7.22668e35 | 0.0927299 | ||||||||
\(895\) | −2.62851e36 | −0.332600 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.74315e37 | 2.14500 | ||||||||
\(898\) | −4.94434e35 | −0.0600004 | ||||||||
\(899\) | −1.76220e37 | −2.10891 | ||||||||
\(900\) | −2.96649e37 | −3.50116 | ||||||||
\(901\) | 4.79030e36 | 0.557574 | ||||||||
\(902\) | 1.55234e35 | 0.0178199 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.88642e35 | −0.0545614 | ||||||||
\(905\) | 2.70522e37 | 2.97917 | ||||||||
\(906\) | 7.72829e35 | 0.0839423 | ||||||||
\(907\) | 1.19643e37 | 1.28173 | 0.640865 | − | 0.767654i | \(-0.278576\pi\) | ||||
0.640865 | + | 0.767654i | \(0.278576\pi\) | |||||||
\(908\) | 9.83355e36 | 1.03905 | ||||||||
\(909\) | 5.01807e36 | 0.522984 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.18003e35 | −0.0626629 | −0.0313315 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313315 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(912\) | 9.94868e36 | 0.995016 | ||||||||
\(913\) | −3.49673e34 | −0.00344967 | ||||||||
\(914\) | 4.48916e34 | 0.00436855 | ||||||||
\(915\) | −4.12713e37 | −3.96172 | ||||||||
\(916\) | 9.15940e36 | 0.867308 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.78372e35 | −0.0809366 | ||||||||
\(919\) | −1.87864e37 | −1.70765 | −0.853826 | − | 0.520558i | \(-0.825724\pi\) | ||||
−0.853826 | + | 0.520558i | \(0.825724\pi\) | |||||||
\(920\) | −3.25136e36 | −0.291553 | ||||||||
\(921\) | 2.47724e37 | 2.19141 | ||||||||
\(922\) | 4.60822e35 | 0.0402158 | ||||||||
\(923\) | 1.38368e37 | 1.19128 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.37645e36 | −0.534327 | ||||||||
\(926\) | 5.19167e35 | 0.0429210 | ||||||||
\(927\) | 2.21907e37 | 1.80998 | ||||||||
\(928\) | 3.54890e36 | 0.285590 | ||||||||
\(929\) | −1.07023e37 | −0.849732 | −0.424866 | − | 0.905256i | \(-0.639679\pi\) | ||||
−0.424866 | + | 0.905256i | \(0.639679\pi\) | |||||||
\(930\) | −2.17802e36 | −0.170618 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.96371e37 | −1.49754 | ||||||||
\(933\) | −2.01926e37 | −1.51940 | ||||||||
\(934\) | 1.65998e35 | 0.0123244 | ||||||||
\(935\) | 6.91748e36 | 0.506761 | ||||||||
\(936\) | −2.00194e36 | −0.144711 | ||||||||
\(937\) | 1.91721e37 | 1.36749 | 0.683746 | − | 0.729720i | \(-0.260350\pi\) | ||||
0.683746 | + | 0.729720i | \(0.260350\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.32423e37 | 1.61421 | ||||||||
\(940\) | 2.18867e37 | 1.49997 | ||||||||
\(941\) | 2.06934e37 | 1.39946 | 0.699732 | − | 0.714405i | \(-0.253303\pi\) | ||||
0.699732 | + | 0.714405i | \(0.253303\pi\) | |||||||
\(942\) | 1.18875e36 | 0.0793329 | ||||||||
\(943\) | 3.57500e37 | 2.35440 | ||||||||
\(944\) | −1.52732e37 | −0.992615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.13987e35 | −0.0135440 | ||||||||
\(947\) | 7.48084e36 | 0.467278 | 0.233639 | − | 0.972323i | \(-0.424937\pi\) | ||||
0.233639 | + | 0.972323i | \(0.424937\pi\) | |||||||
\(948\) | 2.27516e37 | 1.40251 | ||||||||
\(949\) | 2.48959e36 | 0.151461 | ||||||||
\(950\) | −1.03878e36 | −0.0623702 | ||||||||
\(951\) | 1.56653e35 | 0.00928286 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.03734e37 | 1.17599 | 0.587994 | − | 0.808865i | \(-0.299918\pi\) | ||||
0.587994 | + | 0.808865i | \(0.299918\pi\) | |||||||
\(954\) | 7.24959e35 | 0.0413008 | ||||||||
\(955\) | −3.44746e37 | −1.93846 | ||||||||
\(956\) | −2.23808e37 | −1.24209 | ||||||||
\(957\) | 1.32782e37 | 0.727345 | ||||||||
\(958\) | −1.78688e36 | −0.0966112 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.36989e37 | −2.82862 | ||||||||
\(961\) | 5.96261e36 | 0.310023 | ||||||||
\(962\) | −2.14868e35 | −0.0110276 | ||||||||
\(963\) | 6.85274e36 | 0.347165 | ||||||||
\(964\) | −1.34394e37 | −0.672074 | ||||||||
\(965\) | −3.98823e37 | −1.96874 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.36949e37 | −0.658763 | −0.329382 | − | 0.944197i | \(-0.606840\pi\) | ||||
−0.329382 | + | 0.944197i | \(0.606840\pi\) | |||||||
\(968\) | 2.05791e36 | 0.0977203 | ||||||||
\(969\) | 2.63889e37 | 1.23701 | ||||||||
\(970\) | 5.44286e34 | 0.00251872 | ||||||||
\(971\) | 3.88125e37 | 1.77309 | 0.886545 | − | 0.462642i | \(-0.153099\pi\) | ||||
0.886545 | + | 0.462642i | \(0.153099\pi\) | |||||||
\(972\) | −1.54294e37 | −0.695860 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.89654e35 | −0.0171274 | ||||||||
\(975\) | −6.05299e37 | −2.62671 | ||||||||
\(976\) | −3.19059e37 | −1.36693 | ||||||||
\(977\) | −2.41102e35 | −0.0101981 | −0.00509905 | − | 0.999987i | \(-0.501623\pi\) | ||||
−0.00509905 | + | 0.999987i | \(0.501623\pi\) | |||||||
\(978\) | 2.75753e36 | 0.115155 | ||||||||
\(979\) | 7.30192e36 | 0.301060 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.09728e37 | −1.24485 | ||||||||
\(982\) | −5.90765e35 | −0.0234434 | ||||||||
\(983\) | 2.16610e37 | 0.848710 | 0.424355 | − | 0.905496i | \(-0.360501\pi\) | ||||
0.424355 | + | 0.905496i | \(0.360501\pi\) | |||||||
\(984\) | −6.43635e36 | −0.249001 | ||||||||
\(985\) | 3.48766e37 | 1.33224 | ||||||||
\(986\) | 3.12373e36 | 0.117818 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.29844e37 | 0.477484 | ||||||||
\(989\) | −4.92805e37 | −1.78946 | ||||||||
\(990\) | 1.04689e36 | 0.0375370 | ||||||||
\(991\) | 7.62118e36 | 0.269837 | 0.134918 | − | 0.990857i | \(-0.456923\pi\) | ||||
0.134918 | + | 0.990857i | \(0.456923\pi\) | |||||||
\(992\) | −5.07412e36 | −0.177405 | ||||||||
\(993\) | −8.40427e36 | −0.290158 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.07104e37 | −1.37062 | ||||||||
\(996\) | 7.23935e35 | 0.0240690 | ||||||||
\(997\) | −3.72156e37 | −1.22190 | −0.610949 | − | 0.791670i | \(-0.709212\pi\) | ||||
−0.610949 | + | 0.791670i | \(0.709212\pi\) | |||||||
\(998\) | −9.96005e35 | −0.0322946 | ||||||||
\(999\) | 1.05991e37 | 0.339392 |
(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 | 49.26.a.e.1.7 | ✓ | 12 | |
7.6 | odd | 2 | inner | 49.26.a.e.1.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.26.a.e.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
49.26.a.e.1.8 | yes | 12 | 7.6 | odd | 2 | inner |