Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,12,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(4.61005908336\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32.0000 | −0.707107 | ||||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 1024.00 | 0.500000 | ||||||||
\(5\) | 5766.00 | 0.825163 | 0.412581 | − | 0.910921i | \(-0.364627\pi\) | ||||
0.412581 | + | 0.910921i | \(0.364627\pi\) | |||||||
\(6\) | 7776.00 | 0.408248 | ||||||||
\(7\) | 72464.0 | 1.62961 | 0.814804 | − | 0.579737i | \(-0.196845\pi\) | ||||
0.814804 | + | 0.579737i | \(0.196845\pi\) | |||||||
\(8\) | −32768.0 | −0.353553 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −184512. | −0.583478 | ||||||||
\(11\) | −408948. | −0.765611 | −0.382806 | − | 0.923829i | \(-0.625042\pi\) | ||||
−0.382806 | + | 0.923829i | \(0.625042\pi\) | |||||||
\(12\) | −248832. | −0.288675 | ||||||||
\(13\) | 1.36756e6 | 1.02154 | 0.510772 | − | 0.859716i | \(-0.329360\pi\) | ||||
0.510772 | + | 0.859716i | \(0.329360\pi\) | |||||||
\(14\) | −2.31885e6 | −1.15231 | ||||||||
\(15\) | −1.40114e6 | −0.476408 | ||||||||
\(16\) | 1.04858e6 | 0.250000 | ||||||||
\(17\) | 5.42291e6 | 0.926326 | 0.463163 | − | 0.886273i | \(-0.346715\pi\) | ||||
0.463163 | + | 0.886273i | \(0.346715\pi\) | |||||||
\(18\) | −1.88957e6 | −0.235702 | ||||||||
\(19\) | 1.51661e7 | 1.40517 | 0.702585 | − | 0.711599i | \(-0.252029\pi\) | ||||
0.702585 | + | 0.711599i | \(0.252029\pi\) | |||||||
\(20\) | 5.90438e6 | 0.412581 | ||||||||
\(21\) | −1.76088e7 | −0.940854 | ||||||||
\(22\) | 1.30863e7 | 0.541369 | ||||||||
\(23\) | −5.21941e7 | −1.69090 | −0.845450 | − | 0.534054i | \(-0.820668\pi\) | ||||
−0.845450 | + | 0.534054i | \(0.820668\pi\) | |||||||
\(24\) | 7.96262e6 | 0.204124 | ||||||||
\(25\) | −1.55814e7 | −0.319106 | ||||||||
\(26\) | −4.37619e7 | −0.722341 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 7.42031e7 | 0.814804 | ||||||||
\(29\) | 1.18581e8 | 1.07356 | 0.536780 | − | 0.843722i | \(-0.319640\pi\) | ||||
0.536780 | + | 0.843722i | \(0.319640\pi\) | |||||||
\(30\) | 4.48364e7 | 0.336871 | ||||||||
\(31\) | −5.76524e7 | −0.361683 | −0.180842 | − | 0.983512i | \(-0.557882\pi\) | ||||
−0.180842 | + | 0.983512i | \(0.557882\pi\) | |||||||
\(32\) | −3.35544e7 | −0.176777 | ||||||||
\(33\) | 9.93744e7 | 0.442026 | ||||||||
\(34\) | −1.73533e8 | −0.655011 | ||||||||
\(35\) | 4.17827e8 | 1.34469 | ||||||||
\(36\) | 6.04662e7 | 0.166667 | ||||||||
\(37\) | −3.75985e8 | −0.891377 | −0.445688 | − | 0.895188i | \(-0.647041\pi\) | ||||
−0.445688 | + | 0.895188i | \(0.647041\pi\) | |||||||
\(38\) | −4.85315e8 | −0.993606 | ||||||||
\(39\) | −3.32317e8 | −0.589789 | ||||||||
\(40\) | −1.88940e8 | −0.291739 | ||||||||
\(41\) | 8.56316e8 | 1.15431 | 0.577156 | − | 0.816634i | \(-0.304163\pi\) | ||||
0.577156 | + | 0.816634i | \(0.304163\pi\) | |||||||
\(42\) | 5.63480e8 | 0.665285 | ||||||||
\(43\) | −1.24519e9 | −1.29169 | −0.645846 | − | 0.763468i | \(-0.723495\pi\) | ||||
−0.645846 | + | 0.763468i | \(0.723495\pi\) | |||||||
\(44\) | −4.18763e8 | −0.382806 | ||||||||
\(45\) | 3.40477e8 | 0.275054 | ||||||||
\(46\) | 1.67021e9 | 1.19565 | ||||||||
\(47\) | −1.30676e9 | −0.831110 | −0.415555 | − | 0.909568i | \(-0.636413\pi\) | ||||
−0.415555 | + | 0.909568i | \(0.636413\pi\) | |||||||
\(48\) | −2.54804e8 | −0.144338 | ||||||||
\(49\) | 3.27370e9 | 1.65562 | ||||||||
\(50\) | 4.98604e8 | 0.225642 | ||||||||
\(51\) | −1.31777e9 | −0.534814 | ||||||||
\(52\) | 1.40038e9 | 0.510772 | ||||||||
\(53\) | 4.09556e8 | 0.134523 | 0.0672615 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672615 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(54\) | 4.59165e8 | 0.136083 | ||||||||
\(55\) | −2.35799e9 | −0.631754 | ||||||||
\(56\) | −2.37450e9 | −0.576153 | ||||||||
\(57\) | −3.68536e9 | −0.811276 | ||||||||
\(58\) | −3.79460e9 | −0.759122 | ||||||||
\(59\) | −2.88287e9 | −0.524975 | −0.262487 | − | 0.964935i | \(-0.584543\pi\) | ||||
−0.262487 | + | 0.964935i | \(0.584543\pi\) | |||||||
\(60\) | −1.43477e9 | −0.238204 | ||||||||
\(61\) | 5.73177e9 | 0.868909 | 0.434455 | − | 0.900694i | \(-0.356941\pi\) | ||||
0.434455 | + | 0.900694i | \(0.356941\pi\) | |||||||
\(62\) | 1.84488e9 | 0.255749 | ||||||||
\(63\) | 4.27893e9 | 0.543203 | ||||||||
\(64\) | 1.07374e9 | 0.125000 | ||||||||
\(65\) | 7.88534e9 | 0.842941 | ||||||||
\(66\) | −3.17998e9 | −0.312559 | ||||||||
\(67\) | 3.89327e9 | 0.352292 | 0.176146 | − | 0.984364i | \(-0.443637\pi\) | ||||
0.176146 | + | 0.984364i | \(0.443637\pi\) | |||||||
\(68\) | 5.55306e9 | 0.463163 | ||||||||
\(69\) | 1.26832e10 | 0.976242 | ||||||||
\(70\) | −1.33705e10 | −0.950841 | ||||||||
\(71\) | −9.07589e9 | −0.596992 | −0.298496 | − | 0.954411i | \(-0.596485\pi\) | ||||
−0.298496 | + | 0.954411i | \(0.596485\pi\) | |||||||
\(72\) | −1.93492e9 | −0.117851 | ||||||||
\(73\) | −1.55718e10 | −0.879152 | −0.439576 | − | 0.898206i | \(-0.644871\pi\) | ||||
−0.439576 | + | 0.898206i | \(0.644871\pi\) | |||||||
\(74\) | 1.20315e10 | 0.630298 | ||||||||
\(75\) | 3.78627e9 | 0.184236 | ||||||||
\(76\) | 1.55301e10 | 0.702585 | ||||||||
\(77\) | −2.96340e10 | −1.24765 | ||||||||
\(78\) | 1.06341e10 | 0.417044 | ||||||||
\(79\) | −3.01968e10 | −1.10411 | −0.552054 | − | 0.833809i | \(-0.686156\pi\) | ||||
−0.552054 | + | 0.833809i | \(0.686156\pi\) | |||||||
\(80\) | 6.04609e9 | 0.206291 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −2.74021e10 | −0.816221 | ||||||||
\(83\) | 2.31353e10 | 0.644681 | 0.322340 | − | 0.946624i | \(-0.395530\pi\) | ||||
0.322340 | + | 0.946624i | \(0.395530\pi\) | |||||||
\(84\) | −1.80314e10 | −0.470427 | ||||||||
\(85\) | 3.12685e10 | 0.764369 | ||||||||
\(86\) | 3.98461e10 | 0.913364 | ||||||||
\(87\) | −2.88152e10 | −0.619821 | ||||||||
\(88\) | 1.34004e10 | 0.270684 | ||||||||
\(89\) | −2.56148e10 | −0.486235 | −0.243118 | − | 0.969997i | \(-0.578170\pi\) | ||||
−0.243118 | + | 0.969997i | \(0.578170\pi\) | |||||||
\(90\) | −1.08952e10 | −0.194493 | ||||||||
\(91\) | 9.90987e10 | 1.66472 | ||||||||
\(92\) | −5.34467e10 | −0.845450 | ||||||||
\(93\) | 1.40095e10 | 0.208818 | ||||||||
\(94\) | 4.18164e10 | 0.587684 | ||||||||
\(95\) | 8.74477e10 | 1.15949 | ||||||||
\(96\) | 8.15373e9 | 0.102062 | ||||||||
\(97\) | −6.19376e10 | −0.732335 | −0.366167 | − | 0.930549i | \(-0.619330\pi\) | ||||
−0.366167 | + | 0.930549i | \(0.619330\pi\) | |||||||
\(98\) | −1.04759e11 | −1.17070 | ||||||||
\(99\) | −2.41480e10 | −0.255204 | ||||||||
\(100\) | −1.59553e10 | −0.159553 | ||||||||
\(101\) | −9.49642e10 | −0.899067 | −0.449534 | − | 0.893263i | \(-0.648410\pi\) | ||||
−0.449534 | + | 0.893263i | \(0.648410\pi\) | |||||||
\(102\) | 4.21686e10 | 0.378171 | ||||||||
\(103\) | 5.43719e10 | 0.462136 | 0.231068 | − | 0.972938i | \(-0.425778\pi\) | ||||
0.231068 | + | 0.972938i | \(0.425778\pi\) | |||||||
\(104\) | −4.48121e10 | −0.361171 | ||||||||
\(105\) | −1.01532e11 | −0.776358 | ||||||||
\(106\) | −1.31058e10 | −0.0951221 | ||||||||
\(107\) | 5.71348e9 | 0.0393813 | 0.0196906 | − | 0.999806i | \(-0.493732\pi\) | ||||
0.0196906 | + | 0.999806i | \(0.493732\pi\) | |||||||
\(108\) | −1.46933e10 | −0.0962250 | ||||||||
\(109\) | −4.96724e10 | −0.309221 | −0.154611 | − | 0.987975i | \(-0.549412\pi\) | ||||
−0.154611 | + | 0.987975i | \(0.549412\pi\) | |||||||
\(110\) | 7.54558e10 | 0.446717 | ||||||||
\(111\) | 9.13644e10 | 0.514637 | ||||||||
\(112\) | 7.59840e10 | 0.407402 | ||||||||
\(113\) | 1.77803e11 | 0.907834 | 0.453917 | − | 0.891044i | \(-0.350026\pi\) | ||||
0.453917 | + | 0.891044i | \(0.350026\pi\) | |||||||
\(114\) | 1.17932e11 | 0.573659 | ||||||||
\(115\) | −3.00951e11 | −1.39527 | ||||||||
\(116\) | 1.21427e11 | 0.536780 | ||||||||
\(117\) | 8.07529e10 | 0.340515 | ||||||||
\(118\) | 9.22517e10 | 0.371213 | ||||||||
\(119\) | 3.92966e11 | 1.50955 | ||||||||
\(120\) | 4.59125e10 | 0.168436 | ||||||||
\(121\) | −1.18073e11 | −0.413839 | ||||||||
\(122\) | −1.83417e11 | −0.614412 | ||||||||
\(123\) | −2.08085e11 | −0.666442 | ||||||||
\(124\) | −5.90361e10 | −0.180842 | ||||||||
\(125\) | −3.71385e11 | −1.08848 | ||||||||
\(126\) | −1.36926e11 | −0.384102 | ||||||||
\(127\) | −4.73708e11 | −1.27230 | −0.636150 | − | 0.771565i | \(-0.719474\pi\) | ||||
−0.636150 | + | 0.771565i | \(0.719474\pi\) | |||||||
\(128\) | −3.43597e10 | −0.0883883 | ||||||||
\(129\) | 3.02581e11 | 0.745758 | ||||||||
\(130\) | −2.52331e11 | −0.596049 | ||||||||
\(131\) | 1.68574e11 | 0.381767 | 0.190883 | − | 0.981613i | \(-0.438865\pi\) | ||||
0.190883 | + | 0.981613i | \(0.438865\pi\) | |||||||
\(132\) | 1.01759e11 | 0.221013 | ||||||||
\(133\) | 1.09900e12 | 2.28988 | ||||||||
\(134\) | −1.24585e11 | −0.249108 | ||||||||
\(135\) | −8.27358e10 | −0.158803 | ||||||||
\(136\) | −1.77698e11 | −0.327506 | ||||||||
\(137\) | −8.01479e11 | −1.41883 | −0.709413 | − | 0.704793i | \(-0.751040\pi\) | ||||
−0.709413 | + | 0.704793i | \(0.751040\pi\) | |||||||
\(138\) | −4.05861e11 | −0.690307 | ||||||||
\(139\) | 5.24839e11 | 0.857916 | 0.428958 | − | 0.903324i | \(-0.358881\pi\) | ||||
0.428958 | + | 0.903324i | \(0.358881\pi\) | |||||||
\(140\) | 4.27855e11 | 0.672346 | ||||||||
\(141\) | 3.17543e11 | 0.479842 | ||||||||
\(142\) | 2.90428e11 | 0.422137 | ||||||||
\(143\) | −5.59260e11 | −0.782106 | ||||||||
\(144\) | 6.19174e10 | 0.0833333 | ||||||||
\(145\) | 6.83739e11 | 0.885862 | ||||||||
\(146\) | 4.98298e11 | 0.621654 | ||||||||
\(147\) | −7.95510e11 | −0.955873 | ||||||||
\(148\) | −3.85009e11 | −0.445688 | ||||||||
\(149\) | 1.25702e12 | 1.40223 | 0.701113 | − | 0.713051i | \(-0.252687\pi\) | ||||
0.701113 | + | 0.713051i | \(0.252687\pi\) | |||||||
\(150\) | −1.21161e11 | −0.130275 | ||||||||
\(151\) | −4.92117e11 | −0.510147 | −0.255074 | − | 0.966922i | \(-0.582100\pi\) | ||||
−0.255074 | + | 0.966922i | \(0.582100\pi\) | |||||||
\(152\) | −4.96963e11 | −0.496803 | ||||||||
\(153\) | 3.20218e11 | 0.308775 | ||||||||
\(154\) | 9.48288e11 | 0.882219 | ||||||||
\(155\) | −3.32424e11 | −0.298447 | ||||||||
\(156\) | −3.40292e11 | −0.294895 | ||||||||
\(157\) | −9.97092e11 | −0.834232 | −0.417116 | − | 0.908853i | \(-0.636959\pi\) | ||||
−0.417116 | + | 0.908853i | \(0.636959\pi\) | |||||||
\(158\) | 9.66296e11 | 0.780722 | ||||||||
\(159\) | −9.95222e10 | −0.0776669 | ||||||||
\(160\) | −1.93475e11 | −0.145870 | ||||||||
\(161\) | −3.78219e12 | −2.75550 | ||||||||
\(162\) | −1.11577e11 | −0.0785674 | ||||||||
\(163\) | −4.84142e11 | −0.329565 | −0.164782 | − | 0.986330i | \(-0.552692\pi\) | ||||
−0.164782 | + | 0.986330i | \(0.552692\pi\) | |||||||
\(164\) | 8.76868e11 | 0.577156 | ||||||||
\(165\) | 5.72993e11 | 0.364743 | ||||||||
\(166\) | −7.40328e11 | −0.455858 | ||||||||
\(167\) | 2.31537e12 | 1.37937 | 0.689685 | − | 0.724110i | \(-0.257749\pi\) | ||||
0.689685 | + | 0.724110i | \(0.257749\pi\) | |||||||
\(168\) | 5.77004e11 | 0.332642 | ||||||||
\(169\) | 7.80545e10 | 0.0435533 | ||||||||
\(170\) | −1.00059e12 | −0.540491 | ||||||||
\(171\) | 8.95543e11 | 0.468390 | ||||||||
\(172\) | −1.27507e12 | −0.645846 | ||||||||
\(173\) | 3.37157e12 | 1.65416 | 0.827081 | − | 0.562083i | \(-0.190000\pi\) | ||||
0.827081 | + | 0.562083i | \(0.190000\pi\) | |||||||
\(174\) | 9.22087e11 | 0.438279 | ||||||||
\(175\) | −1.12909e12 | −0.520018 | ||||||||
\(176\) | −4.28813e11 | −0.191403 | ||||||||
\(177\) | 7.00537e11 | 0.303094 | ||||||||
\(178\) | 8.19674e11 | 0.343820 | ||||||||
\(179\) | 1.64598e12 | 0.669472 | 0.334736 | − | 0.942312i | \(-0.391353\pi\) | ||||
0.334736 | + | 0.942312i | \(0.391353\pi\) | |||||||
\(180\) | 3.48648e11 | 0.137527 | ||||||||
\(181\) | 2.74217e12 | 1.04921 | 0.524605 | − | 0.851346i | \(-0.324213\pi\) | ||||
0.524605 | + | 0.851346i | \(0.324213\pi\) | |||||||
\(182\) | −3.17116e12 | −1.17713 | ||||||||
\(183\) | −1.39282e12 | −0.501665 | ||||||||
\(184\) | 1.71030e12 | 0.597824 | ||||||||
\(185\) | −2.16793e12 | −0.735531 | ||||||||
\(186\) | −4.48305e11 | −0.147656 | ||||||||
\(187\) | −2.21769e12 | −0.709205 | ||||||||
\(188\) | −1.33812e12 | −0.415555 | ||||||||
\(189\) | −1.03978e12 | −0.313618 | ||||||||
\(190\) | −2.79833e12 | −0.819886 | ||||||||
\(191\) | 4.08409e12 | 1.16255 | 0.581275 | − | 0.813707i | \(-0.302554\pi\) | ||||
0.581275 | + | 0.813707i | \(0.302554\pi\) | |||||||
\(192\) | −2.60919e11 | −0.0721688 | ||||||||
\(193\) | −4.47239e12 | −1.20219 | −0.601097 | − | 0.799176i | \(-0.705269\pi\) | ||||
−0.601097 | + | 0.799176i | \(0.705269\pi\) | |||||||
\(194\) | 1.98200e12 | 0.517839 | ||||||||
\(195\) | −1.91614e12 | −0.486672 | ||||||||
\(196\) | 3.35227e12 | 0.827811 | ||||||||
\(197\) | −7.37025e12 | −1.76977 | −0.884887 | − | 0.465805i | \(-0.845765\pi\) | ||||
−0.884887 | + | 0.465805i | \(0.845765\pi\) | |||||||
\(198\) | 7.72735e11 | 0.180456 | ||||||||
\(199\) | 2.69308e12 | 0.611728 | 0.305864 | − | 0.952075i | \(-0.401055\pi\) | ||||
0.305864 | + | 0.952075i | \(0.401055\pi\) | |||||||
\(200\) | 5.10570e11 | 0.112821 | ||||||||
\(201\) | −9.46065e11 | −0.203396 | ||||||||
\(202\) | 3.03885e12 | 0.635736 | ||||||||
\(203\) | 8.59286e12 | 1.74948 | ||||||||
\(204\) | −1.34939e12 | −0.267407 | ||||||||
\(205\) | 4.93752e12 | 0.952495 | ||||||||
\(206\) | −1.73990e12 | −0.326780 | ||||||||
\(207\) | −3.08201e12 | −0.563634 | ||||||||
\(208\) | 1.43399e12 | 0.255386 | ||||||||
\(209\) | −6.20215e12 | −1.07581 | ||||||||
\(210\) | 3.24903e12 | 0.548968 | ||||||||
\(211\) | 6.63458e12 | 1.09209 | 0.546047 | − | 0.837755i | \(-0.316132\pi\) | ||||
0.546047 | + | 0.837755i | \(0.316132\pi\) | |||||||
\(212\) | 4.19386e11 | 0.0672615 | ||||||||
\(213\) | 2.20544e12 | 0.344673 | ||||||||
\(214\) | −1.82831e11 | −0.0278468 | ||||||||
\(215\) | −7.17976e12 | −1.06586 | ||||||||
\(216\) | 4.70185e11 | 0.0680414 | ||||||||
\(217\) | −4.17772e12 | −0.589401 | ||||||||
\(218\) | 1.58952e12 | 0.218652 | ||||||||
\(219\) | 3.78395e12 | 0.507578 | ||||||||
\(220\) | −2.41459e12 | −0.315877 | ||||||||
\(221\) | 7.41615e12 | 0.946283 | ||||||||
\(222\) | −2.92366e12 | −0.363903 | ||||||||
\(223\) | −5.99559e12 | −0.728040 | −0.364020 | − | 0.931391i | \(-0.618596\pi\) | ||||
−0.364020 | + | 0.931391i | \(0.618596\pi\) | |||||||
\(224\) | −2.43149e12 | −0.288077 | ||||||||
\(225\) | −9.20064e11 | −0.106369 | ||||||||
\(226\) | −5.68968e12 | −0.641936 | ||||||||
\(227\) | −7.74930e12 | −0.853337 | −0.426668 | − | 0.904408i | \(-0.640313\pi\) | ||||
−0.426668 | + | 0.904408i | \(0.640313\pi\) | |||||||
\(228\) | −3.77381e12 | −0.405638 | ||||||||
\(229\) | 3.75804e12 | 0.394336 | 0.197168 | − | 0.980370i | \(-0.436826\pi\) | ||||
0.197168 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(230\) | 9.63043e12 | 0.986604 | ||||||||
\(231\) | 7.20106e12 | 0.720329 | ||||||||
\(232\) | −3.88567e12 | −0.379561 | ||||||||
\(233\) | 9.02676e12 | 0.861141 | 0.430570 | − | 0.902557i | \(-0.358312\pi\) | ||||
0.430570 | + | 0.902557i | \(0.358312\pi\) | |||||||
\(234\) | −2.58409e12 | −0.240780 | ||||||||
\(235\) | −7.53479e12 | −0.685801 | ||||||||
\(236\) | −2.95206e12 | −0.262487 | ||||||||
\(237\) | 7.33781e12 | 0.637457 | ||||||||
\(238\) | −1.25749e13 | −1.06741 | ||||||||
\(239\) | −4.02269e12 | −0.333679 | −0.166839 | − | 0.985984i | \(-0.553356\pi\) | ||||
−0.166839 | + | 0.985984i | \(0.553356\pi\) | |||||||
\(240\) | −1.46920e12 | −0.119102 | ||||||||
\(241\) | −1.49997e13 | −1.18847 | −0.594235 | − | 0.804292i | \(-0.702545\pi\) | ||||
−0.594235 | + | 0.804292i | \(0.702545\pi\) | |||||||
\(242\) | 3.77834e12 | 0.292629 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 5.86933e12 | 0.434455 | ||||||||
\(245\) | 1.88762e13 | 1.36616 | ||||||||
\(246\) | 6.65871e12 | 0.471246 | ||||||||
\(247\) | 2.07405e13 | 1.43544 | ||||||||
\(248\) | 1.88915e12 | 0.127874 | ||||||||
\(249\) | −5.62187e12 | −0.372207 | ||||||||
\(250\) | 1.18843e13 | 0.769670 | ||||||||
\(251\) | −1.46817e13 | −0.930187 | −0.465094 | − | 0.885262i | \(-0.653979\pi\) | ||||
−0.465094 | + | 0.885262i | \(0.653979\pi\) | |||||||
\(252\) | 4.38162e12 | 0.271601 | ||||||||
\(253\) | 2.13447e13 | 1.29457 | ||||||||
\(254\) | 1.51586e13 | 0.899653 | ||||||||
\(255\) | −7.59825e12 | −0.441309 | ||||||||
\(256\) | 1.09951e12 | 0.0625000 | ||||||||
\(257\) | −1.64476e13 | −0.915106 | −0.457553 | − | 0.889182i | \(-0.651274\pi\) | ||||
−0.457553 | + | 0.889182i | \(0.651274\pi\) | |||||||
\(258\) | −9.68259e12 | −0.527331 | ||||||||
\(259\) | −2.72454e13 | −1.45259 | ||||||||
\(260\) | 8.07459e12 | 0.421470 | ||||||||
\(261\) | 7.00210e12 | 0.357854 | ||||||||
\(262\) | −5.39436e12 | −0.269950 | ||||||||
\(263\) | −1.96818e13 | −0.964514 | −0.482257 | − | 0.876030i | \(-0.660183\pi\) | ||||
−0.482257 | + | 0.876030i | \(0.660183\pi\) | |||||||
\(264\) | −3.25630e12 | −0.156280 | ||||||||
\(265\) | 2.36150e12 | 0.111003 | ||||||||
\(266\) | −3.51679e13 | −1.61919 | ||||||||
\(267\) | 6.22440e12 | 0.280728 | ||||||||
\(268\) | 3.98671e12 | 0.176146 | ||||||||
\(269\) | −1.16174e13 | −0.502889 | −0.251444 | − | 0.967872i | \(-0.580906\pi\) | ||||
−0.251444 | + | 0.967872i | \(0.580906\pi\) | |||||||
\(270\) | 2.64755e12 | 0.112290 | ||||||||
\(271\) | 7.46788e12 | 0.310360 | 0.155180 | − | 0.987886i | \(-0.450404\pi\) | ||||
0.155180 | + | 0.987886i | \(0.450404\pi\) | |||||||
\(272\) | 5.68634e12 | 0.231581 | ||||||||
\(273\) | −2.40810e13 | −0.961125 | ||||||||
\(274\) | 2.56473e13 | 1.00326 | ||||||||
\(275\) | 6.37197e12 | 0.244311 | ||||||||
\(276\) | 1.29876e13 | 0.488121 | ||||||||
\(277\) | 1.59564e13 | 0.587892 | 0.293946 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293946 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(278\) | −1.67949e13 | −0.606638 | ||||||||
\(279\) | −3.40432e12 | −0.120561 | ||||||||
\(280\) | −1.36914e13 | −0.475420 | ||||||||
\(281\) | 3.96115e13 | 1.34877 | 0.674383 | − | 0.738382i | \(-0.264410\pi\) | ||||
0.674383 | + | 0.738382i | \(0.264410\pi\) | |||||||
\(282\) | −1.01614e13 | −0.339299 | ||||||||
\(283\) | 1.50001e13 | 0.491211 | 0.245605 | − | 0.969370i | \(-0.421013\pi\) | ||||
0.245605 | + | 0.969370i | \(0.421013\pi\) | |||||||
\(284\) | −9.29371e12 | −0.298496 | ||||||||
\(285\) | −2.12498e13 | −0.669435 | ||||||||
\(286\) | 1.78963e13 | 0.553032 | ||||||||
\(287\) | 6.20521e13 | 1.88107 | ||||||||
\(288\) | −1.98136e12 | −0.0589256 | ||||||||
\(289\) | −4.86390e12 | −0.141921 | ||||||||
\(290\) | −2.18796e13 | −0.626399 | ||||||||
\(291\) | 1.50508e13 | 0.422814 | ||||||||
\(292\) | −1.59455e13 | −0.439576 | ||||||||
\(293\) | 3.88255e13 | 1.05038 | 0.525188 | − | 0.850986i | \(-0.323995\pi\) | ||||
0.525188 | + | 0.850986i | \(0.323995\pi\) | |||||||
\(294\) | 2.54563e13 | 0.675905 | ||||||||
\(295\) | −1.66226e13 | −0.433190 | ||||||||
\(296\) | 1.23203e13 | 0.315149 | ||||||||
\(297\) | 5.86796e12 | 0.147342 | ||||||||
\(298\) | −4.02246e13 | −0.991523 | ||||||||
\(299\) | −7.13784e13 | −1.72733 | ||||||||
\(300\) | 3.87714e12 | 0.0921181 | ||||||||
\(301\) | −9.02314e13 | −2.10495 | ||||||||
\(302\) | 1.57478e13 | 0.360729 | ||||||||
\(303\) | 2.30763e13 | 0.519077 | ||||||||
\(304\) | 1.59028e13 | 0.351293 | ||||||||
\(305\) | 3.30494e13 | 0.716992 | ||||||||
\(306\) | −1.02470e13 | −0.218337 | ||||||||
\(307\) | 7.58194e13 | 1.58679 | 0.793394 | − | 0.608708i | \(-0.208312\pi\) | ||||
0.793394 | + | 0.608708i | \(0.208312\pi\) | |||||||
\(308\) | −3.03452e13 | −0.623823 | ||||||||
\(309\) | −1.32124e13 | −0.266814 | ||||||||
\(310\) | 1.06376e13 | 0.211034 | ||||||||
\(311\) | −7.99907e13 | −1.55904 | −0.779520 | − | 0.626378i | \(-0.784537\pi\) | ||||
−0.779520 | + | 0.626378i | \(0.784537\pi\) | |||||||
\(312\) | 1.08894e13 | 0.208522 | ||||||||
\(313\) | −6.85614e13 | −1.28999 | −0.644994 | − | 0.764187i | \(-0.723140\pi\) | ||||
−0.644994 | + | 0.764187i | \(0.723140\pi\) | |||||||
\(314\) | 3.19069e13 | 0.589891 | ||||||||
\(315\) | 2.46723e13 | 0.448231 | ||||||||
\(316\) | −3.09215e13 | −0.552054 | ||||||||
\(317\) | 6.37891e12 | 0.111923 | 0.0559617 | − | 0.998433i | \(-0.482178\pi\) | ||||
0.0559617 | + | 0.998433i | \(0.482178\pi\) | |||||||
\(318\) | 3.18471e12 | 0.0549188 | ||||||||
\(319\) | −4.84935e13 | −0.821930 | ||||||||
\(320\) | 6.19120e12 | 0.103145 | ||||||||
\(321\) | −1.38838e12 | −0.0227368 | ||||||||
\(322\) | 1.21030e14 | 1.94844 | ||||||||
\(323\) | 8.22445e13 | 1.30165 | ||||||||
\(324\) | 3.57047e12 | 0.0555556 | ||||||||
\(325\) | −2.13084e13 | −0.325981 | ||||||||
\(326\) | 1.54925e13 | 0.233038 | ||||||||
\(327\) | 1.20704e13 | 0.178529 | ||||||||
\(328\) | −2.80598e13 | −0.408111 | ||||||||
\(329\) | −9.46932e13 | −1.35438 | ||||||||
\(330\) | −1.83358e13 | −0.257912 | ||||||||
\(331\) | 8.90210e13 | 1.23151 | 0.615756 | − | 0.787937i | \(-0.288851\pi\) | ||||
0.615756 | + | 0.787937i | \(0.288851\pi\) | |||||||
\(332\) | 2.36905e13 | 0.322340 | ||||||||
\(333\) | −2.22015e13 | −0.297126 | ||||||||
\(334\) | −7.40920e13 | −0.975361 | ||||||||
\(335\) | 2.24486e13 | 0.290699 | ||||||||
\(336\) | −1.84641e13 | −0.235214 | ||||||||
\(337\) | 1.42601e14 | 1.78714 | 0.893568 | − | 0.448928i | \(-0.148194\pi\) | ||||
0.893568 | + | 0.448928i | \(0.148194\pi\) | |||||||
\(338\) | −2.49774e12 | −0.0307968 | ||||||||
\(339\) | −4.32060e13 | −0.524138 | ||||||||
\(340\) | 3.20190e13 | 0.382185 | ||||||||
\(341\) | 2.35768e13 | 0.276909 | ||||||||
\(342\) | −2.86574e13 | −0.331202 | ||||||||
\(343\) | 9.39407e13 | 1.06841 | ||||||||
\(344\) | 4.08024e13 | 0.456682 | ||||||||
\(345\) | 7.31311e13 | 0.805558 | ||||||||
\(346\) | −1.07890e14 | −1.16967 | ||||||||
\(347\) | −1.33726e14 | −1.42693 | −0.713467 | − | 0.700689i | \(-0.752876\pi\) | ||||
−0.713467 | + | 0.700689i | \(0.752876\pi\) | |||||||
\(348\) | −2.95068e13 | −0.309910 | ||||||||
\(349\) | −6.30474e13 | −0.651820 | −0.325910 | − | 0.945401i | \(-0.605671\pi\) | ||||
−0.325910 | + | 0.945401i | \(0.605671\pi\) | |||||||
\(350\) | 3.61308e13 | 0.367708 | ||||||||
\(351\) | −1.96230e13 | −0.196596 | ||||||||
\(352\) | 1.37220e13 | 0.135342 | ||||||||
\(353\) | −2.89749e13 | −0.281359 | −0.140680 | − | 0.990055i | \(-0.544929\pi\) | ||||
−0.140680 | + | 0.990055i | \(0.544929\pi\) | |||||||
\(354\) | −2.24172e13 | −0.214320 | ||||||||
\(355\) | −5.23316e13 | −0.492615 | ||||||||
\(356\) | −2.62296e13 | −0.243118 | ||||||||
\(357\) | −9.54907e13 | −0.871538 | ||||||||
\(358\) | −5.26713e13 | −0.473388 | ||||||||
\(359\) | 4.33108e13 | 0.383334 | 0.191667 | − | 0.981460i | \(-0.438611\pi\) | ||||
0.191667 | + | 0.981460i | \(0.438611\pi\) | |||||||
\(360\) | −1.11567e13 | −0.0972464 | ||||||||
\(361\) | 1.13520e14 | 0.974505 | ||||||||
\(362\) | −8.77495e13 | −0.741904 | ||||||||
\(363\) | 2.86918e13 | 0.238930 | ||||||||
\(364\) | 1.01477e14 | 0.832358 | ||||||||
\(365\) | −8.97871e13 | −0.725443 | ||||||||
\(366\) | 4.45702e13 | 0.354731 | ||||||||
\(367\) | −1.12471e14 | −0.881814 | −0.440907 | − | 0.897553i | \(-0.645343\pi\) | ||||
−0.440907 | + | 0.897553i | \(0.645343\pi\) | |||||||
\(368\) | −5.47295e13 | −0.422725 | ||||||||
\(369\) | 5.05646e13 | 0.384770 | ||||||||
\(370\) | 6.93738e13 | 0.520099 | ||||||||
\(371\) | 2.96781e13 | 0.219220 | ||||||||
\(372\) | 1.43458e13 | 0.104409 | ||||||||
\(373\) | 1.29948e14 | 0.931900 | 0.465950 | − | 0.884811i | \(-0.345713\pi\) | ||||
0.465950 | + | 0.884811i | \(0.345713\pi\) | |||||||
\(374\) | 7.09661e13 | 0.501484 | ||||||||
\(375\) | 9.02466e13 | 0.628433 | ||||||||
\(376\) | 4.28200e13 | 0.293842 | ||||||||
\(377\) | 1.62167e14 | 1.09669 | ||||||||
\(378\) | 3.32729e13 | 0.221762 | ||||||||
\(379\) | −9.45382e13 | −0.621000 | −0.310500 | − | 0.950573i | \(-0.600496\pi\) | ||||
−0.310500 | + | 0.950573i | \(0.600496\pi\) | |||||||
\(380\) | 8.95465e13 | 0.579747 | ||||||||
\(381\) | 1.15111e14 | 0.734563 | ||||||||
\(382\) | −1.30691e14 | −0.822047 | ||||||||
\(383\) | 5.45117e13 | 0.337985 | 0.168992 | − | 0.985617i | \(-0.445949\pi\) | ||||
0.168992 | + | 0.985617i | \(0.445949\pi\) | |||||||
\(384\) | 8.34942e12 | 0.0510310 | ||||||||
\(385\) | −1.70870e14 | −1.02951 | ||||||||
\(386\) | 1.43116e14 | 0.850079 | ||||||||
\(387\) | −7.35272e13 | −0.430564 | ||||||||
\(388\) | −6.34241e13 | −0.366167 | ||||||||
\(389\) | −5.11379e13 | −0.291085 | −0.145543 | − | 0.989352i | \(-0.546493\pi\) | ||||
−0.145543 | + | 0.989352i | \(0.546493\pi\) | |||||||
\(390\) | 6.13164e13 | 0.344129 | ||||||||
\(391\) | −2.83044e14 | −1.56632 | ||||||||
\(392\) | −1.07273e14 | −0.585351 | ||||||||
\(393\) | −4.09634e13 | −0.220413 | ||||||||
\(394\) | 2.35848e14 | 1.25142 | ||||||||
\(395\) | −1.74115e14 | −0.911068 | ||||||||
\(396\) | −2.47275e13 | −0.127602 | ||||||||
\(397\) | −4.87234e13 | −0.247965 | −0.123982 | − | 0.992284i | \(-0.539567\pi\) | ||||
−0.123982 | + | 0.992284i | \(0.539567\pi\) | |||||||
\(398\) | −8.61787e13 | −0.432557 | ||||||||
\(399\) | −2.67056e14 | −1.32206 | ||||||||
\(400\) | −1.63382e13 | −0.0797766 | ||||||||
\(401\) | 3.76407e14 | 1.81286 | 0.906430 | − | 0.422356i | \(-0.138797\pi\) | ||||
0.906430 | + | 0.422356i | \(0.138797\pi\) | |||||||
\(402\) | 3.02741e13 | 0.143823 | ||||||||
\(403\) | −7.88430e13 | −0.369475 | ||||||||
\(404\) | −9.72433e13 | −0.449534 | ||||||||
\(405\) | 2.01048e13 | 0.0916847 | ||||||||
\(406\) | −2.74972e14 | −1.23707 | ||||||||
\(407\) | 1.53758e14 | 0.682448 | ||||||||
\(408\) | 4.31806e13 | 0.189085 | ||||||||
\(409\) | 3.12467e14 | 1.34998 | 0.674988 | − | 0.737828i | \(-0.264149\pi\) | ||||
0.674988 | + | 0.737828i | \(0.264149\pi\) | |||||||
\(410\) | −1.58001e14 | −0.673515 | ||||||||
\(411\) | 1.94759e14 | 0.819160 | ||||||||
\(412\) | 5.56768e13 | 0.231068 | ||||||||
\(413\) | −2.08904e14 | −0.855503 | ||||||||
\(414\) | 9.86242e13 | 0.398549 | ||||||||
\(415\) | 1.33398e14 | 0.531967 | ||||||||
\(416\) | −4.58876e13 | −0.180585 | ||||||||
\(417\) | −1.27536e14 | −0.495318 | ||||||||
\(418\) | 1.98469e14 | 0.760716 | ||||||||
\(419\) | 2.81729e14 | 1.06575 | 0.532874 | − | 0.846195i | \(-0.321112\pi\) | ||||
0.532874 | + | 0.846195i | \(0.321112\pi\) | |||||||
\(420\) | −1.03969e14 | −0.388179 | ||||||||
\(421\) | −3.01064e14 | −1.10945 | −0.554724 | − | 0.832034i | \(-0.687176\pi\) | ||||
−0.554724 | + | 0.832034i | \(0.687176\pi\) | |||||||
\(422\) | −2.12306e14 | −0.772227 | ||||||||
\(423\) | −7.71630e13 | −0.277037 | ||||||||
\(424\) | −1.34203e13 | −0.0475610 | ||||||||
\(425\) | −8.44964e13 | −0.295596 | ||||||||
\(426\) | −7.05741e13 | −0.243721 | ||||||||
\(427\) | 4.15347e14 | 1.41598 | ||||||||
\(428\) | 5.85060e12 | 0.0196906 | ||||||||
\(429\) | 1.35900e14 | 0.451549 | ||||||||
\(430\) | 2.29752e14 | 0.753674 | ||||||||
\(431\) | 3.46694e14 | 1.12285 | 0.561425 | − | 0.827528i | \(-0.310253\pi\) | ||||
0.561425 | + | 0.827528i | \(0.310253\pi\) | |||||||
\(432\) | −1.50459e13 | −0.0481125 | ||||||||
\(433\) | 4.82345e14 | 1.52291 | 0.761456 | − | 0.648217i | \(-0.224485\pi\) | ||||
0.761456 | + | 0.648217i | \(0.224485\pi\) | |||||||
\(434\) | 1.33687e14 | 0.416770 | ||||||||
\(435\) | −1.66149e14 | −0.511453 | ||||||||
\(436\) | −5.08645e13 | −0.154611 | ||||||||
\(437\) | −7.91581e14 | −2.37600 | ||||||||
\(438\) | −1.21086e14 | −0.358912 | ||||||||
\(439\) | 1.18934e14 | 0.348138 | 0.174069 | − | 0.984733i | \(-0.444308\pi\) | ||||
0.174069 | + | 0.984733i | \(0.444308\pi\) | |||||||
\(440\) | 7.72668e13 | 0.223359 | ||||||||
\(441\) | 1.93309e14 | 0.551874 | ||||||||
\(442\) | −2.37317e14 | −0.669123 | ||||||||
\(443\) | −1.99914e14 | −0.556703 | −0.278351 | − | 0.960479i | \(-0.589788\pi\) | ||||
−0.278351 | + | 0.960479i | \(0.589788\pi\) | |||||||
\(444\) | 9.35571e13 | 0.257318 | ||||||||
\(445\) | −1.47695e14 | −0.401223 | ||||||||
\(446\) | 1.91859e14 | 0.514802 | ||||||||
\(447\) | −3.05456e14 | −0.809575 | ||||||||
\(448\) | 7.78076e13 | 0.203701 | ||||||||
\(449\) | −5.06702e14 | −1.31038 | −0.655191 | − | 0.755464i | \(-0.727412\pi\) | ||||
−0.655191 | + | 0.755464i | \(0.727412\pi\) | |||||||
\(450\) | 2.94421e13 | 0.0752141 | ||||||||
\(451\) | −3.50189e14 | −0.883754 | ||||||||
\(452\) | 1.82070e14 | 0.453917 | ||||||||
\(453\) | 1.19585e14 | 0.294534 | ||||||||
\(454\) | 2.47978e14 | 0.603400 | ||||||||
\(455\) | 5.71403e14 | 1.37366 | ||||||||
\(456\) | 1.20762e14 | 0.286829 | ||||||||
\(457\) | −3.62768e14 | −0.851315 | −0.425658 | − | 0.904884i | \(-0.639957\pi\) | ||||
−0.425658 | + | 0.904884i | \(0.639957\pi\) | |||||||
\(458\) | −1.20257e14 | −0.278838 | ||||||||
\(459\) | −7.78129e13 | −0.178271 | ||||||||
\(460\) | −3.08174e14 | −0.697634 | ||||||||
\(461\) | 6.56466e13 | 0.146844 | 0.0734221 | − | 0.997301i | \(-0.476608\pi\) | ||||
0.0734221 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(462\) | −2.30434e14 | −0.509349 | ||||||||
\(463\) | −2.06748e14 | −0.451592 | −0.225796 | − | 0.974175i | \(-0.572498\pi\) | ||||
−0.225796 | + | 0.974175i | \(0.572498\pi\) | |||||||
\(464\) | 1.24341e14 | 0.268390 | ||||||||
\(465\) | 8.07790e13 | 0.172309 | ||||||||
\(466\) | −2.88856e14 | −0.608919 | ||||||||
\(467\) | −3.79401e14 | −0.790416 | −0.395208 | − | 0.918592i | \(-0.629327\pi\) | ||||
−0.395208 | + | 0.918592i | \(0.629327\pi\) | |||||||
\(468\) | 8.26910e13 | 0.170257 | ||||||||
\(469\) | 2.82122e14 | 0.574099 | ||||||||
\(470\) | 2.41113e14 | 0.484935 | ||||||||
\(471\) | 2.42293e14 | 0.481644 | ||||||||
\(472\) | 9.44658e13 | 0.185607 | ||||||||
\(473\) | 5.09218e14 | 0.988934 | ||||||||
\(474\) | −2.34810e14 | −0.450750 | ||||||||
\(475\) | −2.36309e14 | −0.448399 | ||||||||
\(476\) | 4.02397e14 | 0.754774 | ||||||||
\(477\) | 2.41839e13 | 0.0448410 | ||||||||
\(478\) | 1.28726e14 | 0.235946 | ||||||||
\(479\) | 3.67939e14 | 0.666701 | 0.333350 | − | 0.942803i | \(-0.391821\pi\) | ||||
0.333350 | + | 0.942803i | \(0.391821\pi\) | |||||||
\(480\) | 4.70144e13 | 0.0842178 | ||||||||
\(481\) | −5.14182e14 | −0.910581 | ||||||||
\(482\) | 4.79989e14 | 0.840375 | ||||||||
\(483\) | 9.19072e14 | 1.59089 | ||||||||
\(484\) | −1.20907e14 | −0.206920 | ||||||||
\(485\) | −3.57132e14 | −0.604295 | ||||||||
\(486\) | 2.71132e13 | 0.0453609 | ||||||||
\(487\) | 6.31645e14 | 1.04487 | 0.522437 | − | 0.852678i | \(-0.325023\pi\) | ||||
0.522437 | + | 0.852678i | \(0.325023\pi\) | |||||||
\(488\) | −1.87819e14 | −0.307206 | ||||||||
\(489\) | 1.17647e14 | 0.190274 | ||||||||
\(490\) | −6.04038e14 | −0.966019 | ||||||||
\(491\) | 2.78183e14 | 0.439929 | 0.219965 | − | 0.975508i | \(-0.429406\pi\) | ||||
0.219965 | + | 0.975508i | \(0.429406\pi\) | |||||||
\(492\) | −2.13079e14 | −0.333221 | ||||||||
\(493\) | 6.43055e14 | 0.994467 | ||||||||
\(494\) | −6.63697e14 | −1.01501 | ||||||||
\(495\) | −1.39237e14 | −0.210585 | ||||||||
\(496\) | −6.04529e13 | −0.0904208 | ||||||||
\(497\) | −6.57675e14 | −0.972862 | ||||||||
\(498\) | 1.79900e14 | 0.263190 | ||||||||
\(499\) | 4.59050e14 | 0.664213 | 0.332106 | − | 0.943242i | \(-0.392241\pi\) | ||||
0.332106 | + | 0.943242i | \(0.392241\pi\) | |||||||
\(500\) | −3.80298e14 | −0.544239 | ||||||||
\(501\) | −5.62636e14 | −0.796379 | ||||||||
\(502\) | 4.69814e14 | 0.657742 | ||||||||
\(503\) | −9.15703e14 | −1.26803 | −0.634017 | − | 0.773319i | \(-0.718595\pi\) | ||||
−0.634017 | + | 0.773319i | \(0.718595\pi\) | |||||||
\(504\) | −1.40212e14 | −0.192051 | ||||||||
\(505\) | −5.47563e14 | −0.741877 | ||||||||
\(506\) | −6.83029e14 | −0.915401 | ||||||||
\(507\) | −1.89672e13 | −0.0251455 | ||||||||
\(508\) | −4.85077e14 | −0.636150 | ||||||||
\(509\) | 1.08562e15 | 1.40842 | 0.704208 | − | 0.709993i | \(-0.251302\pi\) | ||||
0.704208 | + | 0.709993i | \(0.251302\pi\) | |||||||
\(510\) | 2.43144e14 | 0.312052 | ||||||||
\(511\) | −1.12840e15 | −1.43267 | ||||||||
\(512\) | −3.51844e13 | −0.0441942 | ||||||||
\(513\) | −2.17617e14 | −0.270425 | ||||||||
\(514\) | 5.26324e14 | 0.647077 | ||||||||
\(515\) | 3.13508e14 | 0.381337 | ||||||||
\(516\) | 3.09843e14 | 0.372879 | ||||||||
\(517\) | 5.34398e14 | 0.636307 | ||||||||
\(518\) | 8.71852e14 | 1.02714 | ||||||||
\(519\) | −8.19291e14 | −0.955031 | ||||||||
\(520\) | −2.58387e14 | −0.298024 | ||||||||
\(521\) | −1.63925e14 | −0.187084 | −0.0935422 | − | 0.995615i | \(-0.529819\pi\) | ||||
−0.0935422 | + | 0.995615i | \(0.529819\pi\) | |||||||
\(522\) | −2.24067e14 | −0.253041 | ||||||||
\(523\) | 4.69127e13 | 0.0524241 | 0.0262121 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262121 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(524\) | 1.72620e14 | 0.190883 | ||||||||
\(525\) | 2.74368e14 | 0.300233 | ||||||||
\(526\) | 6.29818e14 | 0.682015 | ||||||||
\(527\) | −3.12644e14 | −0.335036 | ||||||||
\(528\) | 1.04202e14 | 0.110506 | ||||||||
\(529\) | 1.77141e15 | 1.85914 | ||||||||
\(530\) | −7.55681e13 | −0.0784912 | ||||||||
\(531\) | −1.70230e14 | −0.174992 | ||||||||
\(532\) | 1.12537e15 | 1.14494 | ||||||||
\(533\) | 1.17106e15 | 1.17918 | ||||||||
\(534\) | −1.99181e14 | −0.198505 | ||||||||
\(535\) | 3.29439e13 | 0.0324960 | ||||||||
\(536\) | −1.27575e14 | −0.124554 | ||||||||
\(537\) | −3.99972e14 | −0.386520 | ||||||||
\(538\) | 3.71757e14 | 0.355596 | ||||||||
\(539\) | −1.33877e15 | −1.26756 | ||||||||
\(540\) | −8.47215e13 | −0.0794013 | ||||||||
\(541\) | −1.28196e15 | −1.18929 | −0.594647 | − | 0.803987i | \(-0.702708\pi\) | ||||
−0.594647 | + | 0.803987i | \(0.702708\pi\) | |||||||
\(542\) | −2.38972e14 | −0.219458 | ||||||||
\(543\) | −6.66348e14 | −0.605762 | ||||||||
\(544\) | −1.81963e14 | −0.163753 | ||||||||
\(545\) | −2.86411e14 | −0.255158 | ||||||||
\(546\) | 7.70592e14 | 0.679618 | ||||||||
\(547\) | 1.10564e15 | 0.965347 | 0.482673 | − | 0.875801i | \(-0.339666\pi\) | ||||
0.482673 | + | 0.875801i | \(0.339666\pi\) | |||||||
\(548\) | −8.20715e14 | −0.709413 | ||||||||
\(549\) | 3.38455e14 | 0.289636 | ||||||||
\(550\) | −2.03903e14 | −0.172754 | ||||||||
\(551\) | 1.79841e15 | 1.50854 | ||||||||
\(552\) | −4.15602e14 | −0.345154 | ||||||||
\(553\) | −2.18818e15 | −1.79926 | ||||||||
\(554\) | −5.10606e14 | −0.415702 | ||||||||
\(555\) | 5.26807e14 | 0.424659 | ||||||||
\(556\) | 5.37435e14 | 0.428958 | ||||||||
\(557\) | 2.12161e15 | 1.67672 | 0.838362 | − | 0.545113i | \(-0.183513\pi\) | ||||
0.838362 | + | 0.545113i | \(0.183513\pi\) | |||||||
\(558\) | 1.08938e14 | 0.0852495 | ||||||||
\(559\) | −1.70287e15 | −1.31952 | ||||||||
\(560\) | 4.38124e14 | 0.336173 | ||||||||
\(561\) | 5.38899e14 | 0.409460 | ||||||||
\(562\) | −1.26757e15 | −0.953721 | ||||||||
\(563\) | −2.44888e15 | −1.82462 | −0.912309 | − | 0.409503i | \(-0.865702\pi\) | ||||
−0.912309 | + | 0.409503i | \(0.865702\pi\) | |||||||
\(564\) | 3.25164e14 | 0.239921 | ||||||||
\(565\) | 1.02521e15 | 0.749111 | ||||||||
\(566\) | −4.80002e14 | −0.347338 | ||||||||
\(567\) | 2.52666e14 | 0.181068 | ||||||||
\(568\) | 2.97399e14 | 0.211068 | ||||||||
\(569\) | −7.38095e14 | −0.518794 | −0.259397 | − | 0.965771i | \(-0.583524\pi\) | ||||
−0.259397 | + | 0.965771i | \(0.583524\pi\) | |||||||
\(570\) | 6.79994e14 | 0.473362 | ||||||||
\(571\) | −2.10103e13 | −0.0144855 | −0.00724274 | − | 0.999974i | \(-0.502305\pi\) | ||||
−0.00724274 | + | 0.999974i | \(0.502305\pi\) | |||||||
\(572\) | −5.72682e14 | −0.391053 | ||||||||
\(573\) | −9.92434e14 | −0.671199 | ||||||||
\(574\) | −1.98567e15 | −1.33012 | ||||||||
\(575\) | 8.13255e14 | 0.539577 | ||||||||
\(576\) | 6.34034e13 | 0.0416667 | ||||||||
\(577\) | 1.13249e15 | 0.737168 | 0.368584 | − | 0.929594i | \(-0.379843\pi\) | ||||
0.368584 | + | 0.929594i | \(0.379843\pi\) | |||||||
\(578\) | 1.55645e14 | 0.100353 | ||||||||
\(579\) | 1.08679e15 | 0.694087 | ||||||||
\(580\) | 7.00149e14 | 0.442931 | ||||||||
\(581\) | 1.67647e15 | 1.05058 | ||||||||
\(582\) | −4.81626e14 | −0.298974 | ||||||||
\(583\) | −1.67487e14 | −0.102992 | ||||||||
\(584\) | 5.10257e14 | 0.310827 | ||||||||
\(585\) | 4.65621e14 | 0.280980 | ||||||||
\(586\) | −1.24242e15 | −0.742728 | ||||||||
\(587\) | −2.91255e15 | −1.72490 | −0.862448 | − | 0.506145i | \(-0.831070\pi\) | ||||
−0.862448 | + | 0.506145i | \(0.831070\pi\) | |||||||
\(588\) | −8.14602e14 | −0.477937 | ||||||||
\(589\) | −8.74362e14 | −0.508226 | ||||||||
\(590\) | 5.31923e14 | 0.306311 | ||||||||
\(591\) | 1.79097e15 | 1.02178 | ||||||||
\(592\) | −3.94249e14 | −0.222844 | ||||||||
\(593\) | 1.52901e15 | 0.856270 | 0.428135 | − | 0.903715i | \(-0.359171\pi\) | ||||
0.428135 | + | 0.903715i | \(0.359171\pi\) | |||||||
\(594\) | −1.87775e14 | −0.104186 | ||||||||
\(595\) | 2.26584e15 | 1.24562 | ||||||||
\(596\) | 1.28719e15 | 0.701113 | ||||||||
\(597\) | −6.54420e14 | −0.353181 | ||||||||
\(598\) | 2.28411e15 | 1.22141 | ||||||||
\(599\) | 2.71517e15 | 1.43863 | 0.719315 | − | 0.694684i | \(-0.244456\pi\) | ||||
0.719315 | + | 0.694684i | \(0.244456\pi\) | |||||||
\(600\) | −1.24069e14 | −0.0651373 | ||||||||
\(601\) | −2.59104e15 | −1.34792 | −0.673960 | − | 0.738768i | \(-0.735408\pi\) | ||||
−0.673960 | + | 0.738768i | \(0.735408\pi\) | |||||||
\(602\) | 2.88740e15 | 1.48842 | ||||||||
\(603\) | 2.29894e14 | 0.117431 | ||||||||
\(604\) | −5.03928e14 | −0.255074 | ||||||||
\(605\) | −6.80810e14 | −0.341485 | ||||||||
\(606\) | −7.38441e14 | −0.367043 | ||||||||
\(607\) | 1.68761e15 | 0.831255 | 0.415628 | − | 0.909535i | \(-0.363562\pi\) | ||||
0.415628 | + | 0.909535i | \(0.363562\pi\) | |||||||
\(608\) | −5.08890e14 | −0.248401 | ||||||||
\(609\) | −2.08807e15 | −1.01006 | ||||||||
\(610\) | −1.05758e15 | −0.506990 | ||||||||
\(611\) | −1.78707e15 | −0.849016 | ||||||||
\(612\) | 3.27903e14 | 0.154388 | ||||||||
\(613\) | −5.35764e14 | −0.250000 | −0.125000 | − | 0.992157i | \(-0.539893\pi\) | ||||
−0.125000 | + | 0.992157i | \(0.539893\pi\) | |||||||
\(614\) | −2.42622e15 | −1.12203 | ||||||||
\(615\) | −1.19982e15 | −0.549923 | ||||||||
\(616\) | 9.71047e14 | 0.441109 | ||||||||
\(617\) | −2.84367e15 | −1.28030 | −0.640148 | − | 0.768251i | \(-0.721127\pi\) | ||||
−0.640148 | + | 0.768251i | \(0.721127\pi\) | |||||||
\(618\) | 4.22796e14 | 0.188666 | ||||||||
\(619\) | 8.14487e14 | 0.360235 | 0.180117 | − | 0.983645i | \(-0.442352\pi\) | ||||
0.180117 | + | 0.983645i | \(0.442352\pi\) | |||||||
\(620\) | −3.40402e14 | −0.149224 | ||||||||
\(621\) | 7.48928e14 | 0.325414 | ||||||||
\(622\) | 2.55970e15 | 1.10241 | ||||||||
\(623\) | −1.85615e15 | −0.792372 | ||||||||
\(624\) | −3.48459e14 | −0.147447 | ||||||||
\(625\) | −1.38060e15 | −0.579065 | ||||||||
\(626\) | 2.19397e15 | 0.912160 | ||||||||
\(627\) | 1.50712e15 | 0.621122 | ||||||||
\(628\) | −1.02102e15 | −0.417116 | ||||||||
\(629\) | −2.03894e15 | −0.825705 | ||||||||
\(630\) | −7.89513e14 | −0.316947 | ||||||||
\(631\) | −1.45868e15 | −0.580497 | −0.290248 | − | 0.956951i | \(-0.593738\pi\) | ||||
−0.290248 | + | 0.956951i | \(0.593738\pi\) | |||||||
\(632\) | 9.89488e14 | 0.390361 | ||||||||
\(633\) | −1.61220e15 | −0.630520 | ||||||||
\(634\) | −2.04125e14 | −0.0791417 | ||||||||
\(635\) | −2.73140e15 | −1.04986 | ||||||||
\(636\) | −1.01911e14 | −0.0388334 | ||||||||
\(637\) | 4.47698e15 | 1.69129 | ||||||||
\(638\) | 1.55179e15 | 0.581192 | ||||||||
\(639\) | −5.35922e14 | −0.198997 | ||||||||
\(640\) | −1.98118e14 | −0.0729348 | ||||||||
\(641\) | −1.16297e15 | −0.424473 | −0.212236 | − | 0.977218i | \(-0.568075\pi\) | ||||
−0.212236 | + | 0.977218i | \(0.568075\pi\) | |||||||
\(642\) | 4.44280e13 | 0.0160773 | ||||||||
\(643\) | 4.73461e15 | 1.69873 | 0.849364 | − | 0.527807i | \(-0.176985\pi\) | ||||
0.849364 | + | 0.527807i | \(0.176985\pi\) | |||||||
\(644\) | −3.87296e15 | −1.37775 | ||||||||
\(645\) | 1.74468e15 | 0.615372 | ||||||||
\(646\) | −2.63182e15 | −0.920402 | ||||||||
\(647\) | 5.47527e15 | 1.89859 | 0.949297 | − | 0.314380i | \(-0.101797\pi\) | ||||
0.949297 | + | 0.314380i | \(0.101797\pi\) | |||||||
\(648\) | −1.14255e14 | −0.0392837 | ||||||||
\(649\) | 1.17894e15 | 0.401927 | ||||||||
\(650\) | 6.81870e14 | 0.230504 | ||||||||
\(651\) | 1.01519e15 | 0.340291 | ||||||||
\(652\) | −4.95761e14 | −0.164782 | ||||||||
\(653\) | −8.87971e14 | −0.292669 | −0.146334 | − | 0.989235i | \(-0.546748\pi\) | ||||
−0.146334 | + | 0.989235i | \(0.546748\pi\) | |||||||
\(654\) | −3.86252e14 | −0.126239 | ||||||||
\(655\) | 9.71997e14 | 0.315020 | ||||||||
\(656\) | 8.97913e14 | 0.288578 | ||||||||
\(657\) | −9.19501e14 | −0.293051 | ||||||||
\(658\) | 3.03018e15 | 0.957694 | ||||||||
\(659\) | 3.14454e15 | 0.985571 | 0.492785 | − | 0.870151i | \(-0.335979\pi\) | ||||
0.492785 | + | 0.870151i | \(0.335979\pi\) | |||||||
\(660\) | 5.86744e14 | 0.182372 | ||||||||
\(661\) | 1.32982e15 | 0.409907 | 0.204954 | − | 0.978772i | \(-0.434296\pi\) | ||||
0.204954 | + | 0.978772i | \(0.434296\pi\) | |||||||
\(662\) | −2.84867e15 | −0.870810 | ||||||||
\(663\) | −1.80212e15 | −0.546337 | ||||||||
\(664\) | −7.58096e14 | −0.227929 | ||||||||
\(665\) | 6.33681e15 | 1.88952 | ||||||||
\(666\) | 7.10450e14 | 0.210099 | ||||||||
\(667\) | −6.18923e15 | −1.81528 | ||||||||
\(668\) | 2.37094e15 | 0.689685 | ||||||||
\(669\) | 1.45693e15 | 0.420334 | ||||||||
\(670\) | −7.18355e14 | −0.205555 | ||||||||
\(671\) | −2.34399e15 | −0.665247 | ||||||||
\(672\) | 5.90852e14 | 0.166321 | ||||||||
\(673\) | −6.84438e15 | −1.91096 | −0.955479 | − | 0.295058i | \(-0.904661\pi\) | ||||
−0.955479 | + | 0.295058i | \(0.904661\pi\) | |||||||
\(674\) | −4.56323e15 | −1.26370 | ||||||||
\(675\) | 2.23576e14 | 0.0614121 | ||||||||
\(676\) | 7.99278e13 | 0.0217766 | ||||||||
\(677\) | 8.88820e14 | 0.240202 | 0.120101 | − | 0.992762i | \(-0.461678\pi\) | ||||
0.120101 | + | 0.992762i | \(0.461678\pi\) | |||||||
\(678\) | 1.38259e15 | 0.370622 | ||||||||
\(679\) | −4.48824e15 | −1.19342 | ||||||||
\(680\) | −1.02461e15 | −0.270245 | ||||||||
\(681\) | 1.88308e15 | 0.492674 | ||||||||
\(682\) | −7.54459e14 | −0.195804 | ||||||||
\(683\) | 2.22402e15 | 0.572565 | 0.286282 | − | 0.958145i | \(-0.407580\pi\) | ||||
0.286282 | + | 0.958145i | \(0.407580\pi\) | |||||||
\(684\) | 9.17036e14 | 0.234195 | ||||||||
\(685\) | −4.62133e15 | −1.17076 | ||||||||
\(686\) | −3.00610e15 | −0.755477 | ||||||||
\(687\) | −9.13204e14 | −0.227670 | ||||||||
\(688\) | −1.30568e15 | −0.322923 | ||||||||
\(689\) | 5.60092e14 | 0.137421 | ||||||||
\(690\) | −2.34020e15 | −0.569616 | ||||||||
\(691\) | 4.59721e15 | 1.11011 | 0.555053 | − | 0.831815i | \(-0.312698\pi\) | ||||
0.555053 | + | 0.831815i | \(0.312698\pi\) | |||||||
\(692\) | 3.45248e15 | 0.827081 | ||||||||
\(693\) | −1.74986e15 | −0.415882 | ||||||||
\(694\) | 4.27923e15 | 1.00899 | ||||||||
\(695\) | 3.02622e15 | 0.707921 | ||||||||
\(696\) | 9.44217e14 | 0.219140 | ||||||||
\(697\) | 4.64373e15 | 1.06927 | ||||||||
\(698\) | 2.01752e15 | 0.460906 | ||||||||
\(699\) | −2.19350e15 | −0.497180 | ||||||||
\(700\) | −1.15619e15 | −0.260009 | ||||||||
\(701\) | −2.58701e15 | −0.577231 | −0.288616 | − | 0.957445i | \(-0.593195\pi\) | ||||
−0.288616 | + | 0.957445i | \(0.593195\pi\) | |||||||
\(702\) | 6.27935e14 | 0.139015 | ||||||||
\(703\) | −5.70223e15 | −1.25254 | ||||||||
\(704\) | −4.39105e14 | −0.0957014 | ||||||||
\(705\) | 1.83095e15 | 0.395947 | ||||||||
\(706\) | 9.27197e14 | 0.198951 | ||||||||
\(707\) | −6.88148e15 | −1.46513 | ||||||||
\(708\) | 7.17349e14 | 0.151547 | ||||||||
\(709\) | 2.52081e15 | 0.528427 | 0.264214 | − | 0.964464i | \(-0.414888\pi\) | ||||
0.264214 | + | 0.964464i | \(0.414888\pi\) | |||||||
\(710\) | 1.67461e15 | 0.348332 | ||||||||
\(711\) | −1.78309e15 | −0.368036 | ||||||||
\(712\) | 8.39346e14 | 0.171910 | ||||||||
\(713\) | 3.00911e15 | 0.611570 | ||||||||
\(714\) | 3.05570e15 | 0.616270 | ||||||||
\(715\) | −3.22469e15 | −0.645365 | ||||||||
\(716\) | 1.68548e15 | 0.334736 | ||||||||
\(717\) | 9.77514e14 | 0.192649 | ||||||||
\(718\) | −1.38595e15 | −0.271058 | ||||||||
\(719\) | 3.03716e15 | 0.589467 | 0.294733 | − | 0.955580i | \(-0.404769\pi\) | ||||
0.294733 | + | 0.955580i | \(0.404769\pi\) | |||||||
\(720\) | 3.57016e14 | 0.0687636 | ||||||||
\(721\) | 3.94001e15 | 0.753100 | ||||||||
\(722\) | −3.63265e15 | −0.689079 | ||||||||
\(723\) | 3.64492e15 | 0.686163 | ||||||||
\(724\) | 2.80799e15 | 0.524605 | ||||||||
\(725\) | −1.84766e15 | −0.342580 | ||||||||
\(726\) | −9.18137e14 | −0.168949 | ||||||||
\(727\) | 6.52086e15 | 1.19087 | 0.595436 | − | 0.803402i | \(-0.296979\pi\) | ||||
0.595436 | + | 0.803402i | \(0.296979\pi\) | |||||||
\(728\) | −3.24727e15 | −0.588566 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 2.87319e15 | 0.512966 | ||||||||
\(731\) | −6.75255e15 | −1.19653 | ||||||||
\(732\) | −1.42625e15 | −0.250833 | ||||||||
\(733\) | −1.48208e15 | −0.258703 | −0.129351 | − | 0.991599i | \(-0.541290\pi\) | ||||
−0.129351 | + | 0.991599i | \(0.541290\pi\) | |||||||
\(734\) | 3.59907e15 | 0.623536 | ||||||||
\(735\) | −4.58691e15 | −0.788751 | ||||||||
\(736\) | 1.75134e15 | 0.298912 | ||||||||
\(737\) | −1.59215e15 | −0.269719 | ||||||||
\(738\) | −1.61807e15 | −0.272074 | ||||||||
\(739\) | 5.39343e15 | 0.900161 | 0.450081 | − | 0.892988i | \(-0.351395\pi\) | ||||
0.450081 | + | 0.892988i | \(0.351395\pi\) | |||||||
\(740\) | −2.21996e15 | −0.367765 | ||||||||
\(741\) | −5.03995e15 | −0.828754 | ||||||||
\(742\) | −9.49699e14 | −0.155012 | ||||||||
\(743\) | 8.96192e15 | 1.45199 | 0.725993 | − | 0.687702i | \(-0.241380\pi\) | ||||
0.725993 | + | 0.687702i | \(0.241380\pi\) | |||||||
\(744\) | −4.59064e14 | −0.0738282 | ||||||||
\(745\) | 7.24798e15 | 1.15706 | ||||||||
\(746\) | −4.15832e15 | −0.658953 | ||||||||
\(747\) | 1.36611e15 | 0.214894 | ||||||||
\(748\) | −2.27091e15 | −0.354603 | ||||||||
\(749\) | 4.14021e14 | 0.0641760 | ||||||||
\(750\) | −2.88789e15 | −0.444369 | ||||||||
\(751\) | −7.78720e15 | −1.18949 | −0.594746 | − | 0.803913i | \(-0.702747\pi\) | ||||
−0.594746 | + | 0.803913i | \(0.702747\pi\) | |||||||
\(752\) | −1.37024e15 | −0.207777 | ||||||||
\(753\) | 3.56765e15 | 0.537044 | ||||||||
\(754\) | −5.18933e15 | −0.775477 | ||||||||
\(755\) | −2.83755e15 | −0.420955 | ||||||||
\(756\) | −1.06473e15 | −0.156809 | ||||||||
\(757\) | −2.41922e15 | −0.353711 | −0.176856 | − | 0.984237i | \(-0.556593\pi\) | ||||
−0.176856 | + | 0.984237i | \(0.556593\pi\) | |||||||
\(758\) | 3.02522e15 | 0.439113 | ||||||||
\(759\) | −5.18675e15 | −0.747422 | ||||||||
\(760\) | −2.86549e15 | −0.409943 | ||||||||
\(761\) | −5.02552e15 | −0.713782 | −0.356891 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356891 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(762\) | −3.68355e15 | −0.519415 | ||||||||
\(763\) | −3.59946e15 | −0.503909 | ||||||||
\(764\) | 4.18211e15 | 0.581275 | ||||||||
\(765\) | 1.84637e15 | 0.254790 | ||||||||
\(766\) | −1.74438e15 | −0.238991 | ||||||||
\(767\) | −3.94249e15 | −0.536285 | ||||||||
\(768\) | −2.67181e14 | −0.0360844 | ||||||||
\(769\) | 1.21056e16 | 1.62327 | 0.811634 | − | 0.584166i | \(-0.198578\pi\) | ||||
0.811634 | + | 0.584166i | \(0.198578\pi\) | |||||||
\(770\) | 5.46783e15 | 0.727974 | ||||||||
\(771\) | 3.99678e15 | 0.528337 | ||||||||
\(772\) | −4.57973e15 | −0.601097 | ||||||||
\(773\) | −7.45630e15 | −0.971709 | −0.485854 | − | 0.874040i | \(-0.661492\pi\) | ||||
−0.485854 | + | 0.874040i | \(0.661492\pi\) | |||||||
\(774\) | 2.35287e15 | 0.304455 | ||||||||
\(775\) | 8.98303e14 | 0.115415 | ||||||||
\(776\) | 2.02957e15 | 0.258919 | ||||||||
\(777\) | 6.62063e15 | 0.838656 | ||||||||
\(778\) | 1.63641e15 | 0.205828 | ||||||||
\(779\) | 1.29870e16 | 1.62200 | ||||||||
\(780\) | −1.96212e15 | −0.243336 | ||||||||
\(781\) | 3.71157e15 | 0.457064 | ||||||||
\(782\) | 9.05741e15 | 1.10756 | ||||||||
\(783\) | −1.70151e15 | −0.206607 | ||||||||
\(784\) | 3.43273e15 | 0.413905 | ||||||||
\(785\) | −5.74923e15 | −0.688377 | ||||||||
\(786\) | 1.31083e15 | 0.155856 | ||||||||
\(787\) | −1.12580e16 | −1.32923 | −0.664615 | − | 0.747186i | \(-0.731404\pi\) | ||||
−0.664615 | + | 0.747186i | \(0.731404\pi\) | |||||||
\(788\) | −7.54713e15 | −0.884887 | ||||||||
\(789\) | 4.78268e15 | 0.556863 | ||||||||
\(790\) | 5.57167e15 | 0.644223 | ||||||||
\(791\) | 1.28843e16 | 1.47941 | ||||||||
\(792\) | 7.91281e14 | 0.0902282 | ||||||||
\(793\) | 7.83852e15 | 0.887630 | ||||||||
\(794\) | 1.55915e15 | 0.175338 | ||||||||
\(795\) | −5.73845e14 | −0.0640878 | ||||||||
\(796\) | 2.75772e15 | 0.305864 | ||||||||
\(797\) | −1.04669e16 | −1.15291 | −0.576457 | − | 0.817127i | \(-0.695565\pi\) | ||||
−0.576457 | + | 0.817127i | \(0.695565\pi\) | |||||||
\(798\) | 8.54579e15 | 0.934838 | ||||||||
\(799\) | −7.08646e15 | −0.769878 | ||||||||
\(800\) | 5.22824e14 | 0.0564106 | ||||||||
\(801\) | −1.51253e15 | −0.162078 | ||||||||
\(802\) | −1.20450e16 | −1.28189 | ||||||||
\(803\) | 6.36807e15 | 0.673088 | ||||||||
\(804\) | −9.68771e14 | −0.101698 | ||||||||
\(805\) | −2.18081e16 | −2.27374 | ||||||||
\(806\) | 2.52298e15 | 0.261259 | ||||||||
\(807\) | 2.82303e15 | 0.290343 | ||||||||
\(808\) | 3.11179e15 | 0.317868 | ||||||||
\(809\) | −1.28180e16 | −1.30048 | −0.650238 | − | 0.759730i | \(-0.725331\pi\) | ||||
−0.650238 | + | 0.759730i | \(0.725331\pi\) | |||||||
\(810\) | −6.43354e14 | −0.0648309 | ||||||||
\(811\) | 9.79295e15 | 0.980164 | 0.490082 | − | 0.871676i | \(-0.336967\pi\) | ||||
0.490082 | + | 0.871676i | \(0.336967\pi\) | |||||||
\(812\) | 8.79909e15 | 0.874742 | ||||||||
\(813\) | −1.81469e15 | −0.179187 | ||||||||
\(814\) | −4.92027e15 | −0.482564 | ||||||||
\(815\) | −2.79156e15 | −0.271945 | ||||||||
\(816\) | −1.38178e15 | −0.133704 | ||||||||
\(817\) | −1.88847e16 | −1.81505 | ||||||||
\(818\) | −9.99895e15 | −0.954578 | ||||||||
\(819\) | 5.85168e15 | 0.554906 | ||||||||
\(820\) | 5.05602e15 | 0.476247 | ||||||||
\(821\) | 7.08410e15 | 0.662823 | 0.331411 | − | 0.943486i | \(-0.392475\pi\) | ||||
0.331411 | + | 0.943486i | \(0.392475\pi\) | |||||||
\(822\) | −6.23230e15 | −0.579233 | ||||||||
\(823\) | 1.98569e16 | 1.83321 | 0.916606 | − | 0.399792i | \(-0.130918\pi\) | ||||
0.916606 | + | 0.399792i | \(0.130918\pi\) | |||||||
\(824\) | −1.78166e15 | −0.163390 | ||||||||
\(825\) | −1.54839e15 | −0.141053 | ||||||||
\(826\) | 6.68493e15 | 0.604932 | ||||||||
\(827\) | −2.05537e16 | −1.84760 | −0.923802 | − | 0.382871i | \(-0.874935\pi\) | ||||
−0.923802 | + | 0.382871i | \(0.874935\pi\) | |||||||
\(828\) | −3.15598e15 | −0.281817 | ||||||||
\(829\) | −1.45920e16 | −1.29439 | −0.647197 | − | 0.762323i | \(-0.724059\pi\) | ||||
−0.647197 | + | 0.762323i | \(0.724059\pi\) | |||||||
\(830\) | −4.26873e15 | −0.376157 | ||||||||
\(831\) | −3.87742e15 | −0.339419 | ||||||||
\(832\) | 1.46840e15 | 0.127693 | ||||||||
\(833\) | 1.77530e16 | 1.53364 | ||||||||
\(834\) | 4.08115e15 | 0.350243 | ||||||||
\(835\) | 1.33504e16 | 1.13820 | ||||||||
\(836\) | −6.35100e15 | −0.537907 | ||||||||
\(837\) | 8.27249e14 | 0.0696059 | ||||||||
\(838\) | −9.01533e15 | −0.753598 | ||||||||
\(839\) | 6.54963e15 | 0.543909 | 0.271954 | − | 0.962310i | \(-0.412330\pi\) | ||||
0.271954 | + | 0.962310i | \(0.412330\pi\) | |||||||
\(840\) | 3.32700e15 | 0.274484 | ||||||||
\(841\) | 1.86098e15 | 0.152533 | ||||||||
\(842\) | 9.63404e15 | 0.784498 | ||||||||
\(843\) | −9.62559e15 | −0.778710 | ||||||||
\(844\) | 6.79381e15 | 0.546047 | ||||||||
\(845\) | 4.50062e14 | 0.0359386 | ||||||||
\(846\) | 2.46922e15 | 0.195895 | ||||||||
\(847\) | −8.55606e15 | −0.674396 | ||||||||
\(848\) | 4.29451e14 | 0.0336307 | ||||||||
\(849\) | −3.64502e15 | −0.283601 | ||||||||
\(850\) | 2.70389e15 | 0.209018 | ||||||||
\(851\) | 1.96242e16 | 1.50723 | ||||||||
\(852\) | 2.25837e15 | 0.172337 | ||||||||
\(853\) | 1.99244e16 | 1.51066 | 0.755329 | − | 0.655346i | \(-0.227477\pi\) | ||||
0.755329 | + | 0.655346i | \(0.227477\pi\) | |||||||
\(854\) | −1.32911e16 | −1.00125 | ||||||||
\(855\) | 5.16370e15 | 0.386498 | ||||||||
\(856\) | −1.87219e14 | −0.0139234 | ||||||||
\(857\) | 1.59149e16 | 1.17600 | 0.588002 | − | 0.808859i | \(-0.299915\pi\) | ||||
0.588002 | + | 0.808859i | \(0.299915\pi\) | |||||||
\(858\) | −4.34881e15 | −0.319293 | ||||||||
\(859\) | −1.19020e15 | −0.0868272 | −0.0434136 | − | 0.999057i | \(-0.513823\pi\) | ||||
−0.0434136 | + | 0.999057i | \(0.513823\pi\) | |||||||
\(860\) | −7.35208e15 | −0.532928 | ||||||||
\(861\) | −1.50787e16 | −1.08604 | ||||||||
\(862\) | −1.10942e16 | −0.793975 | ||||||||
\(863\) | −1.73343e15 | −0.123267 | −0.0616336 | − | 0.998099i | \(-0.519631\pi\) | ||||
−0.0616336 | + | 0.998099i | \(0.519631\pi\) | |||||||
\(864\) | 4.81469e14 | 0.0340207 | ||||||||
\(865\) | 1.94405e16 | 1.36495 | ||||||||
\(866\) | −1.54351e16 | −1.07686 | ||||||||
\(867\) | 1.18193e15 | 0.0819381 | ||||||||
\(868\) | −4.27799e15 | −0.294701 | ||||||||
\(869\) | 1.23489e16 | 0.845317 | ||||||||
\(870\) | 5.31675e15 | 0.361652 | ||||||||
\(871\) | 5.32428e15 | 0.359882 | ||||||||
\(872\) | 1.62766e15 | 0.109326 | ||||||||
\(873\) | −3.65735e15 | −0.244112 | ||||||||
\(874\) | 2.53306e16 | 1.68009 | ||||||||
\(875\) | −2.69121e16 | −1.77379 | ||||||||
\(876\) | 3.87477e15 | 0.253789 | ||||||||
\(877\) | 1.16602e16 | 0.758943 | 0.379471 | − | 0.925203i | \(-0.376106\pi\) | ||||
0.379471 | + | 0.925203i | \(0.376106\pi\) | |||||||
\(878\) | −3.80589e15 | −0.246171 | ||||||||
\(879\) | −9.43459e15 | −0.606435 | ||||||||
\(880\) | −2.47254e15 | −0.157938 | ||||||||
\(881\) | −1.66091e16 | −1.05434 | −0.527168 | − | 0.849761i | \(-0.676746\pi\) | ||||
−0.527168 | + | 0.849761i | \(0.676746\pi\) | |||||||
\(882\) | −6.18589e15 | −0.390234 | ||||||||
\(883\) | −1.28205e16 | −0.803750 | −0.401875 | − | 0.915695i | \(-0.631641\pi\) | ||||
−0.401875 | + | 0.915695i | \(0.631641\pi\) | |||||||
\(884\) | 7.59414e15 | 0.473141 | ||||||||
\(885\) | 4.03929e15 | 0.250102 | ||||||||
\(886\) | 6.39726e15 | 0.393648 | ||||||||
\(887\) | −2.21358e14 | −0.0135368 | −0.00676840 | − | 0.999977i | \(-0.502154\pi\) | ||||
−0.00676840 | + | 0.999977i | \(0.502154\pi\) | |||||||
\(888\) | −2.99383e15 | −0.181951 | ||||||||
\(889\) | −3.43267e16 | −2.07335 | ||||||||
\(890\) | 4.72624e15 | 0.283708 | ||||||||
\(891\) | −1.42591e15 | −0.0850679 | ||||||||
\(892\) | −6.13948e15 | −0.364020 | ||||||||
\(893\) | −1.98185e16 | −1.16785 | ||||||||
\(894\) | 9.77459e15 | 0.572456 | ||||||||
\(895\) | 9.49070e15 | 0.552423 | ||||||||
\(896\) | −2.48984e15 | −0.144038 | ||||||||
\(897\) | 1.73450e16 | 0.997275 | ||||||||
\(898\) | 1.62145e16 | 0.926579 | ||||||||
\(899\) | −6.83649e15 | −0.388289 | ||||||||
\(900\) | −9.42146e14 | −0.0531844 | ||||||||
\(901\) | 2.22099e15 | 0.124612 | ||||||||
\(902\) | 1.12060e16 | 0.624908 | ||||||||
\(903\) | 2.19262e16 | 1.21529 | ||||||||
\(904\) | −5.82623e15 | −0.320968 | ||||||||
\(905\) | 1.58114e16 | 0.865770 | ||||||||
\(906\) | −3.82671e15 | −0.208267 | ||||||||
\(907\) | −2.48361e16 | −1.34352 | −0.671758 | − | 0.740770i | \(-0.734461\pi\) | ||||
−0.671758 | + | 0.740770i | \(0.734461\pi\) | |||||||
\(908\) | −7.93529e15 | −0.426668 | ||||||||
\(909\) | −5.60754e15 | −0.299689 | ||||||||
\(910\) | −1.82849e16 | −0.971326 | ||||||||
\(911\) | 8.10295e15 | 0.427851 | 0.213925 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213925 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(912\) | −3.86438e15 | −0.202819 | ||||||||
\(913\) | −9.46112e15 | −0.493575 | ||||||||
\(914\) | 1.16086e16 | 0.601971 | ||||||||
\(915\) | −8.03100e15 | −0.413955 | ||||||||
\(916\) | 3.84823e15 | 0.197168 | ||||||||
\(917\) | 1.22155e16 | 0.622130 | ||||||||
\(918\) | 2.49001e15 | 0.126057 | ||||||||
\(919\) | −3.33814e16 | −1.67984 | −0.839922 | − | 0.542707i | \(-0.817399\pi\) | ||||
−0.839922 | + | 0.542707i | \(0.817399\pi\) | |||||||
\(920\) | 9.86156e15 | 0.493302 | ||||||||
\(921\) | −1.84241e16 | −0.916133 | ||||||||
\(922\) | −2.10069e15 | −0.103835 | ||||||||
\(923\) | −1.24118e16 | −0.609854 | ||||||||
\(924\) | 7.37389e15 | 0.360164 | ||||||||
\(925\) | 5.85836e15 | 0.284444 | ||||||||
\(926\) | 6.61595e15 | 0.319324 | ||||||||
\(927\) | 3.21061e15 | 0.154045 | ||||||||
\(928\) | −3.97892e15 | −0.189781 | ||||||||
\(929\) | 3.56713e16 | 1.69134 | 0.845672 | − | 0.533703i | \(-0.179200\pi\) | ||||
0.845672 | + | 0.533703i | \(0.179200\pi\) | |||||||
\(930\) | −2.58493e15 | −0.121841 | ||||||||
\(931\) | 4.96493e16 | 2.32643 | ||||||||
\(932\) | 9.24340e15 | 0.430570 | ||||||||
\(933\) | 1.94377e16 | 0.900112 | ||||||||
\(934\) | 1.21408e16 | 0.558908 | ||||||||
\(935\) | −1.27872e16 | −0.585210 | ||||||||
\(936\) | −2.64611e15 | −0.120390 | ||||||||
\(937\) | 3.96248e16 | 1.79225 | 0.896126 | − | 0.443800i | \(-0.146370\pi\) | ||||
0.896126 | + | 0.443800i | \(0.146370\pi\) | |||||||
\(938\) | −9.02791e15 | −0.405949 | ||||||||
\(939\) | 1.66604e16 | 0.744775 | ||||||||
\(940\) | −7.71563e15 | −0.342900 | ||||||||
\(941\) | 5.37193e15 | 0.237349 | 0.118675 | − | 0.992933i | \(-0.462135\pi\) | ||||
0.118675 | + | 0.992933i | \(0.462135\pi\) | |||||||
\(942\) | −7.75338e15 | −0.340574 | ||||||||
\(943\) | −4.46946e16 | −1.95183 | ||||||||
\(944\) | −3.02290e15 | −0.131244 | ||||||||
\(945\) | −5.99537e15 | −0.258786 | ||||||||
\(946\) | −1.62950e16 | −0.699282 | ||||||||
\(947\) | 2.22241e16 | 0.948199 | 0.474099 | − | 0.880471i | \(-0.342774\pi\) | ||||
0.474099 | + | 0.880471i | \(0.342774\pi\) | |||||||
\(948\) | 7.51392e15 | 0.318728 | ||||||||
\(949\) | −2.12954e16 | −0.898092 | ||||||||
\(950\) | 7.56188e15 | 0.317066 | ||||||||
\(951\) | −1.55008e15 | −0.0646190 | ||||||||
\(952\) | −1.28767e16 | −0.533706 | ||||||||
\(953\) | 7.66867e15 | 0.316016 | 0.158008 | − | 0.987438i | \(-0.449493\pi\) | ||||
0.158008 | + | 0.987438i | \(0.449493\pi\) | |||||||
\(954\) | −7.73885e14 | −0.0317074 | ||||||||
\(955\) | 2.35489e16 | 0.959293 | ||||||||
\(956\) | −4.11924e15 | −0.166839 | ||||||||
\(957\) | 1.17839e16 | 0.474542 | ||||||||
\(958\) | −1.17741e16 | −0.471429 | ||||||||
\(959\) | −5.80784e16 | −2.31213 | ||||||||
\(960\) | −1.50446e15 | −0.0595510 | ||||||||
\(961\) | −2.20847e16 | −0.869185 | ||||||||
\(962\) | 1.64538e16 | 0.643878 | ||||||||
\(963\) | 3.37375e14 | 0.0131271 | ||||||||
\(964\) | −1.53597e16 | −0.594235 | ||||||||
\(965\) | −2.57878e16 | −0.992006 | ||||||||
\(966\) | −2.94103e16 | −1.12493 | ||||||||
\(967\) | 2.80474e16 | 1.06671 | 0.533355 | − | 0.845891i | \(-0.320931\pi\) | ||||
0.533355 | + | 0.845891i | \(0.320931\pi\) | |||||||
\(968\) | 3.86902e15 | 0.146314 | ||||||||
\(969\) | −1.99854e16 | −0.751505 | ||||||||
\(970\) | 1.14282e16 | 0.427301 | ||||||||
\(971\) | −2.43427e16 | −0.905031 | −0.452516 | − | 0.891757i | \(-0.649473\pi\) | ||||
−0.452516 | + | 0.891757i | \(0.649473\pi\) | |||||||
\(972\) | −8.67624e14 | −0.0320750 | ||||||||
\(973\) | 3.80320e16 | 1.39807 | ||||||||
\(974\) | −2.02126e16 | −0.738837 | ||||||||
\(975\) | 5.17795e15 | 0.188205 | ||||||||
\(976\) | 6.01019e15 | 0.217227 | ||||||||
\(977\) | −2.19144e16 | −0.787608 | −0.393804 | − | 0.919194i | \(-0.628841\pi\) | ||||
−0.393804 | + | 0.919194i | \(0.628841\pi\) | |||||||
\(978\) | −3.76469e15 | −0.134544 | ||||||||
\(979\) | 1.04751e16 | 0.372267 | ||||||||
\(980\) | 1.93292e16 | 0.683079 | ||||||||
\(981\) | −2.93310e15 | −0.103074 | ||||||||
\(982\) | −8.90186e15 | −0.311077 | ||||||||
\(983\) | −7.04586e15 | −0.244844 | −0.122422 | − | 0.992478i | \(-0.539066\pi\) | ||||
−0.122422 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(984\) | 6.81852e15 | 0.235623 | ||||||||
\(985\) | −4.24969e16 | −1.46035 | ||||||||
\(986\) | −2.05778e16 | −0.703194 | ||||||||
\(987\) | 2.30105e16 | 0.781954 | ||||||||
\(988\) | 2.12383e16 | 0.717722 | ||||||||
\(989\) | 6.49915e16 | 2.18412 | ||||||||
\(990\) | 4.45559e15 | 0.148906 | ||||||||
\(991\) | 4.04873e16 | 1.34559 | 0.672796 | − | 0.739828i | \(-0.265093\pi\) | ||||
0.672796 | + | 0.739828i | \(0.265093\pi\) | |||||||
\(992\) | 1.93449e15 | 0.0639371 | ||||||||
\(993\) | −2.16321e16 | −0.711013 | ||||||||
\(994\) | 2.10456e16 | 0.687918 | ||||||||
\(995\) | 1.55283e16 | 0.504775 | ||||||||
\(996\) | −5.75679e15 | −0.186103 | ||||||||
\(997\) | 1.79607e16 | 0.577432 | 0.288716 | − | 0.957415i | \(-0.406772\pi\) | ||||
0.288716 | + | 0.957415i | \(0.406772\pi\) | |||||||
\(998\) | −1.46896e16 | −0.469669 | ||||||||
\(999\) | 5.39498e15 | 0.171546 |
(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 | 6.12.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.12.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 48.12.a.h.1.1 | 1 | |||
5.2 | odd | 4 | 150.12.c.f.49.1 | 2 | |||
5.3 | odd | 4 | 150.12.c.f.49.2 | 2 | |||
5.4 | even | 2 | 150.12.a.g.1.1 | 1 | |||
8.3 | odd | 2 | 192.12.a.b.1.1 | 1 | |||
8.5 | even | 2 | 192.12.a.l.1.1 | 1 | |||
9.2 | odd | 6 | 162.12.c.d.109.1 | 2 | |||
9.4 | even | 3 | 162.12.c.g.55.1 | 2 | |||
9.5 | odd | 6 | 162.12.c.d.55.1 | 2 | |||
9.7 | even | 3 | 162.12.c.g.109.1 | 2 | |||
12.11 | even | 2 | 144.12.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.12.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.12.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
48.12.a.h.1.1 | 1 | 4.3 | odd | 2 | |||
144.12.a.b.1.1 | 1 | 12.11 | even | 2 | |||
150.12.a.g.1.1 | 1 | 5.4 | even | 2 | |||
150.12.c.f.49.1 | 2 | 5.2 | odd | 4 | |||
150.12.c.f.49.2 | 2 | 5.3 | odd | 4 | |||
162.12.c.d.55.1 | 2 | 9.5 | odd | 6 | |||
162.12.c.d.109.1 | 2 | 9.2 | odd | 6 | |||
162.12.c.g.55.1 | 2 | 9.4 | even | 3 | |||
162.12.c.g.109.1 | 2 | 9.7 | even | 3 | |||
192.12.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
192.12.a.l.1.1 | 1 | 8.5 | even | 2 |