Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −63.8588 | −0.705547 | −0.352773 | − | 0.935709i | \(-0.614761\pi\) | ||||
−0.352773 | + | 0.935709i | \(0.614761\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | −4114.05 | −0.502204 | ||||||||
\(5\) | 18414.6 | 0.527057 | 0.263528 | − | 0.964652i | \(-0.415114\pi\) | ||||
0.263528 | + | 0.964652i | \(0.415114\pi\) | |||||||
\(6\) | 46553.1 | 0.407348 | ||||||||
\(7\) | 120263. | 0.386361 | 0.193180 | − | 0.981163i | \(-0.438120\pi\) | ||||
0.193180 | + | 0.981163i | \(0.438120\pi\) | |||||||
\(8\) | 785850. | 1.05988 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −1.17593e6 | −0.371863 | ||||||||
\(11\) | −3.91572e6 | −0.666437 | −0.333219 | − | 0.942850i | \(-0.608135\pi\) | ||||
−0.333219 | + | 0.942850i | \(0.608135\pi\) | |||||||
\(12\) | 2.99914e6 | 0.289947 | ||||||||
\(13\) | −9.55466e6 | −0.549014 | −0.274507 | − | 0.961585i | \(-0.588515\pi\) | ||||
−0.274507 | + | 0.961585i | \(0.588515\pi\) | |||||||
\(14\) | −7.67982e6 | −0.272596 | ||||||||
\(15\) | −1.34242e7 | −0.304296 | ||||||||
\(16\) | −1.64811e7 | −0.245588 | ||||||||
\(17\) | 4.69357e6 | 0.0471613 | 0.0235806 | − | 0.999722i | \(-0.492493\pi\) | ||||
0.0235806 | + | 0.999722i | \(0.492493\pi\) | |||||||
\(18\) | −3.39372e7 | −0.235182 | ||||||||
\(19\) | 3.61757e8 | 1.76408 | 0.882041 | − | 0.471172i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471172i | \(0.156169\pi\) | |||||||
\(20\) | −7.57586e7 | −0.264690 | ||||||||
\(21\) | −8.76714e7 | −0.223066 | ||||||||
\(22\) | 2.50053e8 | 0.470203 | ||||||||
\(23\) | 1.17374e9 | 1.65326 | 0.826628 | − | 0.562749i | \(-0.190256\pi\) | ||||
0.826628 | + | 0.562749i | \(0.190256\pi\) | |||||||
\(24\) | −5.72885e8 | −0.611919 | ||||||||
\(25\) | −8.81606e8 | −0.722211 | ||||||||
\(26\) | 6.10149e8 | 0.387355 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | −4.94766e8 | −0.194032 | ||||||||
\(29\) | −4.59818e9 | −1.43549 | −0.717744 | − | 0.696307i | \(-0.754825\pi\) | ||||
−0.717744 | + | 0.696307i | \(0.754825\pi\) | |||||||
\(30\) | 8.57256e8 | 0.214695 | ||||||||
\(31\) | −5.94328e9 | −1.20275 | −0.601375 | − | 0.798967i | \(-0.705380\pi\) | ||||
−0.601375 | + | 0.798967i | \(0.705380\pi\) | |||||||
\(32\) | −5.38522e9 | −0.886601 | ||||||||
\(33\) | 2.85456e9 | 0.384768 | ||||||||
\(34\) | −2.99726e8 | −0.0332745 | ||||||||
\(35\) | 2.21459e9 | 0.203634 | ||||||||
\(36\) | −2.18638e9 | −0.167401 | ||||||||
\(37\) | −1.48917e10 | −0.954185 | −0.477093 | − | 0.878853i | \(-0.658309\pi\) | ||||
−0.477093 | + | 0.878853i | \(0.658309\pi\) | |||||||
\(38\) | −2.31014e10 | −1.24464 | ||||||||
\(39\) | 6.96535e9 | 0.316973 | ||||||||
\(40\) | 1.44711e10 | 0.558614 | ||||||||
\(41\) | −1.83734e10 | −0.604080 | −0.302040 | − | 0.953295i | \(-0.597668\pi\) | ||||
−0.302040 | + | 0.953295i | \(0.597668\pi\) | |||||||
\(42\) | 5.59859e9 | 0.157383 | ||||||||
\(43\) | 1.62479e10 | 0.391970 | 0.195985 | − | 0.980607i | \(-0.437210\pi\) | ||||
0.195985 | + | 0.980607i | \(0.437210\pi\) | |||||||
\(44\) | 1.61095e10 | 0.334687 | ||||||||
\(45\) | 9.78627e9 | 0.175686 | ||||||||
\(46\) | −7.49535e10 | −1.16645 | ||||||||
\(47\) | 1.36551e9 | 0.0184782 | 0.00923911 | − | 0.999957i | \(-0.497059\pi\) | ||||
0.00923911 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(48\) | 1.20147e10 | 0.141790 | ||||||||
\(49\) | −8.24259e10 | −0.850725 | ||||||||
\(50\) | 5.62983e10 | 0.509554 | ||||||||
\(51\) | −3.42161e9 | −0.0272286 | ||||||||
\(52\) | 3.93084e10 | 0.275717 | ||||||||
\(53\) | 1.60234e11 | 0.993026 | 0.496513 | − | 0.868029i | \(-0.334614\pi\) | ||||
0.496513 | + | 0.868029i | \(0.334614\pi\) | |||||||
\(54\) | 2.47402e10 | 0.135783 | ||||||||
\(55\) | −7.21065e10 | −0.351250 | ||||||||
\(56\) | 9.45083e10 | 0.409494 | ||||||||
\(57\) | −2.63721e11 | −1.01849 | ||||||||
\(58\) | 2.93635e11 | 1.01280 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 5.52280e10 | 0.152819 | ||||||||
\(61\) | 2.01713e11 | 0.501291 | 0.250646 | − | 0.968079i | \(-0.419357\pi\) | ||||
0.250646 | + | 0.968079i | \(0.419357\pi\) | |||||||
\(62\) | 3.79531e11 | 0.848596 | ||||||||
\(63\) | 6.39124e10 | 0.128787 | ||||||||
\(64\) | 4.78907e11 | 0.871127 | ||||||||
\(65\) | −1.75945e11 | −0.289362 | ||||||||
\(66\) | −1.82289e11 | −0.271472 | ||||||||
\(67\) | 5.67639e11 | 0.766631 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(68\) | −1.93096e10 | −0.0236846 | ||||||||
\(69\) | −8.55654e11 | −0.954507 | ||||||||
\(70\) | −1.41421e11 | −0.143673 | ||||||||
\(71\) | −2.83595e11 | −0.262736 | −0.131368 | − | 0.991334i | \(-0.541937\pi\) | ||||
−0.131368 | + | 0.991334i | \(0.541937\pi\) | |||||||
\(72\) | 4.17633e11 | 0.353292 | ||||||||
\(73\) | 2.34947e12 | 1.81707 | 0.908534 | − | 0.417812i | \(-0.137203\pi\) | ||||
0.908534 | + | 0.417812i | \(0.137203\pi\) | |||||||
\(74\) | 9.50965e11 | 0.673222 | ||||||||
\(75\) | 6.42690e11 | 0.416969 | ||||||||
\(76\) | −1.48829e12 | −0.885929 | ||||||||
\(77\) | −4.70915e11 | −0.257485 | ||||||||
\(78\) | −4.44799e11 | −0.223640 | ||||||||
\(79\) | 1.78071e12 | 0.824170 | 0.412085 | − | 0.911145i | \(-0.364801\pi\) | ||||
0.412085 | + | 0.911145i | \(0.364801\pi\) | |||||||
\(80\) | −3.03493e11 | −0.129439 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 1.17330e12 | 0.426207 | ||||||||
\(83\) | 1.42768e12 | 0.479319 | 0.239659 | − | 0.970857i | \(-0.422964\pi\) | ||||
0.239659 | + | 0.970857i | \(0.422964\pi\) | |||||||
\(84\) | 3.60685e11 | 0.112024 | ||||||||
\(85\) | 8.64303e10 | 0.0248567 | ||||||||
\(86\) | −1.03757e12 | −0.276553 | ||||||||
\(87\) | 3.35208e12 | 0.828779 | ||||||||
\(88\) | −3.07717e12 | −0.706340 | ||||||||
\(89\) | −5.50543e12 | −1.17424 | −0.587119 | − | 0.809500i | \(-0.699738\pi\) | ||||
−0.587119 | + | 0.809500i | \(0.699738\pi\) | |||||||
\(90\) | −6.24940e11 | −0.123954 | ||||||||
\(91\) | −1.14907e12 | −0.212118 | ||||||||
\(92\) | −4.82882e12 | −0.830271 | ||||||||
\(93\) | 4.33265e12 | 0.694408 | ||||||||
\(94\) | −8.72001e10 | −0.0130372 | ||||||||
\(95\) | 6.66162e12 | 0.929771 | ||||||||
\(96\) | 3.92582e12 | 0.511880 | ||||||||
\(97\) | 1.04921e13 | 1.27893 | 0.639465 | − | 0.768820i | \(-0.279156\pi\) | ||||
0.639465 | + | 0.768820i | \(0.279156\pi\) | |||||||
\(98\) | 5.26362e12 | 0.600227 | ||||||||
\(99\) | −2.08097e12 | −0.222146 | ||||||||
\(100\) | 3.62697e12 | 0.362697 | ||||||||
\(101\) | 1.03017e13 | 0.965648 | 0.482824 | − | 0.875717i | \(-0.339611\pi\) | ||||
0.482824 | + | 0.875717i | \(0.339611\pi\) | |||||||
\(102\) | 2.18500e11 | 0.0192110 | ||||||||
\(103\) | 1.10824e13 | 0.914518 | 0.457259 | − | 0.889334i | \(-0.348831\pi\) | ||||
0.457259 | + | 0.889334i | \(0.348831\pi\) | |||||||
\(104\) | −7.50853e12 | −0.581886 | ||||||||
\(105\) | −1.61443e12 | −0.117568 | ||||||||
\(106\) | −1.02323e13 | −0.700626 | ||||||||
\(107\) | −8.17553e11 | −0.0526649 | −0.0263325 | − | 0.999653i | \(-0.508383\pi\) | ||||
−0.0263325 | + | 0.999653i | \(0.508383\pi\) | |||||||
\(108\) | 1.59387e12 | 0.0966491 | ||||||||
\(109\) | −1.99066e13 | −1.13691 | −0.568455 | − | 0.822715i | \(-0.692458\pi\) | ||||
−0.568455 | + | 0.822715i | \(0.692458\pi\) | |||||||
\(110\) | 4.60463e12 | 0.247824 | ||||||||
\(111\) | 1.08560e13 | 0.550899 | ||||||||
\(112\) | −1.98206e12 | −0.0948855 | ||||||||
\(113\) | 1.70793e12 | 0.0771723 | 0.0385861 | − | 0.999255i | \(-0.487715\pi\) | ||||
0.0385861 | + | 0.999255i | \(0.487715\pi\) | |||||||
\(114\) | 1.68409e13 | 0.718595 | ||||||||
\(115\) | 2.16139e13 | 0.871359 | ||||||||
\(116\) | 1.89172e13 | 0.720907 | ||||||||
\(117\) | −5.07774e12 | −0.183005 | ||||||||
\(118\) | 2.69360e12 | 0.0918544 | ||||||||
\(119\) | 5.64461e11 | 0.0182213 | ||||||||
\(120\) | −1.05494e13 | −0.322516 | ||||||||
\(121\) | −1.91898e13 | −0.555861 | ||||||||
\(122\) | −1.28812e13 | −0.353684 | ||||||||
\(123\) | 1.33942e13 | 0.348766 | ||||||||
\(124\) | 2.44510e13 | 0.604025 | ||||||||
\(125\) | −3.87132e13 | −0.907703 | ||||||||
\(126\) | −4.08137e12 | −0.0908652 | ||||||||
\(127\) | −3.27440e13 | −0.692479 | −0.346240 | − | 0.938146i | \(-0.612542\pi\) | ||||
−0.346240 | + | 0.938146i | \(0.612542\pi\) | |||||||
\(128\) | 1.35333e13 | 0.271981 | ||||||||
\(129\) | −1.18447e13 | −0.226304 | ||||||||
\(130\) | 1.12357e13 | 0.204158 | ||||||||
\(131\) | −4.51213e13 | −0.780043 | −0.390022 | − | 0.920806i | \(-0.627532\pi\) | ||||
−0.390022 | + | 0.920806i | \(0.627532\pi\) | |||||||
\(132\) | −1.17438e13 | −0.193232 | ||||||||
\(133\) | 4.35058e13 | 0.681572 | ||||||||
\(134\) | −3.62488e13 | −0.540894 | ||||||||
\(135\) | −7.13419e12 | −0.101432 | ||||||||
\(136\) | 3.68844e12 | 0.0499851 | ||||||||
\(137\) | −1.29786e14 | −1.67705 | −0.838524 | − | 0.544865i | \(-0.816581\pi\) | ||||
−0.838524 | + | 0.544865i | \(0.816581\pi\) | |||||||
\(138\) | 5.46411e13 | 0.673450 | ||||||||
\(139\) | 8.14124e13 | 0.957402 | 0.478701 | − | 0.877978i | \(-0.341108\pi\) | ||||
0.478701 | + | 0.877978i | \(0.341108\pi\) | |||||||
\(140\) | −9.11093e12 | −0.102266 | ||||||||
\(141\) | −9.95459e11 | −0.0106684 | ||||||||
\(142\) | 1.81100e13 | 0.185372 | ||||||||
\(143\) | 3.74134e13 | 0.365884 | ||||||||
\(144\) | −8.75874e12 | −0.0818626 | ||||||||
\(145\) | −8.46737e13 | −0.756583 | ||||||||
\(146\) | −1.50034e14 | −1.28203 | ||||||||
\(147\) | 6.00885e13 | 0.491166 | ||||||||
\(148\) | 6.12652e13 | 0.479195 | ||||||||
\(149\) | 8.63226e13 | 0.646270 | 0.323135 | − | 0.946353i | \(-0.395263\pi\) | ||||
0.323135 | + | 0.946353i | \(0.395263\pi\) | |||||||
\(150\) | −4.10414e13 | −0.294191 | ||||||||
\(151\) | 2.12012e14 | 1.45550 | 0.727748 | − | 0.685845i | \(-0.240567\pi\) | ||||
0.727748 | + | 0.685845i | \(0.240567\pi\) | |||||||
\(152\) | 2.84287e14 | 1.86971 | ||||||||
\(153\) | 2.49436e12 | 0.0157204 | ||||||||
\(154\) | 3.00720e13 | 0.181668 | ||||||||
\(155\) | −1.09443e14 | −0.633917 | ||||||||
\(156\) | −2.86558e13 | −0.159185 | ||||||||
\(157\) | −1.66693e14 | −0.888321 | −0.444161 | − | 0.895947i | \(-0.646498\pi\) | ||||
−0.444161 | + | 0.895947i | \(0.646498\pi\) | |||||||
\(158\) | −1.13714e14 | −0.581491 | ||||||||
\(159\) | −1.16810e14 | −0.573324 | ||||||||
\(160\) | −9.91666e13 | −0.467289 | ||||||||
\(161\) | 1.41157e14 | 0.638753 | ||||||||
\(162\) | −1.80356e13 | −0.0783941 | ||||||||
\(163\) | −4.64988e13 | −0.194188 | −0.0970940 | − | 0.995275i | \(-0.530955\pi\) | ||||
−0.0970940 | + | 0.995275i | \(0.530955\pi\) | |||||||
\(164\) | 7.55891e13 | 0.303371 | ||||||||
\(165\) | 5.25656e13 | 0.202794 | ||||||||
\(166\) | −9.11702e13 | −0.338182 | ||||||||
\(167\) | 3.31583e14 | 1.18287 | 0.591433 | − | 0.806354i | \(-0.298562\pi\) | ||||
0.591433 | + | 0.806354i | \(0.298562\pi\) | |||||||
\(168\) | −6.88965e13 | −0.236422 | ||||||||
\(169\) | −2.11584e14 | −0.698584 | ||||||||
\(170\) | −5.51933e12 | −0.0175375 | ||||||||
\(171\) | 1.92253e14 | 0.588027 | ||||||||
\(172\) | −6.68448e13 | −0.196849 | ||||||||
\(173\) | 6.09235e13 | 0.172777 | 0.0863883 | − | 0.996262i | \(-0.472467\pi\) | ||||
0.0863883 | + | 0.996262i | \(0.472467\pi\) | |||||||
\(174\) | −2.14060e14 | −0.584743 | ||||||||
\(175\) | −1.06024e14 | −0.279034 | ||||||||
\(176\) | 6.45355e13 | 0.163669 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 3.51570e14 | 0.828481 | ||||||||
\(179\) | 2.22302e14 | 0.505125 | 0.252563 | − | 0.967581i | \(-0.418727\pi\) | ||||
0.252563 | + | 0.967581i | \(0.418727\pi\) | |||||||
\(180\) | −4.02612e13 | −0.0882299 | ||||||||
\(181\) | −3.90444e14 | −0.825368 | −0.412684 | − | 0.910874i | \(-0.635409\pi\) | ||||
−0.412684 | + | 0.910874i | \(0.635409\pi\) | |||||||
\(182\) | 7.33781e13 | 0.149659 | ||||||||
\(183\) | −1.47049e14 | −0.289421 | ||||||||
\(184\) | 9.22381e14 | 1.75224 | ||||||||
\(185\) | −2.74224e14 | −0.502910 | ||||||||
\(186\) | −2.76678e14 | −0.489937 | ||||||||
\(187\) | −1.83787e13 | −0.0314300 | ||||||||
\(188\) | −5.61779e12 | −0.00927983 | ||||||||
\(189\) | −4.65922e13 | −0.0743552 | ||||||||
\(190\) | −4.25403e14 | −0.655997 | ||||||||
\(191\) | −2.60963e14 | −0.388922 | −0.194461 | − | 0.980910i | \(-0.562296\pi\) | ||||
−0.194461 | + | 0.980910i | \(0.562296\pi\) | |||||||
\(192\) | −3.49123e14 | −0.502945 | ||||||||
\(193\) | 1.06191e14 | 0.147899 | 0.0739496 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739496 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(194\) | −6.70014e14 | −0.902345 | ||||||||
\(195\) | 1.28264e14 | 0.167063 | ||||||||
\(196\) | 3.39105e14 | 0.427237 | ||||||||
\(197\) | −7.48053e14 | −0.911804 | −0.455902 | − | 0.890030i | \(-0.650683\pi\) | ||||
−0.455902 | + | 0.890030i | \(0.650683\pi\) | |||||||
\(198\) | 1.32889e14 | 0.156734 | ||||||||
\(199\) | −9.12192e14 | −1.04122 | −0.520608 | − | 0.853796i | \(-0.674295\pi\) | ||||
−0.520608 | + | 0.853796i | \(0.674295\pi\) | |||||||
\(200\) | −6.92810e14 | −0.765454 | ||||||||
\(201\) | −4.13809e14 | −0.442614 | ||||||||
\(202\) | −6.57853e14 | −0.681310 | ||||||||
\(203\) | −5.52989e14 | −0.554616 | ||||||||
\(204\) | 1.40767e13 | 0.0136743 | ||||||||
\(205\) | −3.38339e14 | −0.318384 | ||||||||
\(206\) | −7.07710e14 | −0.645235 | ||||||||
\(207\) | 6.23772e14 | 0.551085 | ||||||||
\(208\) | 1.57472e14 | 0.134831 | ||||||||
\(209\) | −1.41654e15 | −1.17565 | ||||||||
\(210\) | 1.03096e14 | 0.0829498 | ||||||||
\(211\) | 1.88689e15 | 1.47201 | 0.736005 | − | 0.676976i | \(-0.236710\pi\) | ||||
0.736005 | + | 0.676976i | \(0.236710\pi\) | |||||||
\(212\) | −6.59209e14 | −0.498701 | ||||||||
\(213\) | 2.06741e14 | 0.151691 | ||||||||
\(214\) | 5.22080e13 | 0.0371576 | ||||||||
\(215\) | 2.99199e14 | 0.206590 | ||||||||
\(216\) | −3.04454e14 | −0.203973 | ||||||||
\(217\) | −7.14754e14 | −0.464695 | ||||||||
\(218\) | 1.27121e15 | 0.802143 | ||||||||
\(219\) | −1.71276e15 | −1.04908 | ||||||||
\(220\) | 2.96650e14 | 0.176399 | ||||||||
\(221\) | −4.48455e13 | −0.0258922 | ||||||||
\(222\) | −6.93254e14 | −0.388685 | ||||||||
\(223\) | 6.28777e14 | 0.342385 | 0.171193 | − | 0.985238i | \(-0.445238\pi\) | ||||
0.171193 | + | 0.985238i | \(0.445238\pi\) | |||||||
\(224\) | −6.47640e14 | −0.342548 | ||||||||
\(225\) | −4.68521e14 | −0.240737 | ||||||||
\(226\) | −1.09067e14 | −0.0544487 | ||||||||
\(227\) | 1.17064e15 | 0.567879 | 0.283939 | − | 0.958842i | \(-0.408359\pi\) | ||||
0.283939 | + | 0.958842i | \(0.408359\pi\) | |||||||
\(228\) | 1.08496e15 | 0.511491 | ||||||||
\(229\) | −2.26275e14 | −0.103683 | −0.0518414 | − | 0.998655i | \(-0.516509\pi\) | ||||
−0.0518414 | + | 0.998655i | \(0.516509\pi\) | |||||||
\(230\) | −1.38024e15 | −0.614785 | ||||||||
\(231\) | 3.43297e14 | 0.148659 | ||||||||
\(232\) | −3.61348e15 | −1.52144 | ||||||||
\(233\) | −2.85646e15 | −1.16954 | −0.584770 | − | 0.811199i | \(-0.698815\pi\) | ||||
−0.584770 | + | 0.811199i | \(0.698815\pi\) | |||||||
\(234\) | 3.24258e14 | 0.129118 | ||||||||
\(235\) | 2.51454e13 | 0.00973906 | ||||||||
\(236\) | 1.73533e14 | 0.0653813 | ||||||||
\(237\) | −1.29814e15 | −0.475835 | ||||||||
\(238\) | −3.60458e13 | −0.0128560 | ||||||||
\(239\) | 1.01593e15 | 0.352596 | 0.176298 | − | 0.984337i | \(-0.443588\pi\) | ||||
0.176298 | + | 0.984337i | \(0.443588\pi\) | |||||||
\(240\) | 2.21247e14 | 0.0747315 | ||||||||
\(241\) | −8.99146e14 | −0.295610 | −0.147805 | − | 0.989016i | \(-0.547221\pi\) | ||||
−0.147805 | + | 0.989016i | \(0.547221\pi\) | |||||||
\(242\) | 1.22544e15 | 0.392186 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | −8.29858e14 | −0.251750 | ||||||||
\(245\) | −1.51784e15 | −0.448380 | ||||||||
\(246\) | −8.55338e14 | −0.246071 | ||||||||
\(247\) | −3.45647e15 | −0.968506 | ||||||||
\(248\) | −4.67053e15 | −1.27476 | ||||||||
\(249\) | −1.04078e15 | −0.276735 | ||||||||
\(250\) | 2.47218e15 | 0.640427 | ||||||||
\(251\) | −6.61525e15 | −1.66981 | −0.834905 | − | 0.550393i | \(-0.814478\pi\) | ||||
−0.834905 | + | 0.550393i | \(0.814478\pi\) | |||||||
\(252\) | −2.62939e14 | −0.0646773 | ||||||||
\(253\) | −4.59603e15 | −1.10179 | ||||||||
\(254\) | 2.09099e15 | 0.488577 | ||||||||
\(255\) | −6.30077e13 | −0.0143510 | ||||||||
\(256\) | −4.78742e15 | −1.06302 | ||||||||
\(257\) | 2.15487e15 | 0.466504 | 0.233252 | − | 0.972416i | \(-0.425063\pi\) | ||||
0.233252 | + | 0.972416i | \(0.425063\pi\) | |||||||
\(258\) | 7.56391e14 | 0.159668 | ||||||||
\(259\) | −1.79091e15 | −0.368660 | ||||||||
\(260\) | 7.23848e14 | 0.145318 | ||||||||
\(261\) | −2.44366e15 | −0.478496 | ||||||||
\(262\) | 2.88140e15 | 0.550357 | ||||||||
\(263\) | 6.52155e15 | 1.21517 | 0.607587 | − | 0.794253i | \(-0.292137\pi\) | ||||
0.607587 | + | 0.794253i | \(0.292137\pi\) | |||||||
\(264\) | 2.24326e15 | 0.407806 | ||||||||
\(265\) | 2.95064e15 | 0.523381 | ||||||||
\(266\) | −2.77823e15 | −0.480881 | ||||||||
\(267\) | 4.01346e15 | 0.677947 | ||||||||
\(268\) | −2.33530e15 | −0.385005 | ||||||||
\(269\) | −5.06945e15 | −0.815776 | −0.407888 | − | 0.913032i | \(-0.633735\pi\) | ||||
−0.407888 | + | 0.913032i | \(0.633735\pi\) | |||||||
\(270\) | 4.55581e14 | 0.0715651 | ||||||||
\(271\) | −1.22251e16 | −1.87478 | −0.937392 | − | 0.348275i | \(-0.886767\pi\) | ||||
−0.937392 | + | 0.348275i | \(0.886767\pi\) | |||||||
\(272\) | −7.73553e13 | −0.0115822 | ||||||||
\(273\) | 8.37670e14 | 0.122466 | ||||||||
\(274\) | 8.28800e15 | 1.18324 | ||||||||
\(275\) | 3.45212e15 | 0.481309 | ||||||||
\(276\) | 3.52021e15 | 0.479357 | ||||||||
\(277\) | −2.00845e15 | −0.267142 | −0.133571 | − | 0.991039i | \(-0.542644\pi\) | ||||
−0.133571 | + | 0.991039i | \(0.542644\pi\) | |||||||
\(278\) | −5.19890e15 | −0.675492 | ||||||||
\(279\) | −3.15850e15 | −0.400917 | ||||||||
\(280\) | 1.74033e15 | 0.215827 | ||||||||
\(281\) | 3.49015e15 | 0.422915 | 0.211457 | − | 0.977387i | \(-0.432179\pi\) | ||||
0.211457 | + | 0.977387i | \(0.432179\pi\) | |||||||
\(282\) | 6.35688e13 | 0.00752706 | ||||||||
\(283\) | 1.96381e15 | 0.227242 | 0.113621 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113621 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(284\) | 1.16673e15 | 0.131947 | ||||||||
\(285\) | −4.85632e15 | −0.536804 | ||||||||
\(286\) | −2.38917e15 | −0.258148 | ||||||||
\(287\) | −2.20963e15 | −0.233393 | ||||||||
\(288\) | −2.86193e15 | −0.295534 | ||||||||
\(289\) | −9.88255e15 | −0.997776 | ||||||||
\(290\) | 5.40716e15 | 0.533805 | ||||||||
\(291\) | −7.64875e15 | −0.738390 | ||||||||
\(292\) | −9.66584e15 | −0.912538 | ||||||||
\(293\) | 1.34590e16 | 1.24272 | 0.621358 | − | 0.783526i | \(-0.286581\pi\) | ||||
0.621358 | + | 0.783526i | \(0.286581\pi\) | |||||||
\(294\) | −3.83718e15 | −0.346541 | ||||||||
\(295\) | −7.76738e14 | −0.0686169 | ||||||||
\(296\) | −1.17026e16 | −1.01132 | ||||||||
\(297\) | 1.51703e15 | 0.128256 | ||||||||
\(298\) | −5.51246e15 | −0.455974 | ||||||||
\(299\) | −1.12147e16 | −0.907660 | ||||||||
\(300\) | −2.64406e15 | −0.209403 | ||||||||
\(301\) | 1.95402e15 | 0.151442 | ||||||||
\(302\) | −1.35389e16 | −1.02692 | ||||||||
\(303\) | −7.50992e15 | −0.557517 | ||||||||
\(304\) | −5.96216e15 | −0.433237 | ||||||||
\(305\) | 3.71446e15 | 0.264209 | ||||||||
\(306\) | −1.59287e14 | −0.0110915 | ||||||||
\(307\) | −1.54157e16 | −1.05090 | −0.525452 | − | 0.850823i | \(-0.676104\pi\) | ||||
−0.525452 | + | 0.850823i | \(0.676104\pi\) | |||||||
\(308\) | 1.93737e15 | 0.129310 | ||||||||
\(309\) | −8.07908e15 | −0.527997 | ||||||||
\(310\) | 6.98891e15 | 0.447258 | ||||||||
\(311\) | 2.06399e16 | 1.29349 | 0.646747 | − | 0.762705i | \(-0.276129\pi\) | ||||
0.646747 | + | 0.762705i | \(0.276129\pi\) | |||||||
\(312\) | 5.47372e15 | 0.335952 | ||||||||
\(313\) | 1.07125e16 | 0.643948 | 0.321974 | − | 0.946748i | \(-0.395654\pi\) | ||||
0.321974 | + | 0.946748i | \(0.395654\pi\) | |||||||
\(314\) | 1.06448e16 | 0.626752 | ||||||||
\(315\) | 1.17692e15 | 0.0678780 | ||||||||
\(316\) | −7.32593e15 | −0.413901 | ||||||||
\(317\) | 7.10976e15 | 0.393523 | 0.196761 | − | 0.980451i | \(-0.436958\pi\) | ||||
0.196761 | + | 0.980451i | \(0.436958\pi\) | |||||||
\(318\) | 7.45937e15 | 0.404507 | ||||||||
\(319\) | 1.80052e16 | 0.956663 | ||||||||
\(320\) | 8.81888e15 | 0.459133 | ||||||||
\(321\) | 5.95996e14 | 0.0304061 | ||||||||
\(322\) | −9.01409e15 | −0.450670 | ||||||||
\(323\) | 1.69793e15 | 0.0831964 | ||||||||
\(324\) | −1.16193e15 | −0.0558004 | ||||||||
\(325\) | 8.42344e15 | 0.396504 | ||||||||
\(326\) | 2.96936e15 | 0.137009 | ||||||||
\(327\) | 1.45119e16 | 0.656395 | ||||||||
\(328\) | −1.44387e16 | −0.640249 | ||||||||
\(329\) | 1.64220e14 | 0.00713926 | ||||||||
\(330\) | −3.35678e15 | −0.143081 | ||||||||
\(331\) | −4.63238e16 | −1.93607 | −0.968037 | − | 0.250806i | \(-0.919304\pi\) | ||||
−0.968037 | + | 0.250806i | \(0.919304\pi\) | |||||||
\(332\) | −5.87356e15 | −0.240716 | ||||||||
\(333\) | −7.91405e15 | −0.318062 | ||||||||
\(334\) | −2.11745e16 | −0.834567 | ||||||||
\(335\) | 1.04529e16 | 0.404058 | ||||||||
\(336\) | 1.44492e15 | 0.0547822 | ||||||||
\(337\) | 1.40598e16 | 0.522860 | 0.261430 | − | 0.965222i | \(-0.415806\pi\) | ||||
0.261430 | + | 0.965222i | \(0.415806\pi\) | |||||||
\(338\) | 1.35115e16 | 0.492883 | ||||||||
\(339\) | −1.24508e15 | −0.0445554 | ||||||||
\(340\) | −3.55579e14 | −0.0124831 | ||||||||
\(341\) | 2.32722e16 | 0.801557 | ||||||||
\(342\) | −1.22770e16 | −0.414881 | ||||||||
\(343\) | −2.15649e16 | −0.715048 | ||||||||
\(344\) | 1.27684e16 | 0.415439 | ||||||||
\(345\) | −1.57565e16 | −0.503079 | ||||||||
\(346\) | −3.89050e15 | −0.121902 | ||||||||
\(347\) | −3.96808e16 | −1.22022 | −0.610111 | − | 0.792316i | \(-0.708875\pi\) | ||||
−0.610111 | + | 0.792316i | \(0.708875\pi\) | |||||||
\(348\) | −1.37906e16 | −0.416216 | ||||||||
\(349\) | −4.08458e16 | −1.20999 | −0.604996 | − | 0.796229i | \(-0.706825\pi\) | ||||
−0.604996 | + | 0.796229i | \(0.706825\pi\) | |||||||
\(350\) | 6.77057e15 | 0.196872 | ||||||||
\(351\) | 3.70167e15 | 0.105658 | ||||||||
\(352\) | 2.10870e16 | 0.590864 | ||||||||
\(353\) | 5.54402e16 | 1.52507 | 0.762534 | − | 0.646948i | \(-0.223955\pi\) | ||||
0.762534 | + | 0.646948i | \(0.223955\pi\) | |||||||
\(354\) | −1.96363e15 | −0.0530321 | ||||||||
\(355\) | −5.22229e15 | −0.138477 | ||||||||
\(356\) | 2.26496e16 | 0.589707 | ||||||||
\(357\) | −4.11492e14 | −0.0105201 | ||||||||
\(358\) | −1.41960e16 | −0.356390 | ||||||||
\(359\) | −7.48019e16 | −1.84416 | −0.922080 | − | 0.386998i | \(-0.873512\pi\) | ||||
−0.922080 | + | 0.386998i | \(0.873512\pi\) | |||||||
\(360\) | 7.69054e15 | 0.186205 | ||||||||
\(361\) | 8.88153e16 | 2.11199 | ||||||||
\(362\) | 2.49333e16 | 0.582336 | ||||||||
\(363\) | 1.39894e16 | 0.320927 | ||||||||
\(364\) | 4.72732e15 | 0.106526 | ||||||||
\(365\) | 4.32645e16 | 0.957697 | ||||||||
\(366\) | 9.39036e15 | 0.204200 | ||||||||
\(367\) | 2.69332e16 | 0.575384 | 0.287692 | − | 0.957723i | \(-0.407112\pi\) | ||||
0.287692 | + | 0.957723i | \(0.407112\pi\) | |||||||
\(368\) | −1.93445e16 | −0.406019 | ||||||||
\(369\) | −9.76438e15 | −0.201360 | ||||||||
\(370\) | 1.75116e16 | 0.354826 | ||||||||
\(371\) | 1.92701e16 | 0.383666 | ||||||||
\(372\) | −1.78248e16 | −0.348734 | ||||||||
\(373\) | 5.13785e15 | 0.0987812 | 0.0493906 | − | 0.998780i | \(-0.484272\pi\) | ||||
0.0493906 | + | 0.998780i | \(0.484272\pi\) | |||||||
\(374\) | 1.17364e15 | 0.0221754 | ||||||||
\(375\) | 2.82219e16 | 0.524063 | ||||||||
\(376\) | 1.07309e15 | 0.0195846 | ||||||||
\(377\) | 4.39341e16 | 0.788103 | ||||||||
\(378\) | 2.97532e15 | 0.0524611 | ||||||||
\(379\) | −5.72424e15 | −0.0992117 | −0.0496058 | − | 0.998769i | \(-0.515797\pi\) | ||||
−0.0496058 | + | 0.998769i | \(0.515797\pi\) | |||||||
\(380\) | −2.74062e16 | −0.466935 | ||||||||
\(381\) | 2.38703e16 | 0.399803 | ||||||||
\(382\) | 1.66648e16 | 0.274403 | ||||||||
\(383\) | −6.23726e16 | −1.00972 | −0.504861 | − | 0.863201i | \(-0.668456\pi\) | ||||
−0.504861 | + | 0.863201i | \(0.668456\pi\) | |||||||
\(384\) | −9.86576e15 | −0.157028 | ||||||||
\(385\) | −8.67170e15 | −0.135709 | ||||||||
\(386\) | −6.78124e15 | −0.104350 | ||||||||
\(387\) | 8.63481e15 | 0.130657 | ||||||||
\(388\) | −4.31651e16 | −0.642283 | ||||||||
\(389\) | −1.15033e15 | −0.0168325 | −0.00841625 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841625 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(390\) | −8.19079e15 | −0.117871 | ||||||||
\(391\) | 5.50902e15 | 0.0779696 | ||||||||
\(392\) | −6.47744e16 | −0.901663 | ||||||||
\(393\) | 3.28935e16 | 0.450358 | ||||||||
\(394\) | 4.77697e16 | 0.643321 | ||||||||
\(395\) | 3.27910e16 | 0.434384 | ||||||||
\(396\) | 8.56124e15 | 0.111562 | ||||||||
\(397\) | −7.66690e16 | −0.982837 | −0.491418 | − | 0.870924i | \(-0.663521\pi\) | ||||
−0.491418 | + | 0.870924i | \(0.663521\pi\) | |||||||
\(398\) | 5.82515e16 | 0.734627 | ||||||||
\(399\) | −3.17158e16 | −0.393506 | ||||||||
\(400\) | 1.45298e16 | 0.177366 | ||||||||
\(401\) | 2.78495e16 | 0.334487 | 0.167243 | − | 0.985916i | \(-0.446513\pi\) | ||||
0.167243 | + | 0.985916i | \(0.446513\pi\) | |||||||
\(402\) | 2.64254e16 | 0.312285 | ||||||||
\(403\) | 5.67860e16 | 0.660327 | ||||||||
\(404\) | −4.23816e16 | −0.484952 | ||||||||
\(405\) | 5.20083e15 | 0.0585618 | ||||||||
\(406\) | 3.53132e16 | 0.391308 | ||||||||
\(407\) | 5.83117e16 | 0.635905 | ||||||||
\(408\) | −2.68887e15 | −0.0288589 | ||||||||
\(409\) | −8.47371e16 | −0.895101 | −0.447550 | − | 0.894259i | \(-0.647703\pi\) | ||||
−0.447550 | + | 0.894259i | \(0.647703\pi\) | |||||||
\(410\) | 2.16059e16 | 0.224635 | ||||||||
\(411\) | 9.46143e16 | 0.968244 | ||||||||
\(412\) | −4.55936e16 | −0.459274 | ||||||||
\(413\) | −5.07274e15 | −0.0502999 | ||||||||
\(414\) | −3.98333e16 | −0.388816 | ||||||||
\(415\) | 2.62902e16 | 0.252628 | ||||||||
\(416\) | 5.14539e16 | 0.486757 | ||||||||
\(417\) | −5.93496e16 | −0.552756 | ||||||||
\(418\) | 9.04586e16 | 0.829476 | ||||||||
\(419\) | −2.15791e16 | −0.194824 | −0.0974118 | − | 0.995244i | \(-0.531056\pi\) | ||||
−0.0974118 | + | 0.995244i | \(0.531056\pi\) | |||||||
\(420\) | 6.64186e15 | 0.0590432 | ||||||||
\(421\) | −5.87309e15 | −0.0514083 | −0.0257042 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257042 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(422\) | −1.20495e17 | −1.03857 | ||||||||
\(423\) | 7.25690e14 | 0.00615940 | ||||||||
\(424\) | 1.25920e17 | 1.05248 | ||||||||
\(425\) | −4.13788e15 | −0.0340604 | ||||||||
\(426\) | −1.32022e16 | −0.107025 | ||||||||
\(427\) | 2.42585e16 | 0.193679 | ||||||||
\(428\) | 3.36346e15 | 0.0264485 | ||||||||
\(429\) | −2.72744e16 | −0.211243 | ||||||||
\(430\) | −1.91065e16 | −0.145759 | ||||||||
\(431\) | 2.09721e17 | 1.57594 | 0.787970 | − | 0.615713i | \(-0.211132\pi\) | ||||
0.787970 | + | 0.615713i | \(0.211132\pi\) | |||||||
\(432\) | 6.38512e15 | 0.0472634 | ||||||||
\(433\) | −1.91663e17 | −1.39755 | −0.698775 | − | 0.715342i | \(-0.746271\pi\) | ||||
−0.698775 | + | 0.715342i | \(0.746271\pi\) | |||||||
\(434\) | 4.56433e16 | 0.327864 | ||||||||
\(435\) | 6.17272e16 | 0.436814 | ||||||||
\(436\) | 8.18970e16 | 0.570960 | ||||||||
\(437\) | 4.24608e17 | 2.91648 | ||||||||
\(438\) | 1.09375e17 | 0.740178 | ||||||||
\(439\) | 5.54766e16 | 0.369905 | 0.184952 | − | 0.982747i | \(-0.440787\pi\) | ||||
0.184952 | + | 0.982747i | \(0.440787\pi\) | |||||||
\(440\) | −5.66648e16 | −0.372281 | ||||||||
\(441\) | −4.38045e16 | −0.283575 | ||||||||
\(442\) | 2.86378e15 | 0.0182682 | ||||||||
\(443\) | −1.61504e17 | −1.01521 | −0.507607 | − | 0.861589i | \(-0.669470\pi\) | ||||
−0.507607 | + | 0.861589i | \(0.669470\pi\) | |||||||
\(444\) | −4.46623e16 | −0.276664 | ||||||||
\(445\) | −1.01380e17 | −0.618890 | ||||||||
\(446\) | −4.01529e16 | −0.241569 | ||||||||
\(447\) | −6.29292e16 | −0.373124 | ||||||||
\(448\) | 5.75946e16 | 0.336569 | ||||||||
\(449\) | −8.58276e16 | −0.494340 | −0.247170 | − | 0.968972i | \(-0.579501\pi\) | ||||
−0.247170 | + | 0.968972i | \(0.579501\pi\) | |||||||
\(450\) | 2.99192e16 | 0.169851 | ||||||||
\(451\) | 7.19451e16 | 0.402581 | ||||||||
\(452\) | −7.02653e15 | −0.0387562 | ||||||||
\(453\) | −1.54557e17 | −0.840331 | ||||||||
\(454\) | −7.47557e16 | −0.400665 | ||||||||
\(455\) | −2.11596e16 | −0.111798 | ||||||||
\(456\) | −2.07245e17 | −1.07948 | ||||||||
\(457\) | −2.08369e17 | −1.06998 | −0.534992 | − | 0.844857i | \(-0.679686\pi\) | ||||
−0.534992 | + | 0.844857i | \(0.679686\pi\) | |||||||
\(458\) | 1.44497e16 | 0.0731531 | ||||||||
\(459\) | −1.81839e15 | −0.00907619 | ||||||||
\(460\) | −8.89207e16 | −0.437600 | ||||||||
\(461\) | 8.06039e16 | 0.391111 | 0.195555 | − | 0.980693i | \(-0.437349\pi\) | ||||
0.195555 | + | 0.980693i | \(0.437349\pi\) | |||||||
\(462\) | −2.19225e16 | −0.104886 | ||||||||
\(463\) | −3.05515e17 | −1.44131 | −0.720653 | − | 0.693296i | \(-0.756158\pi\) | ||||
−0.720653 | + | 0.693296i | \(0.756158\pi\) | |||||||
\(464\) | 7.57832e16 | 0.352538 | ||||||||
\(465\) | 7.97841e16 | 0.365992 | ||||||||
\(466\) | 1.82410e17 | 0.825165 | ||||||||
\(467\) | −3.37157e16 | −0.150408 | −0.0752042 | − | 0.997168i | \(-0.523961\pi\) | ||||
−0.0752042 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(468\) | 2.08901e16 | 0.0919056 | ||||||||
\(469\) | 6.82657e16 | 0.296196 | ||||||||
\(470\) | −1.60575e15 | −0.00687137 | ||||||||
\(471\) | 1.21519e17 | 0.512873 | ||||||||
\(472\) | −3.31476e16 | −0.137984 | ||||||||
\(473\) | −6.36224e16 | −0.261224 | ||||||||
\(474\) | 8.28975e16 | 0.335724 | ||||||||
\(475\) | −3.18927e17 | −1.27404 | ||||||||
\(476\) | −2.32222e15 | −0.00915079 | ||||||||
\(477\) | 8.51547e16 | 0.331009 | ||||||||
\(478\) | −6.48760e16 | −0.248773 | ||||||||
\(479\) | 1.85402e17 | 0.701350 | 0.350675 | − | 0.936497i | \(-0.385952\pi\) | ||||
0.350675 | + | 0.936497i | \(0.385952\pi\) | |||||||
\(480\) | 7.22925e16 | 0.269790 | ||||||||
\(481\) | 1.42285e17 | 0.523861 | ||||||||
\(482\) | 5.74184e16 | 0.208567 | ||||||||
\(483\) | −1.02903e17 | −0.368784 | ||||||||
\(484\) | 7.89480e16 | 0.279156 | ||||||||
\(485\) | 1.93208e17 | 0.674068 | ||||||||
\(486\) | 1.31480e16 | 0.0452609 | ||||||||
\(487\) | −5.28050e17 | −1.79365 | −0.896824 | − | 0.442388i | \(-0.854131\pi\) | ||||
−0.896824 | + | 0.442388i | \(0.854131\pi\) | |||||||
\(488\) | 1.58516e17 | 0.531306 | ||||||||
\(489\) | 3.38976e16 | 0.112115 | ||||||||
\(490\) | 9.69275e16 | 0.316353 | ||||||||
\(491\) | 9.57612e16 | 0.308432 | 0.154216 | − | 0.988037i | \(-0.450715\pi\) | ||||
0.154216 | + | 0.988037i | \(0.450715\pi\) | |||||||
\(492\) | −5.51045e16 | −0.175151 | ||||||||
\(493\) | −2.15819e16 | −0.0676994 | ||||||||
\(494\) | 2.20726e17 | 0.683326 | ||||||||
\(495\) | −3.83203e16 | −0.117083 | ||||||||
\(496\) | 9.79519e16 | 0.295381 | ||||||||
\(497\) | −3.41059e16 | −0.101511 | ||||||||
\(498\) | 6.64631e16 | 0.195249 | ||||||||
\(499\) | −1.14773e17 | −0.332801 | −0.166401 | − | 0.986058i | \(-0.553215\pi\) | ||||
−0.166401 | + | 0.986058i | \(0.553215\pi\) | |||||||
\(500\) | 1.59268e17 | 0.455852 | ||||||||
\(501\) | −2.41724e17 | −0.682928 | ||||||||
\(502\) | 4.22442e17 | 1.17813 | ||||||||
\(503\) | 9.36677e16 | 0.257868 | 0.128934 | − | 0.991653i | \(-0.458844\pi\) | ||||
0.128934 | + | 0.991653i | \(0.458844\pi\) | |||||||
\(504\) | 5.02256e16 | 0.136498 | ||||||||
\(505\) | 1.89701e17 | 0.508951 | ||||||||
\(506\) | 2.93497e17 | 0.777365 | ||||||||
\(507\) | 1.54244e17 | 0.403327 | ||||||||
\(508\) | 1.34710e17 | 0.347766 | ||||||||
\(509\) | −6.74000e17 | −1.71789 | −0.858943 | − | 0.512071i | \(-0.828879\pi\) | ||||
−0.858943 | + | 0.512071i | \(0.828879\pi\) | |||||||
\(510\) | 4.02359e15 | 0.0101253 | ||||||||
\(511\) | 2.82553e17 | 0.702044 | ||||||||
\(512\) | 1.94855e17 | 0.478031 | ||||||||
\(513\) | −1.40152e17 | −0.339498 | ||||||||
\(514\) | −1.37607e17 | −0.329141 | ||||||||
\(515\) | 2.04078e17 | 0.482003 | ||||||||
\(516\) | 4.87299e16 | 0.113651 | ||||||||
\(517\) | −5.34697e15 | −0.0123146 | ||||||||
\(518\) | 1.14365e17 | 0.260107 | ||||||||
\(519\) | −4.44132e16 | −0.0997526 | ||||||||
\(520\) | −1.38267e17 | −0.306687 | ||||||||
\(521\) | 4.53485e17 | 0.993385 | 0.496693 | − | 0.867927i | \(-0.334548\pi\) | ||||
0.496693 | + | 0.867927i | \(0.334548\pi\) | |||||||
\(522\) | 1.56049e17 | 0.337601 | ||||||||
\(523\) | 8.66889e17 | 1.85226 | 0.926132 | − | 0.377201i | \(-0.123113\pi\) | ||||
0.926132 | + | 0.377201i | \(0.123113\pi\) | |||||||
\(524\) | 1.85632e17 | 0.391740 | ||||||||
\(525\) | 7.72916e16 | 0.161100 | ||||||||
\(526\) | −4.16459e17 | −0.857363 | ||||||||
\(527\) | −2.78952e16 | −0.0567232 | ||||||||
\(528\) | −4.70464e16 | −0.0944943 | ||||||||
\(529\) | 8.73622e17 | 1.73325 | ||||||||
\(530\) | −1.88424e17 | −0.369270 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −1.78985e17 | −0.342288 | ||||||||
\(533\) | 1.75552e17 | 0.331648 | ||||||||
\(534\) | −2.56295e17 | −0.478323 | ||||||||
\(535\) | −1.50549e16 | −0.0277574 | ||||||||
\(536\) | 4.46079e17 | 0.812533 | ||||||||
\(537\) | −1.62058e17 | −0.291634 | ||||||||
\(538\) | 3.23729e17 | 0.575568 | ||||||||
\(539\) | 3.22757e17 | 0.566955 | ||||||||
\(540\) | 2.93504e16 | 0.0509396 | ||||||||
\(541\) | −6.69887e17 | −1.14873 | −0.574367 | − | 0.818598i | \(-0.694752\pi\) | ||||
−0.574367 | + | 0.818598i | \(0.694752\pi\) | |||||||
\(542\) | 7.80679e17 | 1.32275 | ||||||||
\(543\) | 2.84633e17 | 0.476526 | ||||||||
\(544\) | −2.52759e16 | −0.0418132 | ||||||||
\(545\) | −3.66573e17 | −0.599215 | ||||||||
\(546\) | −5.34926e16 | −0.0864056 | ||||||||
\(547\) | 7.81136e17 | 1.24683 | 0.623417 | − | 0.781889i | \(-0.285744\pi\) | ||||
0.623417 | + | 0.781889i | \(0.285744\pi\) | |||||||
\(548\) | 5.33948e17 | 0.842220 | ||||||||
\(549\) | 1.07199e17 | 0.167097 | ||||||||
\(550\) | −2.20448e17 | −0.339586 | ||||||||
\(551\) | −1.66343e18 | −2.53232 | ||||||||
\(552\) | −6.72416e17 | −1.01166 | ||||||||
\(553\) | 2.14153e17 | 0.318427 | ||||||||
\(554\) | 1.28257e17 | 0.188481 | ||||||||
\(555\) | 1.99910e17 | 0.290355 | ||||||||
\(556\) | −3.34935e17 | −0.480811 | ||||||||
\(557\) | 4.27554e17 | 0.606642 | 0.303321 | − | 0.952888i | \(-0.401905\pi\) | ||||
0.303321 | + | 0.952888i | \(0.401905\pi\) | |||||||
\(558\) | 2.01698e17 | 0.282865 | ||||||||
\(559\) | −1.55243e17 | −0.215197 | ||||||||
\(560\) | −3.64989e16 | −0.0500100 | ||||||||
\(561\) | 1.33981e16 | 0.0181461 | ||||||||
\(562\) | −2.22877e17 | −0.298386 | ||||||||
\(563\) | 8.65471e16 | 0.114538 | 0.0572688 | − | 0.998359i | \(-0.481761\pi\) | ||||
0.0572688 | + | 0.998359i | \(0.481761\pi\) | |||||||
\(564\) | 4.09537e15 | 0.00535771 | ||||||||
\(565\) | 3.14509e16 | 0.0406742 | ||||||||
\(566\) | −1.25407e17 | −0.160330 | ||||||||
\(567\) | 3.39657e16 | 0.0429290 | ||||||||
\(568\) | −2.22863e17 | −0.278467 | ||||||||
\(569\) | −1.27671e16 | −0.0157712 | −0.00788558 | − | 0.999969i | \(-0.502510\pi\) | ||||
−0.00788558 | + | 0.999969i | \(0.502510\pi\) | |||||||
\(570\) | 3.10119e17 | 0.378740 | ||||||||
\(571\) | −1.88068e17 | −0.227080 | −0.113540 | − | 0.993533i | \(-0.536219\pi\) | ||||
−0.113540 | + | 0.993533i | \(0.536219\pi\) | |||||||
\(572\) | −1.53921e17 | −0.183748 | ||||||||
\(573\) | 1.90242e17 | 0.224544 | ||||||||
\(574\) | 1.41104e17 | 0.164670 | ||||||||
\(575\) | −1.03477e18 | −1.19400 | ||||||||
\(576\) | 2.54511e17 | 0.290376 | ||||||||
\(577\) | 1.05926e18 | 1.19498 | 0.597491 | − | 0.801876i | \(-0.296164\pi\) | ||||
0.597491 | + | 0.801876i | \(0.296164\pi\) | |||||||
\(578\) | 6.31088e17 | 0.703978 | ||||||||
\(579\) | −7.74133e16 | −0.0853896 | ||||||||
\(580\) | 3.48352e17 | 0.379959 | ||||||||
\(581\) | 1.71697e17 | 0.185190 | ||||||||
\(582\) | 4.88440e17 | 0.520969 | ||||||||
\(583\) | −6.27430e17 | −0.661789 | ||||||||
\(584\) | 1.84633e18 | 1.92586 | ||||||||
\(585\) | −9.35045e16 | −0.0964538 | ||||||||
\(586\) | −8.59474e17 | −0.876795 | ||||||||
\(587\) | 1.21775e18 | 1.22860 | 0.614301 | − | 0.789072i | \(-0.289438\pi\) | ||||
0.614301 | + | 0.789072i | \(0.289438\pi\) | |||||||
\(588\) | −2.47207e17 | −0.246666 | ||||||||
\(589\) | −2.15003e18 | −2.12175 | ||||||||
\(590\) | 4.96015e16 | 0.0484125 | ||||||||
\(591\) | 5.45330e17 | 0.526430 | ||||||||
\(592\) | 2.45432e17 | 0.234336 | ||||||||
\(593\) | −5.86979e17 | −0.554328 | −0.277164 | − | 0.960823i | \(-0.589395\pi\) | ||||
−0.277164 | + | 0.960823i | \(0.589395\pi\) | |||||||
\(594\) | −9.68758e16 | −0.0904906 | ||||||||
\(595\) | 1.03943e16 | 0.00960364 | ||||||||
\(596\) | −3.55136e17 | −0.324559 | ||||||||
\(597\) | 6.64988e17 | 0.601147 | ||||||||
\(598\) | 7.16155e17 | 0.640397 | ||||||||
\(599\) | −1.74292e18 | −1.54171 | −0.770854 | − | 0.637012i | \(-0.780170\pi\) | ||||
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(600\) | 5.05058e17 | 0.441935 | ||||||||
\(601\) | −6.26376e17 | −0.542189 | −0.271095 | − | 0.962553i | \(-0.587386\pi\) | ||||
−0.271095 | + | 0.962553i | \(0.587386\pi\) | |||||||
\(602\) | −1.24781e17 | −0.106849 | ||||||||
\(603\) | 3.01667e17 | 0.255544 | ||||||||
\(604\) | −8.72230e17 | −0.730955 | ||||||||
\(605\) | −3.53373e17 | −0.292970 | ||||||||
\(606\) | 4.79575e17 | 0.393354 | ||||||||
\(607\) | −1.70636e18 | −1.38466 | −0.692331 | − | 0.721580i | \(-0.743416\pi\) | ||||
−0.692331 | + | 0.721580i | \(0.743416\pi\) | |||||||
\(608\) | −1.94814e18 | −1.56404 | ||||||||
\(609\) | 4.03129e17 | 0.320208 | ||||||||
\(610\) | −2.37201e17 | −0.186412 | ||||||||
\(611\) | −1.30470e16 | −0.0101448 | ||||||||
\(612\) | −1.02619e16 | −0.00789485 | ||||||||
\(613\) | −3.36839e17 | −0.256407 | −0.128203 | − | 0.991748i | \(-0.540921\pi\) | ||||
−0.128203 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(614\) | 9.84427e17 | 0.741462 | ||||||||
\(615\) | 2.46649e17 | 0.183819 | ||||||||
\(616\) | −3.70068e17 | −0.272902 | ||||||||
\(617\) | −3.34927e17 | −0.244397 | −0.122199 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(618\) | 5.15920e17 | 0.372527 | ||||||||
\(619\) | −2.03089e18 | −1.45110 | −0.725550 | − | 0.688169i | \(-0.758415\pi\) | ||||
−0.725550 | + | 0.688169i | \(0.758415\pi\) | |||||||
\(620\) | 4.50255e17 | 0.318356 | ||||||||
\(621\) | −4.54730e17 | −0.318169 | ||||||||
\(622\) | −1.31804e18 | −0.912621 | ||||||||
\(623\) | −6.62097e17 | −0.453680 | ||||||||
\(624\) | −1.14797e17 | −0.0778448 | ||||||||
\(625\) | 3.63291e17 | 0.243800 | ||||||||
\(626\) | −6.84085e17 | −0.454336 | ||||||||
\(627\) | 1.03266e18 | 0.678762 | ||||||||
\(628\) | 6.85785e17 | 0.446118 | ||||||||
\(629\) | −6.98952e16 | −0.0450006 | ||||||||
\(630\) | −7.51568e16 | −0.0478911 | ||||||||
\(631\) | −1.93258e18 | −1.21884 | −0.609421 | − | 0.792847i | \(-0.708598\pi\) | ||||
−0.609421 | + | 0.792847i | \(0.708598\pi\) | |||||||
\(632\) | 1.39937e18 | 0.873517 | ||||||||
\(633\) | −1.37554e18 | −0.849865 | ||||||||
\(634\) | −4.54021e17 | −0.277649 | ||||||||
\(635\) | −6.02967e17 | −0.364976 | ||||||||
\(636\) | 4.80564e17 | 0.287925 | ||||||||
\(637\) | 7.87552e17 | 0.467060 | ||||||||
\(638\) | −1.14979e18 | −0.674970 | ||||||||
\(639\) | −1.50714e17 | −0.0875786 | ||||||||
\(640\) | 2.49210e17 | 0.143349 | ||||||||
\(641\) | −3.17896e18 | −1.81012 | −0.905060 | − | 0.425283i | \(-0.860175\pi\) | ||||
−0.905060 | + | 0.425283i | \(0.860175\pi\) | |||||||
\(642\) | −3.80596e16 | −0.0214529 | ||||||||
\(643\) | 1.99242e18 | 1.11176 | 0.555879 | − | 0.831263i | \(-0.312382\pi\) | ||||
0.555879 | + | 0.831263i | \(0.312382\pi\) | |||||||
\(644\) | −5.80726e17 | −0.320784 | ||||||||
\(645\) | −2.18116e17 | −0.119275 | ||||||||
\(646\) | −1.08428e17 | −0.0586989 | ||||||||
\(647\) | −1.34205e18 | −0.719267 | −0.359634 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359634 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(648\) | 2.21947e17 | 0.117764 | ||||||||
\(649\) | 1.65167e17 | 0.0867628 | ||||||||
\(650\) | −5.37911e17 | −0.279752 | ||||||||
\(651\) | 5.21056e17 | 0.268292 | ||||||||
\(652\) | 1.91299e17 | 0.0975220 | ||||||||
\(653\) | −2.21477e18 | −1.11787 | −0.558937 | − | 0.829210i | \(-0.688791\pi\) | ||||
−0.558937 | + | 0.829210i | \(0.688791\pi\) | |||||||
\(654\) | −9.26715e17 | −0.463117 | ||||||||
\(655\) | −8.30892e17 | −0.411127 | ||||||||
\(656\) | 3.02814e17 | 0.148355 | ||||||||
\(657\) | 1.24860e18 | 0.605689 | ||||||||
\(658\) | −1.04869e16 | −0.00503708 | ||||||||
\(659\) | −2.98710e18 | −1.42068 | −0.710338 | − | 0.703861i | \(-0.751458\pi\) | ||||
−0.710338 | + | 0.703861i | \(0.751458\pi\) | |||||||
\(660\) | −2.16258e17 | −0.101844 | ||||||||
\(661\) | −1.01538e18 | −0.473498 | −0.236749 | − | 0.971571i | \(-0.576082\pi\) | ||||
−0.236749 | + | 0.971571i | \(0.576082\pi\) | |||||||
\(662\) | 2.95818e18 | 1.36599 | ||||||||
\(663\) | 3.26924e16 | 0.0149489 | ||||||||
\(664\) | 1.12194e18 | 0.508018 | ||||||||
\(665\) | 8.01143e17 | 0.359227 | ||||||||
\(666\) | 5.05382e17 | 0.224407 | ||||||||
\(667\) | −5.39706e18 | −2.37323 | ||||||||
\(668\) | −1.36415e18 | −0.594040 | ||||||||
\(669\) | −4.58378e17 | −0.197676 | ||||||||
\(670\) | −6.67507e17 | −0.285082 | ||||||||
\(671\) | −7.89852e17 | −0.334079 | ||||||||
\(672\) | 4.72129e17 | 0.197770 | ||||||||
\(673\) | −5.60114e17 | −0.232369 | −0.116185 | − | 0.993228i | \(-0.537066\pi\) | ||||
−0.116185 | + | 0.993228i | \(0.537066\pi\) | |||||||
\(674\) | −8.97843e17 | −0.368902 | ||||||||
\(675\) | 3.41552e17 | 0.138990 | ||||||||
\(676\) | 8.70466e17 | 0.350831 | ||||||||
\(677\) | −8.13286e17 | −0.324651 | −0.162326 | − | 0.986737i | \(-0.551899\pi\) | ||||
−0.162326 | + | 0.986737i | \(0.551899\pi\) | |||||||
\(678\) | 7.95096e16 | 0.0314360 | ||||||||
\(679\) | 1.26181e18 | 0.494128 | ||||||||
\(680\) | 6.79212e16 | 0.0263450 | ||||||||
\(681\) | −8.53397e17 | −0.327865 | ||||||||
\(682\) | −1.48614e18 | −0.565536 | ||||||||
\(683\) | 2.98829e18 | 1.12639 | 0.563195 | − | 0.826324i | \(-0.309572\pi\) | ||||
0.563195 | + | 0.826324i | \(0.309572\pi\) | |||||||
\(684\) | −7.90937e17 | −0.295310 | ||||||||
\(685\) | −2.38996e18 | −0.883899 | ||||||||
\(686\) | 1.37711e18 | 0.504500 | ||||||||
\(687\) | 1.64955e17 | 0.0598613 | ||||||||
\(688\) | −2.67784e17 | −0.0962631 | ||||||||
\(689\) | −1.53098e18 | −0.545185 | ||||||||
\(690\) | 1.00619e18 | 0.354946 | ||||||||
\(691\) | −3.41593e18 | −1.19372 | −0.596858 | − | 0.802347i | \(-0.703585\pi\) | ||||
−0.596858 | + | 0.802347i | \(0.703585\pi\) | |||||||
\(692\) | −2.50642e17 | −0.0867690 | ||||||||
\(693\) | −2.50263e17 | −0.0858284 | ||||||||
\(694\) | 2.53397e18 | 0.860924 | ||||||||
\(695\) | 1.49918e18 | 0.504605 | ||||||||
\(696\) | 2.63423e18 | 0.878402 | ||||||||
\(697\) | −8.62369e16 | −0.0284892 | ||||||||
\(698\) | 2.60836e18 | 0.853705 | ||||||||
\(699\) | 2.08236e18 | 0.675234 | ||||||||
\(700\) | 4.36189e17 | 0.140132 | ||||||||
\(701\) | −6.57222e17 | −0.209192 | −0.104596 | − | 0.994515i | \(-0.533355\pi\) | ||||
−0.104596 | + | 0.994515i | \(0.533355\pi\) | |||||||
\(702\) | −2.36384e17 | −0.0745465 | ||||||||
\(703\) | −5.38718e18 | −1.68326 | ||||||||
\(704\) | −1.87527e18 | −0.580551 | ||||||||
\(705\) | −1.83310e16 | −0.00562285 | ||||||||
\(706\) | −3.54035e18 | −1.07601 | ||||||||
\(707\) | 1.23891e18 | 0.373089 | ||||||||
\(708\) | −1.26506e17 | −0.0377479 | ||||||||
\(709\) | −1.79482e17 | −0.0530665 | −0.0265333 | − | 0.999648i | \(-0.508447\pi\) | ||||
−0.0265333 | + | 0.999648i | \(0.508447\pi\) | |||||||
\(710\) | 3.33489e17 | 0.0977018 | ||||||||
\(711\) | 9.46342e17 | 0.274723 | ||||||||
\(712\) | −4.32644e18 | −1.24455 | ||||||||
\(713\) | −6.97585e18 | −1.98845 | ||||||||
\(714\) | 2.62774e16 | 0.00742239 | ||||||||
\(715\) | 6.88953e17 | 0.192841 | ||||||||
\(716\) | −9.14563e17 | −0.253676 | ||||||||
\(717\) | −7.40612e17 | −0.203571 | ||||||||
\(718\) | 4.77676e18 | 1.30114 | ||||||||
\(719\) | 4.97080e18 | 1.34180 | 0.670902 | − | 0.741546i | \(-0.265907\pi\) | ||||
0.670902 | + | 0.741546i | \(0.265907\pi\) | |||||||
\(720\) | −1.61289e17 | −0.0431462 | ||||||||
\(721\) | 1.33280e18 | 0.353334 | ||||||||
\(722\) | −5.67164e18 | −1.49011 | ||||||||
\(723\) | 6.55478e17 | 0.170671 | ||||||||
\(724\) | 1.60631e18 | 0.414503 | ||||||||
\(725\) | 4.05379e18 | 1.03673 | ||||||||
\(726\) | −8.93346e17 | −0.226429 | ||||||||
\(727\) | 7.59211e17 | 0.190717 | 0.0953583 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953583 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(728\) | −9.02995e17 | −0.224818 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −2.76282e18 | −0.675700 | ||||||||
\(731\) | 7.62608e16 | 0.0184858 | ||||||||
\(732\) | 6.04966e17 | 0.145348 | ||||||||
\(733\) | 6.71055e18 | 1.59802 | 0.799010 | − | 0.601318i | \(-0.205357\pi\) | ||||
0.799010 | + | 0.601318i | \(0.205357\pi\) | |||||||
\(734\) | −1.71992e18 | −0.405960 | ||||||||
\(735\) | 1.10651e18 | 0.258873 | ||||||||
\(736\) | −6.32083e18 | −1.46578 | ||||||||
\(737\) | −2.22272e18 | −0.510911 | ||||||||
\(738\) | 6.23541e17 | 0.142069 | ||||||||
\(739\) | −5.57650e18 | −1.25943 | −0.629713 | − | 0.776828i | \(-0.716827\pi\) | ||||
−0.629713 | + | 0.776828i | \(0.716827\pi\) | |||||||
\(740\) | 1.12817e18 | 0.252563 | ||||||||
\(741\) | 2.51977e18 | 0.559167 | ||||||||
\(742\) | −1.23057e18 | −0.270694 | ||||||||
\(743\) | 8.17239e18 | 1.78206 | 0.891029 | − | 0.453946i | \(-0.149984\pi\) | ||||
0.891029 | + | 0.453946i | \(0.149984\pi\) | |||||||
\(744\) | 3.40481e18 | 0.735986 | ||||||||
\(745\) | 1.58960e18 | 0.340621 | ||||||||
\(746\) | −3.28097e17 | −0.0696948 | ||||||||
\(747\) | 7.58730e17 | 0.159773 | ||||||||
\(748\) | 7.56110e16 | 0.0157843 | ||||||||
\(749\) | −9.83210e16 | −0.0203477 | ||||||||
\(750\) | −1.80222e18 | −0.369751 | ||||||||
\(751\) | −5.17756e18 | −1.05309 | −0.526545 | − | 0.850147i | \(-0.676513\pi\) | ||||
−0.526545 | + | 0.850147i | \(0.676513\pi\) | |||||||
\(752\) | −2.25052e16 | −0.00453802 | ||||||||
\(753\) | 4.82252e18 | 0.964066 | ||||||||
\(754\) | −2.80558e18 | −0.556044 | ||||||||
\(755\) | 3.90412e18 | 0.767129 | ||||||||
\(756\) | 1.91683e17 | 0.0373414 | ||||||||
\(757\) | −9.33308e17 | −0.180261 | −0.0901305 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901305 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(758\) | 3.65543e17 | 0.0699985 | ||||||||
\(759\) | 3.35050e18 | 0.636119 | ||||||||
\(760\) | 5.23503e18 | 0.985441 | ||||||||
\(761\) | 6.65862e18 | 1.24275 | 0.621375 | − | 0.783513i | \(-0.286574\pi\) | ||||
0.621375 | + | 0.783513i | \(0.286574\pi\) | |||||||
\(762\) | −1.52433e18 | −0.282080 | ||||||||
\(763\) | −2.39402e18 | −0.439257 | ||||||||
\(764\) | 1.07362e18 | 0.195318 | ||||||||
\(765\) | 4.59326e16 | 0.00828555 | ||||||||
\(766\) | 3.98304e18 | 0.712406 | ||||||||
\(767\) | 4.03021e17 | 0.0714755 | ||||||||
\(768\) | 3.49003e18 | 0.613736 | ||||||||
\(769\) | −5.49304e18 | −0.957836 | −0.478918 | − | 0.877860i | \(-0.658971\pi\) | ||||
−0.478918 | + | 0.877860i | \(0.658971\pi\) | |||||||
\(770\) | 5.53765e17 | 0.0957493 | ||||||||
\(771\) | −1.57090e18 | −0.269336 | ||||||||
\(772\) | −4.36876e17 | −0.0742755 | ||||||||
\(773\) | −4.56545e18 | −0.769692 | −0.384846 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384846 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(774\) | −5.51409e17 | −0.0921844 | ||||||||
\(775\) | 5.23963e18 | 0.868639 | ||||||||
\(776\) | 8.24523e18 | 1.35551 | ||||||||
\(777\) | 1.30557e18 | 0.212846 | ||||||||
\(778\) | 7.34584e16 | 0.0118761 | ||||||||
\(779\) | −6.64671e18 | −1.06565 | ||||||||
\(780\) | −5.27685e17 | −0.0838996 | ||||||||
\(781\) | 1.11048e18 | 0.175097 | ||||||||
\(782\) | −3.51799e17 | −0.0550112 | ||||||||
\(783\) | 1.78143e18 | 0.276260 | ||||||||
\(784\) | 1.35847e18 | 0.208928 | ||||||||
\(785\) | −3.06959e18 | −0.468196 | ||||||||
\(786\) | −2.10054e18 | −0.317749 | ||||||||
\(787\) | −8.58589e18 | −1.28810 | −0.644050 | − | 0.764983i | \(-0.722747\pi\) | ||||
−0.644050 | + | 0.764983i | \(0.722747\pi\) | |||||||
\(788\) | 3.07753e18 | 0.457911 | ||||||||
\(789\) | −4.75421e18 | −0.701581 | ||||||||
\(790\) | −2.09400e18 | −0.306478 | ||||||||
\(791\) | 2.05401e17 | 0.0298163 | ||||||||
\(792\) | −1.63533e18 | −0.235447 | ||||||||
\(793\) | −1.92730e18 | −0.275216 | ||||||||
\(794\) | 4.89599e18 | 0.693437 | ||||||||
\(795\) | −2.15101e18 | −0.302174 | ||||||||
\(796\) | 3.75280e18 | 0.522903 | ||||||||
\(797\) | 6.84451e18 | 0.945939 | 0.472970 | − | 0.881079i | \(-0.343182\pi\) | ||||
0.472970 | + | 0.881079i | \(0.343182\pi\) | |||||||
\(798\) | 2.02533e18 | 0.277637 | ||||||||
\(799\) | 6.40914e15 | 0.000871456 0 | ||||||||
\(800\) | 4.74764e18 | 0.640313 | ||||||||
\(801\) | −2.92581e18 | −0.391413 | ||||||||
\(802\) | −1.77843e18 | −0.235996 | ||||||||
\(803\) | −9.19986e18 | −1.21096 | ||||||||
\(804\) | 1.70243e18 | 0.222283 | ||||||||
\(805\) | 2.59934e18 | 0.336659 | ||||||||
\(806\) | −3.62629e18 | −0.465891 | ||||||||
\(807\) | 3.69563e18 | 0.470989 | ||||||||
\(808\) | 8.09557e18 | 1.02347 | ||||||||
\(809\) | 1.01211e19 | 1.26930 | 0.634650 | − | 0.772800i | \(-0.281144\pi\) | ||||
0.634650 | + | 0.772800i | \(0.281144\pi\) | |||||||
\(810\) | −3.32119e17 | −0.0413181 | ||||||||
\(811\) | −5.21041e18 | −0.643037 | −0.321519 | − | 0.946903i | \(-0.604193\pi\) | ||||
−0.321519 | + | 0.946903i | \(0.604193\pi\) | |||||||
\(812\) | 2.27503e18 | 0.278530 | ||||||||
\(813\) | 8.91208e18 | 1.08241 | ||||||||
\(814\) | −3.72372e18 | −0.448661 | ||||||||
\(815\) | −8.56257e17 | −0.102348 | ||||||||
\(816\) | 5.63920e16 | 0.00668700 | ||||||||
\(817\) | 5.87781e18 | 0.691468 | ||||||||
\(818\) | 5.41121e18 | 0.631536 | ||||||||
\(819\) | −6.10662e17 | −0.0707058 | ||||||||
\(820\) | 1.39194e18 | 0.159894 | ||||||||
\(821\) | 2.25361e18 | 0.256831 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(822\) | −6.04195e18 | −0.683141 | ||||||||
\(823\) | 1.04493e19 | 1.17217 | 0.586085 | − | 0.810250i | \(-0.300669\pi\) | ||||
0.586085 | + | 0.810250i | \(0.300669\pi\) | |||||||
\(824\) | 8.70911e18 | 0.969275 | ||||||||
\(825\) | −2.51660e18 | −0.277884 | ||||||||
\(826\) | 3.23939e17 | 0.0354889 | ||||||||
\(827\) | 1.23524e19 | 1.34265 | 0.671327 | − | 0.741162i | \(-0.265725\pi\) | ||||
0.671327 | + | 0.741162i | \(0.265725\pi\) | |||||||
\(828\) | −2.56623e18 | −0.276757 | ||||||||
\(829\) | −7.88948e18 | −0.844197 | −0.422098 | − | 0.906550i | \(-0.638706\pi\) | ||||
−0.422098 | + | 0.906550i | \(0.638706\pi\) | |||||||
\(830\) | −1.67886e18 | −0.178241 | ||||||||
\(831\) | 1.46416e18 | 0.154235 | ||||||||
\(832\) | −4.57579e18 | −0.478261 | ||||||||
\(833\) | −3.86872e17 | −0.0401213 | ||||||||
\(834\) | 3.79000e18 | 0.389995 | ||||||||
\(835\) | 6.10597e18 | 0.623437 | ||||||||
\(836\) | 5.82772e18 | 0.590416 | ||||||||
\(837\) | 2.30255e18 | 0.231469 | ||||||||
\(838\) | 1.37801e18 | 0.137457 | ||||||||
\(839\) | 1.36386e19 | 1.34995 | 0.674975 | − | 0.737841i | \(-0.264155\pi\) | ||||
0.674975 | + | 0.737841i | \(0.264155\pi\) | |||||||
\(840\) | −1.26870e18 | −0.124608 | ||||||||
\(841\) | 1.08827e19 | 1.06062 | ||||||||
\(842\) | 3.75049e17 | 0.0362710 | ||||||||
\(843\) | −2.54432e18 | −0.244170 | ||||||||
\(844\) | −7.76277e18 | −0.739249 | ||||||||
\(845\) | −3.89623e18 | −0.368193 | ||||||||
\(846\) | −4.63417e16 | −0.00434575 | ||||||||
\(847\) | −2.30782e18 | −0.214763 | ||||||||
\(848\) | −2.64083e18 | −0.243875 | ||||||||
\(849\) | −1.43162e18 | −0.131198 | ||||||||
\(850\) | 2.64240e17 | 0.0240312 | ||||||||
\(851\) | −1.74789e19 | −1.57751 | ||||||||
\(852\) | −8.50543e17 | −0.0761796 | ||||||||
\(853\) | 4.63570e18 | 0.412047 | 0.206023 | − | 0.978547i | \(-0.433948\pi\) | ||||
0.206023 | + | 0.978547i | \(0.433948\pi\) | |||||||
\(854\) | −1.54912e18 | −0.136650 | ||||||||
\(855\) | 3.54026e18 | 0.309924 | ||||||||
\(856\) | −6.42474e17 | −0.0558182 | ||||||||
\(857\) | 6.54102e18 | 0.563988 | 0.281994 | − | 0.959416i | \(-0.409004\pi\) | ||||
0.281994 | + | 0.959416i | \(0.409004\pi\) | |||||||
\(858\) | 1.74171e18 | 0.149042 | ||||||||
\(859\) | 4.55967e18 | 0.387238 | 0.193619 | − | 0.981077i | \(-0.437977\pi\) | ||||
0.193619 | + | 0.981077i | \(0.437977\pi\) | |||||||
\(860\) | −1.23092e18 | −0.103750 | ||||||||
\(861\) | 1.61082e18 | 0.134749 | ||||||||
\(862\) | −1.33925e19 | −1.11190 | ||||||||
\(863\) | −1.50526e19 | −1.24035 | −0.620173 | − | 0.784465i | \(-0.712937\pi\) | ||||
−0.620173 | + | 0.784465i | \(0.712937\pi\) | |||||||
\(864\) | 2.08634e18 | 0.170627 | ||||||||
\(865\) | 1.12188e18 | 0.0910631 | ||||||||
\(866\) | 1.22394e19 | 0.986037 | ||||||||
\(867\) | 7.20438e18 | 0.576066 | ||||||||
\(868\) | 2.94054e18 | 0.233372 | ||||||||
\(869\) | −6.97276e18 | −0.549258 | ||||||||
\(870\) | −3.94182e18 | −0.308192 | ||||||||
\(871\) | −5.42360e18 | −0.420891 | ||||||||
\(872\) | −1.56436e19 | −1.20498 | ||||||||
\(873\) | 5.57594e18 | 0.426310 | ||||||||
\(874\) | −2.71150e19 | −2.05771 | ||||||||
\(875\) | −4.65574e18 | −0.350701 | ||||||||
\(876\) | 7.04639e18 | 0.526854 | ||||||||
\(877\) | 7.32647e18 | 0.543748 | 0.271874 | − | 0.962333i | \(-0.412357\pi\) | ||||
0.271874 | + | 0.962333i | \(0.412357\pi\) | |||||||
\(878\) | −3.54267e18 | −0.260985 | ||||||||
\(879\) | −9.81159e18 | −0.717483 | ||||||||
\(880\) | 1.18840e18 | 0.0862628 | ||||||||
\(881\) | −7.90227e18 | −0.569388 | −0.284694 | − | 0.958618i | \(-0.591892\pi\) | ||||
−0.284694 | + | 0.958618i | \(0.591892\pi\) | |||||||
\(882\) | 2.79730e18 | 0.200076 | ||||||||
\(883\) | 1.84667e19 | 1.31113 | 0.655563 | − | 0.755140i | \(-0.272431\pi\) | ||||
0.655563 | + | 0.755140i | \(0.272431\pi\) | |||||||
\(884\) | 1.84497e17 | 0.0130032 | ||||||||
\(885\) | 5.66242e17 | 0.0396160 | ||||||||
\(886\) | 1.03134e19 | 0.716281 | ||||||||
\(887\) | 1.78491e19 | 1.23059 | 0.615295 | − | 0.788297i | \(-0.289037\pi\) | ||||
0.615295 | + | 0.788297i | \(0.289037\pi\) | |||||||
\(888\) | 8.53122e18 | 0.583884 | ||||||||
\(889\) | −3.93787e18 | −0.267547 | ||||||||
\(890\) | 6.47403e18 | 0.436656 | ||||||||
\(891\) | −1.10592e18 | −0.0740486 | ||||||||
\(892\) | −2.58682e18 | −0.171947 | ||||||||
\(893\) | 4.93984e17 | 0.0325971 | ||||||||
\(894\) | 4.01858e18 | 0.263257 | ||||||||
\(895\) | 4.09361e18 | 0.266230 | ||||||||
\(896\) | 1.62755e18 | 0.105083 | ||||||||
\(897\) | 8.17549e18 | 0.524038 | ||||||||
\(898\) | 5.48085e18 | 0.348780 | ||||||||
\(899\) | 2.73283e19 | 1.72653 | ||||||||
\(900\) | 1.92752e18 | 0.120899 | ||||||||
\(901\) | 7.52068e17 | 0.0468323 | ||||||||
\(902\) | −4.59433e18 | −0.284040 | ||||||||
\(903\) | −1.42448e18 | −0.0874350 | ||||||||
\(904\) | 1.34218e18 | 0.0817930 | ||||||||
\(905\) | −7.18986e18 | −0.435016 | ||||||||
\(906\) | 9.86982e18 | 0.592893 | ||||||||
\(907\) | −1.78793e18 | −0.106636 | −0.0533178 | − | 0.998578i | \(-0.516980\pi\) | ||||
−0.0533178 | + | 0.998578i | \(0.516980\pi\) | |||||||
\(908\) | −4.81608e18 | −0.285191 | ||||||||
\(909\) | 5.47473e18 | 0.321883 | ||||||||
\(910\) | 1.35123e18 | 0.0788787 | ||||||||
\(911\) | 1.31518e19 | 0.762283 | 0.381142 | − | 0.924517i | \(-0.375531\pi\) | ||||
0.381142 | + | 0.924517i | \(0.375531\pi\) | |||||||
\(912\) | 4.34642e18 | 0.250130 | ||||||||
\(913\) | −5.59041e18 | −0.319436 | ||||||||
\(914\) | 1.33062e19 | 0.754924 | ||||||||
\(915\) | −2.70784e18 | −0.152541 | ||||||||
\(916\) | 9.30909e17 | 0.0520699 | ||||||||
\(917\) | −5.42641e18 | −0.301378 | ||||||||
\(918\) | 1.16120e17 | 0.00640368 | ||||||||
\(919\) | −2.87717e19 | −1.57549 | −0.787743 | − | 0.616004i | \(-0.788750\pi\) | ||||
−0.787743 | + | 0.616004i | \(0.788750\pi\) | |||||||
\(920\) | 1.69853e19 | 0.923532 | ||||||||
\(921\) | 1.12380e19 | 0.606740 | ||||||||
\(922\) | −5.14727e18 | −0.275947 | ||||||||
\(923\) | 2.70965e18 | 0.144246 | ||||||||
\(924\) | −1.41234e18 | −0.0746572 | ||||||||
\(925\) | 1.31286e19 | 0.689123 | ||||||||
\(926\) | 1.95098e19 | 1.01691 | ||||||||
\(927\) | 5.88965e18 | 0.304839 | ||||||||
\(928\) | 2.47622e19 | 1.27271 | ||||||||
\(929\) | 9.56512e18 | 0.488190 | 0.244095 | − | 0.969751i | \(-0.421509\pi\) | ||||
0.244095 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(930\) | −5.09492e18 | −0.258225 | ||||||||
\(931\) | −2.98182e19 | −1.50075 | ||||||||
\(932\) | 1.17516e19 | 0.587347 | ||||||||
\(933\) | −1.50465e19 | −0.746799 | ||||||||
\(934\) | 2.15304e18 | 0.106120 | ||||||||
\(935\) | −3.38437e17 | −0.0165654 | ||||||||
\(936\) | −3.99034e18 | −0.193962 | ||||||||
\(937\) | −2.37281e19 | −1.14540 | −0.572698 | − | 0.819766i | \(-0.694103\pi\) | ||||
−0.572698 | + | 0.819766i | \(0.694103\pi\) | |||||||
\(938\) | −4.35937e18 | −0.208980 | ||||||||
\(939\) | −7.80938e18 | −0.371784 | ||||||||
\(940\) | −1.03449e17 | −0.00489099 | ||||||||
\(941\) | 5.14891e18 | 0.241759 | 0.120880 | − | 0.992667i | \(-0.461429\pi\) | ||||
0.120880 | + | 0.992667i | \(0.461429\pi\) | |||||||
\(942\) | −7.76008e18 | −0.361856 | ||||||||
\(943\) | −2.15655e19 | −0.998698 | ||||||||
\(944\) | 6.95182e17 | 0.0319728 | ||||||||
\(945\) | −8.57976e17 | −0.0391894 | ||||||||
\(946\) | 4.06285e18 | 0.184305 | ||||||||
\(947\) | 2.30511e19 | 1.03852 | 0.519262 | − | 0.854615i | \(-0.326207\pi\) | ||||
0.519262 | + | 0.854615i | \(0.326207\pi\) | |||||||
\(948\) | 5.34060e18 | 0.238966 | ||||||||
\(949\) | −2.24484e19 | −0.997596 | ||||||||
\(950\) | 2.03663e19 | 0.898895 | ||||||||
\(951\) | −5.18302e18 | −0.227201 | ||||||||
\(952\) | 4.43581e17 | 0.0193123 | ||||||||
\(953\) | 5.07741e18 | 0.219552 | 0.109776 | − | 0.993956i | \(-0.464987\pi\) | ||||
0.109776 | + | 0.993956i | \(0.464987\pi\) | |||||||
\(954\) | −5.43788e18 | −0.233542 | ||||||||
\(955\) | −4.80554e18 | −0.204984 | ||||||||
\(956\) | −4.17959e18 | −0.177075 | ||||||||
\(957\) | −1.31258e19 | −0.552329 | ||||||||
\(958\) | −1.18396e19 | −0.494835 | ||||||||
\(959\) | −1.56084e19 | −0.647946 | ||||||||
\(960\) | −6.42896e18 | −0.265081 | ||||||||
\(961\) | 1.09050e19 | 0.446607 | ||||||||
\(962\) | −9.08615e18 | −0.369609 | ||||||||
\(963\) | −4.34481e17 | −0.0175550 | ||||||||
\(964\) | 3.69914e18 | 0.148457 | ||||||||
\(965\) | 1.95547e18 | 0.0779512 | ||||||||
\(966\) | 6.57127e18 | 0.260195 | ||||||||
\(967\) | −4.68899e19 | −1.84420 | −0.922099 | − | 0.386954i | \(-0.873527\pi\) | ||||
−0.922099 | + | 0.386954i | \(0.873527\pi\) | |||||||
\(968\) | −1.50803e19 | −0.589143 | ||||||||
\(969\) | −1.23779e18 | −0.0480334 | ||||||||
\(970\) | −1.23380e19 | −0.475587 | ||||||||
\(971\) | −1.11617e19 | −0.427371 | −0.213686 | − | 0.976902i | \(-0.568547\pi\) | ||||
−0.213686 | + | 0.976902i | \(0.568547\pi\) | |||||||
\(972\) | 8.47047e17 | 0.0322164 | ||||||||
\(973\) | 9.79086e18 | 0.369902 | ||||||||
\(974\) | 3.37207e19 | 1.26550 | ||||||||
\(975\) | −6.14069e18 | −0.228922 | ||||||||
\(976\) | −3.32446e18 | −0.123111 | ||||||||
\(977\) | −4.19466e19 | −1.54306 | −0.771529 | − | 0.636194i | \(-0.780508\pi\) | ||||
−0.771529 | + | 0.636194i | \(0.780508\pi\) | |||||||
\(978\) | −2.16466e18 | −0.0791021 | ||||||||
\(979\) | 2.15577e19 | 0.782557 | ||||||||
\(980\) | 6.24448e18 | 0.225178 | ||||||||
\(981\) | −1.05792e19 | −0.378970 | ||||||||
\(982\) | −6.11520e18 | −0.217613 | ||||||||
\(983\) | −3.57397e19 | −1.26344 | −0.631718 | − | 0.775198i | \(-0.717650\pi\) | ||||
−0.631718 | + | 0.775198i | \(0.717650\pi\) | |||||||
\(984\) | 1.05258e19 | 0.369648 | ||||||||
\(985\) | −1.37751e19 | −0.480573 | ||||||||
\(986\) | 1.37820e18 | 0.0477651 | ||||||||
\(987\) | −1.19716e17 | −0.00412185 | ||||||||
\(988\) | 1.42201e19 | 0.486387 | ||||||||
\(989\) | 1.90708e19 | 0.648027 | ||||||||
\(990\) | 2.44709e18 | 0.0826078 | ||||||||
\(991\) | −1.75515e19 | −0.588620 | −0.294310 | − | 0.955710i | \(-0.595090\pi\) | ||||
−0.294310 | + | 0.955710i | \(0.595090\pi\) | |||||||
\(992\) | 3.20059e19 | 1.06636 | ||||||||
\(993\) | 3.37700e19 | 1.11779 | ||||||||
\(994\) | 2.17796e18 | 0.0716207 | ||||||||
\(995\) | −1.67976e19 | −0.548780 | ||||||||
\(996\) | 4.28183e18 | 0.138977 | ||||||||
\(997\) | 5.23492e18 | 0.168807 | 0.0844036 | − | 0.996432i | \(-0.473101\pi\) | ||||
0.0844036 | + | 0.996432i | \(0.473101\pi\) | |||||||
\(998\) | 7.32925e18 | 0.234807 | ||||||||
\(999\) | 5.76934e18 | 0.183633 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.14.a.b.1.12 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.12 | ✓ | 31 | 1.1 | even | 1 | trivial |