Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,38,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(86.7140381246\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1222518952080 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.10568e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 262144. | 0.707107 | ||||||||
\(3\) | 5.04314e8 | 0.751551 | 0.375775 | − | 0.926711i | \(-0.377376\pi\) | ||||
0.375775 | + | 0.926711i | \(0.377376\pi\) | |||||||
\(4\) | 6.87195e10 | 0.500000 | ||||||||
\(5\) | 3.81470e12 | 0.447214 | ||||||||
\(6\) | 1.32203e14 | 0.531427 | ||||||||
\(7\) | −3.94775e15 | −0.916296 | −0.458148 | − | 0.888876i | \(-0.651487\pi\) | ||||
−0.458148 | + | 0.888876i | \(0.651487\pi\) | |||||||
\(8\) | 1.80144e16 | 0.353553 | ||||||||
\(9\) | −1.95951e17 | −0.435172 | ||||||||
\(10\) | 1.00000e18 | 0.316228 | ||||||||
\(11\) | −2.18005e18 | −0.118223 | −0.0591115 | − | 0.998251i | \(-0.518827\pi\) | ||||
−0.0591115 | + | 0.998251i | \(0.518827\pi\) | |||||||
\(12\) | 3.46562e19 | 0.375775 | ||||||||
\(13\) | 1.81624e20 | 0.447942 | 0.223971 | − | 0.974596i | \(-0.428098\pi\) | ||||
0.223971 | + | 0.974596i | \(0.428098\pi\) | |||||||
\(14\) | −1.03488e21 | −0.647919 | ||||||||
\(15\) | 1.92381e21 | 0.336104 | ||||||||
\(16\) | 4.72237e21 | 0.250000 | ||||||||
\(17\) | −2.91883e22 | −0.503388 | −0.251694 | − | 0.967807i | \(-0.580988\pi\) | ||||
−0.251694 | + | 0.967807i | \(0.580988\pi\) | |||||||
\(18\) | −5.13673e22 | −0.307713 | ||||||||
\(19\) | −4.63426e23 | −1.02103 | −0.510515 | − | 0.859869i | \(-0.670545\pi\) | ||||
−0.510515 | + | 0.859869i | \(0.670545\pi\) | |||||||
\(20\) | 2.62144e23 | 0.223607 | ||||||||
\(21\) | −1.99091e24 | −0.688643 | ||||||||
\(22\) | −5.71488e23 | −0.0835964 | ||||||||
\(23\) | −5.39070e24 | −0.346481 | −0.173241 | − | 0.984880i | \(-0.555424\pi\) | ||||
−0.173241 | + | 0.984880i | \(0.555424\pi\) | |||||||
\(24\) | 9.08492e24 | 0.265713 | ||||||||
\(25\) | 1.45519e25 | 0.200000 | ||||||||
\(26\) | 4.76117e25 | 0.316743 | ||||||||
\(27\) | −3.25906e26 | −1.07860 | ||||||||
\(28\) | −2.71287e26 | −0.458148 | ||||||||
\(29\) | −1.38938e27 | −1.22591 | −0.612956 | − | 0.790117i | \(-0.710020\pi\) | ||||
−0.612956 | + | 0.790117i | \(0.710020\pi\) | |||||||
\(30\) | 5.04314e26 | 0.237661 | ||||||||
\(31\) | 1.08576e27 | 0.278961 | 0.139480 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139480 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(32\) | 1.23794e27 | 0.176777 | ||||||||
\(33\) | −1.09943e27 | −0.0888506 | ||||||||
\(34\) | −7.65153e27 | −0.355949 | ||||||||
\(35\) | −1.50595e28 | −0.409780 | ||||||||
\(36\) | −1.34656e28 | −0.217586 | ||||||||
\(37\) | −8.17276e28 | −0.795494 | −0.397747 | − | 0.917495i | \(-0.630208\pi\) | ||||
−0.397747 | + | 0.917495i | \(0.630208\pi\) | |||||||
\(38\) | −1.21484e29 | −0.721977 | ||||||||
\(39\) | 9.15957e28 | 0.336651 | ||||||||
\(40\) | 6.87195e28 | 0.158114 | ||||||||
\(41\) | 4.55702e29 | 0.664018 | 0.332009 | − | 0.943276i | \(-0.392274\pi\) | ||||
0.332009 | + | 0.943276i | \(0.392274\pi\) | |||||||
\(42\) | −5.21904e29 | −0.486944 | ||||||||
\(43\) | −6.17149e29 | −0.372584 | −0.186292 | − | 0.982494i | \(-0.559647\pi\) | ||||
−0.186292 | + | 0.982494i | \(0.559647\pi\) | |||||||
\(44\) | −1.49812e29 | −0.0591115 | ||||||||
\(45\) | −7.47493e29 | −0.194615 | ||||||||
\(46\) | −1.41314e30 | −0.244999 | ||||||||
\(47\) | −1.66780e30 | −0.194238 | −0.0971191 | − | 0.995273i | \(-0.530963\pi\) | ||||
−0.0971191 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(48\) | 2.38156e30 | 0.187888 | ||||||||
\(49\) | −2.97740e30 | −0.160402 | ||||||||
\(50\) | 3.81470e30 | 0.141421 | ||||||||
\(51\) | −1.47201e31 | −0.378322 | ||||||||
\(52\) | 1.24811e31 | 0.223971 | ||||||||
\(53\) | −5.11828e31 | −0.645684 | −0.322842 | − | 0.946453i | \(-0.604638\pi\) | ||||
−0.322842 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(54\) | −8.54342e31 | −0.762688 | ||||||||
\(55\) | −8.31624e30 | −0.0528710 | ||||||||
\(56\) | −7.11163e31 | −0.323959 | ||||||||
\(57\) | −2.33712e32 | −0.767355 | ||||||||
\(58\) | −3.64219e32 | −0.866851 | ||||||||
\(59\) | −4.79981e32 | −0.832649 | −0.416325 | − | 0.909216i | \(-0.636682\pi\) | ||||
−0.416325 | + | 0.909216i | \(0.636682\pi\) | |||||||
\(60\) | 1.32203e32 | 0.168052 | ||||||||
\(61\) | 1.48774e33 | 1.39292 | 0.696460 | − | 0.717595i | \(-0.254757\pi\) | ||||
0.696460 | + | 0.717595i | \(0.254757\pi\) | |||||||
\(62\) | 2.84626e32 | 0.197255 | ||||||||
\(63\) | 7.73564e32 | 0.398746 | ||||||||
\(64\) | 3.24519e32 | 0.125000 | ||||||||
\(65\) | 6.92841e32 | 0.200326 | ||||||||
\(66\) | −2.88210e32 | −0.0628269 | ||||||||
\(67\) | 1.20039e34 | 1.98125 | 0.990627 | − | 0.136596i | \(-0.0436162\pi\) | ||||
0.990627 | + | 0.136596i | \(0.0436162\pi\) | |||||||
\(68\) | −2.00580e33 | −0.251694 | ||||||||
\(69\) | −2.71861e33 | −0.260398 | ||||||||
\(70\) | −3.94775e33 | −0.289758 | ||||||||
\(71\) | −1.19359e32 | −0.00673869 | −0.00336934 | − | 0.999994i | \(-0.501072\pi\) | ||||
−0.00336934 | + | 0.999994i | \(0.501072\pi\) | |||||||
\(72\) | −3.52994e33 | −0.153856 | ||||||||
\(73\) | −4.41041e33 | −0.148938 | −0.0744691 | − | 0.997223i | \(-0.523726\pi\) | ||||
−0.0744691 | + | 0.997223i | \(0.523726\pi\) | |||||||
\(74\) | −2.14244e34 | −0.562499 | ||||||||
\(75\) | 7.33874e33 | 0.150310 | ||||||||
\(76\) | −3.18464e34 | −0.510515 | ||||||||
\(77\) | 8.60630e33 | 0.108327 | ||||||||
\(78\) | 2.40113e34 | 0.238048 | ||||||||
\(79\) | −1.73547e35 | −1.35930 | −0.679651 | − | 0.733536i | \(-0.737869\pi\) | ||||
−0.679651 | + | 0.733536i | \(0.737869\pi\) | |||||||
\(80\) | 1.80144e34 | 0.111803 | ||||||||
\(81\) | −7.61254e34 | −0.375454 | ||||||||
\(82\) | 1.19460e35 | 0.469532 | ||||||||
\(83\) | −1.57921e35 | −0.496015 | −0.248008 | − | 0.968758i | \(-0.579776\pi\) | ||||
−0.248008 | + | 0.968758i | \(0.579776\pi\) | |||||||
\(84\) | −1.36814e35 | −0.344321 | ||||||||
\(85\) | −1.11344e35 | −0.225122 | ||||||||
\(86\) | −1.61782e35 | −0.263456 | ||||||||
\(87\) | −7.00687e35 | −0.921335 | ||||||||
\(88\) | −3.92723e34 | −0.0417982 | ||||||||
\(89\) | −9.73344e35 | −0.840526 | −0.420263 | − | 0.907402i | \(-0.638062\pi\) | ||||
−0.420263 | + | 0.907402i | \(0.638062\pi\) | |||||||
\(90\) | −1.95951e35 | −0.137613 | ||||||||
\(91\) | −7.17007e35 | −0.410447 | ||||||||
\(92\) | −3.70446e35 | −0.173241 | ||||||||
\(93\) | 5.47565e35 | 0.209653 | ||||||||
\(94\) | −4.37205e35 | −0.137347 | ||||||||
\(95\) | −1.76783e36 | −0.456618 | ||||||||
\(96\) | 6.24311e35 | 0.132857 | ||||||||
\(97\) | −8.76678e36 | −1.54015 | −0.770075 | − | 0.637954i | \(-0.779781\pi\) | ||||
−0.770075 | + | 0.637954i | \(0.779781\pi\) | |||||||
\(98\) | −7.80509e35 | −0.113421 | ||||||||
\(99\) | 4.27183e35 | 0.0514473 | ||||||||
\(100\) | 1.00000e36 | 0.100000 | ||||||||
\(101\) | −9.95992e36 | −0.828534 | −0.414267 | − | 0.910155i | \(-0.635962\pi\) | ||||
−0.414267 | + | 0.910155i | \(0.635962\pi\) | |||||||
\(102\) | −3.85878e36 | −0.267514 | ||||||||
\(103\) | −1.38183e37 | −0.799773 | −0.399887 | − | 0.916565i | \(-0.630951\pi\) | ||||
−0.399887 | + | 0.916565i | \(0.630951\pi\) | |||||||
\(104\) | 3.27185e36 | 0.158371 | ||||||||
\(105\) | −7.59470e36 | −0.307970 | ||||||||
\(106\) | −1.34173e37 | −0.456568 | ||||||||
\(107\) | 1.66394e37 | 0.475924 | 0.237962 | − | 0.971275i | \(-0.423521\pi\) | ||||
0.237962 | + | 0.971275i | \(0.423521\pi\) | |||||||
\(108\) | −2.23961e37 | −0.539302 | ||||||||
\(109\) | −2.15440e37 | −0.437458 | −0.218729 | − | 0.975786i | \(-0.570191\pi\) | ||||
−0.218729 | + | 0.975786i | \(0.570191\pi\) | |||||||
\(110\) | −2.18005e36 | −0.0373854 | ||||||||
\(111\) | −4.12164e37 | −0.597854 | ||||||||
\(112\) | −1.86427e37 | −0.229074 | ||||||||
\(113\) | −7.20846e37 | −0.751435 | −0.375717 | − | 0.926734i | \(-0.622604\pi\) | ||||
−0.375717 | + | 0.926734i | \(0.622604\pi\) | |||||||
\(114\) | −6.12663e37 | −0.542602 | ||||||||
\(115\) | −2.05639e37 | −0.154951 | ||||||||
\(116\) | −9.54778e37 | −0.612956 | ||||||||
\(117\) | −3.55894e37 | −0.194932 | ||||||||
\(118\) | −1.25824e38 | −0.588772 | ||||||||
\(119\) | 1.15228e38 | 0.461253 | ||||||||
\(120\) | 3.46562e37 | 0.118831 | ||||||||
\(121\) | −3.35287e38 | −0.986023 | ||||||||
\(122\) | 3.90003e38 | 0.984944 | ||||||||
\(123\) | 2.29817e38 | 0.499043 | ||||||||
\(124\) | 7.46129e37 | 0.139480 | ||||||||
\(125\) | 5.55112e37 | 0.0894427 | ||||||||
\(126\) | 2.02785e38 | 0.281956 | ||||||||
\(127\) | 5.59928e38 | 0.672610 | 0.336305 | − | 0.941753i | \(-0.390823\pi\) | ||||
0.336305 | + | 0.941753i | \(0.390823\pi\) | |||||||
\(128\) | 8.50706e37 | 0.0883883 | ||||||||
\(129\) | −3.11237e38 | −0.280016 | ||||||||
\(130\) | 1.81624e38 | 0.141652 | ||||||||
\(131\) | 2.41935e39 | 1.63750 | 0.818748 | − | 0.574154i | \(-0.194669\pi\) | ||||
0.818748 | + | 0.574154i | \(0.194669\pi\) | |||||||
\(132\) | −7.55524e37 | −0.0444253 | ||||||||
\(133\) | 1.82949e39 | 0.935565 | ||||||||
\(134\) | 3.14676e39 | 1.40096 | ||||||||
\(135\) | −1.24323e39 | −0.482366 | ||||||||
\(136\) | −5.25809e38 | −0.177975 | ||||||||
\(137\) | 4.22583e39 | 1.24905 | 0.624527 | − | 0.781003i | \(-0.285292\pi\) | ||||
0.624527 | + | 0.781003i | \(0.285292\pi\) | |||||||
\(138\) | −7.12666e38 | −0.184129 | ||||||||
\(139\) | 1.36024e39 | 0.307497 | 0.153748 | − | 0.988110i | \(-0.450866\pi\) | ||||
0.153748 | + | 0.988110i | \(0.450866\pi\) | |||||||
\(140\) | −1.03488e39 | −0.204890 | ||||||||
\(141\) | −8.41097e38 | −0.145980 | ||||||||
\(142\) | −3.12892e37 | −0.00476497 | ||||||||
\(143\) | −3.95950e38 | −0.0529571 | ||||||||
\(144\) | −9.25352e38 | −0.108793 | ||||||||
\(145\) | −5.30008e39 | −0.548245 | ||||||||
\(146\) | −1.15616e39 | −0.105315 | ||||||||
\(147\) | −1.50155e39 | −0.120550 | ||||||||
\(148\) | −5.61628e39 | −0.397747 | ||||||||
\(149\) | 2.43718e39 | 0.152385 | 0.0761924 | − | 0.997093i | \(-0.475724\pi\) | ||||
0.0761924 | + | 0.997093i | \(0.475724\pi\) | |||||||
\(150\) | 1.92381e39 | 0.106285 | ||||||||
\(151\) | 2.40615e40 | 1.17557 | 0.587786 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587786 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(152\) | −8.34833e39 | −0.360989 | ||||||||
\(153\) | 5.71946e39 | 0.219060 | ||||||||
\(154\) | 2.25609e39 | 0.0765990 | ||||||||
\(155\) | 4.14185e39 | 0.124755 | ||||||||
\(156\) | 6.29441e39 | 0.168326 | ||||||||
\(157\) | 3.62213e40 | 0.860638 | 0.430319 | − | 0.902677i | \(-0.358401\pi\) | ||||
0.430319 | + | 0.902677i | \(0.358401\pi\) | |||||||
\(158\) | −4.54943e40 | −0.961172 | ||||||||
\(159\) | −2.58122e40 | −0.485264 | ||||||||
\(160\) | 4.72237e39 | 0.0790569 | ||||||||
\(161\) | 2.12811e40 | 0.317479 | ||||||||
\(162\) | −1.99558e40 | −0.265486 | ||||||||
\(163\) | −1.06162e41 | −1.26037 | −0.630186 | − | 0.776444i | \(-0.717021\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(164\) | 3.13156e40 | 0.332009 | ||||||||
\(165\) | −4.19400e39 | −0.0397352 | ||||||||
\(166\) | −4.13980e40 | −0.350736 | ||||||||
\(167\) | −3.16742e40 | −0.240133 | −0.120066 | − | 0.992766i | \(-0.538311\pi\) | ||||
−0.120066 | + | 0.992766i | \(0.538311\pi\) | |||||||
\(168\) | −3.58650e40 | −0.243472 | ||||||||
\(169\) | −1.31413e41 | −0.799348 | ||||||||
\(170\) | −2.91883e40 | −0.159185 | ||||||||
\(171\) | 9.08086e40 | 0.444323 | ||||||||
\(172\) | −4.24102e40 | −0.186292 | ||||||||
\(173\) | −3.69208e41 | −1.45686 | −0.728431 | − | 0.685119i | \(-0.759750\pi\) | ||||
−0.728431 | + | 0.685119i | \(0.759750\pi\) | |||||||
\(174\) | −1.83681e41 | −0.651482 | ||||||||
\(175\) | −5.74473e40 | −0.183259 | ||||||||
\(176\) | −1.02950e40 | −0.0295558 | ||||||||
\(177\) | −2.42061e41 | −0.625778 | ||||||||
\(178\) | −2.55156e41 | −0.594342 | ||||||||
\(179\) | 4.82779e41 | 1.01384 | 0.506918 | − | 0.861994i | \(-0.330785\pi\) | ||||
0.506918 | + | 0.861994i | \(0.330785\pi\) | |||||||
\(180\) | −5.13673e40 | −0.0973074 | ||||||||
\(181\) | 7.79879e41 | 1.33344 | 0.666720 | − | 0.745308i | \(-0.267698\pi\) | ||||
0.666720 | + | 0.745308i | \(0.267698\pi\) | |||||||
\(182\) | −1.87959e41 | −0.290230 | ||||||||
\(183\) | 7.50291e41 | 1.04685 | ||||||||
\(184\) | −9.71102e40 | −0.122500 | ||||||||
\(185\) | −3.11766e41 | −0.355756 | ||||||||
\(186\) | 1.43541e41 | 0.148247 | ||||||||
\(187\) | 6.36320e40 | 0.0595121 | ||||||||
\(188\) | −1.14611e41 | −0.0971191 | ||||||||
\(189\) | 1.28659e42 | 0.988320 | ||||||||
\(190\) | −4.63426e41 | −0.322878 | ||||||||
\(191\) | 3.29328e41 | 0.208214 | 0.104107 | − | 0.994566i | \(-0.466801\pi\) | ||||
0.104107 | + | 0.994566i | \(0.466801\pi\) | |||||||
\(192\) | 1.63659e41 | 0.0939438 | ||||||||
\(193\) | −1.11821e41 | −0.0583058 | −0.0291529 | − | 0.999575i | \(-0.509281\pi\) | ||||
−0.0291529 | + | 0.999575i | \(0.509281\pi\) | |||||||
\(194\) | −2.29816e42 | −1.08905 | ||||||||
\(195\) | 3.49410e41 | 0.150555 | ||||||||
\(196\) | −2.04606e41 | −0.0802011 | ||||||||
\(197\) | 4.09822e42 | 1.46208 | 0.731038 | − | 0.682337i | \(-0.239036\pi\) | ||||
0.731038 | + | 0.682337i | \(0.239036\pi\) | |||||||
\(198\) | 1.11983e41 | 0.0363788 | ||||||||
\(199\) | 5.54584e42 | 1.64129 | 0.820646 | − | 0.571437i | \(-0.193614\pi\) | ||||
0.820646 | + | 0.571437i | \(0.193614\pi\) | |||||||
\(200\) | 2.62144e41 | 0.0707107 | ||||||||
\(201\) | 6.05376e42 | 1.48901 | ||||||||
\(202\) | −2.61093e42 | −0.585862 | ||||||||
\(203\) | 5.48494e42 | 1.12330 | ||||||||
\(204\) | −1.01156e42 | −0.189161 | ||||||||
\(205\) | 1.73837e42 | 0.296958 | ||||||||
\(206\) | −3.62239e42 | −0.565525 | ||||||||
\(207\) | 1.05631e42 | 0.150779 | ||||||||
\(208\) | 8.57696e41 | 0.111985 | ||||||||
\(209\) | 1.01029e42 | 0.120709 | ||||||||
\(210\) | −1.99091e42 | −0.217768 | ||||||||
\(211\) | −1.56109e43 | −1.56388 | −0.781939 | − | 0.623355i | \(-0.785769\pi\) | ||||
−0.781939 | + | 0.623355i | \(0.785769\pi\) | |||||||
\(212\) | −3.51725e42 | −0.322842 | ||||||||
\(213\) | −6.01944e40 | −0.00506447 | ||||||||
\(214\) | 4.36191e42 | 0.336529 | ||||||||
\(215\) | −2.35424e42 | −0.166625 | ||||||||
\(216\) | −5.87099e42 | −0.381344 | ||||||||
\(217\) | −4.28631e42 | −0.255610 | ||||||||
\(218\) | −5.64764e42 | −0.309330 | ||||||||
\(219\) | −2.22424e42 | −0.111935 | ||||||||
\(220\) | −5.71488e41 | −0.0264355 | ||||||||
\(221\) | −5.30130e42 | −0.225489 | ||||||||
\(222\) | −1.08046e43 | −0.422747 | ||||||||
\(223\) | 3.39504e42 | 0.122238 | 0.0611189 | − | 0.998130i | \(-0.480533\pi\) | ||||
0.0611189 | + | 0.998130i | \(0.480533\pi\) | |||||||
\(224\) | −4.88707e42 | −0.161980 | ||||||||
\(225\) | −2.85146e42 | −0.0870343 | ||||||||
\(226\) | −1.88965e43 | −0.531345 | ||||||||
\(227\) | −5.49026e43 | −1.42271 | −0.711353 | − | 0.702835i | \(-0.751917\pi\) | ||||
−0.711353 | + | 0.702835i | \(0.751917\pi\) | |||||||
\(228\) | −1.60606e43 | −0.383678 | ||||||||
\(229\) | 5.12775e43 | 1.12972 | 0.564860 | − | 0.825187i | \(-0.308930\pi\) | ||||
0.564860 | + | 0.825187i | \(0.308930\pi\) | |||||||
\(230\) | −5.39070e42 | −0.109567 | ||||||||
\(231\) | 4.34028e42 | 0.0814135 | ||||||||
\(232\) | −2.50289e43 | −0.433426 | ||||||||
\(233\) | 9.95511e43 | 1.59207 | 0.796034 | − | 0.605252i | \(-0.206928\pi\) | ||||
0.796034 | + | 0.605252i | \(0.206928\pi\) | |||||||
\(234\) | −9.32955e42 | −0.137837 | ||||||||
\(235\) | −6.36217e42 | −0.0868659 | ||||||||
\(236\) | −3.29841e43 | −0.416325 | ||||||||
\(237\) | −8.75223e43 | −1.02158 | ||||||||
\(238\) | 3.02063e43 | 0.326155 | ||||||||
\(239\) | −4.20147e43 | −0.419798 | −0.209899 | − | 0.977723i | \(-0.567314\pi\) | ||||
−0.209899 | + | 0.977723i | \(0.567314\pi\) | |||||||
\(240\) | 9.08492e42 | 0.0840259 | ||||||||
\(241\) | 9.20589e43 | 0.788407 | 0.394203 | − | 0.919023i | \(-0.371021\pi\) | ||||
0.394203 | + | 0.919023i | \(0.371021\pi\) | |||||||
\(242\) | −8.78934e43 | −0.697224 | ||||||||
\(243\) | 1.08359e44 | 0.796432 | ||||||||
\(244\) | 1.02237e44 | 0.696460 | ||||||||
\(245\) | −1.13579e43 | −0.0717341 | ||||||||
\(246\) | 6.02452e43 | 0.352877 | ||||||||
\(247\) | −8.41693e43 | −0.457362 | ||||||||
\(248\) | 1.95593e43 | 0.0986275 | ||||||||
\(249\) | −7.96418e43 | −0.372780 | ||||||||
\(250\) | 1.45519e43 | 0.0632456 | ||||||||
\(251\) | −8.81367e43 | −0.355789 | −0.177895 | − | 0.984050i | \(-0.556929\pi\) | ||||
−0.177895 | + | 0.984050i | \(0.556929\pi\) | |||||||
\(252\) | 5.31589e43 | 0.199373 | ||||||||
\(253\) | 1.17520e43 | 0.0409621 | ||||||||
\(254\) | 1.46782e44 | 0.475607 | ||||||||
\(255\) | −5.61526e43 | −0.169191 | ||||||||
\(256\) | 2.23007e43 | 0.0625000 | ||||||||
\(257\) | −1.46131e44 | −0.381049 | −0.190524 | − | 0.981682i | \(-0.561019\pi\) | ||||
−0.190524 | + | 0.981682i | \(0.561019\pi\) | |||||||
\(258\) | −8.15890e43 | −0.198001 | ||||||||
\(259\) | 3.22640e44 | 0.728908 | ||||||||
\(260\) | 4.76117e43 | 0.100163 | ||||||||
\(261\) | 2.72251e44 | 0.533482 | ||||||||
\(262\) | 6.34218e44 | 1.15788 | ||||||||
\(263\) | −2.73688e44 | −0.465666 | −0.232833 | − | 0.972517i | \(-0.574800\pi\) | ||||
−0.232833 | + | 0.972517i | \(0.574800\pi\) | |||||||
\(264\) | −1.98056e43 | −0.0314134 | ||||||||
\(265\) | −1.95247e44 | −0.288759 | ||||||||
\(266\) | 4.79589e44 | 0.661544 | ||||||||
\(267\) | −4.90872e44 | −0.631698 | ||||||||
\(268\) | 8.24905e44 | 0.990627 | ||||||||
\(269\) | 1.32425e45 | 1.48440 | 0.742201 | − | 0.670177i | \(-0.233782\pi\) | ||||
0.742201 | + | 0.670177i | \(0.233782\pi\) | |||||||
\(270\) | −3.25906e44 | −0.341085 | ||||||||
\(271\) | 5.21202e44 | 0.509418 | 0.254709 | − | 0.967018i | \(-0.418020\pi\) | ||||
0.254709 | + | 0.967018i | \(0.418020\pi\) | |||||||
\(272\) | −1.37838e44 | −0.125847 | ||||||||
\(273\) | −3.61597e44 | −0.308472 | ||||||||
\(274\) | 1.10777e45 | 0.883214 | ||||||||
\(275\) | −3.17239e43 | −0.0236446 | ||||||||
\(276\) | −1.86821e44 | −0.130199 | ||||||||
\(277\) | −1.63439e45 | −1.06532 | −0.532659 | − | 0.846330i | \(-0.678807\pi\) | ||||
−0.532659 | + | 0.846330i | \(0.678807\pi\) | |||||||
\(278\) | 3.56578e44 | 0.217433 | ||||||||
\(279\) | −2.12756e44 | −0.121396 | ||||||||
\(280\) | −2.71287e44 | −0.144879 | ||||||||
\(281\) | 1.81299e44 | 0.0906420 | 0.0453210 | − | 0.998972i | \(-0.485569\pi\) | ||||
0.0453210 | + | 0.998972i | \(0.485569\pi\) | |||||||
\(282\) | −2.20489e44 | −0.103223 | ||||||||
\(283\) | −3.63001e45 | −1.59169 | −0.795845 | − | 0.605500i | \(-0.792973\pi\) | ||||
−0.795845 | + | 0.605500i | \(0.792973\pi\) | |||||||
\(284\) | −8.20228e42 | −0.00336934 | ||||||||
\(285\) | −8.91541e44 | −0.343172 | ||||||||
\(286\) | −1.03796e44 | −0.0374463 | ||||||||
\(287\) | −1.79900e45 | −0.608437 | ||||||||
\(288\) | −2.42575e44 | −0.0769282 | ||||||||
\(289\) | −2.51014e45 | −0.746600 | ||||||||
\(290\) | −1.38938e45 | −0.387668 | ||||||||
\(291\) | −4.42121e45 | −1.15750 | ||||||||
\(292\) | −3.03081e44 | −0.0744691 | ||||||||
\(293\) | 1.89813e45 | 0.437800 | 0.218900 | − | 0.975747i | \(-0.429753\pi\) | ||||
0.218900 | + | 0.975747i | \(0.429753\pi\) | |||||||
\(294\) | −3.93622e44 | −0.0852420 | ||||||||
\(295\) | −1.83098e45 | −0.372372 | ||||||||
\(296\) | −1.47227e45 | −0.281250 | ||||||||
\(297\) | 7.10491e44 | 0.127516 | ||||||||
\(298\) | 6.38892e44 | 0.107752 | ||||||||
\(299\) | −9.79081e44 | −0.155204 | ||||||||
\(300\) | 5.04314e44 | 0.0751551 | ||||||||
\(301\) | 2.43635e45 | 0.341397 | ||||||||
\(302\) | 6.30757e45 | 0.831254 | ||||||||
\(303\) | −5.02293e45 | −0.622686 | ||||||||
\(304\) | −2.18847e45 | −0.255257 | ||||||||
\(305\) | 5.67529e45 | 0.622933 | ||||||||
\(306\) | 1.49932e45 | 0.154899 | ||||||||
\(307\) | −1.42121e45 | −0.138229 | −0.0691143 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691143 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(308\) | 5.91420e44 | 0.0541637 | ||||||||
\(309\) | −6.96879e45 | −0.601070 | ||||||||
\(310\) | 1.08576e45 | 0.0882151 | ||||||||
\(311\) | 1.48151e46 | 1.13406 | 0.567031 | − | 0.823696i | \(-0.308092\pi\) | ||||
0.567031 | + | 0.823696i | \(0.308092\pi\) | |||||||
\(312\) | 1.65004e45 | 0.119024 | ||||||||
\(313\) | 1.68494e46 | 1.14555 | 0.572775 | − | 0.819713i | \(-0.305867\pi\) | ||||
0.572775 | + | 0.819713i | \(0.305867\pi\) | |||||||
\(314\) | 9.49520e45 | 0.608563 | ||||||||
\(315\) | 2.95091e45 | 0.178325 | ||||||||
\(316\) | −1.19261e46 | −0.679651 | ||||||||
\(317\) | 9.92215e45 | 0.533347 | 0.266673 | − | 0.963787i | \(-0.414076\pi\) | ||||
0.266673 | + | 0.963787i | \(0.414076\pi\) | |||||||
\(318\) | −6.76651e45 | −0.343134 | ||||||||
\(319\) | 3.02893e45 | 0.144931 | ||||||||
\(320\) | 1.23794e45 | 0.0559017 | ||||||||
\(321\) | 8.39148e45 | 0.357681 | ||||||||
\(322\) | 5.57872e45 | 0.224492 | ||||||||
\(323\) | 1.35266e46 | 0.513975 | ||||||||
\(324\) | −5.23130e45 | −0.187727 | ||||||||
\(325\) | 2.64298e45 | 0.0895884 | ||||||||
\(326\) | −2.78297e46 | −0.891217 | ||||||||
\(327\) | −1.08650e46 | −0.328772 | ||||||||
\(328\) | 8.20920e45 | 0.234766 | ||||||||
\(329\) | 6.58407e45 | 0.177980 | ||||||||
\(330\) | −1.09943e45 | −0.0280970 | ||||||||
\(331\) | 4.31846e46 | 1.04354 | 0.521772 | − | 0.853085i | \(-0.325271\pi\) | ||||
0.521772 | + | 0.853085i | \(0.325271\pi\) | |||||||
\(332\) | −1.08522e46 | −0.248008 | ||||||||
\(333\) | 1.60146e46 | 0.346177 | ||||||||
\(334\) | −8.30321e45 | −0.169800 | ||||||||
\(335\) | 4.57914e46 | 0.886044 | ||||||||
\(336\) | −9.40179e45 | −0.172161 | ||||||||
\(337\) | 5.65717e45 | 0.0980497 | 0.0490248 | − | 0.998798i | \(-0.484389\pi\) | ||||
0.0490248 | + | 0.998798i | \(0.484389\pi\) | |||||||
\(338\) | −3.44493e46 | −0.565224 | ||||||||
\(339\) | −3.63533e46 | −0.564741 | ||||||||
\(340\) | −7.65153e45 | −0.112561 | ||||||||
\(341\) | −2.36702e45 | −0.0329796 | ||||||||
\(342\) | 2.38049e46 | 0.314184 | ||||||||
\(343\) | 8.50326e46 | 1.06327 | ||||||||
\(344\) | −1.11176e46 | −0.131728 | ||||||||
\(345\) | −1.03707e46 | −0.116454 | ||||||||
\(346\) | −9.67857e46 | −1.03016 | ||||||||
\(347\) | 5.80965e46 | 0.586211 | 0.293106 | − | 0.956080i | \(-0.405311\pi\) | ||||
0.293106 | + | 0.956080i | \(0.405311\pi\) | |||||||
\(348\) | −4.81508e46 | −0.460668 | ||||||||
\(349\) | −1.34423e47 | −1.21956 | −0.609780 | − | 0.792571i | \(-0.708742\pi\) | ||||
−0.609780 | + | 0.792571i | \(0.708742\pi\) | |||||||
\(350\) | −1.50595e46 | −0.129584 | ||||||||
\(351\) | −5.91923e46 | −0.483152 | ||||||||
\(352\) | −2.69877e45 | −0.0208991 | ||||||||
\(353\) | −1.24862e47 | −0.917484 | −0.458742 | − | 0.888570i | \(-0.651700\pi\) | ||||
−0.458742 | + | 0.888570i | \(0.651700\pi\) | |||||||
\(354\) | −6.34550e46 | −0.442492 | ||||||||
\(355\) | −4.55318e44 | −0.00301363 | ||||||||
\(356\) | −6.68877e46 | −0.420263 | ||||||||
\(357\) | 5.81111e46 | 0.346655 | ||||||||
\(358\) | 1.26558e47 | 0.716890 | ||||||||
\(359\) | −9.59735e46 | −0.516302 | −0.258151 | − | 0.966105i | \(-0.583113\pi\) | ||||
−0.258151 | + | 0.966105i | \(0.583113\pi\) | |||||||
\(360\) | −1.34656e46 | −0.0688067 | ||||||||
\(361\) | 8.75566e45 | 0.0425016 | ||||||||
\(362\) | 2.04441e47 | 0.942884 | ||||||||
\(363\) | −1.69090e47 | −0.741046 | ||||||||
\(364\) | −4.92723e46 | −0.205224 | ||||||||
\(365\) | −1.68244e46 | −0.0666072 | ||||||||
\(366\) | 1.96684e47 | 0.740235 | ||||||||
\(367\) | 1.16622e47 | 0.417310 | 0.208655 | − | 0.977989i | \(-0.433091\pi\) | ||||
0.208655 | + | 0.977989i | \(0.433091\pi\) | |||||||
\(368\) | −2.54568e46 | −0.0866204 | ||||||||
\(369\) | −8.92952e46 | −0.288962 | ||||||||
\(370\) | −8.17276e46 | −0.251557 | ||||||||
\(371\) | 2.02057e47 | 0.591638 | ||||||||
\(372\) | 3.76284e46 | 0.104827 | ||||||||
\(373\) | −3.24328e47 | −0.859749 | −0.429874 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429874 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(374\) | 1.66807e46 | 0.0420814 | ||||||||
\(375\) | 2.79951e46 | 0.0672207 | ||||||||
\(376\) | −3.00445e46 | −0.0686735 | ||||||||
\(377\) | −2.52346e47 | −0.549138 | ||||||||
\(378\) | 3.37273e47 | 0.698848 | ||||||||
\(379\) | −8.85067e46 | −0.174643 | −0.0873214 | − | 0.996180i | \(-0.527831\pi\) | ||||
−0.0873214 | + | 0.996180i | \(0.527831\pi\) | |||||||
\(380\) | −1.21484e47 | −0.228309 | ||||||||
\(381\) | 2.82380e47 | 0.505501 | ||||||||
\(382\) | 8.63313e46 | 0.147230 | ||||||||
\(383\) | −1.64510e46 | −0.0267310 | −0.0133655 | − | 0.999911i | \(-0.504255\pi\) | ||||
−0.0133655 | + | 0.999911i | \(0.504255\pi\) | |||||||
\(384\) | 4.29023e46 | 0.0664283 | ||||||||
\(385\) | 3.28304e46 | 0.0484454 | ||||||||
\(386\) | −2.93131e46 | −0.0412284 | ||||||||
\(387\) | 1.20931e47 | 0.162138 | ||||||||
\(388\) | −6.02448e47 | −0.770075 | ||||||||
\(389\) | 2.33292e47 | 0.284336 | 0.142168 | − | 0.989843i | \(-0.454593\pi\) | ||||
0.142168 | + | 0.989843i | \(0.454593\pi\) | |||||||
\(390\) | 9.15957e46 | 0.106458 | ||||||||
\(391\) | 1.57345e47 | 0.174415 | ||||||||
\(392\) | −5.36362e46 | −0.0567107 | ||||||||
\(393\) | 1.22011e48 | 1.23066 | ||||||||
\(394\) | 1.07432e48 | 1.03384 | ||||||||
\(395\) | −6.62029e47 | −0.607898 | ||||||||
\(396\) | 2.93558e46 | 0.0257237 | ||||||||
\(397\) | −1.77175e48 | −1.48176 | −0.740879 | − | 0.671639i | \(-0.765591\pi\) | ||||
−0.740879 | + | 0.671639i | \(0.765591\pi\) | |||||||
\(398\) | 1.45381e48 | 1.16057 | ||||||||
\(399\) | 9.22637e47 | 0.703125 | ||||||||
\(400\) | 6.87195e46 | 0.0500000 | ||||||||
\(401\) | 9.35091e47 | 0.649656 | 0.324828 | − | 0.945773i | \(-0.394694\pi\) | ||||
0.324828 | + | 0.945773i | \(0.394694\pi\) | |||||||
\(402\) | 1.58696e48 | 1.05289 | ||||||||
\(403\) | 1.97200e47 | 0.124958 | ||||||||
\(404\) | −6.84441e47 | −0.414267 | ||||||||
\(405\) | −2.90395e47 | −0.167908 | ||||||||
\(406\) | 1.43784e48 | 0.794292 | ||||||||
\(407\) | 1.78171e47 | 0.0940458 | ||||||||
\(408\) | −2.65173e47 | −0.133757 | ||||||||
\(409\) | −2.24904e48 | −1.08422 | −0.542108 | − | 0.840309i | \(-0.682374\pi\) | ||||
−0.542108 | + | 0.840309i | \(0.682374\pi\) | |||||||
\(410\) | 4.55702e47 | 0.209981 | ||||||||
\(411\) | 2.13115e48 | 0.938727 | ||||||||
\(412\) | −9.49589e47 | −0.399887 | ||||||||
\(413\) | 1.89484e48 | 0.762953 | ||||||||
\(414\) | 2.76906e47 | 0.106617 | ||||||||
\(415\) | −6.02420e47 | −0.221825 | ||||||||
\(416\) | 2.24840e47 | 0.0791857 | ||||||||
\(417\) | 6.85987e47 | 0.231099 | ||||||||
\(418\) | 2.64842e47 | 0.0853544 | ||||||||
\(419\) | −5.89430e48 | −1.81749 | −0.908747 | − | 0.417348i | \(-0.862960\pi\) | ||||
−0.908747 | + | 0.417348i | \(0.862960\pi\) | |||||||
\(420\) | −5.21904e47 | −0.153985 | ||||||||
\(421\) | −6.89314e48 | −1.94625 | −0.973125 | − | 0.230278i | \(-0.926037\pi\) | ||||
−0.973125 | + | 0.230278i | \(0.926037\pi\) | |||||||
\(422\) | −4.09231e48 | −1.10583 | ||||||||
\(423\) | 3.26807e47 | 0.0845269 | ||||||||
\(424\) | −9.22027e47 | −0.228284 | ||||||||
\(425\) | −4.24745e47 | −0.100678 | ||||||||
\(426\) | −1.57796e46 | −0.00358112 | ||||||||
\(427\) | −5.87324e48 | −1.27633 | ||||||||
\(428\) | 1.14345e48 | 0.237962 | ||||||||
\(429\) | −1.99684e47 | −0.0397999 | ||||||||
\(430\) | −6.17149e47 | −0.117821 | ||||||||
\(431\) | −3.31632e47 | −0.0606495 | −0.0303247 | − | 0.999540i | \(-0.509654\pi\) | ||||
−0.0303247 | + | 0.999540i | \(0.509654\pi\) | |||||||
\(432\) | −1.53905e48 | −0.269651 | ||||||||
\(433\) | 7.05114e48 | 1.18368 | 0.591838 | − | 0.806057i | \(-0.298402\pi\) | ||||
0.591838 | + | 0.806057i | \(0.298402\pi\) | |||||||
\(434\) | −1.12363e48 | −0.180744 | ||||||||
\(435\) | −2.67291e48 | −0.412034 | ||||||||
\(436\) | −1.48049e48 | −0.218729 | ||||||||
\(437\) | 2.49819e48 | 0.353768 | ||||||||
\(438\) | −5.83070e47 | −0.0791498 | ||||||||
\(439\) | −4.37776e48 | −0.569716 | −0.284858 | − | 0.958570i | \(-0.591946\pi\) | ||||
−0.284858 | + | 0.958570i | \(0.591946\pi\) | |||||||
\(440\) | −1.49812e47 | −0.0186927 | ||||||||
\(441\) | 5.83425e47 | 0.0698025 | ||||||||
\(442\) | −1.38970e48 | −0.159445 | ||||||||
\(443\) | 1.23141e49 | 1.35498 | 0.677491 | − | 0.735531i | \(-0.263067\pi\) | ||||
0.677491 | + | 0.735531i | \(0.263067\pi\) | |||||||
\(444\) | −2.83237e48 | −0.298927 | ||||||||
\(445\) | −3.71301e48 | −0.375895 | ||||||||
\(446\) | 8.89990e47 | 0.0864351 | ||||||||
\(447\) | 1.22910e48 | 0.114525 | ||||||||
\(448\) | −1.28112e48 | −0.114537 | ||||||||
\(449\) | 1.51088e49 | 1.29621 | 0.648103 | − | 0.761553i | \(-0.275563\pi\) | ||||
0.648103 | + | 0.761553i | \(0.275563\pi\) | |||||||
\(450\) | −7.47493e47 | −0.0615426 | ||||||||
\(451\) | −9.93455e47 | −0.0785023 | ||||||||
\(452\) | −4.95362e48 | −0.375717 | ||||||||
\(453\) | 1.21346e49 | 0.883501 | ||||||||
\(454\) | −1.43924e49 | −1.00600 | ||||||||
\(455\) | −2.73516e48 | −0.183558 | ||||||||
\(456\) | −4.21019e48 | −0.271301 | ||||||||
\(457\) | 2.42148e49 | 1.49841 | 0.749207 | − | 0.662336i | \(-0.230435\pi\) | ||||
0.749207 | + | 0.662336i | \(0.230435\pi\) | |||||||
\(458\) | 1.34421e49 | 0.798832 | ||||||||
\(459\) | 9.51262e48 | 0.542957 | ||||||||
\(460\) | −1.41314e48 | −0.0774756 | ||||||||
\(461\) | 1.88635e49 | 0.993471 | 0.496736 | − | 0.867902i | \(-0.334532\pi\) | ||||
0.496736 | + | 0.867902i | \(0.334532\pi\) | |||||||
\(462\) | 1.13778e48 | 0.0575680 | ||||||||
\(463\) | 5.15519e48 | 0.250609 | 0.125304 | − | 0.992118i | \(-0.460009\pi\) | ||||
0.125304 | + | 0.992118i | \(0.460009\pi\) | |||||||
\(464\) | −6.56118e48 | −0.306478 | ||||||||
\(465\) | 2.08879e48 | 0.0937597 | ||||||||
\(466\) | 2.60967e49 | 1.12576 | ||||||||
\(467\) | 1.96969e49 | 0.816649 | 0.408324 | − | 0.912837i | \(-0.366113\pi\) | ||||
0.408324 | + | 0.912837i | \(0.366113\pi\) | |||||||
\(468\) | −2.44569e48 | −0.0974658 | ||||||||
\(469\) | −4.73885e49 | −1.81541 | ||||||||
\(470\) | −1.66780e48 | −0.0614235 | ||||||||
\(471\) | 1.82669e49 | 0.646813 | ||||||||
\(472\) | −8.64657e48 | −0.294386 | ||||||||
\(473\) | 1.34542e48 | 0.0440480 | ||||||||
\(474\) | −2.29434e49 | −0.722369 | ||||||||
\(475\) | −6.74373e48 | −0.204206 | ||||||||
\(476\) | 7.91840e48 | 0.230626 | ||||||||
\(477\) | 1.00293e49 | 0.280983 | ||||||||
\(478\) | −1.10139e49 | −0.296842 | ||||||||
\(479\) | −6.22680e49 | −1.61458 | −0.807288 | − | 0.590158i | \(-0.799065\pi\) | ||||
−0.807288 | + | 0.590158i | \(0.799065\pi\) | |||||||
\(480\) | 2.38156e48 | 0.0594153 | ||||||||
\(481\) | −1.48437e49 | −0.356335 | ||||||||
\(482\) | 2.41327e49 | 0.557488 | ||||||||
\(483\) | 1.07324e49 | 0.238602 | ||||||||
\(484\) | −2.30407e49 | −0.493012 | ||||||||
\(485\) | −3.34426e49 | −0.688776 | ||||||||
\(486\) | 2.84056e49 | 0.563162 | ||||||||
\(487\) | 4.56184e49 | 0.870671 | 0.435335 | − | 0.900268i | \(-0.356630\pi\) | ||||
0.435335 | + | 0.900268i | \(0.356630\pi\) | |||||||
\(488\) | 2.68008e49 | 0.492472 | ||||||||
\(489\) | −5.35390e49 | −0.947233 | ||||||||
\(490\) | −2.97740e48 | −0.0507236 | ||||||||
\(491\) | 7.50460e49 | 1.23117 | 0.615587 | − | 0.788069i | \(-0.288919\pi\) | ||||
0.615587 | + | 0.788069i | \(0.288919\pi\) | |||||||
\(492\) | 1.57929e49 | 0.249522 | ||||||||
\(493\) | 4.05537e49 | 0.617110 | ||||||||
\(494\) | −2.20645e49 | −0.323404 | ||||||||
\(495\) | 1.62957e48 | 0.0230080 | ||||||||
\(496\) | 5.12736e48 | 0.0697402 | ||||||||
\(497\) | 4.71199e47 | 0.00617463 | ||||||||
\(498\) | −2.08776e49 | −0.263596 | ||||||||
\(499\) | −1.22644e50 | −1.49206 | −0.746030 | − | 0.665912i | \(-0.768043\pi\) | ||||
−0.746030 | + | 0.665912i | \(0.768043\pi\) | |||||||
\(500\) | 3.81470e48 | 0.0447214 | ||||||||
\(501\) | −1.59738e49 | −0.180472 | ||||||||
\(502\) | −2.31045e49 | −0.251581 | ||||||||
\(503\) | −6.93196e48 | −0.0727526 | −0.0363763 | − | 0.999338i | \(-0.511581\pi\) | ||||
−0.0363763 | + | 0.999338i | \(0.511581\pi\) | |||||||
\(504\) | 1.39353e49 | 0.140978 | ||||||||
\(505\) | −3.79941e49 | −0.370532 | ||||||||
\(506\) | 3.08072e48 | 0.0289646 | ||||||||
\(507\) | −6.62737e49 | −0.600750 | ||||||||
\(508\) | 3.84780e49 | 0.336305 | ||||||||
\(509\) | −1.92494e50 | −1.62233 | −0.811165 | − | 0.584817i | \(-0.801166\pi\) | ||||
−0.811165 | + | 0.584817i | \(0.801166\pi\) | |||||||
\(510\) | −1.47201e49 | −0.119636 | ||||||||
\(511\) | 1.74112e49 | 0.136472 | ||||||||
\(512\) | 5.84601e48 | 0.0441942 | ||||||||
\(513\) | 1.51033e50 | 1.10129 | ||||||||
\(514\) | −3.83075e49 | −0.269442 | ||||||||
\(515\) | −5.27128e49 | −0.357670 | ||||||||
\(516\) | −2.13881e49 | −0.140008 | ||||||||
\(517\) | 3.63590e48 | 0.0229634 | ||||||||
\(518\) | 8.45781e49 | 0.515416 | ||||||||
\(519\) | −1.86197e50 | −1.09491 | ||||||||
\(520\) | 1.24811e49 | 0.0708258 | ||||||||
\(521\) | −7.74303e49 | −0.424046 | −0.212023 | − | 0.977265i | \(-0.568005\pi\) | ||||
−0.212023 | + | 0.977265i | \(0.568005\pi\) | |||||||
\(522\) | 7.13690e49 | 0.377229 | ||||||||
\(523\) | 1.36453e50 | 0.696147 | 0.348074 | − | 0.937467i | \(-0.386836\pi\) | ||||
0.348074 | + | 0.937467i | \(0.386836\pi\) | |||||||
\(524\) | 1.66257e50 | 0.818748 | ||||||||
\(525\) | −2.89715e49 | −0.137729 | ||||||||
\(526\) | −7.17458e49 | −0.329276 | ||||||||
\(527\) | −3.16915e49 | −0.140426 | ||||||||
\(528\) | −5.19192e48 | −0.0222127 | ||||||||
\(529\) | −2.13004e50 | −0.879951 | ||||||||
\(530\) | −5.11828e49 | −0.204183 | ||||||||
\(531\) | 9.40527e49 | 0.362345 | ||||||||
\(532\) | 1.25721e50 | 0.467783 | ||||||||
\(533\) | 8.27666e49 | 0.297442 | ||||||||
\(534\) | −1.28679e50 | −0.446678 | ||||||||
\(535\) | 6.34742e49 | 0.212840 | ||||||||
\(536\) | 2.16244e50 | 0.700479 | ||||||||
\(537\) | 2.43473e50 | 0.761949 | ||||||||
\(538\) | 3.47143e50 | 1.04963 | ||||||||
\(539\) | 6.49090e48 | 0.0189632 | ||||||||
\(540\) | −8.54342e49 | −0.241183 | ||||||||
\(541\) | −3.69295e49 | −0.100745 | −0.0503726 | − | 0.998730i | \(-0.516041\pi\) | ||||
−0.0503726 | + | 0.998730i | \(0.516041\pi\) | |||||||
\(542\) | 1.36630e50 | 0.360213 | ||||||||
\(543\) | 3.93304e50 | 1.00215 | ||||||||
\(544\) | −3.61333e49 | −0.0889873 | ||||||||
\(545\) | −8.21840e49 | −0.195637 | ||||||||
\(546\) | −9.47904e49 | −0.218123 | ||||||||
\(547\) | −3.43870e50 | −0.764942 | −0.382471 | − | 0.923968i | \(-0.624927\pi\) | ||||
−0.382471 | + | 0.923968i | \(0.624927\pi\) | |||||||
\(548\) | 2.90397e50 | 0.624527 | ||||||||
\(549\) | −2.91525e50 | −0.606160 | ||||||||
\(550\) | −8.31624e48 | −0.0167193 | ||||||||
\(551\) | 6.43876e50 | 1.25169 | ||||||||
\(552\) | −4.89741e49 | −0.0920647 | ||||||||
\(553\) | 6.85120e50 | 1.24552 | ||||||||
\(554\) | −4.28445e50 | −0.753294 | ||||||||
\(555\) | −1.57228e50 | −0.267368 | ||||||||
\(556\) | 9.34747e49 | 0.153748 | ||||||||
\(557\) | −1.65111e50 | −0.262697 | −0.131348 | − | 0.991336i | \(-0.541931\pi\) | ||||
−0.131348 | + | 0.991336i | \(0.541931\pi\) | |||||||
\(558\) | −5.57726e49 | −0.0858398 | ||||||||
\(559\) | −1.12089e50 | −0.166896 | ||||||||
\(560\) | −7.11163e49 | −0.102445 | ||||||||
\(561\) | 3.20905e49 | 0.0447264 | ||||||||
\(562\) | 4.75265e49 | 0.0640935 | ||||||||
\(563\) | 8.28221e50 | 1.08079 | 0.540395 | − | 0.841412i | \(-0.318275\pi\) | ||||
0.540395 | + | 0.841412i | \(0.318275\pi\) | |||||||
\(564\) | −5.77998e49 | −0.0729899 | ||||||||
\(565\) | −2.74981e50 | −0.336052 | ||||||||
\(566\) | −9.51585e50 | −1.12550 | ||||||||
\(567\) | 3.00524e50 | 0.344027 | ||||||||
\(568\) | −2.15018e48 | −0.00238249 | ||||||||
\(569\) | 5.31805e50 | 0.570394 | 0.285197 | − | 0.958469i | \(-0.407941\pi\) | ||||
0.285197 | + | 0.958469i | \(0.407941\pi\) | |||||||
\(570\) | −2.33712e50 | −0.242659 | ||||||||
\(571\) | 7.10776e50 | 0.714438 | 0.357219 | − | 0.934021i | \(-0.383725\pi\) | ||||
0.357219 | + | 0.934021i | \(0.383725\pi\) | |||||||
\(572\) | −2.72095e49 | −0.0264785 | ||||||||
\(573\) | 1.66085e50 | 0.156484 | ||||||||
\(574\) | −4.71596e50 | −0.430230 | ||||||||
\(575\) | −7.84450e49 | −0.0692963 | ||||||||
\(576\) | −6.35897e49 | −0.0543965 | ||||||||
\(577\) | −1.53160e51 | −1.26880 | −0.634399 | − | 0.773006i | \(-0.718752\pi\) | ||||
−0.634399 | + | 0.773006i | \(0.718752\pi\) | |||||||
\(578\) | −6.58018e50 | −0.527926 | ||||||||
\(579\) | −5.63928e49 | −0.0438198 | ||||||||
\(580\) | −3.64219e50 | −0.274122 | ||||||||
\(581\) | 6.23432e50 | 0.454496 | ||||||||
\(582\) | −1.15899e51 | −0.818476 | ||||||||
\(583\) | 1.11581e50 | 0.0763348 | ||||||||
\(584\) | −7.94509e49 | −0.0526576 | ||||||||
\(585\) | −1.35763e50 | −0.0871761 | ||||||||
\(586\) | 4.97584e50 | 0.309571 | ||||||||
\(587\) | −3.05746e51 | −1.84313 | −0.921565 | − | 0.388223i | \(-0.873089\pi\) | ||||
−0.921565 | + | 0.388223i | \(0.873089\pi\) | |||||||
\(588\) | −1.03186e50 | −0.0602752 | ||||||||
\(589\) | −5.03169e50 | −0.284827 | ||||||||
\(590\) | −4.79981e50 | −0.263307 | ||||||||
\(591\) | 2.06679e51 | 1.09882 | ||||||||
\(592\) | −3.85948e50 | −0.198874 | ||||||||
\(593\) | −3.18854e51 | −1.59250 | −0.796252 | − | 0.604966i | \(-0.793187\pi\) | ||||
−0.796252 | + | 0.604966i | \(0.793187\pi\) | |||||||
\(594\) | 1.86251e50 | 0.0901674 | ||||||||
\(595\) | 4.39560e50 | 0.206278 | ||||||||
\(596\) | 1.67482e50 | 0.0761924 | ||||||||
\(597\) | 2.79685e51 | 1.23351 | ||||||||
\(598\) | −2.56660e50 | −0.109745 | ||||||||
\(599\) | −2.67703e51 | −1.10983 | −0.554916 | − | 0.831906i | \(-0.687250\pi\) | ||||
−0.554916 | + | 0.831906i | \(0.687250\pi\) | |||||||
\(600\) | 1.32203e50 | 0.0531427 | ||||||||
\(601\) | −1.40525e51 | −0.547743 | −0.273872 | − | 0.961766i | \(-0.588304\pi\) | ||||
−0.273872 | + | 0.961766i | \(0.588304\pi\) | |||||||
\(602\) | 6.38675e50 | 0.241404 | ||||||||
\(603\) | −2.35218e51 | −0.862186 | ||||||||
\(604\) | 1.65349e51 | 0.587786 | ||||||||
\(605\) | −1.27902e51 | −0.440963 | ||||||||
\(606\) | −1.31673e51 | −0.440305 | ||||||||
\(607\) | 2.84184e51 | 0.921741 | 0.460870 | − | 0.887467i | \(-0.347537\pi\) | ||||
0.460870 | + | 0.887467i | \(0.347537\pi\) | |||||||
\(608\) | −5.73693e50 | −0.180494 | ||||||||
\(609\) | 2.76613e51 | 0.844216 | ||||||||
\(610\) | 1.48774e51 | 0.440480 | ||||||||
\(611\) | −3.02913e50 | −0.0870074 | ||||||||
\(612\) | 3.93039e50 | 0.109530 | ||||||||
\(613\) | 5.74303e51 | 1.55282 | 0.776412 | − | 0.630226i | \(-0.217038\pi\) | ||||
0.776412 | + | 0.630226i | \(0.217038\pi\) | |||||||
\(614\) | −3.72561e50 | −0.0977424 | ||||||||
\(615\) | 8.76683e50 | 0.223179 | ||||||||
\(616\) | 1.55037e50 | 0.0382995 | ||||||||
\(617\) | 5.29231e51 | 1.26873 | 0.634366 | − | 0.773033i | \(-0.281261\pi\) | ||||
0.634366 | + | 0.773033i | \(0.281261\pi\) | |||||||
\(618\) | −1.82683e51 | −0.425021 | ||||||||
\(619\) | 1.88485e50 | 0.0425599 | 0.0212799 | − | 0.999774i | \(-0.493226\pi\) | ||||
0.0212799 | + | 0.999774i | \(0.493226\pi\) | |||||||
\(620\) | 2.84626e50 | 0.0623775 | ||||||||
\(621\) | 1.75686e51 | 0.373716 | ||||||||
\(622\) | 3.88369e51 | 0.801903 | ||||||||
\(623\) | 3.84252e51 | 0.770171 | ||||||||
\(624\) | 4.32549e50 | 0.0841628 | ||||||||
\(625\) | 2.11758e50 | 0.0400000 | ||||||||
\(626\) | 4.41697e51 | 0.810026 | ||||||||
\(627\) | 5.09505e50 | 0.0907191 | ||||||||
\(628\) | 2.48911e51 | 0.430319 | ||||||||
\(629\) | 2.38549e51 | 0.400442 | ||||||||
\(630\) | 7.73564e50 | 0.126095 | ||||||||
\(631\) | −5.48789e51 | −0.868685 | −0.434343 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434343 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(632\) | −3.12635e51 | −0.480586 | ||||||||
\(633\) | −7.87281e51 | −1.17533 | ||||||||
\(634\) | 2.60103e51 | 0.377133 | ||||||||
\(635\) | 2.13596e51 | 0.300800 | ||||||||
\(636\) | −1.77380e51 | −0.242632 | ||||||||
\(637\) | −5.40769e50 | −0.0718509 | ||||||||
\(638\) | 7.94016e50 | 0.102482 | ||||||||
\(639\) | 2.33885e49 | 0.00293249 | ||||||||
\(640\) | 3.24519e50 | 0.0395285 | ||||||||
\(641\) | −1.26934e52 | −1.50213 | −0.751063 | − | 0.660231i | \(-0.770458\pi\) | ||||
−0.751063 | + | 0.660231i | \(0.770458\pi\) | |||||||
\(642\) | 2.19978e51 | 0.252918 | ||||||||
\(643\) | −2.67003e50 | −0.0298273 | −0.0149136 | − | 0.999889i | \(-0.504747\pi\) | ||||
−0.0149136 | + | 0.999889i | \(0.504747\pi\) | |||||||
\(644\) | 1.46243e51 | 0.158740 | ||||||||
\(645\) | −1.18728e51 | −0.125227 | ||||||||
\(646\) | 3.54591e51 | 0.363435 | ||||||||
\(647\) | −7.38492e51 | −0.735557 | −0.367778 | − | 0.929913i | \(-0.619882\pi\) | ||||
−0.367778 | + | 0.929913i | \(0.619882\pi\) | |||||||
\(648\) | −1.37135e51 | −0.132743 | ||||||||
\(649\) | 1.04638e51 | 0.0984384 | ||||||||
\(650\) | 6.92841e50 | 0.0633486 | ||||||||
\(651\) | −2.16165e51 | −0.192104 | ||||||||
\(652\) | −7.29540e51 | −0.630186 | ||||||||
\(653\) | −1.43531e52 | −1.20518 | −0.602592 | − | 0.798050i | \(-0.705865\pi\) | ||||
−0.602592 | + | 0.798050i | \(0.705865\pi\) | |||||||
\(654\) | −2.84819e51 | −0.232477 | ||||||||
\(655\) | 9.22909e51 | 0.732310 | ||||||||
\(656\) | 2.15199e51 | 0.166004 | ||||||||
\(657\) | 8.64224e50 | 0.0648137 | ||||||||
\(658\) | 1.72597e51 | 0.125851 | ||||||||
\(659\) | 1.21039e52 | 0.858112 | 0.429056 | − | 0.903278i | \(-0.358846\pi\) | ||||
0.429056 | + | 0.903278i | \(0.358846\pi\) | |||||||
\(660\) | −2.88210e50 | −0.0198676 | ||||||||
\(661\) | −1.90863e52 | −1.27937 | −0.639683 | − | 0.768638i | \(-0.720935\pi\) | ||||
−0.639683 | + | 0.768638i | \(0.720935\pi\) | |||||||
\(662\) | 1.13206e52 | 0.737897 | ||||||||
\(663\) | −2.67352e51 | −0.169466 | ||||||||
\(664\) | −2.84485e51 | −0.175368 | ||||||||
\(665\) | 6.97894e51 | 0.418397 | ||||||||
\(666\) | 4.19813e51 | 0.244784 | ||||||||
\(667\) | 7.48975e51 | 0.424756 | ||||||||
\(668\) | −2.17664e51 | −0.120066 | ||||||||
\(669\) | 1.71217e51 | 0.0918678 | ||||||||
\(670\) | 1.20039e52 | 0.626527 | ||||||||
\(671\) | −3.24336e51 | −0.164675 | ||||||||
\(672\) | −2.46462e51 | −0.121736 | ||||||||
\(673\) | −1.67548e52 | −0.805120 | −0.402560 | − | 0.915394i | \(-0.631879\pi\) | ||||
−0.402560 | + | 0.915394i | \(0.631879\pi\) | |||||||
\(674\) | 1.48299e51 | 0.0693316 | ||||||||
\(675\) | −4.74255e51 | −0.215721 | ||||||||
\(676\) | −9.03067e51 | −0.399674 | ||||||||
\(677\) | −2.49877e52 | −1.07606 | −0.538029 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538029 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(678\) | −9.52980e51 | −0.399332 | ||||||||
\(679\) | 3.46090e52 | 1.41123 | ||||||||
\(680\) | −2.00580e51 | −0.0795927 | ||||||||
\(681\) | −2.76882e52 | −1.06923 | ||||||||
\(682\) | −6.20499e50 | −0.0233201 | ||||||||
\(683\) | −4.73250e52 | −1.73104 | −0.865520 | − | 0.500874i | \(-0.833012\pi\) | ||||
−0.865520 | + | 0.500874i | \(0.833012\pi\) | |||||||
\(684\) | 6.24032e51 | 0.222162 | ||||||||
\(685\) | 1.61202e52 | 0.558594 | ||||||||
\(686\) | 2.22908e52 | 0.751847 | ||||||||
\(687\) | 2.58600e52 | 0.849041 | ||||||||
\(688\) | −2.91441e51 | −0.0931459 | ||||||||
\(689\) | −9.29603e51 | −0.289229 | ||||||||
\(690\) | −2.71861e51 | −0.0823452 | ||||||||
\(691\) | 1.73179e52 | 0.510683 | 0.255341 | − | 0.966851i | \(-0.417812\pi\) | ||||
0.255341 | + | 0.966851i | \(0.417812\pi\) | |||||||
\(692\) | −2.53718e52 | −0.728431 | ||||||||
\(693\) | −1.68641e51 | −0.0471410 | ||||||||
\(694\) | 1.52296e52 | 0.414514 | ||||||||
\(695\) | 5.18889e51 | 0.137517 | ||||||||
\(696\) | −1.26225e52 | −0.325741 | ||||||||
\(697\) | −1.33012e52 | −0.334259 | ||||||||
\(698\) | −3.52382e52 | −0.862359 | ||||||||
\(699\) | 5.02051e52 | 1.19652 | ||||||||
\(700\) | −3.94775e51 | −0.0916296 | ||||||||
\(701\) | 8.62925e51 | 0.195070 | 0.0975348 | − | 0.995232i | \(-0.468904\pi\) | ||||
0.0975348 | + | 0.995232i | \(0.468904\pi\) | |||||||
\(702\) | −1.55169e52 | −0.341640 | ||||||||
\(703\) | 3.78747e52 | 0.812223 | ||||||||
\(704\) | −7.07468e50 | −0.0147779 | ||||||||
\(705\) | −3.20853e51 | −0.0652841 | ||||||||
\(706\) | −3.27318e52 | −0.648759 | ||||||||
\(707\) | 3.93193e52 | 0.759183 | ||||||||
\(708\) | −1.66343e52 | −0.312889 | ||||||||
\(709\) | 2.82932e52 | 0.518473 | 0.259236 | − | 0.965814i | \(-0.416529\pi\) | ||||
0.259236 | + | 0.965814i | \(0.416529\pi\) | |||||||
\(710\) | −1.19359e50 | −0.00213096 | ||||||||
\(711\) | 3.40067e52 | 0.591530 | ||||||||
\(712\) | −1.75342e52 | −0.297171 | ||||||||
\(713\) | −5.85301e51 | −0.0966547 | ||||||||
\(714\) | 1.52335e52 | 0.245122 | ||||||||
\(715\) | −1.51043e51 | −0.0236831 | ||||||||
\(716\) | 3.31763e52 | 0.506918 | ||||||||
\(717\) | −2.11886e52 | −0.315500 | ||||||||
\(718\) | −2.51589e52 | −0.365081 | ||||||||
\(719\) | 1.27280e53 | 1.80001 | 0.900007 | − | 0.435875i | \(-0.143561\pi\) | ||||
0.900007 | + | 0.435875i | \(0.143561\pi\) | |||||||
\(720\) | −3.52994e51 | −0.0486537 | ||||||||
\(721\) | 5.45513e52 | 0.732829 | ||||||||
\(722\) | 2.29524e51 | 0.0300532 | ||||||||
\(723\) | 4.64266e52 | 0.592528 | ||||||||
\(724\) | 5.35929e52 | 0.666720 | ||||||||
\(725\) | −2.02182e52 | −0.245183 | ||||||||
\(726\) | −4.43259e52 | −0.523999 | ||||||||
\(727\) | −5.42190e52 | −0.624834 | −0.312417 | − | 0.949945i | \(-0.601139\pi\) | ||||
−0.312417 | + | 0.949945i | \(0.601139\pi\) | |||||||
\(728\) | −1.29164e52 | −0.145115 | ||||||||
\(729\) | 8.89250e52 | 0.974012 | ||||||||
\(730\) | −4.41041e51 | −0.0470984 | ||||||||
\(731\) | 1.80135e52 | 0.187554 | ||||||||
\(732\) | 5.15596e52 | 0.523425 | ||||||||
\(733\) | −4.67036e52 | −0.462304 | −0.231152 | − | 0.972918i | \(-0.574249\pi\) | ||||
−0.231152 | + | 0.972918i | \(0.574249\pi\) | |||||||
\(734\) | 3.05718e52 | 0.295083 | ||||||||
\(735\) | −5.72795e51 | −0.0539118 | ||||||||
\(736\) | −6.67336e51 | −0.0612498 | ||||||||
\(737\) | −2.61692e52 | −0.234230 | ||||||||
\(738\) | −2.34082e52 | −0.204327 | ||||||||
\(739\) | −3.22372e52 | −0.274432 | −0.137216 | − | 0.990541i | \(-0.543815\pi\) | ||||
−0.137216 | + | 0.990541i | \(0.543815\pi\) | |||||||
\(740\) | −2.14244e52 | −0.177878 | ||||||||
\(741\) | −4.24478e52 | −0.343731 | ||||||||
\(742\) | 5.29679e52 | 0.418351 | ||||||||
\(743\) | −5.43932e52 | −0.419036 | −0.209518 | − | 0.977805i | \(-0.567190\pi\) | ||||
−0.209518 | + | 0.977805i | \(0.567190\pi\) | |||||||
\(744\) | 9.86405e51 | 0.0741235 | ||||||||
\(745\) | 9.29710e51 | 0.0681485 | ||||||||
\(746\) | −8.50207e52 | −0.607934 | ||||||||
\(747\) | 3.09447e52 | 0.215852 | ||||||||
\(748\) | 4.37275e51 | 0.0297561 | ||||||||
\(749\) | −6.56881e52 | −0.436087 | ||||||||
\(750\) | 7.33874e51 | 0.0475322 | ||||||||
\(751\) | −1.15095e53 | −0.727304 | −0.363652 | − | 0.931535i | \(-0.618470\pi\) | ||||
−0.363652 | + | 0.931535i | \(0.618470\pi\) | |||||||
\(752\) | −7.87598e51 | −0.0485595 | ||||||||
\(753\) | −4.44486e52 | −0.267394 | ||||||||
\(754\) | −6.61510e52 | −0.388299 | ||||||||
\(755\) | 9.17873e52 | 0.525731 | ||||||||
\(756\) | 8.84140e52 | 0.494160 | ||||||||
\(757\) | −3.51043e53 | −1.91464 | −0.957318 | − | 0.289038i | \(-0.906665\pi\) | ||||
−0.957318 | + | 0.289038i | \(0.906665\pi\) | |||||||
\(758\) | −2.32015e52 | −0.123491 | ||||||||
\(759\) | 5.92671e51 | 0.0307851 | ||||||||
\(760\) | −3.18464e52 | −0.161439 | ||||||||
\(761\) | −1.73091e53 | −0.856363 | −0.428182 | − | 0.903693i | \(-0.640846\pi\) | ||||
−0.428182 | + | 0.903693i | \(0.640846\pi\) | |||||||
\(762\) | 7.40242e52 | 0.357443 | ||||||||
\(763\) | 8.50504e52 | 0.400841 | ||||||||
\(764\) | 2.26312e52 | 0.104107 | ||||||||
\(765\) | 2.18180e52 | 0.0979668 | ||||||||
\(766\) | −4.31254e51 | −0.0189017 | ||||||||
\(767\) | −8.71762e52 | −0.372978 | ||||||||
\(768\) | 1.12466e52 | 0.0469719 | ||||||||
\(769\) | −3.14722e53 | −1.28319 | −0.641594 | − | 0.767045i | \(-0.721727\pi\) | ||||
−0.641594 | + | 0.767045i | \(0.721727\pi\) | |||||||
\(770\) | 8.60630e51 | 0.0342561 | ||||||||
\(771\) | −7.36961e52 | −0.286377 | ||||||||
\(772\) | −7.68426e51 | −0.0291529 | ||||||||
\(773\) | −1.31709e53 | −0.487861 | −0.243931 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243931 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(774\) | 3.17013e52 | 0.114649 | ||||||||
\(775\) | 1.57999e52 | 0.0557921 | ||||||||
\(776\) | −1.57928e53 | −0.544525 | ||||||||
\(777\) | 1.62712e53 | 0.547811 | ||||||||
\(778\) | 6.11560e52 | 0.201056 | ||||||||
\(779\) | −2.11184e53 | −0.677982 | ||||||||
\(780\) | 2.40113e52 | 0.0752775 | ||||||||
\(781\) | 2.60209e50 | 0.000796669 0 | ||||||||
\(782\) | 4.12471e52 | 0.123330 | ||||||||
\(783\) | 4.52808e53 | 1.32227 | ||||||||
\(784\) | −1.40604e52 | −0.0401006 | ||||||||
\(785\) | 1.38173e53 | 0.384889 | ||||||||
\(786\) | 3.19846e53 | 0.870208 | ||||||||
\(787\) | 2.46211e53 | 0.654296 | 0.327148 | − | 0.944973i | \(-0.393912\pi\) | ||||
0.327148 | + | 0.944973i | \(0.393912\pi\) | |||||||
\(788\) | 2.81628e53 | 0.731038 | ||||||||
\(789\) | −1.38025e53 | −0.349972 | ||||||||
\(790\) | −1.73547e53 | −0.429849 | ||||||||
\(791\) | 2.84572e53 | 0.688536 | ||||||||
\(792\) | 7.69545e51 | 0.0181894 | ||||||||
\(793\) | 2.70210e53 | 0.623948 | ||||||||
\(794\) | −4.64453e53 | −1.04776 | ||||||||
\(795\) | −9.84658e52 | −0.217017 | ||||||||
\(796\) | 3.81107e53 | 0.820646 | ||||||||
\(797\) | −6.55944e53 | −1.38003 | −0.690013 | − | 0.723797i | \(-0.742395\pi\) | ||||
−0.690013 | + | 0.723797i | \(0.742395\pi\) | |||||||
\(798\) | 2.41864e53 | 0.497184 | ||||||||
\(799\) | 4.86803e52 | 0.0977772 | ||||||||
\(800\) | 1.80144e52 | 0.0353553 | ||||||||
\(801\) | 1.90728e53 | 0.365773 | ||||||||
\(802\) | 2.45129e53 | 0.459376 | ||||||||
\(803\) | 9.61493e51 | 0.0176079 | ||||||||
\(804\) | 4.16011e53 | 0.744506 | ||||||||
\(805\) | 8.11810e52 | 0.141981 | ||||||||
\(806\) | 5.16949e52 | 0.0883588 | ||||||||
\(807\) | 6.67837e53 | 1.11560 | ||||||||
\(808\) | −1.79422e53 | −0.292931 | ||||||||
\(809\) | −1.13014e54 | −1.80338 | −0.901688 | − | 0.432387i | \(-0.857671\pi\) | ||||
−0.901688 | + | 0.432387i | \(0.857671\pi\) | |||||||
\(810\) | −7.61254e52 | −0.118729 | ||||||||
\(811\) | 4.98428e53 | 0.759831 | 0.379915 | − | 0.925021i | \(-0.375953\pi\) | ||||
0.379915 | + | 0.925021i | \(0.375953\pi\) | |||||||
\(812\) | 3.76922e53 | 0.561649 | ||||||||
\(813\) | 2.62850e53 | 0.382853 | ||||||||
\(814\) | 4.67063e52 | 0.0665004 | ||||||||
\(815\) | −4.04976e53 | −0.563655 | ||||||||
\(816\) | −6.95135e52 | −0.0945805 | ||||||||
\(817\) | 2.86003e53 | 0.380419 | ||||||||
\(818\) | −5.89572e53 | −0.766656 | ||||||||
\(819\) | 1.40498e53 | 0.178615 | ||||||||
\(820\) | 1.19460e53 | 0.148479 | ||||||||
\(821\) | −6.32222e53 | −0.768283 | −0.384142 | − | 0.923274i | \(-0.625503\pi\) | ||||
−0.384142 | + | 0.923274i | \(0.625503\pi\) | |||||||
\(822\) | 5.58667e53 | 0.663780 | ||||||||
\(823\) | 1.53088e54 | 1.77846 | 0.889228 | − | 0.457465i | \(-0.151243\pi\) | ||||
0.889228 | + | 0.457465i | \(0.151243\pi\) | |||||||
\(824\) | −2.48929e53 | −0.282763 | ||||||||
\(825\) | −1.59988e52 | −0.0177701 | ||||||||
\(826\) | 4.96722e53 | 0.539489 | ||||||||
\(827\) | 1.35864e54 | 1.44295 | 0.721477 | − | 0.692439i | \(-0.243464\pi\) | ||||
0.721477 | + | 0.692439i | \(0.243464\pi\) | |||||||
\(828\) | 7.25892e52 | 0.0753895 | ||||||||
\(829\) | −5.63827e53 | −0.572648 | −0.286324 | − | 0.958133i | \(-0.592433\pi\) | ||||
−0.286324 | + | 0.958133i | \(0.592433\pi\) | |||||||
\(830\) | −1.57921e53 | −0.156854 | ||||||||
\(831\) | −8.24245e53 | −0.800640 | ||||||||
\(832\) | 5.89404e52 | 0.0559927 | ||||||||
\(833\) | 8.69053e52 | 0.0807446 | ||||||||
\(834\) | 1.79827e53 | 0.163412 | ||||||||
\(835\) | −1.20828e53 | −0.107391 | ||||||||
\(836\) | 6.94268e52 | 0.0603546 | ||||||||
\(837\) | −3.53856e53 | −0.300888 | ||||||||
\(838\) | −1.54516e54 | −1.28516 | ||||||||
\(839\) | −2.01357e54 | −1.63821 | −0.819106 | − | 0.573642i | \(-0.805530\pi\) | ||||
−0.819106 | + | 0.573642i | \(0.805530\pi\) | |||||||
\(840\) | −1.36814e53 | −0.108884 | ||||||||
\(841\) | 6.45914e53 | 0.502862 | ||||||||
\(842\) | −1.80700e54 | −1.37621 | ||||||||
\(843\) | 9.14319e52 | 0.0681220 | ||||||||
\(844\) | −1.07277e54 | −0.781939 | ||||||||
\(845\) | −5.01303e53 | −0.357479 | ||||||||
\(846\) | 8.56706e52 | 0.0597696 | ||||||||
\(847\) | 1.32363e54 | 0.903489 | ||||||||
\(848\) | −2.41704e53 | −0.161421 | ||||||||
\(849\) | −1.83067e54 | −1.19624 | ||||||||
\(850\) | −1.11344e53 | −0.0711899 | ||||||||
\(851\) | 4.40569e53 | 0.275624 | ||||||||
\(852\) | −4.13653e51 | −0.00253223 | ||||||||
\(853\) | −5.77259e53 | −0.345791 | −0.172895 | − | 0.984940i | \(-0.555312\pi\) | ||||
−0.172895 | + | 0.984940i | \(0.555312\pi\) | |||||||
\(854\) | −1.53963e54 | −0.902500 | ||||||||
\(855\) | 3.46407e53 | 0.198707 | ||||||||
\(856\) | 2.99748e53 | 0.168264 | ||||||||
\(857\) | −1.17381e54 | −0.644842 | −0.322421 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322421 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(858\) | −5.23458e52 | −0.0281428 | ||||||||
\(859\) | 3.05143e54 | 1.60557 | 0.802786 | − | 0.596267i | \(-0.203350\pi\) | ||||
0.802786 | + | 0.596267i | \(0.203350\pi\) | |||||||
\(860\) | −1.61782e53 | −0.0833123 | ||||||||
\(861\) | −9.07261e53 | −0.457271 | ||||||||
\(862\) | −8.69353e52 | −0.0428856 | ||||||||
\(863\) | 3.37124e54 | 1.62776 | 0.813879 | − | 0.581034i | \(-0.197352\pi\) | ||||
0.813879 | + | 0.581034i | \(0.197352\pi\) | |||||||
\(864\) | −4.03451e53 | −0.190672 | ||||||||
\(865\) | −1.40842e54 | −0.651528 | ||||||||
\(866\) | 1.84841e54 | 0.836986 | ||||||||
\(867\) | −1.26590e54 | −0.561108 | ||||||||
\(868\) | −2.94553e53 | −0.127805 | ||||||||
\(869\) | 3.78342e53 | 0.160701 | ||||||||
\(870\) | −7.00687e53 | −0.291352 | ||||||||
\(871\) | 2.18021e54 | 0.887487 | ||||||||
\(872\) | −3.88103e53 | −0.154665 | ||||||||
\(873\) | 1.71786e54 | 0.670229 | ||||||||
\(874\) | 6.54885e53 | 0.250152 | ||||||||
\(875\) | −2.19144e53 | −0.0819560 | ||||||||
\(876\) | −1.52848e53 | −0.0559673 | ||||||||
\(877\) | 4.59456e52 | 0.0164722 | 0.00823610 | − | 0.999966i | \(-0.497378\pi\) | ||||
0.00823610 | + | 0.999966i | \(0.497378\pi\) | |||||||
\(878\) | −1.14760e54 | −0.402850 | ||||||||
\(879\) | 9.57256e53 | 0.329029 | ||||||||
\(880\) | −3.92723e52 | −0.0132177 | ||||||||
\(881\) | −4.37096e54 | −1.44053 | −0.720266 | − | 0.693698i | \(-0.755980\pi\) | ||||
−0.720266 | + | 0.693698i | \(0.755980\pi\) | |||||||
\(882\) | 1.52941e53 | 0.0493578 | ||||||||
\(883\) | 5.60045e54 | 1.76991 | 0.884953 | − | 0.465680i | \(-0.154190\pi\) | ||||
0.884953 | + | 0.465680i | \(0.154190\pi\) | |||||||
\(884\) | −3.64302e53 | −0.112744 | ||||||||
\(885\) | −9.23391e53 | −0.279856 | ||||||||
\(886\) | 3.22806e54 | 0.958116 | ||||||||
\(887\) | −3.86725e54 | −1.12413 | −0.562064 | − | 0.827094i | \(-0.689992\pi\) | ||||
−0.562064 | + | 0.827094i | \(0.689992\pi\) | |||||||
\(888\) | −7.42489e53 | −0.211373 | ||||||||
\(889\) | −2.21045e54 | −0.616310 | ||||||||
\(890\) | −9.73344e53 | −0.265798 | ||||||||
\(891\) | 1.65957e53 | 0.0443873 | ||||||||
\(892\) | 2.33306e53 | 0.0611189 | ||||||||
\(893\) | 7.72903e53 | 0.198323 | ||||||||
\(894\) | 3.22202e53 | 0.0809813 | ||||||||
\(895\) | 1.84166e54 | 0.453401 | ||||||||
\(896\) | −3.35837e53 | −0.0809899 | ||||||||
\(897\) | −4.93765e53 | −0.116643 | ||||||||
\(898\) | 3.96069e54 | 0.916556 | ||||||||
\(899\) | −1.50854e54 | −0.341981 | ||||||||
\(900\) | −1.95951e53 | −0.0435172 | ||||||||
\(901\) | 1.49394e54 | 0.325030 | ||||||||
\(902\) | −2.60428e53 | −0.0555095 | ||||||||
\(903\) | 1.22869e54 | 0.256577 | ||||||||
\(904\) | −1.29856e54 | −0.265672 | ||||||||
\(905\) | 2.97500e54 | 0.596332 | ||||||||
\(906\) | 3.18100e54 | 0.624730 | ||||||||
\(907\) | 2.47231e54 | 0.475739 | 0.237869 | − | 0.971297i | \(-0.423551\pi\) | ||||
0.237869 | + | 0.971297i | \(0.423551\pi\) | |||||||
\(908\) | −3.77288e54 | −0.711353 | ||||||||
\(909\) | 1.95166e54 | 0.360555 | ||||||||
\(910\) | −7.17007e53 | −0.129795 | ||||||||
\(911\) | −7.75991e54 | −1.37647 | −0.688235 | − | 0.725488i | \(-0.741614\pi\) | ||||
−0.688235 | + | 0.725488i | \(0.741614\pi\) | |||||||
\(912\) | −1.10367e54 | −0.191839 | ||||||||
\(913\) | 3.44276e53 | 0.0586404 | ||||||||
\(914\) | 6.34777e54 | 1.05954 | ||||||||
\(915\) | 2.86213e54 | 0.468166 | ||||||||
\(916\) | 3.52376e54 | 0.564860 | ||||||||
\(917\) | −9.55099e54 | −1.50043 | ||||||||
\(918\) | 2.49368e54 | 0.383928 | ||||||||
\(919\) | −3.05017e53 | −0.0460243 | −0.0230121 | − | 0.999735i | \(-0.507326\pi\) | ||||
−0.0230121 | + | 0.999735i | \(0.507326\pi\) | |||||||
\(920\) | −3.70446e53 | −0.0547835 | ||||||||
\(921\) | −7.16736e53 | −0.103886 | ||||||||
\(922\) | 4.94496e54 | 0.702490 | ||||||||
\(923\) | −2.16785e52 | −0.00301854 | ||||||||
\(924\) | 2.98262e53 | 0.0407067 | ||||||||
\(925\) | −1.18929e54 | −0.159099 | ||||||||
\(926\) | 1.35140e54 | 0.177207 | ||||||||
\(927\) | 2.70771e54 | 0.348039 | ||||||||
\(928\) | −1.71997e54 | −0.216713 | ||||||||
\(929\) | 4.09018e54 | 0.505187 | 0.252593 | − | 0.967573i | \(-0.418717\pi\) | ||||
0.252593 | + | 0.967573i | \(0.418717\pi\) | |||||||
\(930\) | 5.47565e53 | 0.0662981 | ||||||||
\(931\) | 1.37981e54 | 0.163775 | ||||||||
\(932\) | 6.84110e54 | 0.796034 | ||||||||
\(933\) | 7.47146e54 | 0.852305 | ||||||||
\(934\) | 5.16342e54 | 0.577458 | ||||||||
\(935\) | 2.42737e53 | 0.0266146 | ||||||||
\(936\) | −6.41122e53 | −0.0689187 | ||||||||
\(937\) | 6.61227e54 | 0.696897 | 0.348448 | − | 0.937328i | \(-0.386709\pi\) | ||||
0.348448 | + | 0.937328i | \(0.386709\pi\) | |||||||
\(938\) | −1.24226e55 | −1.28369 | ||||||||
\(939\) | 8.49739e54 | 0.860938 | ||||||||
\(940\) | −4.37205e53 | −0.0434330 | ||||||||
\(941\) | −1.99049e55 | −1.93889 | −0.969444 | − | 0.245314i | \(-0.921109\pi\) | ||||
−0.969444 | + | 0.245314i | \(0.921109\pi\) | |||||||
\(942\) | 4.78857e54 | 0.457366 | ||||||||
\(943\) | −2.45655e54 | −0.230070 | ||||||||
\(944\) | −2.26665e54 | −0.208162 | ||||||||
\(945\) | 4.90796e54 | 0.441990 | ||||||||
\(946\) | 3.52693e53 | 0.0311466 | ||||||||
\(947\) | −2.25303e55 | −1.95116 | −0.975580 | − | 0.219644i | \(-0.929510\pi\) | ||||
−0.975580 | + | 0.219644i | \(0.929510\pi\) | |||||||
\(948\) | −6.01448e54 | −0.510792 | ||||||||
\(949\) | −8.01038e53 | −0.0667157 | ||||||||
\(950\) | −1.76783e54 | −0.144395 | ||||||||
\(951\) | 5.00389e54 | 0.400837 | ||||||||
\(952\) | 2.07576e54 | 0.163077 | ||||||||
\(953\) | −1.62950e55 | −1.25555 | −0.627777 | − | 0.778393i | \(-0.716035\pi\) | ||||
−0.627777 | + | 0.778393i | \(0.716035\pi\) | |||||||
\(954\) | 2.62912e54 | 0.198685 | ||||||||
\(955\) | 1.25629e54 | 0.0931163 | ||||||||
\(956\) | −2.88723e54 | −0.209899 | ||||||||
\(957\) | 1.52753e54 | 0.108923 | ||||||||
\(958\) | −1.63232e55 | −1.14168 | ||||||||
\(959\) | −1.66825e55 | −1.14450 | ||||||||
\(960\) | 6.24311e53 | 0.0420130 | ||||||||
\(961\) | −1.39701e55 | −0.922181 | ||||||||
\(962\) | −3.89119e54 | −0.251967 | ||||||||
\(963\) | −3.26050e54 | −0.207109 | ||||||||
\(964\) | 6.32624e54 | 0.394203 | ||||||||
\(965\) | −4.26562e53 | −0.0260751 | ||||||||
\(966\) | 2.81343e54 | 0.168717 | ||||||||
\(967\) | −4.18975e54 | −0.246489 | −0.123245 | − | 0.992376i | \(-0.539330\pi\) | ||||
−0.123245 | + | 0.992376i | \(0.539330\pi\) | |||||||
\(968\) | −6.03999e54 | −0.348612 | ||||||||
\(969\) | 6.82165e54 | 0.386278 | ||||||||
\(970\) | −8.76678e54 | −0.487038 | ||||||||
\(971\) | −9.28589e54 | −0.506137 | −0.253068 | − | 0.967448i | \(-0.581440\pi\) | ||||
−0.253068 | + | 0.967448i | \(0.581440\pi\) | |||||||
\(972\) | 7.44637e54 | 0.398216 | ||||||||
\(973\) | −5.36987e54 | −0.281758 | ||||||||
\(974\) | 1.19586e55 | 0.615657 | ||||||||
\(975\) | 1.33289e54 | 0.0673302 | ||||||||
\(976\) | 7.02567e54 | 0.348230 | ||||||||
\(977\) | 1.35583e55 | 0.659409 | 0.329705 | − | 0.944084i | \(-0.393051\pi\) | ||||
0.329705 | + | 0.944084i | \(0.393051\pi\) | |||||||
\(978\) | −1.40349e55 | −0.669795 | ||||||||
\(979\) | 2.12194e54 | 0.0993696 | ||||||||
\(980\) | −7.80509e53 | −0.0358670 | ||||||||
\(981\) | 4.22157e54 | 0.190370 | ||||||||
\(982\) | 1.96728e55 | 0.870572 | ||||||||
\(983\) | −1.34843e55 | −0.585583 | −0.292791 | − | 0.956176i | \(-0.594584\pi\) | ||||
−0.292791 | + | 0.956176i | \(0.594584\pi\) | |||||||
\(984\) | 4.14002e54 | 0.176438 | ||||||||
\(985\) | 1.56335e55 | 0.653860 | ||||||||
\(986\) | 1.06309e55 | 0.436363 | ||||||||
\(987\) | 3.32044e54 | 0.133761 | ||||||||
\(988\) | −5.78407e54 | −0.228681 | ||||||||
\(989\) | 3.32687e54 | 0.129093 | ||||||||
\(990\) | 4.27183e53 | 0.0162691 | ||||||||
\(991\) | 1.84939e55 | 0.691298 | 0.345649 | − | 0.938364i | \(-0.387659\pi\) | ||||
0.345649 | + | 0.938364i | \(0.387659\pi\) | |||||||
\(992\) | 1.34411e54 | 0.0493137 | ||||||||
\(993\) | 2.17786e55 | 0.784276 | ||||||||
\(994\) | 1.23522e53 | 0.00436612 | ||||||||
\(995\) | 2.11557e55 | 0.734008 | ||||||||
\(996\) | −5.47294e54 | −0.186390 | ||||||||
\(997\) | −2.97900e54 | −0.0995885 | −0.0497943 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497943 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(998\) | −3.21504e55 | −1.05505 | ||||||||
\(999\) | 2.66355e55 | 0.858023 |
(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 | 10.38.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.38.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |