Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,28,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, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
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: | \(46.1855574838\) |
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: | \( x^{2} - x - 19551870 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4422.25\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8192.00 | −0.707107 | ||||||||
\(3\) | −3.52746e6 | −1.27739 | −0.638697 | − | 0.769458i | \(-0.720526\pi\) | ||||
−0.638697 | + | 0.769458i | \(0.720526\pi\) | |||||||
\(4\) | 6.71089e7 | 0.500000 | ||||||||
\(5\) | 1.22070e9 | 0.447214 | ||||||||
\(6\) | 2.88969e10 | 0.903254 | ||||||||
\(7\) | −2.10875e11 | −0.822626 | −0.411313 | − | 0.911494i | \(-0.634930\pi\) | ||||
−0.411313 | + | 0.911494i | \(0.634930\pi\) | |||||||
\(8\) | −5.49756e11 | −0.353553 | ||||||||
\(9\) | 4.81735e12 | 0.631735 | ||||||||
\(10\) | −1.00000e13 | −0.316228 | ||||||||
\(11\) | −2.00632e14 | −1.75226 | −0.876131 | − | 0.482074i | \(-0.839884\pi\) | ||||
−0.876131 | + | 0.482074i | \(0.839884\pi\) | |||||||
\(12\) | −2.36724e14 | −0.638697 | ||||||||
\(13\) | 1.66667e15 | 1.52621 | 0.763105 | − | 0.646275i | \(-0.223674\pi\) | ||||
0.763105 | + | 0.646275i | \(0.223674\pi\) | |||||||
\(14\) | 1.72749e15 | 0.581684 | ||||||||
\(15\) | −4.30598e15 | −0.571268 | ||||||||
\(16\) | 4.50360e15 | 0.250000 | ||||||||
\(17\) | 4.72049e16 | 1.15592 | 0.577959 | − | 0.816066i | \(-0.303849\pi\) | ||||
0.577959 | + | 0.816066i | \(0.303849\pi\) | |||||||
\(18\) | −3.94638e16 | −0.446704 | ||||||||
\(19\) | 2.80684e17 | 1.53124 | 0.765622 | − | 0.643291i | \(-0.222431\pi\) | ||||
0.765622 | + | 0.643291i | \(0.222431\pi\) | |||||||
\(20\) | 8.19200e16 | 0.223607 | ||||||||
\(21\) | 7.43854e17 | 1.05082 | ||||||||
\(22\) | 1.64358e18 | 1.23904 | ||||||||
\(23\) | −3.44510e18 | −1.42520 | −0.712601 | − | 0.701570i | \(-0.752483\pi\) | ||||
−0.712601 | + | 0.701570i | \(0.752483\pi\) | |||||||
\(24\) | 1.93924e18 | 0.451627 | ||||||||
\(25\) | 1.49012e18 | 0.200000 | ||||||||
\(26\) | −1.36534e19 | −1.07919 | ||||||||
\(27\) | 9.90596e18 | 0.470420 | ||||||||
\(28\) | −1.41516e19 | −0.411313 | ||||||||
\(29\) | 5.38410e19 | 0.974407 | 0.487204 | − | 0.873288i | \(-0.338017\pi\) | ||||
0.487204 | + | 0.873288i | \(0.338017\pi\) | |||||||
\(30\) | 3.52746e19 | 0.403947 | ||||||||
\(31\) | −6.02019e19 | −0.442820 | −0.221410 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221410 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(32\) | −3.68935e19 | −0.176777 | ||||||||
\(33\) | 7.07721e20 | 2.23833 | ||||||||
\(34\) | −3.86703e20 | −0.817357 | ||||||||
\(35\) | −2.57416e20 | −0.367889 | ||||||||
\(36\) | 3.23287e20 | 0.315867 | ||||||||
\(37\) | 2.15489e21 | 1.45446 | 0.727231 | − | 0.686393i | \(-0.240807\pi\) | ||||
0.727231 | + | 0.686393i | \(0.240807\pi\) | |||||||
\(38\) | −2.29937e21 | −1.08275 | ||||||||
\(39\) | −5.87910e21 | −1.94957 | ||||||||
\(40\) | −6.71089e20 | −0.158114 | ||||||||
\(41\) | −5.73864e21 | −0.968784 | −0.484392 | − | 0.874851i | \(-0.660959\pi\) | ||||
−0.484392 | + | 0.874851i | \(0.660959\pi\) | |||||||
\(42\) | −6.09365e21 | −0.743040 | ||||||||
\(43\) | 4.73192e20 | 0.0419965 | 0.0209983 | − | 0.999780i | \(-0.493316\pi\) | ||||
0.0209983 | + | 0.999780i | \(0.493316\pi\) | |||||||
\(44\) | −1.34642e22 | −0.876131 | ||||||||
\(45\) | 5.88056e21 | 0.282520 | ||||||||
\(46\) | 2.82223e22 | 1.00777 | ||||||||
\(47\) | −1.36579e22 | −0.364808 | −0.182404 | − | 0.983224i | \(-0.558388\pi\) | ||||
−0.182404 | + | 0.983224i | \(0.558388\pi\) | |||||||
\(48\) | −1.58863e22 | −0.319348 | ||||||||
\(49\) | −2.12439e22 | −0.323287 | ||||||||
\(50\) | −1.22070e22 | −0.141421 | ||||||||
\(51\) | −1.66513e23 | −1.47656 | ||||||||
\(52\) | 1.11848e23 | 0.763105 | ||||||||
\(53\) | 1.17314e23 | 0.618907 | 0.309454 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309454 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(54\) | −8.11496e22 | −0.332637 | ||||||||
\(55\) | −2.44912e23 | −0.783635 | ||||||||
\(56\) | 1.15930e23 | 0.290842 | ||||||||
\(57\) | −9.90101e23 | −1.95600 | ||||||||
\(58\) | −4.41066e23 | −0.689010 | ||||||||
\(59\) | −6.96143e23 | −0.863369 | −0.431684 | − | 0.902025i | \(-0.642081\pi\) | ||||
−0.431684 | + | 0.902025i | \(0.642081\pi\) | |||||||
\(60\) | −2.88969e23 | −0.285634 | ||||||||
\(61\) | −1.66138e24 | −1.31376 | −0.656882 | − | 0.753993i | \(-0.728125\pi\) | ||||
−0.656882 | + | 0.753993i | \(0.728125\pi\) | |||||||
\(62\) | 4.93174e23 | 0.313121 | ||||||||
\(63\) | −1.01586e24 | −0.519681 | ||||||||
\(64\) | 3.02231e23 | 0.125000 | ||||||||
\(65\) | 2.03451e24 | 0.682541 | ||||||||
\(66\) | −5.79765e24 | −1.58274 | ||||||||
\(67\) | −6.87655e22 | −0.0153236 | −0.00766180 | − | 0.999971i | \(-0.502439\pi\) | ||||
−0.00766180 | + | 0.999971i | \(0.502439\pi\) | |||||||
\(68\) | 3.16787e24 | 0.577959 | ||||||||
\(69\) | 1.21524e25 | 1.82054 | ||||||||
\(70\) | 2.10875e24 | 0.260137 | ||||||||
\(71\) | −1.69024e24 | −0.172171 | −0.0860856 | − | 0.996288i | \(-0.527436\pi\) | ||||
−0.0860856 | + | 0.996288i | \(0.527436\pi\) | |||||||
\(72\) | −2.64837e24 | −0.223352 | ||||||||
\(73\) | −5.53884e24 | −0.387758 | −0.193879 | − | 0.981025i | \(-0.562107\pi\) | ||||
−0.193879 | + | 0.981025i | \(0.562107\pi\) | |||||||
\(74\) | −1.76529e25 | −1.02846 | ||||||||
\(75\) | −5.25632e24 | −0.255479 | ||||||||
\(76\) | 1.88364e25 | 0.765622 | ||||||||
\(77\) | 4.23083e25 | 1.44146 | ||||||||
\(78\) | 4.81616e25 | 1.37855 | ||||||||
\(79\) | −5.02072e24 | −0.121004 | −0.0605021 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605021 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(80\) | 5.49756e24 | 0.111803 | ||||||||
\(81\) | −7.16780e25 | −1.23265 | ||||||||
\(82\) | 4.70109e25 | 0.685034 | ||||||||
\(83\) | 1.56395e26 | 1.93494 | 0.967470 | − | 0.252988i | \(-0.0814132\pi\) | ||||
0.967470 | + | 0.252988i | \(0.0814132\pi\) | |||||||
\(84\) | 4.99192e25 | 0.525408 | ||||||||
\(85\) | 5.76232e25 | 0.516942 | ||||||||
\(86\) | −3.87639e24 | −0.0296960 | ||||||||
\(87\) | −1.89922e26 | −1.24470 | ||||||||
\(88\) | 1.10299e26 | 0.619518 | ||||||||
\(89\) | −6.32996e25 | −0.305236 | −0.152618 | − | 0.988285i | \(-0.548770\pi\) | ||||
−0.152618 | + | 0.988285i | \(0.548770\pi\) | |||||||
\(90\) | −4.81735e25 | −0.199772 | ||||||||
\(91\) | −3.51459e26 | −1.25550 | ||||||||
\(92\) | −2.31197e26 | −0.712601 | ||||||||
\(93\) | 2.12360e26 | 0.565656 | ||||||||
\(94\) | 1.11886e26 | 0.257958 | ||||||||
\(95\) | 3.42632e26 | 0.684793 | ||||||||
\(96\) | 1.30140e26 | 0.225813 | ||||||||
\(97\) | −5.95949e26 | −0.899063 | −0.449532 | − | 0.893264i | \(-0.648409\pi\) | ||||
−0.449532 | + | 0.893264i | \(0.648409\pi\) | |||||||
\(98\) | 1.74030e26 | 0.228598 | ||||||||
\(99\) | −9.66515e26 | −1.10696 | ||||||||
\(100\) | 1.00000e26 | 0.100000 | ||||||||
\(101\) | −6.01756e26 | −0.526117 | −0.263058 | − | 0.964780i | \(-0.584731\pi\) | ||||
−0.263058 | + | 0.964780i | \(0.584731\pi\) | |||||||
\(102\) | 1.36408e27 | 1.04409 | ||||||||
\(103\) | 5.34812e26 | 0.358838 | 0.179419 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179419 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(104\) | −9.16261e26 | −0.539596 | ||||||||
\(105\) | 9.08025e26 | 0.469940 | ||||||||
\(106\) | −9.61036e26 | −0.437633 | ||||||||
\(107\) | −2.27447e27 | −0.912429 | −0.456214 | − | 0.889870i | \(-0.650795\pi\) | ||||
−0.456214 | + | 0.889870i | \(0.650795\pi\) | |||||||
\(108\) | 6.64777e26 | 0.235210 | ||||||||
\(109\) | −2.61656e27 | −0.817472 | −0.408736 | − | 0.912653i | \(-0.634030\pi\) | ||||
−0.408736 | + | 0.912653i | \(0.634030\pi\) | |||||||
\(110\) | 2.00632e27 | 0.554114 | ||||||||
\(111\) | −7.60129e27 | −1.85792 | ||||||||
\(112\) | −9.49698e26 | −0.205656 | ||||||||
\(113\) | −9.28514e27 | −1.78332 | −0.891660 | − | 0.452705i | \(-0.850459\pi\) | ||||
−0.891660 | + | 0.452705i | \(0.850459\pi\) | |||||||
\(114\) | 8.11091e27 | 1.38310 | ||||||||
\(115\) | −4.20545e27 | −0.637369 | ||||||||
\(116\) | 3.61321e27 | 0.487204 | ||||||||
\(117\) | 8.02893e27 | 0.964159 | ||||||||
\(118\) | 5.70280e27 | 0.610494 | ||||||||
\(119\) | −9.95436e27 | −0.950888 | ||||||||
\(120\) | 2.36724e27 | 0.201974 | ||||||||
\(121\) | 2.71432e28 | 2.07042 | ||||||||
\(122\) | 1.36101e28 | 0.928972 | ||||||||
\(123\) | 2.02428e28 | 1.23752 | ||||||||
\(124\) | −4.04008e27 | −0.221410 | ||||||||
\(125\) | 1.81899e27 | 0.0894427 | ||||||||
\(126\) | 8.32194e27 | 0.367470 | ||||||||
\(127\) | 1.34819e28 | 0.535058 | 0.267529 | − | 0.963550i | \(-0.413793\pi\) | ||||
0.267529 | + | 0.963550i | \(0.413793\pi\) | |||||||
\(128\) | −2.47588e27 | −0.0883883 | ||||||||
\(129\) | −1.66916e27 | −0.0536461 | ||||||||
\(130\) | −1.66667e28 | −0.482630 | ||||||||
\(131\) | −1.22819e28 | −0.320703 | −0.160351 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160351 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(132\) | 4.74943e28 | 1.11916 | ||||||||
\(133\) | −5.91894e28 | −1.25964 | ||||||||
\(134\) | 5.63327e26 | 0.0108354 | ||||||||
\(135\) | 1.20922e28 | 0.210378 | ||||||||
\(136\) | −2.59512e28 | −0.408679 | ||||||||
\(137\) | 7.77523e28 | 1.10914 | 0.554569 | − | 0.832138i | \(-0.312883\pi\) | ||||
0.554569 | + | 0.832138i | \(0.312883\pi\) | |||||||
\(138\) | −9.95528e28 | −1.28732 | ||||||||
\(139\) | −6.09274e28 | −0.714682 | −0.357341 | − | 0.933974i | \(-0.616317\pi\) | ||||
−0.357341 | + | 0.933974i | \(0.616317\pi\) | |||||||
\(140\) | −1.72749e28 | −0.183945 | ||||||||
\(141\) | 4.81778e28 | 0.466003 | ||||||||
\(142\) | 1.38464e28 | 0.121743 | ||||||||
\(143\) | −3.34387e29 | −2.67432 | ||||||||
\(144\) | 2.16954e28 | 0.157934 | ||||||||
\(145\) | 6.57239e28 | 0.435768 | ||||||||
\(146\) | 4.53742e28 | 0.274186 | ||||||||
\(147\) | 7.49371e28 | 0.412965 | ||||||||
\(148\) | 1.44612e29 | 0.727231 | ||||||||
\(149\) | −1.05900e29 | −0.486276 | −0.243138 | − | 0.969992i | \(-0.578177\pi\) | ||||
−0.243138 | + | 0.969992i | \(0.578177\pi\) | |||||||
\(150\) | 4.30598e28 | 0.180651 | ||||||||
\(151\) | 3.29076e28 | 0.126214 | 0.0631070 | − | 0.998007i | \(-0.479899\pi\) | ||||
0.0631070 | + | 0.998007i | \(0.479899\pi\) | |||||||
\(152\) | −1.54308e29 | −0.541376 | ||||||||
\(153\) | 2.27403e29 | 0.730233 | ||||||||
\(154\) | −3.46590e29 | −1.01926 | ||||||||
\(155\) | −7.34887e28 | −0.198035 | ||||||||
\(156\) | −3.94540e29 | −0.974785 | ||||||||
\(157\) | −1.11931e29 | −0.253692 | −0.126846 | − | 0.991922i | \(-0.540485\pi\) | ||||
−0.126846 | + | 0.991922i | \(0.540485\pi\) | |||||||
\(158\) | 4.11298e28 | 0.0855629 | ||||||||
\(159\) | −4.13820e29 | −0.790588 | ||||||||
\(160\) | −4.50360e28 | −0.0790569 | ||||||||
\(161\) | 7.26487e29 | 1.17241 | ||||||||
\(162\) | 5.87186e29 | 0.871612 | ||||||||
\(163\) | 1.01040e30 | 1.38026 | 0.690128 | − | 0.723687i | \(-0.257554\pi\) | ||||
0.690128 | + | 0.723687i | \(0.257554\pi\) | |||||||
\(164\) | −3.85114e29 | −0.484392 | ||||||||
\(165\) | 8.63917e29 | 1.00101 | ||||||||
\(166\) | −1.28118e30 | −1.36821 | ||||||||
\(167\) | −8.58149e29 | −0.845065 | −0.422533 | − | 0.906348i | \(-0.638859\pi\) | ||||
−0.422533 | + | 0.906348i | \(0.638859\pi\) | |||||||
\(168\) | −4.08938e29 | −0.371520 | ||||||||
\(169\) | 1.58525e30 | 1.32931 | ||||||||
\(170\) | −4.72049e29 | −0.365533 | ||||||||
\(171\) | 1.35216e30 | 0.967340 | ||||||||
\(172\) | 3.17554e28 | 0.0209983 | ||||||||
\(173\) | 1.28043e30 | 0.782949 | 0.391474 | − | 0.920189i | \(-0.371965\pi\) | ||||
0.391474 | + | 0.920189i | \(0.371965\pi\) | |||||||
\(174\) | 1.55584e30 | 0.880137 | ||||||||
\(175\) | −3.14229e29 | −0.164525 | ||||||||
\(176\) | −9.03566e29 | −0.438065 | ||||||||
\(177\) | 2.45561e30 | 1.10286 | ||||||||
\(178\) | 5.18550e29 | 0.215834 | ||||||||
\(179\) | −4.74098e30 | −1.82958 | −0.914791 | − | 0.403928i | \(-0.867645\pi\) | ||||
−0.914791 | + | 0.403928i | \(0.867645\pi\) | |||||||
\(180\) | 3.94638e29 | 0.141260 | ||||||||
\(181\) | −3.96469e30 | −1.31689 | −0.658443 | − | 0.752631i | \(-0.728785\pi\) | ||||
−0.658443 | + | 0.752631i | \(0.728785\pi\) | |||||||
\(182\) | 2.87916e30 | 0.887772 | ||||||||
\(183\) | 5.86046e30 | 1.67819 | ||||||||
\(184\) | 1.89396e30 | 0.503885 | ||||||||
\(185\) | 2.63048e30 | 0.650455 | ||||||||
\(186\) | −1.73965e30 | −0.399979 | ||||||||
\(187\) | −9.47082e30 | −2.02547 | ||||||||
\(188\) | −9.16568e29 | −0.182404 | ||||||||
\(189\) | −2.08892e30 | −0.386979 | ||||||||
\(190\) | −2.80684e30 | −0.484222 | ||||||||
\(191\) | 8.53219e30 | 1.37123 | 0.685615 | − | 0.727964i | \(-0.259533\pi\) | ||||
0.685615 | + | 0.727964i | \(0.259533\pi\) | |||||||
\(192\) | −1.06611e30 | −0.159674 | ||||||||
\(193\) | −1.32910e31 | −1.85582 | −0.927908 | − | 0.372808i | \(-0.878395\pi\) | ||||
−0.927908 | + | 0.372808i | \(0.878395\pi\) | |||||||
\(194\) | 4.88201e30 | 0.635734 | ||||||||
\(195\) | −7.17664e30 | −0.871874 | ||||||||
\(196\) | −1.42566e30 | −0.161643 | ||||||||
\(197\) | −8.40332e30 | −0.889522 | −0.444761 | − | 0.895649i | \(-0.646711\pi\) | ||||
−0.444761 | + | 0.895649i | \(0.646711\pi\) | |||||||
\(198\) | 7.91769e30 | 0.782742 | ||||||||
\(199\) | 1.87522e31 | 1.73195 | 0.865975 | − | 0.500088i | \(-0.166699\pi\) | ||||
0.865975 | + | 0.500088i | \(0.166699\pi\) | |||||||
\(200\) | −8.19200e29 | −0.0707107 | ||||||||
\(201\) | 2.42567e29 | 0.0195743 | ||||||||
\(202\) | 4.92959e30 | 0.372021 | ||||||||
\(203\) | −1.13538e31 | −0.801573 | ||||||||
\(204\) | −1.11745e31 | −0.738281 | ||||||||
\(205\) | −7.00518e30 | −0.433253 | ||||||||
\(206\) | −4.38118e30 | −0.253737 | ||||||||
\(207\) | −1.65963e31 | −0.900349 | ||||||||
\(208\) | 7.50601e30 | 0.381552 | ||||||||
\(209\) | −5.63142e31 | −2.68314 | ||||||||
\(210\) | −7.43854e30 | −0.332297 | ||||||||
\(211\) | 4.59140e31 | 1.92367 | 0.961837 | − | 0.273623i | \(-0.0882219\pi\) | ||||
0.961837 | + | 0.273623i | \(0.0882219\pi\) | |||||||
\(212\) | 7.87281e30 | 0.309454 | ||||||||
\(213\) | 5.96225e30 | 0.219931 | ||||||||
\(214\) | 1.86324e31 | 0.645185 | ||||||||
\(215\) | 5.77627e29 | 0.0187814 | ||||||||
\(216\) | −5.44586e30 | −0.166319 | ||||||||
\(217\) | 1.26951e31 | 0.364275 | ||||||||
\(218\) | 2.14348e31 | 0.578040 | ||||||||
\(219\) | 1.95380e31 | 0.495319 | ||||||||
\(220\) | −1.64358e31 | −0.391817 | ||||||||
\(221\) | 7.86750e31 | 1.76417 | ||||||||
\(222\) | 6.22698e31 | 1.31375 | ||||||||
\(223\) | 5.48895e31 | 1.08987 | 0.544933 | − | 0.838479i | \(-0.316555\pi\) | ||||
0.544933 | + | 0.838479i | \(0.316555\pi\) | |||||||
\(224\) | 7.77993e30 | 0.145421 | ||||||||
\(225\) | 7.17842e30 | 0.126347 | ||||||||
\(226\) | 7.60639e31 | 1.26100 | ||||||||
\(227\) | −4.53524e31 | −0.708355 | −0.354178 | − | 0.935178i | \(-0.615239\pi\) | ||||
−0.354178 | + | 0.935178i | \(0.615239\pi\) | |||||||
\(228\) | −6.64446e31 | −0.978001 | ||||||||
\(229\) | 3.94248e30 | 0.0547004 | 0.0273502 | − | 0.999626i | \(-0.491293\pi\) | ||||
0.0273502 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(230\) | 3.44510e31 | 0.450688 | ||||||||
\(231\) | −1.49241e32 | −1.84131 | ||||||||
\(232\) | −2.95994e31 | −0.344505 | ||||||||
\(233\) | 4.71165e31 | 0.517449 | 0.258725 | − | 0.965951i | \(-0.416698\pi\) | ||||
0.258725 | + | 0.965951i | \(0.416698\pi\) | |||||||
\(234\) | −6.57730e31 | −0.681764 | ||||||||
\(235\) | −1.66723e31 | −0.163147 | ||||||||
\(236\) | −4.67174e31 | −0.431684 | ||||||||
\(237\) | 1.77104e31 | 0.154570 | ||||||||
\(238\) | 8.15461e31 | 0.672379 | ||||||||
\(239\) | −5.90002e31 | −0.459708 | −0.229854 | − | 0.973225i | \(-0.573825\pi\) | ||||
−0.229854 | + | 0.973225i | \(0.573825\pi\) | |||||||
\(240\) | −1.93924e31 | −0.142817 | ||||||||
\(241\) | −1.62357e32 | −1.13042 | −0.565212 | − | 0.824946i | \(-0.691205\pi\) | ||||
−0.565212 | + | 0.824946i | \(0.691205\pi\) | |||||||
\(242\) | −2.22357e32 | −1.46401 | ||||||||
\(243\) | 1.77302e32 | 1.10415 | ||||||||
\(244\) | −1.11494e32 | −0.656882 | ||||||||
\(245\) | −2.59326e31 | −0.144578 | ||||||||
\(246\) | −1.65829e32 | −0.875058 | ||||||||
\(247\) | 4.67808e32 | 2.33700 | ||||||||
\(248\) | 3.30964e31 | 0.156561 | ||||||||
\(249\) | −5.51675e32 | −2.47168 | ||||||||
\(250\) | −1.49012e31 | −0.0632456 | ||||||||
\(251\) | 2.64625e32 | 1.06423 | 0.532115 | − | 0.846672i | \(-0.321397\pi\) | ||||
0.532115 | + | 0.846672i | \(0.321397\pi\) | |||||||
\(252\) | −6.81733e31 | −0.259841 | ||||||||
\(253\) | 6.91197e32 | 2.49732 | ||||||||
\(254\) | −1.10444e32 | −0.378343 | ||||||||
\(255\) | −2.03263e32 | −0.660339 | ||||||||
\(256\) | 2.02824e31 | 0.0625000 | ||||||||
\(257\) | 2.74808e31 | 0.0803402 | 0.0401701 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401701 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(258\) | 1.36738e31 | 0.0379335 | ||||||||
\(259\) | −4.54414e32 | −1.19648 | ||||||||
\(260\) | 1.36534e32 | 0.341271 | ||||||||
\(261\) | 2.59371e32 | 0.615567 | ||||||||
\(262\) | 1.00613e32 | 0.226771 | ||||||||
\(263\) | −6.36864e32 | −1.36346 | −0.681732 | − | 0.731602i | \(-0.738773\pi\) | ||||
−0.681732 | + | 0.731602i | \(0.738773\pi\) | |||||||
\(264\) | −3.89073e32 | −0.791368 | ||||||||
\(265\) | 1.43206e32 | 0.276784 | ||||||||
\(266\) | 4.84879e32 | 0.890700 | ||||||||
\(267\) | 2.23286e32 | 0.389906 | ||||||||
\(268\) | −4.61478e30 | −0.00766180 | ||||||||
\(269\) | −2.64799e32 | −0.418080 | −0.209040 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209040 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(270\) | −9.90596e31 | −0.148760 | ||||||||
\(271\) | −9.06365e32 | −1.29485 | −0.647423 | − | 0.762131i | \(-0.724153\pi\) | ||||
−0.647423 | + | 0.762131i | \(0.724153\pi\) | |||||||
\(272\) | 2.12592e32 | 0.288979 | ||||||||
\(273\) | 1.23976e33 | 1.60377 | ||||||||
\(274\) | −6.36947e32 | −0.784279 | ||||||||
\(275\) | −2.98965e32 | −0.350452 | ||||||||
\(276\) | 8.15537e32 | 0.910271 | ||||||||
\(277\) | 6.76213e32 | 0.718798 | 0.359399 | − | 0.933184i | \(-0.382982\pi\) | ||||
0.359399 | + | 0.933184i | \(0.382982\pi\) | |||||||
\(278\) | 4.99117e32 | 0.505356 | ||||||||
\(279\) | −2.90014e32 | −0.279745 | ||||||||
\(280\) | 1.41516e32 | 0.130069 | ||||||||
\(281\) | 9.77731e32 | 0.856415 | 0.428207 | − | 0.903680i | \(-0.359145\pi\) | ||||
0.428207 | + | 0.903680i | \(0.359145\pi\) | |||||||
\(282\) | −3.94672e32 | −0.329514 | ||||||||
\(283\) | 1.47138e32 | 0.117113 | 0.0585567 | − | 0.998284i | \(-0.481350\pi\) | ||||
0.0585567 | + | 0.998284i | \(0.481350\pi\) | |||||||
\(284\) | −1.13430e32 | −0.0860856 | ||||||||
\(285\) | −1.20862e33 | −0.874750 | ||||||||
\(286\) | 2.73930e33 | 1.89103 | ||||||||
\(287\) | 1.21014e33 | 0.796947 | ||||||||
\(288\) | −1.77729e32 | −0.111676 | ||||||||
\(289\) | 5.60594e32 | 0.336146 | ||||||||
\(290\) | −5.38410e32 | −0.308135 | ||||||||
\(291\) | 2.10218e33 | 1.14846 | ||||||||
\(292\) | −3.71706e32 | −0.193879 | ||||||||
\(293\) | −4.76752e32 | −0.237454 | −0.118727 | − | 0.992927i | \(-0.537881\pi\) | ||||
−0.118727 | + | 0.992927i | \(0.537881\pi\) | |||||||
\(294\) | −6.13885e32 | −0.292010 | ||||||||
\(295\) | −8.49784e32 | −0.386110 | ||||||||
\(296\) | −1.18466e33 | −0.514230 | ||||||||
\(297\) | −1.98745e33 | −0.824298 | ||||||||
\(298\) | 8.67536e32 | 0.343849 | ||||||||
\(299\) | −5.74184e33 | −2.17515 | ||||||||
\(300\) | −3.52746e32 | −0.127739 | ||||||||
\(301\) | −9.97845e31 | −0.0345474 | ||||||||
\(302\) | −2.69579e32 | −0.0892468 | ||||||||
\(303\) | 2.12267e33 | 0.672058 | ||||||||
\(304\) | 1.26409e33 | 0.382811 | ||||||||
\(305\) | −2.02806e33 | −0.587533 | ||||||||
\(306\) | −1.86288e33 | −0.516353 | ||||||||
\(307\) | −1.97700e33 | −0.524370 | −0.262185 | − | 0.965018i | \(-0.584443\pi\) | ||||
−0.262185 | + | 0.965018i | \(0.584443\pi\) | |||||||
\(308\) | 2.83926e33 | 0.720728 | ||||||||
\(309\) | −1.88653e33 | −0.458377 | ||||||||
\(310\) | 6.02019e32 | 0.140032 | ||||||||
\(311\) | −4.03023e33 | −0.897562 | −0.448781 | − | 0.893642i | \(-0.648142\pi\) | ||||
−0.448781 | + | 0.893642i | \(0.648142\pi\) | |||||||
\(312\) | 3.23207e33 | 0.689277 | ||||||||
\(313\) | 1.11971e33 | 0.228696 | 0.114348 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114348 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(314\) | 9.16941e32 | 0.179387 | ||||||||
\(315\) | −1.24007e33 | −0.232409 | ||||||||
\(316\) | −3.36935e32 | −0.0605021 | ||||||||
\(317\) | −6.02275e33 | −1.03632 | −0.518161 | − | 0.855283i | \(-0.673383\pi\) | ||||
−0.518161 | + | 0.855283i | \(0.673383\pi\) | |||||||
\(318\) | 3.39001e33 | 0.559030 | ||||||||
\(319\) | −1.08022e34 | −1.70742 | ||||||||
\(320\) | 3.68935e32 | 0.0559017 | ||||||||
\(321\) | 8.02309e33 | 1.16553 | ||||||||
\(322\) | −5.95138e33 | −0.829017 | ||||||||
\(323\) | 1.32497e34 | 1.76999 | ||||||||
\(324\) | −4.81023e33 | −0.616323 | ||||||||
\(325\) | 2.48353e33 | 0.305242 | ||||||||
\(326\) | −8.27718e33 | −0.975989 | ||||||||
\(327\) | 9.22980e33 | 1.04423 | ||||||||
\(328\) | 3.15485e33 | 0.342517 | ||||||||
\(329\) | 2.88012e33 | 0.300100 | ||||||||
\(330\) | −7.07721e33 | −0.707821 | ||||||||
\(331\) | −3.93423e33 | −0.377730 | −0.188865 | − | 0.982003i | \(-0.560481\pi\) | ||||
−0.188865 | + | 0.982003i | \(0.560481\pi\) | |||||||
\(332\) | 1.04955e34 | 0.967470 | ||||||||
\(333\) | 1.03809e34 | 0.918834 | ||||||||
\(334\) | 7.02996e33 | 0.597551 | ||||||||
\(335\) | −8.39423e31 | −0.00685292 | ||||||||
\(336\) | 3.35002e33 | 0.262704 | ||||||||
\(337\) | −1.77892e34 | −1.34015 | −0.670074 | − | 0.742294i | \(-0.733738\pi\) | ||||
−0.670074 | + | 0.742294i | \(0.733738\pi\) | |||||||
\(338\) | −1.29864e34 | −0.939967 | ||||||||
\(339\) | 3.27529e34 | 2.27800 | ||||||||
\(340\) | 3.86703e33 | 0.258471 | ||||||||
\(341\) | 1.20784e34 | 0.775937 | ||||||||
\(342\) | −1.10769e34 | −0.684013 | ||||||||
\(343\) | 1.83369e34 | 1.08857 | ||||||||
\(344\) | −2.60140e32 | −0.0148480 | ||||||||
\(345\) | 1.48345e34 | 0.814172 | ||||||||
\(346\) | −1.04893e34 | −0.553628 | ||||||||
\(347\) | −6.67131e32 | −0.0338660 | −0.0169330 | − | 0.999857i | \(-0.505390\pi\) | ||||
−0.0169330 | + | 0.999857i | \(0.505390\pi\) | |||||||
\(348\) | −1.27454e34 | −0.622351 | ||||||||
\(349\) | −9.29683e33 | −0.436708 | −0.218354 | − | 0.975870i | \(-0.570069\pi\) | ||||
−0.218354 | + | 0.975870i | \(0.570069\pi\) | |||||||
\(350\) | 2.57416e33 | 0.116337 | ||||||||
\(351\) | 1.65099e34 | 0.717959 | ||||||||
\(352\) | 7.40201e33 | 0.309759 | ||||||||
\(353\) | −2.79504e34 | −1.12572 | −0.562859 | − | 0.826553i | \(-0.690299\pi\) | ||||
−0.562859 | + | 0.826553i | \(0.690299\pi\) | |||||||
\(354\) | −2.01164e34 | −0.779841 | ||||||||
\(355\) | −2.06328e33 | −0.0769973 | ||||||||
\(356\) | −4.24796e33 | −0.152618 | ||||||||
\(357\) | 3.51136e34 | 1.21466 | ||||||||
\(358\) | 3.88381e34 | 1.29371 | ||||||||
\(359\) | −4.42700e34 | −1.42015 | −0.710075 | − | 0.704126i | \(-0.751339\pi\) | ||||
−0.710075 | + | 0.704126i | \(0.751339\pi\) | |||||||
\(360\) | −3.23287e33 | −0.0998860 | ||||||||
\(361\) | 4.51830e34 | 1.34471 | ||||||||
\(362\) | 3.24787e34 | 0.931179 | ||||||||
\(363\) | −9.57464e34 | −2.64474 | ||||||||
\(364\) | −2.35860e34 | −0.627749 | ||||||||
\(365\) | −6.76129e33 | −0.173411 | ||||||||
\(366\) | −4.80089e34 | −1.18666 | ||||||||
\(367\) | −4.21004e34 | −1.00298 | −0.501492 | − | 0.865162i | \(-0.667215\pi\) | ||||
−0.501492 | + | 0.865162i | \(0.667215\pi\) | |||||||
\(368\) | −1.55154e34 | −0.356300 | ||||||||
\(369\) | −2.76451e34 | −0.612015 | ||||||||
\(370\) | −2.15489e34 | −0.459941 | ||||||||
\(371\) | −2.47386e34 | −0.509129 | ||||||||
\(372\) | 1.42512e34 | 0.282828 | ||||||||
\(373\) | −5.44723e34 | −1.04257 | −0.521287 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521287 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(374\) | 7.75849e34 | 1.43222 | ||||||||
\(375\) | −6.41641e33 | −0.114254 | ||||||||
\(376\) | 7.50853e33 | 0.128979 | ||||||||
\(377\) | 8.97352e34 | 1.48715 | ||||||||
\(378\) | 1.71124e34 | 0.273636 | ||||||||
\(379\) | 8.74120e34 | 1.34878 | 0.674391 | − | 0.738374i | \(-0.264406\pi\) | ||||
0.674391 | + | 0.738374i | \(0.264406\pi\) | |||||||
\(380\) | 2.29937e34 | 0.342397 | ||||||||
\(381\) | −4.75568e34 | −0.683480 | ||||||||
\(382\) | −6.98957e34 | −0.969606 | ||||||||
\(383\) | −7.39769e34 | −0.990632 | −0.495316 | − | 0.868713i | \(-0.664948\pi\) | ||||
−0.495316 | + | 0.868713i | \(0.664948\pi\) | |||||||
\(384\) | 8.73356e33 | 0.112907 | ||||||||
\(385\) | 5.16459e34 | 0.644638 | ||||||||
\(386\) | 1.08880e35 | 1.31226 | ||||||||
\(387\) | 2.27953e33 | 0.0265307 | ||||||||
\(388\) | −3.99934e34 | −0.449532 | ||||||||
\(389\) | 6.86864e34 | 0.745677 | 0.372839 | − | 0.927896i | \(-0.378385\pi\) | ||||
0.372839 | + | 0.927896i | \(0.378385\pi\) | |||||||
\(390\) | 5.87910e34 | 0.616508 | ||||||||
\(391\) | −1.62626e35 | −1.64741 | ||||||||
\(392\) | 1.16790e34 | 0.114299 | ||||||||
\(393\) | 4.33238e34 | 0.409664 | ||||||||
\(394\) | 6.88400e34 | 0.628987 | ||||||||
\(395\) | −6.12881e33 | −0.0541147 | ||||||||
\(396\) | −6.48617e34 | −0.553482 | ||||||||
\(397\) | 1.09834e35 | 0.905868 | 0.452934 | − | 0.891544i | \(-0.350377\pi\) | ||||
0.452934 | + | 0.891544i | \(0.350377\pi\) | |||||||
\(398\) | −1.53618e35 | −1.22467 | ||||||||
\(399\) | 2.08788e35 | 1.60906 | ||||||||
\(400\) | 6.71089e33 | 0.0500000 | ||||||||
\(401\) | 1.31925e35 | 0.950336 | 0.475168 | − | 0.879895i | \(-0.342387\pi\) | ||||
0.475168 | + | 0.879895i | \(0.342387\pi\) | |||||||
\(402\) | −1.98711e33 | −0.0138411 | ||||||||
\(403\) | −1.00337e35 | −0.675837 | ||||||||
\(404\) | −4.03832e34 | −0.263058 | ||||||||
\(405\) | −8.74976e34 | −0.551256 | ||||||||
\(406\) | 9.30099e34 | 0.566797 | ||||||||
\(407\) | −4.32340e35 | −2.54860 | ||||||||
\(408\) | 9.15417e34 | 0.522043 | ||||||||
\(409\) | 1.07033e35 | 0.590544 | 0.295272 | − | 0.955413i | \(-0.404590\pi\) | ||||
0.295272 | + | 0.955413i | \(0.404590\pi\) | |||||||
\(410\) | 5.73864e34 | 0.306356 | ||||||||
\(411\) | −2.74268e35 | −1.41681 | ||||||||
\(412\) | 3.58906e34 | 0.179419 | ||||||||
\(413\) | 1.46799e35 | 0.710229 | ||||||||
\(414\) | 1.35957e35 | 0.636643 | ||||||||
\(415\) | 1.90911e35 | 0.865331 | ||||||||
\(416\) | −6.14892e34 | −0.269798 | ||||||||
\(417\) | 2.14919e35 | 0.912930 | ||||||||
\(418\) | 4.61326e35 | 1.89727 | ||||||||
\(419\) | −2.62715e35 | −1.04615 | −0.523076 | − | 0.852286i | \(-0.675216\pi\) | ||||
−0.523076 | + | 0.852286i | \(0.675216\pi\) | |||||||
\(420\) | 6.09365e34 | 0.234970 | ||||||||
\(421\) | −1.82406e35 | −0.681131 | −0.340566 | − | 0.940221i | \(-0.610619\pi\) | ||||
−0.340566 | + | 0.940221i | \(0.610619\pi\) | |||||||
\(422\) | −3.76127e35 | −1.36024 | ||||||||
\(423\) | −6.57951e34 | −0.230462 | ||||||||
\(424\) | −6.44940e34 | −0.218817 | ||||||||
\(425\) | 7.03408e34 | 0.231184 | ||||||||
\(426\) | −4.88427e34 | −0.155514 | ||||||||
\(427\) | 3.50345e35 | 1.08074 | ||||||||
\(428\) | −1.52637e35 | −0.456214 | ||||||||
\(429\) | 1.17954e36 | 3.41616 | ||||||||
\(430\) | −4.73192e33 | −0.0132805 | ||||||||
\(431\) | 1.35228e35 | 0.367810 | 0.183905 | − | 0.982944i | \(-0.441126\pi\) | ||||
0.183905 | + | 0.982944i | \(0.441126\pi\) | |||||||
\(432\) | 4.46125e34 | 0.117605 | ||||||||
\(433\) | −3.26767e35 | −0.834934 | −0.417467 | − | 0.908692i | \(-0.637082\pi\) | ||||
−0.417467 | + | 0.908692i | \(0.637082\pi\) | |||||||
\(434\) | −1.03998e35 | −0.257582 | ||||||||
\(435\) | −2.31838e35 | −0.556648 | ||||||||
\(436\) | −1.75594e35 | −0.408736 | ||||||||
\(437\) | −9.66985e35 | −2.18233 | ||||||||
\(438\) | −1.60056e35 | −0.350244 | ||||||||
\(439\) | −5.20602e35 | −1.10468 | −0.552338 | − | 0.833620i | \(-0.686264\pi\) | ||||
−0.552338 | + | 0.833620i | \(0.686264\pi\) | |||||||
\(440\) | 1.34642e35 | 0.277057 | ||||||||
\(441\) | −1.02340e35 | −0.204232 | ||||||||
\(442\) | −6.44505e35 | −1.24746 | ||||||||
\(443\) | −7.68224e35 | −1.44224 | −0.721120 | − | 0.692810i | \(-0.756372\pi\) | ||||
−0.721120 | + | 0.692810i | \(0.756372\pi\) | |||||||
\(444\) | −5.10114e35 | −0.928960 | ||||||||
\(445\) | −7.72700e34 | −0.136506 | ||||||||
\(446\) | −4.49655e35 | −0.770652 | ||||||||
\(447\) | 3.73559e35 | 0.621166 | ||||||||
\(448\) | −6.37332e34 | −0.102828 | ||||||||
\(449\) | 5.97023e35 | 0.934686 | 0.467343 | − | 0.884076i | \(-0.345211\pi\) | ||||
0.467343 | + | 0.884076i | \(0.345211\pi\) | |||||||
\(450\) | −5.88056e34 | −0.0893408 | ||||||||
\(451\) | 1.15135e36 | 1.69756 | ||||||||
\(452\) | −6.23115e35 | −0.891660 | ||||||||
\(453\) | −1.16080e35 | −0.161225 | ||||||||
\(454\) | 3.71527e35 | 0.500883 | ||||||||
\(455\) | −4.29028e35 | −0.561476 | ||||||||
\(456\) | 5.44314e35 | 0.691551 | ||||||||
\(457\) | 1.24389e36 | 1.53431 | 0.767154 | − | 0.641463i | \(-0.221672\pi\) | ||||
0.767154 | + | 0.641463i | \(0.221672\pi\) | |||||||
\(458\) | −3.22968e34 | −0.0386790 | ||||||||
\(459\) | 4.67610e35 | 0.543767 | ||||||||
\(460\) | −2.82223e35 | −0.318685 | ||||||||
\(461\) | −4.50718e35 | −0.494245 | −0.247122 | − | 0.968984i | \(-0.579485\pi\) | ||||
−0.247122 | + | 0.968984i | \(0.579485\pi\) | |||||||
\(462\) | 1.22258e36 | 1.30200 | ||||||||
\(463\) | 3.06062e35 | 0.316568 | 0.158284 | − | 0.987394i | \(-0.449404\pi\) | ||||
0.158284 | + | 0.987394i | \(0.449404\pi\) | |||||||
\(464\) | 2.42479e35 | 0.243602 | ||||||||
\(465\) | 2.59228e35 | 0.252969 | ||||||||
\(466\) | −3.85978e35 | −0.365892 | ||||||||
\(467\) | 2.48619e35 | 0.228958 | 0.114479 | − | 0.993426i | \(-0.463480\pi\) | ||||
0.114479 | + | 0.993426i | \(0.463480\pi\) | |||||||
\(468\) | 5.38813e35 | 0.482080 | ||||||||
\(469\) | 1.45010e34 | 0.0126056 | ||||||||
\(470\) | 1.36579e35 | 0.115362 | ||||||||
\(471\) | 3.94833e35 | 0.324064 | ||||||||
\(472\) | 3.82709e35 | 0.305247 | ||||||||
\(473\) | −9.49374e34 | −0.0735888 | ||||||||
\(474\) | −1.45083e35 | −0.109298 | ||||||||
\(475\) | 4.18252e35 | 0.306249 | ||||||||
\(476\) | −6.68025e35 | −0.475444 | ||||||||
\(477\) | 5.65143e35 | 0.390985 | ||||||||
\(478\) | 4.83330e35 | 0.325063 | ||||||||
\(479\) | −2.43474e36 | −1.59193 | −0.795964 | − | 0.605344i | \(-0.793036\pi\) | ||||
−0.795964 | + | 0.605344i | \(0.793036\pi\) | |||||||
\(480\) | 1.58863e35 | 0.100987 | ||||||||
\(481\) | 3.59149e36 | 2.21981 | ||||||||
\(482\) | 1.33003e36 | 0.799330 | ||||||||
\(483\) | −2.56265e36 | −1.49763 | ||||||||
\(484\) | 1.82155e36 | 1.03521 | ||||||||
\(485\) | −7.27476e35 | −0.402073 | ||||||||
\(486\) | −1.45246e36 | −0.780755 | ||||||||
\(487\) | −1.21293e35 | −0.0634154 | −0.0317077 | − | 0.999497i | \(-0.510095\pi\) | ||||
−0.0317077 | + | 0.999497i | \(0.510095\pi\) | |||||||
\(488\) | 9.13356e35 | 0.464486 | ||||||||
\(489\) | −3.56414e36 | −1.76313 | ||||||||
\(490\) | 2.12439e35 | 0.102232 | ||||||||
\(491\) | 6.41302e35 | 0.300236 | 0.150118 | − | 0.988668i | \(-0.452035\pi\) | ||||
0.150118 | + | 0.988668i | \(0.452035\pi\) | |||||||
\(492\) | 1.35847e36 | 0.618759 | ||||||||
\(493\) | 2.54156e36 | 1.12633 | ||||||||
\(494\) | −3.83228e36 | −1.65251 | ||||||||
\(495\) | −1.17983e36 | −0.495049 | ||||||||
\(496\) | −2.71125e35 | −0.110705 | ||||||||
\(497\) | 3.56430e35 | 0.141633 | ||||||||
\(498\) | 4.51932e36 | 1.74774 | ||||||||
\(499\) | −4.09067e36 | −1.53970 | −0.769851 | − | 0.638223i | \(-0.779670\pi\) | ||||
−0.769851 | + | 0.638223i | \(0.779670\pi\) | |||||||
\(500\) | 1.22070e35 | 0.0447214 | ||||||||
\(501\) | 3.02708e36 | 1.07948 | ||||||||
\(502\) | −2.16781e36 | −0.752524 | ||||||||
\(503\) | −5.43130e35 | −0.183542 | −0.0917710 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917710 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(504\) | 5.58476e35 | 0.183735 | ||||||||
\(505\) | −7.34566e35 | −0.235287 | ||||||||
\(506\) | −5.66229e36 | −1.76587 | ||||||||
\(507\) | −5.59191e36 | −1.69806 | ||||||||
\(508\) | 9.04756e35 | 0.267529 | ||||||||
\(509\) | −1.01633e36 | −0.292646 | −0.146323 | − | 0.989237i | \(-0.546744\pi\) | ||||
−0.146323 | + | 0.989237i | \(0.546744\pi\) | |||||||
\(510\) | 1.66513e36 | 0.466930 | ||||||||
\(511\) | 1.16801e36 | 0.318980 | ||||||||
\(512\) | −1.66153e35 | −0.0441942 | ||||||||
\(513\) | 2.78045e36 | 0.720327 | ||||||||
\(514\) | −2.25123e35 | −0.0568091 | ||||||||
\(515\) | 6.52846e35 | 0.160477 | ||||||||
\(516\) | −1.12016e35 | −0.0268230 | ||||||||
\(517\) | 2.74022e36 | 0.639238 | ||||||||
\(518\) | 3.72256e36 | 0.846038 | ||||||||
\(519\) | −4.51666e36 | −1.00013 | ||||||||
\(520\) | −1.11848e36 | −0.241315 | ||||||||
\(521\) | −5.75177e36 | −1.20918 | −0.604592 | − | 0.796536i | \(-0.706664\pi\) | ||||
−0.604592 | + | 0.796536i | \(0.706664\pi\) | |||||||
\(522\) | −2.12477e36 | −0.435272 | ||||||||
\(523\) | −7.30952e35 | −0.145920 | −0.0729602 | − | 0.997335i | \(-0.523245\pi\) | ||||
−0.0729602 | + | 0.997335i | \(0.523245\pi\) | |||||||
\(524\) | −8.24224e35 | −0.160351 | ||||||||
\(525\) | 1.10843e36 | 0.210163 | ||||||||
\(526\) | 5.21719e36 | 0.964115 | ||||||||
\(527\) | −2.84183e36 | −0.511864 | ||||||||
\(528\) | 3.18729e36 | 0.559582 | ||||||||
\(529\) | 6.02551e36 | 1.03120 | ||||||||
\(530\) | −1.17314e36 | −0.195716 | ||||||||
\(531\) | −3.35357e36 | −0.545420 | ||||||||
\(532\) | −3.97213e36 | −0.629820 | ||||||||
\(533\) | −9.56441e36 | −1.47857 | ||||||||
\(534\) | −1.82916e36 | −0.275705 | ||||||||
\(535\) | −2.77645e36 | −0.408051 | ||||||||
\(536\) | 3.78042e34 | 0.00541771 | ||||||||
\(537\) | 1.67236e37 | 2.33710 | ||||||||
\(538\) | 2.16923e36 | 0.295628 | ||||||||
\(539\) | 4.26221e36 | 0.566483 | ||||||||
\(540\) | 8.11496e35 | 0.105189 | ||||||||
\(541\) | 1.06277e37 | 1.34362 | 0.671812 | − | 0.740721i | \(-0.265516\pi\) | ||||
0.671812 | + | 0.740721i | \(0.265516\pi\) | |||||||
\(542\) | 7.42494e36 | 0.915594 | ||||||||
\(543\) | 1.39853e37 | 1.68218 | ||||||||
\(544\) | −1.74155e36 | −0.204339 | ||||||||
\(545\) | −3.19404e36 | −0.365584 | ||||||||
\(546\) | −1.01561e37 | −1.13403 | ||||||||
\(547\) | 3.13391e36 | 0.341396 | 0.170698 | − | 0.985323i | \(-0.445398\pi\) | ||||
0.170698 | + | 0.985323i | \(0.445398\pi\) | |||||||
\(548\) | 5.21787e36 | 0.554569 | ||||||||
\(549\) | −8.00348e36 | −0.829950 | ||||||||
\(550\) | 2.44912e36 | 0.247807 | ||||||||
\(551\) | 1.51123e37 | 1.49206 | ||||||||
\(552\) | −6.68088e36 | −0.643659 | ||||||||
\(553\) | 1.05875e36 | 0.0995412 | ||||||||
\(554\) | −5.53954e36 | −0.508267 | ||||||||
\(555\) | −9.27892e36 | −0.830887 | ||||||||
\(556\) | −4.08877e36 | −0.357341 | ||||||||
\(557\) | −1.82733e37 | −1.55874 | −0.779368 | − | 0.626566i | \(-0.784460\pi\) | ||||
−0.779368 | + | 0.626566i | \(0.784460\pi\) | |||||||
\(558\) | 2.37580e36 | 0.197810 | ||||||||
\(559\) | 7.88654e35 | 0.0640954 | ||||||||
\(560\) | −1.15930e36 | −0.0919724 | ||||||||
\(561\) | 3.34079e37 | 2.58732 | ||||||||
\(562\) | −8.00958e36 | −0.605577 | ||||||||
\(563\) | −6.65901e36 | −0.491526 | −0.245763 | − | 0.969330i | \(-0.579038\pi\) | ||||
−0.245763 | + | 0.969330i | \(0.579038\pi\) | |||||||
\(564\) | 3.23315e36 | 0.233001 | ||||||||
\(565\) | −1.13344e37 | −0.797525 | ||||||||
\(566\) | −1.20535e36 | −0.0828117 | ||||||||
\(567\) | 1.51151e37 | 1.01401 | ||||||||
\(568\) | 9.29219e35 | 0.0608717 | ||||||||
\(569\) | 1.71644e37 | 1.09802 | 0.549012 | − | 0.835814i | \(-0.315004\pi\) | ||||
0.549012 | + | 0.835814i | \(0.315004\pi\) | |||||||
\(570\) | 9.90101e36 | 0.618542 | ||||||||
\(571\) | −1.61696e37 | −0.986535 | −0.493267 | − | 0.869878i | \(-0.664198\pi\) | ||||
−0.493267 | + | 0.869878i | \(0.664198\pi\) | |||||||
\(572\) | −2.24403e37 | −1.33716 | ||||||||
\(573\) | −3.00969e37 | −1.75160 | ||||||||
\(574\) | −9.91345e36 | −0.563526 | ||||||||
\(575\) | −5.13360e36 | −0.285040 | ||||||||
\(576\) | 1.45596e36 | 0.0789668 | ||||||||
\(577\) | 2.68745e37 | 1.42386 | 0.711929 | − | 0.702251i | \(-0.247822\pi\) | ||||
0.711929 | + | 0.702251i | \(0.247822\pi\) | |||||||
\(578\) | −4.59238e36 | −0.237691 | ||||||||
\(579\) | 4.68835e37 | 2.37061 | ||||||||
\(580\) | 4.41066e36 | 0.217884 | ||||||||
\(581\) | −3.29797e37 | −1.59173 | ||||||||
\(582\) | −1.72211e37 | −0.812082 | ||||||||
\(583\) | −2.35369e37 | −1.08449 | ||||||||
\(584\) | 3.04501e36 | 0.137093 | ||||||||
\(585\) | 9.80094e36 | 0.431185 | ||||||||
\(586\) | 3.90555e36 | 0.167905 | ||||||||
\(587\) | 2.21802e37 | 0.931860 | 0.465930 | − | 0.884822i | \(-0.345720\pi\) | ||||
0.465930 | + | 0.884822i | \(0.345720\pi\) | |||||||
\(588\) | 5.02894e36 | 0.206482 | ||||||||
\(589\) | −1.68977e37 | −0.678066 | ||||||||
\(590\) | 6.96143e36 | 0.273021 | ||||||||
\(591\) | 2.96424e37 | 1.13627 | ||||||||
\(592\) | 9.70477e36 | 0.363615 | ||||||||
\(593\) | −3.27250e37 | −1.19851 | −0.599255 | − | 0.800558i | \(-0.704536\pi\) | ||||
−0.599255 | + | 0.800558i | \(0.704536\pi\) | |||||||
\(594\) | 1.62812e37 | 0.582867 | ||||||||
\(595\) | −1.21513e37 | −0.425250 | ||||||||
\(596\) | −7.10686e36 | −0.243138 | ||||||||
\(597\) | −6.61475e37 | −2.21238 | ||||||||
\(598\) | 4.70372e37 | 1.53807 | ||||||||
\(599\) | −5.26063e37 | −1.68180 | −0.840902 | − | 0.541187i | \(-0.817975\pi\) | ||||
−0.840902 | + | 0.541187i | \(0.817975\pi\) | |||||||
\(600\) | 2.88969e36 | 0.0903254 | ||||||||
\(601\) | −3.25919e37 | −0.996102 | −0.498051 | − | 0.867148i | \(-0.665951\pi\) | ||||
−0.498051 | + | 0.867148i | \(0.665951\pi\) | |||||||
\(602\) | 8.17435e35 | 0.0244287 | ||||||||
\(603\) | −3.31268e35 | −0.00968045 | ||||||||
\(604\) | 2.20839e36 | 0.0631070 | ||||||||
\(605\) | 3.31338e37 | 0.925919 | ||||||||
\(606\) | −1.73889e37 | −0.475217 | ||||||||
\(607\) | −1.02382e37 | −0.273637 | −0.136818 | − | 0.990596i | \(-0.543688\pi\) | ||||
−0.136818 | + | 0.990596i | \(0.543688\pi\) | |||||||
\(608\) | −1.03554e37 | −0.270688 | ||||||||
\(609\) | 4.00499e37 | 1.02392 | ||||||||
\(610\) | 1.66138e37 | 0.415449 | ||||||||
\(611\) | −2.27632e37 | −0.556773 | ||||||||
\(612\) | 1.52607e37 | 0.365117 | ||||||||
\(613\) | −2.22273e37 | −0.520201 | −0.260100 | − | 0.965582i | \(-0.583756\pi\) | ||||
−0.260100 | + | 0.965582i | \(0.583756\pi\) | |||||||
\(614\) | 1.61956e37 | 0.370786 | ||||||||
\(615\) | 2.47105e37 | 0.553435 | ||||||||
\(616\) | −2.32593e37 | −0.509631 | ||||||||
\(617\) | −3.05546e37 | −0.654978 | −0.327489 | − | 0.944855i | \(-0.606202\pi\) | ||||
−0.327489 | + | 0.944855i | \(0.606202\pi\) | |||||||
\(618\) | 1.54544e37 | 0.324122 | ||||||||
\(619\) | −1.32801e37 | −0.272507 | −0.136254 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136254 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(620\) | −4.93174e36 | −0.0990177 | ||||||||
\(621\) | −3.41270e37 | −0.670443 | ||||||||
\(622\) | 3.30156e37 | 0.634672 | ||||||||
\(623\) | 1.33483e37 | 0.251095 | ||||||||
\(624\) | −2.64771e37 | −0.487392 | ||||||||
\(625\) | 2.22045e36 | 0.0400000 | ||||||||
\(626\) | −9.17269e36 | −0.161712 | ||||||||
\(627\) | 1.98646e38 | 3.42742 | ||||||||
\(628\) | −7.51158e36 | −0.126846 | ||||||||
\(629\) | 1.01722e38 | 1.68124 | ||||||||
\(630\) | 1.01586e37 | 0.164338 | ||||||||
\(631\) | 8.40893e37 | 1.33151 | 0.665755 | − | 0.746171i | \(-0.268110\pi\) | ||||
0.665755 | + | 0.746171i | \(0.268110\pi\) | |||||||
\(632\) | 2.76017e36 | 0.0427815 | ||||||||
\(633\) | −1.61959e38 | −2.45729 | ||||||||
\(634\) | 4.93384e37 | 0.732790 | ||||||||
\(635\) | 1.64574e37 | 0.239285 | ||||||||
\(636\) | −2.77710e37 | −0.395294 | ||||||||
\(637\) | −3.54066e37 | −0.493403 | ||||||||
\(638\) | 8.84919e37 | 1.20733 | ||||||||
\(639\) | −8.14249e36 | −0.108767 | ||||||||
\(640\) | −3.02231e36 | −0.0395285 | ||||||||
\(641\) | 7.86398e37 | 1.00707 | 0.503534 | − | 0.863975i | \(-0.332033\pi\) | ||||
0.503534 | + | 0.863975i | \(0.332033\pi\) | |||||||
\(642\) | −6.57252e37 | −0.824155 | ||||||||
\(643\) | 1.16284e38 | 1.42781 | 0.713904 | − | 0.700243i | \(-0.246925\pi\) | ||||
0.713904 | + | 0.700243i | \(0.246925\pi\) | |||||||
\(644\) | 4.87537e37 | 0.586204 | ||||||||
\(645\) | −2.03755e36 | −0.0239913 | ||||||||
\(646\) | −1.08541e38 | −1.25157 | ||||||||
\(647\) | −7.65469e37 | −0.864410 | −0.432205 | − | 0.901775i | \(-0.642264\pi\) | ||||
−0.432205 | + | 0.901775i | \(0.642264\pi\) | |||||||
\(648\) | 3.94054e37 | 0.435806 | ||||||||
\(649\) | 1.39669e38 | 1.51285 | ||||||||
\(650\) | −2.03451e37 | −0.215839 | ||||||||
\(651\) | −4.47814e37 | −0.465323 | ||||||||
\(652\) | 6.78067e37 | 0.690128 | ||||||||
\(653\) | −1.03403e38 | −1.03087 | −0.515436 | − | 0.856928i | \(-0.672370\pi\) | ||||
−0.515436 | + | 0.856928i | \(0.672370\pi\) | |||||||
\(654\) | −7.56105e37 | −0.738384 | ||||||||
\(655\) | −1.49925e37 | −0.143423 | ||||||||
\(656\) | −2.58445e37 | −0.242196 | ||||||||
\(657\) | −2.66826e37 | −0.244960 | ||||||||
\(658\) | −2.35939e37 | −0.212203 | ||||||||
\(659\) | −5.24833e37 | −0.462453 | −0.231227 | − | 0.972900i | \(-0.574274\pi\) | ||||
−0.231227 | + | 0.972900i | \(0.574274\pi\) | |||||||
\(660\) | 5.79765e37 | 0.500505 | ||||||||
\(661\) | −1.14190e38 | −0.965846 | −0.482923 | − | 0.875663i | \(-0.660425\pi\) | ||||
−0.482923 | + | 0.875663i | \(0.660425\pi\) | |||||||
\(662\) | 3.22292e37 | 0.267096 | ||||||||
\(663\) | −2.77523e38 | −2.25354 | ||||||||
\(664\) | −8.59788e37 | −0.684104 | ||||||||
\(665\) | −7.22527e37 | −0.563328 | ||||||||
\(666\) | −8.50402e37 | −0.649714 | ||||||||
\(667\) | −1.85488e38 | −1.38873 | ||||||||
\(668\) | −5.75894e37 | −0.422533 | ||||||||
\(669\) | −1.93620e38 | −1.39219 | ||||||||
\(670\) | 6.87655e35 | 0.00484575 | ||||||||
\(671\) | 3.33327e38 | 2.30206 | ||||||||
\(672\) | −2.74434e37 | −0.185760 | ||||||||
\(673\) | 3.00048e36 | 0.0199061 | 0.00995307 | − | 0.999950i | \(-0.496832\pi\) | ||||
0.00995307 | + | 0.999950i | \(0.496832\pi\) | |||||||
\(674\) | 1.45729e38 | 0.947628 | ||||||||
\(675\) | 1.47610e37 | 0.0940840 | ||||||||
\(676\) | 1.06384e38 | 0.664657 | ||||||||
\(677\) | 2.27686e38 | 1.39441 | 0.697204 | − | 0.716873i | \(-0.254427\pi\) | ||||
0.697204 | + | 0.716873i | \(0.254427\pi\) | |||||||
\(678\) | −2.68312e38 | −1.61079 | ||||||||
\(679\) | 1.25671e38 | 0.739593 | ||||||||
\(680\) | −3.16787e37 | −0.182767 | ||||||||
\(681\) | 1.59979e38 | 0.904848 | ||||||||
\(682\) | −9.89465e37 | −0.548670 | ||||||||
\(683\) | −1.59944e37 | −0.0869538 | −0.0434769 | − | 0.999054i | \(-0.513843\pi\) | ||||
−0.0434769 | + | 0.999054i | \(0.513843\pi\) | |||||||
\(684\) | 9.07416e37 | 0.483670 | ||||||||
\(685\) | 9.49125e37 | 0.496022 | ||||||||
\(686\) | −1.50216e38 | −0.769735 | ||||||||
\(687\) | −1.39069e37 | −0.0698739 | ||||||||
\(688\) | 2.13107e36 | 0.0104991 | ||||||||
\(689\) | 1.95524e38 | 0.944582 | ||||||||
\(690\) | −1.21524e38 | −0.575706 | ||||||||
\(691\) | 1.56832e38 | 0.728586 | 0.364293 | − | 0.931284i | \(-0.381311\pi\) | ||||
0.364293 | + | 0.931284i | \(0.381311\pi\) | |||||||
\(692\) | 8.59282e37 | 0.391474 | ||||||||
\(693\) | 2.03814e38 | 0.910617 | ||||||||
\(694\) | 5.46514e36 | 0.0239469 | ||||||||
\(695\) | −7.43743e37 | −0.319616 | ||||||||
\(696\) | 1.04411e38 | 0.440069 | ||||||||
\(697\) | −2.70892e38 | −1.11983 | ||||||||
\(698\) | 7.61596e37 | 0.308799 | ||||||||
\(699\) | −1.66201e38 | −0.660987 | ||||||||
\(700\) | −2.10875e37 | −0.0822626 | ||||||||
\(701\) | −2.65673e38 | −1.01661 | −0.508304 | − | 0.861178i | \(-0.669727\pi\) | ||||
−0.508304 | + | 0.861178i | \(0.669727\pi\) | |||||||
\(702\) | −1.35249e38 | −0.507674 | ||||||||
\(703\) | 6.04844e38 | 2.22714 | ||||||||
\(704\) | −6.06373e37 | −0.219033 | ||||||||
\(705\) | 5.88107e37 | 0.208403 | ||||||||
\(706\) | 2.28970e38 | 0.796004 | ||||||||
\(707\) | 1.26896e38 | 0.432797 | ||||||||
\(708\) | 1.64793e38 | 0.551431 | ||||||||
\(709\) | −3.14013e38 | −1.03092 | −0.515458 | − | 0.856915i | \(-0.672378\pi\) | ||||
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(710\) | 1.69024e37 | 0.0544453 | ||||||||
\(711\) | −2.41866e37 | −0.0764426 | ||||||||
\(712\) | 3.47993e37 | 0.107917 | ||||||||
\(713\) | 2.07402e38 | 0.631108 | ||||||||
\(714\) | −2.87650e38 | −0.858893 | ||||||||
\(715\) | −4.08187e38 | −1.19599 | ||||||||
\(716\) | −3.18162e38 | −0.914791 | ||||||||
\(717\) | 2.08121e38 | 0.587228 | ||||||||
\(718\) | 3.62660e38 | 1.00420 | ||||||||
\(719\) | 1.32586e38 | 0.360295 | 0.180147 | − | 0.983640i | \(-0.442343\pi\) | ||||
0.180147 | + | 0.983640i | \(0.442343\pi\) | |||||||
\(720\) | 2.64837e37 | 0.0706301 | ||||||||
\(721\) | −1.12779e38 | −0.295189 | ||||||||
\(722\) | −3.70139e38 | −0.950852 | ||||||||
\(723\) | 5.72708e38 | 1.44400 | ||||||||
\(724\) | −2.66066e38 | −0.658443 | ||||||||
\(725\) | 8.02294e37 | 0.194881 | ||||||||
\(726\) | 7.84354e38 | 1.87011 | ||||||||
\(727\) | −3.02965e38 | −0.709051 | −0.354525 | − | 0.935046i | \(-0.615358\pi\) | ||||
−0.354525 | + | 0.935046i | \(0.615358\pi\) | |||||||
\(728\) | 1.93217e38 | 0.443886 | ||||||||
\(729\) | −7.88385e37 | −0.177794 | ||||||||
\(730\) | 5.53884e37 | 0.122620 | ||||||||
\(731\) | 2.23370e37 | 0.0485445 | ||||||||
\(732\) | 3.93289e38 | 0.839097 | ||||||||
\(733\) | −6.47887e38 | −1.35705 | −0.678525 | − | 0.734578i | \(-0.737380\pi\) | ||||
−0.678525 | + | 0.734578i | \(0.737380\pi\) | |||||||
\(734\) | 3.44886e38 | 0.709217 | ||||||||
\(735\) | 9.14760e37 | 0.184683 | ||||||||
\(736\) | 1.27102e38 | 0.251942 | ||||||||
\(737\) | 1.37966e37 | 0.0268510 | ||||||||
\(738\) | 2.26468e38 | 0.432760 | ||||||||
\(739\) | −5.25007e38 | −0.985065 | −0.492533 | − | 0.870294i | \(-0.663929\pi\) | ||||
−0.492533 | + | 0.870294i | \(0.663929\pi\) | |||||||
\(740\) | 1.76529e38 | 0.325228 | ||||||||
\(741\) | −1.65017e39 | −2.98527 | ||||||||
\(742\) | 2.02659e38 | 0.360009 | ||||||||
\(743\) | 1.07441e39 | 1.87423 | 0.937113 | − | 0.349027i | \(-0.113488\pi\) | ||||
0.937113 | + | 0.349027i | \(0.113488\pi\) | |||||||
\(744\) | −1.16746e38 | −0.199990 | ||||||||
\(745\) | −1.29273e38 | −0.217469 | ||||||||
\(746\) | 4.46237e38 | 0.737211 | ||||||||
\(747\) | 7.53408e38 | 1.22237 | ||||||||
\(748\) | −6.35576e38 | −1.01273 | ||||||||
\(749\) | 4.79629e38 | 0.750587 | ||||||||
\(750\) | 5.25632e37 | 0.0807895 | ||||||||
\(751\) | −6.49718e38 | −0.980812 | −0.490406 | − | 0.871494i | \(-0.663152\pi\) | ||||
−0.490406 | + | 0.871494i | \(0.663152\pi\) | |||||||
\(752\) | −6.15098e37 | −0.0912019 | ||||||||
\(753\) | −9.33453e38 | −1.35944 | ||||||||
\(754\) | −7.35111e38 | −1.05157 | ||||||||
\(755\) | 4.01704e37 | 0.0564446 | ||||||||
\(756\) | −1.40185e38 | −0.193490 | ||||||||
\(757\) | −1.41452e38 | −0.191785 | −0.0958926 | − | 0.995392i | \(-0.530571\pi\) | ||||
−0.0958926 | + | 0.995392i | \(0.530571\pi\) | |||||||
\(758\) | −7.16079e38 | −0.953733 | ||||||||
\(759\) | −2.43817e39 | −3.19007 | ||||||||
\(760\) | −1.88364e38 | −0.242111 | ||||||||
\(761\) | 1.02263e39 | 1.29130 | 0.645650 | − | 0.763634i | \(-0.276587\pi\) | ||||
0.645650 | + | 0.763634i | \(0.276587\pi\) | |||||||
\(762\) | 3.89586e38 | 0.483293 | ||||||||
\(763\) | 5.51768e38 | 0.672473 | ||||||||
\(764\) | 5.72586e38 | 0.685615 | ||||||||
\(765\) | 2.77591e38 | 0.326570 | ||||||||
\(766\) | 6.06019e38 | 0.700483 | ||||||||
\(767\) | −1.16024e39 | −1.31768 | ||||||||
\(768\) | −7.15453e37 | −0.0798371 | ||||||||
\(769\) | 2.43418e38 | 0.266899 | 0.133449 | − | 0.991056i | \(-0.457395\pi\) | ||||
0.133449 | + | 0.991056i | \(0.457395\pi\) | |||||||
\(770\) | −4.23083e38 | −0.455828 | ||||||||
\(771\) | −9.69375e37 | −0.102626 | ||||||||
\(772\) | −8.91946e38 | −0.927908 | ||||||||
\(773\) | 1.87371e39 | 1.91548 | 0.957741 | − | 0.287632i | \(-0.0928679\pi\) | ||||
0.957741 | + | 0.287632i | \(0.0928679\pi\) | |||||||
\(774\) | −1.86739e37 | −0.0187600 | ||||||||
\(775\) | −8.97079e37 | −0.0885641 | ||||||||
\(776\) | 3.27626e38 | 0.317867 | ||||||||
\(777\) | 1.60292e39 | 1.52837 | ||||||||
\(778\) | −5.62679e38 | −0.527273 | ||||||||
\(779\) | −1.61075e39 | −1.48344 | ||||||||
\(780\) | −4.81616e38 | −0.435937 | ||||||||
\(781\) | 3.39116e38 | 0.301689 | ||||||||
\(782\) | 1.33223e39 | 1.16490 | ||||||||
\(783\) | 5.33347e38 | 0.458380 | ||||||||
\(784\) | −9.56742e37 | −0.0808217 | ||||||||
\(785\) | −1.36635e38 | −0.113454 | ||||||||
\(786\) | −3.54909e38 | −0.289676 | ||||||||
\(787\) | 1.05821e39 | 0.849007 | 0.424503 | − | 0.905426i | \(-0.360449\pi\) | ||||
0.424503 | + | 0.905426i | \(0.360449\pi\) | |||||||
\(788\) | −5.63937e38 | −0.444761 | ||||||||
\(789\) | 2.24651e39 | 1.74168 | ||||||||
\(790\) | 5.02072e37 | 0.0382649 | ||||||||
\(791\) | 1.95801e39 | 1.46701 | ||||||||
\(792\) | 5.31347e38 | 0.391371 | ||||||||
\(793\) | −2.76898e39 | −2.00508 | ||||||||
\(794\) | −8.99760e38 | −0.640546 | ||||||||
\(795\) | −5.05151e38 | −0.353562 | ||||||||
\(796\) | 1.25844e39 | 0.865975 | ||||||||
\(797\) | −1.98365e39 | −1.34208 | −0.671041 | − | 0.741421i | \(-0.734152\pi\) | ||||
−0.671041 | + | 0.741421i | \(0.734152\pi\) | |||||||
\(798\) | −1.71039e39 | −1.13778 | ||||||||
\(799\) | −6.44722e38 | −0.421687 | ||||||||
\(800\) | −5.49756e37 | −0.0353553 | ||||||||
\(801\) | −3.04936e38 | −0.192828 | ||||||||
\(802\) | −1.08073e39 | −0.671989 | ||||||||
\(803\) | 1.11127e39 | 0.679453 | ||||||||
\(804\) | 1.62784e37 | 0.00978714 | ||||||||
\(805\) | 8.86825e38 | 0.524316 | ||||||||
\(806\) | 8.21958e38 | 0.477889 | ||||||||
\(807\) | 9.34066e38 | 0.534053 | ||||||||
\(808\) | 3.30819e38 | 0.186010 | ||||||||
\(809\) | 2.34082e39 | 1.29438 | 0.647192 | − | 0.762327i | \(-0.275943\pi\) | ||||
0.647192 | + | 0.762327i | \(0.275943\pi\) | |||||||
\(810\) | 7.16780e38 | 0.389797 | ||||||||
\(811\) | −1.86049e39 | −0.995051 | −0.497525 | − | 0.867449i | \(-0.665758\pi\) | ||||
−0.497525 | + | 0.867449i | \(0.665758\pi\) | |||||||
\(812\) | −7.61937e38 | −0.400786 | ||||||||
\(813\) | 3.19716e39 | 1.65403 | ||||||||
\(814\) | 3.54173e39 | 1.80213 | ||||||||
\(815\) | 1.23340e39 | 0.617270 | ||||||||
\(816\) | −7.49909e38 | −0.369140 | ||||||||
\(817\) | 1.32818e38 | 0.0643069 | ||||||||
\(818\) | −8.76812e38 | −0.417577 | ||||||||
\(819\) | −1.69310e39 | −0.793142 | ||||||||
\(820\) | −4.70109e38 | −0.216627 | ||||||||
\(821\) | 2.17461e39 | 0.985710 | 0.492855 | − | 0.870112i | \(-0.335953\pi\) | ||||
0.492855 | + | 0.870112i | \(0.335953\pi\) | |||||||
\(822\) | 2.24680e39 | 1.00183 | ||||||||
\(823\) | −1.47840e39 | −0.648477 | −0.324239 | − | 0.945975i | \(-0.605108\pi\) | ||||
−0.324239 | + | 0.945975i | \(0.605108\pi\) | |||||||
\(824\) | −2.94016e38 | −0.126868 | ||||||||
\(825\) | 1.05459e39 | 0.447665 | ||||||||
\(826\) | −1.20258e39 | −0.502208 | ||||||||
\(827\) | −1.81409e39 | −0.745307 | −0.372654 | − | 0.927971i | \(-0.621552\pi\) | ||||
−0.372654 | + | 0.927971i | \(0.621552\pi\) | |||||||
\(828\) | −1.11376e39 | −0.450174 | ||||||||
\(829\) | 3.68398e39 | 1.46498 | 0.732489 | − | 0.680779i | \(-0.238359\pi\) | ||||
0.732489 | + | 0.680779i | \(0.238359\pi\) | |||||||
\(830\) | −1.56395e39 | −0.611881 | ||||||||
\(831\) | −2.38531e39 | −0.918188 | ||||||||
\(832\) | 5.03720e38 | 0.190776 | ||||||||
\(833\) | −1.00282e39 | −0.373693 | ||||||||
\(834\) | −1.76061e39 | −0.645539 | ||||||||
\(835\) | −1.04754e39 | −0.377925 | ||||||||
\(836\) | −3.77918e39 | −1.34157 | ||||||||
\(837\) | −5.96358e38 | −0.208311 | ||||||||
\(838\) | 2.15216e39 | 0.739742 | ||||||||
\(839\) | 3.62449e39 | 1.22591 | 0.612957 | − | 0.790116i | \(-0.289980\pi\) | ||||
0.612957 | + | 0.790116i | \(0.289980\pi\) | |||||||
\(840\) | −4.99192e38 | −0.166149 | ||||||||
\(841\) | −1.54276e38 | −0.0505304 | ||||||||
\(842\) | 1.49427e39 | 0.481632 | ||||||||
\(843\) | −3.44891e39 | −1.09398 | ||||||||
\(844\) | 3.08123e39 | 0.961837 | ||||||||
\(845\) | 1.93512e39 | 0.594487 | ||||||||
\(846\) | 5.38993e38 | 0.162961 | ||||||||
\(847\) | −5.72383e39 | −1.70318 | ||||||||
\(848\) | 5.28335e38 | 0.154727 | ||||||||
\(849\) | −5.19021e38 | −0.149600 | ||||||||
\(850\) | −5.76232e38 | −0.163471 | ||||||||
\(851\) | −7.42382e39 | −2.07290 | ||||||||
\(852\) | 4.00120e38 | 0.109965 | ||||||||
\(853\) | 7.16984e39 | 1.93953 | 0.969767 | − | 0.244031i | \(-0.0784699\pi\) | ||||
0.969767 | + | 0.244031i | \(0.0784699\pi\) | |||||||
\(854\) | −2.87003e39 | −0.764196 | ||||||||
\(855\) | 1.65058e39 | 0.432608 | ||||||||
\(856\) | 1.25040e39 | 0.322592 | ||||||||
\(857\) | −5.79545e39 | −1.47179 | −0.735896 | − | 0.677095i | \(-0.763239\pi\) | ||||
−0.735896 | + | 0.677095i | \(0.763239\pi\) | |||||||
\(858\) | −9.66276e39 | −2.41559 | ||||||||
\(859\) | 1.97147e39 | 0.485156 | 0.242578 | − | 0.970132i | \(-0.422007\pi\) | ||||
0.242578 | + | 0.970132i | \(0.422007\pi\) | |||||||
\(860\) | 3.87639e37 | 0.00939070 | ||||||||
\(861\) | −4.26871e39 | −1.01801 | ||||||||
\(862\) | −1.10779e39 | −0.260081 | ||||||||
\(863\) | −1.32958e39 | −0.307305 | −0.153652 | − | 0.988125i | \(-0.549104\pi\) | ||||
−0.153652 | + | 0.988125i | \(0.549104\pi\) | |||||||
\(864\) | −3.65465e38 | −0.0831593 | ||||||||
\(865\) | 1.56302e39 | 0.350145 | ||||||||
\(866\) | 2.67688e39 | 0.590387 | ||||||||
\(867\) | −1.97747e39 | −0.429390 | ||||||||
\(868\) | 8.51954e38 | 0.182138 | ||||||||
\(869\) | 1.00732e39 | 0.212031 | ||||||||
\(870\) | 1.89922e39 | 0.393609 | ||||||||
\(871\) | −1.14609e38 | −0.0233870 | ||||||||
\(872\) | 1.43847e39 | 0.289020 | ||||||||
\(873\) | −2.87090e39 | −0.567970 | ||||||||
\(874\) | 7.92154e39 | 1.54314 | ||||||||
\(875\) | −3.83580e38 | −0.0735779 | ||||||||
\(876\) | 1.31118e39 | 0.247660 | ||||||||
\(877\) | −7.27571e39 | −1.35326 | −0.676629 | − | 0.736324i | \(-0.736560\pi\) | ||||
−0.676629 | + | 0.736324i | \(0.736560\pi\) | |||||||
\(878\) | 4.26477e39 | 0.781124 | ||||||||
\(879\) | 1.68172e39 | 0.303322 | ||||||||
\(880\) | −1.10299e39 | −0.195909 | ||||||||
\(881\) | −6.56252e39 | −1.14788 | −0.573939 | − | 0.818898i | \(-0.694585\pi\) | ||||
−0.573939 | + | 0.818898i | \(0.694585\pi\) | |||||||
\(882\) | 8.38366e38 | 0.144414 | ||||||||
\(883\) | 6.35223e39 | 1.07760 | 0.538799 | − | 0.842434i | \(-0.318878\pi\) | ||||
0.538799 | + | 0.842434i | \(0.318878\pi\) | |||||||
\(884\) | 5.27979e39 | 0.882086 | ||||||||
\(885\) | 2.99758e39 | 0.493215 | ||||||||
\(886\) | 6.29329e39 | 1.01982 | ||||||||
\(887\) | 4.10862e39 | 0.655732 | 0.327866 | − | 0.944724i | \(-0.393670\pi\) | ||||
0.327866 | + | 0.944724i | \(0.393670\pi\) | |||||||
\(888\) | 4.17885e39 | 0.656874 | ||||||||
\(889\) | −2.84300e39 | −0.440153 | ||||||||
\(890\) | 6.32996e38 | 0.0965241 | ||||||||
\(891\) | 1.43809e40 | 2.15992 | ||||||||
\(892\) | 3.68357e39 | 0.544933 | ||||||||
\(893\) | −3.83357e39 | −0.558609 | ||||||||
\(894\) | −3.06020e39 | −0.439231 | ||||||||
\(895\) | −5.78732e39 | −0.818214 | ||||||||
\(896\) | 5.22102e38 | 0.0727105 | ||||||||
\(897\) | 2.02541e40 | 2.77853 | ||||||||
\(898\) | −4.89082e39 | −0.660923 | ||||||||
\(899\) | −3.24134e39 | −0.431487 | ||||||||
\(900\) | 4.81735e38 | 0.0631735 | ||||||||
\(901\) | 5.53780e39 | 0.715406 | ||||||||
\(902\) | −9.43190e39 | −1.20036 | ||||||||
\(903\) | 3.51986e38 | 0.0441306 | ||||||||
\(904\) | 5.10456e39 | 0.630499 | ||||||||
\(905\) | −4.83971e39 | −0.588929 | ||||||||
\(906\) | 9.50929e38 | 0.114003 | ||||||||
\(907\) | 1.26175e40 | 1.49030 | 0.745152 | − | 0.666895i | \(-0.232377\pi\) | ||||
0.745152 | + | 0.666895i | \(0.232377\pi\) | |||||||
\(908\) | −3.04355e39 | −0.354178 | ||||||||
\(909\) | −2.89887e39 | −0.332366 | ||||||||
\(910\) | 3.51459e39 | 0.397024 | ||||||||
\(911\) | −8.55940e39 | −0.952676 | −0.476338 | − | 0.879262i | \(-0.658036\pi\) | ||||
−0.476338 | + | 0.879262i | \(0.658036\pi\) | |||||||
\(912\) | −4.45902e39 | −0.489000 | ||||||||
\(913\) | −3.13777e40 | −3.39052 | ||||||||
\(914\) | −1.01899e40 | −1.08492 | ||||||||
\(915\) | 7.15389e39 | 0.750511 | ||||||||
\(916\) | 2.64575e38 | 0.0273502 | ||||||||
\(917\) | 2.58995e39 | 0.263818 | ||||||||
\(918\) | −3.83066e39 | −0.384501 | ||||||||
\(919\) | 4.48874e39 | 0.443982 | 0.221991 | − | 0.975049i | \(-0.428744\pi\) | ||||
0.221991 | + | 0.975049i | \(0.428744\pi\) | |||||||
\(920\) | 2.31197e39 | 0.225344 | ||||||||
\(921\) | 6.97378e39 | 0.669828 | ||||||||
\(922\) | 3.69228e39 | 0.349484 | ||||||||
\(923\) | −2.81707e39 | −0.262769 | ||||||||
\(924\) | −1.00154e40 | −0.920653 | ||||||||
\(925\) | 3.21104e39 | 0.290892 | ||||||||
\(926\) | −2.50726e39 | −0.223847 | ||||||||
\(927\) | 2.57638e39 | 0.226690 | ||||||||
\(928\) | −1.98638e39 | −0.172253 | ||||||||
\(929\) | 1.47342e40 | 1.25926 | 0.629631 | − | 0.776895i | \(-0.283206\pi\) | ||||
0.629631 | + | 0.776895i | \(0.283206\pi\) | |||||||
\(930\) | −2.12360e39 | −0.178876 | ||||||||
\(931\) | −5.96284e39 | −0.495031 | ||||||||
\(932\) | 3.16193e39 | 0.258725 | ||||||||
\(933\) | 1.42165e40 | 1.14654 | ||||||||
\(934\) | −2.03669e39 | −0.161898 | ||||||||
\(935\) | −1.15611e40 | −0.905817 | ||||||||
\(936\) | −4.41395e39 | −0.340882 | ||||||||
\(937\) | −1.33104e40 | −1.01323 | −0.506614 | − | 0.862173i | \(-0.669103\pi\) | ||||
−0.506614 | + | 0.862173i | \(0.669103\pi\) | |||||||
\(938\) | −1.18792e38 | −0.00891350 | ||||||||
\(939\) | −3.94974e39 | −0.292135 | ||||||||
\(940\) | −1.11886e39 | −0.0815734 | ||||||||
\(941\) | −1.28931e40 | −0.926612 | −0.463306 | − | 0.886198i | \(-0.653337\pi\) | ||||
−0.463306 | + | 0.886198i | \(0.653337\pi\) | |||||||
\(942\) | −3.23447e39 | −0.229148 | ||||||||
\(943\) | 1.97702e40 | 1.38071 | ||||||||
\(944\) | −3.13515e39 | −0.215842 | ||||||||
\(945\) | −2.54995e39 | −0.173062 | ||||||||
\(946\) | 7.77727e38 | 0.0520352 | ||||||||
\(947\) | −1.41966e40 | −0.936396 | −0.468198 | − | 0.883624i | \(-0.655097\pi\) | ||||
−0.468198 | + | 0.883624i | \(0.655097\pi\) | |||||||
\(948\) | 1.18852e39 | 0.0772850 | ||||||||
\(949\) | −9.23142e39 | −0.591800 | ||||||||
\(950\) | −3.42632e39 | −0.216551 | ||||||||
\(951\) | 2.12450e40 | 1.32379 | ||||||||
\(952\) | 5.47246e39 | 0.336190 | ||||||||
\(953\) | 1.53298e40 | 0.928501 | 0.464251 | − | 0.885704i | \(-0.346324\pi\) | ||||
0.464251 | + | 0.885704i | \(0.346324\pi\) | |||||||
\(954\) | −4.62965e39 | −0.276468 | ||||||||
\(955\) | 1.04153e40 | 0.613233 | ||||||||
\(956\) | −3.95944e39 | −0.229854 | ||||||||
\(957\) | 3.81044e40 | 2.18104 | ||||||||
\(958\) | 1.99454e40 | 1.12566 | ||||||||
\(959\) | −1.63961e40 | −0.912406 | ||||||||
\(960\) | −1.30140e39 | −0.0714085 | ||||||||
\(961\) | −1.48584e40 | −0.803910 | ||||||||
\(962\) | −2.94215e40 | −1.56964 | ||||||||
\(963\) | −1.09569e40 | −0.576413 | ||||||||
\(964\) | −1.08956e40 | −0.565212 | ||||||||
\(965\) | −1.62244e40 | −0.829946 | ||||||||
\(966\) | 2.09932e40 | 1.05898 | ||||||||
\(967\) | −6.60284e38 | −0.0328453 | −0.0164226 | − | 0.999865i | \(-0.505228\pi\) | ||||
−0.0164226 | + | 0.999865i | \(0.505228\pi\) | |||||||
\(968\) | −1.49221e40 | −0.732004 | ||||||||
\(969\) | −4.67377e40 | −2.26098 | ||||||||
\(970\) | 5.95949e39 | 0.284309 | ||||||||
\(971\) | 1.76228e40 | 0.829117 | 0.414558 | − | 0.910023i | \(-0.363936\pi\) | ||||
0.414558 | + | 0.910023i | \(0.363936\pi\) | |||||||
\(972\) | 1.18986e40 | 0.552077 | ||||||||
\(973\) | 1.28481e40 | 0.587916 | ||||||||
\(974\) | 9.93633e38 | 0.0448415 | ||||||||
\(975\) | −8.76054e39 | −0.389914 | ||||||||
\(976\) | −7.48221e39 | −0.328441 | ||||||||
\(977\) | 2.50038e39 | 0.108250 | 0.0541251 | − | 0.998534i | \(-0.482763\pi\) | ||||
0.0541251 | + | 0.998534i | \(0.482763\pi\) | |||||||
\(978\) | 2.91974e40 | 1.24672 | ||||||||
\(979\) | 1.26999e40 | 0.534853 | ||||||||
\(980\) | −1.74030e39 | −0.0722892 | ||||||||
\(981\) | −1.26049e40 | −0.516425 | ||||||||
\(982\) | −5.25355e39 | −0.212299 | ||||||||
\(983\) | 2.38859e40 | 0.952069 | 0.476034 | − | 0.879427i | \(-0.342074\pi\) | ||||
0.476034 | + | 0.879427i | \(0.342074\pi\) | |||||||
\(984\) | −1.11286e40 | −0.437529 | ||||||||
\(985\) | −1.02580e40 | −0.397807 | ||||||||
\(986\) | −2.08205e40 | −0.796439 | ||||||||
\(987\) | −1.01595e40 | −0.383346 | ||||||||
\(988\) | 3.13940e40 | 1.16850 | ||||||||
\(989\) | −1.63019e39 | −0.0598535 | ||||||||
\(990\) | 9.66515e39 | 0.350053 | ||||||||
\(991\) | −1.88335e40 | −0.672879 | −0.336440 | − | 0.941705i | \(-0.609223\pi\) | ||||
−0.336440 | + | 0.941705i | \(0.609223\pi\) | |||||||
\(992\) | 2.22106e39 | 0.0782803 | ||||||||
\(993\) | 1.38778e40 | 0.482510 | ||||||||
\(994\) | −2.91987e39 | −0.100149 | ||||||||
\(995\) | 2.28908e40 | 0.774551 | ||||||||
\(996\) | −3.70223e40 | −1.23584 | ||||||||
\(997\) | −3.07289e40 | −1.01196 | −0.505979 | − | 0.862546i | \(-0.668869\pi\) | ||||
−0.505979 | + | 0.862546i | \(0.668869\pi\) | |||||||
\(998\) | 3.35107e40 | 1.08873 | ||||||||
\(999\) | 2.13463e40 | 0.684208 |
(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 | 10.28.a.a.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.28.b.e.49.2 | 4 | |||
5.3 | odd | 4 | 50.28.b.e.49.3 | 4 | |||
5.4 | even | 2 | 50.28.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.28.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.28.a.e.1.2 | 2 | 5.4 | even | 2 | |||
50.28.b.e.49.2 | 4 | 5.2 | odd | 4 | |||
50.28.b.e.49.3 | 4 | 5.3 | odd | 4 |