Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −645.655 | −1.78339 | −0.891693 | − | 0.452640i | \(-0.850482\pi\) | ||||
−0.891693 | + | 0.452640i | \(0.850482\pi\) | |||||||
\(3\) | 14883.2 | 1.30968 | 0.654842 | − | 0.755766i | \(-0.272735\pi\) | ||||
0.654842 | + | 0.755766i | \(0.272735\pi\) | |||||||
\(4\) | 285798. | 2.18047 | ||||||||
\(5\) | 954733. | 1.09304 | 0.546521 | − | 0.837445i | \(-0.315952\pi\) | ||||
0.546521 | + | 0.837445i | \(0.315952\pi\) | |||||||
\(6\) | −9.60943e6 | −2.33567 | ||||||||
\(7\) | 1.80737e7 | 1.18499 | 0.592495 | − | 0.805574i | \(-0.298143\pi\) | ||||
0.592495 | + | 0.805574i | \(0.298143\pi\) | |||||||
\(8\) | −9.98999e7 | −2.10523 | ||||||||
\(9\) | 9.23704e7 | 0.715273 | ||||||||
\(10\) | −6.16428e8 | −1.94932 | ||||||||
\(11\) | −1.63616e8 | −0.230138 | −0.115069 | − | 0.993358i | \(-0.536709\pi\) | ||||
−0.115069 | + | 0.993358i | \(0.536709\pi\) | |||||||
\(12\) | 4.25360e9 | 2.85573 | ||||||||
\(13\) | 4.33002e9 | 1.47222 | 0.736108 | − | 0.676864i | \(-0.236661\pi\) | ||||
0.736108 | + | 0.676864i | \(0.236661\pi\) | |||||||
\(14\) | −1.16694e10 | −2.11330 | ||||||||
\(15\) | 1.42095e10 | 1.43154 | ||||||||
\(16\) | 2.70407e10 | 1.57398 | ||||||||
\(17\) | 5.11795e10 | 1.77943 | 0.889714 | − | 0.456518i | \(-0.150904\pi\) | ||||
0.889714 | + | 0.456518i | \(0.150904\pi\) | |||||||
\(18\) | −5.96394e10 | −1.27561 | ||||||||
\(19\) | 8.96514e10 | 1.21102 | 0.605510 | − | 0.795838i | \(-0.292969\pi\) | ||||
0.605510 | + | 0.795838i | \(0.292969\pi\) | |||||||
\(20\) | 2.72861e11 | 2.38334 | ||||||||
\(21\) | 2.68996e11 | 1.55196 | ||||||||
\(22\) | 1.05639e11 | 0.410424 | ||||||||
\(23\) | −2.78368e11 | −0.741197 | −0.370598 | − | 0.928793i | \(-0.620847\pi\) | ||||
−0.370598 | + | 0.928793i | \(0.620847\pi\) | |||||||
\(24\) | −1.48683e12 | −2.75719 | ||||||||
\(25\) | 1.48576e11 | 0.194741 | ||||||||
\(26\) | −2.79570e12 | −2.62553 | ||||||||
\(27\) | −5.47252e11 | −0.372903 | ||||||||
\(28\) | 5.16545e12 | 2.58383 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | −9.17444e12 | −2.55299 | ||||||||
\(31\) | −2.36840e12 | −0.498748 | −0.249374 | − | 0.968407i | \(-0.580225\pi\) | ||||
−0.249374 | + | 0.968407i | \(0.580225\pi\) | |||||||
\(32\) | −4.36488e12 | −0.701775 | ||||||||
\(33\) | −2.43513e12 | −0.301408 | ||||||||
\(34\) | −3.30443e13 | −3.17341 | ||||||||
\(35\) | 1.72556e13 | 1.29524 | ||||||||
\(36\) | 2.63993e13 | 1.55963 | ||||||||
\(37\) | 3.03597e13 | 1.42096 | 0.710482 | − | 0.703715i | \(-0.248477\pi\) | ||||
0.710482 | + | 0.703715i | \(0.248477\pi\) | |||||||
\(38\) | −5.78839e13 | −2.15972 | ||||||||
\(39\) | 6.44448e13 | 1.92814 | ||||||||
\(40\) | −9.53777e13 | −2.30111 | ||||||||
\(41\) | −8.45031e13 | −1.65276 | −0.826380 | − | 0.563113i | \(-0.809604\pi\) | ||||
−0.826380 | + | 0.563113i | \(0.809604\pi\) | |||||||
\(42\) | −1.73678e14 | −2.76775 | ||||||||
\(43\) | −1.94211e13 | −0.253392 | −0.126696 | − | 0.991942i | \(-0.540437\pi\) | ||||
−0.126696 | + | 0.991942i | \(0.540437\pi\) | |||||||
\(44\) | −4.67611e13 | −0.501808 | ||||||||
\(45\) | 8.81891e13 | 0.781823 | ||||||||
\(46\) | 1.79730e14 | 1.32184 | ||||||||
\(47\) | 9.65771e13 | 0.591619 | 0.295810 | − | 0.955247i | \(-0.404411\pi\) | ||||
0.295810 | + | 0.955247i | \(0.404411\pi\) | |||||||
\(48\) | 4.02453e14 | 2.06141 | ||||||||
\(49\) | 9.40296e13 | 0.404202 | ||||||||
\(50\) | −9.59287e13 | −0.347299 | ||||||||
\(51\) | 7.61717e14 | 2.33049 | ||||||||
\(52\) | 1.23751e15 | 3.21012 | ||||||||
\(53\) | −5.94756e14 | −1.31218 | −0.656090 | − | 0.754682i | \(-0.727791\pi\) | ||||
−0.656090 | + | 0.754682i | \(0.727791\pi\) | |||||||
\(54\) | 3.53336e14 | 0.665030 | ||||||||
\(55\) | −1.56209e14 | −0.251550 | ||||||||
\(56\) | −1.80556e15 | −2.49468 | ||||||||
\(57\) | 1.33430e15 | 1.58605 | ||||||||
\(58\) | −3.22987e14 | −0.331167 | ||||||||
\(59\) | −1.80184e14 | −0.159763 | −0.0798813 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798813 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(60\) | 4.06106e15 | 3.12143 | ||||||||
\(61\) | −1.33081e15 | −0.888820 | −0.444410 | − | 0.895824i | \(-0.646587\pi\) | ||||
−0.444410 | + | 0.895824i | \(0.646587\pi\) | |||||||
\(62\) | 1.52917e15 | 0.889461 | ||||||||
\(63\) | 1.66948e15 | 0.847591 | ||||||||
\(64\) | −7.26069e14 | −0.322439 | ||||||||
\(65\) | 4.13402e15 | 1.60920 | ||||||||
\(66\) | 1.57226e15 | 0.537526 | ||||||||
\(67\) | 2.44049e15 | 0.734245 | 0.367122 | − | 0.930173i | \(-0.380343\pi\) | ||||
0.367122 | + | 0.930173i | \(0.380343\pi\) | |||||||
\(68\) | 1.46270e16 | 3.87999 | ||||||||
\(69\) | −4.14302e15 | −0.970733 | ||||||||
\(70\) | −1.11412e16 | −2.30992 | ||||||||
\(71\) | −5.66814e15 | −1.04171 | −0.520853 | − | 0.853647i | \(-0.674386\pi\) | ||||
−0.520853 | + | 0.853647i | \(0.674386\pi\) | |||||||
\(72\) | −9.22780e15 | −1.50582 | ||||||||
\(73\) | −1.53697e15 | −0.223060 | −0.111530 | − | 0.993761i | \(-0.535575\pi\) | ||||
−0.111530 | + | 0.993761i | \(0.535575\pi\) | |||||||
\(74\) | −1.96019e16 | −2.53413 | ||||||||
\(75\) | 2.21129e15 | 0.255050 | ||||||||
\(76\) | 2.56222e16 | 2.64059 | ||||||||
\(77\) | −2.95715e15 | −0.272711 | ||||||||
\(78\) | −4.16091e16 | −3.43862 | ||||||||
\(79\) | −1.72129e16 | −1.27651 | −0.638256 | − | 0.769824i | \(-0.720344\pi\) | ||||
−0.638256 | + | 0.769824i | \(0.720344\pi\) | |||||||
\(80\) | 2.58166e16 | 1.72042 | ||||||||
\(81\) | −2.00736e16 | −1.20366 | ||||||||
\(82\) | 5.45599e16 | 2.94751 | ||||||||
\(83\) | 8.38378e15 | 0.408579 | 0.204290 | − | 0.978911i | \(-0.434512\pi\) | ||||
0.204290 | + | 0.978911i | \(0.434512\pi\) | |||||||
\(84\) | 7.68785e16 | 3.38401 | ||||||||
\(85\) | 4.88628e16 | 1.94499 | ||||||||
\(86\) | 1.25393e16 | 0.451895 | ||||||||
\(87\) | 7.44528e15 | 0.243202 | ||||||||
\(88\) | 1.63452e16 | 0.484493 | ||||||||
\(89\) | −3.85946e16 | −1.03923 | −0.519615 | − | 0.854400i | \(-0.673925\pi\) | ||||
−0.519615 | + | 0.854400i | \(0.673925\pi\) | |||||||
\(90\) | −5.69397e16 | −1.39429 | ||||||||
\(91\) | 7.82597e16 | 1.74456 | ||||||||
\(92\) | −7.95573e16 | −1.61616 | ||||||||
\(93\) | −3.52495e16 | −0.653202 | ||||||||
\(94\) | −6.23555e16 | −1.05509 | ||||||||
\(95\) | 8.55931e16 | 1.32370 | ||||||||
\(96\) | −6.49636e16 | −0.919104 | ||||||||
\(97\) | 8.15125e16 | 1.05600 | 0.528001 | − | 0.849244i | \(-0.322942\pi\) | ||||
0.528001 | + | 0.849244i | \(0.322942\pi\) | |||||||
\(98\) | −6.07107e16 | −0.720848 | ||||||||
\(99\) | −1.51133e16 | −0.164611 | ||||||||
\(100\) | 4.24627e16 | 0.424627 | ||||||||
\(101\) | 1.67885e17 | 1.54270 | 0.771349 | − | 0.636412i | \(-0.219582\pi\) | ||||
0.771349 | + | 0.636412i | \(0.219582\pi\) | |||||||
\(102\) | −4.91806e17 | −4.15616 | ||||||||
\(103\) | 1.21257e17 | 0.943169 | 0.471585 | − | 0.881821i | \(-0.343682\pi\) | ||||
0.471585 | + | 0.881821i | \(0.343682\pi\) | |||||||
\(104\) | −4.32569e17 | −3.09936 | ||||||||
\(105\) | 2.56819e17 | 1.69636 | ||||||||
\(106\) | 3.84007e17 | 2.34013 | ||||||||
\(107\) | −9.11858e16 | −0.513056 | −0.256528 | − | 0.966537i | \(-0.582579\pi\) | ||||
−0.256528 | + | 0.966537i | \(0.582579\pi\) | |||||||
\(108\) | −1.56404e17 | −0.813103 | ||||||||
\(109\) | −3.65713e17 | −1.75799 | −0.878994 | − | 0.476834i | \(-0.841784\pi\) | ||||
−0.878994 | + | 0.476834i | \(0.841784\pi\) | |||||||
\(110\) | 1.00857e17 | 0.448611 | ||||||||
\(111\) | 4.51851e17 | 1.86101 | ||||||||
\(112\) | 4.88727e17 | 1.86515 | ||||||||
\(113\) | 1.69688e15 | 0.00600459 | 0.00300230 | − | 0.999995i | \(-0.499044\pi\) | ||||
0.00300230 | + | 0.999995i | \(0.499044\pi\) | |||||||
\(114\) | −8.61499e17 | −2.82855 | ||||||||
\(115\) | −2.65768e17 | −0.810159 | ||||||||
\(116\) | 1.42970e17 | 0.404903 | ||||||||
\(117\) | 3.99966e17 | 1.05304 | ||||||||
\(118\) | 1.16337e17 | 0.284918 | ||||||||
\(119\) | 9.25006e17 | 2.10860 | ||||||||
\(120\) | −1.41953e18 | −3.01373 | ||||||||
\(121\) | −4.78677e17 | −0.947037 | ||||||||
\(122\) | 8.59247e17 | 1.58511 | ||||||||
\(123\) | −1.25768e18 | −2.16459 | ||||||||
\(124\) | −6.76886e17 | −1.08750 | ||||||||
\(125\) | −5.86553e17 | −0.880182 | ||||||||
\(126\) | −1.07791e18 | −1.51158 | ||||||||
\(127\) | 1.08499e18 | 1.42264 | 0.711320 | − | 0.702868i | \(-0.248098\pi\) | ||||
0.711320 | + | 0.702868i | \(0.248098\pi\) | |||||||
\(128\) | 1.04090e18 | 1.27681 | ||||||||
\(129\) | −2.89049e17 | −0.331863 | ||||||||
\(130\) | −2.66915e18 | −2.86982 | ||||||||
\(131\) | −5.51328e17 | −0.555398 | −0.277699 | − | 0.960668i | \(-0.589572\pi\) | ||||
−0.277699 | + | 0.960668i | \(0.589572\pi\) | |||||||
\(132\) | −6.95957e17 | −0.657210 | ||||||||
\(133\) | 1.62034e18 | 1.43505 | ||||||||
\(134\) | −1.57571e18 | −1.30944 | ||||||||
\(135\) | −5.22480e17 | −0.407598 | ||||||||
\(136\) | −5.11283e18 | −3.74611 | ||||||||
\(137\) | 2.01819e18 | 1.38943 | 0.694717 | − | 0.719283i | \(-0.255530\pi\) | ||||
0.694717 | + | 0.719283i | \(0.255530\pi\) | |||||||
\(138\) | 2.67496e18 | 1.73119 | ||||||||
\(139\) | 1.76829e18 | 1.07628 | 0.538142 | − | 0.842854i | \(-0.319126\pi\) | ||||
0.538142 | + | 0.842854i | \(0.319126\pi\) | |||||||
\(140\) | 4.93162e18 | 2.82424 | ||||||||
\(141\) | 1.43738e18 | 0.774834 | ||||||||
\(142\) | 3.65966e18 | 1.85776 | ||||||||
\(143\) | −7.08460e17 | −0.338812 | ||||||||
\(144\) | 2.49776e18 | 1.12582 | ||||||||
\(145\) | 4.77602e17 | 0.202973 | ||||||||
\(146\) | 9.92354e17 | 0.397803 | ||||||||
\(147\) | 1.39946e18 | 0.529376 | ||||||||
\(148\) | 8.67676e18 | 3.09837 | ||||||||
\(149\) | −1.28596e17 | −0.0433656 | −0.0216828 | − | 0.999765i | \(-0.506902\pi\) | ||||
−0.0216828 | + | 0.999765i | \(0.506902\pi\) | |||||||
\(150\) | −1.42773e18 | −0.454852 | ||||||||
\(151\) | −1.87304e18 | −0.563953 | −0.281977 | − | 0.959421i | \(-0.590990\pi\) | ||||
−0.281977 | + | 0.959421i | \(0.590990\pi\) | |||||||
\(152\) | −8.95616e18 | −2.54948 | ||||||||
\(153\) | 4.72748e18 | 1.27278 | ||||||||
\(154\) | 1.90930e18 | 0.486349 | ||||||||
\(155\) | −2.26119e18 | −0.545153 | ||||||||
\(156\) | 1.84182e19 | 4.20425 | ||||||||
\(157\) | −1.37344e18 | −0.296935 | −0.148468 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148468 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(158\) | 1.11136e19 | 2.27651 | ||||||||
\(159\) | −8.85189e18 | −1.71854 | ||||||||
\(160\) | −4.16730e18 | −0.767070 | ||||||||
\(161\) | −5.03116e18 | −0.878311 | ||||||||
\(162\) | 1.29606e19 | 2.14659 | ||||||||
\(163\) | 8.00163e18 | 1.25772 | 0.628860 | − | 0.777519i | \(-0.283522\pi\) | ||||
0.628860 | + | 0.777519i | \(0.283522\pi\) | |||||||
\(164\) | −2.41509e19 | −3.60379 | ||||||||
\(165\) | −2.32490e18 | −0.329451 | ||||||||
\(166\) | −5.41303e18 | −0.728655 | ||||||||
\(167\) | 9.77713e18 | 1.25061 | 0.625304 | − | 0.780381i | \(-0.284975\pi\) | ||||
0.625304 | + | 0.780381i | \(0.284975\pi\) | |||||||
\(168\) | −2.68726e19 | −3.26724 | ||||||||
\(169\) | 1.00987e19 | 1.16742 | ||||||||
\(170\) | −3.15485e19 | −3.46867 | ||||||||
\(171\) | 8.28114e18 | 0.866210 | ||||||||
\(172\) | −5.55052e18 | −0.552512 | ||||||||
\(173\) | −1.06185e19 | −1.00617 | −0.503084 | − | 0.864238i | \(-0.667801\pi\) | ||||
−0.503084 | + | 0.864238i | \(0.667801\pi\) | |||||||
\(174\) | −4.80708e18 | −0.433724 | ||||||||
\(175\) | 2.68532e18 | 0.230766 | ||||||||
\(176\) | −4.42429e18 | −0.362231 | ||||||||
\(177\) | −2.68173e18 | −0.209238 | ||||||||
\(178\) | 2.49188e19 | 1.85335 | ||||||||
\(179\) | −2.29142e19 | −1.62500 | −0.812501 | − | 0.582960i | \(-0.801895\pi\) | ||||
−0.812501 | + | 0.582960i | \(0.801895\pi\) | |||||||
\(180\) | 2.52043e19 | 1.70474 | ||||||||
\(181\) | 2.24468e19 | 1.44840 | 0.724198 | − | 0.689592i | \(-0.242210\pi\) | ||||
0.724198 | + | 0.689592i | \(0.242210\pi\) | |||||||
\(182\) | −5.05288e19 | −3.11123 | ||||||||
\(183\) | −1.98068e19 | −1.16407 | ||||||||
\(184\) | 2.78090e19 | 1.56039 | ||||||||
\(185\) | 2.89854e19 | 1.55317 | ||||||||
\(186\) | 2.27590e19 | 1.16491 | ||||||||
\(187\) | −8.37378e18 | −0.409513 | ||||||||
\(188\) | 2.76016e19 | 1.29001 | ||||||||
\(189\) | −9.89090e18 | −0.441886 | ||||||||
\(190\) | −5.52636e19 | −2.36066 | ||||||||
\(191\) | 8.15204e18 | 0.333029 | 0.166515 | − | 0.986039i | \(-0.446749\pi\) | ||||
0.166515 | + | 0.986039i | \(0.446749\pi\) | |||||||
\(192\) | −1.08063e19 | −0.422294 | ||||||||
\(193\) | −5.90065e18 | −0.220629 | −0.110315 | − | 0.993897i | \(-0.535186\pi\) | ||||
−0.110315 | + | 0.993897i | \(0.535186\pi\) | |||||||
\(194\) | −5.26290e19 | −1.88326 | ||||||||
\(195\) | 6.15275e19 | 2.10754 | ||||||||
\(196\) | 2.68735e19 | 0.881349 | ||||||||
\(197\) | −2.48407e18 | −0.0780191 | −0.0390095 | − | 0.999239i | \(-0.512420\pi\) | ||||
−0.0390095 | + | 0.999239i | \(0.512420\pi\) | |||||||
\(198\) | 9.75796e18 | 0.293565 | ||||||||
\(199\) | 4.88334e19 | 1.40756 | 0.703778 | − | 0.710420i | \(-0.251495\pi\) | ||||
0.703778 | + | 0.710420i | \(0.251495\pi\) | |||||||
\(200\) | −1.48427e19 | −0.409976 | ||||||||
\(201\) | 3.63223e19 | 0.961628 | ||||||||
\(202\) | −1.08396e20 | −2.75123 | ||||||||
\(203\) | 9.04132e18 | 0.220047 | ||||||||
\(204\) | 2.17697e20 | 5.08156 | ||||||||
\(205\) | −8.06779e19 | −1.80654 | ||||||||
\(206\) | −7.82901e19 | −1.68204 | ||||||||
\(207\) | −2.57130e19 | −0.530158 | ||||||||
\(208\) | 1.17087e20 | 2.31723 | ||||||||
\(209\) | −1.46684e19 | −0.278701 | ||||||||
\(210\) | −1.65817e20 | −3.02527 | ||||||||
\(211\) | −3.00726e19 | −0.526952 | −0.263476 | − | 0.964666i | \(-0.584869\pi\) | ||||
−0.263476 | + | 0.964666i | \(0.584869\pi\) | |||||||
\(212\) | −1.69980e20 | −2.86117 | ||||||||
\(213\) | −8.43603e19 | −1.36430 | ||||||||
\(214\) | 5.88746e19 | 0.914978 | ||||||||
\(215\) | −1.85420e19 | −0.276968 | ||||||||
\(216\) | 5.46704e19 | 0.785047 | ||||||||
\(217\) | −4.28059e19 | −0.591012 | ||||||||
\(218\) | 2.36125e20 | 3.13517 | ||||||||
\(219\) | −2.28751e19 | −0.292138 | ||||||||
\(220\) | −4.46444e19 | −0.548497 | ||||||||
\(221\) | 2.21609e20 | 2.61970 | ||||||||
\(222\) | −2.91740e20 | −3.31891 | ||||||||
\(223\) | 1.29928e20 | 1.42269 | 0.711347 | − | 0.702841i | \(-0.248085\pi\) | ||||
0.711347 | + | 0.702841i | \(0.248085\pi\) | |||||||
\(224\) | −7.88898e19 | −0.831597 | ||||||||
\(225\) | 1.37240e19 | 0.139293 | ||||||||
\(226\) | −1.09560e18 | −0.0107085 | ||||||||
\(227\) | 1.87841e19 | 0.176836 | 0.0884180 | − | 0.996083i | \(-0.471819\pi\) | ||||
0.0884180 | + | 0.996083i | \(0.471819\pi\) | |||||||
\(228\) | 3.81341e20 | 3.45834 | ||||||||
\(229\) | 7.75871e19 | 0.677935 | 0.338968 | − | 0.940798i | \(-0.389922\pi\) | ||||
0.338968 | + | 0.940798i | \(0.389922\pi\) | |||||||
\(230\) | 1.71594e20 | 1.44483 | ||||||||
\(231\) | −4.40120e19 | −0.357165 | ||||||||
\(232\) | −4.99746e19 | −0.390932 | ||||||||
\(233\) | −1.91389e20 | −1.44341 | −0.721707 | − | 0.692199i | \(-0.756642\pi\) | ||||
−0.721707 | + | 0.692199i | \(0.756642\pi\) | |||||||
\(234\) | −2.58240e20 | −1.87797 | ||||||||
\(235\) | 9.22053e19 | 0.646665 | ||||||||
\(236\) | −5.14964e19 | −0.348357 | ||||||||
\(237\) | −2.56184e20 | −1.67183 | ||||||||
\(238\) | −5.97235e20 | −3.76046 | ||||||||
\(239\) | −2.52552e20 | −1.53451 | −0.767253 | − | 0.641345i | \(-0.778377\pi\) | ||||
−0.767253 | + | 0.641345i | \(0.778377\pi\) | |||||||
\(240\) | 3.84235e20 | 2.25321 | ||||||||
\(241\) | −1.27038e20 | −0.719102 | −0.359551 | − | 0.933125i | \(-0.617070\pi\) | ||||
−0.359551 | + | 0.933125i | \(0.617070\pi\) | |||||||
\(242\) | 3.09060e20 | 1.68893 | ||||||||
\(243\) | −2.28088e20 | −1.20351 | ||||||||
\(244\) | −3.80345e20 | −1.93804 | ||||||||
\(245\) | 8.97732e19 | 0.441809 | ||||||||
\(246\) | 8.12027e20 | 3.86031 | ||||||||
\(247\) | 3.88193e20 | 1.78288 | ||||||||
\(248\) | 2.36603e20 | 1.04998 | ||||||||
\(249\) | 1.24778e20 | 0.535110 | ||||||||
\(250\) | 3.78711e20 | 1.56970 | ||||||||
\(251\) | −1.19032e20 | −0.476912 | −0.238456 | − | 0.971153i | \(-0.576641\pi\) | ||||
−0.238456 | + | 0.971153i | \(0.576641\pi\) | |||||||
\(252\) | 4.77135e20 | 1.84815 | ||||||||
\(253\) | 4.55455e19 | 0.170577 | ||||||||
\(254\) | −7.00531e20 | −2.53712 | ||||||||
\(255\) | 7.27236e20 | 2.54732 | ||||||||
\(256\) | −5.76898e20 | −1.95461 | ||||||||
\(257\) | −5.11555e20 | −1.67672 | −0.838360 | − | 0.545117i | \(-0.816485\pi\) | ||||
−0.838360 | + | 0.545117i | \(0.816485\pi\) | |||||||
\(258\) | 1.86626e20 | 0.591840 | ||||||||
\(259\) | 5.48714e20 | 1.68383 | ||||||||
\(260\) | 1.18150e21 | 3.50880 | ||||||||
\(261\) | 4.62080e19 | 0.132823 | ||||||||
\(262\) | 3.55968e20 | 0.990490 | ||||||||
\(263\) | −4.69281e20 | −1.26418 | −0.632091 | − | 0.774895i | \(-0.717803\pi\) | ||||
−0.632091 | + | 0.774895i | \(0.717803\pi\) | |||||||
\(264\) | 2.43269e20 | 0.634533 | ||||||||
\(265\) | −5.67833e20 | −1.43427 | ||||||||
\(266\) | −1.04618e21 | −2.55924 | ||||||||
\(267\) | −5.74413e20 | −1.36106 | ||||||||
\(268\) | 6.97487e20 | 1.60100 | ||||||||
\(269\) | 5.98639e20 | 1.33128 | 0.665642 | − | 0.746271i | \(-0.268158\pi\) | ||||
0.665642 | + | 0.746271i | \(0.268158\pi\) | |||||||
\(270\) | 3.37342e20 | 0.726906 | ||||||||
\(271\) | 1.92263e20 | 0.401474 | 0.200737 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200737 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(272\) | 1.38393e21 | 2.80078 | ||||||||
\(273\) | 1.16476e21 | 2.28483 | ||||||||
\(274\) | −1.30306e21 | −2.47790 | ||||||||
\(275\) | −2.43094e19 | −0.0448173 | ||||||||
\(276\) | −1.18407e21 | −2.11665 | ||||||||
\(277\) | −8.40638e20 | −1.45724 | −0.728620 | − | 0.684918i | \(-0.759838\pi\) | ||||
−0.728620 | + | 0.684918i | \(0.759838\pi\) | |||||||
\(278\) | −1.14170e21 | −1.91943 | ||||||||
\(279\) | −2.18770e20 | −0.356741 | ||||||||
\(280\) | −1.72383e21 | −2.72679 | ||||||||
\(281\) | 2.84695e20 | 0.436893 | 0.218447 | − | 0.975849i | \(-0.429901\pi\) | ||||
0.218447 | + | 0.975849i | \(0.429901\pi\) | |||||||
\(282\) | −9.28051e20 | −1.38183 | ||||||||
\(283\) | 8.90156e20 | 1.28612 | 0.643060 | − | 0.765816i | \(-0.277664\pi\) | ||||
0.643060 | + | 0.765816i | \(0.277664\pi\) | |||||||
\(284\) | −1.61995e21 | −2.27141 | ||||||||
\(285\) | 1.27390e21 | 1.73362 | ||||||||
\(286\) | 4.57421e20 | 0.604234 | ||||||||
\(287\) | −1.52729e21 | −1.95850 | ||||||||
\(288\) | −4.03186e20 | −0.501961 | ||||||||
\(289\) | 1.79210e21 | 2.16636 | ||||||||
\(290\) | −3.08366e20 | −0.361979 | ||||||||
\(291\) | 1.21317e21 | 1.38303 | ||||||||
\(292\) | −4.39264e20 | −0.486376 | ||||||||
\(293\) | −5.73524e20 | −0.616846 | −0.308423 | − | 0.951249i | \(-0.599801\pi\) | ||||
−0.308423 | + | 0.951249i | \(0.599801\pi\) | |||||||
\(294\) | −9.03571e20 | −0.944083 | ||||||||
\(295\) | −1.72028e20 | −0.174627 | ||||||||
\(296\) | −3.03293e21 | −2.99146 | ||||||||
\(297\) | 8.95391e19 | 0.0858189 | ||||||||
\(298\) | 8.30289e19 | 0.0773377 | ||||||||
\(299\) | −1.20534e21 | −1.09120 | ||||||||
\(300\) | 6.31983e20 | 0.556128 | ||||||||
\(301\) | −3.51012e20 | −0.300266 | ||||||||
\(302\) | 1.20934e21 | 1.00575 | ||||||||
\(303\) | 2.49868e21 | 2.02045 | ||||||||
\(304\) | 2.42424e21 | 1.90612 | ||||||||
\(305\) | −1.27057e21 | −0.971518 | ||||||||
\(306\) | −3.05232e21 | −2.26985 | ||||||||
\(307\) | 8.21971e20 | 0.594539 | 0.297270 | − | 0.954794i | \(-0.403924\pi\) | ||||
0.297270 | + | 0.954794i | \(0.403924\pi\) | |||||||
\(308\) | −8.45149e20 | −0.594637 | ||||||||
\(309\) | 1.80469e21 | 1.23525 | ||||||||
\(310\) | 1.45995e21 | 0.972218 | ||||||||
\(311\) | 1.53791e21 | 0.996477 | 0.498239 | − | 0.867040i | \(-0.333980\pi\) | ||||
0.498239 | + | 0.867040i | \(0.333980\pi\) | |||||||
\(312\) | −6.43802e21 | −4.05918 | ||||||||
\(313\) | 1.42511e21 | 0.874421 | 0.437211 | − | 0.899359i | \(-0.355966\pi\) | ||||
0.437211 | + | 0.899359i | \(0.355966\pi\) | |||||||
\(314\) | 8.86767e20 | 0.529551 | ||||||||
\(315\) | 1.59391e21 | 0.926453 | ||||||||
\(316\) | −4.91943e21 | −2.78339 | ||||||||
\(317\) | 1.64676e21 | 0.907038 | 0.453519 | − | 0.891247i | \(-0.350168\pi\) | ||||
0.453519 | + | 0.891247i | \(0.350168\pi\) | |||||||
\(318\) | 5.71527e21 | 3.06483 | ||||||||
\(319\) | −8.18482e19 | −0.0427355 | ||||||||
\(320\) | −6.93202e20 | −0.352440 | ||||||||
\(321\) | −1.35714e21 | −0.671942 | ||||||||
\(322\) | 3.24839e21 | 1.56637 | ||||||||
\(323\) | 4.58831e21 | 2.15492 | ||||||||
\(324\) | −5.73701e21 | −2.62454 | ||||||||
\(325\) | 6.43337e20 | 0.286701 | ||||||||
\(326\) | −5.16629e21 | −2.24300 | ||||||||
\(327\) | −5.44300e21 | −2.30241 | ||||||||
\(328\) | 8.44185e21 | 3.47945 | ||||||||
\(329\) | 1.74551e21 | 0.701063 | ||||||||
\(330\) | 1.50108e21 | 0.587539 | ||||||||
\(331\) | −4.54685e21 | −1.73449 | −0.867247 | − | 0.497878i | \(-0.834113\pi\) | ||||
−0.867247 | + | 0.497878i | \(0.834113\pi\) | |||||||
\(332\) | 2.39607e21 | 0.890894 | ||||||||
\(333\) | 2.80434e21 | 1.01638 | ||||||||
\(334\) | −6.31265e21 | −2.23032 | ||||||||
\(335\) | 2.33001e21 | 0.802560 | ||||||||
\(336\) | 7.27383e21 | 2.44275 | ||||||||
\(337\) | 5.00380e21 | 1.63850 | 0.819248 | − | 0.573439i | \(-0.194391\pi\) | ||||
0.819248 | + | 0.573439i | \(0.194391\pi\) | |||||||
\(338\) | −6.52027e21 | −2.08197 | ||||||||
\(339\) | 2.52550e19 | 0.00786412 | ||||||||
\(340\) | 1.39649e22 | 4.24099 | ||||||||
\(341\) | 3.87508e20 | 0.114781 | ||||||||
\(342\) | −5.34676e21 | −1.54479 | ||||||||
\(343\) | −2.50504e21 | −0.706015 | ||||||||
\(344\) | 1.94017e21 | 0.533448 | ||||||||
\(345\) | −3.95548e21 | −1.06105 | ||||||||
\(346\) | 6.85587e21 | 1.79439 | ||||||||
\(347\) | −4.17722e21 | −1.06681 | −0.533404 | − | 0.845861i | \(-0.679088\pi\) | ||||
−0.533404 | + | 0.845861i | \(0.679088\pi\) | |||||||
\(348\) | 2.12785e21 | 0.530295 | ||||||||
\(349\) | 5.82193e21 | 1.41596 | 0.707979 | − | 0.706233i | \(-0.249607\pi\) | ||||
0.707979 | + | 0.706233i | \(0.249607\pi\) | |||||||
\(350\) | −1.73379e21 | −0.411546 | ||||||||
\(351\) | −2.36962e21 | −0.548994 | ||||||||
\(352\) | 7.14164e20 | 0.161505 | ||||||||
\(353\) | −2.45544e21 | −0.542057 | −0.271028 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271028 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(354\) | 1.73147e21 | 0.373153 | ||||||||
\(355\) | −5.41156e21 | −1.13863 | ||||||||
\(356\) | −1.10303e22 | −2.26601 | ||||||||
\(357\) | 1.37671e22 | 2.76161 | ||||||||
\(358\) | 1.47947e22 | 2.89801 | ||||||||
\(359\) | 9.63080e20 | 0.184230 | 0.0921148 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921148 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(360\) | −8.81008e21 | −1.64592 | ||||||||
\(361\) | 2.55698e21 | 0.466569 | ||||||||
\(362\) | −1.44929e22 | −2.58305 | ||||||||
\(363\) | −7.12426e21 | −1.24032 | ||||||||
\(364\) | 2.23665e22 | 3.80396 | ||||||||
\(365\) | −1.46740e21 | −0.243814 | ||||||||
\(366\) | 1.27884e22 | 2.07599 | ||||||||
\(367\) | −3.28839e21 | −0.521581 | −0.260791 | − | 0.965395i | \(-0.583983\pi\) | ||||
−0.260791 | + | 0.965395i | \(0.583983\pi\) | |||||||
\(368\) | −7.52728e21 | −1.16663 | ||||||||
\(369\) | −7.80559e21 | −1.18217 | ||||||||
\(370\) | −1.87146e22 | −2.76991 | ||||||||
\(371\) | −1.07495e22 | −1.55492 | ||||||||
\(372\) | −1.00743e22 | −1.42429 | ||||||||
\(373\) | 9.77462e21 | 1.35075 | 0.675375 | − | 0.737474i | \(-0.263982\pi\) | ||||
0.675375 | + | 0.737474i | \(0.263982\pi\) | |||||||
\(374\) | 5.40657e21 | 0.730321 | ||||||||
\(375\) | −8.72981e21 | −1.15276 | ||||||||
\(376\) | −9.64804e21 | −1.24550 | ||||||||
\(377\) | 2.16608e21 | 0.273384 | ||||||||
\(378\) | 6.38611e21 | 0.788054 | ||||||||
\(379\) | −7.55961e21 | −0.912149 | −0.456075 | − | 0.889942i | \(-0.650745\pi\) | ||||
−0.456075 | + | 0.889942i | \(0.650745\pi\) | |||||||
\(380\) | 2.44624e22 | 2.88628 | ||||||||
\(381\) | 1.61482e22 | 1.86321 | ||||||||
\(382\) | −5.26340e21 | −0.593920 | ||||||||
\(383\) | −9.38965e21 | −1.03624 | −0.518119 | − | 0.855308i | \(-0.673368\pi\) | ||||
−0.518119 | + | 0.855308i | \(0.673368\pi\) | |||||||
\(384\) | 1.54920e22 | 1.67222 | ||||||||
\(385\) | −2.82329e21 | −0.298084 | ||||||||
\(386\) | 3.80979e21 | 0.393467 | ||||||||
\(387\) | −1.79394e21 | −0.181244 | ||||||||
\(388\) | 2.32962e22 | 2.30258 | ||||||||
\(389\) | 3.43837e21 | 0.332492 | 0.166246 | − | 0.986084i | \(-0.446835\pi\) | ||||
0.166246 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(390\) | −3.97256e22 | −3.75855 | ||||||||
\(391\) | −1.42468e22 | −1.31891 | ||||||||
\(392\) | −9.39355e21 | −0.850938 | ||||||||
\(393\) | −8.20555e21 | −0.727396 | ||||||||
\(394\) | 1.60385e21 | 0.139138 | ||||||||
\(395\) | −1.64338e22 | −1.39528 | ||||||||
\(396\) | −4.31935e21 | −0.358929 | ||||||||
\(397\) | 3.71243e21 | 0.301953 | 0.150976 | − | 0.988537i | \(-0.451758\pi\) | ||||
0.150976 | + | 0.988537i | \(0.451758\pi\) | |||||||
\(398\) | −3.15295e22 | −2.51022 | ||||||||
\(399\) | 2.41158e22 | 1.87946 | ||||||||
\(400\) | 4.01759e21 | 0.306518 | ||||||||
\(401\) | −2.30999e21 | −0.172538 | −0.0862688 | − | 0.996272i | \(-0.527494\pi\) | ||||
−0.0862688 | + | 0.996272i | \(0.527494\pi\) | |||||||
\(402\) | −2.34517e22 | −1.71496 | ||||||||
\(403\) | −1.02552e22 | −0.734265 | ||||||||
\(404\) | 4.79814e22 | 3.36381 | ||||||||
\(405\) | −1.91649e22 | −1.31565 | ||||||||
\(406\) | −5.83758e21 | −0.392429 | ||||||||
\(407\) | −4.96733e21 | −0.327017 | ||||||||
\(408\) | −7.60954e22 | −4.90622 | ||||||||
\(409\) | −3.38041e21 | −0.213462 | −0.106731 | − | 0.994288i | \(-0.534038\pi\) | ||||
−0.106731 | + | 0.994288i | \(0.534038\pi\) | |||||||
\(410\) | 5.20901e22 | 3.22175 | ||||||||
\(411\) | 3.00372e22 | 1.81972 | ||||||||
\(412\) | 3.46550e22 | 2.05655 | ||||||||
\(413\) | −3.25660e21 | −0.189317 | ||||||||
\(414\) | 1.66017e22 | 0.945476 | ||||||||
\(415\) | 8.00427e21 | 0.446594 | ||||||||
\(416\) | −1.89001e22 | −1.03317 | ||||||||
\(417\) | 2.63178e22 | 1.40959 | ||||||||
\(418\) | 9.47072e21 | 0.497032 | ||||||||
\(419\) | −1.91876e22 | −0.986739 | −0.493369 | − | 0.869820i | \(-0.664235\pi\) | ||||
−0.493369 | + | 0.869820i | \(0.664235\pi\) | |||||||
\(420\) | 7.33985e22 | 3.69886 | ||||||||
\(421\) | −3.06665e22 | −1.51449 | −0.757244 | − | 0.653132i | \(-0.773455\pi\) | ||||
−0.757244 | + | 0.653132i | \(0.773455\pi\) | |||||||
\(422\) | 1.94166e22 | 0.939759 | ||||||||
\(423\) | 8.92087e21 | 0.423169 | ||||||||
\(424\) | 5.94160e22 | 2.76245 | ||||||||
\(425\) | 7.60404e21 | 0.346528 | ||||||||
\(426\) | 5.44676e22 | 2.43308 | ||||||||
\(427\) | −2.40528e22 | −1.05324 | ||||||||
\(428\) | −2.60608e22 | −1.11870 | ||||||||
\(429\) | −1.05442e22 | −0.443737 | ||||||||
\(430\) | 1.19717e22 | 0.493941 | ||||||||
\(431\) | 2.41512e22 | 0.976971 | 0.488486 | − | 0.872572i | \(-0.337549\pi\) | ||||
0.488486 | + | 0.872572i | \(0.337549\pi\) | |||||||
\(432\) | −1.47981e22 | −0.586940 | ||||||||
\(433\) | −3.26498e22 | −1.26979 | −0.634897 | − | 0.772597i | \(-0.718958\pi\) | ||||
−0.634897 | + | 0.772597i | \(0.718958\pi\) | |||||||
\(434\) | 2.76378e22 | 1.05400 | ||||||||
\(435\) | 7.10826e21 | 0.265830 | ||||||||
\(436\) | −1.04520e23 | −3.83324 | ||||||||
\(437\) | −2.49561e22 | −0.897604 | ||||||||
\(438\) | 1.47694e22 | 0.520996 | ||||||||
\(439\) | −3.33883e22 | −1.15517 | −0.577586 | − | 0.816330i | \(-0.696005\pi\) | ||||
−0.577586 | + | 0.816330i | \(0.696005\pi\) | |||||||
\(440\) | 1.56053e22 | 0.529571 | ||||||||
\(441\) | 8.68556e21 | 0.289114 | ||||||||
\(442\) | −1.43083e23 | −4.67195 | ||||||||
\(443\) | 1.88444e22 | 0.603601 | 0.301800 | − | 0.953371i | \(-0.402412\pi\) | ||||
0.301800 | + | 0.953371i | \(0.402412\pi\) | |||||||
\(444\) | 1.29138e23 | 4.05788 | ||||||||
\(445\) | −3.68476e22 | −1.13592 | ||||||||
\(446\) | −8.38887e22 | −2.53722 | ||||||||
\(447\) | −1.91393e21 | −0.0567952 | ||||||||
\(448\) | −1.31228e22 | −0.382087 | ||||||||
\(449\) | −3.26676e22 | −0.933304 | −0.466652 | − | 0.884441i | \(-0.654540\pi\) | ||||
−0.466652 | + | 0.884441i | \(0.654540\pi\) | |||||||
\(450\) | −8.86098e21 | −0.248414 | ||||||||
\(451\) | 1.38260e22 | 0.380362 | ||||||||
\(452\) | 4.84965e20 | 0.0130928 | ||||||||
\(453\) | −2.78769e22 | −0.738601 | ||||||||
\(454\) | −1.21281e22 | −0.315367 | ||||||||
\(455\) | 7.47172e22 | 1.90688 | ||||||||
\(456\) | −1.33297e23 | −3.33901 | ||||||||
\(457\) | 9.67539e21 | 0.237893 | 0.118946 | − | 0.992901i | \(-0.462048\pi\) | ||||
0.118946 | + | 0.992901i | \(0.462048\pi\) | |||||||
\(458\) | −5.00945e22 | −1.20902 | ||||||||
\(459\) | −2.80081e22 | −0.663554 | ||||||||
\(460\) | −7.59559e22 | −1.76653 | ||||||||
\(461\) | 1.83202e21 | 0.0418286 | 0.0209143 | − | 0.999781i | \(-0.493342\pi\) | ||||
0.0209143 | + | 0.999781i | \(0.493342\pi\) | |||||||
\(462\) | 2.84165e22 | 0.636963 | ||||||||
\(463\) | 1.56727e22 | 0.344910 | 0.172455 | − | 0.985017i | \(-0.444830\pi\) | ||||
0.172455 | + | 0.985017i | \(0.444830\pi\) | |||||||
\(464\) | 1.35270e22 | 0.292280 | ||||||||
\(465\) | −3.36539e22 | −0.713978 | ||||||||
\(466\) | 1.23571e23 | 2.57417 | ||||||||
\(467\) | 5.80904e22 | 1.18826 | 0.594129 | − | 0.804370i | \(-0.297497\pi\) | ||||
0.594129 | + | 0.804370i | \(0.297497\pi\) | |||||||
\(468\) | 1.14310e23 | 2.29611 | ||||||||
\(469\) | 4.41087e22 | 0.870072 | ||||||||
\(470\) | −5.95328e22 | −1.15325 | ||||||||
\(471\) | −2.04412e22 | −0.388891 | ||||||||
\(472\) | 1.80004e22 | 0.336337 | ||||||||
\(473\) | 3.17760e21 | 0.0583149 | ||||||||
\(474\) | 1.65407e23 | 2.98152 | ||||||||
\(475\) | 1.33200e22 | 0.235836 | ||||||||
\(476\) | 2.64365e23 | 4.59775 | ||||||||
\(477\) | −5.49378e22 | −0.938567 | ||||||||
\(478\) | 1.63061e23 | 2.73662 | ||||||||
\(479\) | 8.51939e22 | 1.40461 | 0.702307 | − | 0.711875i | \(-0.252154\pi\) | ||||
0.702307 | + | 0.711875i | \(0.252154\pi\) | |||||||
\(480\) | −6.20229e22 | −1.00462 | ||||||||
\(481\) | 1.31458e23 | 2.09197 | ||||||||
\(482\) | 8.20230e22 | 1.28244 | ||||||||
\(483\) | −7.48799e22 | −1.15031 | ||||||||
\(484\) | −1.36805e23 | −2.06498 | ||||||||
\(485\) | 7.78227e22 | 1.15425 | ||||||||
\(486\) | 1.47266e23 | 2.14632 | ||||||||
\(487\) | −4.47381e22 | −0.640739 | −0.320370 | − | 0.947293i | \(-0.603807\pi\) | ||||
−0.320370 | + | 0.947293i | \(0.603807\pi\) | |||||||
\(488\) | 1.32948e23 | 1.87117 | ||||||||
\(489\) | 1.19090e23 | 1.64722 | ||||||||
\(490\) | −5.79625e22 | −0.787917 | ||||||||
\(491\) | 2.24806e22 | 0.300341 | 0.150171 | − | 0.988660i | \(-0.452018\pi\) | ||||
0.150171 | + | 0.988660i | \(0.452018\pi\) | |||||||
\(492\) | −3.59443e23 | −4.71983 | ||||||||
\(493\) | 2.56024e22 | 0.330432 | ||||||||
\(494\) | −2.50638e23 | −3.17957 | ||||||||
\(495\) | −1.44291e22 | −0.179927 | ||||||||
\(496\) | −6.40433e22 | −0.785017 | ||||||||
\(497\) | −1.02445e23 | −1.23441 | ||||||||
\(498\) | −8.05634e22 | −0.954307 | ||||||||
\(499\) | −1.50494e23 | −1.75252 | −0.876262 | − | 0.481836i | \(-0.839970\pi\) | ||||
−0.876262 | + | 0.481836i | \(0.839970\pi\) | |||||||
\(500\) | −1.67636e23 | −1.91921 | ||||||||
\(501\) | 1.45515e23 | 1.63790 | ||||||||
\(502\) | 7.68538e22 | 0.850518 | ||||||||
\(503\) | −9.48795e22 | −1.03239 | −0.516196 | − | 0.856471i | \(-0.672652\pi\) | ||||
−0.516196 | + | 0.856471i | \(0.672652\pi\) | |||||||
\(504\) | −1.66781e23 | −1.78438 | ||||||||
\(505\) | 1.60286e23 | 1.68623 | ||||||||
\(506\) | −2.94067e22 | −0.304205 | ||||||||
\(507\) | 1.50301e23 | 1.52895 | ||||||||
\(508\) | 3.10089e23 | 3.10202 | ||||||||
\(509\) | 3.53997e22 | 0.348256 | 0.174128 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174128 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(510\) | −4.69544e23 | −4.54286 | ||||||||
\(511\) | −2.77789e22 | −0.264324 | ||||||||
\(512\) | 2.36044e23 | 2.20901 | ||||||||
\(513\) | −4.90619e22 | −0.451593 | ||||||||
\(514\) | 3.30288e23 | 2.99024 | ||||||||
\(515\) | 1.15768e23 | 1.03092 | ||||||||
\(516\) | −8.26097e22 | −0.723617 | ||||||||
\(517\) | −1.58015e22 | −0.136154 | ||||||||
\(518\) | −3.54280e23 | −3.00292 | ||||||||
\(519\) | −1.58037e23 | −1.31776 | ||||||||
\(520\) | −4.12988e23 | −3.38773 | ||||||||
\(521\) | 5.25323e22 | 0.423942 | 0.211971 | − | 0.977276i | \(-0.432012\pi\) | ||||
0.211971 | + | 0.977276i | \(0.432012\pi\) | |||||||
\(522\) | −2.98344e22 | −0.236874 | ||||||||
\(523\) | 3.45072e22 | 0.269554 | 0.134777 | − | 0.990876i | \(-0.456968\pi\) | ||||
0.134777 | + | 0.990876i | \(0.456968\pi\) | |||||||
\(524\) | −1.57569e23 | −1.21103 | ||||||||
\(525\) | 3.99662e22 | 0.302231 | ||||||||
\(526\) | 3.02994e23 | 2.25452 | ||||||||
\(527\) | −1.21214e23 | −0.887486 | ||||||||
\(528\) | −6.58477e22 | −0.474408 | ||||||||
\(529\) | −6.35611e22 | −0.450628 | ||||||||
\(530\) | 3.66624e23 | 2.55786 | ||||||||
\(531\) | −1.66437e22 | −0.114274 | ||||||||
\(532\) | 4.63089e23 | 3.12907 | ||||||||
\(533\) | −3.65900e23 | −2.43322 | ||||||||
\(534\) | 3.70873e23 | 2.42730 | ||||||||
\(535\) | −8.70581e22 | −0.560792 | ||||||||
\(536\) | −2.43804e23 | −1.54576 | ||||||||
\(537\) | −3.41037e23 | −2.12824 | ||||||||
\(538\) | −3.86514e23 | −2.37419 | ||||||||
\(539\) | −1.53847e22 | −0.0930220 | ||||||||
\(540\) | −1.49324e23 | −0.888756 | ||||||||
\(541\) | −2.71733e23 | −1.59208 | −0.796041 | − | 0.605242i | \(-0.793076\pi\) | ||||
−0.796041 | + | 0.605242i | \(0.793076\pi\) | |||||||
\(542\) | −1.24136e23 | −0.715983 | ||||||||
\(543\) | 3.34081e23 | 1.89694 | ||||||||
\(544\) | −2.23393e23 | −1.24876 | ||||||||
\(545\) | −3.49159e23 | −1.92155 | ||||||||
\(546\) | −7.52032e23 | −4.07473 | ||||||||
\(547\) | 7.86656e22 | 0.419655 | 0.209828 | − | 0.977738i | \(-0.432710\pi\) | ||||
0.209828 | + | 0.977738i | \(0.432710\pi\) | |||||||
\(548\) | 5.76796e23 | 3.02962 | ||||||||
\(549\) | −1.22928e23 | −0.635749 | ||||||||
\(550\) | 1.56955e22 | 0.0799265 | ||||||||
\(551\) | 4.48478e22 | 0.224881 | ||||||||
\(552\) | 4.13887e23 | 2.04362 | ||||||||
\(553\) | −3.11102e23 | −1.51265 | ||||||||
\(554\) | 5.42762e23 | 2.59882 | ||||||||
\(555\) | 4.31397e23 | 2.03417 | ||||||||
\(556\) | 5.05374e23 | 2.34680 | ||||||||
\(557\) | 3.77522e23 | 1.72652 | 0.863262 | − | 0.504756i | \(-0.168417\pi\) | ||||
0.863262 | + | 0.504756i | \(0.168417\pi\) | |||||||
\(558\) | 1.41250e23 | 0.636207 | ||||||||
\(559\) | −8.40939e22 | −0.373047 | ||||||||
\(560\) | 4.66603e23 | 2.03868 | ||||||||
\(561\) | −1.24629e23 | −0.536333 | ||||||||
\(562\) | −1.83815e23 | −0.779150 | ||||||||
\(563\) | 4.39470e23 | 1.83488 | 0.917440 | − | 0.397874i | \(-0.130252\pi\) | ||||
0.917440 | + | 0.397874i | \(0.130252\pi\) | |||||||
\(564\) | 4.10801e23 | 1.68950 | ||||||||
\(565\) | 1.62006e21 | 0.00656327 | ||||||||
\(566\) | −5.74734e23 | −2.29365 | ||||||||
\(567\) | −3.62805e23 | −1.42632 | ||||||||
\(568\) | 5.66247e23 | 2.19303 | ||||||||
\(569\) | 8.19442e22 | 0.312654 | 0.156327 | − | 0.987705i | \(-0.450035\pi\) | ||||
0.156327 | + | 0.987705i | \(0.450035\pi\) | |||||||
\(570\) | −8.22501e23 | −3.09172 | ||||||||
\(571\) | −4.04798e23 | −1.49910 | −0.749551 | − | 0.661947i | \(-0.769730\pi\) | ||||
−0.749551 | + | 0.661947i | \(0.769730\pi\) | |||||||
\(572\) | −2.02477e23 | −0.738770 | ||||||||
\(573\) | 1.21329e23 | 0.436163 | ||||||||
\(574\) | 9.86101e23 | 3.49277 | ||||||||
\(575\) | −4.13588e22 | −0.144342 | ||||||||
\(576\) | −6.70673e22 | −0.230632 | ||||||||
\(577\) | 1.88491e23 | 0.638698 | 0.319349 | − | 0.947637i | \(-0.396536\pi\) | ||||
0.319349 | + | 0.947637i | \(0.396536\pi\) | |||||||
\(578\) | −1.15708e24 | −3.86347 | ||||||||
\(579\) | −8.78208e22 | −0.288955 | ||||||||
\(580\) | 1.36498e23 | 0.442576 | ||||||||
\(581\) | 1.51526e23 | 0.484162 | ||||||||
\(582\) | −7.83289e23 | −2.46648 | ||||||||
\(583\) | 9.73115e22 | 0.301982 | ||||||||
\(584\) | 1.53543e23 | 0.469594 | ||||||||
\(585\) | 3.81861e23 | 1.15101 | ||||||||
\(586\) | 3.70299e23 | 1.10007 | ||||||||
\(587\) | 7.10981e22 | 0.208178 | 0.104089 | − | 0.994568i | \(-0.466807\pi\) | ||||
0.104089 | + | 0.994568i | \(0.466807\pi\) | |||||||
\(588\) | 3.99965e23 | 1.15429 | ||||||||
\(589\) | −2.12331e23 | −0.603994 | ||||||||
\(590\) | 1.11071e23 | 0.311428 | ||||||||
\(591\) | −3.69710e22 | −0.102180 | ||||||||
\(592\) | 8.20948e23 | 2.23656 | ||||||||
\(593\) | −1.17349e23 | −0.315148 | −0.157574 | − | 0.987507i | \(-0.550367\pi\) | ||||
−0.157574 | + | 0.987507i | \(0.550367\pi\) | |||||||
\(594\) | −5.78114e22 | −0.153048 | ||||||||
\(595\) | 8.83133e23 | 2.30479 | ||||||||
\(596\) | −3.67526e22 | −0.0945574 | ||||||||
\(597\) | 7.26799e23 | 1.84345 | ||||||||
\(598\) | 7.78235e23 | 1.94604 | ||||||||
\(599\) | 4.09095e23 | 1.00855 | 0.504273 | − | 0.863544i | \(-0.331760\pi\) | ||||
0.504273 | + | 0.863544i | \(0.331760\pi\) | |||||||
\(600\) | −2.20907e23 | −0.536939 | ||||||||
\(601\) | −3.75264e23 | −0.899299 | −0.449649 | − | 0.893205i | \(-0.648451\pi\) | ||||
−0.449649 | + | 0.893205i | \(0.648451\pi\) | |||||||
\(602\) | 2.26633e23 | 0.535491 | ||||||||
\(603\) | 2.25429e23 | 0.525185 | ||||||||
\(604\) | −5.35312e23 | −1.22968 | ||||||||
\(605\) | −4.57009e23 | −1.03515 | ||||||||
\(606\) | −1.61328e24 | −3.60324 | ||||||||
\(607\) | 1.43973e23 | 0.317086 | 0.158543 | − | 0.987352i | \(-0.449320\pi\) | ||||
0.158543 | + | 0.987352i | \(0.449320\pi\) | |||||||
\(608\) | −3.91318e23 | −0.849864 | ||||||||
\(609\) | 1.34564e23 | 0.288192 | ||||||||
\(610\) | 8.20351e23 | 1.73259 | ||||||||
\(611\) | 4.18181e23 | 0.870992 | ||||||||
\(612\) | 1.35111e24 | 2.77525 | ||||||||
\(613\) | 5.25038e23 | 1.06360 | 0.531799 | − | 0.846871i | \(-0.321516\pi\) | ||||
0.531799 | + | 0.846871i | \(0.321516\pi\) | |||||||
\(614\) | −5.30710e23 | −1.06029 | ||||||||
\(615\) | −1.20075e24 | −2.36599 | ||||||||
\(616\) | 2.95419e23 | 0.574120 | ||||||||
\(617\) | −3.49285e22 | −0.0669508 | −0.0334754 | − | 0.999440i | \(-0.510658\pi\) | ||||
−0.0334754 | + | 0.999440i | \(0.510658\pi\) | |||||||
\(618\) | −1.16521e24 | −2.20294 | ||||||||
\(619\) | −1.47469e23 | −0.274998 | −0.137499 | − | 0.990502i | \(-0.543906\pi\) | ||||
−0.137499 | + | 0.990502i | \(0.543906\pi\) | |||||||
\(620\) | −6.46245e23 | −1.18869 | ||||||||
\(621\) | 1.52338e23 | 0.276394 | ||||||||
\(622\) | −9.92959e23 | −1.77710 | ||||||||
\(623\) | −6.97550e23 | −1.23148 | ||||||||
\(624\) | 1.74263e24 | 3.03484 | ||||||||
\(625\) | −6.73356e23 | −1.15682 | ||||||||
\(626\) | −9.20128e23 | −1.55943 | ||||||||
\(627\) | −2.18313e23 | −0.365011 | ||||||||
\(628\) | −3.92526e23 | −0.647458 | ||||||||
\(629\) | 1.55380e24 | 2.52850 | ||||||||
\(630\) | −1.02911e24 | −1.65222 | ||||||||
\(631\) | 7.40740e23 | 1.17332 | 0.586660 | − | 0.809833i | \(-0.300443\pi\) | ||||
0.586660 | + | 0.809833i | \(0.300443\pi\) | |||||||
\(632\) | 1.71957e24 | 2.68736 | ||||||||
\(633\) | −4.47578e23 | −0.690140 | ||||||||
\(634\) | −1.06324e24 | −1.61760 | ||||||||
\(635\) | 1.03588e24 | 1.55501 | ||||||||
\(636\) | −2.52986e24 | −3.74723 | ||||||||
\(637\) | 4.07150e23 | 0.595072 | ||||||||
\(638\) | 5.28457e22 | 0.0762139 | ||||||||
\(639\) | −5.23569e23 | −0.745103 | ||||||||
\(640\) | 9.93786e23 | 1.39561 | ||||||||
\(641\) | −3.50461e23 | −0.485676 | −0.242838 | − | 0.970067i | \(-0.578078\pi\) | ||||
−0.242838 | + | 0.970067i | \(0.578078\pi\) | |||||||
\(642\) | 8.76244e23 | 1.19833 | ||||||||
\(643\) | −6.96395e23 | −0.939858 | −0.469929 | − | 0.882704i | \(-0.655721\pi\) | ||||
−0.469929 | + | 0.882704i | \(0.655721\pi\) | |||||||
\(644\) | −1.43790e24 | −1.91513 | ||||||||
\(645\) | −2.75965e23 | −0.362740 | ||||||||
\(646\) | −2.96247e24 | −3.84306 | ||||||||
\(647\) | −2.63794e23 | −0.337738 | −0.168869 | − | 0.985639i | \(-0.554011\pi\) | ||||
−0.168869 | + | 0.985639i | \(0.554011\pi\) | |||||||
\(648\) | 2.00535e24 | 2.53398 | ||||||||
\(649\) | 2.94810e22 | 0.0367674 | ||||||||
\(650\) | −4.15374e23 | −0.511299 | ||||||||
\(651\) | −6.37090e23 | −0.774039 | ||||||||
\(652\) | 2.28685e24 | 2.74242 | ||||||||
\(653\) | −1.64108e24 | −1.94253 | −0.971263 | − | 0.238007i | \(-0.923506\pi\) | ||||
−0.971263 | + | 0.238007i | \(0.923506\pi\) | |||||||
\(654\) | 3.51430e24 | 4.10608 | ||||||||
\(655\) | −5.26371e23 | −0.607074 | ||||||||
\(656\) | −2.28502e24 | −2.60140 | ||||||||
\(657\) | −1.41971e23 | −0.159549 | ||||||||
\(658\) | −1.12700e24 | −1.25027 | ||||||||
\(659\) | 5.73508e22 | 0.0628078 | 0.0314039 | − | 0.999507i | \(-0.490002\pi\) | ||||
0.0314039 | + | 0.999507i | \(0.490002\pi\) | |||||||
\(660\) | −6.64453e23 | −0.718358 | ||||||||
\(661\) | −1.04064e24 | −1.11067 | −0.555336 | − | 0.831626i | \(-0.687410\pi\) | ||||
−0.555336 | + | 0.831626i | \(0.687410\pi\) | |||||||
\(662\) | 2.93570e24 | 3.09327 | ||||||||
\(663\) | 3.29825e24 | 3.43099 | ||||||||
\(664\) | −8.37539e23 | −0.860154 | ||||||||
\(665\) | 1.54699e24 | 1.56857 | ||||||||
\(666\) | −1.81064e24 | −1.81259 | ||||||||
\(667\) | −1.39253e23 | −0.137637 | ||||||||
\(668\) | 2.79429e24 | 2.72691 | ||||||||
\(669\) | 1.93375e24 | 1.86328 | ||||||||
\(670\) | −1.50439e24 | −1.43128 | ||||||||
\(671\) | 2.17742e23 | 0.204551 | ||||||||
\(672\) | −1.17414e24 | −1.08913 | ||||||||
\(673\) | −3.50405e23 | −0.320953 | −0.160477 | − | 0.987040i | \(-0.551303\pi\) | ||||
−0.160477 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(674\) | −3.23073e24 | −2.92207 | ||||||||
\(675\) | −8.13084e22 | −0.0726195 | ||||||||
\(676\) | 2.88619e24 | 2.54553 | ||||||||
\(677\) | −6.35949e23 | −0.553884 | −0.276942 | − | 0.960887i | \(-0.589321\pi\) | ||||
−0.276942 | + | 0.960887i | \(0.589321\pi\) | |||||||
\(678\) | −1.63060e22 | −0.0140248 | ||||||||
\(679\) | 1.47324e24 | 1.25135 | ||||||||
\(680\) | −4.88139e24 | −4.09466 | ||||||||
\(681\) | 2.79568e23 | 0.231599 | ||||||||
\(682\) | −2.50197e23 | −0.204698 | ||||||||
\(683\) | −8.56675e23 | −0.692214 | −0.346107 | − | 0.938195i | \(-0.612497\pi\) | ||||
−0.346107 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(684\) | 2.36674e24 | 1.88874 | ||||||||
\(685\) | 1.92684e24 | 1.51871 | ||||||||
\(686\) | 1.61739e24 | 1.25910 | ||||||||
\(687\) | 1.15475e24 | 0.887881 | ||||||||
\(688\) | −5.25160e23 | −0.398832 | ||||||||
\(689\) | −2.57531e24 | −1.93181 | ||||||||
\(690\) | 2.55388e24 | 1.89227 | ||||||||
\(691\) | 1.21066e24 | 0.886053 | 0.443027 | − | 0.896508i | \(-0.353905\pi\) | ||||
0.443027 | + | 0.896508i | \(0.353905\pi\) | |||||||
\(692\) | −3.03474e24 | −2.19392 | ||||||||
\(693\) | −2.73153e23 | −0.195063 | ||||||||
\(694\) | 2.69704e24 | 1.90253 | ||||||||
\(695\) | 1.68824e24 | 1.17642 | ||||||||
\(696\) | −7.43783e23 | −0.511997 | ||||||||
\(697\) | −4.32483e24 | −2.94097 | ||||||||
\(698\) | −3.75896e24 | −2.52520 | ||||||||
\(699\) | −2.84848e24 | −1.89042 | ||||||||
\(700\) | 7.67460e23 | 0.503179 | ||||||||
\(701\) | 8.06024e23 | 0.522089 | 0.261045 | − | 0.965327i | \(-0.415933\pi\) | ||||
0.261045 | + | 0.965327i | \(0.415933\pi\) | |||||||
\(702\) | 1.52995e24 | 0.979068 | ||||||||
\(703\) | 2.72179e24 | 1.72082 | ||||||||
\(704\) | 1.18796e23 | 0.0742054 | ||||||||
\(705\) | 1.37231e24 | 0.846927 | ||||||||
\(706\) | 1.58537e24 | 0.966697 | ||||||||
\(707\) | 3.03432e24 | 1.82808 | ||||||||
\(708\) | −7.66433e23 | −0.456238 | ||||||||
\(709\) | −5.09200e22 | −0.0299499 | −0.0149749 | − | 0.999888i | \(-0.504767\pi\) | ||||
−0.0149749 | + | 0.999888i | \(0.504767\pi\) | |||||||
\(710\) | 3.49400e24 | 2.03061 | ||||||||
\(711\) | −1.58997e24 | −0.913054 | ||||||||
\(712\) | 3.85560e24 | 2.18782 | ||||||||
\(713\) | 6.59289e23 | 0.369670 | ||||||||
\(714\) | −8.88878e24 | −4.92501 | ||||||||
\(715\) | −6.76391e23 | −0.370336 | ||||||||
\(716\) | −6.54884e24 | −3.54327 | ||||||||
\(717\) | −3.75879e24 | −2.00972 | ||||||||
\(718\) | −6.21817e23 | −0.328553 | ||||||||
\(719\) | 1.84407e24 | 0.962902 | 0.481451 | − | 0.876473i | \(-0.340110\pi\) | ||||
0.481451 | + | 0.876473i | \(0.340110\pi\) | |||||||
\(720\) | 2.38470e24 | 1.23057 | ||||||||
\(721\) | 2.19156e24 | 1.11765 | ||||||||
\(722\) | −1.65093e24 | −0.832074 | ||||||||
\(723\) | −1.89074e24 | −0.941796 | ||||||||
\(724\) | 6.41527e24 | 3.15818 | ||||||||
\(725\) | 7.43245e22 | 0.0361625 | ||||||||
\(726\) | 4.59981e24 | 2.21197 | ||||||||
\(727\) | 9.59151e23 | 0.455873 | 0.227937 | − | 0.973676i | \(-0.426802\pi\) | ||||
0.227937 | + | 0.973676i | \(0.426802\pi\) | |||||||
\(728\) | −7.81814e24 | −3.67271 | ||||||||
\(729\) | −8.02377e23 | −0.372559 | ||||||||
\(730\) | 9.47434e23 | 0.434815 | ||||||||
\(731\) | −9.93963e23 | −0.450892 | ||||||||
\(732\) | −5.66076e24 | −2.53823 | ||||||||
\(733\) | −3.35057e24 | −1.48503 | −0.742514 | − | 0.669831i | \(-0.766367\pi\) | ||||
−0.742514 | + | 0.669831i | \(0.766367\pi\) | |||||||
\(734\) | 2.12317e24 | 0.930181 | ||||||||
\(735\) | 1.33612e24 | 0.578631 | ||||||||
\(736\) | 1.21505e24 | 0.520153 | ||||||||
\(737\) | −3.99302e23 | −0.168977 | ||||||||
\(738\) | 5.03972e24 | 2.10827 | ||||||||
\(739\) | −8.18867e23 | −0.338638 | −0.169319 | − | 0.985561i | \(-0.554157\pi\) | ||||
−0.169319 | + | 0.985561i | \(0.554157\pi\) | |||||||
\(740\) | 8.28399e24 | 3.38665 | ||||||||
\(741\) | 5.77756e24 | 2.33502 | ||||||||
\(742\) | 6.94044e24 | 2.77303 | ||||||||
\(743\) | −2.28443e24 | −0.902347 | −0.451173 | − | 0.892436i | \(-0.648994\pi\) | ||||
−0.451173 | + | 0.892436i | \(0.648994\pi\) | |||||||
\(744\) | 3.52142e24 | 1.37514 | ||||||||
\(745\) | −1.22775e23 | −0.0474004 | ||||||||
\(746\) | −6.31103e24 | −2.40891 | ||||||||
\(747\) | 7.74414e23 | 0.292245 | ||||||||
\(748\) | −2.39321e24 | −0.892931 | ||||||||
\(749\) | −1.64807e24 | −0.607967 | ||||||||
\(750\) | 5.63645e24 | 2.05582 | ||||||||
\(751\) | 3.36388e24 | 1.21311 | 0.606557 | − | 0.795040i | \(-0.292550\pi\) | ||||
0.606557 | + | 0.795040i | \(0.292550\pi\) | |||||||
\(752\) | 2.61151e24 | 0.931194 | ||||||||
\(753\) | −1.77159e24 | −0.624604 | ||||||||
\(754\) | −1.39854e24 | −0.487549 | ||||||||
\(755\) | −1.78825e24 | −0.616425 | ||||||||
\(756\) | −2.82680e24 | −0.963519 | ||||||||
\(757\) | 2.85798e24 | 0.963261 | 0.481631 | − | 0.876374i | \(-0.340045\pi\) | ||||
0.481631 | + | 0.876374i | \(0.340045\pi\) | |||||||
\(758\) | 4.88090e24 | 1.62671 | ||||||||
\(759\) | 6.77864e23 | 0.223402 | ||||||||
\(760\) | −8.55074e24 | −2.78669 | ||||||||
\(761\) | −4.10866e24 | −1.32413 | −0.662065 | − | 0.749447i | \(-0.730320\pi\) | ||||
−0.662065 | + | 0.749447i | \(0.730320\pi\) | |||||||
\(762\) | −1.04262e25 | −3.32282 | ||||||||
\(763\) | −6.60981e24 | −2.08320 | ||||||||
\(764\) | 2.32984e24 | 0.726160 | ||||||||
\(765\) | 4.51348e24 | 1.39120 | ||||||||
\(766\) | 6.06248e24 | 1.84802 | ||||||||
\(767\) | −7.80202e23 | −0.235205 | ||||||||
\(768\) | −8.58610e24 | −2.55992 | ||||||||
\(769\) | 2.31222e24 | 0.681797 | 0.340898 | − | 0.940100i | \(-0.389269\pi\) | ||||
0.340898 | + | 0.940100i | \(0.389269\pi\) | |||||||
\(770\) | 1.82287e24 | 0.531600 | ||||||||
\(771\) | −7.61359e24 | −2.19597 | ||||||||
\(772\) | −1.68640e24 | −0.481075 | ||||||||
\(773\) | 2.16669e24 | 0.611323 | 0.305661 | − | 0.952140i | \(-0.401122\pi\) | ||||
0.305661 | + | 0.952140i | \(0.401122\pi\) | |||||||
\(774\) | 1.15826e24 | 0.323228 | ||||||||
\(775\) | −3.51887e23 | −0.0971268 | ||||||||
\(776\) | −8.14309e24 | −2.22313 | ||||||||
\(777\) | 8.16663e24 | 2.20528 | ||||||||
\(778\) | −2.22000e24 | −0.592961 | ||||||||
\(779\) | −7.57582e24 | −2.00153 | ||||||||
\(780\) | 1.75845e25 | 4.59542 | ||||||||
\(781\) | 9.27398e23 | 0.239735 | ||||||||
\(782\) | 9.19850e24 | 2.35212 | ||||||||
\(783\) | −2.73761e23 | −0.0692463 | ||||||||
\(784\) | 2.54263e24 | 0.636204 | ||||||||
\(785\) | −1.31127e24 | −0.324563 | ||||||||
\(786\) | 5.29795e24 | 1.29723 | ||||||||
\(787\) | −4.02529e24 | −0.975018 | −0.487509 | − | 0.873118i | \(-0.662094\pi\) | ||||
−0.487509 | + | 0.873118i | \(0.662094\pi\) | |||||||
\(788\) | −7.09943e23 | −0.170118 | ||||||||
\(789\) | −6.98442e24 | −1.65568 | ||||||||
\(790\) | 1.06105e25 | 2.48833 | ||||||||
\(791\) | 3.06689e22 | 0.00711538 | ||||||||
\(792\) | 1.50981e24 | 0.346545 | ||||||||
\(793\) | −5.76246e24 | −1.30854 | ||||||||
\(794\) | −2.39695e24 | −0.538499 | ||||||||
\(795\) | −8.45119e24 | −1.87844 | ||||||||
\(796\) | 1.39565e25 | 3.06913 | ||||||||
\(797\) | −5.44766e24 | −1.18526 | −0.592631 | − | 0.805474i | \(-0.701911\pi\) | ||||
−0.592631 | + | 0.805474i | \(0.701911\pi\) | |||||||
\(798\) | −1.55705e25 | −3.35180 | ||||||||
\(799\) | 4.94277e24 | 1.05274 | ||||||||
\(800\) | −6.48516e23 | −0.136665 | ||||||||
\(801\) | −3.56500e24 | −0.743333 | ||||||||
\(802\) | 1.49146e24 | 0.307701 | ||||||||
\(803\) | 2.51473e23 | 0.0513345 | ||||||||
\(804\) | 1.03809e25 | 2.09680 | ||||||||
\(805\) | −4.80341e24 | −0.960031 | ||||||||
\(806\) | 6.62135e24 | 1.30948 | ||||||||
\(807\) | 8.90968e24 | 1.74356 | ||||||||
\(808\) | −1.67717e25 | −3.24774 | ||||||||
\(809\) | 5.80752e23 | 0.111283 | 0.0556414 | − | 0.998451i | \(-0.482280\pi\) | ||||
0.0556414 | + | 0.998451i | \(0.482280\pi\) | |||||||
\(810\) | 1.23739e25 | 2.34631 | ||||||||
\(811\) | 3.19811e24 | 0.600090 | 0.300045 | − | 0.953925i | \(-0.402998\pi\) | ||||
0.300045 | + | 0.953925i | \(0.402998\pi\) | |||||||
\(812\) | 2.58400e24 | 0.479806 | ||||||||
\(813\) | 2.86150e24 | 0.525804 | ||||||||
\(814\) | 3.20718e24 | 0.583198 | ||||||||
\(815\) | 7.63942e24 | 1.37474 | ||||||||
\(816\) | 2.05974e25 | 3.66813 | ||||||||
\(817\) | −1.74113e24 | −0.306862 | ||||||||
\(818\) | 2.18258e24 | 0.380686 | ||||||||
\(819\) | 7.22889e24 | 1.24784 | ||||||||
\(820\) | −2.30576e25 | −3.93910 | ||||||||
\(821\) | −7.56232e24 | −1.27861 | −0.639305 | − | 0.768953i | \(-0.720778\pi\) | ||||
−0.639305 | + | 0.768953i | \(0.720778\pi\) | |||||||
\(822\) | −1.93937e25 | −3.24526 | ||||||||
\(823\) | −4.16723e24 | −0.690158 | −0.345079 | − | 0.938574i | \(-0.612148\pi\) | ||||
−0.345079 | + | 0.938574i | \(0.612148\pi\) | |||||||
\(824\) | −1.21135e25 | −1.98559 | ||||||||
\(825\) | −3.61802e23 | −0.0586965 | ||||||||
\(826\) | 2.10264e24 | 0.337625 | ||||||||
\(827\) | −8.45598e24 | −1.34390 | −0.671950 | − | 0.740596i | \(-0.734543\pi\) | ||||
−0.671950 | + | 0.740596i | \(0.734543\pi\) | |||||||
\(828\) | −7.34874e24 | −1.15599 | ||||||||
\(829\) | 7.30805e24 | 1.13786 | 0.568929 | − | 0.822386i | \(-0.307358\pi\) | ||||
0.568929 | + | 0.822386i | \(0.307358\pi\) | |||||||
\(830\) | −5.16800e24 | −0.796450 | ||||||||
\(831\) | −1.25114e25 | −1.90852 | ||||||||
\(832\) | −3.14390e24 | −0.474701 | ||||||||
\(833\) | 4.81239e24 | 0.719248 | ||||||||
\(834\) | −1.69922e25 | −2.51385 | ||||||||
\(835\) | 9.33455e24 | 1.36697 | ||||||||
\(836\) | −4.19220e24 | −0.607699 | ||||||||
\(837\) | 1.29611e24 | 0.185985 | ||||||||
\(838\) | 1.23886e25 | 1.75974 | ||||||||
\(839\) | 8.35418e24 | 1.17470 | 0.587350 | − | 0.809333i | \(-0.300171\pi\) | ||||
0.587350 | + | 0.809333i | \(0.300171\pi\) | |||||||
\(840\) | −2.56562e25 | −3.57123 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | 1.98000e25 | 2.70092 | ||||||||
\(843\) | 4.23718e24 | 0.572192 | ||||||||
\(844\) | −8.59471e24 | −1.14900 | ||||||||
\(845\) | 9.64155e24 | 1.27604 | ||||||||
\(846\) | −5.75980e24 | −0.754674 | ||||||||
\(847\) | −8.65148e24 | −1.12223 | ||||||||
\(848\) | −1.60826e25 | −2.06534 | ||||||||
\(849\) | 1.32484e25 | 1.68441 | ||||||||
\(850\) | −4.90959e24 | −0.617994 | ||||||||
\(851\) | −8.45119e24 | −1.05321 | ||||||||
\(852\) | −2.41100e25 | −2.97482 | ||||||||
\(853\) | −1.19530e25 | −1.46020 | −0.730098 | − | 0.683342i | \(-0.760526\pi\) | ||||
−0.730098 | + | 0.683342i | \(0.760526\pi\) | |||||||
\(854\) | 1.55298e25 | 1.87834 | ||||||||
\(855\) | 7.90627e24 | 0.946804 | ||||||||
\(856\) | 9.10945e24 | 1.08010 | ||||||||
\(857\) | −5.32682e24 | −0.625361 | −0.312681 | − | 0.949858i | \(-0.601227\pi\) | ||||
−0.312681 | + | 0.949858i | \(0.601227\pi\) | |||||||
\(858\) | 6.80790e24 | 0.791355 | ||||||||
\(859\) | 3.60851e24 | 0.415323 | 0.207661 | − | 0.978201i | \(-0.433415\pi\) | ||||
0.207661 | + | 0.978201i | \(0.433415\pi\) | |||||||
\(860\) | −5.29927e24 | −0.603919 | ||||||||
\(861\) | −2.27310e25 | −2.56502 | ||||||||
\(862\) | −1.55933e25 | −1.74232 | ||||||||
\(863\) | −1.28137e24 | −0.141770 | −0.0708848 | − | 0.997485i | \(-0.522582\pi\) | ||||
−0.0708848 | + | 0.997485i | \(0.522582\pi\) | |||||||
\(864\) | 2.38869e24 | 0.261694 | ||||||||
\(865\) | −1.01378e25 | −1.09978 | ||||||||
\(866\) | 2.10805e25 | 2.26453 | ||||||||
\(867\) | 2.66723e25 | 2.83725 | ||||||||
\(868\) | −1.22339e25 | −1.28868 | ||||||||
\(869\) | 2.81631e24 | 0.293773 | ||||||||
\(870\) | −4.58948e24 | −0.474078 | ||||||||
\(871\) | 1.05674e25 | 1.08097 | ||||||||
\(872\) | 3.65347e25 | 3.70097 | ||||||||
\(873\) | 7.52935e24 | 0.755329 | ||||||||
\(874\) | 1.61130e25 | 1.60077 | ||||||||
\(875\) | −1.06012e25 | −1.04301 | ||||||||
\(876\) | −6.53768e24 | −0.636999 | ||||||||
\(877\) | −1.06601e25 | −1.02864 | −0.514322 | − | 0.857597i | \(-0.671956\pi\) | ||||
−0.514322 | + | 0.857597i | \(0.671956\pi\) | |||||||
\(878\) | 2.15574e25 | 2.06012 | ||||||||
\(879\) | −8.53589e24 | −0.807873 | ||||||||
\(880\) | −4.22401e24 | −0.395934 | ||||||||
\(881\) | 6.83036e24 | 0.634087 | 0.317043 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317043 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(882\) | −5.60787e24 | −0.515603 | ||||||||
\(883\) | 5.77117e24 | 0.525530 | 0.262765 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262765 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(884\) | 6.33354e25 | 5.71218 | ||||||||
\(885\) | −2.56033e24 | −0.228706 | ||||||||
\(886\) | −1.21670e25 | −1.07645 | ||||||||
\(887\) | −5.24053e24 | −0.459224 | −0.229612 | − | 0.973282i | \(-0.573746\pi\) | ||||
−0.229612 | + | 0.973282i | \(0.573746\pi\) | |||||||
\(888\) | −4.51398e25 | −3.91787 | ||||||||
\(889\) | 1.96099e25 | 1.68581 | ||||||||
\(890\) | 2.37908e25 | 2.02579 | ||||||||
\(891\) | 3.28436e24 | 0.277007 | ||||||||
\(892\) | 3.71332e25 | 3.10214 | ||||||||
\(893\) | 8.65827e24 | 0.716463 | ||||||||
\(894\) | 1.23574e24 | 0.101288 | ||||||||
\(895\) | −2.18769e25 | −1.77620 | ||||||||
\(896\) | 1.88130e25 | 1.51301 | ||||||||
\(897\) | −1.79394e25 | −1.42913 | ||||||||
\(898\) | 2.10920e25 | 1.66444 | ||||||||
\(899\) | −1.18479e24 | −0.0926152 | ||||||||
\(900\) | 3.92230e24 | 0.303724 | ||||||||
\(901\) | −3.04393e25 | −2.33493 | ||||||||
\(902\) | −8.92686e24 | −0.678333 | ||||||||
\(903\) | −5.22419e24 | −0.393254 | ||||||||
\(904\) | −1.69518e23 | −0.0126411 | ||||||||
\(905\) | 2.14307e25 | 1.58316 | ||||||||
\(906\) | 1.79989e25 | 1.31721 | ||||||||
\(907\) | 1.51449e25 | 1.09801 | 0.549003 | − | 0.835820i | \(-0.315008\pi\) | ||||
0.549003 | + | 0.835820i | \(0.315008\pi\) | |||||||
\(908\) | 5.36847e24 | 0.385586 | ||||||||
\(909\) | 1.55076e25 | 1.10345 | ||||||||
\(910\) | −4.82415e25 | −3.40071 | ||||||||
\(911\) | 1.28115e25 | 0.894732 | 0.447366 | − | 0.894351i | \(-0.352362\pi\) | ||||
0.447366 | + | 0.894351i | \(0.352362\pi\) | |||||||
\(912\) | 3.60805e25 | 2.49641 | ||||||||
\(913\) | −1.37172e24 | −0.0940294 | ||||||||
\(914\) | −6.24697e24 | −0.424255 | ||||||||
\(915\) | −1.89102e25 | −1.27238 | ||||||||
\(916\) | 2.21743e25 | 1.47822 | ||||||||
\(917\) | −9.96457e24 | −0.658141 | ||||||||
\(918\) | 1.80836e25 | 1.18337 | ||||||||
\(919\) | −3.21309e24 | −0.208325 | −0.104162 | − | 0.994560i | \(-0.533216\pi\) | ||||
−0.104162 | + | 0.994560i | \(0.533216\pi\) | |||||||
\(920\) | 2.65501e25 | 1.70557 | ||||||||
\(921\) | 1.22336e25 | 0.778659 | ||||||||
\(922\) | −1.18285e24 | −0.0745965 | ||||||||
\(923\) | −2.45432e25 | −1.53362 | ||||||||
\(924\) | −1.25785e25 | −0.778787 | ||||||||
\(925\) | 4.51072e24 | 0.276720 | ||||||||
\(926\) | −1.01192e25 | −0.615108 | ||||||||
\(927\) | 1.12005e25 | 0.674623 | ||||||||
\(928\) | −2.18352e24 | −0.130316 | ||||||||
\(929\) | −1.54037e25 | −0.910944 | −0.455472 | − | 0.890250i | \(-0.650529\pi\) | ||||
−0.455472 | + | 0.890250i | \(0.650529\pi\) | |||||||
\(930\) | 2.17288e25 | 1.27330 | ||||||||
\(931\) | 8.42988e24 | 0.489496 | ||||||||
\(932\) | −5.46986e25 | −3.14732 | ||||||||
\(933\) | 2.28891e25 | 1.30507 | ||||||||
\(934\) | −3.75064e25 | −2.11912 | ||||||||
\(935\) | −7.99473e24 | −0.447615 | ||||||||
\(936\) | −3.99566e25 | −2.21689 | ||||||||
\(937\) | −1.65163e25 | −0.908083 | −0.454042 | − | 0.890981i | \(-0.650018\pi\) | ||||
−0.454042 | + | 0.890981i | \(0.650018\pi\) | |||||||
\(938\) | −2.84790e25 | −1.55168 | ||||||||
\(939\) | 2.12102e25 | 1.14522 | ||||||||
\(940\) | 2.63521e25 | 1.41003 | ||||||||
\(941\) | 1.13211e25 | 0.600312 | 0.300156 | − | 0.953890i | \(-0.402961\pi\) | ||||
0.300156 | + | 0.953890i | \(0.402961\pi\) | |||||||
\(942\) | 1.31980e25 | 0.693544 | ||||||||
\(943\) | 2.35230e25 | 1.22502 | ||||||||
\(944\) | −4.87231e24 | −0.251462 | ||||||||
\(945\) | −9.44317e24 | −0.483000 | ||||||||
\(946\) | −2.05163e24 | −0.103998 | ||||||||
\(947\) | 2.69015e25 | 1.35145 | 0.675727 | − | 0.737152i | \(-0.263830\pi\) | ||||
0.675727 | + | 0.737152i | \(0.263830\pi\) | |||||||
\(948\) | −7.32171e25 | −3.64537 | ||||||||
\(949\) | −6.65513e24 | −0.328393 | ||||||||
\(950\) | −8.60014e24 | −0.420586 | ||||||||
\(951\) | 2.45090e25 | 1.18793 | ||||||||
\(952\) | −9.24080e25 | −4.43910 | ||||||||
\(953\) | 2.54029e25 | 1.20947 | 0.604733 | − | 0.796428i | \(-0.293280\pi\) | ||||
0.604733 | + | 0.796428i | \(0.293280\pi\) | |||||||
\(954\) | 3.54709e25 | 1.67383 | ||||||||
\(955\) | 7.78302e24 | 0.364015 | ||||||||
\(956\) | −7.21789e25 | −3.34594 | ||||||||
\(957\) | −1.21817e24 | −0.0559700 | ||||||||
\(958\) | −5.50059e25 | −2.50497 | ||||||||
\(959\) | 3.64763e25 | 1.64647 | ||||||||
\(960\) | −1.03171e25 | −0.461585 | ||||||||
\(961\) | −1.69408e25 | −0.751250 | ||||||||
\(962\) | −8.48767e25 | −3.73079 | ||||||||
\(963\) | −8.42287e24 | −0.366975 | ||||||||
\(964\) | −3.63074e25 | −1.56798 | ||||||||
\(965\) | −5.63355e24 | −0.241157 | ||||||||
\(966\) | 4.83466e25 | 2.05145 | ||||||||
\(967\) | −1.75933e25 | −0.739984 | −0.369992 | − | 0.929035i | \(-0.620640\pi\) | ||||
−0.369992 | + | 0.929035i | \(0.620640\pi\) | |||||||
\(968\) | 4.78198e25 | 1.99373 | ||||||||
\(969\) | 6.82890e25 | 2.82227 | ||||||||
\(970\) | −5.02466e25 | −2.05848 | ||||||||
\(971\) | −3.77277e24 | −0.153214 | −0.0766068 | − | 0.997061i | \(-0.524409\pi\) | ||||
−0.0766068 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(972\) | −6.51872e25 | −2.62421 | ||||||||
\(973\) | 3.19596e25 | 1.27539 | ||||||||
\(974\) | 2.88854e25 | 1.14269 | ||||||||
\(975\) | 9.57493e24 | 0.375488 | ||||||||
\(976\) | −3.59861e25 | −1.39898 | ||||||||
\(977\) | −8.08742e24 | −0.311678 | −0.155839 | − | 0.987782i | \(-0.549808\pi\) | ||||
−0.155839 | + | 0.987782i | \(0.549808\pi\) | |||||||
\(978\) | −7.68912e25 | −2.93762 | ||||||||
\(979\) | 6.31469e24 | 0.239166 | ||||||||
\(980\) | 2.56570e25 | 0.963352 | ||||||||
\(981\) | −3.37811e25 | −1.25744 | ||||||||
\(982\) | −1.45147e25 | −0.535625 | ||||||||
\(983\) | 3.50594e25 | 1.28262 | 0.641312 | − | 0.767280i | \(-0.278390\pi\) | ||||
0.641312 | + | 0.767280i | \(0.278390\pi\) | |||||||
\(984\) | 1.25642e26 | 4.55697 | ||||||||
\(985\) | −2.37162e24 | −0.0852781 | ||||||||
\(986\) | −1.65303e25 | −0.589287 | ||||||||
\(987\) | 2.59788e25 | 0.918171 | ||||||||
\(988\) | 1.10945e26 | 3.88752 | ||||||||
\(989\) | 5.40622e24 | 0.187813 | ||||||||
\(990\) | 9.31624e24 | 0.320879 | ||||||||
\(991\) | −1.27204e25 | −0.434386 | −0.217193 | − | 0.976129i | \(-0.569690\pi\) | ||||
−0.217193 | + | 0.976129i | \(0.569690\pi\) | |||||||
\(992\) | 1.03378e25 | 0.350009 | ||||||||
\(993\) | −6.76719e25 | −2.27164 | ||||||||
\(994\) | 6.61438e25 | 2.20143 | ||||||||
\(995\) | 4.66229e25 | 1.53852 | ||||||||
\(996\) | 3.56613e25 | 1.16679 | ||||||||
\(997\) | −7.57365e24 | −0.245695 | −0.122847 | − | 0.992426i | \(-0.539203\pi\) | ||||
−0.122847 | + | 0.992426i | \(0.539203\pi\) | |||||||
\(998\) | 9.71670e25 | 3.12543 | ||||||||
\(999\) | −1.66144e25 | −0.529881 |
(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 | 29.18.a.b.1.3 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.3 | ✓ | 21 | 1.1 | even | 1 | trivial |