Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.1747 | −1.59871 | −0.799355 | − | 0.600859i | \(-0.794825\pi\) | ||||
−0.799355 | + | 0.600859i | \(0.794825\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 796.607 | 1.55587 | ||||||||
\(5\) | 898.892 | 0.643195 | 0.321597 | − | 0.946876i | \(-0.395780\pi\) | ||||
0.321597 | + | 0.946876i | \(0.395780\pi\) | |||||||
\(6\) | 2930.15 | 0.923015 | ||||||||
\(7\) | −4674.69 | −0.735888 | −0.367944 | − | 0.929848i | \(-0.619938\pi\) | ||||
−0.367944 | + | 0.929848i | \(0.619938\pi\) | |||||||
\(8\) | −10295.5 | −0.888678 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −32517.1 | −1.02828 | ||||||||
\(11\) | −58345.2 | −1.20154 | −0.600769 | − | 0.799422i | \(-0.705139\pi\) | ||||
−0.600769 | + | 0.799422i | \(0.705139\pi\) | |||||||
\(12\) | −64525.1 | −0.898283 | ||||||||
\(13\) | 57332.9 | 0.556748 | 0.278374 | − | 0.960473i | \(-0.410204\pi\) | ||||
0.278374 | + | 0.960473i | \(0.410204\pi\) | |||||||
\(14\) | 169105. | 1.17647 | ||||||||
\(15\) | −72810.3 | −0.371349 | ||||||||
\(16\) | −35424.5 | −0.135134 | ||||||||
\(17\) | −510308. | −1.48188 | −0.740939 | − | 0.671573i | \(-0.765619\pi\) | ||||
−0.740939 | + | 0.671573i | \(0.765619\pi\) | |||||||
\(18\) | −237342. | −0.532903 | ||||||||
\(19\) | −168147. | −0.296004 | −0.148002 | − | 0.988987i | \(-0.547284\pi\) | ||||
−0.148002 | + | 0.988987i | \(0.547284\pi\) | |||||||
\(20\) | 716063. | 1.00073 | ||||||||
\(21\) | 378650. | 0.424865 | ||||||||
\(22\) | 2.11062e6 | 1.92091 | ||||||||
\(23\) | 2.17501e6 | 1.62064 | 0.810318 | − | 0.585990i | \(-0.199294\pi\) | ||||
0.810318 | + | 0.585990i | \(0.199294\pi\) | |||||||
\(24\) | 833939. | 0.513079 | ||||||||
\(25\) | −1.14512e6 | −0.586300 | ||||||||
\(26\) | −2.07400e6 | −0.890079 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −3.72389e6 | −1.14495 | ||||||||
\(29\) | 244852. | 0.0642853 | 0.0321427 | − | 0.999483i | \(-0.489767\pi\) | ||||
0.0321427 | + | 0.999483i | \(0.489767\pi\) | |||||||
\(30\) | 2.63389e6 | 0.593679 | ||||||||
\(31\) | 6.46606e6 | 1.25751 | 0.628756 | − | 0.777603i | \(-0.283565\pi\) | ||||
0.628756 | + | 0.777603i | \(0.283565\pi\) | |||||||
\(32\) | 6.55279e6 | 1.10472 | ||||||||
\(33\) | 4.72596e6 | 0.693709 | ||||||||
\(34\) | 1.84602e7 | 2.36909 | ||||||||
\(35\) | −4.20204e6 | −0.473319 | ||||||||
\(36\) | 5.22654e6 | 0.518624 | ||||||||
\(37\) | −4.04614e6 | −0.354922 | −0.177461 | − | 0.984128i | \(-0.556788\pi\) | ||||
−0.177461 | + | 0.984128i | \(0.556788\pi\) | |||||||
\(38\) | 6.08266e6 | 0.473224 | ||||||||
\(39\) | −4.64396e6 | −0.321439 | ||||||||
\(40\) | −9.25459e6 | −0.571593 | ||||||||
\(41\) | −8.50617e6 | −0.470118 | −0.235059 | − | 0.971981i | \(-0.575528\pi\) | ||||
−0.235059 | + | 0.971981i | \(0.575528\pi\) | |||||||
\(42\) | −1.36975e7 | −0.679236 | ||||||||
\(43\) | −1.02337e7 | −0.456485 | −0.228242 | − | 0.973604i | \(-0.573298\pi\) | ||||
−0.228242 | + | 0.973604i | \(0.573298\pi\) | |||||||
\(44\) | −4.64781e7 | −1.86944 | ||||||||
\(45\) | 5.89763e6 | 0.214398 | ||||||||
\(46\) | −7.86802e7 | −2.59093 | ||||||||
\(47\) | −3.48588e7 | −1.04201 | −0.521005 | − | 0.853554i | \(-0.674443\pi\) | ||||
−0.521005 | + | 0.853554i | \(0.674443\pi\) | |||||||
\(48\) | 2.86939e6 | 0.0780195 | ||||||||
\(49\) | −1.85009e7 | −0.458470 | ||||||||
\(50\) | 4.14243e7 | 0.937324 | ||||||||
\(51\) | 4.13350e7 | 0.855562 | ||||||||
\(52\) | 4.56718e7 | 0.866229 | ||||||||
\(53\) | −5.20000e7 | −0.905237 | −0.452618 | − | 0.891704i | \(-0.649510\pi\) | ||||
−0.452618 | + | 0.891704i | \(0.649510\pi\) | |||||||
\(54\) | 1.92247e7 | 0.307672 | ||||||||
\(55\) | −5.24460e7 | −0.772823 | ||||||||
\(56\) | 4.81285e7 | 0.653967 | ||||||||
\(57\) | 1.36199e7 | 0.170898 | ||||||||
\(58\) | −8.85743e6 | −0.102774 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −5.80011e7 | −0.577771 | ||||||||
\(61\) | 2.99414e7 | 0.276878 | 0.138439 | − | 0.990371i | \(-0.455792\pi\) | ||||
0.138439 | + | 0.990371i | \(0.455792\pi\) | |||||||
\(62\) | −2.33907e8 | −2.01040 | ||||||||
\(63\) | −3.06706e7 | −0.245296 | ||||||||
\(64\) | −2.18908e8 | −1.63099 | ||||||||
\(65\) | 5.15361e7 | 0.358098 | ||||||||
\(66\) | −1.70960e8 | −1.10904 | ||||||||
\(67\) | −2.13498e8 | −1.29437 | −0.647183 | − | 0.762335i | \(-0.724053\pi\) | ||||
−0.647183 | + | 0.762335i | \(0.724053\pi\) | |||||||
\(68\) | −4.06515e8 | −2.30561 | ||||||||
\(69\) | −1.76176e8 | −0.935675 | ||||||||
\(70\) | 1.52007e8 | 0.756700 | ||||||||
\(71\) | −1.52154e8 | −0.710592 | −0.355296 | − | 0.934754i | \(-0.615620\pi\) | ||||
−0.355296 | + | 0.934754i | \(0.615620\pi\) | |||||||
\(72\) | −6.75491e7 | −0.296226 | ||||||||
\(73\) | 1.83932e8 | 0.758063 | 0.379032 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379032 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(74\) | 1.46368e8 | 0.567417 | ||||||||
\(75\) | 9.27546e7 | 0.338501 | ||||||||
\(76\) | −1.33947e8 | −0.460544 | ||||||||
\(77\) | 2.72745e8 | 0.884197 | ||||||||
\(78\) | 1.67994e8 | 0.513887 | ||||||||
\(79\) | 7.72399e7 | 0.223110 | 0.111555 | − | 0.993758i | \(-0.464417\pi\) | ||||
0.111555 | + | 0.993758i | \(0.464417\pi\) | |||||||
\(80\) | −3.18428e7 | −0.0869174 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 3.07708e8 | 0.751582 | ||||||||
\(83\) | −1.73619e8 | −0.401555 | −0.200778 | − | 0.979637i | \(-0.564347\pi\) | ||||
−0.200778 | + | 0.979637i | \(0.564347\pi\) | |||||||
\(84\) | 3.01635e8 | 0.661035 | ||||||||
\(85\) | −4.58712e8 | −0.953136 | ||||||||
\(86\) | 3.70202e8 | 0.729787 | ||||||||
\(87\) | −1.98330e7 | −0.0371152 | ||||||||
\(88\) | 6.00695e8 | 1.06778 | ||||||||
\(89\) | −6.72303e8 | −1.13582 | −0.567911 | − | 0.823090i | \(-0.692248\pi\) | ||||
−0.567911 | + | 0.823090i | \(0.692248\pi\) | |||||||
\(90\) | −2.13345e8 | −0.342761 | ||||||||
\(91\) | −2.68013e8 | −0.409704 | ||||||||
\(92\) | 1.73263e9 | 2.52150 | ||||||||
\(93\) | −5.23751e8 | −0.726024 | ||||||||
\(94\) | 1.26100e9 | 1.66587 | ||||||||
\(95\) | −1.51146e8 | −0.190388 | ||||||||
\(96\) | −5.30776e8 | −0.637809 | ||||||||
\(97\) | 1.37731e9 | 1.57964 | 0.789820 | − | 0.613338i | \(-0.210174\pi\) | ||||
0.789820 | + | 0.613338i | \(0.210174\pi\) | |||||||
\(98\) | 6.69264e8 | 0.732960 | ||||||||
\(99\) | −3.82803e8 | −0.400513 | ||||||||
\(100\) | −9.12209e8 | −0.912209 | ||||||||
\(101\) | −7.06551e7 | −0.0675612 | −0.0337806 | − | 0.999429i | \(-0.510755\pi\) | ||||
−0.0337806 | + | 0.999429i | \(0.510755\pi\) | |||||||
\(102\) | −1.49528e9 | −1.36780 | ||||||||
\(103\) | 3.47159e8 | 0.303921 | 0.151961 | − | 0.988387i | \(-0.451441\pi\) | ||||
0.151961 | + | 0.988387i | \(0.451441\pi\) | |||||||
\(104\) | −5.90274e8 | −0.494770 | ||||||||
\(105\) | 3.40365e8 | 0.273271 | ||||||||
\(106\) | 1.88108e9 | 1.44721 | ||||||||
\(107\) | −2.17084e9 | −1.60103 | −0.800516 | − | 0.599311i | \(-0.795441\pi\) | ||||
−0.800516 | + | 0.599311i | \(0.795441\pi\) | |||||||
\(108\) | −4.23349e8 | −0.299428 | ||||||||
\(109\) | 1.68021e9 | 1.14010 | 0.570051 | − | 0.821609i | \(-0.306923\pi\) | ||||
0.570051 | + | 0.821609i | \(0.306923\pi\) | |||||||
\(110\) | 1.89722e9 | 1.23552 | ||||||||
\(111\) | 3.27737e8 | 0.204914 | ||||||||
\(112\) | 1.65599e8 | 0.0994433 | ||||||||
\(113\) | −3.34940e8 | −0.193248 | −0.0966239 | − | 0.995321i | \(-0.530804\pi\) | ||||
−0.0966239 | + | 0.995321i | \(0.530804\pi\) | |||||||
\(114\) | −4.92695e8 | −0.273216 | ||||||||
\(115\) | 1.95510e9 | 1.04238 | ||||||||
\(116\) | 1.95050e8 | 0.100020 | ||||||||
\(117\) | 3.76161e8 | 0.185583 | ||||||||
\(118\) | −4.38342e8 | −0.208134 | ||||||||
\(119\) | 2.38553e9 | 1.09050 | ||||||||
\(120\) | 7.49622e8 | 0.330010 | ||||||||
\(121\) | 1.04621e9 | 0.443695 | ||||||||
\(122\) | −1.08312e9 | −0.442647 | ||||||||
\(123\) | 6.89000e8 | 0.271423 | ||||||||
\(124\) | 5.15090e9 | 1.95653 | ||||||||
\(125\) | −2.78499e9 | −1.02030 | ||||||||
\(126\) | 1.10950e9 | 0.392157 | ||||||||
\(127\) | 4.31503e9 | 1.47186 | 0.735931 | − | 0.677056i | \(-0.236745\pi\) | ||||
0.735931 | + | 0.677056i | \(0.236745\pi\) | |||||||
\(128\) | 4.56388e9 | 1.50276 | ||||||||
\(129\) | 8.28933e8 | 0.263552 | ||||||||
\(130\) | −1.86430e9 | −0.572494 | ||||||||
\(131\) | −4.44468e9 | −1.31862 | −0.659310 | − | 0.751871i | \(-0.729152\pi\) | ||||
−0.659310 | + | 0.751871i | \(0.729152\pi\) | |||||||
\(132\) | 3.76473e9 | 1.07932 | ||||||||
\(133\) | 7.86034e8 | 0.217826 | ||||||||
\(134\) | 7.72322e9 | 2.06932 | ||||||||
\(135\) | −4.77708e8 | −0.123783 | ||||||||
\(136\) | 5.25390e9 | 1.31691 | ||||||||
\(137\) | −2.71704e9 | −0.658951 | −0.329476 | − | 0.944164i | \(-0.606872\pi\) | ||||
−0.329476 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(138\) | 6.37310e9 | 1.49587 | ||||||||
\(139\) | −1.44384e9 | −0.328060 | −0.164030 | − | 0.986455i | \(-0.552449\pi\) | ||||
−0.164030 | + | 0.986455i | \(0.552449\pi\) | |||||||
\(140\) | −3.34737e9 | −0.736424 | ||||||||
\(141\) | 2.82356e9 | 0.601605 | ||||||||
\(142\) | 5.50411e9 | 1.13603 | ||||||||
\(143\) | −3.34510e9 | −0.668954 | ||||||||
\(144\) | −2.32420e8 | −0.0450446 | ||||||||
\(145\) | 2.20095e8 | 0.0413480 | ||||||||
\(146\) | −6.65369e9 | −1.21192 | ||||||||
\(147\) | 1.49857e9 | 0.264698 | ||||||||
\(148\) | −3.22318e9 | −0.552213 | ||||||||
\(149\) | 2.95833e9 | 0.491709 | 0.245855 | − | 0.969307i | \(-0.420931\pi\) | ||||
0.245855 | + | 0.969307i | \(0.420931\pi\) | |||||||
\(150\) | −3.35537e9 | −0.541164 | ||||||||
\(151\) | 4.00966e9 | 0.627640 | 0.313820 | − | 0.949482i | \(-0.398391\pi\) | ||||
0.313820 | + | 0.949482i | \(0.398391\pi\) | |||||||
\(152\) | 1.73116e9 | 0.263052 | ||||||||
\(153\) | −3.34813e9 | −0.493959 | ||||||||
\(154\) | −9.86647e9 | −1.41357 | ||||||||
\(155\) | 5.81229e9 | 0.808825 | ||||||||
\(156\) | −3.69941e9 | −0.500118 | ||||||||
\(157\) | 1.25451e10 | 1.64788 | 0.823940 | − | 0.566678i | \(-0.191771\pi\) | ||||
0.823940 | + | 0.566678i | \(0.191771\pi\) | |||||||
\(158\) | −2.79413e9 | −0.356689 | ||||||||
\(159\) | 4.21200e9 | 0.522639 | ||||||||
\(160\) | 5.89025e9 | 0.710549 | ||||||||
\(161\) | −1.01675e10 | −1.19261 | ||||||||
\(162\) | −1.55720e9 | −0.177634 | ||||||||
\(163\) | 1.20770e10 | 1.34003 | 0.670013 | − | 0.742349i | \(-0.266288\pi\) | ||||
0.670013 | + | 0.742349i | \(0.266288\pi\) | |||||||
\(164\) | −6.77607e9 | −0.731443 | ||||||||
\(165\) | 4.24813e9 | 0.446190 | ||||||||
\(166\) | 6.28060e9 | 0.641970 | ||||||||
\(167\) | −8.77986e9 | −0.873501 | −0.436750 | − | 0.899583i | \(-0.643871\pi\) | ||||
−0.436750 | + | 0.899583i | \(0.643871\pi\) | |||||||
\(168\) | −3.89841e9 | −0.377568 | ||||||||
\(169\) | −7.31744e9 | −0.690031 | ||||||||
\(170\) | 1.65937e10 | 1.52379 | ||||||||
\(171\) | −1.10321e9 | −0.0986680 | ||||||||
\(172\) | −8.15226e9 | −0.710232 | ||||||||
\(173\) | −3.23450e9 | −0.274536 | −0.137268 | − | 0.990534i | \(-0.543832\pi\) | ||||
−0.137268 | + | 0.990534i | \(0.543832\pi\) | |||||||
\(174\) | 7.17451e8 | 0.0593364 | ||||||||
\(175\) | 5.35307e9 | 0.431451 | ||||||||
\(176\) | 2.06685e9 | 0.162368 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 2.43204e10 | 1.81585 | ||||||||
\(179\) | 2.22715e10 | 1.62147 | 0.810737 | − | 0.585411i | \(-0.199067\pi\) | ||||
0.810737 | + | 0.585411i | \(0.199067\pi\) | |||||||
\(180\) | 4.69809e9 | 0.333576 | ||||||||
\(181\) | −2.16773e10 | −1.50125 | −0.750623 | − | 0.660731i | \(-0.770247\pi\) | ||||
−0.750623 | + | 0.660731i | \(0.770247\pi\) | |||||||
\(182\) | 9.69530e9 | 0.654998 | ||||||||
\(183\) | −2.42526e9 | −0.159856 | ||||||||
\(184\) | −2.23929e10 | −1.44022 | ||||||||
\(185\) | −3.63704e9 | −0.228284 | ||||||||
\(186\) | 1.89465e10 | 1.16070 | ||||||||
\(187\) | 2.97740e10 | 1.78053 | ||||||||
\(188\) | −2.77687e10 | −1.62123 | ||||||||
\(189\) | 2.48432e9 | 0.141622 | ||||||||
\(190\) | 5.46765e9 | 0.304375 | ||||||||
\(191\) | 2.81443e10 | 1.53017 | 0.765086 | − | 0.643928i | \(-0.222696\pi\) | ||||
0.765086 | + | 0.643928i | \(0.222696\pi\) | |||||||
\(192\) | 1.77315e10 | 0.941652 | ||||||||
\(193\) | −4.41397e9 | −0.228992 | −0.114496 | − | 0.993424i | \(-0.536525\pi\) | ||||
−0.114496 | + | 0.993424i | \(0.536525\pi\) | |||||||
\(194\) | −4.98237e10 | −2.52539 | ||||||||
\(195\) | −4.17442e9 | −0.206748 | ||||||||
\(196\) | −1.47379e10 | −0.713320 | ||||||||
\(197\) | −2.04044e10 | −0.965219 | −0.482609 | − | 0.875836i | \(-0.660311\pi\) | ||||
−0.482609 | + | 0.875836i | \(0.660311\pi\) | |||||||
\(198\) | 1.38478e10 | 0.640304 | ||||||||
\(199\) | 1.01977e10 | 0.460962 | 0.230481 | − | 0.973077i | \(-0.425970\pi\) | ||||
0.230481 | + | 0.973077i | \(0.425970\pi\) | |||||||
\(200\) | 1.17896e10 | 0.521032 | ||||||||
\(201\) | 1.72933e10 | 0.747303 | ||||||||
\(202\) | 2.55592e9 | 0.108011 | ||||||||
\(203\) | −1.14460e9 | −0.0473068 | ||||||||
\(204\) | 3.29277e10 | 1.33115 | ||||||||
\(205\) | −7.64613e9 | −0.302377 | ||||||||
\(206\) | −1.25584e10 | −0.485882 | ||||||||
\(207\) | 1.42702e10 | 0.540212 | ||||||||
\(208\) | −2.03099e9 | −0.0752355 | ||||||||
\(209\) | 9.81055e9 | 0.355660 | ||||||||
\(210\) | −1.23126e10 | −0.436881 | ||||||||
\(211\) | −1.33425e10 | −0.463410 | −0.231705 | − | 0.972786i | \(-0.574430\pi\) | ||||
−0.231705 | + | 0.972786i | \(0.574430\pi\) | |||||||
\(212\) | −4.14236e10 | −1.40843 | ||||||||
\(213\) | 1.23245e10 | 0.410260 | ||||||||
\(214\) | 7.85293e10 | 2.55959 | ||||||||
\(215\) | −9.19903e9 | −0.293609 | ||||||||
\(216\) | 5.47148e9 | 0.171026 | ||||||||
\(217\) | −3.02268e10 | −0.925387 | ||||||||
\(218\) | −6.07810e10 | −1.82269 | ||||||||
\(219\) | −1.48985e10 | −0.437668 | ||||||||
\(220\) | −4.17788e10 | −1.20241 | ||||||||
\(221\) | −2.92574e10 | −0.825033 | ||||||||
\(222\) | −1.18558e10 | −0.327598 | ||||||||
\(223\) | −2.17210e10 | −0.588178 | −0.294089 | − | 0.955778i | \(-0.595016\pi\) | ||||
−0.294089 | + | 0.955778i | \(0.595016\pi\) | |||||||
\(224\) | −3.06323e10 | −0.812948 | ||||||||
\(225\) | −7.51312e9 | −0.195433 | ||||||||
\(226\) | 1.21164e10 | 0.308947 | ||||||||
\(227\) | 3.32500e10 | 0.831141 | 0.415571 | − | 0.909561i | \(-0.363582\pi\) | ||||
0.415571 | + | 0.909561i | \(0.363582\pi\) | |||||||
\(228\) | 1.08497e10 | 0.265895 | ||||||||
\(229\) | −9.20653e9 | −0.221226 | −0.110613 | − | 0.993864i | \(-0.535281\pi\) | ||||
−0.110613 | + | 0.993864i | \(0.535281\pi\) | |||||||
\(230\) | −7.07250e10 | −1.66647 | ||||||||
\(231\) | −2.20924e10 | −0.510492 | ||||||||
\(232\) | −2.52088e9 | −0.0571290 | ||||||||
\(233\) | 5.05237e10 | 1.12303 | 0.561517 | − | 0.827465i | \(-0.310218\pi\) | ||||
0.561517 | + | 0.827465i | \(0.310218\pi\) | |||||||
\(234\) | −1.36075e10 | −0.296693 | ||||||||
\(235\) | −3.13343e10 | −0.670215 | ||||||||
\(236\) | 9.65277e9 | 0.202557 | ||||||||
\(237\) | −6.25643e9 | −0.128813 | ||||||||
\(238\) | −8.62958e10 | −1.74338 | ||||||||
\(239\) | 1.89053e10 | 0.374794 | 0.187397 | − | 0.982284i | \(-0.439995\pi\) | ||||
0.187397 | + | 0.982284i | \(0.439995\pi\) | |||||||
\(240\) | 2.57927e9 | 0.0501818 | ||||||||
\(241\) | −3.30262e10 | −0.630640 | −0.315320 | − | 0.948985i | \(-0.602112\pi\) | ||||
−0.315320 | + | 0.948985i | \(0.602112\pi\) | |||||||
\(242\) | −3.78463e10 | −0.709340 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 2.38515e10 | 0.430787 | ||||||||
\(245\) | −1.66303e10 | −0.294885 | ||||||||
\(246\) | −2.49243e10 | −0.433926 | ||||||||
\(247\) | −9.64035e9 | −0.164800 | ||||||||
\(248\) | −6.65716e10 | −1.11752 | ||||||||
\(249\) | 1.40631e10 | 0.231838 | ||||||||
\(250\) | 1.00746e11 | 1.63116 | ||||||||
\(251\) | −8.61853e8 | −0.0137057 | −0.00685285 | − | 0.999977i | \(-0.502181\pi\) | ||||
−0.00685285 | + | 0.999977i | \(0.502181\pi\) | |||||||
\(252\) | −2.44324e10 | −0.381649 | ||||||||
\(253\) | −1.26901e11 | −1.94726 | ||||||||
\(254\) | −1.56095e11 | −2.35308 | ||||||||
\(255\) | 3.71557e10 | 0.550293 | ||||||||
\(256\) | −5.30162e10 | −0.771488 | ||||||||
\(257\) | 1.23018e11 | 1.75902 | 0.879510 | − | 0.475881i | \(-0.157871\pi\) | ||||
0.879510 | + | 0.475881i | \(0.157871\pi\) | |||||||
\(258\) | −2.99864e10 | −0.421342 | ||||||||
\(259\) | 1.89144e10 | 0.261183 | ||||||||
\(260\) | 4.10540e10 | 0.557154 | ||||||||
\(261\) | 1.60647e9 | 0.0214284 | ||||||||
\(262\) | 1.60785e11 | 2.10809 | ||||||||
\(263\) | 2.48000e10 | 0.319632 | 0.159816 | − | 0.987147i | \(-0.448910\pi\) | ||||
0.159816 | + | 0.987147i | \(0.448910\pi\) | |||||||
\(264\) | −4.86563e10 | −0.616484 | ||||||||
\(265\) | −4.67424e10 | −0.582244 | ||||||||
\(266\) | −2.84345e10 | −0.348240 | ||||||||
\(267\) | 5.44566e10 | 0.655767 | ||||||||
\(268\) | −1.70074e11 | −2.01387 | ||||||||
\(269\) | −1.65665e11 | −1.92906 | −0.964528 | − | 0.263979i | \(-0.914965\pi\) | ||||
−0.964528 | + | 0.263979i | \(0.914965\pi\) | |||||||
\(270\) | 1.72809e10 | 0.197893 | ||||||||
\(271\) | 3.14041e10 | 0.353691 | 0.176846 | − | 0.984239i | \(-0.443411\pi\) | ||||
0.176846 | + | 0.984239i | \(0.443411\pi\) | |||||||
\(272\) | 1.80774e10 | 0.200252 | ||||||||
\(273\) | 2.17091e10 | 0.236543 | ||||||||
\(274\) | 9.82880e10 | 1.05347 | ||||||||
\(275\) | 6.68121e10 | 0.704463 | ||||||||
\(276\) | −1.40343e11 | −1.45579 | ||||||||
\(277\) | 1.64597e11 | 1.67982 | 0.839911 | − | 0.542725i | \(-0.182607\pi\) | ||||
0.839911 | + | 0.542725i | \(0.182607\pi\) | |||||||
\(278\) | 5.22306e10 | 0.524473 | ||||||||
\(279\) | 4.24238e10 | 0.419170 | ||||||||
\(280\) | 4.32623e10 | 0.420628 | ||||||||
\(281\) | −1.74325e11 | −1.66794 | −0.833971 | − | 0.551808i | \(-0.813938\pi\) | ||||
−0.833971 | + | 0.551808i | \(0.813938\pi\) | |||||||
\(282\) | −1.02141e11 | −0.961791 | ||||||||
\(283\) | 1.53298e11 | 1.42069 | 0.710344 | − | 0.703855i | \(-0.248540\pi\) | ||||
0.710344 | + | 0.703855i | \(0.248540\pi\) | |||||||
\(284\) | −1.21207e11 | −1.10559 | ||||||||
\(285\) | 1.22428e10 | 0.109921 | ||||||||
\(286\) | 1.21008e11 | 1.06946 | ||||||||
\(287\) | 3.97637e10 | 0.345954 | ||||||||
\(288\) | 4.29929e10 | 0.368239 | ||||||||
\(289\) | 1.41826e11 | 1.19596 | ||||||||
\(290\) | −7.96187e9 | −0.0661034 | ||||||||
\(291\) | −1.11562e11 | −0.912006 | ||||||||
\(292\) | 1.46522e11 | 1.17945 | ||||||||
\(293\) | 5.26361e10 | 0.417233 | 0.208617 | − | 0.977997i | \(-0.433104\pi\) | ||||
0.208617 | + | 0.977997i | \(0.433104\pi\) | |||||||
\(294\) | −5.42104e10 | −0.423174 | ||||||||
\(295\) | 1.08922e10 | 0.0837368 | ||||||||
\(296\) | 4.16572e10 | 0.315411 | ||||||||
\(297\) | 3.10070e10 | 0.231236 | ||||||||
\(298\) | −1.07017e11 | −0.786100 | ||||||||
\(299\) | 1.24700e11 | 0.902286 | ||||||||
\(300\) | 7.38889e10 | 0.526664 | ||||||||
\(301\) | 4.78395e10 | 0.335921 | ||||||||
\(302\) | −1.45048e11 | −1.00341 | ||||||||
\(303\) | 5.72306e9 | 0.0390064 | ||||||||
\(304\) | 5.95652e9 | 0.0400001 | ||||||||
\(305\) | 2.69141e10 | 0.178086 | ||||||||
\(306\) | 1.21118e11 | 0.789697 | ||||||||
\(307\) | 2.34703e11 | 1.50798 | 0.753991 | − | 0.656885i | \(-0.228126\pi\) | ||||
0.753991 | + | 0.656885i | \(0.228126\pi\) | |||||||
\(308\) | 2.17271e11 | 1.37570 | ||||||||
\(309\) | −2.81199e10 | −0.175469 | ||||||||
\(310\) | −2.10258e11 | −1.29308 | ||||||||
\(311\) | 3.48562e10 | 0.211280 | 0.105640 | − | 0.994404i | \(-0.466311\pi\) | ||||
0.105640 | + | 0.994404i | \(0.466311\pi\) | |||||||
\(312\) | 4.78122e10 | 0.285656 | ||||||||
\(313\) | 1.77039e11 | 1.04260 | 0.521301 | − | 0.853373i | \(-0.325447\pi\) | ||||
0.521301 | + | 0.853373i | \(0.325447\pi\) | |||||||
\(314\) | −4.53814e11 | −2.63448 | ||||||||
\(315\) | −2.75696e10 | −0.157773 | ||||||||
\(316\) | 6.15298e10 | 0.347131 | ||||||||
\(317\) | 2.30912e8 | 0.00128434 | 0.000642169 | − | 1.00000i | \(-0.499796\pi\) | ||||
0.000642169 | 1.00000i | \(0.499796\pi\) | ||||||||
\(318\) | −1.52368e11 | −0.835547 | ||||||||
\(319\) | −1.42859e10 | −0.0772413 | ||||||||
\(320\) | −1.96774e11 | −1.04904 | ||||||||
\(321\) | 1.75838e11 | 0.924357 | ||||||||
\(322\) | 3.67805e11 | 1.90663 | ||||||||
\(323\) | 8.58067e10 | 0.438642 | ||||||||
\(324\) | 3.42913e10 | 0.172875 | ||||||||
\(325\) | −6.56529e10 | −0.326422 | ||||||||
\(326\) | −4.36880e11 | −2.14231 | ||||||||
\(327\) | −1.36097e11 | −0.658238 | ||||||||
\(328\) | 8.75757e10 | 0.417783 | ||||||||
\(329\) | 1.62954e11 | 0.766802 | ||||||||
\(330\) | −1.53675e11 | −0.713328 | ||||||||
\(331\) | 7.38318e9 | 0.0338078 | 0.0169039 | − | 0.999857i | \(-0.494619\pi\) | ||||
0.0169039 | + | 0.999857i | \(0.494619\pi\) | |||||||
\(332\) | −1.38306e11 | −0.624769 | ||||||||
\(333\) | −2.65467e10 | −0.118307 | ||||||||
\(334\) | 3.17608e11 | 1.39647 | ||||||||
\(335\) | −1.91912e11 | −0.832530 | ||||||||
\(336\) | −1.34135e10 | −0.0574136 | ||||||||
\(337\) | 4.06055e11 | 1.71495 | 0.857473 | − | 0.514530i | \(-0.172033\pi\) | ||||
0.857473 | + | 0.514530i | \(0.172033\pi\) | |||||||
\(338\) | 2.64706e11 | 1.10316 | ||||||||
\(339\) | 2.71302e10 | 0.111572 | ||||||||
\(340\) | −3.65413e11 | −1.48296 | ||||||||
\(341\) | −3.77263e11 | −1.51095 | ||||||||
\(342\) | 3.99083e10 | 0.157741 | ||||||||
\(343\) | 2.75126e11 | 1.07327 | ||||||||
\(344\) | 1.05362e11 | 0.405668 | ||||||||
\(345\) | −1.58363e11 | −0.601821 | ||||||||
\(346\) | 1.17007e11 | 0.438904 | ||||||||
\(347\) | 5.29349e11 | 1.96002 | 0.980008 | − | 0.198957i | \(-0.0637555\pi\) | ||||
0.980008 | + | 0.198957i | \(0.0637555\pi\) | |||||||
\(348\) | −1.57991e10 | −0.0577464 | ||||||||
\(349\) | 3.08680e11 | 1.11377 | 0.556884 | − | 0.830591i | \(-0.311997\pi\) | ||||
0.556884 | + | 0.830591i | \(0.311997\pi\) | |||||||
\(350\) | −1.93646e11 | −0.689765 | ||||||||
\(351\) | −3.04691e10 | −0.107146 | ||||||||
\(352\) | −3.82324e11 | −1.32736 | ||||||||
\(353\) | 3.72155e11 | 1.27567 | 0.637833 | − | 0.770175i | \(-0.279831\pi\) | ||||
0.637833 | + | 0.770175i | \(0.279831\pi\) | |||||||
\(354\) | 3.55057e10 | 0.120166 | ||||||||
\(355\) | −1.36770e11 | −0.457049 | ||||||||
\(356\) | −5.35561e11 | −1.76719 | ||||||||
\(357\) | −1.93228e11 | −0.629598 | ||||||||
\(358\) | −8.05663e11 | −2.59227 | ||||||||
\(359\) | 5.49485e11 | 1.74595 | 0.872973 | − | 0.487769i | \(-0.162189\pi\) | ||||
0.872973 | + | 0.487769i | \(0.162189\pi\) | |||||||
\(360\) | −6.07193e10 | −0.190531 | ||||||||
\(361\) | −2.94414e11 | −0.912382 | ||||||||
\(362\) | 7.84170e11 | 2.40006 | ||||||||
\(363\) | −8.47430e10 | −0.256167 | ||||||||
\(364\) | −2.13501e11 | −0.637447 | ||||||||
\(365\) | 1.65335e11 | 0.487582 | ||||||||
\(366\) | 8.77328e10 | 0.255563 | ||||||||
\(367\) | −3.94449e11 | −1.13499 | −0.567497 | − | 0.823376i | \(-0.692088\pi\) | ||||
−0.567497 | + | 0.823376i | \(0.692088\pi\) | |||||||
\(368\) | −7.70486e10 | −0.219003 | ||||||||
\(369\) | −5.58090e10 | −0.156706 | ||||||||
\(370\) | 1.31569e11 | 0.364960 | ||||||||
\(371\) | 2.43084e11 | 0.666152 | ||||||||
\(372\) | −4.17223e11 | −1.12960 | ||||||||
\(373\) | −3.12062e11 | −0.834739 | −0.417369 | − | 0.908737i | \(-0.637048\pi\) | ||||
−0.417369 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(374\) | −1.07706e12 | −2.84656 | ||||||||
\(375\) | 2.25584e11 | 0.589071 | ||||||||
\(376\) | 3.58890e11 | 0.926011 | ||||||||
\(377\) | 1.40381e10 | 0.0357908 | ||||||||
\(378\) | −8.98695e10 | −0.226412 | ||||||||
\(379\) | −1.54226e11 | −0.383955 | −0.191977 | − | 0.981399i | \(-0.561490\pi\) | ||||
−0.191977 | + | 0.981399i | \(0.561490\pi\) | |||||||
\(380\) | −1.20404e11 | −0.296220 | ||||||||
\(381\) | −3.49518e11 | −0.849780 | ||||||||
\(382\) | −1.01811e12 | −2.44630 | ||||||||
\(383\) | 4.33365e11 | 1.02911 | 0.514553 | − | 0.857459i | \(-0.327958\pi\) | ||||
0.514553 | + | 0.857459i | \(0.327958\pi\) | |||||||
\(384\) | −3.69675e11 | −0.867619 | ||||||||
\(385\) | 2.45169e11 | 0.568711 | ||||||||
\(386\) | 1.59674e11 | 0.366092 | ||||||||
\(387\) | −6.71436e10 | −0.152162 | ||||||||
\(388\) | 1.09717e12 | 2.45772 | ||||||||
\(389\) | −2.14366e11 | −0.474660 | −0.237330 | − | 0.971429i | \(-0.576272\pi\) | ||||
−0.237330 | + | 0.971429i | \(0.576272\pi\) | |||||||
\(390\) | 1.51008e11 | 0.330530 | ||||||||
\(391\) | −1.10992e12 | −2.40158 | ||||||||
\(392\) | 1.90477e11 | 0.407432 | ||||||||
\(393\) | 3.60019e11 | 0.761306 | ||||||||
\(394\) | 7.38122e11 | 1.54310 | ||||||||
\(395\) | 6.94303e10 | 0.143503 | ||||||||
\(396\) | −3.04943e11 | −0.623147 | ||||||||
\(397\) | 3.59774e10 | 0.0726895 | 0.0363448 | − | 0.999339i | \(-0.488429\pi\) | ||||
0.0363448 | + | 0.999339i | \(0.488429\pi\) | |||||||
\(398\) | −3.68900e11 | −0.736944 | ||||||||
\(399\) | −6.36688e10 | −0.125762 | ||||||||
\(400\) | 4.05652e10 | 0.0792290 | ||||||||
\(401\) | 2.39655e11 | 0.462846 | 0.231423 | − | 0.972853i | \(-0.425662\pi\) | ||||
0.231423 | + | 0.972853i | \(0.425662\pi\) | |||||||
\(402\) | −6.25581e11 | −1.19472 | ||||||||
\(403\) | 3.70718e11 | 0.700117 | ||||||||
\(404\) | −5.62843e10 | −0.105117 | ||||||||
\(405\) | 3.86944e10 | 0.0714661 | ||||||||
\(406\) | 4.14057e10 | 0.0756298 | ||||||||
\(407\) | 2.36073e11 | 0.426452 | ||||||||
\(408\) | −4.25566e11 | −0.760320 | ||||||||
\(409\) | 8.16510e11 | 1.44280 | 0.721401 | − | 0.692518i | \(-0.243499\pi\) | ||||
0.721401 | + | 0.692518i | \(0.243499\pi\) | |||||||
\(410\) | 2.76596e11 | 0.483414 | ||||||||
\(411\) | 2.20080e11 | 0.380446 | ||||||||
\(412\) | 2.76549e11 | 0.472862 | ||||||||
\(413\) | −5.66449e10 | −0.0958044 | ||||||||
\(414\) | −5.16221e11 | −0.863642 | ||||||||
\(415\) | −1.56065e11 | −0.258278 | ||||||||
\(416\) | 3.75691e11 | 0.615050 | ||||||||
\(417\) | 1.16951e11 | 0.189406 | ||||||||
\(418\) | −3.54894e11 | −0.568597 | ||||||||
\(419\) | 1.35929e10 | 0.0215452 | 0.0107726 | − | 0.999942i | \(-0.496571\pi\) | ||||
0.0107726 | + | 0.999942i | \(0.496571\pi\) | |||||||
\(420\) | 2.71137e11 | 0.425175 | ||||||||
\(421\) | −1.99138e11 | −0.308948 | −0.154474 | − | 0.987997i | \(-0.549368\pi\) | ||||
−0.154474 | + | 0.987997i | \(0.549368\pi\) | |||||||
\(422\) | 4.82660e11 | 0.740858 | ||||||||
\(423\) | −2.28708e11 | −0.347337 | ||||||||
\(424\) | 5.35369e11 | 0.804464 | ||||||||
\(425\) | 5.84363e11 | 0.868825 | ||||||||
\(426\) | −4.45833e11 | −0.655887 | ||||||||
\(427\) | −1.39967e11 | −0.203751 | ||||||||
\(428\) | −1.72930e12 | −2.49100 | ||||||||
\(429\) | 2.70953e11 | 0.386221 | ||||||||
\(430\) | 3.32772e11 | 0.469395 | ||||||||
\(431\) | 7.02282e11 | 0.980310 | 0.490155 | − | 0.871635i | \(-0.336940\pi\) | ||||
0.490155 | + | 0.871635i | \(0.336940\pi\) | |||||||
\(432\) | 1.88260e10 | 0.0260065 | ||||||||
\(433\) | −2.80736e11 | −0.383798 | −0.191899 | − | 0.981415i | \(-0.561465\pi\) | ||||
−0.191899 | + | 0.981415i | \(0.561465\pi\) | |||||||
\(434\) | 1.09344e12 | 1.47942 | ||||||||
\(435\) | −1.78277e10 | −0.0238723 | ||||||||
\(436\) | 1.33846e12 | 1.77385 | ||||||||
\(437\) | −3.65721e11 | −0.479715 | ||||||||
\(438\) | 5.38949e11 | 0.699704 | ||||||||
\(439\) | 5.49999e11 | 0.706760 | 0.353380 | − | 0.935480i | \(-0.385032\pi\) | ||||
0.353380 | + | 0.935480i | \(0.385032\pi\) | |||||||
\(440\) | 5.39960e11 | 0.686791 | ||||||||
\(441\) | −1.21384e11 | −0.152823 | ||||||||
\(442\) | 1.05838e12 | 1.31899 | ||||||||
\(443\) | −1.23621e11 | −0.152501 | −0.0762507 | − | 0.997089i | \(-0.524295\pi\) | ||||
−0.0762507 | + | 0.997089i | \(0.524295\pi\) | |||||||
\(444\) | 2.61078e11 | 0.318820 | ||||||||
\(445\) | −6.04328e11 | −0.730555 | ||||||||
\(446\) | 7.85751e11 | 0.940325 | ||||||||
\(447\) | −2.39625e11 | −0.283888 | ||||||||
\(448\) | 1.02333e12 | 1.20022 | ||||||||
\(449\) | −8.83485e11 | −1.02587 | −0.512933 | − | 0.858429i | \(-0.671441\pi\) | ||||
−0.512933 | + | 0.858429i | \(0.671441\pi\) | |||||||
\(450\) | 2.71785e11 | 0.312441 | ||||||||
\(451\) | 4.96294e11 | 0.564865 | ||||||||
\(452\) | −2.66816e11 | −0.300669 | ||||||||
\(453\) | −3.24782e11 | −0.362368 | ||||||||
\(454\) | −1.20281e12 | −1.32875 | ||||||||
\(455\) | −2.40915e11 | −0.263520 | ||||||||
\(456\) | −1.40224e11 | −0.151873 | ||||||||
\(457\) | −9.77143e11 | −1.04794 | −0.523969 | − | 0.851738i | \(-0.675549\pi\) | ||||
−0.523969 | + | 0.851738i | \(0.675549\pi\) | |||||||
\(458\) | 3.33043e11 | 0.353676 | ||||||||
\(459\) | 2.71199e11 | 0.285187 | ||||||||
\(460\) | 1.55744e12 | 1.62182 | ||||||||
\(461\) | 2.51148e11 | 0.258986 | 0.129493 | − | 0.991580i | \(-0.458665\pi\) | ||||
0.129493 | + | 0.991580i | \(0.458665\pi\) | |||||||
\(462\) | 7.99184e11 | 0.816128 | ||||||||
\(463\) | 4.80930e11 | 0.486371 | 0.243185 | − | 0.969980i | \(-0.421808\pi\) | ||||
0.243185 | + | 0.969980i | \(0.421808\pi\) | |||||||
\(464\) | −8.67375e9 | −0.00868712 | ||||||||
\(465\) | −4.70795e11 | −0.466975 | ||||||||
\(466\) | −1.82768e12 | −1.79541 | ||||||||
\(467\) | −5.63309e10 | −0.0548051 | −0.0274026 | − | 0.999624i | \(-0.508724\pi\) | ||||
−0.0274026 | + | 0.999624i | \(0.508724\pi\) | |||||||
\(468\) | 2.99652e11 | 0.288743 | ||||||||
\(469\) | 9.98036e11 | 0.952508 | ||||||||
\(470\) | 1.13351e12 | 1.07148 | ||||||||
\(471\) | −1.01615e12 | −0.951404 | ||||||||
\(472\) | −1.24755e11 | −0.115696 | ||||||||
\(473\) | 5.97089e11 | 0.548484 | ||||||||
\(474\) | 2.26324e11 | 0.205934 | ||||||||
\(475\) | 1.92548e11 | 0.173547 | ||||||||
\(476\) | 1.90033e12 | 1.69667 | ||||||||
\(477\) | −3.41172e11 | −0.301746 | ||||||||
\(478\) | −6.83892e11 | −0.599186 | ||||||||
\(479\) | 2.33976e11 | 0.203078 | 0.101539 | − | 0.994832i | \(-0.467623\pi\) | ||||
0.101539 | + | 0.994832i | \(0.467623\pi\) | |||||||
\(480\) | −4.77110e11 | −0.410236 | ||||||||
\(481\) | −2.31977e11 | −0.197602 | ||||||||
\(482\) | 1.19471e12 | 1.00821 | ||||||||
\(483\) | 8.23566e11 | 0.688552 | ||||||||
\(484\) | 8.33418e11 | 0.690333 | ||||||||
\(485\) | 1.23805e12 | 1.01602 | ||||||||
\(486\) | 1.26133e11 | 0.102557 | ||||||||
\(487\) | −1.54104e12 | −1.24147 | −0.620733 | − | 0.784022i | \(-0.713165\pi\) | ||||
−0.620733 | + | 0.784022i | \(0.713165\pi\) | |||||||
\(488\) | −3.08264e11 | −0.246055 | ||||||||
\(489\) | −9.78234e11 | −0.773665 | ||||||||
\(490\) | 6.01596e11 | 0.471436 | ||||||||
\(491\) | −4.63630e11 | −0.360002 | −0.180001 | − | 0.983666i | \(-0.557610\pi\) | ||||
−0.180001 | + | 0.983666i | \(0.557610\pi\) | |||||||
\(492\) | 5.48862e11 | 0.422299 | ||||||||
\(493\) | −1.24950e11 | −0.0952630 | ||||||||
\(494\) | 3.48736e11 | 0.263467 | ||||||||
\(495\) | −3.44098e11 | −0.257608 | ||||||||
\(496\) | −2.29057e11 | −0.169932 | ||||||||
\(497\) | 7.11272e11 | 0.522916 | ||||||||
\(498\) | −5.08729e11 | −0.370642 | ||||||||
\(499\) | 2.14250e12 | 1.54692 | 0.773462 | − | 0.633843i | \(-0.218523\pi\) | ||||
0.773462 | + | 0.633843i | \(0.218523\pi\) | |||||||
\(500\) | −2.21854e12 | −1.58746 | ||||||||
\(501\) | 7.11168e11 | 0.504316 | ||||||||
\(502\) | 3.11772e10 | 0.0219114 | ||||||||
\(503\) | 8.16297e11 | 0.568581 | 0.284291 | − | 0.958738i | \(-0.408242\pi\) | ||||
0.284291 | + | 0.958738i | \(0.408242\pi\) | |||||||
\(504\) | 3.15771e11 | 0.217989 | ||||||||
\(505\) | −6.35113e10 | −0.0434550 | ||||||||
\(506\) | 4.59061e12 | 3.11310 | ||||||||
\(507\) | 5.92712e11 | 0.398390 | ||||||||
\(508\) | 3.43738e12 | 2.29003 | ||||||||
\(509\) | −1.36465e12 | −0.901136 | −0.450568 | − | 0.892742i | \(-0.648779\pi\) | ||||
−0.450568 | + | 0.892742i | \(0.648779\pi\) | |||||||
\(510\) | −1.34409e12 | −0.879759 | ||||||||
\(511\) | −8.59827e11 | −0.557849 | ||||||||
\(512\) | −4.18863e11 | −0.269375 | ||||||||
\(513\) | 8.93601e10 | 0.0569660 | ||||||||
\(514\) | −4.45015e12 | −2.81216 | ||||||||
\(515\) | 3.12058e11 | 0.195480 | ||||||||
\(516\) | 6.60333e11 | 0.410053 | ||||||||
\(517\) | 2.03384e12 | 1.25202 | ||||||||
\(518\) | −6.84223e11 | −0.417555 | ||||||||
\(519\) | 2.61995e11 | 0.158504 | ||||||||
\(520\) | −5.30592e11 | −0.318234 | ||||||||
\(521\) | −1.64297e12 | −0.976920 | −0.488460 | − | 0.872586i | \(-0.662441\pi\) | ||||
−0.488460 | + | 0.872586i | \(0.662441\pi\) | |||||||
\(522\) | −5.81136e10 | −0.0342579 | ||||||||
\(523\) | 2.27813e12 | 1.33144 | 0.665719 | − | 0.746203i | \(-0.268125\pi\) | ||||
0.665719 | + | 0.746203i | \(0.268125\pi\) | |||||||
\(524\) | −3.54066e12 | −2.05160 | ||||||||
\(525\) | −4.33599e11 | −0.249098 | ||||||||
\(526\) | −8.97132e11 | −0.511000 | ||||||||
\(527\) | −3.29968e12 | −1.86348 | ||||||||
\(528\) | −1.67415e11 | −0.0937435 | ||||||||
\(529\) | 2.92951e12 | 1.62646 | ||||||||
\(530\) | 1.69089e12 | 0.930838 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 6.26160e11 | 0.338909 | ||||||||
\(533\) | −4.87683e11 | −0.261737 | ||||||||
\(534\) | −1.96995e12 | −1.04838 | ||||||||
\(535\) | −1.95135e12 | −1.02978 | ||||||||
\(536\) | 2.19808e12 | 1.15028 | ||||||||
\(537\) | −1.80399e12 | −0.936158 | ||||||||
\(538\) | 5.99287e12 | 3.08400 | ||||||||
\(539\) | 1.07944e12 | 0.550869 | ||||||||
\(540\) | −3.80545e11 | −0.192590 | ||||||||
\(541\) | −3.39774e12 | −1.70530 | −0.852652 | − | 0.522479i | \(-0.825007\pi\) | ||||
−0.852652 | + | 0.522479i | \(0.825007\pi\) | |||||||
\(542\) | −1.13603e12 | −0.565450 | ||||||||
\(543\) | 1.75586e12 | 0.866745 | ||||||||
\(544\) | −3.34394e12 | −1.63706 | ||||||||
\(545\) | 1.51033e12 | 0.733308 | ||||||||
\(546\) | −7.85319e11 | −0.378163 | ||||||||
\(547\) | −2.14411e11 | −0.102401 | −0.0512005 | − | 0.998688i | \(-0.516305\pi\) | ||||
−0.0512005 | + | 0.998688i | \(0.516305\pi\) | |||||||
\(548\) | −2.16441e12 | −1.02524 | ||||||||
\(549\) | 1.96446e11 | 0.0922927 | ||||||||
\(550\) | −2.41691e12 | −1.12623 | ||||||||
\(551\) | −4.11710e10 | −0.0190287 | ||||||||
\(552\) | 1.81383e12 | 0.831514 | ||||||||
\(553\) | −3.61072e11 | −0.164184 | ||||||||
\(554\) | −5.95424e12 | −2.68555 | ||||||||
\(555\) | 2.94600e11 | 0.131800 | ||||||||
\(556\) | −1.15018e12 | −0.510420 | ||||||||
\(557\) | 2.17048e12 | 0.955450 | 0.477725 | − | 0.878510i | \(-0.341462\pi\) | ||||
0.477725 | + | 0.878510i | \(0.341462\pi\) | |||||||
\(558\) | −1.53467e12 | −0.670132 | ||||||||
\(559\) | −5.86730e11 | −0.254147 | ||||||||
\(560\) | 1.48855e11 | 0.0639614 | ||||||||
\(561\) | −2.41169e12 | −1.02799 | ||||||||
\(562\) | 6.30615e12 | 2.66656 | ||||||||
\(563\) | 9.89772e11 | 0.415191 | 0.207595 | − | 0.978215i | \(-0.433436\pi\) | ||||
0.207595 | + | 0.978215i | \(0.433436\pi\) | |||||||
\(564\) | 2.24927e12 | 0.936020 | ||||||||
\(565\) | −3.01075e11 | −0.124296 | ||||||||
\(566\) | −5.54552e12 | −2.27127 | ||||||||
\(567\) | −2.01230e11 | −0.0817653 | ||||||||
\(568\) | 1.56651e12 | 0.631488 | ||||||||
\(569\) | −3.94076e12 | −1.57607 | −0.788033 | − | 0.615632i | \(-0.788901\pi\) | ||||
−0.788033 | + | 0.615632i | \(0.788901\pi\) | |||||||
\(570\) | −4.42880e11 | −0.175731 | ||||||||
\(571\) | −8.16947e11 | −0.321611 | −0.160806 | − | 0.986986i | \(-0.551409\pi\) | ||||
−0.160806 | + | 0.986986i | \(0.551409\pi\) | |||||||
\(572\) | −2.66473e12 | −1.04081 | ||||||||
\(573\) | −2.27969e12 | −0.883446 | ||||||||
\(574\) | −1.43844e12 | −0.553080 | ||||||||
\(575\) | −2.49064e12 | −0.950180 | ||||||||
\(576\) | −1.43625e12 | −0.543663 | ||||||||
\(577\) | 7.47676e11 | 0.280816 | 0.140408 | − | 0.990094i | \(-0.455159\pi\) | ||||
0.140408 | + | 0.990094i | \(0.455159\pi\) | |||||||
\(578\) | −5.13052e12 | −1.91199 | ||||||||
\(579\) | 3.57531e11 | 0.132209 | ||||||||
\(580\) | 1.75329e11 | 0.0643322 | ||||||||
\(581\) | 8.11614e11 | 0.295499 | ||||||||
\(582\) | 4.03572e12 | 1.45803 | ||||||||
\(583\) | 3.03395e12 | 1.08768 | ||||||||
\(584\) | −1.89369e12 | −0.673674 | ||||||||
\(585\) | 3.38128e11 | 0.119366 | ||||||||
\(586\) | −1.90409e12 | −0.667035 | ||||||||
\(587\) | −2.57396e12 | −0.894808 | −0.447404 | − | 0.894332i | \(-0.647651\pi\) | ||||
−0.447404 | + | 0.894332i | \(0.647651\pi\) | |||||||
\(588\) | 1.19377e12 | 0.411836 | ||||||||
\(589\) | −1.08725e12 | −0.372228 | ||||||||
\(590\) | −3.94022e11 | −0.133871 | ||||||||
\(591\) | 1.65276e12 | 0.557269 | ||||||||
\(592\) | 1.43332e11 | 0.0479619 | ||||||||
\(593\) | 2.53540e12 | 0.841979 | 0.420989 | − | 0.907066i | \(-0.361683\pi\) | ||||
0.420989 | + | 0.907066i | \(0.361683\pi\) | |||||||
\(594\) | −1.12167e12 | −0.369680 | ||||||||
\(595\) | 2.14433e12 | 0.701401 | ||||||||
\(596\) | 2.35662e12 | 0.765037 | ||||||||
\(597\) | −8.26017e11 | −0.266136 | ||||||||
\(598\) | −4.51096e12 | −1.44249 | ||||||||
\(599\) | 3.20638e12 | 1.01764 | 0.508820 | − | 0.860873i | \(-0.330082\pi\) | ||||
0.508820 | + | 0.860873i | \(0.330082\pi\) | |||||||
\(600\) | −9.54959e11 | −0.300818 | ||||||||
\(601\) | −2.22462e12 | −0.695537 | −0.347769 | − | 0.937580i | \(-0.613061\pi\) | ||||
−0.347769 | + | 0.937580i | \(0.613061\pi\) | |||||||
\(602\) | −1.73058e12 | −0.537041 | ||||||||
\(603\) | −1.40076e12 | −0.431455 | ||||||||
\(604\) | 3.19412e12 | 0.976528 | ||||||||
\(605\) | 9.40430e11 | 0.285382 | ||||||||
\(606\) | −2.07030e11 | −0.0623600 | ||||||||
\(607\) | 1.85983e12 | 0.556062 | 0.278031 | − | 0.960572i | \(-0.410318\pi\) | ||||
0.278031 | + | 0.960572i | \(0.410318\pi\) | |||||||
\(608\) | −1.10183e12 | −0.327001 | ||||||||
\(609\) | 9.27130e10 | 0.0273126 | ||||||||
\(610\) | −9.73609e11 | −0.284709 | ||||||||
\(611\) | −1.99855e12 | −0.580137 | ||||||||
\(612\) | −2.66714e12 | −0.768537 | ||||||||
\(613\) | 4.96907e11 | 0.142136 | 0.0710679 | − | 0.997471i | \(-0.477359\pi\) | ||||
0.0710679 | + | 0.997471i | \(0.477359\pi\) | |||||||
\(614\) | −8.49031e12 | −2.41083 | ||||||||
\(615\) | 6.19336e11 | 0.174578 | ||||||||
\(616\) | −2.80806e12 | −0.785767 | ||||||||
\(617\) | −4.67093e12 | −1.29754 | −0.648769 | − | 0.760985i | \(-0.724716\pi\) | ||||
−0.648769 | + | 0.760985i | \(0.724716\pi\) | |||||||
\(618\) | 1.01723e12 | 0.280524 | ||||||||
\(619\) | −3.58040e11 | −0.0980220 | −0.0490110 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490110 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(620\) | 4.63011e12 | 1.25843 | ||||||||
\(621\) | −1.15589e12 | −0.311892 | ||||||||
\(622\) | −1.26091e12 | −0.337776 | ||||||||
\(623\) | 3.14281e12 | 0.835837 | ||||||||
\(624\) | 1.64510e11 | 0.0434372 | ||||||||
\(625\) | −2.66843e11 | −0.0699514 | ||||||||
\(626\) | −6.40432e12 | −1.66682 | ||||||||
\(627\) | −7.94655e11 | −0.205341 | ||||||||
\(628\) | 9.99350e12 | 2.56389 | ||||||||
\(629\) | 2.06478e12 | 0.525951 | ||||||||
\(630\) | 9.97321e11 | 0.252233 | ||||||||
\(631\) | 9.90994e11 | 0.248851 | 0.124425 | − | 0.992229i | \(-0.460291\pi\) | ||||
0.124425 | + | 0.992229i | \(0.460291\pi\) | |||||||
\(632\) | −7.95227e11 | −0.198273 | ||||||||
\(633\) | 1.08074e12 | 0.267550 | ||||||||
\(634\) | −8.35315e9 | −0.00205328 | ||||||||
\(635\) | 3.87875e12 | 0.946694 | ||||||||
\(636\) | 3.35531e12 | 0.813159 | ||||||||
\(637\) | −1.06071e12 | −0.255252 | ||||||||
\(638\) | 5.16788e11 | 0.123486 | ||||||||
\(639\) | −9.98281e11 | −0.236864 | ||||||||
\(640\) | 4.10244e12 | 0.966568 | ||||||||
\(641\) | −3.94375e12 | −0.922675 | −0.461337 | − | 0.887225i | \(-0.652630\pi\) | ||||
−0.461337 | + | 0.887225i | \(0.652630\pi\) | |||||||
\(642\) | −6.36087e12 | −1.47778 | ||||||||
\(643\) | 6.09002e12 | 1.40498 | 0.702489 | − | 0.711695i | \(-0.252072\pi\) | ||||
0.702489 | + | 0.711695i | \(0.252072\pi\) | |||||||
\(644\) | −8.09948e12 | −1.85554 | ||||||||
\(645\) | 7.45121e11 | 0.169515 | ||||||||
\(646\) | −3.10403e12 | −0.701260 | ||||||||
\(647\) | −8.53763e12 | −1.91544 | −0.957719 | − | 0.287704i | \(-0.907108\pi\) | ||||
−0.957719 | + | 0.287704i | \(0.907108\pi\) | |||||||
\(648\) | −4.43190e11 | −0.0987420 | ||||||||
\(649\) | −7.06989e11 | −0.156427 | ||||||||
\(650\) | 2.37497e12 | 0.521854 | ||||||||
\(651\) | 2.44837e12 | 0.534272 | ||||||||
\(652\) | 9.62059e12 | 2.08491 | ||||||||
\(653\) | −2.31918e12 | −0.499144 | −0.249572 | − | 0.968356i | \(-0.580290\pi\) | ||||
−0.249572 | + | 0.968356i | \(0.580290\pi\) | |||||||
\(654\) | 4.92326e12 | 1.05233 | ||||||||
\(655\) | −3.99529e12 | −0.848130 | ||||||||
\(656\) | 3.01327e11 | 0.0635288 | ||||||||
\(657\) | 1.20678e12 | 0.252688 | ||||||||
\(658\) | −5.89480e12 | −1.22589 | ||||||||
\(659\) | 3.93884e12 | 0.813549 | 0.406774 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406774 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(660\) | 3.38409e12 | 0.694214 | ||||||||
\(661\) | −4.00845e12 | −0.816714 | −0.408357 | − | 0.912822i | \(-0.633898\pi\) | ||||
−0.408357 | + | 0.912822i | \(0.633898\pi\) | |||||||
\(662\) | −2.67084e11 | −0.0540489 | ||||||||
\(663\) | 2.36985e12 | 0.476333 | ||||||||
\(664\) | 1.78750e12 | 0.356853 | ||||||||
\(665\) | 7.06560e11 | 0.140104 | ||||||||
\(666\) | 9.60318e11 | 0.189139 | ||||||||
\(667\) | 5.32554e11 | 0.104183 | ||||||||
\(668\) | −6.99409e12 | −1.35906 | ||||||||
\(669\) | 1.75940e12 | 0.339584 | ||||||||
\(670\) | 6.94234e12 | 1.33097 | ||||||||
\(671\) | −1.74694e12 | −0.332680 | ||||||||
\(672\) | 2.48121e12 | 0.469356 | ||||||||
\(673\) | −1.29844e12 | −0.243979 | −0.121990 | − | 0.992531i | \(-0.538927\pi\) | ||||
−0.121990 | + | 0.992531i | \(0.538927\pi\) | |||||||
\(674\) | −1.46889e13 | −2.74170 | ||||||||
\(675\) | 6.08563e11 | 0.112834 | ||||||||
\(676\) | −5.82912e12 | −1.07360 | ||||||||
\(677\) | 8.66231e12 | 1.58484 | 0.792419 | − | 0.609978i | \(-0.208822\pi\) | ||||
0.792419 | + | 0.609978i | \(0.208822\pi\) | |||||||
\(678\) | −9.81425e11 | −0.178371 | ||||||||
\(679\) | −6.43849e12 | −1.16244 | ||||||||
\(680\) | 4.72269e12 | 0.847031 | ||||||||
\(681\) | −2.69325e12 | −0.479860 | ||||||||
\(682\) | 1.36474e13 | 2.41557 | ||||||||
\(683\) | 3.03372e12 | 0.533436 | 0.266718 | − | 0.963775i | \(-0.414061\pi\) | ||||
0.266718 | + | 0.963775i | \(0.414061\pi\) | |||||||
\(684\) | −8.78825e11 | −0.153515 | ||||||||
\(685\) | −2.44233e12 | −0.423834 | ||||||||
\(686\) | −9.95261e12 | −1.71585 | ||||||||
\(687\) | 7.45729e11 | 0.127725 | ||||||||
\(688\) | 3.62525e11 | 0.0616865 | ||||||||
\(689\) | −2.98131e12 | −0.503989 | ||||||||
\(690\) | 5.72873e12 | 0.962137 | ||||||||
\(691\) | 7.07473e11 | 0.118048 | 0.0590240 | − | 0.998257i | \(-0.481201\pi\) | ||||
0.0590240 | + | 0.998257i | \(0.481201\pi\) | |||||||
\(692\) | −2.57663e12 | −0.427144 | ||||||||
\(693\) | 1.78948e12 | 0.294732 | ||||||||
\(694\) | −1.91490e13 | −3.13350 | ||||||||
\(695\) | −1.29786e12 | −0.211007 | ||||||||
\(696\) | 2.04191e11 | 0.0329834 | ||||||||
\(697\) | 4.34077e12 | 0.696657 | ||||||||
\(698\) | −1.11664e13 | −1.78059 | ||||||||
\(699\) | −4.09242e12 | −0.648384 | ||||||||
\(700\) | 4.26429e12 | 0.671283 | ||||||||
\(701\) | 5.38606e12 | 0.842442 | 0.421221 | − | 0.906958i | \(-0.361602\pi\) | ||||
0.421221 | + | 0.906958i | \(0.361602\pi\) | |||||||
\(702\) | 1.10221e12 | 0.171296 | ||||||||
\(703\) | 6.80345e11 | 0.105058 | ||||||||
\(704\) | 1.27722e13 | 1.95970 | ||||||||
\(705\) | 2.53808e12 | 0.386949 | ||||||||
\(706\) | −1.34626e13 | −2.03942 | ||||||||
\(707\) | 3.30290e11 | 0.0497174 | ||||||||
\(708\) | −7.81874e11 | −0.116947 | ||||||||
\(709\) | −5.97478e12 | −0.888002 | −0.444001 | − | 0.896026i | \(-0.646441\pi\) | ||||
−0.444001 | + | 0.896026i | \(0.646441\pi\) | |||||||
\(710\) | 4.94760e12 | 0.730689 | ||||||||
\(711\) | 5.06771e11 | 0.0743701 | ||||||||
\(712\) | 6.92173e12 | 1.00938 | ||||||||
\(713\) | 1.40637e13 | 2.03797 | ||||||||
\(714\) | 6.98996e12 | 1.00654 | ||||||||
\(715\) | −3.00688e12 | −0.430268 | ||||||||
\(716\) | 1.77416e13 | 2.52281 | ||||||||
\(717\) | −1.53133e12 | −0.216387 | ||||||||
\(718\) | −1.98774e13 | −2.79126 | ||||||||
\(719\) | −3.16517e12 | −0.441689 | −0.220844 | − | 0.975309i | \(-0.570881\pi\) | ||||
−0.220844 | + | 0.975309i | \(0.570881\pi\) | |||||||
\(720\) | −2.08921e11 | −0.0289725 | ||||||||
\(721\) | −1.62286e12 | −0.223652 | ||||||||
\(722\) | 1.06503e13 | 1.45863 | ||||||||
\(723\) | 2.67512e12 | 0.364100 | ||||||||
\(724\) | −1.72683e13 | −2.33575 | ||||||||
\(725\) | −2.80384e11 | −0.0376905 | ||||||||
\(726\) | 3.06555e12 | 0.409537 | ||||||||
\(727\) | 5.47097e12 | 0.726372 | 0.363186 | − | 0.931717i | \(-0.381689\pi\) | ||||
0.363186 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(728\) | 2.75935e12 | 0.364095 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −5.98095e12 | −0.779502 | ||||||||
\(731\) | 5.22236e12 | 0.676454 | ||||||||
\(732\) | −1.93198e12 | −0.248715 | ||||||||
\(733\) | −2.58003e12 | −0.330108 | −0.165054 | − | 0.986285i | \(-0.552780\pi\) | ||||
−0.165054 | + | 0.986285i | \(0.552780\pi\) | |||||||
\(734\) | 1.42691e13 | 1.81452 | ||||||||
\(735\) | 1.34706e12 | 0.170252 | ||||||||
\(736\) | 1.42524e13 | 1.79035 | ||||||||
\(737\) | 1.24566e13 | 1.55523 | ||||||||
\(738\) | 2.01887e12 | 0.250527 | ||||||||
\(739\) | 7.87394e12 | 0.971163 | 0.485582 | − | 0.874191i | \(-0.338608\pi\) | ||||
0.485582 | + | 0.874191i | \(0.338608\pi\) | |||||||
\(740\) | −2.89729e12 | −0.355181 | ||||||||
\(741\) | 7.80868e11 | 0.0951471 | ||||||||
\(742\) | −8.79348e12 | −1.06498 | ||||||||
\(743\) | 1.97110e12 | 0.237279 | 0.118640 | − | 0.992937i | \(-0.462147\pi\) | ||||
0.118640 | + | 0.992937i | \(0.462147\pi\) | |||||||
\(744\) | 5.39230e12 | 0.645202 | ||||||||
\(745\) | 2.65922e12 | 0.316265 | ||||||||
\(746\) | 1.12887e13 | 1.33450 | ||||||||
\(747\) | −1.13911e12 | −0.133852 | ||||||||
\(748\) | 2.37182e13 | 2.77028 | ||||||||
\(749\) | 1.01480e13 | 1.17818 | ||||||||
\(750\) | −8.16042e12 | −0.941753 | ||||||||
\(751\) | 1.05866e13 | 1.21444 | 0.607219 | − | 0.794535i | \(-0.292285\pi\) | ||||
0.607219 | + | 0.794535i | \(0.292285\pi\) | |||||||
\(752\) | 1.23486e12 | 0.140811 | ||||||||
\(753\) | 6.98101e10 | 0.00791299 | ||||||||
\(754\) | −5.07822e11 | −0.0572190 | ||||||||
\(755\) | 3.60425e12 | 0.403695 | ||||||||
\(756\) | 1.97903e12 | 0.220345 | ||||||||
\(757\) | 6.82958e12 | 0.755897 | 0.377949 | − | 0.925827i | \(-0.376630\pi\) | ||||
0.377949 | + | 0.925827i | \(0.376630\pi\) | |||||||
\(758\) | 5.57906e12 | 0.613832 | ||||||||
\(759\) | 1.02790e13 | 1.12425 | ||||||||
\(760\) | 1.55613e12 | 0.169194 | ||||||||
\(761\) | 3.87107e12 | 0.418409 | 0.209204 | − | 0.977872i | \(-0.432913\pi\) | ||||
0.209204 | + | 0.977872i | \(0.432913\pi\) | |||||||
\(762\) | 1.26437e13 | 1.35855 | ||||||||
\(763\) | −7.85445e12 | −0.838987 | ||||||||
\(764\) | 2.24199e13 | 2.38075 | ||||||||
\(765\) | −3.00961e12 | −0.317712 | ||||||||
\(766\) | −1.56769e13 | −1.64524 | ||||||||
\(767\) | 6.94723e11 | 0.0724824 | ||||||||
\(768\) | 4.29432e12 | 0.445419 | ||||||||
\(769\) | −3.32827e12 | −0.343202 | −0.171601 | − | 0.985167i | \(-0.554894\pi\) | ||||
−0.171601 | + | 0.985167i | \(0.554894\pi\) | |||||||
\(770\) | −8.86890e12 | −0.909204 | ||||||||
\(771\) | −9.96448e12 | −1.01557 | ||||||||
\(772\) | −3.51619e12 | −0.356283 | ||||||||
\(773\) | 1.09993e13 | 1.10805 | 0.554023 | − | 0.832502i | \(-0.313092\pi\) | ||||
0.554023 | + | 0.832502i | \(0.313092\pi\) | |||||||
\(774\) | 2.42890e12 | 0.243262 | ||||||||
\(775\) | −7.40440e12 | −0.737279 | ||||||||
\(776\) | −1.41801e13 | −1.40379 | ||||||||
\(777\) | −1.53207e12 | −0.150794 | ||||||||
\(778\) | 7.75462e12 | 0.758844 | ||||||||
\(779\) | 1.43029e12 | 0.139157 | ||||||||
\(780\) | −3.32537e12 | −0.321673 | ||||||||
\(781\) | 8.87744e12 | 0.853804 | ||||||||
\(782\) | 4.01511e13 | 3.83944 | ||||||||
\(783\) | −1.30124e11 | −0.0123717 | ||||||||
\(784\) | 6.55385e11 | 0.0619547 | ||||||||
\(785\) | 1.12767e13 | 1.05991 | ||||||||
\(786\) | −1.30236e13 | −1.21711 | ||||||||
\(787\) | −4.00733e12 | −0.372365 | −0.186182 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186182 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(788\) | −1.62543e13 | −1.50176 | ||||||||
\(789\) | −2.00880e12 | −0.184540 | ||||||||
\(790\) | −2.51162e12 | −0.229420 | ||||||||
\(791\) | 1.56574e12 | 0.142209 | ||||||||
\(792\) | 3.94116e12 | 0.355927 | ||||||||
\(793\) | 1.71663e12 | 0.154151 | ||||||||
\(794\) | −1.30147e12 | −0.116209 | ||||||||
\(795\) | 3.78614e12 | 0.336158 | ||||||||
\(796\) | 8.12358e12 | 0.717198 | ||||||||
\(797\) | −1.15951e13 | −1.01792 | −0.508959 | − | 0.860791i | \(-0.669970\pi\) | ||||
−0.508959 | + | 0.860791i | \(0.669970\pi\) | |||||||
\(798\) | 2.30320e12 | 0.201056 | ||||||||
\(799\) | 1.77887e13 | 1.54413 | ||||||||
\(800\) | −7.50372e12 | −0.647697 | ||||||||
\(801\) | −4.41098e12 | −0.378607 | ||||||||
\(802\) | −8.66944e12 | −0.739956 | ||||||||
\(803\) | −1.07316e13 | −0.910842 | ||||||||
\(804\) | 1.37760e13 | 1.16271 | ||||||||
\(805\) | −9.13947e12 | −0.767078 | ||||||||
\(806\) | −1.34106e13 | −1.11928 | ||||||||
\(807\) | 1.34188e13 | 1.11374 | ||||||||
\(808\) | 7.27433e11 | 0.0600401 | ||||||||
\(809\) | 8.25765e12 | 0.677779 | 0.338890 | − | 0.940826i | \(-0.389949\pi\) | ||||
0.338890 | + | 0.940826i | \(0.389949\pi\) | |||||||
\(810\) | −1.39976e12 | −0.114254 | ||||||||
\(811\) | −8.98093e12 | −0.729000 | −0.364500 | − | 0.931203i | \(-0.618760\pi\) | ||||
−0.364500 | + | 0.931203i | \(0.618760\pi\) | |||||||
\(812\) | −9.11800e11 | −0.0736033 | ||||||||
\(813\) | −2.54373e12 | −0.204204 | ||||||||
\(814\) | −8.53984e12 | −0.681774 | ||||||||
\(815\) | 1.08559e13 | 0.861898 | ||||||||
\(816\) | −1.46427e12 | −0.115615 | ||||||||
\(817\) | 1.72077e12 | 0.135121 | ||||||||
\(818\) | −2.95370e13 | −2.30662 | ||||||||
\(819\) | −1.75844e12 | −0.136568 | ||||||||
\(820\) | −6.09096e12 | −0.470461 | ||||||||
\(821\) | −1.51505e13 | −1.16381 | −0.581905 | − | 0.813257i | \(-0.697692\pi\) | ||||
−0.581905 | + | 0.813257i | \(0.697692\pi\) | |||||||
\(822\) | −7.96133e12 | −0.608222 | ||||||||
\(823\) | 1.47489e12 | 0.112063 | 0.0560313 | − | 0.998429i | \(-0.482155\pi\) | ||||
0.0560313 | + | 0.998429i | \(0.482155\pi\) | |||||||
\(824\) | −3.57419e12 | −0.270088 | ||||||||
\(825\) | −5.41178e12 | −0.406722 | ||||||||
\(826\) | 2.04911e12 | 0.153163 | ||||||||
\(827\) | 1.16616e13 | 0.866925 | 0.433463 | − | 0.901172i | \(-0.357292\pi\) | ||||
0.433463 | + | 0.901172i | \(0.357292\pi\) | |||||||
\(828\) | 1.13678e13 | 0.840501 | ||||||||
\(829\) | 2.04853e13 | 1.50642 | 0.753210 | − | 0.657780i | \(-0.228505\pi\) | ||||
0.753210 | + | 0.657780i | \(0.228505\pi\) | |||||||
\(830\) | 5.64558e12 | 0.412912 | ||||||||
\(831\) | −1.33324e13 | −0.969845 | ||||||||
\(832\) | −1.25506e13 | −0.908050 | ||||||||
\(833\) | 9.44116e12 | 0.679396 | ||||||||
\(834\) | −4.23068e12 | −0.302805 | ||||||||
\(835\) | −7.89214e12 | −0.561831 | ||||||||
\(836\) | 7.81515e12 | 0.553362 | ||||||||
\(837\) | −3.43633e12 | −0.242008 | ||||||||
\(838\) | −4.91720e11 | −0.0344445 | ||||||||
\(839\) | 8.04580e12 | 0.560584 | 0.280292 | − | 0.959915i | \(-0.409569\pi\) | ||||
0.280292 | + | 0.959915i | \(0.409569\pi\) | |||||||
\(840\) | −3.50425e12 | −0.242850 | ||||||||
\(841\) | −1.44472e13 | −0.995867 | ||||||||
\(842\) | 7.20376e12 | 0.493918 | ||||||||
\(843\) | 1.41203e13 | 0.962987 | ||||||||
\(844\) | −1.06287e13 | −0.721007 | ||||||||
\(845\) | −6.57759e12 | −0.443825 | ||||||||
\(846\) | 8.27345e12 | 0.555290 | ||||||||
\(847\) | −4.89070e12 | −0.326510 | ||||||||
\(848\) | 1.84208e12 | 0.122328 | ||||||||
\(849\) | −1.24172e13 | −0.820234 | ||||||||
\(850\) | −2.11391e13 | −1.38900 | ||||||||
\(851\) | −8.80038e12 | −0.575199 | ||||||||
\(852\) | 9.81775e12 | 0.638313 | ||||||||
\(853\) | −2.14040e13 | −1.38428 | −0.692140 | − | 0.721763i | \(-0.743332\pi\) | ||||
−0.692140 | + | 0.721763i | \(0.743332\pi\) | |||||||
\(854\) | 5.06326e12 | 0.325739 | ||||||||
\(855\) | −9.91668e11 | −0.0634627 | ||||||||
\(856\) | 2.23500e13 | 1.42280 | ||||||||
\(857\) | 2.80212e13 | 1.77449 | 0.887245 | − | 0.461299i | \(-0.152617\pi\) | ||||
0.887245 | + | 0.461299i | \(0.152617\pi\) | |||||||
\(858\) | −9.80163e12 | −0.617455 | ||||||||
\(859\) | −1.79329e13 | −1.12378 | −0.561891 | − | 0.827211i | \(-0.689926\pi\) | ||||
−0.561891 | + | 0.827211i | \(0.689926\pi\) | |||||||
\(860\) | −7.32801e12 | −0.456818 | ||||||||
\(861\) | −3.22086e12 | −0.199737 | ||||||||
\(862\) | −2.54048e13 | −1.56723 | ||||||||
\(863\) | −1.96418e13 | −1.20540 | −0.602701 | − | 0.797967i | \(-0.705909\pi\) | ||||
−0.602701 | + | 0.797967i | \(0.705909\pi\) | |||||||
\(864\) | −3.48242e12 | −0.212603 | ||||||||
\(865\) | −2.90747e12 | −0.176580 | ||||||||
\(866\) | 1.01555e13 | 0.613582 | ||||||||
\(867\) | −1.14879e13 | −0.690488 | ||||||||
\(868\) | −2.40789e13 | −1.43978 | ||||||||
\(869\) | −4.50657e12 | −0.268076 | ||||||||
\(870\) | 6.44911e11 | 0.0381648 | ||||||||
\(871\) | −1.22405e13 | −0.720636 | ||||||||
\(872\) | −1.72987e13 | −1.01318 | ||||||||
\(873\) | 9.03652e12 | 0.526547 | ||||||||
\(874\) | 1.32298e13 | 0.766925 | ||||||||
\(875\) | 1.30189e13 | 0.750826 | ||||||||
\(876\) | −1.18683e13 | −0.680955 | ||||||||
\(877\) | 2.23088e12 | 0.127344 | 0.0636718 | − | 0.997971i | \(-0.479719\pi\) | ||||
0.0636718 | + | 0.997971i | \(0.479719\pi\) | |||||||
\(878\) | −1.98960e13 | −1.12990 | ||||||||
\(879\) | −4.26352e12 | −0.240890 | ||||||||
\(880\) | 1.85787e12 | 0.104435 | ||||||||
\(881\) | −2.49429e13 | −1.39494 | −0.697469 | − | 0.716615i | \(-0.745691\pi\) | ||||
−0.697469 | + | 0.716615i | \(0.745691\pi\) | |||||||
\(882\) | 4.39104e12 | 0.244320 | ||||||||
\(883\) | −1.27104e13 | −0.703614 | −0.351807 | − | 0.936073i | \(-0.614433\pi\) | ||||
−0.351807 | + | 0.936073i | \(0.614433\pi\) | |||||||
\(884\) | −2.33067e13 | −1.28365 | ||||||||
\(885\) | −8.82268e11 | −0.0483455 | ||||||||
\(886\) | 4.47193e12 | 0.243805 | ||||||||
\(887\) | −1.03838e13 | −0.563251 | −0.281625 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281625 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(888\) | −3.37423e12 | −0.182103 | ||||||||
\(889\) | −2.01714e13 | −1.08313 | ||||||||
\(890\) | 2.18614e13 | 1.16794 | ||||||||
\(891\) | −2.51157e12 | −0.133504 | ||||||||
\(892\) | −1.73031e13 | −0.915129 | ||||||||
\(893\) | 5.86139e12 | 0.308439 | ||||||||
\(894\) | 8.66834e12 | 0.453855 | ||||||||
\(895\) | 2.00196e13 | 1.04292 | ||||||||
\(896\) | −2.13347e13 | −1.10586 | ||||||||
\(897\) | −1.01007e13 | −0.520935 | ||||||||
\(898\) | 3.19598e13 | 1.64006 | ||||||||
\(899\) | 1.58322e12 | 0.0808395 | ||||||||
\(900\) | −5.98500e12 | −0.304070 | ||||||||
\(901\) | 2.65360e13 | 1.34145 | ||||||||
\(902\) | −1.79533e13 | −0.903055 | ||||||||
\(903\) | −3.87500e12 | −0.193944 | ||||||||
\(904\) | 3.44840e12 | 0.171735 | ||||||||
\(905\) | −1.94856e13 | −0.965594 | ||||||||
\(906\) | 1.17489e13 | 0.579322 | ||||||||
\(907\) | 1.26702e13 | 0.621659 | 0.310829 | − | 0.950466i | \(-0.399393\pi\) | ||||
0.310829 | + | 0.950466i | \(0.399393\pi\) | |||||||
\(908\) | 2.64871e13 | 1.29315 | ||||||||
\(909\) | −4.63568e11 | −0.0225204 | ||||||||
\(910\) | 8.71503e12 | 0.421291 | ||||||||
\(911\) | 2.60368e13 | 1.25243 | 0.626217 | − | 0.779649i | \(-0.284602\pi\) | ||||
0.626217 | + | 0.779649i | \(0.284602\pi\) | |||||||
\(912\) | −4.82478e11 | −0.0230941 | ||||||||
\(913\) | 1.01298e13 | 0.482484 | ||||||||
\(914\) | 3.53478e13 | 1.67535 | ||||||||
\(915\) | −2.18004e12 | −0.102818 | ||||||||
\(916\) | −7.33398e12 | −0.344199 | ||||||||
\(917\) | 2.07775e13 | 0.970356 | ||||||||
\(918\) | −9.81052e12 | −0.455932 | ||||||||
\(919\) | 1.59208e13 | 0.736283 | 0.368141 | − | 0.929770i | \(-0.379994\pi\) | ||||
0.368141 | + | 0.929770i | \(0.379994\pi\) | |||||||
\(920\) | −2.01288e13 | −0.926345 | ||||||||
\(921\) | −1.90110e13 | −0.870634 | ||||||||
\(922\) | −9.08521e12 | −0.414043 | ||||||||
\(923\) | −8.72342e12 | −0.395621 | ||||||||
\(924\) | −1.75989e13 | −0.794260 | ||||||||
\(925\) | 4.63330e12 | 0.208091 | ||||||||
\(926\) | −1.73975e13 | −0.777566 | ||||||||
\(927\) | 2.27771e12 | 0.101307 | ||||||||
\(928\) | 1.60446e12 | 0.0710172 | ||||||||
\(929\) | 1.91960e13 | 0.845551 | 0.422775 | − | 0.906234i | \(-0.361056\pi\) | ||||
0.422775 | + | 0.906234i | \(0.361056\pi\) | |||||||
\(930\) | 1.70309e13 | 0.746558 | ||||||||
\(931\) | 3.11087e12 | 0.135709 | ||||||||
\(932\) | 4.02475e13 | 1.74730 | ||||||||
\(933\) | −2.82336e12 | −0.121983 | ||||||||
\(934\) | 2.03775e12 | 0.0876175 | ||||||||
\(935\) | 2.67636e13 | 1.14523 | ||||||||
\(936\) | −3.87279e12 | −0.164923 | ||||||||
\(937\) | 4.35148e13 | 1.84421 | 0.922103 | − | 0.386946i | \(-0.126470\pi\) | ||||
0.922103 | + | 0.386946i | \(0.126470\pi\) | |||||||
\(938\) | −3.61036e13 | −1.52278 | ||||||||
\(939\) | −1.43401e13 | −0.601947 | ||||||||
\(940\) | −2.49611e13 | −1.04277 | ||||||||
\(941\) | −3.71803e13 | −1.54582 | −0.772912 | − | 0.634514i | \(-0.781200\pi\) | ||||
−0.772912 | + | 0.634514i | \(0.781200\pi\) | |||||||
\(942\) | 3.67590e13 | 1.52102 | ||||||||
\(943\) | −1.85010e13 | −0.761890 | ||||||||
\(944\) | −4.29252e11 | −0.0175929 | ||||||||
\(945\) | 2.23314e12 | 0.0910903 | ||||||||
\(946\) | −2.15995e13 | −0.876867 | ||||||||
\(947\) | 2.06568e13 | 0.834620 | 0.417310 | − | 0.908764i | \(-0.362973\pi\) | ||||
0.417310 | + | 0.908764i | \(0.362973\pi\) | |||||||
\(948\) | −4.98391e12 | −0.200416 | ||||||||
\(949\) | 1.05454e13 | 0.422050 | ||||||||
\(950\) | −6.96536e12 | −0.277452 | ||||||||
\(951\) | −1.87038e10 | −0.000741512 0 | ||||||||
\(952\) | −2.45604e13 | −0.969099 | ||||||||
\(953\) | −1.41965e13 | −0.557525 | −0.278763 | − | 0.960360i | \(-0.589924\pi\) | ||||
−0.278763 | + | 0.960360i | \(0.589924\pi\) | |||||||
\(954\) | 1.23418e13 | 0.482404 | ||||||||
\(955\) | 2.52987e13 | 0.984199 | ||||||||
\(956\) | 1.50601e13 | 0.583131 | ||||||||
\(957\) | 1.15716e12 | 0.0445953 | ||||||||
\(958\) | −8.46402e12 | −0.324662 | ||||||||
\(959\) | 1.27013e13 | 0.484914 | ||||||||
\(960\) | 1.59387e13 | 0.605666 | ||||||||
\(961\) | 1.53703e13 | 0.581334 | ||||||||
\(962\) | 8.39168e12 | 0.315908 | ||||||||
\(963\) | −1.42429e13 | −0.533678 | ||||||||
\(964\) | −2.63089e13 | −0.981195 | ||||||||
\(965\) | −3.96768e12 | −0.147287 | ||||||||
\(966\) | −2.97922e13 | −1.10079 | ||||||||
\(967\) | −4.32059e13 | −1.58900 | −0.794500 | − | 0.607264i | \(-0.792267\pi\) | ||||
−0.794500 | + | 0.607264i | \(0.792267\pi\) | |||||||
\(968\) | −1.07713e13 | −0.394302 | ||||||||
\(969\) | −6.95034e12 | −0.253250 | ||||||||
\(970\) | −4.47861e13 | −1.62432 | ||||||||
\(971\) | 2.39954e13 | 0.866245 | 0.433123 | − | 0.901335i | \(-0.357412\pi\) | ||||
0.433123 | + | 0.901335i | \(0.357412\pi\) | |||||||
\(972\) | −2.77760e12 | −0.0998093 | ||||||||
\(973\) | 6.74952e12 | 0.241416 | ||||||||
\(974\) | 5.57468e13 | 1.98474 | ||||||||
\(975\) | 5.31789e12 | 0.188460 | ||||||||
\(976\) | −1.06066e12 | −0.0374156 | ||||||||
\(977\) | 1.45550e13 | 0.511077 | 0.255538 | − | 0.966799i | \(-0.417747\pi\) | ||||
0.255538 | + | 0.966799i | \(0.417747\pi\) | |||||||
\(978\) | 3.53873e13 | 1.23687 | ||||||||
\(979\) | 3.92256e13 | 1.36473 | ||||||||
\(980\) | −1.32478e13 | −0.458804 | ||||||||
\(981\) | 1.10238e13 | 0.380034 | ||||||||
\(982\) | 1.67717e13 | 0.575539 | ||||||||
\(983\) | 4.62268e13 | 1.57908 | 0.789538 | − | 0.613701i | \(-0.210320\pi\) | ||||
0.789538 | + | 0.613701i | \(0.210320\pi\) | |||||||
\(984\) | −7.09363e12 | −0.241207 | ||||||||
\(985\) | −1.83414e13 | −0.620824 | ||||||||
\(986\) | 4.52002e12 | 0.152298 | ||||||||
\(987\) | −1.31993e13 | −0.442713 | ||||||||
\(988\) | −7.67956e12 | −0.256407 | ||||||||
\(989\) | −2.22585e13 | −0.739796 | ||||||||
\(990\) | 1.24476e13 | 0.411840 | ||||||||
\(991\) | 1.20817e13 | 0.397922 | 0.198961 | − | 0.980007i | \(-0.436243\pi\) | ||||
0.198961 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(992\) | 4.23707e13 | 1.38920 | ||||||||
\(993\) | −5.98038e11 | −0.0195190 | ||||||||
\(994\) | −2.57300e13 | −0.835991 | ||||||||
\(995\) | 9.16666e12 | 0.296488 | ||||||||
\(996\) | 1.12028e13 | 0.360710 | ||||||||
\(997\) | −5.11913e13 | −1.64085 | −0.820423 | − | 0.571757i | \(-0.806262\pi\) | ||||
−0.820423 | + | 0.571757i | \(0.806262\pi\) | |||||||
\(998\) | −7.75043e13 | −2.47308 | ||||||||
\(999\) | 2.15028e12 | 0.0683048 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.c.1.4 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.4 | ✓ | 22 | 1.1 | even | 1 | trivial |