Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −155.970 | −1.72324 | −0.861620 | − | 0.507553i | \(-0.830550\pi\) | ||||
−0.861620 | + | 0.507553i | \(0.830550\pi\) | |||||||
\(3\) | 2509.18 | 1.98721 | 0.993605 | − | 0.112915i | \(-0.0360187\pi\) | ||||
0.993605 | + | 0.112915i | \(0.0360187\pi\) | |||||||
\(4\) | 16134.6 | 1.96956 | ||||||||
\(5\) | −12965.5 | −0.371095 | −0.185547 | − | 0.982635i | \(-0.559406\pi\) | ||||
−0.185547 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(6\) | −391357. | −3.42444 | ||||||||
\(7\) | 428722. | 1.37733 | 0.688666 | − | 0.725078i | \(-0.258196\pi\) | ||||
0.688666 | + | 0.725078i | \(0.258196\pi\) | |||||||
\(8\) | −1.23881e6 | −1.67078 | ||||||||
\(9\) | 4.70166e6 | 2.94900 | ||||||||
\(10\) | 2.02223e6 | 0.639486 | ||||||||
\(11\) | −1.10577e7 | −1.88196 | −0.940982 | − | 0.338456i | \(-0.890095\pi\) | ||||
−0.940982 | + | 0.338456i | \(0.890095\pi\) | |||||||
\(12\) | 4.04847e7 | 3.91393 | ||||||||
\(13\) | 1.87853e7 | 1.07941 | 0.539706 | − | 0.841854i | \(-0.318535\pi\) | ||||
0.539706 | + | 0.841854i | \(0.318535\pi\) | |||||||
\(14\) | −6.68678e7 | −2.37348 | ||||||||
\(15\) | −3.25328e7 | −0.737443 | ||||||||
\(16\) | 6.10426e7 | 0.909605 | ||||||||
\(17\) | −1.84750e7 | −0.185638 | −0.0928190 | − | 0.995683i | \(-0.529588\pi\) | ||||
−0.0928190 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(18\) | −7.33318e8 | −5.08184 | ||||||||
\(19\) | 2.47569e8 | 1.20725 | 0.603626 | − | 0.797268i | \(-0.293722\pi\) | ||||
0.603626 | + | 0.797268i | \(0.293722\pi\) | |||||||
\(20\) | −2.09194e8 | −0.730893 | ||||||||
\(21\) | 1.07574e9 | 2.73705 | ||||||||
\(22\) | 1.72467e9 | 3.24308 | ||||||||
\(23\) | 5.09140e8 | 0.717144 | 0.358572 | − | 0.933502i | \(-0.383264\pi\) | ||||
0.358572 | + | 0.933502i | \(0.383264\pi\) | |||||||
\(24\) | −3.10840e9 | −3.32020 | ||||||||
\(25\) | −1.05260e9 | −0.862289 | ||||||||
\(26\) | −2.92995e9 | −1.86009 | ||||||||
\(27\) | 7.79687e9 | 3.87307 | ||||||||
\(28\) | 6.91728e9 | 2.71274 | ||||||||
\(29\) | 9.32197e8 | 0.291019 | 0.145509 | − | 0.989357i | \(-0.453518\pi\) | ||||
0.145509 | + | 0.989357i | \(0.453518\pi\) | |||||||
\(30\) | 5.07414e9 | 1.27079 | ||||||||
\(31\) | −1.35265e8 | −0.0273737 | −0.0136869 | − | 0.999906i | \(-0.504357\pi\) | ||||
−0.0136869 | + | 0.999906i | \(0.504357\pi\) | |||||||
\(32\) | 6.27540e8 | 0.103316 | ||||||||
\(33\) | −2.77457e10 | −3.73986 | ||||||||
\(34\) | 2.88155e9 | 0.319899 | ||||||||
\(35\) | −5.55861e9 | −0.511121 | ||||||||
\(36\) | 7.58596e10 | 5.80823 | ||||||||
\(37\) | 7.65238e8 | 0.0490327 | 0.0245163 | − | 0.999699i | \(-0.492195\pi\) | ||||
0.0245163 | + | 0.999699i | \(0.492195\pi\) | |||||||
\(38\) | −3.86133e10 | −2.08039 | ||||||||
\(39\) | 4.71358e10 | 2.14502 | ||||||||
\(40\) | 1.60618e10 | 0.620020 | ||||||||
\(41\) | −4.53532e10 | −1.49112 | −0.745560 | − | 0.666438i | \(-0.767818\pi\) | ||||
−0.745560 | + | 0.666438i | \(0.767818\pi\) | |||||||
\(42\) | −1.67783e11 | −4.71659 | ||||||||
\(43\) | −6.13610e10 | −1.48029 | −0.740146 | − | 0.672447i | \(-0.765243\pi\) | ||||
−0.740146 | + | 0.672447i | \(0.765243\pi\) | |||||||
\(44\) | −1.78412e11 | −3.70664 | ||||||||
\(45\) | −6.09595e10 | −1.09436 | ||||||||
\(46\) | −7.94105e10 | −1.23581 | ||||||||
\(47\) | 9.71747e10 | 1.31497 | 0.657487 | − | 0.753466i | \(-0.271619\pi\) | ||||
0.657487 | + | 0.753466i | \(0.271619\pi\) | |||||||
\(48\) | 1.53167e11 | 1.80758 | ||||||||
\(49\) | 8.69139e10 | 0.897046 | ||||||||
\(50\) | 1.64174e11 | 1.48593 | ||||||||
\(51\) | −4.63571e10 | −0.368901 | ||||||||
\(52\) | 3.03094e11 | 2.12597 | ||||||||
\(53\) | 1.05544e11 | 0.654095 | 0.327047 | − | 0.945008i | \(-0.393946\pi\) | ||||
0.327047 | + | 0.945008i | \(0.393946\pi\) | |||||||
\(54\) | −1.21608e12 | −6.67424 | ||||||||
\(55\) | 1.43369e11 | 0.698387 | ||||||||
\(56\) | −5.31106e11 | −2.30123 | ||||||||
\(57\) | 6.21195e11 | 2.39906 | ||||||||
\(58\) | −1.45395e11 | −0.501495 | ||||||||
\(59\) | 4.85318e11 | 1.49792 | 0.748959 | − | 0.662616i | \(-0.230554\pi\) | ||||
0.748959 | + | 0.662616i | \(0.230554\pi\) | |||||||
\(60\) | −5.24905e11 | −1.45244 | ||||||||
\(61\) | 1.08531e11 | 0.269717 | 0.134859 | − | 0.990865i | \(-0.456942\pi\) | ||||
0.134859 | + | 0.990865i | \(0.456942\pi\) | |||||||
\(62\) | 2.10973e10 | 0.0471716 | ||||||||
\(63\) | 2.01571e12 | 4.06176 | ||||||||
\(64\) | −5.97938e11 | −1.08764 | ||||||||
\(65\) | −2.43562e11 | −0.400564 | ||||||||
\(66\) | 4.32750e12 | 6.44468 | ||||||||
\(67\) | −3.62070e11 | −0.488997 | −0.244498 | − | 0.969650i | \(-0.578623\pi\) | ||||
−0.244498 | + | 0.969650i | \(0.578623\pi\) | |||||||
\(68\) | −2.98088e11 | −0.365625 | ||||||||
\(69\) | 1.27752e12 | 1.42511 | ||||||||
\(70\) | 8.66976e11 | 0.880785 | ||||||||
\(71\) | −9.45914e11 | −0.876339 | −0.438170 | − | 0.898892i | \(-0.644373\pi\) | ||||
−0.438170 | + | 0.898892i | \(0.644373\pi\) | |||||||
\(72\) | −5.82447e12 | −4.92715 | ||||||||
\(73\) | 2.20920e12 | 1.70859 | 0.854294 | − | 0.519791i | \(-0.173990\pi\) | ||||
0.854294 | + | 0.519791i | \(0.173990\pi\) | |||||||
\(74\) | −1.19354e11 | −0.0844951 | ||||||||
\(75\) | −2.64116e12 | −1.71355 | ||||||||
\(76\) | 3.99443e12 | 2.37775 | ||||||||
\(77\) | −4.74067e12 | −2.59209 | ||||||||
\(78\) | −7.35177e12 | −3.69638 | ||||||||
\(79\) | 1.65336e12 | 0.765227 | 0.382614 | − | 0.923908i | \(-0.375024\pi\) | ||||
0.382614 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(80\) | −7.91449e11 | −0.337550 | ||||||||
\(81\) | 1.20678e13 | 4.74761 | ||||||||
\(82\) | 7.07373e12 | 2.56956 | ||||||||
\(83\) | −1.35427e11 | −0.0454673 | −0.0227336 | − | 0.999742i | \(-0.507237\pi\) | ||||
−0.0227336 | + | 0.999742i | \(0.507237\pi\) | |||||||
\(84\) | 1.73567e13 | 5.39078 | ||||||||
\(85\) | 2.39538e11 | 0.0688893 | ||||||||
\(86\) | 9.57047e12 | 2.55090 | ||||||||
\(87\) | 2.33905e12 | 0.578315 | ||||||||
\(88\) | 1.36984e13 | 3.14436 | ||||||||
\(89\) | −2.58441e11 | −0.0551221 | −0.0275610 | − | 0.999620i | \(-0.508774\pi\) | ||||
−0.0275610 | + | 0.999620i | \(0.508774\pi\) | |||||||
\(90\) | 9.50785e12 | 1.88584 | ||||||||
\(91\) | 8.05369e12 | 1.48671 | ||||||||
\(92\) | 8.21478e12 | 1.41246 | ||||||||
\(93\) | −3.39404e11 | −0.0543974 | ||||||||
\(94\) | −1.51563e13 | −2.26602 | ||||||||
\(95\) | −3.20986e12 | −0.448005 | ||||||||
\(96\) | 1.57461e12 | 0.205310 | ||||||||
\(97\) | 1.26391e13 | 1.54064 | 0.770320 | − | 0.637657i | \(-0.220096\pi\) | ||||
0.770320 | + | 0.637657i | \(0.220096\pi\) | |||||||
\(98\) | −1.35560e13 | −1.54583 | ||||||||
\(99\) | −5.19894e13 | −5.54992 | ||||||||
\(100\) | −1.69833e13 | −1.69833 | ||||||||
\(101\) | −1.20790e13 | −1.13225 | −0.566124 | − | 0.824320i | \(-0.691557\pi\) | ||||
−0.566124 | + | 0.824320i | \(0.691557\pi\) | |||||||
\(102\) | 7.23032e12 | 0.635706 | ||||||||
\(103\) | 1.93406e13 | 1.59598 | 0.797992 | − | 0.602668i | \(-0.205896\pi\) | ||||
0.797992 | + | 0.602668i | \(0.205896\pi\) | |||||||
\(104\) | −2.32715e13 | −1.80346 | ||||||||
\(105\) | −1.39475e13 | −1.01570 | ||||||||
\(106\) | −1.64617e13 | −1.12716 | ||||||||
\(107\) | 6.57218e12 | 0.423365 | 0.211683 | − | 0.977338i | \(-0.432106\pi\) | ||||
0.211683 | + | 0.977338i | \(0.432106\pi\) | |||||||
\(108\) | 1.25800e14 | 7.62825 | ||||||||
\(109\) | 1.38956e13 | 0.793607 | 0.396803 | − | 0.917904i | \(-0.370119\pi\) | ||||
0.396803 | + | 0.917904i | \(0.370119\pi\) | |||||||
\(110\) | −2.23612e13 | −1.20349 | ||||||||
\(111\) | 1.92012e12 | 0.0974382 | ||||||||
\(112\) | 2.61703e13 | 1.25283 | ||||||||
\(113\) | −2.01596e13 | −0.910904 | −0.455452 | − | 0.890260i | \(-0.650522\pi\) | ||||
−0.455452 | + | 0.890260i | \(0.650522\pi\) | |||||||
\(114\) | −9.68878e13 | −4.13416 | ||||||||
\(115\) | −6.60126e12 | −0.266128 | ||||||||
\(116\) | 1.50407e13 | 0.573178 | ||||||||
\(117\) | 8.83223e13 | 3.18319 | ||||||||
\(118\) | −7.56950e13 | −2.58127 | ||||||||
\(119\) | −7.92065e12 | −0.255685 | ||||||||
\(120\) | 4.03021e13 | 1.23211 | ||||||||
\(121\) | 8.77495e13 | 2.54179 | ||||||||
\(122\) | −1.69275e13 | −0.464788 | ||||||||
\(123\) | −1.13799e14 | −2.96317 | ||||||||
\(124\) | −2.18245e12 | −0.0539142 | ||||||||
\(125\) | 2.94745e13 | 0.691086 | ||||||||
\(126\) | −3.14390e14 | −6.99938 | ||||||||
\(127\) | 5.03593e13 | 1.06502 | 0.532508 | − | 0.846425i | \(-0.321250\pi\) | ||||
0.532508 | + | 0.846425i | \(0.321250\pi\) | |||||||
\(128\) | 8.81196e13 | 1.77096 | ||||||||
\(129\) | −1.53966e14 | −2.94165 | ||||||||
\(130\) | 3.79883e13 | 0.690269 | ||||||||
\(131\) | −4.70768e13 | −0.813848 | −0.406924 | − | 0.913462i | \(-0.633399\pi\) | ||||
−0.406924 | + | 0.913462i | \(0.633399\pi\) | |||||||
\(132\) | −4.47667e14 | −7.36587 | ||||||||
\(133\) | 1.06138e14 | 1.66279 | ||||||||
\(134\) | 5.64720e13 | 0.842659 | ||||||||
\(135\) | −1.01090e14 | −1.43728 | ||||||||
\(136\) | 2.28871e13 | 0.310161 | ||||||||
\(137\) | −7.19811e13 | −0.930111 | −0.465055 | − | 0.885282i | \(-0.653966\pi\) | ||||
−0.465055 | + | 0.885282i | \(0.653966\pi\) | |||||||
\(138\) | −1.99255e14 | −2.45582 | ||||||||
\(139\) | −1.21312e14 | −1.42661 | −0.713307 | − | 0.700852i | \(-0.752803\pi\) | ||||
−0.713307 | + | 0.700852i | \(0.752803\pi\) | |||||||
\(140\) | −8.96861e13 | −1.00668 | ||||||||
\(141\) | 2.43829e14 | 2.61313 | ||||||||
\(142\) | 1.47534e14 | 1.51014 | ||||||||
\(143\) | −2.07722e14 | −2.03141 | ||||||||
\(144\) | 2.87001e14 | 2.68243 | ||||||||
\(145\) | −1.20864e13 | −0.107995 | ||||||||
\(146\) | −3.44569e14 | −2.94431 | ||||||||
\(147\) | 2.18082e14 | 1.78262 | ||||||||
\(148\) | 1.23468e13 | 0.0965728 | ||||||||
\(149\) | 8.87453e13 | 0.664408 | 0.332204 | − | 0.943208i | \(-0.392208\pi\) | ||||
0.332204 | + | 0.943208i | \(0.392208\pi\) | |||||||
\(150\) | 4.11941e14 | 2.95286 | ||||||||
\(151\) | 1.15727e14 | 0.794481 | 0.397240 | − | 0.917715i | \(-0.369968\pi\) | ||||
0.397240 | + | 0.917715i | \(0.369968\pi\) | |||||||
\(152\) | −3.06691e14 | −2.01706 | ||||||||
\(153\) | −8.68632e13 | −0.547447 | ||||||||
\(154\) | 7.39403e14 | 4.46680 | ||||||||
\(155\) | 1.75378e12 | 0.0101583 | ||||||||
\(156\) | 7.60518e14 | 4.22474 | ||||||||
\(157\) | −2.99206e14 | −1.59449 | −0.797246 | − | 0.603655i | \(-0.793711\pi\) | ||||
−0.797246 | + | 0.603655i | \(0.793711\pi\) | |||||||
\(158\) | −2.57874e14 | −1.31867 | ||||||||
\(159\) | 2.64829e14 | 1.29982 | ||||||||
\(160\) | −8.13638e12 | −0.0383399 | ||||||||
\(161\) | 2.18280e14 | 0.987746 | ||||||||
\(162\) | −1.88221e15 | −8.18127 | ||||||||
\(163\) | −7.83819e13 | −0.327338 | −0.163669 | − | 0.986515i | \(-0.552333\pi\) | ||||
−0.163669 | + | 0.986515i | \(0.552333\pi\) | |||||||
\(164\) | −7.31757e14 | −2.93685 | ||||||||
\(165\) | 3.59737e14 | 1.38784 | ||||||||
\(166\) | 2.11226e13 | 0.0783511 | ||||||||
\(167\) | 7.91587e13 | 0.282385 | 0.141192 | − | 0.989982i | \(-0.454906\pi\) | ||||
0.141192 | + | 0.989982i | \(0.454906\pi\) | |||||||
\(168\) | −1.33264e15 | −4.57302 | ||||||||
\(169\) | 5.00137e13 | 0.165130 | ||||||||
\(170\) | −3.73608e13 | −0.118713 | ||||||||
\(171\) | 1.16399e15 | 3.56019 | ||||||||
\(172\) | −9.90036e14 | −2.91552 | ||||||||
\(173\) | 5.35739e14 | 1.51933 | 0.759667 | − | 0.650312i | \(-0.225362\pi\) | ||||
0.759667 | + | 0.650312i | \(0.225362\pi\) | |||||||
\(174\) | −3.64822e14 | −0.996576 | ||||||||
\(175\) | −4.51272e14 | −1.18766 | ||||||||
\(176\) | −6.74989e14 | −1.71184 | ||||||||
\(177\) | 1.21775e15 | 2.97668 | ||||||||
\(178\) | 4.03090e13 | 0.0949886 | ||||||||
\(179\) | −2.80170e14 | −0.636615 | −0.318307 | − | 0.947988i | \(-0.603114\pi\) | ||||
−0.318307 | + | 0.947988i | \(0.603114\pi\) | |||||||
\(180\) | −9.83559e14 | −2.15541 | ||||||||
\(181\) | 5.14060e14 | 1.08668 | 0.543342 | − | 0.839511i | \(-0.317159\pi\) | ||||
0.543342 | + | 0.839511i | \(0.317159\pi\) | |||||||
\(182\) | −1.25613e15 | −2.56196 | ||||||||
\(183\) | 2.72323e14 | 0.535984 | ||||||||
\(184\) | −6.30729e14 | −1.19819 | ||||||||
\(185\) | −9.92172e12 | −0.0181958 | ||||||||
\(186\) | 5.29368e13 | 0.0937398 | ||||||||
\(187\) | 2.04291e14 | 0.349364 | ||||||||
\(188\) | 1.56788e15 | 2.58992 | ||||||||
\(189\) | 3.34269e15 | 5.33451 | ||||||||
\(190\) | 5.00642e14 | 0.772020 | ||||||||
\(191\) | −1.00129e15 | −1.49225 | −0.746124 | − | 0.665807i | \(-0.768087\pi\) | ||||
−0.746124 | + | 0.665807i | \(0.768087\pi\) | |||||||
\(192\) | −1.50033e15 | −2.16137 | ||||||||
\(193\) | −4.90266e14 | −0.682825 | −0.341412 | − | 0.939914i | \(-0.610905\pi\) | ||||
−0.341412 | + | 0.939914i | \(0.610905\pi\) | |||||||
\(194\) | −1.97133e15 | −2.65490 | ||||||||
\(195\) | −6.11140e14 | −0.796005 | ||||||||
\(196\) | 1.40232e15 | 1.76678 | ||||||||
\(197\) | 5.84517e13 | 0.0712470 | ||||||||
\(198\) | 8.10879e15 | 9.56384 | ||||||||
\(199\) | −5.81232e14 | −0.663444 | −0.331722 | − | 0.943377i | \(-0.607630\pi\) | ||||
−0.331722 | + | 0.943377i | \(0.607630\pi\) | |||||||
\(200\) | 1.30397e15 | 1.44070 | ||||||||
\(201\) | −9.08498e14 | −0.971739 | ||||||||
\(202\) | 1.88396e15 | 1.95113 | ||||||||
\(203\) | 3.99654e14 | 0.400829 | ||||||||
\(204\) | −7.47955e14 | −0.726573 | ||||||||
\(205\) | 5.88028e14 | 0.553347 | ||||||||
\(206\) | −3.01656e15 | −2.75026 | ||||||||
\(207\) | 2.39380e15 | 2.11486 | ||||||||
\(208\) | 1.14671e15 | 0.981839 | ||||||||
\(209\) | −2.73754e15 | −2.27200 | ||||||||
\(210\) | 2.17540e15 | 1.75030 | ||||||||
\(211\) | 4.92372e14 | 0.384111 | 0.192056 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192056 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(212\) | 1.70292e15 | 1.28828 | ||||||||
\(213\) | −2.37347e15 | −1.74147 | ||||||||
\(214\) | −1.02506e15 | −0.729560 | ||||||||
\(215\) | 7.95577e14 | 0.549328 | ||||||||
\(216\) | −9.65885e15 | −6.47107 | ||||||||
\(217\) | −5.79911e13 | −0.0377028 | ||||||||
\(218\) | −2.16730e15 | −1.36758 | ||||||||
\(219\) | 5.54329e15 | 3.39532 | ||||||||
\(220\) | 2.31320e15 | 1.37552 | ||||||||
\(221\) | −3.47059e14 | −0.200380 | ||||||||
\(222\) | −2.99481e14 | −0.167909 | ||||||||
\(223\) | −1.35774e15 | −0.739322 | −0.369661 | − | 0.929167i | \(-0.620526\pi\) | ||||
−0.369661 | + | 0.929167i | \(0.620526\pi\) | |||||||
\(224\) | 2.69040e14 | 0.142300 | ||||||||
\(225\) | −4.94896e15 | −2.54289 | ||||||||
\(226\) | 3.14429e15 | 1.56971 | ||||||||
\(227\) | −1.74739e15 | −0.847661 | −0.423831 | − | 0.905741i | \(-0.639315\pi\) | ||||
−0.423831 | + | 0.905741i | \(0.639315\pi\) | |||||||
\(228\) | 1.00228e16 | 4.72510 | ||||||||
\(229\) | 7.26003e14 | 0.332666 | 0.166333 | − | 0.986070i | \(-0.446807\pi\) | ||||
0.166333 | + | 0.986070i | \(0.446807\pi\) | |||||||
\(230\) | 1.02960e15 | 0.458603 | ||||||||
\(231\) | −1.18952e16 | −5.15103 | ||||||||
\(232\) | −1.15482e15 | −0.486229 | ||||||||
\(233\) | −2.41004e15 | −0.986756 | −0.493378 | − | 0.869815i | \(-0.664238\pi\) | ||||
−0.493378 | + | 0.869815i | \(0.664238\pi\) | |||||||
\(234\) | −1.37756e16 | −5.48540 | ||||||||
\(235\) | −1.25992e15 | −0.487980 | ||||||||
\(236\) | 7.83042e15 | 2.95024 | ||||||||
\(237\) | 4.14857e15 | 1.52067 | ||||||||
\(238\) | 1.23538e15 | 0.440607 | ||||||||
\(239\) | 1.43672e15 | 0.498639 | 0.249320 | − | 0.968421i | \(-0.419793\pi\) | ||||
0.249320 | + | 0.968421i | \(0.419793\pi\) | |||||||
\(240\) | −1.98589e15 | −0.670782 | ||||||||
\(241\) | −2.05994e15 | −0.677242 | −0.338621 | − | 0.940923i | \(-0.609960\pi\) | ||||
−0.338621 | + | 0.940923i | \(0.609960\pi\) | |||||||
\(242\) | −1.36863e16 | −4.38012 | ||||||||
\(243\) | 1.78495e16 | 5.56142 | ||||||||
\(244\) | 1.75110e15 | 0.531224 | ||||||||
\(245\) | −1.12688e15 | −0.332889 | ||||||||
\(246\) | 1.77493e16 | 5.10625 | ||||||||
\(247\) | 4.65067e15 | 1.30312 | ||||||||
\(248\) | 1.67568e14 | 0.0457356 | ||||||||
\(249\) | −3.39812e14 | −0.0903530 | ||||||||
\(250\) | −4.59714e15 | −1.19091 | ||||||||
\(251\) | 2.86312e15 | 0.722704 | 0.361352 | − | 0.932430i | \(-0.382315\pi\) | ||||
0.361352 | + | 0.932430i | \(0.382315\pi\) | |||||||
\(252\) | 3.25227e16 | 7.99987 | ||||||||
\(253\) | −5.62990e15 | −1.34964 | ||||||||
\(254\) | −7.85454e15 | −1.83528 | ||||||||
\(255\) | 6.01044e14 | 0.136897 | ||||||||
\(256\) | −8.84570e15 | −1.96414 | ||||||||
\(257\) | 1.18597e15 | 0.256749 | 0.128375 | − | 0.991726i | \(-0.459024\pi\) | ||||
0.128375 | + | 0.991726i | \(0.459024\pi\) | |||||||
\(258\) | 2.40140e16 | 5.06917 | ||||||||
\(259\) | 3.28075e14 | 0.0675343 | ||||||||
\(260\) | −3.92978e15 | −0.788935 | ||||||||
\(261\) | 4.38287e15 | 0.858214 | ||||||||
\(262\) | 7.34257e15 | 1.40246 | ||||||||
\(263\) | 2.56539e15 | 0.478015 | 0.239008 | − | 0.971018i | \(-0.423178\pi\) | ||||
0.239008 | + | 0.971018i | \(0.423178\pi\) | |||||||
\(264\) | 3.43717e16 | 6.24850 | ||||||||
\(265\) | −1.36843e15 | −0.242731 | ||||||||
\(266\) | −1.65544e16 | −2.86538 | ||||||||
\(267\) | −6.48474e14 | −0.109539 | ||||||||
\(268\) | −5.84186e15 | −0.963108 | ||||||||
\(269\) | 2.62105e14 | 0.0421780 | 0.0210890 | − | 0.999778i | \(-0.493287\pi\) | ||||
0.0210890 | + | 0.999778i | \(0.493287\pi\) | |||||||
\(270\) | 1.57671e16 | 2.47678 | ||||||||
\(271\) | 1.23467e16 | 1.89344 | 0.946722 | − | 0.322053i | \(-0.104373\pi\) | ||||
0.946722 | + | 0.322053i | \(0.104373\pi\) | |||||||
\(272\) | −1.12776e15 | −0.168857 | ||||||||
\(273\) | 2.02082e16 | 2.95440 | ||||||||
\(274\) | 1.12269e16 | 1.60280 | ||||||||
\(275\) | 1.16393e16 | 1.62280 | ||||||||
\(276\) | 2.06124e16 | 2.80685 | ||||||||
\(277\) | 3.96634e15 | 0.527560 | 0.263780 | − | 0.964583i | \(-0.415031\pi\) | ||||
0.263780 | + | 0.964583i | \(0.415031\pi\) | |||||||
\(278\) | 1.89210e16 | 2.45840 | ||||||||
\(279\) | −6.35970e14 | −0.0807252 | ||||||||
\(280\) | 6.88607e15 | 0.853973 | ||||||||
\(281\) | −8.18647e14 | −0.0991986 | −0.0495993 | − | 0.998769i | \(-0.515794\pi\) | ||||
−0.0495993 | + | 0.998769i | \(0.515794\pi\) | |||||||
\(282\) | −3.80300e16 | −4.50305 | ||||||||
\(283\) | 8.53591e15 | 0.987729 | 0.493865 | − | 0.869539i | \(-0.335584\pi\) | ||||
0.493865 | + | 0.869539i | \(0.335584\pi\) | |||||||
\(284\) | −1.52620e16 | −1.72600 | ||||||||
\(285\) | −8.05412e15 | −0.890280 | ||||||||
\(286\) | 3.23984e16 | 3.50062 | ||||||||
\(287\) | −1.94439e16 | −2.05377 | ||||||||
\(288\) | 2.95048e15 | 0.304678 | ||||||||
\(289\) | −9.56325e15 | −0.965539 | ||||||||
\(290\) | 1.88512e15 | 0.186102 | ||||||||
\(291\) | 3.17139e16 | 3.06158 | ||||||||
\(292\) | 3.56447e16 | 3.36516 | ||||||||
\(293\) | −2.13064e15 | −0.196730 | −0.0983650 | − | 0.995150i | \(-0.531361\pi\) | ||||
−0.0983650 | + | 0.995150i | \(0.531361\pi\) | |||||||
\(294\) | −3.40143e16 | −3.07188 | ||||||||
\(295\) | −6.29240e15 | −0.555870 | ||||||||
\(296\) | −9.47987e14 | −0.0819230 | ||||||||
\(297\) | −8.62152e16 | −7.28899 | ||||||||
\(298\) | −1.38416e16 | −1.14493 | ||||||||
\(299\) | 9.56436e15 | 0.774093 | ||||||||
\(300\) | −4.26141e16 | −3.37493 | ||||||||
\(301\) | −2.63068e16 | −2.03885 | ||||||||
\(302\) | −1.80499e16 | −1.36908 | ||||||||
\(303\) | −3.03083e16 | −2.25001 | ||||||||
\(304\) | 1.51122e16 | 1.09812 | ||||||||
\(305\) | −1.40716e15 | −0.100091 | ||||||||
\(306\) | 1.35481e16 | 0.943382 | ||||||||
\(307\) | −1.20030e16 | −0.818261 | −0.409131 | − | 0.912476i | \(-0.634168\pi\) | ||||
−0.409131 | + | 0.912476i | \(0.634168\pi\) | |||||||
\(308\) | −7.64890e16 | −5.10528 | ||||||||
\(309\) | 4.85291e16 | 3.17155 | ||||||||
\(310\) | −2.73537e14 | −0.0175051 | ||||||||
\(311\) | 6.73209e15 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(312\) | −5.83924e16 | −3.58386 | ||||||||
\(313\) | 2.20435e16 | 1.32508 | 0.662541 | − | 0.749025i | \(-0.269478\pi\) | ||||
0.662541 | + | 0.749025i | \(0.269478\pi\) | |||||||
\(314\) | 4.66671e16 | 2.74769 | ||||||||
\(315\) | −2.61347e16 | −1.50730 | ||||||||
\(316\) | 2.66763e16 | 1.50716 | ||||||||
\(317\) | −2.09394e16 | −1.15899 | −0.579495 | − | 0.814976i | \(-0.696750\pi\) | ||||
−0.579495 | + | 0.814976i | \(0.696750\pi\) | |||||||
\(318\) | −4.13054e16 | −2.23991 | ||||||||
\(319\) | −1.03079e16 | −0.547687 | ||||||||
\(320\) | 7.75258e15 | 0.403619 | ||||||||
\(321\) | 1.64908e16 | 0.841315 | ||||||||
\(322\) | −3.40451e16 | −1.70212 | ||||||||
\(323\) | −4.57384e15 | −0.224112 | ||||||||
\(324\) | 1.94709e17 | 9.35069 | ||||||||
\(325\) | −1.97734e16 | −0.930764 | ||||||||
\(326\) | 1.22252e16 | 0.564082 | ||||||||
\(327\) | 3.48666e16 | 1.57706 | ||||||||
\(328\) | 5.61841e16 | 2.49134 | ||||||||
\(329\) | 4.16610e16 | 1.81116 | ||||||||
\(330\) | −5.61082e16 | −2.39159 | ||||||||
\(331\) | 8.50904e15 | 0.355630 | 0.177815 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177815 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(332\) | −2.18507e15 | −0.0895505 | ||||||||
\(333\) | 3.59789e15 | 0.144597 | ||||||||
\(334\) | −1.23464e16 | −0.486617 | ||||||||
\(335\) | 4.69442e15 | 0.181464 | ||||||||
\(336\) | 6.56660e16 | 2.48963 | ||||||||
\(337\) | −2.12037e16 | −0.788528 | −0.394264 | − | 0.918997i | \(-0.629001\pi\) | ||||
−0.394264 | + | 0.918997i | \(0.629001\pi\) | |||||||
\(338\) | −7.80063e15 | −0.284558 | ||||||||
\(339\) | −5.05841e16 | −1.81016 | ||||||||
\(340\) | 3.86486e15 | 0.135682 | ||||||||
\(341\) | 1.49572e15 | 0.0515164 | ||||||||
\(342\) | −1.81547e17 | −6.13506 | ||||||||
\(343\) | −4.27657e15 | −0.141803 | ||||||||
\(344\) | 7.60147e16 | 2.47325 | ||||||||
\(345\) | −1.65638e16 | −0.528853 | ||||||||
\(346\) | −8.35592e16 | −2.61818 | ||||||||
\(347\) | −5.39081e16 | −1.65773 | −0.828863 | − | 0.559452i | \(-0.811012\pi\) | ||||
−0.828863 | + | 0.559452i | \(0.811012\pi\) | |||||||
\(348\) | 3.77397e16 | 1.13903 | ||||||||
\(349\) | 2.21791e16 | 0.657020 | 0.328510 | − | 0.944500i | \(-0.393454\pi\) | ||||
0.328510 | + | 0.944500i | \(0.393454\pi\) | |||||||
\(350\) | 7.03850e16 | 2.04662 | ||||||||
\(351\) | 1.46467e17 | 4.18064 | ||||||||
\(352\) | −6.93913e15 | −0.194436 | ||||||||
\(353\) | 1.65766e16 | 0.455995 | 0.227998 | − | 0.973662i | \(-0.426782\pi\) | ||||
0.227998 | + | 0.973662i | \(0.426782\pi\) | |||||||
\(354\) | −1.89932e17 | −5.12953 | ||||||||
\(355\) | 1.22643e16 | 0.325205 | ||||||||
\(356\) | −4.16984e15 | −0.108566 | ||||||||
\(357\) | −1.98743e16 | −0.508100 | ||||||||
\(358\) | 4.36981e16 | 1.09704 | ||||||||
\(359\) | 6.16736e16 | 1.52050 | 0.760248 | − | 0.649633i | \(-0.225077\pi\) | ||||
0.760248 | + | 0.649633i | \(0.225077\pi\) | |||||||
\(360\) | 7.55173e16 | 1.82844 | ||||||||
\(361\) | 1.92374e16 | 0.457457 | ||||||||
\(362\) | −8.01780e16 | −1.87262 | ||||||||
\(363\) | 2.20179e17 | 5.05107 | ||||||||
\(364\) | 1.29943e17 | 2.92816 | ||||||||
\(365\) | −2.86435e16 | −0.634048 | ||||||||
\(366\) | −4.24742e16 | −0.923630 | ||||||||
\(367\) | 3.90178e16 | 0.833554 | 0.416777 | − | 0.909009i | \(-0.363160\pi\) | ||||
0.416777 | + | 0.909009i | \(0.363160\pi\) | |||||||
\(368\) | 3.10792e16 | 0.652318 | ||||||||
\(369\) | −2.13235e17 | −4.39732 | ||||||||
\(370\) | 1.54749e15 | 0.0313557 | ||||||||
\(371\) | 4.52491e16 | 0.900906 | ||||||||
\(372\) | −5.47616e15 | −0.107139 | ||||||||
\(373\) | 5.39763e16 | 1.03776 | 0.518879 | − | 0.854848i | \(-0.326350\pi\) | ||||
0.518879 | + | 0.854848i | \(0.326350\pi\) | |||||||
\(374\) | −3.18632e16 | −0.602038 | ||||||||
\(375\) | 7.39569e16 | 1.37333 | ||||||||
\(376\) | −1.20381e17 | −2.19704 | ||||||||
\(377\) | 1.75116e16 | 0.314129 | ||||||||
\(378\) | −5.21360e17 | −9.19265 | ||||||||
\(379\) | −1.78707e16 | −0.309732 | −0.154866 | − | 0.987935i | \(-0.549495\pi\) | ||||
−0.154866 | + | 0.987935i | \(0.549495\pi\) | |||||||
\(380\) | −5.17899e16 | −0.882372 | ||||||||
\(381\) | 1.26361e17 | 2.11641 | ||||||||
\(382\) | 1.56170e17 | 2.57150 | ||||||||
\(383\) | 5.22730e16 | 0.846224 | 0.423112 | − | 0.906077i | \(-0.360938\pi\) | ||||
0.423112 | + | 0.906077i | \(0.360938\pi\) | |||||||
\(384\) | 2.21108e17 | 3.51926 | ||||||||
\(385\) | 6.14653e16 | 0.961912 | ||||||||
\(386\) | 7.64668e16 | 1.17667 | ||||||||
\(387\) | −2.88498e17 | −4.36538 | ||||||||
\(388\) | 2.03928e17 | 3.03438 | ||||||||
\(389\) | 8.13700e16 | 1.19067 | 0.595336 | − | 0.803477i | \(-0.297019\pi\) | ||||
0.595336 | + | 0.803477i | \(0.297019\pi\) | |||||||
\(390\) | 9.53195e16 | 1.37171 | ||||||||
\(391\) | −9.40637e15 | −0.133129 | ||||||||
\(392\) | −1.07670e17 | −1.49877 | ||||||||
\(393\) | −1.18124e17 | −1.61729 | ||||||||
\(394\) | −9.11671e15 | −0.122776 | ||||||||
\(395\) | −2.14366e16 | −0.283972 | ||||||||
\(396\) | −8.38830e17 | −10.9309 | ||||||||
\(397\) | −2.21999e16 | −0.284586 | −0.142293 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142293 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(398\) | 9.06547e16 | 1.14327 | ||||||||
\(399\) | 2.66320e17 | 3.30431 | ||||||||
\(400\) | −6.42533e16 | −0.784342 | ||||||||
\(401\) | 3.18496e15 | 0.0382530 | 0.0191265 | − | 0.999817i | \(-0.493911\pi\) | ||||
0.0191265 | + | 0.999817i | \(0.493911\pi\) | |||||||
\(402\) | 1.41698e17 | 1.67454 | ||||||||
\(403\) | −2.54100e15 | −0.0295475 | ||||||||
\(404\) | −1.94890e17 | −2.23003 | ||||||||
\(405\) | −1.56465e17 | −1.76181 | ||||||||
\(406\) | −6.23340e16 | −0.690726 | ||||||||
\(407\) | −8.46176e15 | −0.0922778 | ||||||||
\(408\) | 5.74278e16 | 0.616355 | ||||||||
\(409\) | 4.57706e16 | 0.483487 | 0.241744 | − | 0.970340i | \(-0.422281\pi\) | ||||
0.241744 | + | 0.970340i | \(0.422281\pi\) | |||||||
\(410\) | −9.17146e16 | −0.953550 | ||||||||
\(411\) | −1.80613e17 | −1.84832 | ||||||||
\(412\) | 3.12054e17 | 3.14338 | ||||||||
\(413\) | 2.08067e17 | 2.06313 | ||||||||
\(414\) | −3.73361e17 | −3.64441 | ||||||||
\(415\) | 1.75589e15 | 0.0168727 | ||||||||
\(416\) | 1.17885e16 | 0.111520 | ||||||||
\(417\) | −3.04393e17 | −2.83498 | ||||||||
\(418\) | 4.26974e17 | 3.91521 | ||||||||
\(419\) | 5.97703e15 | 0.0539628 | 0.0269814 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269814 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(420\) | −2.25039e17 | −2.00049 | ||||||||
\(421\) | 1.74495e17 | 1.52739 | 0.763695 | − | 0.645577i | \(-0.223383\pi\) | ||||
0.763695 | + | 0.645577i | \(0.223383\pi\) | |||||||
\(422\) | −7.67952e16 | −0.661917 | ||||||||
\(423\) | 4.56883e17 | 3.87786 | ||||||||
\(424\) | −1.30749e17 | −1.09285 | ||||||||
\(425\) | 1.94468e16 | 0.160073 | ||||||||
\(426\) | 3.70190e17 | 3.00097 | ||||||||
\(427\) | 4.65295e16 | 0.371490 | ||||||||
\(428\) | 1.06040e17 | 0.833843 | ||||||||
\(429\) | −5.21212e17 | −4.03685 | ||||||||
\(430\) | −1.24086e17 | −0.946625 | ||||||||
\(431\) | −6.38154e16 | −0.479538 | −0.239769 | − | 0.970830i | \(-0.577072\pi\) | ||||
−0.239769 | + | 0.970830i | \(0.577072\pi\) | |||||||
\(432\) | 4.75941e17 | 3.52297 | ||||||||
\(433\) | −2.60358e17 | −1.89845 | −0.949226 | − | 0.314595i | \(-0.898131\pi\) | ||||
−0.949226 | + | 0.314595i | \(0.898131\pi\) | |||||||
\(434\) | 9.04487e15 | 0.0649709 | ||||||||
\(435\) | −3.03270e16 | −0.214610 | ||||||||
\(436\) | 2.24201e17 | 1.56306 | ||||||||
\(437\) | 1.26047e17 | 0.865773 | ||||||||
\(438\) | −8.64587e17 | −5.85096 | ||||||||
\(439\) | −5.47246e16 | −0.364891 | −0.182446 | − | 0.983216i | \(-0.558401\pi\) | ||||
−0.182446 | + | 0.983216i | \(0.558401\pi\) | |||||||
\(440\) | −1.77607e17 | −1.16685 | ||||||||
\(441\) | 4.08639e17 | 2.64539 | ||||||||
\(442\) | 5.41308e16 | 0.345303 | ||||||||
\(443\) | −9.11386e15 | −0.0572899 | −0.0286450 | − | 0.999590i | \(-0.509119\pi\) | ||||
−0.0286450 | + | 0.999590i | \(0.509119\pi\) | |||||||
\(444\) | 3.09804e16 | 0.191910 | ||||||||
\(445\) | 3.35082e15 | 0.0204555 | ||||||||
\(446\) | 2.11766e17 | 1.27403 | ||||||||
\(447\) | 2.22678e17 | 1.32032 | ||||||||
\(448\) | −2.56349e17 | −1.49805 | ||||||||
\(449\) | −3.97393e16 | −0.228886 | −0.114443 | − | 0.993430i | \(-0.536508\pi\) | ||||
−0.114443 | + | 0.993430i | \(0.536508\pi\) | |||||||
\(450\) | 7.71889e17 | 4.38201 | ||||||||
\(451\) | 5.01501e17 | 2.80624 | ||||||||
\(452\) | −3.25268e17 | −1.79408 | ||||||||
\(453\) | 2.90379e17 | 1.57880 | ||||||||
\(454\) | 2.72541e17 | 1.46072 | ||||||||
\(455\) | −1.04420e17 | −0.551710 | ||||||||
\(456\) | −7.69544e17 | −4.00832 | ||||||||
\(457\) | −2.70719e17 | −1.39016 | −0.695078 | − | 0.718935i | \(-0.744630\pi\) | ||||
−0.695078 | + | 0.718935i | \(0.744630\pi\) | |||||||
\(458\) | −1.13235e17 | −0.573263 | ||||||||
\(459\) | −1.44047e17 | −0.718989 | ||||||||
\(460\) | −1.06509e17 | −0.524156 | ||||||||
\(461\) | 3.70630e17 | 1.79839 | 0.899197 | − | 0.437545i | \(-0.144152\pi\) | ||||
0.899197 | + | 0.437545i | \(0.144152\pi\) | |||||||
\(462\) | 1.85529e18 | 8.87646 | ||||||||
\(463\) | 2.17407e17 | 1.02565 | 0.512823 | − | 0.858494i | \(-0.328600\pi\) | ||||
0.512823 | + | 0.858494i | \(0.328600\pi\) | |||||||
\(464\) | 5.69037e16 | 0.264712 | ||||||||
\(465\) | 4.40055e15 | 0.0201866 | ||||||||
\(466\) | 3.75893e17 | 1.70042 | ||||||||
\(467\) | 1.82256e17 | 0.813058 | 0.406529 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406529 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(468\) | 1.42505e18 | 6.26948 | ||||||||
\(469\) | −1.55227e17 | −0.673511 | ||||||||
\(470\) | 1.96510e17 | 0.840908 | ||||||||
\(471\) | −7.50761e17 | −3.16859 | ||||||||
\(472\) | −6.01217e17 | −2.50270 | ||||||||
\(473\) | 6.78510e17 | 2.78586 | ||||||||
\(474\) | −6.47052e17 | −2.62047 | ||||||||
\(475\) | −2.60591e17 | −1.04100 | ||||||||
\(476\) | −1.27797e17 | −0.503587 | ||||||||
\(477\) | 4.96232e17 | 1.92893 | ||||||||
\(478\) | −2.24085e17 | −0.859275 | ||||||||
\(479\) | 1.08405e17 | 0.410080 | 0.205040 | − | 0.978754i | \(-0.434268\pi\) | ||||
0.205040 | + | 0.978754i | \(0.434268\pi\) | |||||||
\(480\) | −2.04156e16 | −0.0761895 | ||||||||
\(481\) | 1.43753e16 | 0.0529264 | ||||||||
\(482\) | 3.21289e17 | 1.16705 | ||||||||
\(483\) | 5.47703e17 | 1.96286 | ||||||||
\(484\) | 1.41581e18 | 5.00621 | ||||||||
\(485\) | −1.63873e17 | −0.571724 | ||||||||
\(486\) | −2.78399e18 | −9.58366 | ||||||||
\(487\) | −1.41298e17 | −0.479951 | −0.239976 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239976 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(488\) | −1.34449e17 | −0.450639 | ||||||||
\(489\) | −1.96674e17 | −0.650489 | ||||||||
\(490\) | 1.75760e17 | 0.573648 | ||||||||
\(491\) | −2.70485e17 | −0.871191 | −0.435595 | − | 0.900143i | \(-0.643462\pi\) | ||||
−0.435595 | + | 0.900143i | \(0.643462\pi\) | |||||||
\(492\) | −1.83611e18 | −5.83614 | ||||||||
\(493\) | −1.72224e16 | −0.0540241 | ||||||||
\(494\) | −7.25364e17 | −2.24559 | ||||||||
\(495\) | 6.74070e17 | 2.05955 | ||||||||
\(496\) | −8.25692e15 | −0.0248993 | ||||||||
\(497\) | −4.05534e17 | −1.20701 | ||||||||
\(498\) | 5.30004e16 | 0.155700 | ||||||||
\(499\) | 3.23433e17 | 0.937844 | 0.468922 | − | 0.883240i | \(-0.344643\pi\) | ||||
0.468922 | + | 0.883240i | \(0.344643\pi\) | |||||||
\(500\) | 4.75561e17 | 1.36113 | ||||||||
\(501\) | 1.98623e17 | 0.561158 | ||||||||
\(502\) | −4.46561e17 | −1.24539 | ||||||||
\(503\) | −9.51693e16 | −0.262002 | −0.131001 | − | 0.991382i | \(-0.541819\pi\) | ||||
−0.131001 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(504\) | −2.49708e18 | −6.78632 | ||||||||
\(505\) | 1.56610e17 | 0.420171 | ||||||||
\(506\) | 8.78096e17 | 2.32575 | ||||||||
\(507\) | 1.25493e17 | 0.328147 | ||||||||
\(508\) | 8.12529e17 | 2.09761 | ||||||||
\(509\) | 6.94544e17 | 1.77025 | 0.885124 | − | 0.465355i | \(-0.154073\pi\) | ||||
0.885124 | + | 0.465355i | \(0.154073\pi\) | |||||||
\(510\) | −9.37449e16 | −0.235907 | ||||||||
\(511\) | 9.47135e17 | 2.35329 | ||||||||
\(512\) | 6.57788e17 | 1.61373 | ||||||||
\(513\) | 1.93026e18 | 4.67577 | ||||||||
\(514\) | −1.84976e17 | −0.442441 | ||||||||
\(515\) | −2.50761e17 | −0.592261 | ||||||||
\(516\) | −2.48418e18 | −5.79375 | ||||||||
\(517\) | −1.07453e18 | −2.47473 | ||||||||
\(518\) | −5.11698e16 | −0.116378 | ||||||||
\(519\) | 1.34426e18 | 3.01924 | ||||||||
\(520\) | 3.01727e17 | 0.669256 | ||||||||
\(521\) | −7.54275e17 | −1.65228 | −0.826142 | − | 0.563463i | \(-0.809469\pi\) | ||||
−0.826142 | + | 0.563463i | \(0.809469\pi\) | |||||||
\(522\) | −6.83597e17 | −1.47891 | ||||||||
\(523\) | 5.73990e17 | 1.22643 | 0.613216 | − | 0.789915i | \(-0.289875\pi\) | ||||
0.613216 | + | 0.789915i | \(0.289875\pi\) | |||||||
\(524\) | −7.59567e17 | −1.60292 | ||||||||
\(525\) | −1.13232e18 | −2.36013 | ||||||||
\(526\) | −4.00125e17 | −0.823736 | ||||||||
\(527\) | 2.49902e15 | 0.00508161 | ||||||||
\(528\) | −1.69367e18 | −3.40179 | ||||||||
\(529\) | −2.44813e17 | −0.485705 | ||||||||
\(530\) | 2.13435e17 | 0.418284 | ||||||||
\(531\) | 2.28180e18 | 4.41736 | ||||||||
\(532\) | 1.71250e18 | 3.27496 | ||||||||
\(533\) | −8.51975e17 | −1.60953 | ||||||||
\(534\) | 1.01142e17 | 0.188762 | ||||||||
\(535\) | −8.52117e16 | −0.157109 | ||||||||
\(536\) | 4.48536e17 | 0.817008 | ||||||||
\(537\) | −7.02996e17 | −1.26509 | ||||||||
\(538\) | −4.08805e16 | −0.0726828 | ||||||||
\(539\) | −9.61065e17 | −1.68821 | ||||||||
\(540\) | −1.63106e18 | −2.83080 | ||||||||
\(541\) | 1.64531e17 | 0.282141 | 0.141071 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141071 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(542\) | −1.92572e18 | −3.26286 | ||||||||
\(543\) | 1.28987e18 | 2.15947 | ||||||||
\(544\) | −1.15938e16 | −0.0191793 | ||||||||
\(545\) | −1.80164e17 | −0.294503 | ||||||||
\(546\) | −3.15187e18 | −5.09115 | ||||||||
\(547\) | −1.13121e18 | −1.80562 | −0.902810 | − | 0.430040i | \(-0.858500\pi\) | ||||
−0.902810 | + | 0.430040i | \(0.858500\pi\) | |||||||
\(548\) | −1.16139e18 | −1.83191 | ||||||||
\(549\) | 5.10274e17 | 0.795396 | ||||||||
\(550\) | −1.81538e18 | −2.79647 | ||||||||
\(551\) | 2.30783e17 | 0.351333 | ||||||||
\(552\) | −1.58261e18 | −2.38106 | ||||||||
\(553\) | 7.08831e17 | 1.05397 | ||||||||
\(554\) | −6.18630e17 | −0.909112 | ||||||||
\(555\) | −2.48954e16 | −0.0361588 | ||||||||
\(556\) | −1.95732e18 | −2.80980 | ||||||||
\(557\) | 5.20463e17 | 0.738467 | 0.369233 | − | 0.929337i | \(-0.379620\pi\) | ||||
0.369233 | + | 0.929337i | \(0.379620\pi\) | |||||||
\(558\) | 9.91922e16 | 0.139109 | ||||||||
\(559\) | −1.15269e18 | −1.59784 | ||||||||
\(560\) | −3.39312e17 | −0.464918 | ||||||||
\(561\) | 5.12602e17 | 0.694260 | ||||||||
\(562\) | 1.27684e17 | 0.170943 | ||||||||
\(563\) | 4.15047e17 | 0.549278 | 0.274639 | − | 0.961547i | \(-0.411442\pi\) | ||||
0.274639 | + | 0.961547i | \(0.411442\pi\) | |||||||
\(564\) | 3.93409e18 | 5.14671 | ||||||||
\(565\) | 2.61380e17 | 0.338032 | ||||||||
\(566\) | −1.33135e18 | −1.70210 | ||||||||
\(567\) | 5.17373e18 | 6.53903 | ||||||||
\(568\) | 1.17181e18 | 1.46417 | ||||||||
\(569\) | 7.54991e17 | 0.932636 | 0.466318 | − | 0.884617i | \(-0.345580\pi\) | ||||
0.466318 | + | 0.884617i | \(0.345580\pi\) | |||||||
\(570\) | 1.25620e18 | 1.53417 | ||||||||
\(571\) | −4.09580e17 | −0.494544 | −0.247272 | − | 0.968946i | \(-0.579534\pi\) | ||||
−0.247272 | + | 0.968946i | \(0.579534\pi\) | |||||||
\(572\) | −3.35152e18 | −4.00099 | ||||||||
\(573\) | −2.51241e18 | −2.96541 | ||||||||
\(574\) | 3.03267e18 | 3.53914 | ||||||||
\(575\) | −5.35920e17 | −0.618385 | ||||||||
\(576\) | −2.81130e18 | −3.20746 | ||||||||
\(577\) | −2.64267e17 | −0.298126 | −0.149063 | − | 0.988828i | \(-0.547626\pi\) | ||||
−0.149063 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(578\) | 1.49158e18 | 1.66386 | ||||||||
\(579\) | −1.23017e18 | −1.35692 | ||||||||
\(580\) | −1.95010e17 | −0.212704 | ||||||||
\(581\) | −5.80608e16 | −0.0626236 | ||||||||
\(582\) | −4.94641e18 | −5.27583 | ||||||||
\(583\) | −1.16707e18 | −1.23098 | ||||||||
\(584\) | −2.73679e18 | −2.85468 | ||||||||
\(585\) | −1.14514e18 | −1.18126 | ||||||||
\(586\) | 3.32316e17 | 0.339013 | ||||||||
\(587\) | 3.22129e17 | 0.324999 | 0.162500 | − | 0.986709i | \(-0.448044\pi\) | ||||
0.162500 | + | 0.986709i | \(0.448044\pi\) | |||||||
\(588\) | 3.51868e18 | 3.51097 | ||||||||
\(589\) | −3.34874e16 | −0.0330470 | ||||||||
\(590\) | 9.81425e17 | 0.957898 | ||||||||
\(591\) | 1.46666e17 | 0.141583 | ||||||||
\(592\) | 4.67121e16 | 0.0446004 | ||||||||
\(593\) | −2.59941e15 | −0.00245482 | −0.00122741 | − | 0.999999i | \(-0.500391\pi\) | ||||
−0.00122741 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(594\) | 1.34470e19 | 12.5607 | ||||||||
\(595\) | 1.02695e17 | 0.0948835 | ||||||||
\(596\) | 1.43187e18 | 1.30859 | ||||||||
\(597\) | −1.45842e18 | −1.31840 | ||||||||
\(598\) | −1.49175e18 | −1.33395 | ||||||||
\(599\) | −7.33415e17 | −0.648747 | −0.324373 | − | 0.945929i | \(-0.605153\pi\) | ||||
−0.324373 | + | 0.945929i | \(0.605153\pi\) | |||||||
\(600\) | 3.27190e18 | 2.86297 | ||||||||
\(601\) | −1.30126e18 | −1.12637 | −0.563184 | − | 0.826331i | \(-0.690424\pi\) | ||||
−0.563184 | + | 0.826331i | \(0.690424\pi\) | |||||||
\(602\) | 4.10307e18 | 3.51344 | ||||||||
\(603\) | −1.70233e18 | −1.44205 | ||||||||
\(604\) | 1.86721e18 | 1.56478 | ||||||||
\(605\) | −1.13772e18 | −0.943245 | ||||||||
\(606\) | 4.72719e18 | 3.87731 | ||||||||
\(607\) | 1.97868e18 | 1.60564 | 0.802820 | − | 0.596222i | \(-0.203332\pi\) | ||||
0.802820 | + | 0.596222i | \(0.203332\pi\) | |||||||
\(608\) | 1.55359e17 | 0.124728 | ||||||||
\(609\) | 1.00280e18 | 0.796532 | ||||||||
\(610\) | 2.19474e17 | 0.172480 | ||||||||
\(611\) | 1.82546e18 | 1.41940 | ||||||||
\(612\) | −1.40151e18 | −1.07823 | ||||||||
\(613\) | −2.65013e17 | −0.201732 | −0.100866 | − | 0.994900i | \(-0.532161\pi\) | ||||
−0.100866 | + | 0.994900i | \(0.532161\pi\) | |||||||
\(614\) | 1.87211e18 | 1.41006 | ||||||||
\(615\) | 1.47547e18 | 1.09962 | ||||||||
\(616\) | 5.87280e18 | 4.33083 | ||||||||
\(617\) | 7.81798e17 | 0.570481 | 0.285241 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285241 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(618\) | −7.56908e18 | −5.46535 | ||||||||
\(619\) | −1.63363e18 | −1.16725 | −0.583625 | − | 0.812023i | \(-0.698366\pi\) | ||||
−0.583625 | + | 0.812023i | \(0.698366\pi\) | |||||||
\(620\) | 2.82966e16 | 0.0200073 | ||||||||
\(621\) | 3.96970e18 | 2.77755 | ||||||||
\(622\) | −1.05000e18 | −0.727032 | ||||||||
\(623\) | −1.10799e17 | −0.0759215 | ||||||||
\(624\) | 2.87729e18 | 1.95112 | ||||||||
\(625\) | 9.02757e17 | 0.605830 | ||||||||
\(626\) | −3.43813e18 | −2.28344 | ||||||||
\(627\) | −6.86897e18 | −4.51495 | ||||||||
\(628\) | −4.82758e18 | −3.14045 | ||||||||
\(629\) | −1.41378e16 | −0.00910233 | ||||||||
\(630\) | 4.07623e18 | 2.59744 | ||||||||
\(631\) | −1.12255e18 | −0.707970 | −0.353985 | − | 0.935251i | \(-0.615174\pi\) | ||||
−0.353985 | + | 0.935251i | \(0.615174\pi\) | |||||||
\(632\) | −2.04820e18 | −1.27853 | ||||||||
\(633\) | 1.23545e18 | 0.763310 | ||||||||
\(634\) | 3.26592e18 | 1.99722 | ||||||||
\(635\) | −6.52935e17 | −0.395222 | ||||||||
\(636\) | 4.27292e18 | 2.56008 | ||||||||
\(637\) | 1.63271e18 | 0.968281 | ||||||||
\(638\) | 1.60773e18 | 0.943796 | ||||||||
\(639\) | −4.44736e18 | −2.58433 | ||||||||
\(640\) | −1.14252e18 | −0.657192 | ||||||||
\(641\) | 6.57260e17 | 0.374248 | 0.187124 | − | 0.982336i | \(-0.440083\pi\) | ||||
0.187124 | + | 0.982336i | \(0.440083\pi\) | |||||||
\(642\) | −2.57207e18 | −1.44979 | ||||||||
\(643\) | −1.71692e17 | −0.0958029 | −0.0479014 | − | 0.998852i | \(-0.515253\pi\) | ||||
−0.0479014 | + | 0.998852i | \(0.515253\pi\) | |||||||
\(644\) | 3.52186e18 | 1.94542 | ||||||||
\(645\) | 1.99625e18 | 1.09163 | ||||||||
\(646\) | 7.13382e17 | 0.386199 | ||||||||
\(647\) | −3.32550e18 | −1.78229 | −0.891146 | − | 0.453717i | \(-0.850098\pi\) | ||||
−0.891146 | + | 0.453717i | \(0.850098\pi\) | |||||||
\(648\) | −1.49497e19 | −7.93223 | ||||||||
\(649\) | −5.36649e18 | −2.81903 | ||||||||
\(650\) | 3.08406e18 | 1.60393 | ||||||||
\(651\) | −1.45510e17 | −0.0749233 | ||||||||
\(652\) | −1.26466e18 | −0.644712 | ||||||||
\(653\) | −1.08906e18 | −0.549687 | −0.274844 | − | 0.961489i | \(-0.588626\pi\) | ||||
−0.274844 | + | 0.961489i | \(0.588626\pi\) | |||||||
\(654\) | −5.43814e18 | −2.71766 | ||||||||
\(655\) | 6.10375e17 | 0.302015 | ||||||||
\(656\) | −2.76847e18 | −1.35633 | ||||||||
\(657\) | 1.03869e19 | 5.03863 | ||||||||
\(658\) | −6.49786e18 | −3.12106 | ||||||||
\(659\) | −1.12429e18 | −0.534717 | −0.267359 | − | 0.963597i | \(-0.586151\pi\) | ||||
−0.267359 | + | 0.963597i | \(0.586151\pi\) | |||||||
\(660\) | 5.80423e18 | 2.73344 | ||||||||
\(661\) | 2.44785e18 | 1.14150 | 0.570748 | − | 0.821125i | \(-0.306653\pi\) | ||||
0.570748 | + | 0.821125i | \(0.306653\pi\) | |||||||
\(662\) | −1.32715e18 | −0.612836 | ||||||||
\(663\) | −8.70834e17 | −0.398197 | ||||||||
\(664\) | 1.67769e17 | 0.0759660 | ||||||||
\(665\) | −1.37614e18 | −0.617052 | ||||||||
\(666\) | −5.61163e17 | −0.249176 | ||||||||
\(667\) | 4.74619e17 | 0.208702 | ||||||||
\(668\) | 1.27720e18 | 0.556174 | ||||||||
\(669\) | −3.40680e18 | −1.46919 | ||||||||
\(670\) | −7.32189e17 | −0.312707 | ||||||||
\(671\) | −1.20010e18 | −0.507598 | ||||||||
\(672\) | 6.75070e17 | 0.282780 | ||||||||
\(673\) | −2.91529e17 | −0.120944 | −0.0604719 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604719 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(674\) | 3.30714e18 | 1.35882 | ||||||||
\(675\) | −8.20697e18 | −3.33971 | ||||||||
\(676\) | 8.06952e17 | 0.325233 | ||||||||
\(677\) | −2.22878e18 | −0.889696 | −0.444848 | − | 0.895606i | \(-0.646742\pi\) | ||||
−0.444848 | + | 0.895606i | \(0.646742\pi\) | |||||||
\(678\) | 7.88960e18 | 3.11934 | ||||||||
\(679\) | 5.41868e18 | 2.12197 | ||||||||
\(680\) | −2.96743e17 | −0.115099 | ||||||||
\(681\) | −4.38452e18 | −1.68448 | ||||||||
\(682\) | −2.33287e17 | −0.0887752 | ||||||||
\(683\) | −2.24637e18 | −0.846732 | −0.423366 | − | 0.905959i | \(-0.639152\pi\) | ||||
−0.423366 | + | 0.905959i | \(0.639152\pi\) | |||||||
\(684\) | 1.87805e19 | 7.01200 | ||||||||
\(685\) | 9.33272e17 | 0.345159 | ||||||||
\(686\) | 6.67017e17 | 0.244360 | ||||||||
\(687\) | 1.82167e18 | 0.661076 | ||||||||
\(688\) | −3.74563e18 | −1.34648 | ||||||||
\(689\) | 1.98268e18 | 0.706038 | ||||||||
\(690\) | 2.58345e18 | 0.911341 | ||||||||
\(691\) | 5.41506e17 | 0.189233 | 0.0946163 | − | 0.995514i | \(-0.469838\pi\) | ||||
0.0946163 | + | 0.995514i | \(0.469838\pi\) | |||||||
\(692\) | 8.64395e18 | 2.99242 | ||||||||
\(693\) | −2.22890e19 | −7.64408 | ||||||||
\(694\) | 8.40805e18 | 2.85666 | ||||||||
\(695\) | 1.57287e18 | 0.529409 | ||||||||
\(696\) | −2.89764e18 | −0.966240 | ||||||||
\(697\) | 8.37901e17 | 0.276809 | ||||||||
\(698\) | −3.45927e18 | −1.13220 | ||||||||
\(699\) | −6.04721e18 | −1.96089 | ||||||||
\(700\) | −7.28112e18 | −2.33916 | ||||||||
\(701\) | 5.35148e17 | 0.170336 | 0.0851681 | − | 0.996367i | \(-0.472857\pi\) | ||||
0.0851681 | + | 0.996367i | \(0.472857\pi\) | |||||||
\(702\) | −2.28444e19 | −7.20425 | ||||||||
\(703\) | 1.89449e17 | 0.0591948 | ||||||||
\(704\) | 6.61181e18 | 2.04691 | ||||||||
\(705\) | −3.16137e18 | −0.969719 | ||||||||
\(706\) | −2.58545e18 | −0.785789 | ||||||||
\(707\) | −5.17853e18 | −1.55948 | ||||||||
\(708\) | 1.96479e19 | 5.86274 | ||||||||
\(709\) | 6.13908e18 | 1.81511 | 0.907555 | − | 0.419933i | \(-0.137946\pi\) | ||||
0.907555 | + | 0.419933i | \(0.137946\pi\) | |||||||
\(710\) | −1.91286e18 | −0.560407 | ||||||||
\(711\) | 7.77352e18 | 2.25666 | ||||||||
\(712\) | 3.20159e17 | 0.0920971 | ||||||||
\(713\) | −6.88688e16 | −0.0196309 | ||||||||
\(714\) | 3.09980e18 | 0.875579 | ||||||||
\(715\) | 2.69323e18 | 0.753847 | ||||||||
\(716\) | −4.52044e18 | −1.25385 | ||||||||
\(717\) | 3.60499e18 | 0.990900 | ||||||||
\(718\) | −9.61923e18 | −2.62018 | ||||||||
\(719\) | 5.94931e18 | 1.60594 | 0.802969 | − | 0.596021i | \(-0.203253\pi\) | ||||
0.802969 | + | 0.596021i | \(0.203253\pi\) | |||||||
\(720\) | −3.72112e18 | −0.995435 | ||||||||
\(721\) | 8.29176e18 | 2.19820 | ||||||||
\(722\) | −3.00046e18 | −0.788308 | ||||||||
\(723\) | −5.16876e18 | −1.34582 | ||||||||
\(724\) | 8.29417e18 | 2.14029 | ||||||||
\(725\) | −9.81229e17 | −0.250942 | ||||||||
\(726\) | −3.43414e19 | −8.70421 | ||||||||
\(727\) | 1.70242e18 | 0.427654 | 0.213827 | − | 0.976871i | \(-0.431407\pi\) | ||||
0.213827 | + | 0.976871i | \(0.431407\pi\) | |||||||
\(728\) | −9.97701e18 | −2.48397 | ||||||||
\(729\) | 2.55477e19 | 6.30409 | ||||||||
\(730\) | 4.46752e18 | 1.09262 | ||||||||
\(731\) | 1.13364e18 | 0.274798 | ||||||||
\(732\) | 4.39383e18 | 1.05565 | ||||||||
\(733\) | −2.77760e18 | −0.661445 | −0.330722 | − | 0.943728i | \(-0.607292\pi\) | ||||
−0.330722 | + | 0.943728i | \(0.607292\pi\) | |||||||
\(734\) | −6.08561e18 | −1.43641 | ||||||||
\(735\) | −2.82755e18 | −0.661520 | ||||||||
\(736\) | 3.19505e17 | 0.0740922 | ||||||||
\(737\) | 4.00365e18 | 0.920275 | ||||||||
\(738\) | 3.32583e19 | 7.57763 | ||||||||
\(739\) | −1.72660e17 | −0.0389945 | −0.0194972 | − | 0.999810i | \(-0.506207\pi\) | ||||
−0.0194972 | + | 0.999810i | \(0.506207\pi\) | |||||||
\(740\) | −1.60083e17 | −0.0358377 | ||||||||
\(741\) | 1.16694e19 | 2.58958 | ||||||||
\(742\) | −7.05750e18 | −1.55248 | ||||||||
\(743\) | −2.60998e18 | −0.569127 | −0.284564 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284564 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(744\) | 4.20458e17 | 0.0908863 | ||||||||
\(745\) | −1.15063e18 | −0.246558 | ||||||||
\(746\) | −8.41869e18 | −1.78831 | ||||||||
\(747\) | −6.36734e17 | −0.134083 | ||||||||
\(748\) | 3.29616e18 | 0.688093 | ||||||||
\(749\) | 2.81764e18 | 0.583114 | ||||||||
\(750\) | −1.15351e19 | −2.36658 | ||||||||
\(751\) | 6.40691e17 | 0.130313 | 0.0651567 | − | 0.997875i | \(-0.479245\pi\) | ||||
0.0651567 | + | 0.997875i | \(0.479245\pi\) | |||||||
\(752\) | 5.93180e18 | 1.19611 | ||||||||
\(753\) | 7.18408e18 | 1.43616 | ||||||||
\(754\) | −2.73129e18 | −0.541320 | ||||||||
\(755\) | −1.50046e18 | −0.294828 | ||||||||
\(756\) | 5.39331e19 | 10.5066 | ||||||||
\(757\) | −1.11215e18 | −0.214804 | −0.107402 | − | 0.994216i | \(-0.534253\pi\) | ||||
−0.107402 | + | 0.994216i | \(0.534253\pi\) | |||||||
\(758\) | 2.78729e18 | 0.533743 | ||||||||
\(759\) | −1.41264e19 | −2.68202 | ||||||||
\(760\) | 3.97641e18 | 0.748520 | ||||||||
\(761\) | 2.07797e18 | 0.387829 | 0.193914 | − | 0.981018i | \(-0.437882\pi\) | ||||
0.193914 | + | 0.981018i | \(0.437882\pi\) | |||||||
\(762\) | −1.97085e19 | −3.64708 | ||||||||
\(763\) | 5.95736e18 | 1.09306 | ||||||||
\(764\) | −1.61554e19 | −2.93907 | ||||||||
\(765\) | 1.12623e18 | 0.203155 | ||||||||
\(766\) | −8.15302e18 | −1.45825 | ||||||||
\(767\) | 9.11686e18 | 1.61687 | ||||||||
\(768\) | −2.21955e19 | −3.90316 | ||||||||
\(769\) | 5.93573e18 | 1.03503 | 0.517515 | − | 0.855674i | \(-0.326857\pi\) | ||||
0.517515 | + | 0.855674i | \(0.326857\pi\) | |||||||
\(770\) | −9.58674e18 | −1.65761 | ||||||||
\(771\) | 2.97582e18 | 0.510214 | ||||||||
\(772\) | −7.91026e18 | −1.34486 | ||||||||
\(773\) | 1.57618e18 | 0.265729 | 0.132865 | − | 0.991134i | \(-0.457582\pi\) | ||||
0.132865 | + | 0.991134i | \(0.457582\pi\) | |||||||
\(774\) | 4.49971e19 | 7.52260 | ||||||||
\(775\) | 1.42380e17 | 0.0236041 | ||||||||
\(776\) | −1.56575e19 | −2.57408 | ||||||||
\(777\) | 8.23199e17 | 0.134205 | ||||||||
\(778\) | −1.26913e19 | −2.05181 | ||||||||
\(779\) | −1.12280e19 | −1.80016 | ||||||||
\(780\) | −9.86052e18 | −1.56778 | ||||||||
\(781\) | 1.04596e19 | 1.64924 | ||||||||
\(782\) | 1.46711e18 | 0.229414 | ||||||||
\(783\) | 7.26822e18 | 1.12714 | ||||||||
\(784\) | 5.30545e18 | 0.815957 | ||||||||
\(785\) | 3.87936e18 | 0.591708 | ||||||||
\(786\) | 1.84238e19 | 2.78697 | ||||||||
\(787\) | −1.59516e18 | −0.239314 | −0.119657 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119657 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(788\) | 9.43097e17 | 0.140325 | ||||||||
\(789\) | 6.43704e18 | 0.949916 | ||||||||
\(790\) | 3.34347e18 | 0.489352 | ||||||||
\(791\) | −8.64288e18 | −1.25462 | ||||||||
\(792\) | 6.44051e19 | 9.27271 | ||||||||
\(793\) | 2.03878e18 | 0.291136 | ||||||||
\(794\) | 3.46252e18 | 0.490410 | ||||||||
\(795\) | −3.43365e18 | −0.482358 | ||||||||
\(796\) | −9.37796e18 | −1.30669 | ||||||||
\(797\) | 7.08181e18 | 0.978735 | 0.489368 | − | 0.872078i | \(-0.337228\pi\) | ||||
0.489368 | + | 0.872078i | \(0.337228\pi\) | |||||||
\(798\) | −4.15380e19 | −5.69412 | ||||||||
\(799\) | −1.79530e18 | −0.244109 | ||||||||
\(800\) | −6.60547e17 | −0.0890880 | ||||||||
\(801\) | −1.21510e18 | −0.162555 | ||||||||
\(802\) | −4.96758e17 | −0.0659191 | ||||||||
\(803\) | −2.44287e19 | −3.21550 | ||||||||
\(804\) | −1.46583e19 | −1.91390 | ||||||||
\(805\) | −2.83011e18 | −0.366547 | ||||||||
\(806\) | 3.96319e17 | 0.0509175 | ||||||||
\(807\) | 6.57669e17 | 0.0838164 | ||||||||
\(808\) | 1.49636e19 | 1.89174 | ||||||||
\(809\) | −9.56351e18 | −1.19937 | −0.599684 | − | 0.800237i | \(-0.704707\pi\) | ||||
−0.599684 | + | 0.800237i | \(0.704707\pi\) | |||||||
\(810\) | 2.44038e19 | 3.03603 | ||||||||
\(811\) | −6.66298e17 | −0.0822304 | −0.0411152 | − | 0.999154i | \(-0.513091\pi\) | ||||
−0.0411152 | + | 0.999154i | \(0.513091\pi\) | |||||||
\(812\) | 6.44826e18 | 0.789457 | ||||||||
\(813\) | 3.09802e19 | 3.76267 | ||||||||
\(814\) | 1.31978e18 | 0.159017 | ||||||||
\(815\) | 1.01626e18 | 0.121473 | ||||||||
\(816\) | −2.82976e18 | −0.335555 | ||||||||
\(817\) | −1.51911e19 | −1.78708 | ||||||||
\(818\) | −7.13884e18 | −0.833165 | ||||||||
\(819\) | 3.78657e19 | 4.38431 | ||||||||
\(820\) | 9.48761e18 | 1.08985 | ||||||||
\(821\) | −8.62414e18 | −0.982845 | −0.491423 | − | 0.870921i | \(-0.663523\pi\) | ||||
−0.491423 | + | 0.870921i | \(0.663523\pi\) | |||||||
\(822\) | 2.81703e19 | 3.18511 | ||||||||
\(823\) | 5.17351e18 | 0.580345 | 0.290173 | − | 0.956974i | \(-0.406287\pi\) | ||||
0.290173 | + | 0.956974i | \(0.406287\pi\) | |||||||
\(824\) | −2.39594e19 | −2.66655 | ||||||||
\(825\) | 2.92051e19 | 3.22484 | ||||||||
\(826\) | −3.24521e19 | −3.55527 | ||||||||
\(827\) | −1.51864e19 | −1.65070 | −0.825351 | − | 0.564620i | \(-0.809023\pi\) | ||||
−0.825351 | + | 0.564620i | \(0.809023\pi\) | |||||||
\(828\) | 3.86231e19 | 4.16534 | ||||||||
\(829\) | −6.55630e18 | −0.701543 | −0.350772 | − | 0.936461i | \(-0.614081\pi\) | ||||
−0.350772 | + | 0.936461i | \(0.614081\pi\) | |||||||
\(830\) | −2.73866e17 | −0.0290757 | ||||||||
\(831\) | 9.95226e18 | 1.04837 | ||||||||
\(832\) | −1.12325e19 | −1.17401 | ||||||||
\(833\) | −1.60573e18 | −0.166526 | ||||||||
\(834\) | 4.74761e19 | 4.88535 | ||||||||
\(835\) | −1.02633e18 | −0.104792 | ||||||||
\(836\) | −4.41692e19 | −4.47485 | ||||||||
\(837\) | −1.05464e18 | −0.106021 | ||||||||
\(838\) | −9.32237e17 | −0.0929909 | ||||||||
\(839\) | −9.08342e17 | −0.0899076 | −0.0449538 | − | 0.998989i | \(-0.514314\pi\) | ||||
−0.0449538 | + | 0.998989i | \(0.514314\pi\) | |||||||
\(840\) | 1.72784e19 | 1.69702 | ||||||||
\(841\) | −9.39164e18 | −0.915308 | ||||||||
\(842\) | −2.72160e19 | −2.63206 | ||||||||
\(843\) | −2.05413e18 | −0.197128 | ||||||||
\(844\) | 7.94424e18 | 0.756530 | ||||||||
\(845\) | −6.48453e17 | −0.0612788 | ||||||||
\(846\) | −7.12600e19 | −6.68249 | ||||||||
\(847\) | 3.76202e19 | 3.50089 | ||||||||
\(848\) | 6.44268e18 | 0.594968 | ||||||||
\(849\) | 2.14181e19 | 1.96283 | ||||||||
\(850\) | −3.03311e18 | −0.275845 | ||||||||
\(851\) | 3.89613e17 | 0.0351635 | ||||||||
\(852\) | −3.82950e19 | −3.42993 | ||||||||
\(853\) | 8.27209e18 | 0.735270 | 0.367635 | − | 0.929970i | \(-0.380168\pi\) | ||||
0.367635 | + | 0.929970i | \(0.380168\pi\) | |||||||
\(854\) | −7.25721e18 | −0.640167 | ||||||||
\(855\) | −1.50917e19 | −1.32117 | ||||||||
\(856\) | −8.14170e18 | −0.707352 | ||||||||
\(857\) | −3.68435e18 | −0.317677 | −0.158838 | − | 0.987305i | \(-0.550775\pi\) | ||||
−0.158838 | + | 0.987305i | \(0.550775\pi\) | |||||||
\(858\) | 8.12935e19 | 6.95646 | ||||||||
\(859\) | 2.27542e19 | 1.93244 | 0.966219 | − | 0.257724i | \(-0.0829725\pi\) | ||||
0.966219 | + | 0.257724i | \(0.0829725\pi\) | |||||||
\(860\) | 1.28363e19 | 1.08194 | ||||||||
\(861\) | −4.87883e19 | −4.08127 | ||||||||
\(862\) | 9.95328e18 | 0.826360 | ||||||||
\(863\) | 4.98035e18 | 0.410384 | 0.205192 | − | 0.978722i | \(-0.434218\pi\) | ||||
0.205192 | + | 0.978722i | \(0.434218\pi\) | |||||||
\(864\) | 4.89284e18 | 0.400149 | ||||||||
\(865\) | −6.94613e18 | −0.563817 | ||||||||
\(866\) | 4.06080e19 | 3.27149 | ||||||||
\(867\) | −2.39959e19 | −1.91873 | ||||||||
\(868\) | −9.35665e17 | −0.0742578 | ||||||||
\(869\) | −1.82823e19 | −1.44013 | ||||||||
\(870\) | 4.73010e18 | 0.369824 | ||||||||
\(871\) | −6.80160e18 | −0.527829 | ||||||||
\(872\) | −1.72141e19 | −1.32595 | ||||||||
\(873\) | 5.94250e19 | 4.54335 | ||||||||
\(874\) | −1.96596e19 | −1.49194 | ||||||||
\(875\) | 1.26364e19 | 0.951855 | ||||||||
\(876\) | 8.94389e19 | 6.68729 | ||||||||
\(877\) | −1.48476e19 | −1.10194 | −0.550970 | − | 0.834525i | \(-0.685742\pi\) | ||||
−0.550970 | + | 0.834525i | \(0.685742\pi\) | |||||||
\(878\) | 8.53539e18 | 0.628795 | ||||||||
\(879\) | −5.34616e18 | −0.390944 | ||||||||
\(880\) | 8.75158e18 | 0.635257 | ||||||||
\(881\) | 7.50276e18 | 0.540602 | 0.270301 | − | 0.962776i | \(-0.412877\pi\) | ||||
0.270301 | + | 0.962776i | \(0.412877\pi\) | |||||||
\(882\) | −6.37355e19 | −4.55864 | ||||||||
\(883\) | 5.81660e18 | 0.412976 | 0.206488 | − | 0.978449i | \(-0.433797\pi\) | ||||
0.206488 | + | 0.978449i | \(0.433797\pi\) | |||||||
\(884\) | −5.59967e18 | −0.394660 | ||||||||
\(885\) | −1.57888e19 | −1.10463 | ||||||||
\(886\) | 1.42149e18 | 0.0987243 | ||||||||
\(887\) | 2.13508e18 | 0.147201 | 0.0736006 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0736006 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(888\) | −2.37867e18 | −0.162798 | ||||||||
\(889\) | 2.15902e19 | 1.46688 | ||||||||
\(890\) | −5.22627e17 | −0.0352498 | ||||||||
\(891\) | −1.33442e20 | −8.93483 | ||||||||
\(892\) | −2.19066e19 | −1.45614 | ||||||||
\(893\) | 2.40574e19 | 1.58750 | ||||||||
\(894\) | −3.47311e19 | −2.27523 | ||||||||
\(895\) | 3.63255e18 | 0.236244 | ||||||||
\(896\) | 3.77788e19 | 2.43919 | ||||||||
\(897\) | 2.39987e19 | 1.53829 | ||||||||
\(898\) | 6.19814e18 | 0.394425 | ||||||||
\(899\) | −1.26094e17 | −0.00796627 | ||||||||
\(900\) | −7.98496e19 | −5.00837 | ||||||||
\(901\) | −1.94993e18 | −0.121425 | ||||||||
\(902\) | −7.82191e19 | −4.83582 | ||||||||
\(903\) | −6.60085e19 | −4.05163 | ||||||||
\(904\) | 2.49740e19 | 1.52192 | ||||||||
\(905\) | −6.66506e18 | −0.403263 | ||||||||
\(906\) | −4.52904e19 | −2.72065 | ||||||||
\(907\) | 2.34252e19 | 1.39713 | 0.698564 | − | 0.715548i | \(-0.253823\pi\) | ||||
0.698564 | + | 0.715548i | \(0.253823\pi\) | |||||||
\(908\) | −2.81935e19 | −1.66952 | ||||||||
\(909\) | −5.67912e19 | −3.33900 | ||||||||
\(910\) | 1.62864e19 | 0.950729 | ||||||||
\(911\) | −1.13703e18 | −0.0659028 | −0.0329514 | − | 0.999457i | \(-0.510491\pi\) | ||||
−0.0329514 | + | 0.999457i | \(0.510491\pi\) | |||||||
\(912\) | 3.79193e19 | 2.18220 | ||||||||
\(913\) | 1.49751e18 | 0.0855678 | ||||||||
\(914\) | 4.22240e19 | 2.39557 | ||||||||
\(915\) | −3.53081e18 | −0.198901 | ||||||||
\(916\) | 1.17138e19 | 0.655205 | ||||||||
\(917\) | −2.01829e19 | −1.12094 | ||||||||
\(918\) | 2.24670e19 | 1.23899 | ||||||||
\(919\) | −2.69929e18 | −0.147808 | −0.0739041 | − | 0.997265i | \(-0.523546\pi\) | ||||
−0.0739041 | + | 0.997265i | \(0.523546\pi\) | |||||||
\(920\) | 8.17773e18 | 0.444643 | ||||||||
\(921\) | −3.01178e19 | −1.62606 | ||||||||
\(922\) | −5.78072e19 | −3.09906 | ||||||||
\(923\) | −1.77693e19 | −0.945931 | ||||||||
\(924\) | −1.91925e20 | −10.1453 | ||||||||
\(925\) | −8.05489e17 | −0.0422803 | ||||||||
\(926\) | −3.39090e19 | −1.76744 | ||||||||
\(927\) | 9.09330e19 | 4.70656 | ||||||||
\(928\) | 5.84991e17 | 0.0300668 | ||||||||
\(929\) | 3.67718e19 | 1.87678 | 0.938390 | − | 0.345579i | \(-0.112317\pi\) | ||||
0.938390 | + | 0.345579i | \(0.112317\pi\) | |||||||
\(930\) | −6.86354e17 | −0.0347863 | ||||||||
\(931\) | 2.15172e19 | 1.08296 | ||||||||
\(932\) | −3.88850e19 | −1.94348 | ||||||||
\(933\) | 1.68920e19 | 0.838399 | ||||||||
\(934\) | −2.84264e19 | −1.40110 | ||||||||
\(935\) | −2.64874e18 | −0.129647 | ||||||||
\(936\) | −1.09415e20 | −5.31842 | ||||||||
\(937\) | 1.61659e19 | 0.780356 | 0.390178 | − | 0.920739i | \(-0.372413\pi\) | ||||
0.390178 | + | 0.920739i | \(0.372413\pi\) | |||||||
\(938\) | 2.42108e19 | 1.16062 | ||||||||
\(939\) | 5.53112e19 | 2.63322 | ||||||||
\(940\) | −2.03284e19 | −0.961106 | ||||||||
\(941\) | 2.89880e19 | 1.36109 | 0.680544 | − | 0.732707i | \(-0.261744\pi\) | ||||
0.680544 | + | 0.732707i | \(0.261744\pi\) | |||||||
\(942\) | 1.17096e20 | 5.46024 | ||||||||
\(943\) | −2.30911e19 | −1.06935 | ||||||||
\(944\) | 2.96250e19 | 1.36251 | ||||||||
\(945\) | −4.33397e19 | −1.97961 | ||||||||
\(946\) | −1.05827e20 | −4.80070 | ||||||||
\(947\) | 4.32869e19 | 1.95021 | 0.975106 | − | 0.221741i | \(-0.0711741\pi\) | ||||
0.975106 | + | 0.221741i | \(0.0711741\pi\) | |||||||
\(948\) | 6.69356e19 | 2.99504 | ||||||||
\(949\) | 4.15006e19 | 1.84427 | ||||||||
\(950\) | 4.06443e19 | 1.79389 | ||||||||
\(951\) | −5.25408e19 | −2.30316 | ||||||||
\(952\) | 9.81220e18 | 0.427195 | ||||||||
\(953\) | 1.12843e19 | 0.487944 | 0.243972 | − | 0.969782i | \(-0.421549\pi\) | ||||
0.243972 | + | 0.969782i | \(0.421549\pi\) | |||||||
\(954\) | −7.73974e19 | −3.32401 | ||||||||
\(955\) | 1.29822e19 | 0.553766 | ||||||||
\(956\) | 2.31810e19 | 0.982099 | ||||||||
\(957\) | −2.58645e19 | −1.08837 | ||||||||
\(958\) | −1.69079e19 | −0.706667 | ||||||||
\(959\) | −3.08599e19 | −1.28107 | ||||||||
\(960\) | 1.94526e19 | 0.802075 | ||||||||
\(961\) | −2.43992e19 | −0.999251 | ||||||||
\(962\) | −2.24211e18 | −0.0912050 | ||||||||
\(963\) | 3.09002e19 | 1.24850 | ||||||||
\(964\) | −3.32364e19 | −1.33387 | ||||||||
\(965\) | 6.35656e18 | 0.253393 | ||||||||
\(966\) | −8.54252e19 | −3.38248 | ||||||||
\(967\) | −2.87228e19 | −1.12968 | −0.564840 | − | 0.825201i | \(-0.691062\pi\) | ||||
−0.564840 | + | 0.825201i | \(0.691062\pi\) | |||||||
\(968\) | −1.08705e20 | −4.24678 | ||||||||
\(969\) | −1.14766e19 | −0.445357 | ||||||||
\(970\) | 2.55593e19 | 0.985218 | ||||||||
\(971\) | 2.53595e19 | 0.970991 | 0.485495 | − | 0.874239i | \(-0.338639\pi\) | ||||
0.485495 | + | 0.874239i | \(0.338639\pi\) | |||||||
\(972\) | 2.87995e20 | 10.9535 | ||||||||
\(973\) | −5.20090e19 | −1.96492 | ||||||||
\(974\) | 2.20382e19 | 0.827072 | ||||||||
\(975\) | −4.96150e19 | −1.84962 | ||||||||
\(976\) | 6.62499e18 | 0.245336 | ||||||||
\(977\) | 1.75793e19 | 0.646678 | 0.323339 | − | 0.946283i | \(-0.395195\pi\) | ||||
0.323339 | + | 0.946283i | \(0.395195\pi\) | |||||||
\(978\) | 3.06753e19 | 1.12095 | ||||||||
\(979\) | 2.85775e18 | 0.103738 | ||||||||
\(980\) | −1.81818e19 | −0.655645 | ||||||||
\(981\) | 6.53324e19 | 2.34035 | ||||||||
\(982\) | 4.21875e19 | 1.50127 | ||||||||
\(983\) | −5.51691e18 | −0.195029 | −0.0975143 | − | 0.995234i | \(-0.531089\pi\) | ||||
−0.0975143 | + | 0.995234i | \(0.531089\pi\) | |||||||
\(984\) | 1.40976e20 | 4.95082 | ||||||||
\(985\) | −7.57857e17 | −0.0264394 | ||||||||
\(986\) | 2.68617e18 | 0.0930965 | ||||||||
\(987\) | 1.04535e20 | 3.59915 | ||||||||
\(988\) | 7.50368e19 | 2.56658 | ||||||||
\(989\) | −3.12413e19 | −1.06158 | ||||||||
\(990\) | −1.05135e20 | −3.54909 | ||||||||
\(991\) | 3.31548e19 | 1.11190 | 0.555952 | − | 0.831214i | \(-0.312354\pi\) | ||||
0.555952 | + | 0.831214i | \(0.312354\pi\) | |||||||
\(992\) | −8.48841e16 | −0.00282814 | ||||||||
\(993\) | 2.13507e19 | 0.706711 | ||||||||
\(994\) | 6.32512e19 | 2.07997 | ||||||||
\(995\) | 7.53597e18 | 0.246201 | ||||||||
\(996\) | −5.48274e18 | −0.177956 | ||||||||
\(997\) | −4.04706e19 | −1.30503 | −0.652517 | − | 0.757775i | \(-0.726287\pi\) | ||||
−0.652517 | + | 0.757775i | \(0.726287\pi\) | |||||||
\(998\) | −5.04458e19 | −1.61613 | ||||||||
\(999\) | 5.96646e18 | 0.189907 |
(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 | 197.14.a.b.1.10 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.b.1.10 | ✓ | 109 | 1.1 | even | 1 | trivial |