Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −86.5721 | −1.91299 | −0.956496 | − | 0.291746i | \(-0.905764\pi\) | ||||
−0.956496 | + | 0.291746i | \(0.905764\pi\) | |||||||
\(3\) | −287.043 | −0.681993 | −0.340996 | − | 0.940065i | \(-0.610764\pi\) | ||||
−0.340996 | + | 0.940065i | \(0.610764\pi\) | |||||||
\(4\) | 5446.73 | 2.65954 | ||||||||
\(5\) | −10768.4 | −1.54105 | −0.770523 | − | 0.637412i | \(-0.780005\pi\) | ||||
−0.770523 | + | 0.637412i | \(0.780005\pi\) | |||||||
\(6\) | 24849.9 | 1.30465 | ||||||||
\(7\) | −50234.8 | −1.12971 | −0.564853 | − | 0.825192i | \(-0.691067\pi\) | ||||
−0.564853 | + | 0.825192i | \(0.691067\pi\) | |||||||
\(8\) | −294236. | −3.17468 | ||||||||
\(9\) | −94753.4 | −0.534886 | ||||||||
\(10\) | 932242. | 2.94801 | ||||||||
\(11\) | 137694. | 0.257784 | 0.128892 | − | 0.991659i | \(-0.458858\pi\) | ||||
0.128892 | + | 0.991659i | \(0.458858\pi\) | |||||||
\(12\) | −1.56345e6 | −1.81379 | ||||||||
\(13\) | 1.89680e6 | 1.41688 | 0.708441 | − | 0.705770i | \(-0.249399\pi\) | ||||
0.708441 | + | 0.705770i | \(0.249399\pi\) | |||||||
\(14\) | 4.34893e6 | 2.16112 | ||||||||
\(15\) | 3.09099e6 | 1.05098 | ||||||||
\(16\) | 1.43177e7 | 3.41360 | ||||||||
\(17\) | 4.71231e6 | 0.804942 | 0.402471 | − | 0.915433i | \(-0.368151\pi\) | ||||
0.402471 | + | 0.915433i | \(0.368151\pi\) | |||||||
\(18\) | 8.20300e6 | 1.02323 | ||||||||
\(19\) | −1.54798e7 | −1.43423 | −0.717116 | − | 0.696954i | \(-0.754538\pi\) | ||||
−0.717116 | + | 0.696954i | \(0.754538\pi\) | |||||||
\(20\) | −5.86525e7 | −4.09847 | ||||||||
\(21\) | 1.44195e7 | 0.770451 | ||||||||
\(22\) | −1.19205e7 | −0.493138 | ||||||||
\(23\) | −4.55820e7 | −1.47669 | −0.738347 | − | 0.674421i | \(-0.764393\pi\) | ||||
−0.738347 | + | 0.674421i | \(0.764393\pi\) | |||||||
\(24\) | 8.44582e7 | 2.16511 | ||||||||
\(25\) | 6.71300e7 | 1.37482 | ||||||||
\(26\) | −1.64210e8 | −2.71048 | ||||||||
\(27\) | 7.80471e7 | 1.04678 | ||||||||
\(28\) | −2.73615e8 | −3.00449 | ||||||||
\(29\) | 3.92624e7 | 0.355458 | 0.177729 | − | 0.984079i | \(-0.443125\pi\) | ||||
0.177729 | + | 0.984079i | \(0.443125\pi\) | |||||||
\(30\) | −2.67593e8 | −2.01052 | ||||||||
\(31\) | 5.48803e7 | 0.344292 | 0.172146 | − | 0.985071i | \(-0.444930\pi\) | ||||
0.172146 | + | 0.985071i | \(0.444930\pi\) | |||||||
\(32\) | −6.36919e8 | −3.35551 | ||||||||
\(33\) | −3.95241e7 | −0.175807 | ||||||||
\(34\) | −4.07954e8 | −1.53985 | ||||||||
\(35\) | 5.40948e8 | 1.74093 | ||||||||
\(36\) | −5.16096e8 | −1.42255 | ||||||||
\(37\) | 6.58234e8 | 1.56052 | 0.780262 | − | 0.625452i | \(-0.215086\pi\) | ||||
0.780262 | + | 0.625452i | \(0.215086\pi\) | |||||||
\(38\) | 1.34012e9 | 2.74367 | ||||||||
\(39\) | −5.44464e8 | −0.966304 | ||||||||
\(40\) | 3.16844e9 | 4.89233 | ||||||||
\(41\) | 2.72100e8 | 0.366790 | 0.183395 | − | 0.983039i | \(-0.441291\pi\) | ||||
0.183395 | + | 0.983039i | \(0.441291\pi\) | |||||||
\(42\) | −1.24833e9 | −1.47387 | ||||||||
\(43\) | 2.65418e8 | 0.275330 | 0.137665 | − | 0.990479i | \(-0.456040\pi\) | ||||
0.137665 | + | 0.990479i | \(0.456040\pi\) | |||||||
\(44\) | 7.49983e8 | 0.685585 | ||||||||
\(45\) | 1.02034e9 | 0.824283 | ||||||||
\(46\) | 3.94613e9 | 2.82490 | ||||||||
\(47\) | −2.92021e9 | −1.85727 | −0.928637 | − | 0.370989i | \(-0.879019\pi\) | ||||
−0.928637 | + | 0.370989i | \(0.879019\pi\) | |||||||
\(48\) | −4.10979e9 | −2.32805 | ||||||||
\(49\) | 5.46206e8 | 0.276235 | ||||||||
\(50\) | −5.81159e9 | −2.63003 | ||||||||
\(51\) | −1.35263e9 | −0.548965 | ||||||||
\(52\) | 1.03314e10 | 3.76825 | ||||||||
\(53\) | −4.21817e9 | −1.38550 | −0.692750 | − | 0.721177i | \(-0.743601\pi\) | ||||
−0.692750 | + | 0.721177i | \(0.743601\pi\) | |||||||
\(54\) | −6.75670e9 | −2.00248 | ||||||||
\(55\) | −1.48274e9 | −0.397256 | ||||||||
\(56\) | 1.47809e10 | 3.58646 | ||||||||
\(57\) | 4.44336e9 | 0.978136 | ||||||||
\(58\) | −3.39903e9 | −0.679988 | ||||||||
\(59\) | 1.55089e9 | 0.282420 | 0.141210 | − | 0.989980i | \(-0.454901\pi\) | ||||
0.141210 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(60\) | 1.68358e10 | 2.79513 | ||||||||
\(61\) | −7.70506e9 | −1.16805 | −0.584026 | − | 0.811735i | \(-0.698523\pi\) | ||||
−0.584026 | + | 0.811735i | \(0.698523\pi\) | |||||||
\(62\) | −4.75111e9 | −0.658629 | ||||||||
\(63\) | 4.75992e9 | 0.604263 | ||||||||
\(64\) | 2.58168e10 | 3.00547 | ||||||||
\(65\) | −2.04255e10 | −2.18348 | ||||||||
\(66\) | 3.42168e9 | 0.336317 | ||||||||
\(67\) | 1.50199e10 | 1.35912 | 0.679558 | − | 0.733622i | \(-0.262171\pi\) | ||||
0.679558 | + | 0.733622i | \(0.262171\pi\) | |||||||
\(68\) | 2.56667e10 | 2.14077 | ||||||||
\(69\) | 1.30840e10 | 1.00709 | ||||||||
\(70\) | −4.68310e10 | −3.33038 | ||||||||
\(71\) | 8.58511e9 | 0.564709 | 0.282354 | − | 0.959310i | \(-0.408885\pi\) | ||||
0.282354 | + | 0.959310i | \(0.408885\pi\) | |||||||
\(72\) | 2.78798e10 | 1.69809 | ||||||||
\(73\) | −1.81116e10 | −1.02254 | −0.511271 | − | 0.859419i | \(-0.670825\pi\) | ||||
−0.511271 | + | 0.859419i | \(0.670825\pi\) | |||||||
\(74\) | −5.69847e10 | −2.98527 | ||||||||
\(75\) | −1.92692e10 | −0.937620 | ||||||||
\(76\) | −8.43142e10 | −3.81440 | ||||||||
\(77\) | −6.91703e9 | −0.291220 | ||||||||
\(78\) | 4.71354e10 | 1.84853 | ||||||||
\(79\) | −2.21343e10 | −0.809314 | −0.404657 | − | 0.914469i | \(-0.632609\pi\) | ||||
−0.404657 | + | 0.914469i | \(0.632609\pi\) | |||||||
\(80\) | −1.54178e11 | −5.26052 | ||||||||
\(81\) | −5.61758e9 | −0.179012 | ||||||||
\(82\) | −2.35563e10 | −0.701666 | ||||||||
\(83\) | 7.17506e9 | 0.199938 | 0.0999692 | − | 0.994991i | \(-0.468126\pi\) | ||||
0.0999692 | + | 0.994991i | \(0.468126\pi\) | |||||||
\(84\) | 7.85394e10 | 2.04904 | ||||||||
\(85\) | −5.07439e10 | −1.24045 | ||||||||
\(86\) | −2.29778e10 | −0.526705 | ||||||||
\(87\) | −1.12700e10 | −0.242420 | ||||||||
\(88\) | −4.05145e10 | −0.818381 | ||||||||
\(89\) | 3.68534e10 | 0.699571 | 0.349786 | − | 0.936830i | \(-0.386254\pi\) | ||||
0.349786 | + | 0.936830i | \(0.386254\pi\) | |||||||
\(90\) | −8.83331e10 | −1.57685 | ||||||||
\(91\) | −9.52855e10 | −1.60066 | ||||||||
\(92\) | −2.48273e11 | −3.92732 | ||||||||
\(93\) | −1.57530e10 | −0.234805 | ||||||||
\(94\) | 2.52809e11 | 3.55295 | ||||||||
\(95\) | 1.66692e11 | 2.21022 | ||||||||
\(96\) | 1.82823e11 | 2.28844 | ||||||||
\(97\) | 4.00765e9 | 0.0473855 | 0.0236927 | − | 0.999719i | \(-0.492458\pi\) | ||||
0.0236927 | + | 0.999719i | \(0.492458\pi\) | |||||||
\(98\) | −4.72862e10 | −0.528435 | ||||||||
\(99\) | −1.30470e10 | −0.137885 | ||||||||
\(100\) | 3.65639e11 | 3.65639 | ||||||||
\(101\) | −1.84185e11 | −1.74376 | −0.871878 | − | 0.489722i | \(-0.837098\pi\) | ||||
−0.871878 | + | 0.489722i | \(0.837098\pi\) | |||||||
\(102\) | 1.17100e11 | 1.05016 | ||||||||
\(103\) | 4.37962e10 | 0.372248 | 0.186124 | − | 0.982526i | \(-0.440407\pi\) | ||||
0.186124 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(104\) | −5.58107e11 | −4.49815 | ||||||||
\(105\) | −1.55275e11 | −1.18730 | ||||||||
\(106\) | 3.65176e11 | 2.65045 | ||||||||
\(107\) | −1.62314e11 | −1.11878 | −0.559392 | − | 0.828903i | \(-0.688965\pi\) | ||||
−0.559392 | + | 0.828903i | \(0.688965\pi\) | |||||||
\(108\) | 4.25102e11 | 2.78395 | ||||||||
\(109\) | −2.64387e11 | −1.64587 | −0.822933 | − | 0.568139i | \(-0.807664\pi\) | ||||
−0.822933 | + | 0.568139i | \(0.807664\pi\) | |||||||
\(110\) | 1.28364e11 | 0.759948 | ||||||||
\(111\) | −1.88941e11 | −1.06427 | ||||||||
\(112\) | −7.19246e11 | −3.85637 | ||||||||
\(113\) | −1.69277e11 | −0.864302 | −0.432151 | − | 0.901801i | \(-0.642245\pi\) | ||||
−0.432151 | + | 0.901801i | \(0.642245\pi\) | |||||||
\(114\) | −3.84671e11 | −1.87117 | ||||||||
\(115\) | 4.90845e11 | 2.27565 | ||||||||
\(116\) | 2.13852e11 | 0.945354 | ||||||||
\(117\) | −1.79728e11 | −0.757870 | ||||||||
\(118\) | −1.34264e11 | −0.540267 | ||||||||
\(119\) | −2.36722e11 | −0.909347 | ||||||||
\(120\) | −9.09479e11 | −3.33654 | ||||||||
\(121\) | −2.66352e11 | −0.933548 | ||||||||
\(122\) | 6.67044e11 | 2.23447 | ||||||||
\(123\) | −7.81044e10 | −0.250148 | ||||||||
\(124\) | 2.98919e11 | 0.915659 | ||||||||
\(125\) | −1.97082e11 | −0.577619 | ||||||||
\(126\) | −4.12076e11 | −1.15595 | ||||||||
\(127\) | −1.22516e11 | −0.329057 | −0.164528 | − | 0.986372i | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(128\) | −9.30604e11 | −2.39392 | ||||||||
\(129\) | −7.61864e10 | −0.187773 | ||||||||
\(130\) | 1.76828e12 | 4.17698 | ||||||||
\(131\) | −2.36127e11 | −0.534754 | −0.267377 | − | 0.963592i | \(-0.586157\pi\) | ||||
−0.267377 | + | 0.963592i | \(0.586157\pi\) | |||||||
\(132\) | −2.15277e11 | −0.467564 | ||||||||
\(133\) | 7.77623e11 | 1.62026 | ||||||||
\(134\) | −1.30031e12 | −2.59998 | ||||||||
\(135\) | −8.40441e11 | −1.61314 | ||||||||
\(136\) | −1.38653e12 | −2.55543 | ||||||||
\(137\) | −7.36038e11 | −1.30298 | −0.651489 | − | 0.758658i | \(-0.725855\pi\) | ||||
−0.651489 | + | 0.758658i | \(0.725855\pi\) | |||||||
\(138\) | −1.13271e12 | −1.92656 | ||||||||
\(139\) | −1.63487e11 | −0.267239 | −0.133620 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133620 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(140\) | 2.94640e12 | 4.63006 | ||||||||
\(141\) | 8.38226e11 | 1.26665 | ||||||||
\(142\) | −7.43231e11 | −1.08028 | ||||||||
\(143\) | 2.61178e11 | 0.365249 | ||||||||
\(144\) | −1.35665e12 | −1.82589 | ||||||||
\(145\) | −4.22793e11 | −0.547777 | ||||||||
\(146\) | 1.56796e12 | 1.95612 | ||||||||
\(147\) | −1.56785e11 | −0.188390 | ||||||||
\(148\) | 3.58522e12 | 4.15027 | ||||||||
\(149\) | −1.43510e12 | −1.60088 | −0.800439 | − | 0.599414i | \(-0.795400\pi\) | ||||
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(150\) | 1.66818e12 | 1.79366 | ||||||||
\(151\) | −8.46040e10 | −0.0877036 | −0.0438518 | − | 0.999038i | \(-0.513963\pi\) | ||||
−0.0438518 | + | 0.999038i | \(0.513963\pi\) | |||||||
\(152\) | 4.55470e12 | 4.55323 | ||||||||
\(153\) | −4.46507e11 | −0.430552 | ||||||||
\(154\) | 5.98822e11 | 0.557101 | ||||||||
\(155\) | −5.90973e11 | −0.530570 | ||||||||
\(156\) | −2.96555e12 | −2.56992 | ||||||||
\(157\) | 7.09827e11 | 0.593888 | 0.296944 | − | 0.954895i | \(-0.404033\pi\) | ||||
0.296944 | + | 0.954895i | \(0.404033\pi\) | |||||||
\(158\) | 1.91621e12 | 1.54821 | ||||||||
\(159\) | 1.21080e12 | 0.944902 | ||||||||
\(160\) | 6.85859e12 | 5.17100 | ||||||||
\(161\) | 2.28980e12 | 1.66823 | ||||||||
\(162\) | 4.86326e11 | 0.342448 | ||||||||
\(163\) | 2.02859e12 | 1.38090 | 0.690449 | − | 0.723381i | \(-0.257413\pi\) | ||||
0.690449 | + | 0.723381i | \(0.257413\pi\) | |||||||
\(164\) | 1.48206e12 | 0.975492 | ||||||||
\(165\) | 4.25611e11 | 0.270926 | ||||||||
\(166\) | −6.21160e11 | −0.382480 | ||||||||
\(167\) | 1.03298e12 | 0.615391 | 0.307695 | − | 0.951485i | \(-0.400442\pi\) | ||||
0.307695 | + | 0.951485i | \(0.400442\pi\) | |||||||
\(168\) | −4.24274e12 | −2.44594 | ||||||||
\(169\) | 1.80570e12 | 1.00755 | ||||||||
\(170\) | 4.39301e12 | 2.37298 | ||||||||
\(171\) | 1.46676e12 | 0.767150 | ||||||||
\(172\) | 1.44566e12 | 0.732251 | ||||||||
\(173\) | −1.77073e12 | −0.868756 | −0.434378 | − | 0.900731i | \(-0.643032\pi\) | ||||
−0.434378 | + | 0.900731i | \(0.643032\pi\) | |||||||
\(174\) | 9.75668e11 | 0.463747 | ||||||||
\(175\) | −3.37226e12 | −1.55315 | ||||||||
\(176\) | 1.97146e12 | 0.879971 | ||||||||
\(177\) | −4.45172e11 | −0.192608 | ||||||||
\(178\) | −3.19047e12 | −1.33827 | ||||||||
\(179\) | −1.80189e12 | −0.732888 | −0.366444 | − | 0.930440i | \(-0.619425\pi\) | ||||
−0.366444 | + | 0.930440i | \(0.619425\pi\) | |||||||
\(180\) | 5.55753e12 | 2.19221 | ||||||||
\(181\) | −4.45615e12 | −1.70501 | −0.852506 | − | 0.522718i | \(-0.824918\pi\) | ||||
−0.852506 | + | 0.522718i | \(0.824918\pi\) | |||||||
\(182\) | 8.24906e12 | 3.06205 | ||||||||
\(183\) | 2.21168e12 | 0.796603 | ||||||||
\(184\) | 1.34118e13 | 4.68803 | ||||||||
\(185\) | −7.08811e12 | −2.40484 | ||||||||
\(186\) | 1.36377e12 | 0.449180 | ||||||||
\(187\) | 6.48856e11 | 0.207501 | ||||||||
\(188\) | −1.59056e13 | −4.93949 | ||||||||
\(189\) | −3.92068e12 | −1.18255 | ||||||||
\(190\) | −1.44309e13 | −4.22813 | ||||||||
\(191\) | 1.41157e12 | 0.401809 | 0.200905 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200905 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(192\) | −7.41052e12 | −2.04971 | ||||||||
\(193\) | −3.62567e12 | −0.974593 | −0.487297 | − | 0.873236i | \(-0.662017\pi\) | ||||
−0.487297 | + | 0.873236i | \(0.662017\pi\) | |||||||
\(194\) | −3.46951e11 | −0.0906481 | ||||||||
\(195\) | 5.86300e12 | 1.48912 | ||||||||
\(196\) | 2.97504e12 | 0.734657 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | 1.12950e12 | 0.263772 | ||||||||
\(199\) | 7.07088e12 | 1.60613 | 0.803066 | − | 0.595890i | \(-0.203200\pi\) | ||||
0.803066 | + | 0.595890i | \(0.203200\pi\) | |||||||
\(200\) | −1.97520e13 | −4.36463 | ||||||||
\(201\) | −4.31137e12 | −0.926908 | ||||||||
\(202\) | 1.59453e13 | 3.33579 | ||||||||
\(203\) | −1.97234e12 | −0.401563 | ||||||||
\(204\) | −7.36744e12 | −1.45999 | ||||||||
\(205\) | −2.93008e12 | −0.565240 | ||||||||
\(206\) | −3.79153e12 | −0.712107 | ||||||||
\(207\) | 4.31905e12 | 0.789862 | ||||||||
\(208\) | 2.71578e13 | 4.83667 | ||||||||
\(209\) | −2.13147e12 | −0.369722 | ||||||||
\(210\) | 1.34425e13 | 2.27130 | ||||||||
\(211\) | −1.19056e12 | −0.195974 | −0.0979870 | − | 0.995188i | \(-0.531240\pi\) | ||||
−0.0979870 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(212\) | −2.29752e13 | −3.68479 | ||||||||
\(213\) | −2.46429e12 | −0.385128 | ||||||||
\(214\) | 1.40519e13 | 2.14023 | ||||||||
\(215\) | −2.85812e12 | −0.424297 | ||||||||
\(216\) | −2.29642e13 | −3.32320 | ||||||||
\(217\) | −2.75690e12 | −0.388949 | ||||||||
\(218\) | 2.28885e13 | 3.14853 | ||||||||
\(219\) | 5.19881e12 | 0.697367 | ||||||||
\(220\) | −8.07610e12 | −1.05652 | ||||||||
\(221\) | 8.93831e12 | 1.14051 | ||||||||
\(222\) | 1.63570e13 | 2.03593 | ||||||||
\(223\) | −9.73013e12 | −1.18152 | −0.590761 | − | 0.806846i | \(-0.701173\pi\) | ||||
−0.590761 | + | 0.806846i | \(0.701173\pi\) | |||||||
\(224\) | 3.19955e13 | 3.79074 | ||||||||
\(225\) | −6.36080e12 | −0.735373 | ||||||||
\(226\) | 1.46546e13 | 1.65340 | ||||||||
\(227\) | −2.93570e12 | −0.323273 | −0.161636 | − | 0.986850i | \(-0.551677\pi\) | ||||
−0.161636 | + | 0.986850i | \(0.551677\pi\) | |||||||
\(228\) | 2.42018e13 | 2.60139 | ||||||||
\(229\) | −9.50474e12 | −0.997344 | −0.498672 | − | 0.866791i | \(-0.666179\pi\) | ||||
−0.498672 | + | 0.866791i | \(0.666179\pi\) | |||||||
\(230\) | −4.24935e13 | −4.35330 | ||||||||
\(231\) | 1.98548e12 | 0.198610 | ||||||||
\(232\) | −1.15524e13 | −1.12847 | ||||||||
\(233\) | 6.96508e12 | 0.664459 | 0.332230 | − | 0.943199i | \(-0.392199\pi\) | ||||
0.332230 | + | 0.943199i | \(0.392199\pi\) | |||||||
\(234\) | 1.55595e13 | 1.44980 | ||||||||
\(235\) | 3.14460e13 | 2.86215 | ||||||||
\(236\) | 8.44729e12 | 0.751106 | ||||||||
\(237\) | 6.35350e12 | 0.551946 | ||||||||
\(238\) | 2.04935e13 | 1.73957 | ||||||||
\(239\) | −9.66194e11 | −0.0801449 | −0.0400725 | − | 0.999197i | \(-0.512759\pi\) | ||||
−0.0400725 | + | 0.999197i | \(0.512759\pi\) | |||||||
\(240\) | 4.42558e13 | 3.58764 | ||||||||
\(241\) | 1.46440e13 | 1.16029 | 0.580143 | − | 0.814514i | \(-0.302997\pi\) | ||||
0.580143 | + | 0.814514i | \(0.302997\pi\) | |||||||
\(242\) | 2.30587e13 | 1.78587 | ||||||||
\(243\) | −1.22133e13 | −0.924696 | ||||||||
\(244\) | −4.19674e13 | −3.10648 | ||||||||
\(245\) | −5.88176e12 | −0.425690 | ||||||||
\(246\) | 6.76166e12 | 0.478532 | ||||||||
\(247\) | −2.93621e13 | −2.03214 | ||||||||
\(248\) | −1.61478e13 | −1.09302 | ||||||||
\(249\) | −2.05955e12 | −0.136357 | ||||||||
\(250\) | 1.70618e13 | 1.10498 | ||||||||
\(251\) | −2.23763e13 | −1.41769 | −0.708847 | − | 0.705362i | \(-0.750784\pi\) | ||||
−0.708847 | + | 0.705362i | \(0.750784\pi\) | |||||||
\(252\) | 2.59260e13 | 1.60706 | ||||||||
\(253\) | −6.27637e12 | −0.380667 | ||||||||
\(254\) | 1.06064e13 | 0.629483 | ||||||||
\(255\) | 1.45657e13 | 0.845980 | ||||||||
\(256\) | 2.76916e13 | 1.57408 | ||||||||
\(257\) | 2.09807e13 | 1.16731 | 0.583656 | − | 0.812001i | \(-0.301622\pi\) | ||||
0.583656 | + | 0.812001i | \(0.301622\pi\) | |||||||
\(258\) | 6.59562e12 | 0.359209 | ||||||||
\(259\) | −3.30662e13 | −1.76293 | ||||||||
\(260\) | −1.11252e14 | −5.80705 | ||||||||
\(261\) | −3.72025e12 | −0.190129 | ||||||||
\(262\) | 2.04421e13 | 1.02298 | ||||||||
\(263\) | 2.05205e13 | 1.00561 | 0.502807 | − | 0.864399i | \(-0.332301\pi\) | ||||
0.502807 | + | 0.864399i | \(0.332301\pi\) | |||||||
\(264\) | 1.16294e13 | 0.558130 | ||||||||
\(265\) | 4.54229e13 | 2.13512 | ||||||||
\(266\) | −6.73204e13 | −3.09954 | ||||||||
\(267\) | −1.05785e13 | −0.477103 | ||||||||
\(268\) | 8.18096e13 | 3.61462 | ||||||||
\(269\) | −3.41149e13 | −1.47675 | −0.738374 | − | 0.674391i | \(-0.764406\pi\) | ||||
−0.738374 | + | 0.674391i | \(0.764406\pi\) | |||||||
\(270\) | 7.27588e13 | 3.08592 | ||||||||
\(271\) | 3.17092e13 | 1.31781 | 0.658907 | − | 0.752224i | \(-0.271019\pi\) | ||||
0.658907 | + | 0.752224i | \(0.271019\pi\) | |||||||
\(272\) | 6.74694e13 | 2.74775 | ||||||||
\(273\) | 2.73510e13 | 1.09164 | ||||||||
\(274\) | 6.37204e13 | 2.49259 | ||||||||
\(275\) | 9.24340e12 | 0.354407 | ||||||||
\(276\) | 7.12650e13 | 2.67841 | ||||||||
\(277\) | 3.73768e13 | 1.37709 | 0.688546 | − | 0.725192i | \(-0.258249\pi\) | ||||
0.688546 | + | 0.725192i | \(0.258249\pi\) | |||||||
\(278\) | 1.41534e13 | 0.511227 | ||||||||
\(279\) | −5.20010e12 | −0.184157 | ||||||||
\(280\) | −1.59166e14 | −5.52690 | ||||||||
\(281\) | −5.20161e12 | −0.177114 | −0.0885571 | − | 0.996071i | \(-0.528226\pi\) | ||||
−0.0885571 | + | 0.996071i | \(0.528226\pi\) | |||||||
\(282\) | −7.25670e13 | −2.42309 | ||||||||
\(283\) | 6.29189e11 | 0.0206042 | 0.0103021 | − | 0.999947i | \(-0.496721\pi\) | ||||
0.0103021 | + | 0.999947i | \(0.496721\pi\) | |||||||
\(284\) | 4.67608e13 | 1.50187 | ||||||||
\(285\) | −4.78478e13 | −1.50735 | ||||||||
\(286\) | −2.26108e13 | −0.698718 | ||||||||
\(287\) | −1.36689e13 | −0.414365 | ||||||||
\(288\) | 6.03502e13 | 1.79482 | ||||||||
\(289\) | −1.20661e13 | −0.352069 | ||||||||
\(290\) | 3.66021e13 | 1.04789 | ||||||||
\(291\) | −1.15037e12 | −0.0323166 | ||||||||
\(292\) | −9.86491e13 | −2.71949 | ||||||||
\(293\) | 1.47114e13 | 0.397998 | 0.198999 | − | 0.980000i | \(-0.436231\pi\) | ||||
0.198999 | + | 0.980000i | \(0.436231\pi\) | |||||||
\(294\) | 1.35732e13 | 0.360389 | ||||||||
\(295\) | −1.67006e13 | −0.435222 | ||||||||
\(296\) | −1.93676e14 | −4.95417 | ||||||||
\(297\) | 1.07466e13 | 0.269843 | ||||||||
\(298\) | 1.24240e14 | 3.06247 | ||||||||
\(299\) | −8.64601e13 | −2.09230 | ||||||||
\(300\) | −1.04954e14 | −2.49363 | ||||||||
\(301\) | −1.33332e13 | −0.311042 | ||||||||
\(302\) | 7.32434e12 | 0.167776 | ||||||||
\(303\) | 5.28689e13 | 1.18923 | ||||||||
\(304\) | −2.21635e14 | −4.89590 | ||||||||
\(305\) | 8.29711e13 | 1.80002 | ||||||||
\(306\) | 3.86551e13 | 0.823642 | ||||||||
\(307\) | 6.24695e13 | 1.30739 | 0.653697 | − | 0.756756i | \(-0.273217\pi\) | ||||
0.653697 | + | 0.756756i | \(0.273217\pi\) | |||||||
\(308\) | −3.76752e13 | −0.774510 | ||||||||
\(309\) | −1.25714e13 | −0.253870 | ||||||||
\(310\) | 5.11618e13 | 1.01498 | ||||||||
\(311\) | −3.35568e13 | −0.654032 | −0.327016 | − | 0.945019i | \(-0.606043\pi\) | ||||
−0.327016 | + | 0.945019i | \(0.606043\pi\) | |||||||
\(312\) | 1.60201e14 | 3.06771 | ||||||||
\(313\) | 8.44273e13 | 1.58851 | 0.794253 | − | 0.607587i | \(-0.207862\pi\) | ||||
0.794253 | + | 0.607587i | \(0.207862\pi\) | |||||||
\(314\) | −6.14513e13 | −1.13610 | ||||||||
\(315\) | −5.12566e13 | −0.931198 | ||||||||
\(316\) | −1.20560e14 | −2.15240 | ||||||||
\(317\) | −7.78116e13 | −1.36527 | −0.682635 | − | 0.730759i | \(-0.739166\pi\) | ||||
−0.682635 | + | 0.730759i | \(0.739166\pi\) | |||||||
\(318\) | −1.04821e14 | −1.80759 | ||||||||
\(319\) | 5.40620e12 | 0.0916312 | ||||||||
\(320\) | −2.78005e14 | −4.63157 | ||||||||
\(321\) | 4.65912e13 | 0.763003 | ||||||||
\(322\) | −1.98233e14 | −3.19131 | ||||||||
\(323\) | −7.29454e13 | −1.15447 | ||||||||
\(324\) | −3.05975e13 | −0.476089 | ||||||||
\(325\) | 1.27332e14 | 1.94796 | ||||||||
\(326\) | −1.75619e14 | −2.64165 | ||||||||
\(327\) | 7.58904e13 | 1.12247 | ||||||||
\(328\) | −8.00616e13 | −1.16444 | ||||||||
\(329\) | 1.46696e14 | 2.09817 | ||||||||
\(330\) | −3.68460e13 | −0.518279 | ||||||||
\(331\) | 1.18497e14 | 1.63929 | 0.819643 | − | 0.572874i | \(-0.194172\pi\) | ||||
0.819643 | + | 0.572874i | \(0.194172\pi\) | |||||||
\(332\) | 3.90806e13 | 0.531744 | ||||||||
\(333\) | −6.23699e13 | −0.834702 | ||||||||
\(334\) | −8.94272e13 | −1.17724 | ||||||||
\(335\) | −1.61740e14 | −2.09446 | ||||||||
\(336\) | 2.06455e14 | 2.63002 | ||||||||
\(337\) | 7.08465e13 | 0.887880 | 0.443940 | − | 0.896057i | \(-0.353580\pi\) | ||||
0.443940 | + | 0.896057i | \(0.353580\pi\) | |||||||
\(338\) | −1.56323e14 | −1.92744 | ||||||||
\(339\) | 4.85897e13 | 0.589448 | ||||||||
\(340\) | −2.76389e14 | −3.29903 | ||||||||
\(341\) | 7.55669e12 | 0.0887529 | ||||||||
\(342\) | −1.26981e14 | −1.46755 | ||||||||
\(343\) | 7.18920e13 | 0.817642 | ||||||||
\(344\) | −7.80955e13 | −0.874086 | ||||||||
\(345\) | −1.40893e14 | −1.55198 | ||||||||
\(346\) | 1.53296e14 | 1.66192 | ||||||||
\(347\) | 1.33342e14 | 1.42284 | 0.711418 | − | 0.702769i | \(-0.248053\pi\) | ||||
0.711418 | + | 0.702769i | \(0.248053\pi\) | |||||||
\(348\) | −6.13847e13 | −0.644724 | ||||||||
\(349\) | −1.62451e14 | −1.67951 | −0.839756 | − | 0.542964i | \(-0.817302\pi\) | ||||
−0.839756 | + | 0.542964i | \(0.817302\pi\) | |||||||
\(350\) | 2.91944e14 | 2.97115 | ||||||||
\(351\) | 1.48040e14 | 1.48317 | ||||||||
\(352\) | −8.76999e13 | −0.864997 | ||||||||
\(353\) | −1.03309e14 | −1.00318 | −0.501588 | − | 0.865107i | \(-0.667251\pi\) | ||||
−0.501588 | + | 0.865107i | \(0.667251\pi\) | |||||||
\(354\) | 3.85395e13 | 0.368458 | ||||||||
\(355\) | −9.24477e13 | −0.870243 | ||||||||
\(356\) | 2.00730e14 | 1.86054 | ||||||||
\(357\) | 6.79493e13 | 0.620168 | ||||||||
\(358\) | 1.55994e14 | 1.40201 | ||||||||
\(359\) | 1.35380e14 | 1.19821 | 0.599107 | − | 0.800669i | \(-0.295523\pi\) | ||||
0.599107 | + | 0.800669i | \(0.295523\pi\) | |||||||
\(360\) | −3.00221e14 | −2.61684 | ||||||||
\(361\) | 1.23133e14 | 1.05702 | ||||||||
\(362\) | 3.85778e14 | 3.26167 | ||||||||
\(363\) | 7.64545e13 | 0.636673 | ||||||||
\(364\) | −5.18995e14 | −4.25701 | ||||||||
\(365\) | 1.95033e14 | 1.57578 | ||||||||
\(366\) | −1.91470e14 | −1.52390 | ||||||||
\(367\) | −2.12613e14 | −1.66696 | −0.833481 | − | 0.552549i | \(-0.813655\pi\) | ||||
−0.833481 | + | 0.552549i | \(0.813655\pi\) | |||||||
\(368\) | −6.52629e14 | −5.04085 | ||||||||
\(369\) | −2.57824e13 | −0.196191 | ||||||||
\(370\) | 6.13633e14 | 4.60044 | ||||||||
\(371\) | 2.11899e14 | 1.56521 | ||||||||
\(372\) | −8.58025e13 | −0.624473 | ||||||||
\(373\) | −1.85839e14 | −1.33272 | −0.666360 | − | 0.745630i | \(-0.732149\pi\) | ||||
−0.666360 | + | 0.745630i | \(0.732149\pi\) | |||||||
\(374\) | −5.61729e13 | −0.396947 | ||||||||
\(375\) | 5.65710e13 | 0.393932 | ||||||||
\(376\) | 8.59230e14 | 5.89626 | ||||||||
\(377\) | 7.44731e13 | 0.503642 | ||||||||
\(378\) | 3.39421e14 | 2.26222 | ||||||||
\(379\) | −1.50749e14 | −0.990235 | −0.495117 | − | 0.868826i | \(-0.664875\pi\) | ||||
−0.495117 | + | 0.868826i | \(0.664875\pi\) | |||||||
\(380\) | 9.07927e14 | 5.87816 | ||||||||
\(381\) | 3.51672e13 | 0.224414 | ||||||||
\(382\) | −1.22203e14 | −0.768658 | ||||||||
\(383\) | −8.05851e13 | −0.499645 | −0.249823 | − | 0.968292i | \(-0.580372\pi\) | ||||
−0.249823 | + | 0.968292i | \(0.580372\pi\) | |||||||
\(384\) | 2.67123e14 | 1.63264 | ||||||||
\(385\) | 7.44852e13 | 0.448783 | ||||||||
\(386\) | 3.13882e14 | 1.86439 | ||||||||
\(387\) | −2.51493e13 | −0.147270 | ||||||||
\(388\) | 2.18286e13 | 0.126024 | ||||||||
\(389\) | 2.01229e13 | 0.114543 | 0.0572714 | − | 0.998359i | \(-0.481760\pi\) | ||||
0.0572714 | + | 0.998359i | \(0.481760\pi\) | |||||||
\(390\) | −5.07572e14 | −2.84867 | ||||||||
\(391\) | −2.14796e14 | −1.18865 | ||||||||
\(392\) | −1.60713e14 | −0.876957 | ||||||||
\(393\) | 6.77787e13 | 0.364699 | ||||||||
\(394\) | 2.56868e13 | 0.136295 | ||||||||
\(395\) | 2.38351e14 | 1.24719 | ||||||||
\(396\) | −7.10634e13 | −0.366710 | ||||||||
\(397\) | 1.21538e14 | 0.618536 | 0.309268 | − | 0.950975i | \(-0.399916\pi\) | ||||
0.309268 | + | 0.950975i | \(0.399916\pi\) | |||||||
\(398\) | −6.12141e14 | −3.07252 | ||||||||
\(399\) | −2.23211e14 | −1.10501 | ||||||||
\(400\) | 9.61147e14 | 4.69310 | ||||||||
\(401\) | −1.70320e14 | −0.820298 | −0.410149 | − | 0.912019i | \(-0.634523\pi\) | ||||
−0.410149 | + | 0.912019i | \(0.634523\pi\) | |||||||
\(402\) | 3.73244e14 | 1.77317 | ||||||||
\(403\) | 1.04097e14 | 0.487822 | ||||||||
\(404\) | −1.00320e15 | −4.63759 | ||||||||
\(405\) | 6.04922e13 | 0.275865 | ||||||||
\(406\) | 1.70750e14 | 0.768186 | ||||||||
\(407\) | 9.06348e13 | 0.402278 | ||||||||
\(408\) | 3.97993e14 | 1.74279 | ||||||||
\(409\) | −2.53767e14 | −1.09637 | −0.548186 | − | 0.836357i | \(-0.684681\pi\) | ||||
−0.548186 | + | 0.836357i | \(0.684681\pi\) | |||||||
\(410\) | 2.53663e14 | 1.08130 | ||||||||
\(411\) | 2.11274e14 | 0.888622 | ||||||||
\(412\) | 2.38546e14 | 0.990007 | ||||||||
\(413\) | −7.79087e13 | −0.319051 | ||||||||
\(414\) | −3.73909e14 | −1.51100 | ||||||||
\(415\) | −7.72638e13 | −0.308114 | ||||||||
\(416\) | −1.20811e15 | −4.75437 | ||||||||
\(417\) | 4.69276e13 | 0.182255 | ||||||||
\(418\) | 1.84526e14 | 0.707274 | ||||||||
\(419\) | −2.74281e14 | −1.03757 | −0.518786 | − | 0.854904i | \(-0.673616\pi\) | ||||
−0.518786 | + | 0.854904i | \(0.673616\pi\) | |||||||
\(420\) | −8.45742e14 | −3.15767 | ||||||||
\(421\) | −3.68411e14 | −1.35763 | −0.678815 | − | 0.734310i | \(-0.737506\pi\) | ||||
−0.678815 | + | 0.734310i | \(0.737506\pi\) | |||||||
\(422\) | 1.03069e14 | 0.374897 | ||||||||
\(423\) | 2.76700e14 | 0.993429 | ||||||||
\(424\) | 1.24114e15 | 4.39853 | ||||||||
\(425\) | 3.16337e14 | 1.10665 | ||||||||
\(426\) | 2.13339e14 | 0.736746 | ||||||||
\(427\) | 3.87062e14 | 1.31955 | ||||||||
\(428\) | −8.84083e14 | −2.97545 | ||||||||
\(429\) | −7.49694e13 | −0.249097 | ||||||||
\(430\) | 2.47434e14 | 0.811676 | ||||||||
\(431\) | 2.94489e13 | 0.0953770 | 0.0476885 | − | 0.998862i | \(-0.484815\pi\) | ||||
0.0476885 | + | 0.998862i | \(0.484815\pi\) | |||||||
\(432\) | 1.11745e15 | 3.57330 | ||||||||
\(433\) | 4.56308e14 | 1.44070 | 0.720351 | − | 0.693610i | \(-0.243981\pi\) | ||||
0.720351 | + | 0.693610i | \(0.243981\pi\) | |||||||
\(434\) | 2.38671e14 | 0.744056 | ||||||||
\(435\) | 1.21360e14 | 0.373580 | ||||||||
\(436\) | −1.44005e15 | −4.37724 | ||||||||
\(437\) | 7.05599e14 | 2.11792 | ||||||||
\(438\) | −4.50072e14 | −1.33406 | ||||||||
\(439\) | −8.72119e13 | −0.255282 | −0.127641 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127641 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(440\) | 4.36276e14 | 1.26116 | ||||||||
\(441\) | −5.17549e13 | −0.147754 | ||||||||
\(442\) | −7.73809e14 | −2.18178 | ||||||||
\(443\) | 1.35402e14 | 0.377054 | 0.188527 | − | 0.982068i | \(-0.439629\pi\) | ||||
0.188527 | + | 0.982068i | \(0.439629\pi\) | |||||||
\(444\) | −1.02911e15 | −2.83046 | ||||||||
\(445\) | −3.96851e14 | −1.07807 | ||||||||
\(446\) | 8.42358e14 | 2.26024 | ||||||||
\(447\) | 4.11936e14 | 1.09179 | ||||||||
\(448\) | −1.29690e15 | −3.39529 | ||||||||
\(449\) | −2.35281e14 | −0.608460 | −0.304230 | − | 0.952599i | \(-0.598399\pi\) | ||||
−0.304230 | + | 0.952599i | \(0.598399\pi\) | |||||||
\(450\) | 5.50668e14 | 1.40676 | ||||||||
\(451\) | 3.74666e13 | 0.0945525 | ||||||||
\(452\) | −9.22005e14 | −2.29864 | ||||||||
\(453\) | 2.42850e13 | 0.0598132 | ||||||||
\(454\) | 2.54149e14 | 0.618418 | ||||||||
\(455\) | 1.02607e15 | 2.46669 | ||||||||
\(456\) | −1.30739e15 | −3.10527 | ||||||||
\(457\) | −5.78531e14 | −1.35765 | −0.678825 | − | 0.734300i | \(-0.737510\pi\) | ||||
−0.678825 | + | 0.734300i | \(0.737510\pi\) | |||||||
\(458\) | 8.22846e14 | 1.90791 | ||||||||
\(459\) | 3.67782e14 | 0.842598 | ||||||||
\(460\) | 2.67350e15 | 6.05218 | ||||||||
\(461\) | −2.60112e14 | −0.581842 | −0.290921 | − | 0.956747i | \(-0.593962\pi\) | ||||
−0.290921 | + | 0.956747i | \(0.593962\pi\) | |||||||
\(462\) | −1.71888e14 | −0.379939 | ||||||||
\(463\) | 5.07415e14 | 1.10833 | 0.554164 | − | 0.832408i | \(-0.313038\pi\) | ||||
0.554164 | + | 0.832408i | \(0.313038\pi\) | |||||||
\(464\) | 5.62147e14 | 1.21339 | ||||||||
\(465\) | 1.69635e14 | 0.361845 | ||||||||
\(466\) | −6.02981e14 | −1.27110 | ||||||||
\(467\) | −8.80591e14 | −1.83456 | −0.917279 | − | 0.398245i | \(-0.869619\pi\) | ||||
−0.917279 | + | 0.398245i | \(0.869619\pi\) | |||||||
\(468\) | −9.78933e14 | −2.01558 | ||||||||
\(469\) | −7.54523e14 | −1.53540 | ||||||||
\(470\) | −2.72234e15 | −5.47526 | ||||||||
\(471\) | −2.03751e14 | −0.405027 | ||||||||
\(472\) | −4.56327e14 | −0.896593 | ||||||||
\(473\) | 3.65465e13 | 0.0709756 | ||||||||
\(474\) | −5.50036e14 | −1.05587 | ||||||||
\(475\) | −1.03916e15 | −1.97182 | ||||||||
\(476\) | −1.28936e15 | −2.41844 | ||||||||
\(477\) | 3.99686e14 | 0.741085 | ||||||||
\(478\) | 8.36455e13 | 0.153317 | ||||||||
\(479\) | −6.61023e14 | −1.19776 | −0.598882 | − | 0.800837i | \(-0.704388\pi\) | ||||
−0.598882 | + | 0.800837i | \(0.704388\pi\) | |||||||
\(480\) | −1.96871e15 | −3.52659 | ||||||||
\(481\) | 1.24854e15 | 2.21108 | ||||||||
\(482\) | −1.26776e15 | −2.21962 | ||||||||
\(483\) | −6.57271e14 | −1.13772 | ||||||||
\(484\) | −1.45075e15 | −2.48281 | ||||||||
\(485\) | −4.31559e13 | −0.0730232 | ||||||||
\(486\) | 1.05733e15 | 1.76894 | ||||||||
\(487\) | 6.47398e14 | 1.07093 | 0.535466 | − | 0.844557i | \(-0.320136\pi\) | ||||
0.535466 | + | 0.844557i | \(0.320136\pi\) | |||||||
\(488\) | 2.26710e15 | 3.70819 | ||||||||
\(489\) | −5.82291e14 | −0.941763 | ||||||||
\(490\) | 5.09196e14 | 0.814342 | ||||||||
\(491\) | 6.23604e14 | 0.986190 | 0.493095 | − | 0.869975i | \(-0.335865\pi\) | ||||
0.493095 | + | 0.869975i | \(0.335865\pi\) | |||||||
\(492\) | −4.25414e14 | −0.665279 | ||||||||
\(493\) | 1.85017e14 | 0.286123 | ||||||||
\(494\) | 2.54194e15 | 3.88746 | ||||||||
\(495\) | 1.40495e14 | 0.212487 | ||||||||
\(496\) | 7.85760e14 | 1.17528 | ||||||||
\(497\) | −4.31271e14 | −0.637955 | ||||||||
\(498\) | 1.78300e14 | 0.260849 | ||||||||
\(499\) | −5.85885e14 | −0.847734 | −0.423867 | − | 0.905724i | \(-0.639328\pi\) | ||||
−0.423867 | + | 0.905724i | \(0.639328\pi\) | |||||||
\(500\) | −1.07345e15 | −1.53620 | ||||||||
\(501\) | −2.96509e14 | −0.419692 | ||||||||
\(502\) | 1.93716e15 | 2.71204 | ||||||||
\(503\) | −7.59409e13 | −0.105160 | −0.0525801 | − | 0.998617i | \(-0.516744\pi\) | ||||
−0.0525801 | + | 0.998617i | \(0.516744\pi\) | |||||||
\(504\) | −1.40054e15 | −1.91834 | ||||||||
\(505\) | 1.98337e15 | 2.68721 | ||||||||
\(506\) | 5.43359e14 | 0.728214 | ||||||||
\(507\) | −5.18313e14 | −0.687145 | ||||||||
\(508\) | −6.67310e14 | −0.875139 | ||||||||
\(509\) | 1.24817e15 | 1.61929 | 0.809645 | − | 0.586920i | \(-0.199660\pi\) | ||||
0.809645 | + | 0.586920i | \(0.199660\pi\) | |||||||
\(510\) | −1.26098e15 | −1.61835 | ||||||||
\(511\) | 9.09833e14 | 1.15517 | ||||||||
\(512\) | −4.91443e14 | −0.617289 | ||||||||
\(513\) | −1.20815e15 | −1.50133 | ||||||||
\(514\) | −1.81634e15 | −2.23306 | ||||||||
\(515\) | −4.71615e14 | −0.573651 | ||||||||
\(516\) | −4.14967e14 | −0.499390 | ||||||||
\(517\) | −4.02096e14 | −0.478775 | ||||||||
\(518\) | 2.86261e15 | 3.37248 | ||||||||
\(519\) | 5.08275e14 | 0.592486 | ||||||||
\(520\) | 6.00991e15 | 6.93186 | ||||||||
\(521\) | −6.33330e14 | −0.722808 | −0.361404 | − | 0.932409i | \(-0.617702\pi\) | ||||
−0.361404 | + | 0.932409i | \(0.617702\pi\) | |||||||
\(522\) | 3.22070e14 | 0.363716 | ||||||||
\(523\) | 1.66720e15 | 1.86306 | 0.931531 | − | 0.363663i | \(-0.118474\pi\) | ||||
0.931531 | + | 0.363663i | \(0.118474\pi\) | |||||||
\(524\) | −1.28612e15 | −1.42220 | ||||||||
\(525\) | 9.67984e14 | 1.05923 | ||||||||
\(526\) | −1.77650e15 | −1.92373 | ||||||||
\(527\) | 2.58613e14 | 0.277135 | ||||||||
\(528\) | −5.65894e14 | −0.600134 | ||||||||
\(529\) | 1.12491e15 | 1.18062 | ||||||||
\(530\) | −3.93236e15 | −4.08447 | ||||||||
\(531\) | −1.46952e14 | −0.151062 | ||||||||
\(532\) | 4.23550e15 | 4.30914 | ||||||||
\(533\) | 5.16120e14 | 0.519698 | ||||||||
\(534\) | 9.15803e14 | 0.912694 | ||||||||
\(535\) | 1.74786e15 | 1.72410 | ||||||||
\(536\) | −4.41940e15 | −4.31476 | ||||||||
\(537\) | 5.17221e14 | 0.499824 | ||||||||
\(538\) | 2.95340e15 | 2.82501 | ||||||||
\(539\) | 7.52093e13 | 0.0712088 | ||||||||
\(540\) | −4.57766e15 | −4.29020 | ||||||||
\(541\) | 6.70038e14 | 0.621605 | 0.310802 | − | 0.950475i | \(-0.399402\pi\) | ||||
0.310802 | + | 0.950475i | \(0.399402\pi\) | |||||||
\(542\) | −2.74513e15 | −2.52097 | ||||||||
\(543\) | 1.27911e15 | 1.16281 | ||||||||
\(544\) | −3.00136e15 | −2.70099 | ||||||||
\(545\) | 2.84702e15 | 2.53636 | ||||||||
\(546\) | −2.36784e15 | −2.08830 | ||||||||
\(547\) | −2.04406e15 | −1.78470 | −0.892348 | − | 0.451348i | \(-0.850943\pi\) | ||||
−0.892348 | + | 0.451348i | \(0.850943\pi\) | |||||||
\(548\) | −4.00900e15 | −3.46532 | ||||||||
\(549\) | 7.30081e14 | 0.624774 | ||||||||
\(550\) | −8.00221e14 | −0.677977 | ||||||||
\(551\) | −6.07773e14 | −0.509809 | ||||||||
\(552\) | −3.84978e15 | −3.19721 | ||||||||
\(553\) | 1.11191e15 | 0.914286 | ||||||||
\(554\) | −3.23579e15 | −2.63437 | ||||||||
\(555\) | 2.03459e15 | 1.64008 | ||||||||
\(556\) | −8.90468e14 | −0.710733 | ||||||||
\(557\) | −7.15674e14 | −0.565603 | −0.282801 | − | 0.959179i | \(-0.591264\pi\) | ||||
−0.282801 | + | 0.959179i | \(0.591264\pi\) | |||||||
\(558\) | 4.50184e14 | 0.352291 | ||||||||
\(559\) | 5.03446e14 | 0.390111 | ||||||||
\(560\) | 7.74512e15 | 5.94284 | ||||||||
\(561\) | −1.86250e14 | −0.141514 | ||||||||
\(562\) | 4.50315e14 | 0.338818 | ||||||||
\(563\) | −3.38439e14 | −0.252164 | −0.126082 | − | 0.992020i | \(-0.540240\pi\) | ||||
−0.126082 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(564\) | 4.56559e15 | 3.36870 | ||||||||
\(565\) | 1.82284e15 | 1.33193 | ||||||||
\(566\) | −5.44702e13 | −0.0394156 | ||||||||
\(567\) | 2.82198e14 | 0.202231 | ||||||||
\(568\) | −2.52604e15 | −1.79277 | ||||||||
\(569\) | 1.78757e14 | 0.125645 | 0.0628225 | − | 0.998025i | \(-0.479990\pi\) | ||||
0.0628225 | + | 0.998025i | \(0.479990\pi\) | |||||||
\(570\) | 4.14228e15 | 2.88355 | ||||||||
\(571\) | 3.91659e14 | 0.270028 | 0.135014 | − | 0.990844i | \(-0.456892\pi\) | ||||
0.135014 | + | 0.990844i | \(0.456892\pi\) | |||||||
\(572\) | 1.42257e15 | 0.971394 | ||||||||
\(573\) | −4.05182e14 | −0.274031 | ||||||||
\(574\) | 1.18334e15 | 0.792676 | ||||||||
\(575\) | −3.05992e15 | −2.03019 | ||||||||
\(576\) | −2.44623e15 | −1.60758 | ||||||||
\(577\) | 5.05916e14 | 0.329315 | 0.164658 | − | 0.986351i | \(-0.447348\pi\) | ||||
0.164658 | + | 0.986351i | \(0.447348\pi\) | |||||||
\(578\) | 1.04458e15 | 0.673505 | ||||||||
\(579\) | 1.04072e15 | 0.664666 | ||||||||
\(580\) | −2.30284e15 | −1.45683 | ||||||||
\(581\) | −3.60438e14 | −0.225871 | ||||||||
\(582\) | 9.95898e13 | 0.0618213 | ||||||||
\(583\) | −5.80817e14 | −0.357159 | ||||||||
\(584\) | 5.32908e15 | 3.24625 | ||||||||
\(585\) | 1.93539e15 | 1.16791 | ||||||||
\(586\) | −1.27359e15 | −0.761367 | ||||||||
\(587\) | 1.73810e15 | 1.02936 | 0.514678 | − | 0.857384i | \(-0.327912\pi\) | ||||
0.514678 | + | 0.857384i | \(0.327912\pi\) | |||||||
\(588\) | −8.53964e14 | −0.501031 | ||||||||
\(589\) | −8.49535e14 | −0.493795 | ||||||||
\(590\) | 1.44581e15 | 0.832576 | ||||||||
\(591\) | 8.51683e13 | 0.0485900 | ||||||||
\(592\) | 9.42439e15 | 5.32701 | ||||||||
\(593\) | −1.47703e15 | −0.827156 | −0.413578 | − | 0.910469i | \(-0.635721\pi\) | ||||
−0.413578 | + | 0.910469i | \(0.635721\pi\) | |||||||
\(594\) | −9.30357e14 | −0.516208 | ||||||||
\(595\) | 2.54911e15 | 1.40135 | ||||||||
\(596\) | −7.81662e15 | −4.25760 | ||||||||
\(597\) | −2.02965e15 | −1.09537 | ||||||||
\(598\) | 7.48503e15 | 4.00255 | ||||||||
\(599\) | −2.58595e15 | −1.37016 | −0.685081 | − | 0.728467i | \(-0.740233\pi\) | ||||
−0.685081 | + | 0.728467i | \(0.740233\pi\) | |||||||
\(600\) | 5.66968e15 | 2.97664 | ||||||||
\(601\) | −2.84322e15 | −1.47911 | −0.739555 | − | 0.673096i | \(-0.764964\pi\) | ||||
−0.739555 | + | 0.673096i | \(0.764964\pi\) | |||||||
\(602\) | 1.15429e15 | 0.595021 | ||||||||
\(603\) | −1.42319e15 | −0.726972 | ||||||||
\(604\) | −4.60815e14 | −0.233251 | ||||||||
\(605\) | 2.86818e15 | 1.43864 | ||||||||
\(606\) | −4.57697e15 | −2.27499 | ||||||||
\(607\) | −5.45615e14 | −0.268750 | −0.134375 | − | 0.990931i | \(-0.542903\pi\) | ||||
−0.134375 | + | 0.990931i | \(0.542903\pi\) | |||||||
\(608\) | 9.85935e15 | 4.81259 | ||||||||
\(609\) | 5.66146e14 | 0.273863 | ||||||||
\(610\) | −7.18298e15 | −3.44343 | ||||||||
\(611\) | −5.53907e15 | −2.63154 | ||||||||
\(612\) | −2.43200e15 | −1.14507 | ||||||||
\(613\) | −3.67185e15 | −1.71338 | −0.856688 | − | 0.515834i | \(-0.827482\pi\) | ||||
−0.856688 | + | 0.515834i | \(0.827482\pi\) | |||||||
\(614\) | −5.40811e15 | −2.50104 | ||||||||
\(615\) | 8.41058e14 | 0.385490 | ||||||||
\(616\) | 2.03524e15 | 0.924530 | ||||||||
\(617\) | 3.26263e15 | 1.46893 | 0.734463 | − | 0.678648i | \(-0.237434\pi\) | ||||
0.734463 | + | 0.678648i | \(0.237434\pi\) | |||||||
\(618\) | 1.08833e15 | 0.485652 | ||||||||
\(619\) | 1.64075e15 | 0.725676 | 0.362838 | − | 0.931852i | \(-0.381808\pi\) | ||||
0.362838 | + | 0.931852i | \(0.381808\pi\) | |||||||
\(620\) | −3.21887e15 | −1.41107 | ||||||||
\(621\) | −3.55754e15 | −1.54577 | ||||||||
\(622\) | 2.90509e15 | 1.25116 | ||||||||
\(623\) | −1.85132e15 | −0.790310 | ||||||||
\(624\) | −7.79546e15 | −3.29858 | ||||||||
\(625\) | −1.15558e15 | −0.484685 | ||||||||
\(626\) | −7.30905e15 | −3.03880 | ||||||||
\(627\) | 6.11824e14 | 0.252148 | ||||||||
\(628\) | 3.86624e15 | 1.57947 | ||||||||
\(629\) | 3.10180e15 | 1.25613 | ||||||||
\(630\) | 4.43739e15 | 1.78137 | ||||||||
\(631\) | −3.46678e15 | −1.37964 | −0.689818 | − | 0.723983i | \(-0.742310\pi\) | ||||
−0.689818 | + | 0.723983i | \(0.742310\pi\) | |||||||
\(632\) | 6.51270e15 | 2.56931 | ||||||||
\(633\) | 3.41742e14 | 0.133653 | ||||||||
\(634\) | 6.73632e15 | 2.61175 | ||||||||
\(635\) | 1.31929e15 | 0.507092 | ||||||||
\(636\) | 6.59488e15 | 2.51300 | ||||||||
\(637\) | 1.03605e15 | 0.391392 | ||||||||
\(638\) | −4.68026e14 | −0.175290 | ||||||||
\(639\) | −8.13468e14 | −0.302055 | ||||||||
\(640\) | 1.00211e16 | 3.68914 | ||||||||
\(641\) | −1.65515e15 | −0.604111 | −0.302056 | − | 0.953290i | \(-0.597673\pi\) | ||||
−0.302056 | + | 0.953290i | \(0.597673\pi\) | |||||||
\(642\) | −4.03350e15 | −1.45962 | ||||||||
\(643\) | 2.68040e14 | 0.0961701 | 0.0480850 | − | 0.998843i | \(-0.484688\pi\) | ||||
0.0480850 | + | 0.998843i | \(0.484688\pi\) | |||||||
\(644\) | 1.24719e16 | 4.43672 | ||||||||
\(645\) | 8.20404e14 | 0.289367 | ||||||||
\(646\) | 6.31504e15 | 2.20850 | ||||||||
\(647\) | 1.15109e15 | 0.399151 | 0.199575 | − | 0.979882i | \(-0.436044\pi\) | ||||
0.199575 | + | 0.979882i | \(0.436044\pi\) | |||||||
\(648\) | 1.65289e15 | 0.568305 | ||||||||
\(649\) | 2.13548e14 | 0.0728032 | ||||||||
\(650\) | −1.10234e16 | −3.72644 | ||||||||
\(651\) | 7.91349e14 | 0.265261 | ||||||||
\(652\) | 1.10492e16 | 3.67255 | ||||||||
\(653\) | −2.70126e15 | −0.890316 | −0.445158 | − | 0.895452i | \(-0.646852\pi\) | ||||
−0.445158 | + | 0.895452i | \(0.646852\pi\) | |||||||
\(654\) | −6.57000e15 | −2.14727 | ||||||||
\(655\) | 2.54271e15 | 0.824081 | ||||||||
\(656\) | 3.89585e15 | 1.25208 | ||||||||
\(657\) | 1.71614e15 | 0.546943 | ||||||||
\(658\) | −1.26998e16 | −4.01379 | ||||||||
\(659\) | −2.06804e14 | −0.0648170 | −0.0324085 | − | 0.999475i | \(-0.510318\pi\) | ||||
−0.0324085 | + | 0.999475i | \(0.510318\pi\) | |||||||
\(660\) | 2.31819e15 | 0.720538 | ||||||||
\(661\) | 4.36563e15 | 1.34567 | 0.672836 | − | 0.739792i | \(-0.265076\pi\) | ||||
0.672836 | + | 0.739792i | \(0.265076\pi\) | |||||||
\(662\) | −1.02586e16 | −3.13594 | ||||||||
\(663\) | −2.56568e15 | −0.777818 | ||||||||
\(664\) | −2.11116e15 | −0.634741 | ||||||||
\(665\) | −8.37374e15 | −2.49690 | ||||||||
\(666\) | 5.39949e15 | 1.59678 | ||||||||
\(667\) | −1.78966e15 | −0.524902 | ||||||||
\(668\) | 5.62636e15 | 1.63666 | ||||||||
\(669\) | 2.79297e15 | 0.805790 | ||||||||
\(670\) | 1.40022e16 | 4.00669 | ||||||||
\(671\) | −1.06094e15 | −0.301105 | ||||||||
\(672\) | −9.18407e15 | −2.58526 | ||||||||
\(673\) | −2.70502e15 | −0.755244 | −0.377622 | − | 0.925960i | \(-0.623258\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(674\) | −6.13334e15 | −1.69851 | ||||||||
\(675\) | 5.23930e15 | 1.43914 | ||||||||
\(676\) | 9.83517e15 | 2.67963 | ||||||||
\(677\) | −3.32057e14 | −0.0897376 | −0.0448688 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448688 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(678\) | −4.20651e15 | −1.12761 | ||||||||
\(679\) | −2.01323e14 | −0.0535317 | ||||||||
\(680\) | 1.49307e16 | 3.93804 | ||||||||
\(681\) | 8.42671e14 | 0.220470 | ||||||||
\(682\) | −6.54199e14 | −0.169784 | ||||||||
\(683\) | 1.95787e15 | 0.504047 | 0.252023 | − | 0.967721i | \(-0.418904\pi\) | ||||
0.252023 | + | 0.967721i | \(0.418904\pi\) | |||||||
\(684\) | 7.98905e15 | 2.04027 | ||||||||
\(685\) | 7.92594e15 | 2.00795 | ||||||||
\(686\) | −6.22385e15 | −1.56414 | ||||||||
\(687\) | 2.72827e15 | 0.680182 | ||||||||
\(688\) | 3.80018e15 | 0.939869 | ||||||||
\(689\) | −8.00104e15 | −1.96309 | ||||||||
\(690\) | 1.21974e16 | 2.96892 | ||||||||
\(691\) | −2.61062e15 | −0.630397 | −0.315199 | − | 0.949026i | \(-0.602071\pi\) | ||||
−0.315199 | + | 0.949026i | \(0.602071\pi\) | |||||||
\(692\) | −9.64468e15 | −2.31049 | ||||||||
\(693\) | 6.55412e14 | 0.155769 | ||||||||
\(694\) | −1.15437e16 | −2.72187 | ||||||||
\(695\) | 1.76049e15 | 0.411828 | ||||||||
\(696\) | 3.31603e15 | 0.769606 | ||||||||
\(697\) | 1.28222e15 | 0.295245 | ||||||||
\(698\) | 1.40637e16 | 3.21289 | ||||||||
\(699\) | −1.99928e15 | −0.453156 | ||||||||
\(700\) | −1.83678e16 | −4.13065 | ||||||||
\(701\) | 4.45543e15 | 0.994125 | 0.497062 | − | 0.867715i | \(-0.334412\pi\) | ||||
0.497062 | + | 0.867715i | \(0.334412\pi\) | |||||||
\(702\) | −1.28161e16 | −2.83728 | ||||||||
\(703\) | −1.01893e16 | −2.23815 | ||||||||
\(704\) | 3.55482e15 | 0.774761 | ||||||||
\(705\) | −9.02634e15 | −1.95196 | ||||||||
\(706\) | 8.94368e15 | 1.91907 | ||||||||
\(707\) | 9.25248e15 | 1.96993 | ||||||||
\(708\) | −2.42473e15 | −0.512249 | ||||||||
\(709\) | 3.60048e14 | 0.0754756 | 0.0377378 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377378 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(710\) | 8.00340e15 | 1.66477 | ||||||||
\(711\) | 2.09730e15 | 0.432890 | ||||||||
\(712\) | −1.08436e16 | −2.22092 | ||||||||
\(713\) | −2.50156e15 | −0.508414 | ||||||||
\(714\) | −5.88251e15 | −1.18638 | ||||||||
\(715\) | −2.81247e15 | −0.562866 | ||||||||
\(716\) | −9.81444e15 | −1.94914 | ||||||||
\(717\) | 2.77339e14 | 0.0546583 | ||||||||
\(718\) | −1.17201e16 | −2.29217 | ||||||||
\(719\) | 7.57262e14 | 0.146973 | 0.0734864 | − | 0.997296i | \(-0.476587\pi\) | ||||
0.0734864 | + | 0.997296i | \(0.476587\pi\) | |||||||
\(720\) | 1.46089e16 | 2.81378 | ||||||||
\(721\) | −2.20009e15 | −0.420530 | ||||||||
\(722\) | −1.06599e16 | −2.02208 | ||||||||
\(723\) | −4.20345e15 | −0.791307 | ||||||||
\(724\) | −2.42714e16 | −4.53454 | ||||||||
\(725\) | 2.63569e15 | 0.488692 | ||||||||
\(726\) | −6.61882e15 | −1.21795 | ||||||||
\(727\) | −4.77912e15 | −0.872789 | −0.436394 | − | 0.899756i | \(-0.643745\pi\) | ||||
−0.436394 | + | 0.899756i | \(0.643745\pi\) | |||||||
\(728\) | 2.80364e16 | 5.08159 | ||||||||
\(729\) | 4.50088e15 | 0.809648 | ||||||||
\(730\) | −1.68844e16 | −3.01446 | ||||||||
\(731\) | 1.25073e15 | 0.221625 | ||||||||
\(732\) | 1.20465e16 | 2.11860 | ||||||||
\(733\) | 1.92867e14 | 0.0336656 | 0.0168328 | − | 0.999858i | \(-0.494642\pi\) | ||||
0.0168328 | + | 0.999858i | \(0.494642\pi\) | |||||||
\(734\) | 1.84063e16 | 3.18888 | ||||||||
\(735\) | 1.68832e15 | 0.290318 | ||||||||
\(736\) | 2.90320e16 | 4.95507 | ||||||||
\(737\) | 2.06816e15 | 0.350358 | ||||||||
\(738\) | 2.23204e15 | 0.375311 | ||||||||
\(739\) | 8.60815e15 | 1.43670 | 0.718349 | − | 0.695683i | \(-0.244898\pi\) | ||||
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(740\) | −3.86071e16 | −6.39576 | ||||||||
\(741\) | 8.42817e15 | 1.38590 | ||||||||
\(742\) | −1.83445e16 | −2.99423 | ||||||||
\(743\) | 5.66593e15 | 0.917979 | 0.458990 | − | 0.888442i | \(-0.348212\pi\) | ||||
0.458990 | + | 0.888442i | \(0.348212\pi\) | |||||||
\(744\) | 4.63510e15 | 0.745431 | ||||||||
\(745\) | 1.54537e16 | 2.46703 | ||||||||
\(746\) | 1.60885e16 | 2.54948 | ||||||||
\(747\) | −6.79861e14 | −0.106944 | ||||||||
\(748\) | 3.53415e15 | 0.551856 | ||||||||
\(749\) | 8.15383e15 | 1.26390 | ||||||||
\(750\) | −4.89747e15 | −0.753589 | ||||||||
\(751\) | −1.28689e16 | −1.96572 | −0.982862 | − | 0.184341i | \(-0.940985\pi\) | ||||
−0.982862 | + | 0.184341i | \(0.940985\pi\) | |||||||
\(752\) | −4.18107e16 | −6.34000 | ||||||||
\(753\) | 6.42296e15 | 0.966858 | ||||||||
\(754\) | −6.44729e15 | −0.963463 | ||||||||
\(755\) | 9.11048e14 | 0.135155 | ||||||||
\(756\) | −2.13549e16 | −3.14505 | ||||||||
\(757\) | −4.18693e15 | −0.612164 | −0.306082 | − | 0.952005i | \(-0.599018\pi\) | ||||
−0.306082 | + | 0.952005i | \(0.599018\pi\) | |||||||
\(758\) | 1.30506e16 | 1.89431 | ||||||||
\(759\) | 1.80159e15 | 0.259612 | ||||||||
\(760\) | −4.90468e16 | −7.01674 | ||||||||
\(761\) | −6.59676e15 | −0.936948 | −0.468474 | − | 0.883477i | \(-0.655196\pi\) | ||||
−0.468474 | + | 0.883477i | \(0.655196\pi\) | |||||||
\(762\) | −3.04450e15 | −0.429303 | ||||||||
\(763\) | 1.32814e16 | 1.85934 | ||||||||
\(764\) | 7.68846e15 | 1.06863 | ||||||||
\(765\) | 4.80816e15 | 0.663500 | ||||||||
\(766\) | 6.97642e15 | 0.955817 | ||||||||
\(767\) | 2.94173e15 | 0.400156 | ||||||||
\(768\) | −7.94867e15 | −1.07351 | ||||||||
\(769\) | −3.82006e15 | −0.512242 | −0.256121 | − | 0.966645i | \(-0.582445\pi\) | ||||
−0.256121 | + | 0.966645i | \(0.582445\pi\) | |||||||
\(770\) | −6.44835e15 | −0.858518 | ||||||||
\(771\) | −6.02235e15 | −0.796099 | ||||||||
\(772\) | −1.97481e16 | −2.59197 | ||||||||
\(773\) | 6.98362e15 | 0.910108 | 0.455054 | − | 0.890464i | \(-0.349620\pi\) | ||||
0.455054 | + | 0.890464i | \(0.349620\pi\) | |||||||
\(774\) | 2.17723e15 | 0.281727 | ||||||||
\(775\) | 3.68412e15 | 0.473341 | ||||||||
\(776\) | −1.17919e15 | −0.150434 | ||||||||
\(777\) | 9.49142e15 | 1.20231 | ||||||||
\(778\) | −1.74208e15 | −0.219120 | ||||||||
\(779\) | −4.21205e15 | −0.526062 | ||||||||
\(780\) | 3.19342e16 | 3.96037 | ||||||||
\(781\) | 1.18212e15 | 0.145573 | ||||||||
\(782\) | 1.85954e16 | 2.27388 | ||||||||
\(783\) | 3.06432e15 | 0.372087 | ||||||||
\(784\) | 7.82041e15 | 0.942956 | ||||||||
\(785\) | −7.64369e15 | −0.915209 | ||||||||
\(786\) | −5.86775e15 | −0.697666 | ||||||||
\(787\) | 1.25624e16 | 1.48324 | 0.741618 | − | 0.670823i | \(-0.234059\pi\) | ||||
0.741618 | + | 0.670823i | \(0.234059\pi\) | |||||||
\(788\) | −1.61610e15 | −0.189484 | ||||||||
\(789\) | −5.89026e15 | −0.685822 | ||||||||
\(790\) | −2.06345e16 | −2.38586 | ||||||||
\(791\) | 8.50358e15 | 0.976407 | ||||||||
\(792\) | 3.83888e15 | 0.437740 | ||||||||
\(793\) | −1.46150e16 | −1.65499 | ||||||||
\(794\) | −1.05218e16 | −1.18325 | ||||||||
\(795\) | −1.30383e16 | −1.45614 | ||||||||
\(796\) | 3.85132e16 | 4.27157 | ||||||||
\(797\) | 9.12350e15 | 1.00494 | 0.502471 | − | 0.864594i | \(-0.332424\pi\) | ||||
0.502471 | + | 0.864594i | \(0.332424\pi\) | |||||||
\(798\) | 1.93239e16 | 2.11387 | ||||||||
\(799\) | −1.37609e16 | −1.49500 | ||||||||
\(800\) | −4.27564e16 | −4.61324 | ||||||||
\(801\) | −3.49198e15 | −0.374191 | ||||||||
\(802\) | 1.47450e16 | 1.56922 | ||||||||
\(803\) | −2.49386e15 | −0.263595 | ||||||||
\(804\) | −2.34829e16 | −2.46515 | ||||||||
\(805\) | −2.46575e16 | −2.57082 | ||||||||
\(806\) | −9.01191e15 | −0.933199 | ||||||||
\(807\) | 9.79244e15 | 1.00713 | ||||||||
\(808\) | 5.41937e16 | 5.53587 | ||||||||
\(809\) | 1.40131e16 | 1.42174 | 0.710868 | − | 0.703326i | \(-0.248303\pi\) | ||||
0.710868 | + | 0.703326i | \(0.248303\pi\) | |||||||
\(810\) | −5.23694e15 | −0.527728 | ||||||||
\(811\) | −9.89235e15 | −0.990114 | −0.495057 | − | 0.868861i | \(-0.664853\pi\) | ||||
−0.495057 | + | 0.868861i | \(0.664853\pi\) | |||||||
\(812\) | −1.07428e16 | −1.06797 | ||||||||
\(813\) | −9.10191e15 | −0.898741 | ||||||||
\(814\) | −7.84645e15 | −0.769554 | ||||||||
\(815\) | −2.18446e16 | −2.12803 | ||||||||
\(816\) | −1.93666e16 | −1.87395 | ||||||||
\(817\) | −4.10861e15 | −0.394888 | ||||||||
\(818\) | 2.19692e16 | 2.09735 | ||||||||
\(819\) | 9.02862e15 | 0.856170 | ||||||||
\(820\) | −1.59594e16 | −1.50328 | ||||||||
\(821\) | −4.49746e15 | −0.420804 | −0.210402 | − | 0.977615i | \(-0.567477\pi\) | ||||
−0.210402 | + | 0.977615i | \(0.567477\pi\) | |||||||
\(822\) | −1.82905e16 | −1.69993 | ||||||||
\(823\) | −6.75910e15 | −0.624007 | −0.312004 | − | 0.950081i | \(-0.601000\pi\) | ||||
−0.312004 | + | 0.950081i | \(0.601000\pi\) | |||||||
\(824\) | −1.28864e16 | −1.18177 | ||||||||
\(825\) | −2.65325e15 | −0.241703 | ||||||||
\(826\) | 6.74472e15 | 0.610342 | ||||||||
\(827\) | 9.35357e14 | 0.0840808 | 0.0420404 | − | 0.999116i | \(-0.486614\pi\) | ||||
0.0420404 | + | 0.999116i | \(0.486614\pi\) | |||||||
\(828\) | 2.35247e16 | 2.10067 | ||||||||
\(829\) | −2.13470e16 | −1.89359 | −0.946797 | − | 0.321830i | \(-0.895702\pi\) | ||||
−0.946797 | + | 0.321830i | \(0.895702\pi\) | |||||||
\(830\) | 6.68889e15 | 0.589420 | ||||||||
\(831\) | −1.07287e16 | −0.939168 | ||||||||
\(832\) | 4.89693e16 | 4.25839 | ||||||||
\(833\) | 2.57389e15 | 0.222353 | ||||||||
\(834\) | −4.06263e15 | −0.348653 | ||||||||
\(835\) | −1.11235e16 | −0.948346 | ||||||||
\(836\) | −1.16096e16 | −0.983289 | ||||||||
\(837\) | 4.28325e15 | 0.360399 | ||||||||
\(838\) | 2.37451e16 | 1.98487 | ||||||||
\(839\) | −5.95088e15 | −0.494186 | −0.247093 | − | 0.968992i | \(-0.579475\pi\) | ||||
−0.247093 | + | 0.968992i | \(0.579475\pi\) | |||||||
\(840\) | 4.56875e16 | 3.76930 | ||||||||
\(841\) | −1.06590e16 | −0.873650 | ||||||||
\(842\) | 3.18941e16 | 2.59713 | ||||||||
\(843\) | 1.49309e15 | 0.120791 | ||||||||
\(844\) | −6.48467e15 | −0.521200 | ||||||||
\(845\) | −1.94445e16 | −1.55269 | ||||||||
\(846\) | −2.39545e16 | −1.90042 | ||||||||
\(847\) | 1.33801e16 | 1.05463 | ||||||||
\(848\) | −6.03945e16 | −4.72955 | ||||||||
\(849\) | −1.80604e14 | −0.0140519 | ||||||||
\(850\) | −2.73860e16 | −2.11702 | ||||||||
\(851\) | −3.00036e16 | −2.30442 | ||||||||
\(852\) | −1.34223e16 | −1.02426 | ||||||||
\(853\) | −3.56735e15 | −0.270474 | −0.135237 | − | 0.990813i | \(-0.543180\pi\) | ||||
−0.135237 | + | 0.990813i | \(0.543180\pi\) | |||||||
\(854\) | −3.35088e16 | −2.52430 | ||||||||
\(855\) | −1.57946e16 | −1.18221 | ||||||||
\(856\) | 4.77587e16 | 3.55178 | ||||||||
\(857\) | −2.04044e16 | −1.50775 | −0.753873 | − | 0.657020i | \(-0.771817\pi\) | ||||
−0.753873 | + | 0.657020i | \(0.771817\pi\) | |||||||
\(858\) | 6.49026e15 | 0.476521 | ||||||||
\(859\) | −8.33941e15 | −0.608377 | −0.304189 | − | 0.952612i | \(-0.598385\pi\) | ||||
−0.304189 | + | 0.952612i | \(0.598385\pi\) | |||||||
\(860\) | −1.55674e16 | −1.12843 | ||||||||
\(861\) | 3.92356e15 | 0.282594 | ||||||||
\(862\) | −2.54945e15 | −0.182455 | ||||||||
\(863\) | 2.61014e16 | 1.85611 | 0.928057 | − | 0.372438i | \(-0.121478\pi\) | ||||
0.928057 | + | 0.372438i | \(0.121478\pi\) | |||||||
\(864\) | −4.97096e16 | −3.51249 | ||||||||
\(865\) | 1.90679e16 | 1.33879 | ||||||||
\(866\) | −3.95035e16 | −2.75605 | ||||||||
\(867\) | 3.46348e15 | 0.240108 | ||||||||
\(868\) | −1.50161e16 | −1.03442 | ||||||||
\(869\) | −3.04776e15 | −0.208628 | ||||||||
\(870\) | −1.05064e16 | −0.714655 | ||||||||
\(871\) | 2.84899e16 | 1.92571 | ||||||||
\(872\) | 7.77921e16 | 5.22510 | ||||||||
\(873\) | −3.79739e14 | −0.0253458 | ||||||||
\(874\) | −6.10852e16 | −4.05157 | ||||||||
\(875\) | 9.90037e15 | 0.652540 | ||||||||
\(876\) | 2.83165e16 | 1.85467 | ||||||||
\(877\) | −5.51813e15 | −0.359165 | −0.179583 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179583 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(878\) | 7.55012e15 | 0.488353 | ||||||||
\(879\) | −4.22279e15 | −0.271432 | ||||||||
\(880\) | −2.12295e16 | −1.35608 | ||||||||
\(881\) | 9.48757e14 | 0.0602265 | 0.0301132 | − | 0.999546i | \(-0.490413\pi\) | ||||
0.0301132 | + | 0.999546i | \(0.490413\pi\) | |||||||
\(882\) | 4.48053e15 | 0.282652 | ||||||||
\(883\) | −1.39775e16 | −0.876284 | −0.438142 | − | 0.898906i | \(-0.644363\pi\) | ||||
−0.438142 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(884\) | 4.86846e16 | 3.03322 | ||||||||
\(885\) | 4.79379e15 | 0.296818 | ||||||||
\(886\) | −1.17220e16 | −0.721302 | ||||||||
\(887\) | −1.77585e16 | −1.08599 | −0.542996 | − | 0.839735i | \(-0.682710\pi\) | ||||
−0.542996 | + | 0.839735i | \(0.682710\pi\) | |||||||
\(888\) | 5.55933e16 | 3.37871 | ||||||||
\(889\) | 6.15454e15 | 0.371737 | ||||||||
\(890\) | 3.43563e16 | 2.06234 | ||||||||
\(891\) | −7.73507e14 | −0.0461463 | ||||||||
\(892\) | −5.29974e16 | −3.14230 | ||||||||
\(893\) | 4.52042e16 | 2.66376 | ||||||||
\(894\) | −3.56622e16 | −2.08858 | ||||||||
\(895\) | 1.94035e16 | 1.12941 | ||||||||
\(896\) | 4.67487e16 | 2.70443 | ||||||||
\(897\) | 2.48177e16 | 1.42693 | ||||||||
\(898\) | 2.03688e16 | 1.16398 | ||||||||
\(899\) | 2.15473e15 | 0.122381 | ||||||||
\(900\) | −3.46456e16 | −1.95575 | ||||||||
\(901\) | −1.98773e16 | −1.11525 | ||||||||
\(902\) | −3.24356e15 | −0.180878 | ||||||||
\(903\) | 3.82721e15 | 0.212129 | ||||||||
\(904\) | 4.98072e16 | 2.74389 | ||||||||
\(905\) | 4.79855e16 | 2.62750 | ||||||||
\(906\) | −2.10240e15 | −0.114422 | ||||||||
\(907\) | −9.03137e15 | −0.488555 | −0.244278 | − | 0.969705i | \(-0.578551\pi\) | ||||
−0.244278 | + | 0.969705i | \(0.578551\pi\) | |||||||
\(908\) | −1.59900e16 | −0.859756 | ||||||||
\(909\) | 1.74521e16 | 0.932710 | ||||||||
\(910\) | −8.88291e16 | −4.71876 | ||||||||
\(911\) | −1.47302e16 | −0.777784 | −0.388892 | − | 0.921283i | \(-0.627142\pi\) | ||||
−0.388892 | + | 0.921283i | \(0.627142\pi\) | |||||||
\(912\) | 6.36186e16 | 3.33897 | ||||||||
\(913\) | 9.87963e14 | 0.0515408 | ||||||||
\(914\) | 5.00847e16 | 2.59717 | ||||||||
\(915\) | −2.38163e16 | −1.22760 | ||||||||
\(916\) | −5.17698e16 | −2.65247 | ||||||||
\(917\) | 1.18618e16 | 0.604115 | ||||||||
\(918\) | −3.18396e16 | −1.61188 | ||||||||
\(919\) | 2.51043e16 | 1.26332 | 0.631659 | − | 0.775247i | \(-0.282374\pi\) | ||||
0.631659 | + | 0.775247i | \(0.282374\pi\) | |||||||
\(920\) | −1.44424e17 | −7.22447 | ||||||||
\(921\) | −1.79314e16 | −0.891634 | ||||||||
\(922\) | 2.25184e16 | 1.11306 | ||||||||
\(923\) | 1.62842e16 | 0.800126 | ||||||||
\(924\) | 1.08144e16 | 0.528210 | ||||||||
\(925\) | 4.41872e16 | 2.14544 | ||||||||
\(926\) | −4.39280e16 | −2.12022 | ||||||||
\(927\) | −4.14984e15 | −0.199110 | ||||||||
\(928\) | −2.50070e16 | −1.19274 | ||||||||
\(929\) | −3.40423e16 | −1.61411 | −0.807054 | − | 0.590477i | \(-0.798940\pi\) | ||||
−0.807054 | + | 0.590477i | \(0.798940\pi\) | |||||||
\(930\) | −1.46856e16 | −0.692207 | ||||||||
\(931\) | −8.45514e15 | −0.396185 | ||||||||
\(932\) | 3.79369e16 | 1.76715 | ||||||||
\(933\) | 9.63225e15 | 0.446045 | ||||||||
\(934\) | 7.62346e16 | 3.50949 | ||||||||
\(935\) | −6.98714e15 | −0.319768 | ||||||||
\(936\) | 5.28825e16 | 2.40600 | ||||||||
\(937\) | −1.60071e16 | −0.724010 | −0.362005 | − | 0.932176i | \(-0.617908\pi\) | ||||
−0.362005 | + | 0.932176i | \(0.617908\pi\) | |||||||
\(938\) | 6.53207e16 | 2.93721 | ||||||||
\(939\) | −2.42342e16 | −1.08335 | ||||||||
\(940\) | 1.71278e17 | 7.61199 | ||||||||
\(941\) | 1.79408e16 | 0.792683 | 0.396341 | − | 0.918103i | \(-0.370280\pi\) | ||||
0.396341 | + | 0.918103i | \(0.370280\pi\) | |||||||
\(942\) | 1.76391e16 | 0.774814 | ||||||||
\(943\) | −1.24029e16 | −0.541636 | ||||||||
\(944\) | 2.22052e16 | 0.964069 | ||||||||
\(945\) | 4.22194e16 | 1.82237 | ||||||||
\(946\) | −3.16391e15 | −0.135776 | ||||||||
\(947\) | 1.31442e16 | 0.560800 | 0.280400 | − | 0.959883i | \(-0.409533\pi\) | ||||
0.280400 | + | 0.959883i | \(0.409533\pi\) | |||||||
\(948\) | 3.46058e16 | 1.46792 | ||||||||
\(949\) | −3.43541e16 | −1.44882 | ||||||||
\(950\) | 8.99620e16 | 3.77207 | ||||||||
\(951\) | 2.23353e16 | 0.931105 | ||||||||
\(952\) | 6.96519e16 | 2.88689 | ||||||||
\(953\) | −4.39785e16 | −1.81230 | −0.906150 | − | 0.422958i | \(-0.860992\pi\) | ||||
−0.906150 | + | 0.422958i | \(0.860992\pi\) | |||||||
\(954\) | −3.46017e16 | −1.41769 | ||||||||
\(955\) | −1.52004e16 | −0.619207 | ||||||||
\(956\) | −5.26260e15 | −0.213148 | ||||||||
\(957\) | −1.55181e15 | −0.0624918 | ||||||||
\(958\) | 5.72262e16 | 2.29131 | ||||||||
\(959\) | 3.69747e16 | 1.47198 | ||||||||
\(960\) | 7.97994e16 | 3.15869 | ||||||||
\(961\) | −2.23966e16 | −0.881463 | ||||||||
\(962\) | −1.08089e17 | −4.22978 | ||||||||
\(963\) | 1.53798e16 | 0.598422 | ||||||||
\(964\) | 7.97618e16 | 3.08583 | ||||||||
\(965\) | 3.90427e16 | 1.50189 | ||||||||
\(966\) | 5.69014e16 | 2.17645 | ||||||||
\(967\) | 8.85236e15 | 0.336677 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(968\) | 7.83703e16 | 2.96372 | ||||||||
\(969\) | 2.09385e16 | 0.787343 | ||||||||
\(970\) | 3.73610e15 | 0.139693 | ||||||||
\(971\) | 2.16728e16 | 0.805766 | 0.402883 | − | 0.915251i | \(-0.368008\pi\) | ||||
0.402883 | + | 0.915251i | \(0.368008\pi\) | |||||||
\(972\) | −6.65227e16 | −2.45927 | ||||||||
\(973\) | 8.21271e15 | 0.301902 | ||||||||
\(974\) | −5.60466e16 | −2.04868 | ||||||||
\(975\) | −3.65499e16 | −1.32850 | ||||||||
\(976\) | −1.10319e17 | −3.98727 | ||||||||
\(977\) | 2.25522e16 | 0.810531 | 0.405265 | − | 0.914199i | \(-0.367179\pi\) | ||||
0.405265 | + | 0.914199i | \(0.367179\pi\) | |||||||
\(978\) | 5.04102e16 | 1.80158 | ||||||||
\(979\) | 5.07449e15 | 0.180338 | ||||||||
\(980\) | −3.20364e16 | −1.13214 | ||||||||
\(981\) | 2.50516e16 | 0.880350 | ||||||||
\(982\) | −5.39867e16 | −1.88657 | ||||||||
\(983\) | −1.07495e16 | −0.373547 | −0.186773 | − | 0.982403i | \(-0.559803\pi\) | ||||
−0.186773 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(984\) | 2.29811e16 | 0.794141 | ||||||||
\(985\) | 3.19508e15 | 0.109795 | ||||||||
\(986\) | −1.60173e16 | −0.547351 | ||||||||
\(987\) | −4.21081e16 | −1.43094 | ||||||||
\(988\) | −1.59927e17 | −5.40455 | ||||||||
\(989\) | −1.20983e16 | −0.406578 | ||||||||
\(990\) | −1.21629e16 | −0.406485 | ||||||||
\(991\) | 4.13282e16 | 1.37354 | 0.686770 | − | 0.726874i | \(-0.259028\pi\) | ||||
0.686770 | + | 0.726874i | \(0.259028\pi\) | |||||||
\(992\) | −3.49543e16 | −1.15528 | ||||||||
\(993\) | −3.40138e16 | −1.11798 | ||||||||
\(994\) | 3.73360e16 | 1.22040 | ||||||||
\(995\) | −7.61420e16 | −2.47512 | ||||||||
\(996\) | −1.12178e16 | −0.362645 | ||||||||
\(997\) | 4.17879e16 | 1.34347 | 0.671734 | − | 0.740793i | \(-0.265550\pi\) | ||||
0.671734 | + | 0.740793i | \(0.265550\pi\) | |||||||
\(998\) | 5.07214e16 | 1.62171 | ||||||||
\(999\) | 5.13732e16 | 1.63353 |
(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 | 197.12.a.b.1.3 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.3 | ✓ | 92 | 1.1 | even | 1 | trivial |