Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [529,8,Mod(1,529)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(529, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("529.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 529 = 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 529.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: | \(165.251678481\) |
Analytic rank: | \(0\) |
Dimension: | \(65\) |
Twist minimal: | no (minimal twist has level 23) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.55 | ||
Character | \(\chi\) | \(=\) | 529.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.3929 | 1.44894 | 0.724471 | − | 0.689305i | \(-0.242084\pi\) | ||||
0.724471 | + | 0.689305i | \(0.242084\pi\) | |||||||
\(3\) | 83.4847 | 1.78518 | 0.892591 | − | 0.450868i | \(-0.148885\pi\) | ||||
0.892591 | + | 0.450868i | \(0.148885\pi\) | |||||||
\(4\) | 140.728 | 1.09944 | ||||||||
\(5\) | 338.591 | 1.21138 | 0.605690 | − | 0.795701i | \(-0.292897\pi\) | ||||
0.605690 | + | 0.795701i | \(0.292897\pi\) | |||||||
\(6\) | 1368.56 | 2.58663 | ||||||||
\(7\) | −736.684 | −0.811779 | −0.405890 | − | 0.913922i | \(-0.633038\pi\) | ||||
−0.405890 | + | 0.913922i | \(0.633038\pi\) | |||||||
\(8\) | 208.646 | 0.144077 | ||||||||
\(9\) | 4782.69 | 2.18687 | ||||||||
\(10\) | 5550.49 | 1.75522 | ||||||||
\(11\) | 3210.44 | 0.727260 | 0.363630 | − | 0.931543i | \(-0.381537\pi\) | ||||
0.363630 | + | 0.931543i | \(0.381537\pi\) | |||||||
\(12\) | 11748.6 | 1.96269 | ||||||||
\(13\) | −9074.76 | −1.14560 | −0.572801 | − | 0.819695i | \(-0.694143\pi\) | ||||
−0.572801 | + | 0.819695i | \(0.694143\pi\) | |||||||
\(14\) | −12076.4 | −1.17622 | ||||||||
\(15\) | 28267.1 | 2.16253 | ||||||||
\(16\) | −14592.8 | −0.890677 | ||||||||
\(17\) | 21664.5 | 1.06949 | 0.534746 | − | 0.845013i | \(-0.320407\pi\) | ||||
0.534746 | + | 0.845013i | \(0.320407\pi\) | |||||||
\(18\) | 78402.2 | 3.16865 | ||||||||
\(19\) | 41497.5 | 1.38798 | 0.693991 | − | 0.719983i | \(-0.255851\pi\) | ||||
0.693991 | + | 0.719983i | \(0.255851\pi\) | |||||||
\(20\) | 47649.1 | 1.33183 | ||||||||
\(21\) | −61501.8 | −1.44917 | ||||||||
\(22\) | 52628.5 | 1.05376 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 17418.7 | 0.257203 | ||||||||
\(25\) | 36518.7 | 0.467440 | ||||||||
\(26\) | −148762. | −1.65991 | ||||||||
\(27\) | 216700. | 2.11878 | ||||||||
\(28\) | −103672. | −0.892499 | ||||||||
\(29\) | 186237. | 1.41799 | 0.708995 | − | 0.705213i | \(-0.249149\pi\) | ||||
0.708995 | + | 0.705213i | \(0.249149\pi\) | |||||||
\(30\) | 463381. | 3.13338 | ||||||||
\(31\) | −26969.2 | −0.162593 | −0.0812967 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812967 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(32\) | −265926. | −1.43462 | ||||||||
\(33\) | 268022. | 1.29829 | ||||||||
\(34\) | 355145. | 1.54963 | ||||||||
\(35\) | −249434. | −0.983372 | ||||||||
\(36\) | 673057. | 2.40433 | ||||||||
\(37\) | 335309. | 1.08828 | 0.544139 | − | 0.838995i | \(-0.316857\pi\) | ||||
0.544139 | + | 0.838995i | \(0.316857\pi\) | |||||||
\(38\) | 680265. | 2.01111 | ||||||||
\(39\) | −757603. | −2.04511 | ||||||||
\(40\) | 70645.4 | 0.174532 | ||||||||
\(41\) | −282583. | −0.640328 | −0.320164 | − | 0.947362i | \(-0.603738\pi\) | ||||
−0.320164 | + | 0.947362i | \(0.603738\pi\) | |||||||
\(42\) | −1.00819e6 | −2.09977 | ||||||||
\(43\) | 235425. | 0.451558 | 0.225779 | − | 0.974179i | \(-0.427507\pi\) | ||||
0.225779 | + | 0.974179i | \(0.427507\pi\) | |||||||
\(44\) | 451798. | 0.799576 | ||||||||
\(45\) | 1.61937e6 | 2.64913 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.13207e6 | 1.59049 | 0.795243 | − | 0.606291i | \(-0.207343\pi\) | ||||
0.795243 | + | 0.606291i | \(0.207343\pi\) | |||||||
\(48\) | −1.21828e6 | −1.59002 | ||||||||
\(49\) | −280840. | −0.341015 | ||||||||
\(50\) | 598648. | 0.677293 | ||||||||
\(51\) | 1.80865e6 | 1.90924 | ||||||||
\(52\) | −1.27707e6 | −1.25952 | ||||||||
\(53\) | 72039.4 | 0.0664667 | 0.0332334 | − | 0.999448i | \(-0.489420\pi\) | ||||
0.0332334 | + | 0.999448i | \(0.489420\pi\) | |||||||
\(54\) | 3.55235e6 | 3.06999 | ||||||||
\(55\) | 1.08702e6 | 0.880988 | ||||||||
\(56\) | −153706. | −0.116959 | ||||||||
\(57\) | 3.46440e6 | 2.47780 | ||||||||
\(58\) | 3.05297e6 | 2.05459 | ||||||||
\(59\) | −1.87957e6 | −1.19145 | −0.595726 | − | 0.803188i | \(-0.703136\pi\) | ||||
−0.595726 | + | 0.803188i | \(0.703136\pi\) | |||||||
\(60\) | 3.97797e6 | 2.37756 | ||||||||
\(61\) | 258.019 | 0.000145545 0 | 7.27725e−5 | − | 1.00000i | \(-0.499977\pi\) | ||||
7.27725e−5 | 1.00000i | \(0.499977\pi\) | ||||||||
\(62\) | −442104. | −0.235588 | ||||||||
\(63\) | −3.52333e6 | −1.77526 | ||||||||
\(64\) | −2.49142e6 | −1.18800 | ||||||||
\(65\) | −3.07263e6 | −1.38776 | ||||||||
\(66\) | 4.39367e6 | 1.88115 | ||||||||
\(67\) | −3.36449e6 | −1.36665 | −0.683325 | − | 0.730114i | \(-0.739467\pi\) | ||||
−0.683325 | + | 0.730114i | \(0.739467\pi\) | |||||||
\(68\) | 3.04880e6 | 1.17584 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.08896e6 | −1.42485 | ||||||||
\(71\) | 3.80823e6 | 1.26276 | 0.631378 | − | 0.775475i | \(-0.282490\pi\) | ||||
0.631378 | + | 0.775475i | \(0.282490\pi\) | |||||||
\(72\) | 997887. | 0.315078 | ||||||||
\(73\) | −1.70273e6 | −0.512291 | −0.256145 | − | 0.966638i | \(-0.582453\pi\) | ||||
−0.256145 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(74\) | 5.49670e6 | 1.57685 | ||||||||
\(75\) | 3.04875e6 | 0.834465 | ||||||||
\(76\) | 5.83985e6 | 1.52600 | ||||||||
\(77\) | −2.36508e6 | −0.590375 | ||||||||
\(78\) | −1.24193e7 | −2.96324 | ||||||||
\(79\) | −1.49616e6 | −0.341415 | −0.170707 | − | 0.985322i | \(-0.554605\pi\) | ||||
−0.170707 | + | 0.985322i | \(0.554605\pi\) | |||||||
\(80\) | −4.94100e6 | −1.07895 | ||||||||
\(81\) | 7.63141e6 | 1.59554 | ||||||||
\(82\) | −4.63236e6 | −0.927799 | ||||||||
\(83\) | 8.57869e6 | 1.64683 | 0.823413 | − | 0.567443i | \(-0.192067\pi\) | ||||
0.823413 | + | 0.567443i | \(0.192067\pi\) | |||||||
\(84\) | −8.65501e6 | −1.59327 | ||||||||
\(85\) | 7.33541e6 | 1.29556 | ||||||||
\(86\) | 3.85931e6 | 0.654282 | ||||||||
\(87\) | 1.55479e7 | 2.53137 | ||||||||
\(88\) | 669844. | 0.104781 | ||||||||
\(89\) | −1.75273e6 | −0.263542 | −0.131771 | − | 0.991280i | \(-0.542066\pi\) | ||||
−0.131771 | + | 0.991280i | \(0.542066\pi\) | |||||||
\(90\) | 2.65463e7 | 3.83844 | ||||||||
\(91\) | 6.68523e6 | 0.929975 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.25152e6 | −0.290259 | ||||||||
\(94\) | 1.85579e7 | 2.30452 | ||||||||
\(95\) | 1.40507e7 | 1.68137 | ||||||||
\(96\) | −2.22007e7 | −2.56105 | ||||||||
\(97\) | −3.50274e6 | −0.389678 | −0.194839 | − | 0.980835i | \(-0.562419\pi\) | ||||
−0.194839 | + | 0.980835i | \(0.562419\pi\) | |||||||
\(98\) | −4.60379e6 | −0.494111 | ||||||||
\(99\) | 1.53545e7 | 1.59043 | ||||||||
\(100\) | 5.13920e6 | 0.513920 | ||||||||
\(101\) | −1.01898e6 | −0.0984104 | −0.0492052 | − | 0.998789i | \(-0.515669\pi\) | ||||
−0.0492052 | + | 0.998789i | \(0.515669\pi\) | |||||||
\(102\) | 2.96491e7 | 2.76638 | ||||||||
\(103\) | −1.07208e7 | −0.966713 | −0.483356 | − | 0.875424i | \(-0.660582\pi\) | ||||
−0.483356 | + | 0.875424i | \(0.660582\pi\) | |||||||
\(104\) | −1.89341e6 | −0.165055 | ||||||||
\(105\) | −2.08239e7 | −1.75550 | ||||||||
\(106\) | 1.18094e6 | 0.0963065 | ||||||||
\(107\) | −1.11949e7 | −0.883440 | −0.441720 | − | 0.897153i | \(-0.645632\pi\) | ||||
−0.441720 | + | 0.897153i | \(0.645632\pi\) | |||||||
\(108\) | 3.04958e7 | 2.32946 | ||||||||
\(109\) | −1.30249e7 | −0.963344 | −0.481672 | − | 0.876352i | \(-0.659970\pi\) | ||||
−0.481672 | + | 0.876352i | \(0.659970\pi\) | |||||||
\(110\) | 1.78195e7 | 1.27650 | ||||||||
\(111\) | 2.79932e7 | 1.94277 | ||||||||
\(112\) | 1.07503e7 | 0.723033 | ||||||||
\(113\) | 1.30597e7 | 0.851451 | 0.425725 | − | 0.904852i | \(-0.360019\pi\) | ||||
0.425725 | + | 0.904852i | \(0.360019\pi\) | |||||||
\(114\) | 5.67917e7 | 3.59019 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.62087e7 | 1.55899 | ||||||||
\(117\) | −4.34018e7 | −2.50528 | ||||||||
\(118\) | −3.08117e7 | −1.72635 | ||||||||
\(119\) | −1.59599e7 | −0.868192 | ||||||||
\(120\) | 5.89781e6 | 0.311571 | ||||||||
\(121\) | −9.18026e6 | −0.471092 | ||||||||
\(122\) | 4229.69 | 0.000210886 0 | ||||||||
\(123\) | −2.35913e7 | −1.14310 | ||||||||
\(124\) | −3.79532e6 | −0.178761 | ||||||||
\(125\) | −1.40875e7 | −0.645133 | ||||||||
\(126\) | −5.77576e7 | −2.57225 | ||||||||
\(127\) | −769876. | −0.0333509 | −0.0166755 | − | 0.999861i | \(-0.505308\pi\) | ||||
−0.0166755 | + | 0.999861i | \(0.505308\pi\) | |||||||
\(128\) | −6.80310e6 | −0.286729 | ||||||||
\(129\) | 1.96544e7 | 0.806113 | ||||||||
\(130\) | −5.03694e7 | −2.01078 | ||||||||
\(131\) | −2.76562e7 | −1.07484 | −0.537419 | − | 0.843315i | \(-0.680601\pi\) | ||||
−0.537419 | + | 0.843315i | \(0.680601\pi\) | |||||||
\(132\) | 3.77182e7 | 1.42739 | ||||||||
\(133\) | −3.05705e7 | −1.12674 | ||||||||
\(134\) | −5.51538e7 | −1.98020 | ||||||||
\(135\) | 7.33727e7 | 2.56665 | ||||||||
\(136\) | 4.52020e6 | 0.154089 | ||||||||
\(137\) | −2.71467e7 | −0.901977 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.58689e6 | 0.176449 | 0.0882243 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882243 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(140\) | −3.51023e7 | −1.08115 | ||||||||
\(141\) | 9.45103e7 | 2.83931 | ||||||||
\(142\) | 6.24280e7 | 1.82966 | ||||||||
\(143\) | −2.91340e7 | −0.833150 | ||||||||
\(144\) | −6.97931e7 | −1.94780 | ||||||||
\(145\) | 6.30582e7 | 1.71772 | ||||||||
\(146\) | −2.79128e7 | −0.742280 | ||||||||
\(147\) | −2.34459e7 | −0.608773 | ||||||||
\(148\) | 4.71873e7 | 1.19649 | ||||||||
\(149\) | 3.74459e7 | 0.927368 | 0.463684 | − | 0.886001i | \(-0.346527\pi\) | ||||
0.463684 | + | 0.886001i | \(0.346527\pi\) | |||||||
\(150\) | 4.99780e7 | 1.20909 | ||||||||
\(151\) | −7.41132e7 | −1.75177 | −0.875883 | − | 0.482523i | \(-0.839721\pi\) | ||||
−0.875883 | + | 0.482523i | \(0.839721\pi\) | |||||||
\(152\) | 8.65826e6 | 0.199976 | ||||||||
\(153\) | 1.03615e8 | 2.33884 | ||||||||
\(154\) | −3.87705e7 | −0.855419 | ||||||||
\(155\) | −9.13153e6 | −0.196962 | ||||||||
\(156\) | −1.06616e8 | −2.24846 | ||||||||
\(157\) | 1.54008e7 | 0.317610 | 0.158805 | − | 0.987310i | \(-0.449236\pi\) | ||||
0.158805 | + | 0.987310i | \(0.449236\pi\) | |||||||
\(158\) | −2.45264e7 | −0.494691 | ||||||||
\(159\) | 6.01418e6 | 0.118655 | ||||||||
\(160\) | −9.00401e7 | −1.73786 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.25101e8 | 2.31184 | ||||||||
\(163\) | −2.40562e7 | −0.435081 | −0.217540 | − | 0.976051i | \(-0.569803\pi\) | ||||
−0.217540 | + | 0.976051i | \(0.569803\pi\) | |||||||
\(164\) | −3.97673e7 | −0.703999 | ||||||||
\(165\) | 9.07499e7 | 1.57272 | ||||||||
\(166\) | 1.40630e8 | 2.38616 | ||||||||
\(167\) | −8.90659e7 | −1.47980 | −0.739901 | − | 0.672715i | \(-0.765128\pi\) | ||||
−0.739901 | + | 0.672715i | \(0.765128\pi\) | |||||||
\(168\) | −1.28321e7 | −0.208792 | ||||||||
\(169\) | 1.96028e7 | 0.312402 | ||||||||
\(170\) | 1.20249e8 | 1.87719 | ||||||||
\(171\) | 1.98470e8 | 3.03534 | ||||||||
\(172\) | 3.31309e7 | 0.496459 | ||||||||
\(173\) | 4.46616e7 | 0.655802 | 0.327901 | − | 0.944712i | \(-0.393659\pi\) | ||||
0.327901 | + | 0.944712i | \(0.393659\pi\) | |||||||
\(174\) | 2.54876e8 | 3.66781 | ||||||||
\(175\) | −2.69027e7 | −0.379458 | ||||||||
\(176\) | −4.68494e7 | −0.647754 | ||||||||
\(177\) | −1.56915e8 | −2.12696 | ||||||||
\(178\) | −2.87324e7 | −0.381857 | ||||||||
\(179\) | 5.91332e7 | 0.770629 | 0.385315 | − | 0.922785i | \(-0.374093\pi\) | ||||
0.385315 | + | 0.922785i | \(0.374093\pi\) | |||||||
\(180\) | 2.27891e8 | 2.91255 | ||||||||
\(181\) | −1.97550e7 | −0.247630 | −0.123815 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123815 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(182\) | 1.09590e8 | 1.34748 | ||||||||
\(183\) | 21540.6 | 0.000259824 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.13533e8 | 1.31832 | ||||||||
\(186\) | −3.69089e7 | −0.420568 | ||||||||
\(187\) | 6.95526e7 | 0.777800 | ||||||||
\(188\) | 1.59313e8 | 1.74864 | ||||||||
\(189\) | −1.59640e8 | −1.71998 | ||||||||
\(190\) | 2.30331e8 | 2.43621 | ||||||||
\(191\) | −6.95746e7 | −0.722494 | −0.361247 | − | 0.932470i | \(-0.617649\pi\) | ||||
−0.361247 | + | 0.932470i | \(0.617649\pi\) | |||||||
\(192\) | −2.07995e8 | −2.12080 | ||||||||
\(193\) | −3.80027e6 | −0.0380508 | −0.0190254 | − | 0.999819i | \(-0.506056\pi\) | ||||
−0.0190254 | + | 0.999819i | \(0.506056\pi\) | |||||||
\(194\) | −5.74201e7 | −0.564622 | ||||||||
\(195\) | −2.56518e8 | −2.47740 | ||||||||
\(196\) | −3.95220e7 | −0.374924 | ||||||||
\(197\) | −5.64335e7 | −0.525902 | −0.262951 | − | 0.964809i | \(-0.584696\pi\) | ||||
−0.262951 | + | 0.964809i | \(0.584696\pi\) | |||||||
\(198\) | 2.51706e8 | 2.30444 | ||||||||
\(199\) | −1.36312e6 | −0.0122617 | −0.00613083 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613083 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(200\) | 7.61947e6 | 0.0673472 | ||||||||
\(201\) | −2.80883e8 | −2.43972 | ||||||||
\(202\) | −1.67041e7 | −0.142591 | ||||||||
\(203\) | −1.37198e8 | −1.15109 | ||||||||
\(204\) | 2.54528e8 | 2.09908 | ||||||||
\(205\) | −9.56800e7 | −0.775680 | ||||||||
\(206\) | −1.75745e8 | −1.40071 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.32427e8 | 1.02036 | ||||||||
\(209\) | 1.33225e8 | 1.00942 | ||||||||
\(210\) | −3.41365e8 | −2.54362 | ||||||||
\(211\) | −1.15332e8 | −0.845207 | −0.422603 | − | 0.906315i | \(-0.638884\pi\) | ||||
−0.422603 | + | 0.906315i | \(0.638884\pi\) | |||||||
\(212\) | 1.01379e7 | 0.0730759 | ||||||||
\(213\) | 3.17929e8 | 2.25425 | ||||||||
\(214\) | −1.83517e8 | −1.28005 | ||||||||
\(215\) | 7.97129e7 | 0.547008 | ||||||||
\(216\) | 4.52135e7 | 0.305267 | ||||||||
\(217\) | 1.98678e7 | 0.131990 | ||||||||
\(218\) | −2.13516e8 | −1.39583 | ||||||||
\(219\) | −1.42152e8 | −0.914532 | ||||||||
\(220\) | 1.52975e8 | 0.968590 | ||||||||
\(221\) | −1.96600e8 | −1.22521 | ||||||||
\(222\) | 4.58890e8 | 2.81497 | ||||||||
\(223\) | 1.40708e7 | 0.0849670 | 0.0424835 | − | 0.999097i | \(-0.486473\pi\) | ||||
0.0424835 | + | 0.999097i | \(0.486473\pi\) | |||||||
\(224\) | 1.95903e8 | 1.16459 | ||||||||
\(225\) | 1.74658e8 | 1.02223 | ||||||||
\(226\) | 2.14087e8 | 1.23370 | ||||||||
\(227\) | −1.13960e8 | −0.646639 | −0.323320 | − | 0.946290i | \(-0.604799\pi\) | ||||
−0.323320 | + | 0.946290i | \(0.604799\pi\) | |||||||
\(228\) | 4.87538e8 | 2.72418 | ||||||||
\(229\) | −1.05245e8 | −0.579132 | −0.289566 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289566 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.97448e8 | −1.05393 | ||||||||
\(232\) | 3.88575e7 | 0.204299 | ||||||||
\(233\) | 8.52263e7 | 0.441395 | 0.220698 | − | 0.975342i | \(-0.429167\pi\) | ||||
0.220698 | + | 0.975342i | \(0.429167\pi\) | |||||||
\(234\) | −7.11482e8 | −3.63001 | ||||||||
\(235\) | 3.83308e8 | 1.92668 | ||||||||
\(236\) | −2.64508e8 | −1.30993 | ||||||||
\(237\) | −1.24906e8 | −0.609487 | ||||||||
\(238\) | −2.61629e8 | −1.25796 | ||||||||
\(239\) | 1.65538e6 | 0.00784344 | 0.00392172 | − | 0.999992i | \(-0.498752\pi\) | ||||
0.00392172 | + | 0.999992i | \(0.498752\pi\) | |||||||
\(240\) | −4.12498e8 | −1.92612 | ||||||||
\(241\) | 1.95902e8 | 0.901530 | 0.450765 | − | 0.892643i | \(-0.351151\pi\) | ||||
0.450765 | + | 0.892643i | \(0.351151\pi\) | |||||||
\(242\) | −1.50491e8 | −0.682586 | ||||||||
\(243\) | 1.63182e8 | 0.729543 | ||||||||
\(244\) | 36310.5 | 0.000160017 0 | ||||||||
\(245\) | −9.50900e7 | −0.413098 | ||||||||
\(246\) | −3.86731e8 | −1.65629 | ||||||||
\(247\) | −3.76580e8 | −1.59007 | ||||||||
\(248\) | −5.62701e6 | −0.0234259 | ||||||||
\(249\) | 7.16189e8 | 2.93988 | ||||||||
\(250\) | −2.30935e8 | −0.934760 | ||||||||
\(251\) | −2.55891e8 | −1.02140 | −0.510701 | − | 0.859758i | \(-0.670614\pi\) | ||||
−0.510701 | + | 0.859758i | \(0.670614\pi\) | |||||||
\(252\) | −4.95830e8 | −1.95178 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.26205e7 | −0.0483236 | ||||||||
\(255\) | 6.12394e8 | 2.31281 | ||||||||
\(256\) | 2.07379e8 | 0.772547 | ||||||||
\(257\) | −4.54892e8 | −1.67164 | −0.835819 | − | 0.549005i | \(-0.815007\pi\) | ||||
−0.835819 | + | 0.549005i | \(0.815007\pi\) | |||||||
\(258\) | 3.22193e8 | 1.16801 | ||||||||
\(259\) | −2.47017e8 | −0.883441 | ||||||||
\(260\) | −4.32405e8 | −1.52575 | ||||||||
\(261\) | 8.90714e8 | 3.10096 | ||||||||
\(262\) | −4.53366e8 | −1.55738 | ||||||||
\(263\) | 4.08065e8 | 1.38320 | 0.691600 | − | 0.722281i | \(-0.256906\pi\) | ||||
0.691600 | + | 0.722281i | \(0.256906\pi\) | |||||||
\(264\) | 5.59217e7 | 0.187054 | ||||||||
\(265\) | 2.43919e7 | 0.0805164 | ||||||||
\(266\) | −5.01140e8 | −1.63258 | ||||||||
\(267\) | −1.46326e8 | −0.470470 | ||||||||
\(268\) | −4.73477e8 | −1.50254 | ||||||||
\(269\) | 1.38988e7 | 0.0435356 | 0.0217678 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217678 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(270\) | 1.20279e9 | 3.71893 | ||||||||
\(271\) | −6.47803e8 | −1.97720 | −0.988600 | − | 0.150568i | \(-0.951890\pi\) | ||||
−0.988600 | + | 0.150568i | \(0.951890\pi\) | |||||||
\(272\) | −3.16147e8 | −0.952572 | ||||||||
\(273\) | 5.58114e8 | 1.66017 | ||||||||
\(274\) | −4.45014e8 | −1.30691 | ||||||||
\(275\) | 1.17241e8 | 0.339950 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.55887e7 | −0.0440688 | −0.0220344 | − | 0.999757i | \(-0.507014\pi\) | ||||
−0.0220344 | + | 0.999757i | \(0.507014\pi\) | |||||||
\(278\) | 9.15854e7 | 0.255664 | ||||||||
\(279\) | −1.28985e8 | −0.355571 | ||||||||
\(280\) | −5.20433e7 | −0.141681 | ||||||||
\(281\) | 5.18521e7 | 0.139410 | 0.0697050 | − | 0.997568i | \(-0.477794\pi\) | ||||
0.0697050 | + | 0.997568i | \(0.477794\pi\) | |||||||
\(282\) | 1.54930e9 | 4.11399 | ||||||||
\(283\) | 1.08344e8 | 0.284152 | 0.142076 | − | 0.989856i | \(-0.454622\pi\) | ||||
0.142076 | + | 0.989856i | \(0.454622\pi\) | |||||||
\(284\) | 5.35924e8 | 1.38832 | ||||||||
\(285\) | 1.17301e9 | 3.00156 | ||||||||
\(286\) | −4.77591e8 | −1.20719 | ||||||||
\(287\) | 2.08174e8 | 0.519805 | ||||||||
\(288\) | −1.27184e9 | −3.13732 | ||||||||
\(289\) | 5.90126e7 | 0.143814 | ||||||||
\(290\) | 1.03371e9 | 2.48888 | ||||||||
\(291\) | −2.92425e8 | −0.695647 | ||||||||
\(292\) | −2.39622e8 | −0.563231 | ||||||||
\(293\) | 5.11610e8 | 1.18824 | 0.594118 | − | 0.804378i | \(-0.297501\pi\) | ||||
0.594118 | + | 0.804378i | \(0.297501\pi\) | |||||||
\(294\) | −3.84346e8 | −0.882078 | ||||||||
\(295\) | −6.36405e8 | −1.44330 | ||||||||
\(296\) | 6.99608e7 | 0.156796 | ||||||||
\(297\) | 6.95703e8 | 1.54091 | ||||||||
\(298\) | 6.13847e8 | 1.34370 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.29044e8 | 0.917440 | ||||||||
\(301\) | −1.73434e8 | −0.366566 | ||||||||
\(302\) | −1.21493e9 | −2.53821 | ||||||||
\(303\) | −8.50692e7 | −0.175680 | ||||||||
\(304\) | −6.05566e8 | −1.23624 | ||||||||
\(305\) | 87362.9 | 0.000176310 0 | ||||||||
\(306\) | 1.69855e9 | 3.38885 | ||||||||
\(307\) | 5.64382e8 | 1.11324 | 0.556620 | − | 0.830767i | \(-0.312098\pi\) | ||||
0.556620 | + | 0.830767i | \(0.312098\pi\) | |||||||
\(308\) | −3.32832e8 | −0.649079 | ||||||||
\(309\) | −8.95024e8 | −1.72576 | ||||||||
\(310\) | −1.49693e8 | −0.285387 | ||||||||
\(311\) | 1.90079e8 | 0.358321 | 0.179161 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179161 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(312\) | −1.58071e8 | −0.294652 | ||||||||
\(313\) | −4.22148e8 | −0.778143 | −0.389071 | − | 0.921208i | \(-0.627204\pi\) | ||||
−0.389071 | + | 0.921208i | \(0.627204\pi\) | |||||||
\(314\) | 2.52464e8 | 0.460198 | ||||||||
\(315\) | −1.19297e9 | −2.15051 | ||||||||
\(316\) | −2.10551e8 | −0.375364 | ||||||||
\(317\) | 5.33001e8 | 0.939768 | 0.469884 | − | 0.882728i | \(-0.344296\pi\) | ||||
0.469884 | + | 0.882728i | \(0.344296\pi\) | |||||||
\(318\) | 9.85900e7 | 0.171925 | ||||||||
\(319\) | 5.97903e8 | 1.03125 | ||||||||
\(320\) | −8.43571e8 | −1.43912 | ||||||||
\(321\) | −9.34603e8 | −1.57710 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.99023e8 | 1.48444 | ||||||||
\(324\) | 1.07395e9 | 1.75419 | ||||||||
\(325\) | −3.31399e8 | −0.535499 | ||||||||
\(326\) | −3.94351e8 | −0.630408 | ||||||||
\(327\) | −1.08738e9 | −1.71974 | ||||||||
\(328\) | −5.89597e7 | −0.0922564 | ||||||||
\(329\) | −8.33975e8 | −1.29112 | ||||||||
\(330\) | 1.48766e9 | 2.27879 | ||||||||
\(331\) | 1.20778e9 | 1.83059 | 0.915295 | − | 0.402784i | \(-0.131958\pi\) | ||||
0.915295 | + | 0.402784i | \(0.131958\pi\) | |||||||
\(332\) | 1.20726e9 | 1.81058 | ||||||||
\(333\) | 1.60368e9 | 2.37992 | ||||||||
\(334\) | −1.46005e9 | −2.14415 | ||||||||
\(335\) | −1.13918e9 | −1.65553 | ||||||||
\(336\) | 8.97486e8 | 1.29074 | ||||||||
\(337\) | 3.38170e8 | 0.481316 | 0.240658 | − | 0.970610i | \(-0.422637\pi\) | ||||
0.240658 | + | 0.970610i | \(0.422637\pi\) | |||||||
\(338\) | 3.21347e8 | 0.452653 | ||||||||
\(339\) | 1.09029e9 | 1.51999 | ||||||||
\(340\) | 1.03230e9 | 1.42439 | ||||||||
\(341\) | −8.65831e7 | −0.118248 | ||||||||
\(342\) | 3.25349e9 | 4.39804 | ||||||||
\(343\) | 8.13581e8 | 1.08861 | ||||||||
\(344\) | 4.91205e7 | 0.0650591 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.32133e8 | 0.950219 | ||||||||
\(347\) | −3.04174e8 | −0.390813 | −0.195406 | − | 0.980722i | \(-0.562603\pi\) | ||||
−0.195406 | + | 0.980722i | \(0.562603\pi\) | |||||||
\(348\) | 2.18803e9 | 2.78308 | ||||||||
\(349\) | 2.67516e8 | 0.336869 | 0.168435 | − | 0.985713i | \(-0.446129\pi\) | ||||
0.168435 | + | 0.985713i | \(0.446129\pi\) | |||||||
\(350\) | −4.41014e8 | −0.549813 | ||||||||
\(351\) | −1.96650e9 | −2.42728 | ||||||||
\(352\) | −8.53739e8 | −1.04334 | ||||||||
\(353\) | 5.64113e8 | 0.682581 | 0.341291 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341291 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(354\) | −2.57230e9 | −3.08184 | ||||||||
\(355\) | 1.28943e9 | 1.52968 | ||||||||
\(356\) | −2.46658e8 | −0.289748 | ||||||||
\(357\) | −1.33241e9 | −1.54988 | ||||||||
\(358\) | 9.69365e8 | 1.11660 | ||||||||
\(359\) | 6.17291e8 | 0.704141 | 0.352071 | − | 0.935973i | \(-0.385478\pi\) | ||||
0.352071 | + | 0.935973i | \(0.385478\pi\) | |||||||
\(360\) | 3.37875e8 | 0.381678 | ||||||||
\(361\) | 8.28169e8 | 0.926496 | ||||||||
\(362\) | −3.23843e8 | −0.358801 | ||||||||
\(363\) | −7.66411e8 | −0.840985 | ||||||||
\(364\) | 9.40797e8 | 1.02245 | ||||||||
\(365\) | −5.76530e8 | −0.620578 | ||||||||
\(366\) | 353114. | 0.000376471 0 | ||||||||
\(367\) | 1.21530e9 | 1.28337 | 0.641687 | − | 0.766966i | \(-0.278235\pi\) | ||||
0.641687 | + | 0.766966i | \(0.278235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.35151e9 | −1.40032 | ||||||||
\(370\) | 1.86113e9 | 1.91017 | ||||||||
\(371\) | −5.30702e7 | −0.0539563 | ||||||||
\(372\) | −3.16851e8 | −0.319121 | ||||||||
\(373\) | 1.21138e9 | 1.20865 | 0.604325 | − | 0.796738i | \(-0.293443\pi\) | ||||
0.604325 | + | 0.796738i | \(0.293443\pi\) | |||||||
\(374\) | 1.14017e9 | 1.12699 | ||||||||
\(375\) | −1.17609e9 | −1.15168 | ||||||||
\(376\) | 2.36201e8 | 0.229152 | ||||||||
\(377\) | −1.69006e9 | −1.62445 | ||||||||
\(378\) | −2.61696e9 | −2.49216 | ||||||||
\(379\) | −1.05619e9 | −0.996565 | −0.498283 | − | 0.867015i | \(-0.666036\pi\) | ||||
−0.498283 | + | 0.867015i | \(0.666036\pi\) | |||||||
\(380\) | 1.97732e9 | 1.84856 | ||||||||
\(381\) | −6.42728e7 | −0.0595374 | ||||||||
\(382\) | −1.14053e9 | −1.04685 | ||||||||
\(383\) | 3.69197e8 | 0.335786 | 0.167893 | − | 0.985805i | \(-0.446304\pi\) | ||||
0.167893 | + | 0.985805i | \(0.446304\pi\) | |||||||
\(384\) | −5.67954e8 | −0.511863 | ||||||||
\(385\) | −8.00793e8 | −0.715168 | ||||||||
\(386\) | −6.22975e7 | −0.0551335 | ||||||||
\(387\) | 1.12597e9 | 0.987500 | ||||||||
\(388\) | −4.92932e8 | −0.428426 | ||||||||
\(389\) | 8.75745e8 | 0.754317 | 0.377159 | − | 0.926149i | \(-0.376901\pi\) | ||||
0.377159 | + | 0.926149i | \(0.376901\pi\) | |||||||
\(390\) | −4.20507e9 | −3.58961 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.85961e7 | −0.0491323 | ||||||||
\(393\) | −2.30887e9 | −1.91878 | ||||||||
\(394\) | −9.25109e8 | −0.762002 | ||||||||
\(395\) | −5.06585e8 | −0.413583 | ||||||||
\(396\) | 2.16081e9 | 1.74857 | ||||||||
\(397\) | 1.89164e9 | 1.51730 | 0.758648 | − | 0.651500i | \(-0.225860\pi\) | ||||
0.758648 | + | 0.651500i | \(0.225860\pi\) | |||||||
\(398\) | −2.23456e7 | −0.0177665 | ||||||||
\(399\) | −2.55217e9 | −2.01143 | ||||||||
\(400\) | −5.32912e8 | −0.416338 | ||||||||
\(401\) | −2.07582e9 | −1.60763 | −0.803813 | − | 0.594882i | \(-0.797199\pi\) | ||||
−0.803813 | + | 0.594882i | \(0.797199\pi\) | |||||||
\(402\) | −4.60450e9 | −3.53501 | ||||||||
\(403\) | 2.44739e8 | 0.186267 | ||||||||
\(404\) | −1.43399e8 | −0.108196 | ||||||||
\(405\) | 2.58392e9 | 1.93280 | ||||||||
\(406\) | −2.24907e9 | −1.66787 | ||||||||
\(407\) | 1.07649e9 | 0.791461 | ||||||||
\(408\) | 3.77368e8 | 0.275077 | ||||||||
\(409\) | 2.40073e9 | 1.73505 | 0.867524 | − | 0.497396i | \(-0.165710\pi\) | ||||
0.867524 | + | 0.497396i | \(0.165710\pi\) | |||||||
\(410\) | −1.56847e9 | −1.12392 | ||||||||
\(411\) | −2.26633e9 | −1.61019 | ||||||||
\(412\) | −1.50872e9 | −1.06284 | ||||||||
\(413\) | 1.38465e9 | 0.967196 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.90466e9 | 1.99493 | ||||||||
\(416\) | 2.41321e9 | 1.64350 | ||||||||
\(417\) | 4.66420e8 | 0.314993 | ||||||||
\(418\) | 2.18395e9 | 1.46260 | ||||||||
\(419\) | 2.28736e9 | 1.51910 | 0.759549 | − | 0.650451i | \(-0.225420\pi\) | ||||
0.759549 | + | 0.650451i | \(0.225420\pi\) | |||||||
\(420\) | −2.93051e9 | −1.93006 | ||||||||
\(421\) | −2.54375e9 | −1.66145 | −0.830724 | − | 0.556684i | \(-0.812073\pi\) | ||||
−0.830724 | + | 0.556684i | \(0.812073\pi\) | |||||||
\(422\) | −1.89064e9 | −1.22466 | ||||||||
\(423\) | 5.41433e9 | 3.47819 | ||||||||
\(424\) | 1.50307e7 | 0.00957632 | ||||||||
\(425\) | 7.91160e8 | 0.499923 | ||||||||
\(426\) | 5.21178e9 | 3.26628 | ||||||||
\(427\) | −190078. | −0.000118150 0 | ||||||||
\(428\) | −1.57543e9 | −0.971286 | ||||||||
\(429\) | −2.43224e9 | −1.48732 | ||||||||
\(430\) | 1.30673e9 | 0.792584 | ||||||||
\(431\) | −2.76344e9 | −1.66257 | −0.831284 | − | 0.555848i | \(-0.812393\pi\) | ||||
−0.831284 | + | 0.555848i | \(0.812393\pi\) | |||||||
\(432\) | −3.16227e9 | −1.88715 | ||||||||
\(433\) | 2.67047e9 | 1.58081 | 0.790406 | − | 0.612583i | \(-0.209870\pi\) | ||||
0.790406 | + | 0.612583i | \(0.209870\pi\) | |||||||
\(434\) | 3.25691e8 | 0.191246 | ||||||||
\(435\) | 5.26439e9 | 3.06645 | ||||||||
\(436\) | −1.83296e9 | −1.05913 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.33029e9 | −1.32510 | ||||||||
\(439\) | −2.54512e9 | −1.43576 | −0.717880 | − | 0.696167i | \(-0.754887\pi\) | ||||
−0.717880 | + | 0.696167i | \(0.754887\pi\) | |||||||
\(440\) | 2.26803e8 | 0.126930 | ||||||||
\(441\) | −1.34317e9 | −0.745756 | ||||||||
\(442\) | −3.22285e9 | −1.77526 | ||||||||
\(443\) | −3.89455e7 | −0.0212835 | −0.0106418 | − | 0.999943i | \(-0.503387\pi\) | ||||
−0.0106418 | + | 0.999943i | \(0.503387\pi\) | |||||||
\(444\) | 3.93942e9 | 2.13595 | ||||||||
\(445\) | −5.93458e8 | −0.319249 | ||||||||
\(446\) | 2.30661e8 | 0.123112 | ||||||||
\(447\) | 3.12616e9 | 1.65552 | ||||||||
\(448\) | 1.83539e9 | 0.964394 | ||||||||
\(449\) | −2.07530e9 | −1.08198 | −0.540990 | − | 0.841029i | \(-0.681950\pi\) | ||||
−0.540990 | + | 0.841029i | \(0.681950\pi\) | |||||||
\(450\) | 2.86315e9 | 1.48115 | ||||||||
\(451\) | −9.07215e8 | −0.465685 | ||||||||
\(452\) | 1.83787e9 | 0.936115 | ||||||||
\(453\) | −6.18732e9 | −3.12722 | ||||||||
\(454\) | −1.86814e9 | −0.936943 | ||||||||
\(455\) | 2.26356e9 | 1.12655 | ||||||||
\(456\) | 7.22832e8 | 0.356994 | ||||||||
\(457\) | −2.06112e9 | −1.01018 | −0.505088 | − | 0.863068i | \(-0.668540\pi\) | ||||
−0.505088 | + | 0.863068i | \(0.668540\pi\) | |||||||
\(458\) | −1.72527e9 | −0.839129 | ||||||||
\(459\) | 4.69471e9 | 2.26602 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.32245e8 | 0.0628676 | 0.0314338 | − | 0.999506i | \(-0.489993\pi\) | ||||
0.0314338 | + | 0.999506i | \(0.489993\pi\) | |||||||
\(462\) | −3.23674e9 | −1.52708 | ||||||||
\(463\) | −1.50363e9 | −0.704058 | −0.352029 | − | 0.935989i | \(-0.614508\pi\) | ||||
−0.352029 | + | 0.935989i | \(0.614508\pi\) | |||||||
\(464\) | −2.71773e9 | −1.26297 | ||||||||
\(465\) | −7.62343e8 | −0.351613 | ||||||||
\(466\) | 1.39711e9 | 0.639557 | ||||||||
\(467\) | 2.26520e9 | 1.02919 | 0.514596 | − | 0.857433i | \(-0.327942\pi\) | ||||
0.514596 | + | 0.857433i | \(0.327942\pi\) | |||||||
\(468\) | −6.10783e9 | −2.75440 | ||||||||
\(469\) | 2.47856e9 | 1.10942 | ||||||||
\(470\) | 6.28353e9 | 2.79165 | ||||||||
\(471\) | 1.28573e9 | 0.566991 | ||||||||
\(472\) | −3.92164e8 | −0.171661 | ||||||||
\(473\) | 7.55819e8 | 0.328400 | ||||||||
\(474\) | −2.04758e9 | −0.883113 | ||||||||
\(475\) | 1.51543e9 | 0.648798 | ||||||||
\(476\) | −2.24600e9 | −0.954521 | ||||||||
\(477\) | 3.44542e8 | 0.145354 | ||||||||
\(478\) | 2.71366e7 | 0.0113647 | ||||||||
\(479\) | 2.14676e8 | 0.0892501 | 0.0446251 | − | 0.999004i | \(-0.485791\pi\) | ||||
0.0446251 | + | 0.999004i | \(0.485791\pi\) | |||||||
\(480\) | −7.51697e9 | −3.10240 | ||||||||
\(481\) | −3.04285e9 | −1.24673 | ||||||||
\(482\) | 3.21141e9 | 1.30627 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.29192e9 | −0.517936 | ||||||||
\(485\) | −1.18599e9 | −0.472048 | ||||||||
\(486\) | 2.67503e9 | 1.05707 | ||||||||
\(487\) | 2.33496e9 | 0.916069 | 0.458034 | − | 0.888935i | \(-0.348554\pi\) | ||||
0.458034 | + | 0.888935i | \(0.348554\pi\) | |||||||
\(488\) | 53834.5 | 2.09697e−5 0 | ||||||||
\(489\) | −2.00832e9 | −0.776698 | ||||||||
\(490\) | −1.55880e9 | −0.598556 | ||||||||
\(491\) | 1.35244e9 | 0.515623 | 0.257811 | − | 0.966195i | \(-0.416999\pi\) | ||||
0.257811 | + | 0.966195i | \(0.416999\pi\) | |||||||
\(492\) | −3.31996e9 | −1.25677 | ||||||||
\(493\) | 4.03474e9 | 1.51653 | ||||||||
\(494\) | −6.17324e9 | −2.30393 | ||||||||
\(495\) | 5.19890e9 | 1.92661 | ||||||||
\(496\) | 3.93558e8 | 0.144818 | ||||||||
\(497\) | −2.80546e9 | −1.02508 | ||||||||
\(498\) | 1.17404e10 | 4.25972 | ||||||||
\(499\) | 3.49248e9 | 1.25829 | 0.629147 | − | 0.777286i | \(-0.283404\pi\) | ||||
0.629147 | + | 0.777286i | \(0.283404\pi\) | |||||||
\(500\) | −1.98250e9 | −0.709282 | ||||||||
\(501\) | −7.43564e9 | −2.64172 | ||||||||
\(502\) | −4.19480e9 | −1.47995 | ||||||||
\(503\) | 3.47841e9 | 1.21869 | 0.609345 | − | 0.792905i | \(-0.291433\pi\) | ||||
0.609345 | + | 0.792905i | \(0.291433\pi\) | |||||||
\(504\) | −7.35127e8 | −0.255773 | ||||||||
\(505\) | −3.45017e8 | −0.119212 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.63653e9 | 0.557695 | ||||||||
\(508\) | −1.08343e8 | −0.0366672 | ||||||||
\(509\) | −2.41614e9 | −0.812101 | −0.406051 | − | 0.913851i | \(-0.633094\pi\) | ||||
−0.406051 | + | 0.913851i | \(0.633094\pi\) | |||||||
\(510\) | 1.00389e10 | 3.35113 | ||||||||
\(511\) | 1.25438e9 | 0.415867 | ||||||||
\(512\) | 4.27034e9 | 1.40611 | ||||||||
\(513\) | 8.99251e9 | 2.94083 | ||||||||
\(514\) | −7.45700e9 | −2.42211 | ||||||||
\(515\) | −3.62997e9 | −1.17106 | ||||||||
\(516\) | 2.76592e9 | 0.886270 | ||||||||
\(517\) | 3.63443e9 | 1.15670 | ||||||||
\(518\) | −4.04933e9 | −1.28006 | ||||||||
\(519\) | 3.72856e9 | 1.17072 | ||||||||
\(520\) | −6.41091e8 | −0.199944 | ||||||||
\(521\) | −4.86999e8 | −0.150868 | −0.0754339 | − | 0.997151i | \(-0.524034\pi\) | ||||
−0.0754339 | + | 0.997151i | \(0.524034\pi\) | |||||||
\(522\) | 1.46014e10 | 4.49312 | ||||||||
\(523\) | −7.85974e8 | −0.240244 | −0.120122 | − | 0.992759i | \(-0.538329\pi\) | ||||
−0.120122 | + | 0.992759i | \(0.538329\pi\) | |||||||
\(524\) | −3.89199e9 | −1.18171 | ||||||||
\(525\) | −2.24597e9 | −0.677401 | ||||||||
\(526\) | 6.68938e9 | 2.00418 | ||||||||
\(527\) | −5.84275e8 | −0.173892 | ||||||||
\(528\) | −3.91121e9 | −1.15636 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 3.99854e8 | 0.116664 | ||||||||
\(531\) | −8.98940e9 | −2.60555 | ||||||||
\(532\) | −4.30212e9 | −1.23877 | ||||||||
\(533\) | 2.56437e9 | 0.733560 | ||||||||
\(534\) | −2.39871e9 | −0.681685 | ||||||||
\(535\) | −3.79049e9 | −1.07018 | ||||||||
\(536\) | −7.01985e8 | −0.196903 | ||||||||
\(537\) | 4.93671e9 | 1.37571 | ||||||||
\(538\) | 2.27842e8 | 0.0630806 | ||||||||
\(539\) | −9.01621e8 | −0.248007 | ||||||||
\(540\) | 1.03256e10 | 2.82187 | ||||||||
\(541\) | −1.83492e9 | −0.498228 | −0.249114 | − | 0.968474i | \(-0.580139\pi\) | ||||
−0.249114 | + | 0.968474i | \(0.580139\pi\) | |||||||
\(542\) | −1.06194e10 | −2.86485 | ||||||||
\(543\) | −1.64924e9 | −0.442064 | ||||||||
\(544\) | −5.76116e9 | −1.53431 | ||||||||
\(545\) | −4.41011e9 | −1.16697 | ||||||||
\(546\) | 9.14912e9 | 2.40550 | ||||||||
\(547\) | 1.69712e8 | 0.0443360 | 0.0221680 | − | 0.999754i | \(-0.492943\pi\) | ||||
0.0221680 | + | 0.999754i | \(0.492943\pi\) | |||||||
\(548\) | −3.82030e9 | −0.991665 | ||||||||
\(549\) | 1.23403e6 | 0.000318288 0 | ||||||||
\(550\) | 1.92192e9 | 0.492569 | ||||||||
\(551\) | 7.72837e9 | 1.96815 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.10219e9 | 0.277153 | ||||||||
\(554\) | −2.55544e8 | −0.0638531 | ||||||||
\(555\) | 9.47824e9 | 2.35343 | ||||||||
\(556\) | 7.86231e8 | 0.193994 | ||||||||
\(557\) | 7.57295e8 | 0.185683 | 0.0928415 | − | 0.995681i | \(-0.470405\pi\) | ||||
0.0928415 | + | 0.995681i | \(0.470405\pi\) | |||||||
\(558\) | −2.11445e9 | −0.515202 | ||||||||
\(559\) | −2.13643e9 | −0.517306 | ||||||||
\(560\) | 3.63996e9 | 0.875867 | ||||||||
\(561\) | 5.80658e9 | 1.38851 | ||||||||
\(562\) | 8.50007e8 | 0.201997 | ||||||||
\(563\) | −5.25817e9 | −1.24181 | −0.620905 | − | 0.783886i | \(-0.713235\pi\) | ||||
−0.620905 | + | 0.783886i | \(0.713235\pi\) | |||||||
\(564\) | 1.33002e10 | 3.12163 | ||||||||
\(565\) | 4.42190e9 | 1.03143 | ||||||||
\(566\) | 1.77607e9 | 0.411720 | ||||||||
\(567\) | −5.62193e9 | −1.29522 | ||||||||
\(568\) | 7.94571e8 | 0.181934 | ||||||||
\(569\) | −5.63278e9 | −1.28183 | −0.640914 | − | 0.767612i | \(-0.721445\pi\) | ||||
−0.640914 | + | 0.767612i | \(0.721445\pi\) | |||||||
\(570\) | 1.92291e10 | 4.34908 | ||||||||
\(571\) | −4.15588e9 | −0.934192 | −0.467096 | − | 0.884207i | \(-0.654700\pi\) | ||||
−0.467096 | + | 0.884207i | \(0.654700\pi\) | |||||||
\(572\) | −4.09996e9 | −0.915995 | ||||||||
\(573\) | −5.80842e9 | −1.28978 | ||||||||
\(574\) | 3.41258e9 | 0.753167 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.19157e10 | −2.59801 | ||||||||
\(577\) | 5.68728e9 | 1.23251 | 0.616253 | − | 0.787548i | \(-0.288650\pi\) | ||||
0.616253 | + | 0.787548i | \(0.288650\pi\) | |||||||
\(578\) | 9.67388e8 | 0.208379 | ||||||||
\(579\) | −3.17264e8 | −0.0679276 | ||||||||
\(580\) | 8.87404e9 | 1.88853 | ||||||||
\(581\) | −6.31978e9 | −1.33686 | ||||||||
\(582\) | −4.79370e9 | −1.00795 | ||||||||
\(583\) | 2.31278e8 | 0.0483386 | ||||||||
\(584\) | −3.55268e8 | −0.0738092 | ||||||||
\(585\) | −1.46954e10 | −3.03485 | ||||||||
\(586\) | 8.38679e9 | 1.72169 | ||||||||
\(587\) | 1.95305e9 | 0.398548 | 0.199274 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199274 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(588\) | −3.29948e9 | −0.669307 | ||||||||
\(589\) | −1.11916e9 | −0.225677 | ||||||||
\(590\) | −1.04325e10 | −2.09126 | ||||||||
\(591\) | −4.71133e9 | −0.938831 | ||||||||
\(592\) | −4.89312e9 | −0.969303 | ||||||||
\(593\) | −9.14464e9 | −1.80084 | −0.900420 | − | 0.435021i | \(-0.856741\pi\) | ||||
−0.900420 | + | 0.435021i | \(0.856741\pi\) | |||||||
\(594\) | 1.14046e10 | 2.23269 | ||||||||
\(595\) | −5.40387e9 | −1.05171 | ||||||||
\(596\) | 5.26968e9 | 1.01958 | ||||||||
\(597\) | −1.13800e8 | −0.0218893 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.48547e9 | −1.23296 | −0.616478 | − | 0.787372i | \(-0.711441\pi\) | ||||
−0.616478 | + | 0.787372i | \(0.711441\pi\) | |||||||
\(600\) | 6.36109e8 | 0.120227 | ||||||||
\(601\) | 1.56871e9 | 0.294769 | 0.147384 | − | 0.989079i | \(-0.452915\pi\) | ||||
0.147384 | + | 0.989079i | \(0.452915\pi\) | |||||||
\(602\) | −2.84309e9 | −0.531133 | ||||||||
\(603\) | −1.60913e10 | −2.98869 | ||||||||
\(604\) | −1.04298e10 | −1.92595 | ||||||||
\(605\) | −3.10835e9 | −0.570671 | ||||||||
\(606\) | −1.39453e9 | −0.254551 | ||||||||
\(607\) | −1.36381e9 | −0.247510 | −0.123755 | − | 0.992313i | \(-0.539494\pi\) | ||||
−0.123755 | + | 0.992313i | \(0.539494\pi\) | |||||||
\(608\) | −1.10353e10 | −1.99122 | ||||||||
\(609\) | −1.14539e10 | −2.05491 | ||||||||
\(610\) | 1.43213e6 | 0.000255463 0 | ||||||||
\(611\) | −1.02732e10 | −1.82206 | ||||||||
\(612\) | 1.45815e10 | 2.57141 | ||||||||
\(613\) | −4.12622e9 | −0.723504 | −0.361752 | − | 0.932274i | \(-0.617821\pi\) | ||||
−0.361752 | + | 0.932274i | \(0.617821\pi\) | |||||||
\(614\) | 9.25187e9 | 1.61302 | ||||||||
\(615\) | −7.98781e9 | −1.38473 | ||||||||
\(616\) | −4.93463e8 | −0.0850593 | ||||||||
\(617\) | −1.01139e10 | −1.73349 | −0.866747 | − | 0.498749i | \(-0.833793\pi\) | ||||
−0.866747 | + | 0.498749i | \(0.833793\pi\) | |||||||
\(618\) | −1.46720e10 | −2.50052 | ||||||||
\(619\) | 6.33691e9 | 1.07389 | 0.536946 | − | 0.843617i | \(-0.319578\pi\) | ||||
0.536946 | + | 0.843617i | \(0.319578\pi\) | |||||||
\(620\) | −1.28506e9 | −0.216547 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.11595e9 | 0.519187 | ||||||||
\(623\) | 1.29121e9 | 0.213938 | ||||||||
\(624\) | 1.10556e10 | 1.82153 | ||||||||
\(625\) | −7.62292e9 | −1.24894 | ||||||||
\(626\) | −6.92023e9 | −1.12748 | ||||||||
\(627\) | 1.11223e10 | 1.80201 | ||||||||
\(628\) | 2.16732e9 | 0.349191 | ||||||||
\(629\) | 7.26431e9 | 1.16390 | ||||||||
\(630\) | −1.95562e10 | −3.11597 | ||||||||
\(631\) | 6.10946e8 | 0.0968055 | 0.0484027 | − | 0.998828i | \(-0.484587\pi\) | ||||
0.0484027 | + | 0.998828i | \(0.484587\pi\) | |||||||
\(632\) | −3.12167e8 | −0.0491900 | ||||||||
\(633\) | −9.62849e9 | −1.50885 | ||||||||
\(634\) | 8.73745e9 | 1.36167 | ||||||||
\(635\) | −2.60673e8 | −0.0404006 | ||||||||
\(636\) | 8.46363e8 | 0.130454 | ||||||||
\(637\) | 2.54856e9 | 0.390667 | ||||||||
\(638\) | 9.80137e9 | 1.49422 | ||||||||
\(639\) | 1.82136e10 | 2.76148 | ||||||||
\(640\) | −2.30347e9 | −0.347338 | ||||||||
\(641\) | 9.91656e9 | 1.48716 | 0.743580 | − | 0.668647i | \(-0.233126\pi\) | ||||
0.743580 | + | 0.668647i | \(0.233126\pi\) | |||||||
\(642\) | −1.53209e10 | −2.28513 | ||||||||
\(643\) | −1.11784e10 | −1.65821 | −0.829107 | − | 0.559090i | \(-0.811151\pi\) | ||||
−0.829107 | + | 0.559090i | \(0.811151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.65480e9 | 0.976509 | ||||||||
\(646\) | 1.47376e10 | 2.15086 | ||||||||
\(647\) | −7.54635e8 | −0.109540 | −0.0547699 | − | 0.998499i | \(-0.517443\pi\) | ||||
−0.0547699 | + | 0.998499i | \(0.517443\pi\) | |||||||
\(648\) | 1.59226e9 | 0.229880 | ||||||||
\(649\) | −6.03425e9 | −0.866496 | ||||||||
\(650\) | −5.43259e9 | −0.775908 | ||||||||
\(651\) | 1.65866e9 | 0.235626 | ||||||||
\(652\) | −3.38537e9 | −0.478344 | ||||||||
\(653\) | −9.84811e9 | −1.38407 | −0.692033 | − | 0.721866i | \(-0.743285\pi\) | ||||
−0.692033 | + | 0.721866i | \(0.743285\pi\) | |||||||
\(654\) | −1.78253e10 | −2.49181 | ||||||||
\(655\) | −9.36413e9 | −1.30204 | ||||||||
\(656\) | 4.12369e9 | 0.570325 | ||||||||
\(657\) | −8.14364e9 | −1.12031 | ||||||||
\(658\) | −1.36713e10 | −1.87076 | ||||||||
\(659\) | −5.14935e9 | −0.700896 | −0.350448 | − | 0.936582i | \(-0.613971\pi\) | ||||
−0.350448 | + | 0.936582i | \(0.613971\pi\) | |||||||
\(660\) | 1.27710e10 | 1.72911 | ||||||||
\(661\) | 1.13653e9 | 0.153066 | 0.0765328 | − | 0.997067i | \(-0.475615\pi\) | ||||
0.0765328 | + | 0.997067i | \(0.475615\pi\) | |||||||
\(662\) | 1.97991e10 | 2.65242 | ||||||||
\(663\) | −1.64131e10 | −2.18723 | ||||||||
\(664\) | 1.78990e9 | 0.237269 | ||||||||
\(665\) | −1.03509e10 | −1.36490 | ||||||||
\(666\) | 2.62890e10 | 3.44837 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.25340e10 | −1.62695 | ||||||||
\(669\) | 1.17469e9 | 0.151682 | ||||||||
\(670\) | −1.86746e10 | −2.39877 | ||||||||
\(671\) | 828354. | 0.000105849 0 | ||||||||
\(672\) | 1.63549e10 | 2.07901 | ||||||||
\(673\) | 2.35285e9 | 0.297537 | 0.148769 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148769 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(674\) | 5.54359e9 | 0.697399 | ||||||||
\(675\) | 7.91362e9 | 0.990403 | ||||||||
\(676\) | 2.75866e9 | 0.343466 | ||||||||
\(677\) | 2.05267e9 | 0.254248 | 0.127124 | − | 0.991887i | \(-0.459425\pi\) | ||||
0.127124 | + | 0.991887i | \(0.459425\pi\) | |||||||
\(678\) | 1.78730e10 | 2.20238 | ||||||||
\(679\) | 2.58041e9 | 0.316333 | ||||||||
\(680\) | 1.53050e9 | 0.186660 | ||||||||
\(681\) | −9.51391e9 | −1.15437 | ||||||||
\(682\) | −1.41935e9 | −0.171334 | ||||||||
\(683\) | −4.54809e9 | −0.546206 | −0.273103 | − | 0.961985i | \(-0.588050\pi\) | ||||
−0.273103 | + | 0.961985i | \(0.588050\pi\) | |||||||
\(684\) | 2.79302e10 | 3.33716 | ||||||||
\(685\) | −9.19163e9 | −1.09264 | ||||||||
\(686\) | 1.33370e10 | 1.57733 | ||||||||
\(687\) | −8.78635e9 | −1.03386 | ||||||||
\(688\) | −3.43553e9 | −0.402192 | ||||||||
\(689\) | −6.53740e8 | −0.0761444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.21067e8 | −0.0139589 | −0.00697945 | − | 0.999976i | \(-0.502222\pi\) | ||||
−0.00697945 | + | 0.999976i | \(0.502222\pi\) | |||||||
\(692\) | 6.28512e9 | 0.721012 | ||||||||
\(693\) | −1.13114e10 | −1.29107 | ||||||||
\(694\) | −4.98630e9 | −0.566265 | ||||||||
\(695\) | 1.89167e9 | 0.213746 | ||||||||
\(696\) | 3.24401e9 | 0.364712 | ||||||||
\(697\) | −6.12202e9 | −0.684826 | ||||||||
\(698\) | 4.38537e9 | 0.488104 | ||||||||
\(699\) | 7.11509e9 | 0.787971 | ||||||||
\(700\) | −3.78596e9 | −0.417189 | ||||||||
\(701\) | 1.61317e10 | 1.76875 | 0.884376 | − | 0.466776i | \(-0.154584\pi\) | ||||
0.884376 | + | 0.466776i | \(0.154584\pi\) | |||||||
\(702\) | −3.22367e10 | −3.51699 | ||||||||
\(703\) | 1.39145e10 | 1.51051 | ||||||||
\(704\) | −7.99855e9 | −0.863986 | ||||||||
\(705\) | 3.20003e10 | 3.43948 | ||||||||
\(706\) | 9.24745e9 | 0.989021 | ||||||||
\(707\) | 7.50666e8 | 0.0798875 | ||||||||
\(708\) | −2.20824e10 | −2.33845 | ||||||||
\(709\) | 5.01882e9 | 0.528859 | 0.264430 | − | 0.964405i | \(-0.414816\pi\) | ||||
0.264430 | + | 0.964405i | \(0.414816\pi\) | |||||||
\(710\) | 2.11376e10 | 2.21641 | ||||||||
\(711\) | −7.15566e9 | −0.746631 | ||||||||
\(712\) | −3.65699e8 | −0.0379703 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −2.18420e10 | −2.24569 | ||||||||
\(715\) | −9.86449e9 | −1.00926 | ||||||||
\(716\) | 8.32168e9 | 0.847258 | ||||||||
\(717\) | 1.38199e8 | 0.0140020 | ||||||||
\(718\) | 1.01192e10 | 1.02026 | ||||||||
\(719\) | 5.38688e9 | 0.540488 | 0.270244 | − | 0.962792i | \(-0.412896\pi\) | ||||
0.270244 | + | 0.962792i | \(0.412896\pi\) | |||||||
\(720\) | −2.36313e10 | −2.35952 | ||||||||
\(721\) | 7.89785e9 | 0.784757 | ||||||||
\(722\) | 1.35761e10 | 1.34244 | ||||||||
\(723\) | 1.63548e10 | 1.60939 | ||||||||
\(724\) | −2.78008e9 | −0.272253 | ||||||||
\(725\) | 6.80114e9 | 0.662825 | ||||||||
\(726\) | −1.25637e10 | −1.21854 | ||||||||
\(727\) | 5.69764e9 | 0.549951 | 0.274976 | − | 0.961451i | \(-0.411330\pi\) | ||||
0.274976 | + | 0.961451i | \(0.411330\pi\) | |||||||
\(728\) | 1.39484e9 | 0.133988 | ||||||||
\(729\) | −3.06669e9 | −0.293172 | ||||||||
\(730\) | −9.45101e9 | −0.899183 | ||||||||
\(731\) | 5.10038e9 | 0.482938 | ||||||||
\(732\) | 3.03137e6 | 0.000285660 0 | ||||||||
\(733\) | 4.65441e8 | 0.0436517 | 0.0218258 | − | 0.999762i | \(-0.493052\pi\) | ||||
0.0218258 | + | 0.999762i | \(0.493052\pi\) | |||||||
\(734\) | 1.99224e10 | 1.85954 | ||||||||
\(735\) | −7.93855e9 | −0.737455 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.08015e10 | −0.993910 | ||||||||
\(738\) | −2.21551e10 | −2.02898 | ||||||||
\(739\) | −6.28218e9 | −0.572604 | −0.286302 | − | 0.958139i | \(-0.592426\pi\) | ||||
−0.286302 | + | 0.958139i | \(0.592426\pi\) | |||||||
\(740\) | 1.59772e10 | 1.44940 | ||||||||
\(741\) | −3.14386e10 | −2.83857 | ||||||||
\(742\) | −8.69976e8 | −0.0781796 | ||||||||
\(743\) | 1.42657e10 | 1.27595 | 0.637973 | − | 0.770058i | \(-0.279773\pi\) | ||||
0.637973 | + | 0.770058i | \(0.279773\pi\) | |||||||
\(744\) | −4.69769e8 | −0.0418195 | ||||||||
\(745\) | 1.26788e10 | 1.12339 | ||||||||
\(746\) | 1.98581e10 | 1.75127 | ||||||||
\(747\) | 4.10292e10 | 3.60140 | ||||||||
\(748\) | 9.78798e9 | 0.855141 | ||||||||
\(749\) | 8.24710e9 | 0.717158 | ||||||||
\(750\) | −1.92796e10 | −1.66872 | ||||||||
\(751\) | 2.12149e9 | 0.182769 | 0.0913844 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913844 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(752\) | −1.65201e10 | −1.41661 | ||||||||
\(753\) | −2.13630e10 | −1.82339 | ||||||||
\(754\) | −2.77050e10 | −2.35374 | ||||||||
\(755\) | −2.50940e10 | −2.12205 | ||||||||
\(756\) | −2.24657e10 | −1.89101 | ||||||||
\(757\) | −1.18334e9 | −0.0991457 | −0.0495729 | − | 0.998771i | \(-0.515786\pi\) | ||||
−0.0495729 | + | 0.998771i | \(0.515786\pi\) | |||||||
\(758\) | −1.73141e10 | −1.44397 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.93161e9 | 0.242247 | ||||||||
\(761\) | −3.32564e9 | −0.273545 | −0.136772 | − | 0.990602i | \(-0.543673\pi\) | ||||
−0.136772 | + | 0.990602i | \(0.543673\pi\) | |||||||
\(762\) | −1.05362e9 | −0.0862663 | ||||||||
\(763\) | 9.59522e9 | 0.782022 | ||||||||
\(764\) | −9.79108e9 | −0.794336 | ||||||||
\(765\) | 3.50830e10 | 2.83323 | ||||||||
\(766\) | 6.05221e9 | 0.486535 | ||||||||
\(767\) | 1.70567e10 | 1.36493 | ||||||||
\(768\) | 1.73130e10 | 1.37914 | ||||||||
\(769\) | −2.21919e10 | −1.75975 | −0.879876 | − | 0.475203i | \(-0.842374\pi\) | ||||
−0.879876 | + | 0.475203i | \(0.842374\pi\) | |||||||
\(770\) | −1.31273e10 | −1.03624 | ||||||||
\(771\) | −3.79765e10 | −2.98418 | ||||||||
\(772\) | −5.34804e8 | −0.0418344 | ||||||||
\(773\) | 9.36140e9 | 0.728975 | 0.364487 | − | 0.931208i | \(-0.381244\pi\) | ||||
0.364487 | + | 0.931208i | \(0.381244\pi\) | |||||||
\(774\) | 1.84579e10 | 1.43083 | ||||||||
\(775\) | −9.84882e8 | −0.0760026 | ||||||||
\(776\) | −7.30830e8 | −0.0561436 | ||||||||
\(777\) | −2.06221e10 | −1.57710 | ||||||||
\(778\) | 1.43560e10 | 1.09296 | ||||||||
\(779\) | −1.17265e10 | −0.888764 | ||||||||
\(780\) | −3.60991e10 | −2.72374 | ||||||||
\(781\) | 1.22261e10 | 0.918352 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.03576e10 | 3.00441 | ||||||||
\(784\) | 4.09826e9 | 0.303734 | ||||||||
\(785\) | 5.21456e9 | 0.384746 | ||||||||
\(786\) | −3.78491e10 | −2.78020 | ||||||||
\(787\) | −1.14447e9 | −0.0836937 | −0.0418469 | − | 0.999124i | \(-0.513324\pi\) | ||||
−0.0418469 | + | 0.999124i | \(0.513324\pi\) | |||||||
\(788\) | −7.94176e9 | −0.578196 | ||||||||
\(789\) | 3.40672e10 | 2.46926 | ||||||||
\(790\) | −8.30441e9 | −0.599258 | ||||||||
\(791\) | −9.62088e9 | −0.691190 | ||||||||
\(792\) | 3.20365e9 | 0.229143 | ||||||||
\(793\) | −2.34146e6 | −0.000166737 0 | ||||||||
\(794\) | 3.10094e10 | 2.19848 | ||||||||
\(795\) | 2.03635e9 | 0.143736 | ||||||||
\(796\) | −1.91829e8 | −0.0134809 | ||||||||
\(797\) | −2.51562e10 | −1.76012 | −0.880058 | − | 0.474867i | \(-0.842496\pi\) | ||||
−0.880058 | + | 0.474867i | \(0.842496\pi\) | |||||||
\(798\) | −4.18375e10 | −2.91444 | ||||||||
\(799\) | 2.45257e10 | 1.70101 | ||||||||
\(800\) | −9.71128e9 | −0.670597 | ||||||||
\(801\) | −8.38276e9 | −0.576333 | ||||||||
\(802\) | −3.40288e10 | −2.32936 | ||||||||
\(803\) | −5.46652e9 | −0.372569 | ||||||||
\(804\) | −3.95281e10 | −2.68231 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.01199e9 | 0.269890 | ||||||||
\(807\) | 1.16034e9 | 0.0777190 | ||||||||
\(808\) | −2.12606e8 | −0.0141787 | ||||||||
\(809\) | −1.75441e10 | −1.16496 | −0.582482 | − | 0.812844i | \(-0.697918\pi\) | ||||
−0.582482 | + | 0.812844i | \(0.697918\pi\) | |||||||
\(810\) | 4.23581e10 | 2.80052 | ||||||||
\(811\) | 1.03172e10 | 0.679183 | 0.339592 | − | 0.940573i | \(-0.389711\pi\) | ||||
0.339592 | + | 0.940573i | \(0.389711\pi\) | |||||||
\(812\) | −1.93075e10 | −1.26555 | ||||||||
\(813\) | −5.40816e10 | −3.52966 | ||||||||
\(814\) | 1.76468e10 | 1.14678 | ||||||||
\(815\) | −8.14520e9 | −0.527048 | ||||||||
\(816\) | −2.63934e10 | −1.70051 | ||||||||
\(817\) | 9.76956e9 | 0.626755 | ||||||||
\(818\) | 3.93549e10 | 2.51398 | ||||||||
\(819\) | 3.19734e10 | 2.03374 | ||||||||
\(820\) | −1.34648e10 | −0.852810 | ||||||||
\(821\) | 1.90058e10 | 1.19863 | 0.599316 | − | 0.800512i | \(-0.295439\pi\) | ||||
0.599316 | + | 0.800512i | \(0.295439\pi\) | |||||||
\(822\) | −3.71518e10 | −2.33308 | ||||||||
\(823\) | −2.38126e10 | −1.48904 | −0.744521 | − | 0.667599i | \(-0.767322\pi\) | ||||
−0.744521 | + | 0.667599i | \(0.767322\pi\) | |||||||
\(824\) | −2.23685e9 | −0.139281 | ||||||||
\(825\) | 9.78783e9 | 0.606873 | ||||||||
\(826\) | 2.26984e10 | 1.40141 | ||||||||
\(827\) | −9.78569e9 | −0.601620 | −0.300810 | − | 0.953684i | \(-0.597257\pi\) | ||||
−0.300810 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.01748e10 | −1.83951 | −0.919757 | − | 0.392489i | \(-0.871614\pi\) | ||||
−0.919757 | + | 0.392489i | \(0.871614\pi\) | |||||||
\(830\) | 4.76159e10 | 2.89054 | ||||||||
\(831\) | −1.30142e9 | −0.0786708 | ||||||||
\(832\) | 2.26090e10 | 1.36098 | ||||||||
\(833\) | −6.08427e9 | −0.364713 | ||||||||
\(834\) | 7.64598e9 | 0.456407 | ||||||||
\(835\) | −3.01569e10 | −1.79260 | ||||||||
\(836\) | 1.87485e10 | 1.10980 | ||||||||
\(837\) | −5.84424e9 | −0.344500 | ||||||||
\(838\) | 3.74965e10 | 2.20109 | ||||||||
\(839\) | 9.58551e9 | 0.560336 | 0.280168 | − | 0.959951i | \(-0.409610\pi\) | ||||
0.280168 | + | 0.959951i | \(0.409610\pi\) | |||||||
\(840\) | −4.34482e9 | −0.252927 | ||||||||
\(841\) | 1.74344e10 | 1.01070 | ||||||||
\(842\) | −4.16995e10 | −2.40734 | ||||||||
\(843\) | 4.32885e9 | 0.248872 | ||||||||
\(844\) | −1.62305e10 | −0.929251 | ||||||||
\(845\) | 6.63732e9 | 0.378438 | ||||||||
\(846\) | 8.87566e10 | 5.03970 | ||||||||
\(847\) | 6.76294e9 | 0.382423 | ||||||||
\(848\) | −1.05126e9 | −0.0592004 | ||||||||
\(849\) | 9.04503e9 | 0.507263 | ||||||||
\(850\) | 1.29694e10 | 0.724360 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.47414e10 | 2.47840 | ||||||||
\(853\) | −7.19448e9 | −0.396897 | −0.198448 | − | 0.980111i | \(-0.563590\pi\) | ||||
−0.198448 | + | 0.980111i | \(0.563590\pi\) | |||||||
\(854\) | −3.11594e6 | −0.000171193 0 | ||||||||
\(855\) | 6.72000e10 | 3.67695 | ||||||||
\(856\) | −2.33577e9 | −0.127283 | ||||||||
\(857\) | −2.79450e10 | −1.51660 | −0.758301 | − | 0.651904i | \(-0.773970\pi\) | ||||
−0.758301 | + | 0.651904i | \(0.773970\pi\) | |||||||
\(858\) | −3.98715e10 | −2.15505 | ||||||||
\(859\) | −8.91616e9 | −0.479957 | −0.239978 | − | 0.970778i | \(-0.577140\pi\) | ||||
−0.239978 | + | 0.970778i | \(0.577140\pi\) | |||||||
\(860\) | 1.12178e10 | 0.601401 | ||||||||
\(861\) | 1.73794e10 | 0.927946 | ||||||||
\(862\) | −4.53008e10 | −2.40897 | ||||||||
\(863\) | 2.01312e10 | 1.06618 | 0.533092 | − | 0.846057i | \(-0.321030\pi\) | ||||
0.533092 | + | 0.846057i | \(0.321030\pi\) | |||||||
\(864\) | −5.76262e10 | −3.03964 | ||||||||
\(865\) | 1.51220e10 | 0.794425 | ||||||||
\(866\) | 4.37768e10 | 2.29051 | ||||||||
\(867\) | 4.92664e9 | 0.256735 | ||||||||
\(868\) | 2.79595e9 | 0.145114 | ||||||||
\(869\) | −4.80332e9 | −0.248298 | ||||||||
\(870\) | 8.62987e10 | 4.44311 | ||||||||
\(871\) | 3.05319e10 | 1.56564 | ||||||||
\(872\) | −2.71759e9 | −0.138796 | ||||||||
\(873\) | −1.67525e10 | −0.852177 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.03780e10 | 0.523705 | ||||||||
\(876\) | −2.00048e10 | −1.00547 | ||||||||
\(877\) | −1.09704e10 | −0.549191 | −0.274595 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274595 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(878\) | −4.17219e10 | −2.08033 | ||||||||
\(879\) | 4.27116e10 | 2.12122 | ||||||||
\(880\) | −1.58628e10 | −0.784676 | ||||||||
\(881\) | 3.81338e10 | 1.87886 | 0.939431 | − | 0.342738i | \(-0.111354\pi\) | ||||
0.939431 | + | 0.342738i | \(0.111354\pi\) | |||||||
\(882\) | −2.20185e10 | −1.08056 | ||||||||
\(883\) | 2.10556e10 | 1.02921 | 0.514605 | − | 0.857427i | \(-0.327938\pi\) | ||||
0.514605 | + | 0.857427i | \(0.327938\pi\) | |||||||
\(884\) | −2.76671e10 | −1.34704 | ||||||||
\(885\) | −5.31301e10 | −2.57655 | ||||||||
\(886\) | −6.38430e8 | −0.0308386 | ||||||||
\(887\) | −5.78634e9 | −0.278401 | −0.139201 | − | 0.990264i | \(-0.544453\pi\) | ||||
−0.139201 | + | 0.990264i | \(0.544453\pi\) | |||||||
\(888\) | 5.84065e9 | 0.279908 | ||||||||
\(889\) | 5.67155e8 | 0.0270736 | ||||||||
\(890\) | −9.72851e9 | −0.462574 | ||||||||
\(891\) | 2.45002e10 | 1.16037 | ||||||||
\(892\) | 1.98015e9 | 0.0934158 | ||||||||
\(893\) | 4.69779e10 | 2.20757 | ||||||||
\(894\) | 5.12469e10 | 2.39875 | ||||||||
\(895\) | 2.00219e10 | 0.933524 | ||||||||
\(896\) | 5.01173e9 | 0.232761 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.40203e10 | −1.56773 | ||||||||
\(899\) | −5.02267e9 | −0.230556 | ||||||||
\(900\) | 2.45792e10 | 1.12388 | ||||||||
\(901\) | 1.56070e9 | 0.0710857 | ||||||||
\(902\) | −1.48719e10 | −0.674751 | ||||||||
\(903\) | −1.44791e10 | −0.654386 | ||||||||
\(904\) | 2.72485e9 | 0.122674 | ||||||||
\(905\) | −6.68887e9 | −0.299974 | ||||||||
\(906\) | −1.01428e11 | −4.53117 | ||||||||
\(907\) | −1.31715e10 | −0.586150 | −0.293075 | − | 0.956089i | \(-0.594679\pi\) | ||||
−0.293075 | + | 0.956089i | \(0.594679\pi\) | |||||||
\(908\) | −1.60373e10 | −0.710938 | ||||||||
\(909\) | −4.87347e9 | −0.215211 | ||||||||
\(910\) | 3.71063e10 | 1.63231 | ||||||||
\(911\) | 9.00072e9 | 0.394423 | 0.197212 | − | 0.980361i | \(-0.436811\pi\) | ||||
0.197212 | + | 0.980361i | \(0.436811\pi\) | |||||||
\(912\) | −5.05555e10 | −2.20692 | ||||||||
\(913\) | 2.75413e10 | 1.19767 | ||||||||
\(914\) | −3.37878e10 | −1.46369 | ||||||||
\(915\) | 7.29346e6 | 0.000314746 0 | ||||||||
\(916\) | −1.48109e10 | −0.636718 | ||||||||
\(917\) | 2.03739e10 | 0.872531 | ||||||||
\(918\) | 7.69599e10 | 3.28334 | ||||||||
\(919\) | 1.41113e10 | 0.599739 | 0.299869 | − | 0.953980i | \(-0.403057\pi\) | ||||
0.299869 | + | 0.953980i | \(0.403057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.71173e10 | 1.98734 | ||||||||
\(922\) | 2.16789e9 | 0.0910916 | ||||||||
\(923\) | −3.45588e10 | −1.44661 | ||||||||
\(924\) | −2.77864e10 | −1.15872 | ||||||||
\(925\) | 1.22451e10 | 0.508704 | ||||||||
\(926\) | −2.46489e10 | −1.02014 | ||||||||
\(927\) | −5.12743e10 | −2.11408 | ||||||||
\(928\) | −4.95253e10 | −2.03427 | ||||||||
\(929\) | −8.66251e9 | −0.354477 | −0.177239 | − | 0.984168i | \(-0.556716\pi\) | ||||
−0.177239 | + | 0.984168i | \(0.556716\pi\) | |||||||
\(930\) | −1.24970e10 | −0.509467 | ||||||||
\(931\) | −1.16542e10 | −0.473323 | ||||||||
\(932\) | 1.19937e10 | 0.485286 | ||||||||
\(933\) | 1.58687e10 | 0.639668 | ||||||||
\(934\) | 3.71332e10 | 1.49124 | ||||||||
\(935\) | 2.35499e10 | 0.942210 | ||||||||
\(936\) | −9.05558e9 | −0.360953 | ||||||||
\(937\) | 2.24359e10 | 0.890954 | 0.445477 | − | 0.895293i | \(-0.353034\pi\) | ||||
0.445477 | + | 0.895293i | \(0.353034\pi\) | |||||||
\(938\) | 4.06309e10 | 1.60748 | ||||||||
\(939\) | −3.52429e10 | −1.38913 | ||||||||
\(940\) | 5.39420e10 | 2.11826 | ||||||||
\(941\) | 4.12869e10 | 1.61528 | 0.807642 | − | 0.589674i | \(-0.200744\pi\) | ||||
0.807642 | + | 0.589674i | \(0.200744\pi\) | |||||||
\(942\) | 2.10768e10 | 0.821537 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.74283e10 | 1.06120 | ||||||||
\(945\) | −5.40525e10 | −2.08355 | ||||||||
\(946\) | 1.23901e10 | 0.475834 | ||||||||
\(947\) | −3.68012e10 | −1.40811 | −0.704057 | − | 0.710144i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710144i | \(0.748630\pi\) | |||||||
\(948\) | −1.75778e10 | −0.670092 | ||||||||
\(949\) | 1.54519e10 | 0.586881 | ||||||||
\(950\) | 2.48424e10 | 0.940072 | ||||||||
\(951\) | 4.44974e10 | 1.67766 | ||||||||
\(952\) | −3.32996e9 | −0.125086 | ||||||||
\(953\) | 3.96218e10 | 1.48289 | 0.741445 | − | 0.671014i | \(-0.234141\pi\) | ||||
0.741445 | + | 0.671014i | \(0.234141\pi\) | |||||||
\(954\) | 5.64805e9 | 0.210610 | ||||||||
\(955\) | −2.35573e10 | −0.875214 | ||||||||
\(956\) | 2.32959e8 | 0.00862335 | ||||||||
\(957\) | 4.99157e10 | 1.84096 | ||||||||
\(958\) | 3.51916e9 | 0.129318 | ||||||||
\(959\) | 1.99985e10 | 0.732206 | ||||||||
\(960\) | −7.04253e10 | −2.56909 | ||||||||
\(961\) | −2.67853e10 | −0.973563 | ||||||||
\(962\) | −4.98812e10 | −1.80644 | ||||||||
\(963\) | −5.35418e10 | −1.93197 | ||||||||
\(964\) | 2.75689e10 | 0.991174 | ||||||||
\(965\) | −1.28674e9 | −0.0460940 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.31992e10 | 1.18069 | 0.590343 | − | 0.807153i | \(-0.298993\pi\) | ||||
0.590343 | + | 0.807153i | \(0.298993\pi\) | |||||||
\(968\) | −1.91542e9 | −0.0678735 | ||||||||
\(969\) | 7.50546e10 | 2.64999 | ||||||||
\(970\) | −1.94419e10 | −0.683971 | ||||||||
\(971\) | −2.23646e10 | −0.783961 | −0.391981 | − | 0.919974i | \(-0.628210\pi\) | ||||
−0.391981 | + | 0.919974i | \(0.628210\pi\) | |||||||
\(972\) | 2.29643e10 | 0.802085 | ||||||||
\(973\) | −4.11577e9 | −0.143237 | ||||||||
\(974\) | 3.82768e10 | 1.32733 | ||||||||
\(975\) | −2.76667e10 | −0.955964 | ||||||||
\(976\) | −3.76523e6 | −0.000129634 0 | ||||||||
\(977\) | 2.31233e10 | 0.793266 | 0.396633 | − | 0.917977i | \(-0.370179\pi\) | ||||
0.396633 | + | 0.917977i | \(0.370179\pi\) | |||||||
\(978\) | −3.29223e10 | −1.12539 | ||||||||
\(979\) | −5.62703e9 | −0.191664 | ||||||||
\(980\) | −1.33818e10 | −0.454175 | ||||||||
\(981\) | −6.22940e10 | −2.10671 | ||||||||
\(982\) | 2.21704e10 | 0.747108 | ||||||||
\(983\) | −1.42260e10 | −0.477691 | −0.238845 | − | 0.971058i | \(-0.576769\pi\) | ||||
−0.238845 | + | 0.971058i | \(0.576769\pi\) | |||||||
\(984\) | −4.92223e9 | −0.164694 | ||||||||
\(985\) | −1.91078e10 | −0.637067 | ||||||||
\(986\) | 6.61411e10 | 2.19737 | ||||||||
\(987\) | −6.96242e10 | −2.30489 | ||||||||
\(988\) | −5.29952e10 | −1.74819 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 8.52252e10 | 2.79155 | ||||||||
\(991\) | 3.34542e10 | 1.09192 | 0.545962 | − | 0.837810i | \(-0.316164\pi\) | ||||
0.545962 | + | 0.837810i | \(0.316164\pi\) | |||||||
\(992\) | 7.17182e9 | 0.233259 | ||||||||
\(993\) | 1.00831e11 | 3.26793 | ||||||||
\(994\) | −4.59897e10 | −1.48528 | ||||||||
\(995\) | −4.61541e8 | −0.0148535 | ||||||||
\(996\) | 1.00788e11 | 3.23221 | ||||||||
\(997\) | 2.24944e10 | 0.718855 | 0.359427 | − | 0.933173i | \(-0.382972\pi\) | ||||
0.359427 | + | 0.933173i | \(0.382972\pi\) | |||||||
\(998\) | 5.72520e10 | 1.82320 | ||||||||
\(999\) | 7.26616e10 | 2.30582 |
(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 | 529.8.a.k.1.55 | 65 | ||
23.9 | even | 11 | 23.8.c.a.12.12 | yes | 130 | ||
23.18 | even | 11 | 23.8.c.a.2.12 | ✓ | 130 | ||
23.22 | odd | 2 | 529.8.a.j.1.55 | 65 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.8.c.a.2.12 | ✓ | 130 | 23.18 | even | 11 | ||
23.8.c.a.12.12 | yes | 130 | 23.9 | even | 11 | ||
529.8.a.j.1.55 | 65 | 23.22 | odd | 2 | |||
529.8.a.k.1.55 | 65 | 1.1 | even | 1 | trivial |