Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,10,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(19.5713617742\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000 | 0.707107 | ||||||||
\(3\) | 102.000 | 0.727034 | 0.363517 | − | 0.931588i | \(-0.381576\pi\) | ||||
0.363517 | + | 0.931588i | \(0.381576\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | −1581.00 | −1.13127 | −0.565636 | − | 0.824655i | \(-0.691369\pi\) | ||||
−0.565636 | + | 0.824655i | \(0.691369\pi\) | |||||||
\(6\) | 1632.00 | 0.514090 | ||||||||
\(7\) | −4865.00 | −0.765846 | −0.382923 | − | 0.923780i | \(-0.625083\pi\) | ||||
−0.382923 | + | 0.923780i | \(0.625083\pi\) | |||||||
\(8\) | 4096.00 | 0.353553 | ||||||||
\(9\) | −9279.00 | −0.471422 | ||||||||
\(10\) | −25296.0 | −0.799930 | ||||||||
\(11\) | −64189.0 | −1.32188 | −0.660942 | − | 0.750437i | \(-0.729843\pi\) | ||||
−0.660942 | + | 0.750437i | \(0.729843\pi\) | |||||||
\(12\) | 26112.0 | 0.363517 | ||||||||
\(13\) | −48516.0 | −0.471129 | −0.235565 | − | 0.971859i | \(-0.575694\pi\) | ||||
−0.235565 | + | 0.971859i | \(0.575694\pi\) | |||||||
\(14\) | −77840.0 | −0.541535 | ||||||||
\(15\) | −161262. | −0.822472 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 314477. | 0.913206 | 0.456603 | − | 0.889671i | \(-0.349066\pi\) | ||||
0.456603 | + | 0.889671i | \(0.349066\pi\) | |||||||
\(18\) | −148464. | −0.333346 | ||||||||
\(19\) | 130321. | 0.229416 | ||||||||
\(20\) | −404736. | −0.565636 | ||||||||
\(21\) | −496230. | −0.556796 | ||||||||
\(22\) | −1.02702e6 | −0.934714 | ||||||||
\(23\) | −51088.0 | −0.0380666 | −0.0190333 | − | 0.999819i | \(-0.506059\pi\) | ||||
−0.0190333 | + | 0.999819i | \(0.506059\pi\) | |||||||
\(24\) | 417792. | 0.257045 | ||||||||
\(25\) | 546436. | 0.279775 | ||||||||
\(26\) | −776256. | −0.333139 | ||||||||
\(27\) | −2.95412e6 | −1.06977 | ||||||||
\(28\) | −1.24544e6 | −0.382923 | ||||||||
\(29\) | −1.54322e6 | −0.405169 | −0.202585 | − | 0.979265i | \(-0.564934\pi\) | ||||
−0.202585 | + | 0.979265i | \(0.564934\pi\) | |||||||
\(30\) | −2.58019e6 | −0.581576 | ||||||||
\(31\) | 153108. | 0.0297763 | 0.0148881 | − | 0.999889i | \(-0.495261\pi\) | ||||
0.0148881 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(32\) | 1.04858e6 | 0.176777 | ||||||||
\(33\) | −6.54728e6 | −0.961055 | ||||||||
\(34\) | 5.03163e6 | 0.645734 | ||||||||
\(35\) | 7.69156e6 | 0.866380 | ||||||||
\(36\) | −2.37542e6 | −0.235711 | ||||||||
\(37\) | 71578.0 | 0.00627873 | 0.00313936 | − | 0.999995i | \(-0.499001\pi\) | ||||
0.00313936 | + | 0.999995i | \(0.499001\pi\) | |||||||
\(38\) | 2.08514e6 | 0.162221 | ||||||||
\(39\) | −4.94863e6 | −0.342527 | ||||||||
\(40\) | −6.47578e6 | −0.399965 | ||||||||
\(41\) | −2.41906e7 | −1.33696 | −0.668482 | − | 0.743729i | \(-0.733055\pi\) | ||||
−0.668482 | + | 0.743729i | \(0.733055\pi\) | |||||||
\(42\) | −7.93968e6 | −0.393714 | ||||||||
\(43\) | −2.90653e6 | −0.129648 | −0.0648241 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648241 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(44\) | −1.64324e7 | −0.660942 | ||||||||
\(45\) | 1.46701e7 | 0.533306 | ||||||||
\(46\) | −817408. | −0.0269171 | ||||||||
\(47\) | 1.46874e7 | 0.439041 | 0.219520 | − | 0.975608i | \(-0.429551\pi\) | ||||
0.219520 | + | 0.975608i | \(0.429551\pi\) | |||||||
\(48\) | 6.68467e6 | 0.181758 | ||||||||
\(49\) | −1.66854e7 | −0.413479 | ||||||||
\(50\) | 8.74298e6 | 0.197831 | ||||||||
\(51\) | 3.20767e7 | 0.663931 | ||||||||
\(52\) | −1.24201e7 | −0.235565 | ||||||||
\(53\) | 1.07478e8 | 1.87102 | 0.935510 | − | 0.353301i | \(-0.114941\pi\) | ||||
0.935510 | + | 0.353301i | \(0.114941\pi\) | |||||||
\(54\) | −4.72660e7 | −0.756444 | ||||||||
\(55\) | 1.01483e8 | 1.49541 | ||||||||
\(56\) | −1.99270e7 | −0.270768 | ||||||||
\(57\) | 1.32927e7 | 0.166793 | ||||||||
\(58\) | −2.46915e7 | −0.286498 | ||||||||
\(59\) | 1.38113e8 | 1.48388 | 0.741941 | − | 0.670465i | \(-0.233906\pi\) | ||||
0.741941 | + | 0.670465i | \(0.233906\pi\) | |||||||
\(60\) | −4.12831e7 | −0.411236 | ||||||||
\(61\) | −1.22366e8 | −1.13156 | −0.565779 | − | 0.824557i | \(-0.691424\pi\) | ||||
−0.565779 | + | 0.824557i | \(0.691424\pi\) | |||||||
\(62\) | 2.44973e6 | 0.0210550 | ||||||||
\(63\) | 4.51423e7 | 0.361037 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 7.67038e7 | 0.532975 | ||||||||
\(66\) | −1.04756e8 | −0.679568 | ||||||||
\(67\) | 6.72966e7 | 0.407997 | 0.203998 | − | 0.978971i | \(-0.434606\pi\) | ||||
0.203998 | + | 0.978971i | \(0.434606\pi\) | |||||||
\(68\) | 8.05061e7 | 0.456603 | ||||||||
\(69\) | −5.21098e6 | −0.0276757 | ||||||||
\(70\) | 1.23065e8 | 0.612623 | ||||||||
\(71\) | 2.53993e8 | 1.18620 | 0.593101 | − | 0.805128i | \(-0.297903\pi\) | ||||
0.593101 | + | 0.805128i | \(0.297903\pi\) | |||||||
\(72\) | −3.80068e7 | −0.166673 | ||||||||
\(73\) | 2.55181e7 | 0.105171 | 0.0525855 | − | 0.998616i | \(-0.483254\pi\) | ||||
0.0525855 | + | 0.998616i | \(0.483254\pi\) | |||||||
\(74\) | 1.14525e6 | 0.00443973 | ||||||||
\(75\) | 5.57365e7 | 0.203406 | ||||||||
\(76\) | 3.33622e7 | 0.114708 | ||||||||
\(77\) | 3.12279e8 | 1.01236 | ||||||||
\(78\) | −7.91781e7 | −0.242203 | ||||||||
\(79\) | −2.64202e8 | −0.763158 | −0.381579 | − | 0.924336i | \(-0.624620\pi\) | ||||
−0.381579 | + | 0.924336i | \(0.624620\pi\) | |||||||
\(80\) | −1.03612e8 | −0.282818 | ||||||||
\(81\) | −1.18682e8 | −0.306339 | ||||||||
\(82\) | −3.87050e8 | −0.945376 | ||||||||
\(83\) | −7.24058e8 | −1.67464 | −0.837321 | − | 0.546711i | \(-0.815880\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(84\) | −1.27035e8 | −0.278398 | ||||||||
\(85\) | −4.97188e8 | −1.03308 | ||||||||
\(86\) | −4.65045e7 | −0.0916751 | ||||||||
\(87\) | −1.57408e8 | −0.294572 | ||||||||
\(88\) | −2.62918e8 | −0.467357 | ||||||||
\(89\) | −1.07504e9 | −1.81622 | −0.908110 | − | 0.418732i | \(-0.862475\pi\) | ||||
−0.908110 | + | 0.418732i | \(0.862475\pi\) | |||||||
\(90\) | 2.34722e8 | 0.377105 | ||||||||
\(91\) | 2.36030e8 | 0.360812 | ||||||||
\(92\) | −1.30785e7 | −0.0190333 | ||||||||
\(93\) | 1.56170e7 | 0.0216483 | ||||||||
\(94\) | 2.34998e8 | 0.310449 | ||||||||
\(95\) | −2.06038e8 | −0.259531 | ||||||||
\(96\) | 1.06955e8 | 0.128523 | ||||||||
\(97\) | 1.17323e9 | 1.34558 | 0.672792 | − | 0.739832i | \(-0.265095\pi\) | ||||
0.672792 | + | 0.739832i | \(0.265095\pi\) | |||||||
\(98\) | −2.66966e8 | −0.292374 | ||||||||
\(99\) | 5.95610e8 | 0.623166 | ||||||||
\(100\) | 1.39888e8 | 0.139888 | ||||||||
\(101\) | −1.20251e9 | −1.14985 | −0.574926 | − | 0.818205i | \(-0.694969\pi\) | ||||
−0.574926 | + | 0.818205i | \(0.694969\pi\) | |||||||
\(102\) | 5.13226e8 | 0.469470 | ||||||||
\(103\) | −1.30419e9 | −1.14175 | −0.570877 | − | 0.821036i | \(-0.693397\pi\) | ||||
−0.570877 | + | 0.821036i | \(0.693397\pi\) | |||||||
\(104\) | −1.98722e8 | −0.166569 | ||||||||
\(105\) | 7.84540e8 | 0.629888 | ||||||||
\(106\) | 1.71965e9 | 1.32301 | ||||||||
\(107\) | 3.28531e8 | 0.242297 | 0.121149 | − | 0.992634i | \(-0.461342\pi\) | ||||
0.121149 | + | 0.992634i | \(0.461342\pi\) | |||||||
\(108\) | −7.56256e8 | −0.534887 | ||||||||
\(109\) | 1.26912e9 | 0.861161 | 0.430581 | − | 0.902552i | \(-0.358309\pi\) | ||||
0.430581 | + | 0.902552i | \(0.358309\pi\) | |||||||
\(110\) | 1.62372e9 | 1.05741 | ||||||||
\(111\) | 7.30096e6 | 0.00456485 | ||||||||
\(112\) | −3.18833e8 | −0.191462 | ||||||||
\(113\) | −6.03462e8 | −0.348175 | −0.174087 | − | 0.984730i | \(-0.555698\pi\) | ||||
−0.174087 | + | 0.984730i | \(0.555698\pi\) | |||||||
\(114\) | 2.12684e8 | 0.117940 | ||||||||
\(115\) | 8.07701e7 | 0.0430636 | ||||||||
\(116\) | −3.95064e8 | −0.202585 | ||||||||
\(117\) | 4.50180e8 | 0.222101 | ||||||||
\(118\) | 2.20980e9 | 1.04926 | ||||||||
\(119\) | −1.52993e9 | −0.699375 | ||||||||
\(120\) | −6.60529e8 | −0.290788 | ||||||||
\(121\) | 1.76228e9 | 0.747379 | ||||||||
\(122\) | −1.95786e9 | −0.800132 | ||||||||
\(123\) | −2.46744e9 | −0.972017 | ||||||||
\(124\) | 3.91956e7 | 0.0148881 | ||||||||
\(125\) | 2.22398e9 | 0.814770 | ||||||||
\(126\) | 7.22277e8 | 0.255292 | ||||||||
\(127\) | −9.19867e8 | −0.313768 | −0.156884 | − | 0.987617i | \(-0.550145\pi\) | ||||
−0.156884 | + | 0.987617i | \(0.550145\pi\) | |||||||
\(128\) | 2.68435e8 | 0.0883883 | ||||||||
\(129\) | −2.96466e8 | −0.0942586 | ||||||||
\(130\) | 1.22726e9 | 0.376870 | ||||||||
\(131\) | 2.13372e9 | 0.633020 | 0.316510 | − | 0.948589i | \(-0.397489\pi\) | ||||
0.316510 | + | 0.948589i | \(0.397489\pi\) | |||||||
\(132\) | −1.67610e9 | −0.480527 | ||||||||
\(133\) | −6.34012e8 | −0.175697 | ||||||||
\(134\) | 1.07675e9 | 0.288497 | ||||||||
\(135\) | 4.67047e9 | 1.21020 | ||||||||
\(136\) | 1.28810e9 | 0.322867 | ||||||||
\(137\) | −4.83513e9 | −1.17264 | −0.586321 | − | 0.810079i | \(-0.699424\pi\) | ||||
−0.586321 | + | 0.810079i | \(0.699424\pi\) | |||||||
\(138\) | −8.33756e7 | −0.0195697 | ||||||||
\(139\) | −5.89855e9 | −1.34023 | −0.670114 | − | 0.742258i | \(-0.733755\pi\) | ||||
−0.670114 | + | 0.742258i | \(0.733755\pi\) | |||||||
\(140\) | 1.96904e9 | 0.433190 | ||||||||
\(141\) | 1.49812e9 | 0.319197 | ||||||||
\(142\) | 4.06388e9 | 0.838772 | ||||||||
\(143\) | 3.11419e9 | 0.622778 | ||||||||
\(144\) | −6.08109e8 | −0.117856 | ||||||||
\(145\) | 2.43983e9 | 0.458356 | ||||||||
\(146\) | 4.08290e8 | 0.0743671 | ||||||||
\(147\) | −1.70191e9 | −0.300613 | ||||||||
\(148\) | 1.83240e7 | 0.00313936 | ||||||||
\(149\) | −1.64663e9 | −0.273690 | −0.136845 | − | 0.990592i | \(-0.543696\pi\) | ||||
−0.136845 | + | 0.990592i | \(0.543696\pi\) | |||||||
\(150\) | 8.91784e8 | 0.143830 | ||||||||
\(151\) | −1.21642e9 | −0.190409 | −0.0952046 | − | 0.995458i | \(-0.530351\pi\) | ||||
−0.0952046 | + | 0.995458i | \(0.530351\pi\) | |||||||
\(152\) | 5.33795e8 | 0.0811107 | ||||||||
\(153\) | −2.91803e9 | −0.430505 | ||||||||
\(154\) | 4.99647e9 | 0.715847 | ||||||||
\(155\) | −2.42064e8 | −0.0336850 | ||||||||
\(156\) | −1.26685e9 | −0.171263 | ||||||||
\(157\) | −6.68596e9 | −0.878244 | −0.439122 | − | 0.898427i | \(-0.644710\pi\) | ||||
−0.439122 | + | 0.898427i | \(0.644710\pi\) | |||||||
\(158\) | −4.22723e9 | −0.539634 | ||||||||
\(159\) | 1.09628e10 | 1.36029 | ||||||||
\(160\) | −1.65780e9 | −0.199982 | ||||||||
\(161\) | 2.48543e8 | 0.0291531 | ||||||||
\(162\) | −1.89891e9 | −0.216615 | ||||||||
\(163\) | −1.09773e10 | −1.21802 | −0.609008 | − | 0.793164i | \(-0.708432\pi\) | ||||
−0.609008 | + | 0.793164i | \(0.708432\pi\) | |||||||
\(164\) | −6.19280e9 | −0.668482 | ||||||||
\(165\) | 1.03512e10 | 1.08721 | ||||||||
\(166\) | −1.15849e10 | −1.18415 | ||||||||
\(167\) | 2.11768e9 | 0.210686 | 0.105343 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105343 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(168\) | −2.03256e9 | −0.196857 | ||||||||
\(169\) | −8.25070e9 | −0.778037 | ||||||||
\(170\) | −7.95501e9 | −0.730501 | ||||||||
\(171\) | −1.20925e9 | −0.108152 | ||||||||
\(172\) | −7.44071e8 | −0.0648241 | ||||||||
\(173\) | 1.84114e10 | 1.56271 | 0.781355 | − | 0.624087i | \(-0.214529\pi\) | ||||
0.781355 | + | 0.624087i | \(0.214529\pi\) | |||||||
\(174\) | −2.51853e9 | −0.208294 | ||||||||
\(175\) | −2.65841e9 | −0.214265 | ||||||||
\(176\) | −4.20669e9 | −0.330471 | ||||||||
\(177\) | 1.40875e10 | 1.07883 | ||||||||
\(178\) | −1.72006e10 | −1.28426 | ||||||||
\(179\) | −1.82020e10 | −1.32520 | −0.662599 | − | 0.748974i | \(-0.730547\pi\) | ||||
−0.662599 | + | 0.748974i | \(0.730547\pi\) | |||||||
\(180\) | 3.75555e9 | 0.266653 | ||||||||
\(181\) | 1.11247e10 | 0.770431 | 0.385216 | − | 0.922827i | \(-0.374127\pi\) | ||||
0.385216 | + | 0.922827i | \(0.374127\pi\) | |||||||
\(182\) | 3.77649e9 | 0.255133 | ||||||||
\(183\) | −1.24813e10 | −0.822680 | ||||||||
\(184\) | −2.09256e8 | −0.0134586 | ||||||||
\(185\) | −1.13165e8 | −0.00710295 | ||||||||
\(186\) | 2.49872e8 | 0.0153077 | ||||||||
\(187\) | −2.01860e10 | −1.20715 | ||||||||
\(188\) | 3.75998e9 | 0.219520 | ||||||||
\(189\) | 1.43718e10 | 0.819282 | ||||||||
\(190\) | −3.29660e9 | −0.183516 | ||||||||
\(191\) | −2.23310e10 | −1.21411 | −0.607056 | − | 0.794659i | \(-0.707649\pi\) | ||||
−0.607056 | + | 0.794659i | \(0.707649\pi\) | |||||||
\(192\) | 1.71128e9 | 0.0908792 | ||||||||
\(193\) | 4.35980e9 | 0.226182 | 0.113091 | − | 0.993585i | \(-0.463925\pi\) | ||||
0.113091 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(194\) | 1.87717e10 | 0.951471 | ||||||||
\(195\) | 7.82379e9 | 0.387491 | ||||||||
\(196\) | −4.27146e9 | −0.206740 | ||||||||
\(197\) | 2.47577e10 | 1.17115 | 0.585574 | − | 0.810619i | \(-0.300869\pi\) | ||||
0.585574 | + | 0.810619i | \(0.300869\pi\) | |||||||
\(198\) | 9.52976e9 | 0.440645 | ||||||||
\(199\) | 2.57114e10 | 1.16222 | 0.581108 | − | 0.813827i | \(-0.302620\pi\) | ||||
0.581108 | + | 0.813827i | \(0.302620\pi\) | |||||||
\(200\) | 2.23820e9 | 0.0989155 | ||||||||
\(201\) | 6.86425e9 | 0.296627 | ||||||||
\(202\) | −1.92401e10 | −0.813068 | ||||||||
\(203\) | 7.50776e9 | 0.310297 | ||||||||
\(204\) | 8.21162e9 | 0.331966 | ||||||||
\(205\) | 3.82453e10 | 1.51247 | ||||||||
\(206\) | −2.08670e10 | −0.807341 | ||||||||
\(207\) | 4.74046e8 | 0.0179454 | ||||||||
\(208\) | −3.17954e9 | −0.117782 | ||||||||
\(209\) | −8.36517e9 | −0.303261 | ||||||||
\(210\) | 1.25526e10 | 0.445398 | ||||||||
\(211\) | −4.87650e10 | −1.69370 | −0.846852 | − | 0.531829i | \(-0.821505\pi\) | ||||
−0.846852 | + | 0.531829i | \(0.821505\pi\) | |||||||
\(212\) | 2.75144e10 | 0.935510 | ||||||||
\(213\) | 2.59073e10 | 0.862409 | ||||||||
\(214\) | 5.25649e9 | 0.171330 | ||||||||
\(215\) | 4.59522e9 | 0.146667 | ||||||||
\(216\) | −1.21001e10 | −0.378222 | ||||||||
\(217\) | −7.44870e8 | −0.0228040 | ||||||||
\(218\) | 2.03060e10 | 0.608933 | ||||||||
\(219\) | 2.60285e9 | 0.0764628 | ||||||||
\(220\) | 2.59796e10 | 0.747705 | ||||||||
\(221\) | −1.52572e10 | −0.430238 | ||||||||
\(222\) | 1.16815e8 | 0.00322784 | ||||||||
\(223\) | −1.99213e10 | −0.539443 | −0.269722 | − | 0.962938i | \(-0.586932\pi\) | ||||
−0.269722 | + | 0.962938i | \(0.586932\pi\) | |||||||
\(224\) | −5.10132e9 | −0.135384 | ||||||||
\(225\) | −5.07038e9 | −0.131892 | ||||||||
\(226\) | −9.65540e9 | −0.246197 | ||||||||
\(227\) | 6.30952e10 | 1.57718 | 0.788588 | − | 0.614922i | \(-0.210812\pi\) | ||||
0.788588 | + | 0.614922i | \(0.210812\pi\) | |||||||
\(228\) | 3.40294e9 | 0.0833965 | ||||||||
\(229\) | −2.98031e10 | −0.716147 | −0.358073 | − | 0.933693i | \(-0.616566\pi\) | ||||
−0.358073 | + | 0.933693i | \(0.616566\pi\) | |||||||
\(230\) | 1.29232e9 | 0.0304506 | ||||||||
\(231\) | 3.18525e10 | 0.736020 | ||||||||
\(232\) | −6.32102e9 | −0.143249 | ||||||||
\(233\) | 4.49049e9 | 0.0998141 | 0.0499070 | − | 0.998754i | \(-0.484107\pi\) | ||||
0.0499070 | + | 0.998754i | \(0.484107\pi\) | |||||||
\(234\) | 7.20288e9 | 0.157049 | ||||||||
\(235\) | −2.32208e10 | −0.496674 | ||||||||
\(236\) | 3.53568e10 | 0.741941 | ||||||||
\(237\) | −2.69486e10 | −0.554841 | ||||||||
\(238\) | −2.44789e10 | −0.494533 | ||||||||
\(239\) | −1.55900e10 | −0.309069 | −0.154534 | − | 0.987987i | \(-0.549388\pi\) | ||||
−0.154534 | + | 0.987987i | \(0.549388\pi\) | |||||||
\(240\) | −1.05685e10 | −0.205618 | ||||||||
\(241\) | 1.02707e9 | 0.0196121 | 0.00980605 | − | 0.999952i | \(-0.496879\pi\) | ||||
0.00980605 | + | 0.999952i | \(0.496879\pi\) | |||||||
\(242\) | 2.81965e10 | 0.528477 | ||||||||
\(243\) | 4.60404e10 | 0.847054 | ||||||||
\(244\) | −3.13257e10 | −0.565779 | ||||||||
\(245\) | 2.63796e10 | 0.467757 | ||||||||
\(246\) | −3.94791e10 | −0.687320 | ||||||||
\(247\) | −6.32265e9 | −0.108084 | ||||||||
\(248\) | 6.27130e8 | 0.0105275 | ||||||||
\(249\) | −7.38540e10 | −1.21752 | ||||||||
\(250\) | 3.55836e10 | 0.576129 | ||||||||
\(251\) | −8.57726e10 | −1.36401 | −0.682004 | − | 0.731349i | \(-0.738891\pi\) | ||||
−0.682004 | + | 0.731349i | \(0.738891\pi\) | |||||||
\(252\) | 1.15564e10 | 0.180518 | ||||||||
\(253\) | 3.27929e9 | 0.0503196 | ||||||||
\(254\) | −1.47179e10 | −0.221867 | ||||||||
\(255\) | −5.07132e10 | −0.751087 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 2.45603e10 | 0.351184 | 0.175592 | − | 0.984463i | \(-0.443816\pi\) | ||||
0.175592 | + | 0.984463i | \(0.443816\pi\) | |||||||
\(258\) | −4.74346e9 | −0.0666509 | ||||||||
\(259\) | −3.48227e8 | −0.00480854 | ||||||||
\(260\) | 1.96362e10 | 0.266487 | ||||||||
\(261\) | 1.43195e10 | 0.191006 | ||||||||
\(262\) | 3.41396e10 | 0.447612 | ||||||||
\(263\) | −7.30924e10 | −0.942044 | −0.471022 | − | 0.882121i | \(-0.656115\pi\) | ||||
−0.471022 | + | 0.882121i | \(0.656115\pi\) | |||||||
\(264\) | −2.68177e10 | −0.339784 | ||||||||
\(265\) | −1.69923e11 | −2.11663 | ||||||||
\(266\) | −1.01442e10 | −0.124237 | ||||||||
\(267\) | −1.09654e11 | −1.32045 | ||||||||
\(268\) | 1.72279e10 | 0.203998 | ||||||||
\(269\) | 6.31008e10 | 0.734767 | 0.367384 | − | 0.930070i | \(-0.380254\pi\) | ||||
0.367384 | + | 0.930070i | \(0.380254\pi\) | |||||||
\(270\) | 7.47275e10 | 0.855744 | ||||||||
\(271\) | −9.88889e10 | −1.11375 | −0.556873 | − | 0.830598i | \(-0.687999\pi\) | ||||
−0.556873 | + | 0.830598i | \(0.687999\pi\) | |||||||
\(272\) | 2.06096e10 | 0.228301 | ||||||||
\(273\) | 2.40751e10 | 0.262323 | ||||||||
\(274\) | −7.73621e10 | −0.829183 | ||||||||
\(275\) | −3.50752e10 | −0.369831 | ||||||||
\(276\) | −1.33401e9 | −0.0138378 | ||||||||
\(277\) | −1.18609e11 | −1.21048 | −0.605242 | − | 0.796041i | \(-0.706924\pi\) | ||||
−0.605242 | + | 0.796041i | \(0.706924\pi\) | |||||||
\(278\) | −9.43768e10 | −0.947684 | ||||||||
\(279\) | −1.42069e9 | −0.0140372 | ||||||||
\(280\) | 3.15047e10 | 0.306312 | ||||||||
\(281\) | 1.93961e11 | 1.85582 | 0.927910 | − | 0.372805i | \(-0.121604\pi\) | ||||
0.927910 | + | 0.372805i | \(0.121604\pi\) | |||||||
\(282\) | 2.39698e10 | 0.225707 | ||||||||
\(283\) | 1.11144e11 | 1.03003 | 0.515013 | − | 0.857183i | \(-0.327787\pi\) | ||||
0.515013 | + | 0.857183i | \(0.327787\pi\) | |||||||
\(284\) | 6.50222e10 | 0.593101 | ||||||||
\(285\) | −2.10158e10 | −0.188688 | ||||||||
\(286\) | 4.98271e10 | 0.440371 | ||||||||
\(287\) | 1.17687e11 | 1.02391 | ||||||||
\(288\) | −9.72974e9 | −0.0833364 | ||||||||
\(289\) | −1.96921e10 | −0.166055 | ||||||||
\(290\) | 3.90372e10 | 0.324107 | ||||||||
\(291\) | 1.19670e11 | 0.978284 | ||||||||
\(292\) | 6.53264e9 | 0.0525855 | ||||||||
\(293\) | 1.83473e11 | 1.45435 | 0.727175 | − | 0.686452i | \(-0.240833\pi\) | ||||
0.727175 | + | 0.686452i | \(0.240833\pi\) | |||||||
\(294\) | −2.72305e10 | −0.212566 | ||||||||
\(295\) | −2.18356e11 | −1.67867 | ||||||||
\(296\) | 2.93183e8 | 0.00221987 | ||||||||
\(297\) | 1.89622e11 | 1.41412 | ||||||||
\(298\) | −2.63461e10 | −0.193528 | ||||||||
\(299\) | 2.47859e9 | 0.0179343 | ||||||||
\(300\) | 1.42685e10 | 0.101703 | ||||||||
\(301\) | 1.41403e10 | 0.0992906 | ||||||||
\(302\) | −1.94627e10 | −0.134640 | ||||||||
\(303\) | −1.22656e11 | −0.835981 | ||||||||
\(304\) | 8.54072e9 | 0.0573539 | ||||||||
\(305\) | 1.93461e11 | 1.28010 | ||||||||
\(306\) | −4.66885e10 | −0.304413 | ||||||||
\(307\) | −1.04516e11 | −0.671525 | −0.335762 | − | 0.941947i | \(-0.608994\pi\) | ||||
−0.335762 | + | 0.941947i | \(0.608994\pi\) | |||||||
\(308\) | 7.99435e10 | 0.506180 | ||||||||
\(309\) | −1.33027e11 | −0.830093 | ||||||||
\(310\) | −3.87302e9 | −0.0238189 | ||||||||
\(311\) | 2.51394e11 | 1.52382 | 0.761909 | − | 0.647685i | \(-0.224263\pi\) | ||||
0.761909 | + | 0.647685i | \(0.224263\pi\) | |||||||
\(312\) | −2.02696e10 | −0.121101 | ||||||||
\(313\) | −6.58635e10 | −0.387878 | −0.193939 | − | 0.981014i | \(-0.562126\pi\) | ||||
−0.193939 | + | 0.981014i | \(0.562126\pi\) | |||||||
\(314\) | −1.06975e11 | −0.621012 | ||||||||
\(315\) | −7.13700e10 | −0.408431 | ||||||||
\(316\) | −6.76357e10 | −0.381579 | ||||||||
\(317\) | 3.05617e11 | 1.69985 | 0.849925 | − | 0.526904i | \(-0.176647\pi\) | ||||
0.849925 | + | 0.526904i | \(0.176647\pi\) | |||||||
\(318\) | 1.75404e11 | 0.961873 | ||||||||
\(319\) | 9.90576e10 | 0.535587 | ||||||||
\(320\) | −2.65248e10 | −0.141409 | ||||||||
\(321\) | 3.35101e10 | 0.176158 | ||||||||
\(322\) | 3.97669e9 | 0.0206144 | ||||||||
\(323\) | 4.09830e10 | 0.209504 | ||||||||
\(324\) | −3.03826e10 | −0.153170 | ||||||||
\(325\) | −2.65109e10 | −0.131810 | ||||||||
\(326\) | −1.75637e11 | −0.861267 | ||||||||
\(327\) | 1.29451e11 | 0.626093 | ||||||||
\(328\) | −9.90847e10 | −0.472688 | ||||||||
\(329\) | −7.14542e10 | −0.336238 | ||||||||
\(330\) | 1.65620e11 | 0.768776 | ||||||||
\(331\) | −1.42404e10 | −0.0652073 | −0.0326036 | − | 0.999468i | \(-0.510380\pi\) | ||||
−0.0326036 | + | 0.999468i | \(0.510380\pi\) | |||||||
\(332\) | −1.85359e11 | −0.837321 | ||||||||
\(333\) | −6.64172e8 | −0.00295993 | ||||||||
\(334\) | 3.38828e10 | 0.148977 | ||||||||
\(335\) | −1.06396e11 | −0.461555 | ||||||||
\(336\) | −3.25209e10 | −0.139199 | ||||||||
\(337\) | 1.41523e11 | 0.597714 | 0.298857 | − | 0.954298i | \(-0.403395\pi\) | ||||
0.298857 | + | 0.954298i | \(0.403395\pi\) | |||||||
\(338\) | −1.32011e11 | −0.550156 | ||||||||
\(339\) | −6.15532e10 | −0.253135 | ||||||||
\(340\) | −1.27280e11 | −0.516542 | ||||||||
\(341\) | −9.82785e9 | −0.0393608 | ||||||||
\(342\) | −1.93480e10 | −0.0764748 | ||||||||
\(343\) | 2.77495e11 | 1.08251 | ||||||||
\(344\) | −1.19051e10 | −0.0458376 | ||||||||
\(345\) | 8.23855e9 | 0.0313087 | ||||||||
\(346\) | 2.94582e11 | 1.10500 | ||||||||
\(347\) | −5.29148e11 | −1.95927 | −0.979635 | − | 0.200788i | \(-0.935650\pi\) | ||||
−0.979635 | + | 0.200788i | \(0.935650\pi\) | |||||||
\(348\) | −4.02965e10 | −0.147286 | ||||||||
\(349\) | 5.76493e10 | 0.208008 | 0.104004 | − | 0.994577i | \(-0.466835\pi\) | ||||
0.104004 | + | 0.994577i | \(0.466835\pi\) | |||||||
\(350\) | −4.25346e10 | −0.151508 | ||||||||
\(351\) | 1.43322e11 | 0.504001 | ||||||||
\(352\) | −6.73070e10 | −0.233678 | ||||||||
\(353\) | 3.89169e11 | 1.33399 | 0.666993 | − | 0.745064i | \(-0.267581\pi\) | ||||
0.666993 | + | 0.745064i | \(0.267581\pi\) | |||||||
\(354\) | 2.25400e11 | 0.762849 | ||||||||
\(355\) | −4.01563e11 | −1.34192 | ||||||||
\(356\) | −2.75209e11 | −0.908110 | ||||||||
\(357\) | −1.56053e11 | −0.508470 | ||||||||
\(358\) | −2.91232e11 | −0.937057 | ||||||||
\(359\) | 1.06143e11 | 0.337262 | 0.168631 | − | 0.985679i | \(-0.446065\pi\) | ||||
0.168631 | + | 0.985679i | \(0.446065\pi\) | |||||||
\(360\) | 6.00887e10 | 0.188552 | ||||||||
\(361\) | 1.69836e10 | 0.0526316 | ||||||||
\(362\) | 1.77995e11 | 0.544777 | ||||||||
\(363\) | 1.79753e11 | 0.543370 | ||||||||
\(364\) | 6.04238e10 | 0.180406 | ||||||||
\(365\) | −4.03441e10 | −0.118977 | ||||||||
\(366\) | −1.99701e11 | −0.581723 | ||||||||
\(367\) | −6.95837e10 | −0.200221 | −0.100111 | − | 0.994976i | \(-0.531920\pi\) | ||||
−0.100111 | + | 0.994976i | \(0.531920\pi\) | |||||||
\(368\) | −3.34810e9 | −0.00951664 | ||||||||
\(369\) | 2.24465e11 | 0.630274 | ||||||||
\(370\) | −1.81064e9 | −0.00502254 | ||||||||
\(371\) | −5.22881e11 | −1.43291 | ||||||||
\(372\) | 3.99796e9 | 0.0108242 | ||||||||
\(373\) | −1.74159e11 | −0.465861 | −0.232930 | − | 0.972493i | \(-0.574831\pi\) | ||||
−0.232930 | + | 0.972493i | \(0.574831\pi\) | |||||||
\(374\) | −3.22975e11 | −0.853586 | ||||||||
\(375\) | 2.26845e11 | 0.592365 | ||||||||
\(376\) | 6.01596e10 | 0.155224 | ||||||||
\(377\) | 7.48708e10 | 0.190887 | ||||||||
\(378\) | 2.29949e11 | 0.579320 | ||||||||
\(379\) | 8.64873e10 | 0.215316 | 0.107658 | − | 0.994188i | \(-0.465665\pi\) | ||||
0.107658 | + | 0.994188i | \(0.465665\pi\) | |||||||
\(380\) | −5.27456e10 | −0.129766 | ||||||||
\(381\) | −9.38264e10 | −0.228120 | ||||||||
\(382\) | −3.57296e11 | −0.858506 | ||||||||
\(383\) | 8.93812e10 | 0.212252 | 0.106126 | − | 0.994353i | \(-0.466155\pi\) | ||||
0.106126 | + | 0.994353i | \(0.466155\pi\) | |||||||
\(384\) | 2.73804e10 | 0.0642613 | ||||||||
\(385\) | −4.93714e11 | −1.14525 | ||||||||
\(386\) | 6.97568e10 | 0.159935 | ||||||||
\(387\) | 2.69697e10 | 0.0611190 | ||||||||
\(388\) | 3.00347e11 | 0.672792 | ||||||||
\(389\) | −4.19755e11 | −0.929444 | −0.464722 | − | 0.885457i | \(-0.653846\pi\) | ||||
−0.464722 | + | 0.885457i | \(0.653846\pi\) | |||||||
\(390\) | 1.25181e11 | 0.273997 | ||||||||
\(391\) | −1.60660e10 | −0.0347626 | ||||||||
\(392\) | −6.83433e10 | −0.146187 | ||||||||
\(393\) | 2.17640e11 | 0.460227 | ||||||||
\(394\) | 3.96123e11 | 0.828126 | ||||||||
\(395\) | 4.17704e11 | 0.863339 | ||||||||
\(396\) | 1.52476e11 | 0.311583 | ||||||||
\(397\) | −2.97495e11 | −0.601065 | −0.300533 | − | 0.953772i | \(-0.597164\pi\) | ||||
−0.300533 | + | 0.953772i | \(0.597164\pi\) | |||||||
\(398\) | 4.11382e11 | 0.821810 | ||||||||
\(399\) | −6.46692e10 | −0.127738 | ||||||||
\(400\) | 3.58112e10 | 0.0699438 | ||||||||
\(401\) | −9.27957e10 | −0.179217 | −0.0896083 | − | 0.995977i | \(-0.528562\pi\) | ||||
−0.0896083 | + | 0.995977i | \(0.528562\pi\) | |||||||
\(402\) | 1.09828e11 | 0.209747 | ||||||||
\(403\) | −7.42819e9 | −0.0140285 | ||||||||
\(404\) | −3.07842e11 | −0.574926 | ||||||||
\(405\) | 1.87636e11 | 0.346553 | ||||||||
\(406\) | 1.20124e11 | 0.219413 | ||||||||
\(407\) | −4.59452e9 | −0.00829976 | ||||||||
\(408\) | 1.31386e11 | 0.234735 | ||||||||
\(409\) | −1.05127e12 | −1.85763 | −0.928815 | − | 0.370543i | \(-0.879172\pi\) | ||||
−0.928815 | + | 0.370543i | \(0.879172\pi\) | |||||||
\(410\) | 6.11926e11 | 1.06948 | ||||||||
\(411\) | −4.93183e11 | −0.852550 | ||||||||
\(412\) | −3.33872e11 | −0.570877 | ||||||||
\(413\) | −6.71918e11 | −1.13643 | ||||||||
\(414\) | 7.58473e9 | 0.0126893 | ||||||||
\(415\) | 1.14474e12 | 1.89448 | ||||||||
\(416\) | −5.08727e10 | −0.0832846 | ||||||||
\(417\) | −6.01652e11 | −0.974391 | ||||||||
\(418\) | −1.33843e11 | −0.214438 | ||||||||
\(419\) | −7.46398e11 | −1.18306 | −0.591531 | − | 0.806282i | \(-0.701476\pi\) | ||||
−0.591531 | + | 0.806282i | \(0.701476\pi\) | |||||||
\(420\) | 2.00842e11 | 0.314944 | ||||||||
\(421\) | −1.02671e12 | −1.59286 | −0.796432 | − | 0.604728i | \(-0.793282\pi\) | ||||
−0.796432 | + | 0.604728i | \(0.793282\pi\) | |||||||
\(422\) | −7.80240e11 | −1.19763 | ||||||||
\(423\) | −1.36284e11 | −0.206973 | ||||||||
\(424\) | 4.40230e11 | 0.661505 | ||||||||
\(425\) | 1.71842e11 | 0.255492 | ||||||||
\(426\) | 4.14516e11 | 0.609815 | ||||||||
\(427\) | 5.95311e11 | 0.866599 | ||||||||
\(428\) | 8.41038e10 | 0.121149 | ||||||||
\(429\) | 3.17648e11 | 0.452781 | ||||||||
\(430\) | 7.35236e10 | 0.103709 | ||||||||
\(431\) | 6.01842e11 | 0.840108 | 0.420054 | − | 0.907499i | \(-0.362011\pi\) | ||||
0.420054 | + | 0.907499i | \(0.362011\pi\) | |||||||
\(432\) | −1.93601e11 | −0.267443 | ||||||||
\(433\) | 3.80261e11 | 0.519860 | 0.259930 | − | 0.965627i | \(-0.416300\pi\) | ||||
0.259930 | + | 0.965627i | \(0.416300\pi\) | |||||||
\(434\) | −1.19179e10 | −0.0161249 | ||||||||
\(435\) | 2.48862e11 | 0.333240 | ||||||||
\(436\) | 3.24895e11 | 0.430581 | ||||||||
\(437\) | −6.65784e9 | −0.00873307 | ||||||||
\(438\) | 4.16456e10 | 0.0540674 | ||||||||
\(439\) | 5.52278e11 | 0.709688 | 0.354844 | − | 0.934926i | \(-0.384534\pi\) | ||||
0.354844 | + | 0.934926i | \(0.384534\pi\) | |||||||
\(440\) | 4.15674e11 | 0.528707 | ||||||||
\(441\) | 1.54824e11 | 0.194923 | ||||||||
\(442\) | −2.44115e11 | −0.304224 | ||||||||
\(443\) | 1.44599e12 | 1.78381 | 0.891906 | − | 0.452221i | \(-0.149368\pi\) | ||||
0.891906 | + | 0.452221i | \(0.149368\pi\) | |||||||
\(444\) | 1.86904e9 | 0.00228242 | ||||||||
\(445\) | 1.69963e12 | 2.05464 | ||||||||
\(446\) | −3.18741e11 | −0.381444 | ||||||||
\(447\) | −1.67957e11 | −0.198982 | ||||||||
\(448\) | −8.16212e10 | −0.0957308 | ||||||||
\(449\) | −4.28462e11 | −0.497513 | −0.248756 | − | 0.968566i | \(-0.580022\pi\) | ||||
−0.248756 | + | 0.968566i | \(0.580022\pi\) | |||||||
\(450\) | −8.11261e10 | −0.0932619 | ||||||||
\(451\) | 1.55277e12 | 1.76731 | ||||||||
\(452\) | −1.54486e11 | −0.174087 | ||||||||
\(453\) | −1.24075e11 | −0.138434 | ||||||||
\(454\) | 1.00952e12 | 1.11523 | ||||||||
\(455\) | −3.73164e11 | −0.408177 | ||||||||
\(456\) | 5.44471e10 | 0.0589702 | ||||||||
\(457\) | −1.40485e12 | −1.50663 | −0.753314 | − | 0.657661i | \(-0.771546\pi\) | ||||
−0.753314 | + | 0.657661i | \(0.771546\pi\) | |||||||
\(458\) | −4.76850e11 | −0.506392 | ||||||||
\(459\) | −9.29004e11 | −0.976923 | ||||||||
\(460\) | 2.06772e10 | 0.0215318 | ||||||||
\(461\) | 1.37738e12 | 1.42037 | 0.710183 | − | 0.704018i | \(-0.248612\pi\) | ||||
0.710183 | + | 0.704018i | \(0.248612\pi\) | |||||||
\(462\) | 5.09640e11 | 0.520445 | ||||||||
\(463\) | 1.35301e12 | 1.36832 | 0.684160 | − | 0.729332i | \(-0.260169\pi\) | ||||
0.684160 | + | 0.729332i | \(0.260169\pi\) | |||||||
\(464\) | −1.01136e11 | −0.101292 | ||||||||
\(465\) | −2.46905e10 | −0.0244902 | ||||||||
\(466\) | 7.18478e10 | 0.0705792 | ||||||||
\(467\) | 1.13537e12 | 1.10462 | 0.552310 | − | 0.833639i | \(-0.313746\pi\) | ||||
0.552310 | + | 0.833639i | \(0.313746\pi\) | |||||||
\(468\) | 1.15246e11 | 0.111050 | ||||||||
\(469\) | −3.27398e11 | −0.312463 | ||||||||
\(470\) | −3.71533e11 | −0.351202 | ||||||||
\(471\) | −6.81968e11 | −0.638513 | ||||||||
\(472\) | 5.65709e11 | 0.524631 | ||||||||
\(473\) | 1.86567e11 | 0.171380 | ||||||||
\(474\) | −4.31178e11 | −0.392332 | ||||||||
\(475\) | 7.12121e10 | 0.0641848 | ||||||||
\(476\) | −3.91662e11 | −0.349688 | ||||||||
\(477\) | −9.97289e11 | −0.882040 | ||||||||
\(478\) | −2.49440e11 | −0.218545 | ||||||||
\(479\) | −1.03514e12 | −0.898440 | −0.449220 | − | 0.893421i | \(-0.648298\pi\) | ||||
−0.449220 | + | 0.893421i | \(0.648298\pi\) | |||||||
\(480\) | −1.69095e11 | −0.145394 | ||||||||
\(481\) | −3.47268e9 | −0.00295809 | ||||||||
\(482\) | 1.64332e10 | 0.0138679 | ||||||||
\(483\) | 2.53514e10 | 0.0211953 | ||||||||
\(484\) | 4.51144e11 | 0.373689 | ||||||||
\(485\) | −1.85488e12 | −1.52222 | ||||||||
\(486\) | 7.36647e11 | 0.598958 | ||||||||
\(487\) | −1.77896e12 | −1.43313 | −0.716567 | − | 0.697519i | \(-0.754287\pi\) | ||||
−0.716567 | + | 0.697519i | \(0.754287\pi\) | |||||||
\(488\) | −5.01211e11 | −0.400066 | ||||||||
\(489\) | −1.11969e12 | −0.885538 | ||||||||
\(490\) | 4.22073e11 | 0.330754 | ||||||||
\(491\) | −2.22425e12 | −1.72710 | −0.863548 | − | 0.504267i | \(-0.831763\pi\) | ||||
−0.863548 | + | 0.504267i | \(0.831763\pi\) | |||||||
\(492\) | −6.31665e11 | −0.486009 | ||||||||
\(493\) | −4.85307e11 | −0.370003 | ||||||||
\(494\) | −1.01162e11 | −0.0764272 | ||||||||
\(495\) | −9.41659e11 | −0.704969 | ||||||||
\(496\) | 1.00341e10 | 0.00744407 | ||||||||
\(497\) | −1.23567e12 | −0.908449 | ||||||||
\(498\) | −1.18166e12 | −0.860918 | ||||||||
\(499\) | 1.97300e12 | 1.42454 | 0.712268 | − | 0.701907i | \(-0.247668\pi\) | ||||
0.712268 | + | 0.701907i | \(0.247668\pi\) | |||||||
\(500\) | 5.69338e11 | 0.407385 | ||||||||
\(501\) | 2.16003e11 | 0.153176 | ||||||||
\(502\) | −1.37236e12 | −0.964499 | ||||||||
\(503\) | 1.01903e12 | 0.709795 | 0.354897 | − | 0.934905i | \(-0.384516\pi\) | ||||
0.354897 | + | 0.934905i | \(0.384516\pi\) | |||||||
\(504\) | 1.84903e11 | 0.127646 | ||||||||
\(505\) | 1.90117e12 | 1.30080 | ||||||||
\(506\) | 5.24686e10 | 0.0355813 | ||||||||
\(507\) | −8.41571e11 | −0.565659 | ||||||||
\(508\) | −2.35486e11 | −0.156884 | ||||||||
\(509\) | 8.88315e11 | 0.586593 | 0.293297 | − | 0.956021i | \(-0.405248\pi\) | ||||
0.293297 | + | 0.956021i | \(0.405248\pi\) | |||||||
\(510\) | −8.11411e11 | −0.531099 | ||||||||
\(511\) | −1.24146e11 | −0.0805448 | ||||||||
\(512\) | 6.87195e10 | 0.0441942 | ||||||||
\(513\) | −3.84984e11 | −0.245423 | ||||||||
\(514\) | 3.92965e11 | 0.248325 | ||||||||
\(515\) | 2.06192e12 | 1.29163 | ||||||||
\(516\) | −7.58953e10 | −0.0471293 | ||||||||
\(517\) | −9.42770e11 | −0.580361 | ||||||||
\(518\) | −5.57163e9 | −0.00340015 | ||||||||
\(519\) | 1.87796e12 | 1.13614 | ||||||||
\(520\) | 3.14179e11 | 0.188435 | ||||||||
\(521\) | 1.58630e12 | 0.943228 | 0.471614 | − | 0.881805i | \(-0.343672\pi\) | ||||
0.471614 | + | 0.881805i | \(0.343672\pi\) | |||||||
\(522\) | 2.29112e11 | 0.135061 | ||||||||
\(523\) | 1.49701e11 | 0.0874915 | 0.0437458 | − | 0.999043i | \(-0.486071\pi\) | ||||
0.0437458 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(524\) | 5.46233e11 | 0.316510 | ||||||||
\(525\) | −2.71158e11 | −0.155778 | ||||||||
\(526\) | −1.16948e12 | −0.666126 | ||||||||
\(527\) | 4.81489e10 | 0.0271919 | ||||||||
\(528\) | −4.29082e11 | −0.240264 | ||||||||
\(529\) | −1.79854e12 | −0.998551 | ||||||||
\(530\) | −2.71876e12 | −1.49668 | ||||||||
\(531\) | −1.28155e12 | −0.699534 | ||||||||
\(532\) | −1.62307e11 | −0.0878486 | ||||||||
\(533\) | 1.17363e12 | 0.629882 | ||||||||
\(534\) | −1.75446e12 | −0.933701 | ||||||||
\(535\) | −5.19407e11 | −0.274104 | ||||||||
\(536\) | 2.75647e11 | 0.144249 | ||||||||
\(537\) | −1.85661e12 | −0.963464 | ||||||||
\(538\) | 1.00961e12 | 0.519559 | ||||||||
\(539\) | 1.07102e12 | 0.546572 | ||||||||
\(540\) | 1.19564e12 | 0.605102 | ||||||||
\(541\) | 3.19362e12 | 1.60286 | 0.801431 | − | 0.598088i | \(-0.204073\pi\) | ||||
0.801431 | + | 0.598088i | \(0.204073\pi\) | |||||||
\(542\) | −1.58222e12 | −0.787537 | ||||||||
\(543\) | 1.13472e12 | 0.560129 | ||||||||
\(544\) | 3.29753e11 | 0.161434 | ||||||||
\(545\) | −2.00648e12 | −0.974207 | ||||||||
\(546\) | 3.85202e11 | 0.185490 | ||||||||
\(547\) | −4.19272e11 | −0.200241 | −0.100120 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100120 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(548\) | −1.23779e12 | −0.586321 | ||||||||
\(549\) | 1.13543e12 | 0.533441 | ||||||||
\(550\) | −5.61203e11 | −0.261510 | ||||||||
\(551\) | −2.01114e11 | −0.0929522 | ||||||||
\(552\) | −2.13442e10 | −0.00978483 | ||||||||
\(553\) | 1.28534e12 | 0.584462 | ||||||||
\(554\) | −1.89775e12 | −0.855942 | ||||||||
\(555\) | −1.15428e10 | −0.00516408 | ||||||||
\(556\) | −1.51003e12 | −0.670114 | ||||||||
\(557\) | 3.22232e12 | 1.41847 | 0.709234 | − | 0.704973i | \(-0.249041\pi\) | ||||
0.709234 | + | 0.704973i | \(0.249041\pi\) | |||||||
\(558\) | −2.27310e10 | −0.00992579 | ||||||||
\(559\) | 1.41013e11 | 0.0610811 | ||||||||
\(560\) | 5.04074e11 | 0.216595 | ||||||||
\(561\) | −2.05897e12 | −0.877641 | ||||||||
\(562\) | 3.10337e12 | 1.31226 | ||||||||
\(563\) | 3.54247e12 | 1.48600 | 0.743000 | − | 0.669291i | \(-0.233402\pi\) | ||||
0.743000 | + | 0.669291i | \(0.233402\pi\) | |||||||
\(564\) | 3.83518e11 | 0.159599 | ||||||||
\(565\) | 9.54074e11 | 0.393880 | ||||||||
\(566\) | 1.77831e12 | 0.728338 | ||||||||
\(567\) | 5.77388e11 | 0.234609 | ||||||||
\(568\) | 1.04035e12 | 0.419386 | ||||||||
\(569\) | 1.05951e12 | 0.423742 | 0.211871 | − | 0.977298i | \(-0.432044\pi\) | ||||
0.211871 | + | 0.977298i | \(0.432044\pi\) | |||||||
\(570\) | −3.36253e11 | −0.133423 | ||||||||
\(571\) | 1.87884e12 | 0.739650 | 0.369825 | − | 0.929101i | \(-0.379418\pi\) | ||||
0.369825 | + | 0.929101i | \(0.379418\pi\) | |||||||
\(572\) | 7.97234e11 | 0.311389 | ||||||||
\(573\) | −2.27776e12 | −0.882700 | ||||||||
\(574\) | 1.88300e12 | 0.724012 | ||||||||
\(575\) | −2.79163e10 | −0.0106501 | ||||||||
\(576\) | −1.55676e11 | −0.0589278 | ||||||||
\(577\) | 1.10245e12 | 0.414065 | 0.207032 | − | 0.978334i | \(-0.433619\pi\) | ||||
0.207032 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(578\) | −3.15073e11 | −0.117419 | ||||||||
\(579\) | 4.44700e11 | 0.164442 | ||||||||
\(580\) | 6.24596e11 | 0.229178 | ||||||||
\(581\) | 3.52254e12 | 1.28252 | ||||||||
\(582\) | 1.91471e12 | 0.691752 | ||||||||
\(583\) | −6.89891e12 | −2.47327 | ||||||||
\(584\) | 1.04522e11 | 0.0371835 | ||||||||
\(585\) | −7.11735e11 | −0.251256 | ||||||||
\(586\) | 2.93558e12 | 1.02838 | ||||||||
\(587\) | −5.10026e12 | −1.77305 | −0.886525 | − | 0.462680i | \(-0.846888\pi\) | ||||
−0.886525 | + | 0.462680i | \(0.846888\pi\) | |||||||
\(588\) | −4.35689e11 | −0.150307 | ||||||||
\(589\) | 1.99532e10 | 0.00683114 | ||||||||
\(590\) | −3.49370e12 | −1.18700 | ||||||||
\(591\) | 2.52528e12 | 0.851464 | ||||||||
\(592\) | 4.69094e9 | 0.00156968 | ||||||||
\(593\) | −2.73128e12 | −0.907026 | −0.453513 | − | 0.891250i | \(-0.649829\pi\) | ||||
−0.453513 | + | 0.891250i | \(0.649829\pi\) | |||||||
\(594\) | 3.03396e12 | 0.999932 | ||||||||
\(595\) | 2.41882e12 | 0.791184 | ||||||||
\(596\) | −4.21538e11 | −0.136845 | ||||||||
\(597\) | 2.62256e12 | 0.844970 | ||||||||
\(598\) | 3.96574e10 | 0.0126814 | ||||||||
\(599\) | 2.10529e11 | 0.0668177 | 0.0334089 | − | 0.999442i | \(-0.489364\pi\) | ||||
0.0334089 | + | 0.999442i | \(0.489364\pi\) | |||||||
\(600\) | 2.28297e11 | 0.0719149 | ||||||||
\(601\) | 3.31426e12 | 1.03622 | 0.518110 | − | 0.855314i | \(-0.326636\pi\) | ||||
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(602\) | 2.26244e11 | 0.0702091 | ||||||||
\(603\) | −6.24445e11 | −0.192339 | ||||||||
\(604\) | −3.11404e11 | −0.0952046 | ||||||||
\(605\) | −2.78616e12 | −0.845488 | ||||||||
\(606\) | −1.96249e12 | −0.591128 | ||||||||
\(607\) | −3.75897e12 | −1.12388 | −0.561940 | − | 0.827178i | \(-0.689945\pi\) | ||||
−0.561940 | + | 0.827178i | \(0.689945\pi\) | |||||||
\(608\) | 1.36651e11 | 0.0405554 | ||||||||
\(609\) | 7.65791e11 | 0.225597 | ||||||||
\(610\) | 3.09537e12 | 0.905166 | ||||||||
\(611\) | −7.12574e11 | −0.206845 | ||||||||
\(612\) | −7.47016e11 | −0.215253 | ||||||||
\(613\) | −4.35989e12 | −1.24711 | −0.623553 | − | 0.781781i | \(-0.714311\pi\) | ||||
−0.623553 | + | 0.781781i | \(0.714311\pi\) | |||||||
\(614\) | −1.67226e12 | −0.474840 | ||||||||
\(615\) | 3.90103e12 | 1.09962 | ||||||||
\(616\) | 1.27910e12 | 0.357923 | ||||||||
\(617\) | 3.10182e11 | 0.0861655 | 0.0430827 | − | 0.999072i | \(-0.486282\pi\) | ||||
0.0430827 | + | 0.999072i | \(0.486282\pi\) | |||||||
\(618\) | −2.12843e12 | −0.586964 | ||||||||
\(619\) | 5.58231e11 | 0.152829 | 0.0764145 | − | 0.997076i | \(-0.475653\pi\) | ||||
0.0764145 | + | 0.997076i | \(0.475653\pi\) | |||||||
\(620\) | −6.19683e10 | −0.0168425 | ||||||||
\(621\) | 1.50920e11 | 0.0407226 | ||||||||
\(622\) | 4.02230e12 | 1.07750 | ||||||||
\(623\) | 5.23006e12 | 1.39095 | ||||||||
\(624\) | −3.24314e11 | −0.0856317 | ||||||||
\(625\) | −4.58336e12 | −1.20150 | ||||||||
\(626\) | −1.05382e12 | −0.274271 | ||||||||
\(627\) | −8.53248e11 | −0.220481 | ||||||||
\(628\) | −1.71161e12 | −0.439122 | ||||||||
\(629\) | 2.25096e10 | 0.00573377 | ||||||||
\(630\) | −1.14192e12 | −0.288804 | ||||||||
\(631\) | −3.12950e12 | −0.785856 | −0.392928 | − | 0.919569i | \(-0.628538\pi\) | ||||
−0.392928 | + | 0.919569i | \(0.628538\pi\) | |||||||
\(632\) | −1.08217e12 | −0.269817 | ||||||||
\(633\) | −4.97403e12 | −1.23138 | ||||||||
\(634\) | 4.88987e12 | 1.20198 | ||||||||
\(635\) | 1.45431e12 | 0.354956 | ||||||||
\(636\) | 2.80647e12 | 0.680147 | ||||||||
\(637\) | 8.09508e11 | 0.194802 | ||||||||
\(638\) | 1.58492e12 | 0.378717 | ||||||||
\(639\) | −2.35680e12 | −0.559202 | ||||||||
\(640\) | −4.24396e11 | −0.0999912 | ||||||||
\(641\) | 1.74234e12 | 0.407635 | 0.203817 | − | 0.979009i | \(-0.434665\pi\) | ||||
0.203817 | + | 0.979009i | \(0.434665\pi\) | |||||||
\(642\) | 5.36162e11 | 0.124563 | ||||||||
\(643\) | −2.16462e12 | −0.499381 | −0.249690 | − | 0.968326i | \(-0.580329\pi\) | ||||
−0.249690 | + | 0.968326i | \(0.580329\pi\) | |||||||
\(644\) | 6.36270e10 | 0.0145766 | ||||||||
\(645\) | 4.68713e11 | 0.106632 | ||||||||
\(646\) | 6.55727e11 | 0.148142 | ||||||||
\(647\) | −8.45274e12 | −1.89639 | −0.948197 | − | 0.317683i | \(-0.897095\pi\) | ||||
−0.948197 | + | 0.317683i | \(0.897095\pi\) | |||||||
\(648\) | −4.86122e11 | −0.108307 | ||||||||
\(649\) | −8.86531e12 | −1.96152 | ||||||||
\(650\) | −4.24174e11 | −0.0932039 | ||||||||
\(651\) | −7.59768e10 | −0.0165793 | ||||||||
\(652\) | −2.81020e12 | −0.609008 | ||||||||
\(653\) | 1.94287e12 | 0.418153 | 0.209076 | − | 0.977899i | \(-0.432954\pi\) | ||||
0.209076 | + | 0.977899i | \(0.432954\pi\) | |||||||
\(654\) | 2.07121e12 | 0.442715 | ||||||||
\(655\) | −3.37342e12 | −0.716117 | ||||||||
\(656\) | −1.58536e12 | −0.334241 | ||||||||
\(657\) | −2.36783e11 | −0.0495799 | ||||||||
\(658\) | −1.14327e12 | −0.237756 | ||||||||
\(659\) | −1.78479e12 | −0.368640 | −0.184320 | − | 0.982866i | \(-0.559008\pi\) | ||||
−0.184320 | + | 0.982866i | \(0.559008\pi\) | |||||||
\(660\) | 2.64992e12 | 0.543607 | ||||||||
\(661\) | 6.08589e12 | 1.23999 | 0.619994 | − | 0.784607i | \(-0.287135\pi\) | ||||
0.619994 | + | 0.784607i | \(0.287135\pi\) | |||||||
\(662\) | −2.27846e11 | −0.0461085 | ||||||||
\(663\) | −1.55623e12 | −0.312797 | ||||||||
\(664\) | −2.96574e12 | −0.592076 | ||||||||
\(665\) | 1.00237e12 | 0.198761 | ||||||||
\(666\) | −1.06268e10 | −0.00209299 | ||||||||
\(667\) | 7.88399e10 | 0.0154234 | ||||||||
\(668\) | 5.42125e11 | 0.105343 | ||||||||
\(669\) | −2.03197e12 | −0.392193 | ||||||||
\(670\) | −1.70234e12 | −0.326369 | ||||||||
\(671\) | 7.85455e12 | 1.49579 | ||||||||
\(672\) | −5.20335e11 | −0.0984286 | ||||||||
\(673\) | 4.24160e12 | 0.797007 | 0.398504 | − | 0.917167i | \(-0.369530\pi\) | ||||
0.398504 | + | 0.917167i | \(0.369530\pi\) | |||||||
\(674\) | 2.26437e12 | 0.422648 | ||||||||
\(675\) | −1.61424e12 | −0.299296 | ||||||||
\(676\) | −2.11218e12 | −0.389019 | ||||||||
\(677\) | −2.61978e12 | −0.479310 | −0.239655 | − | 0.970858i | \(-0.577034\pi\) | ||||
−0.239655 | + | 0.970858i | \(0.577034\pi\) | |||||||
\(678\) | −9.84851e11 | −0.178993 | ||||||||
\(679\) | −5.70777e12 | −1.03051 | ||||||||
\(680\) | −2.03648e12 | −0.365250 | ||||||||
\(681\) | 6.43571e12 | 1.14666 | ||||||||
\(682\) | −1.57246e11 | −0.0278323 | ||||||||
\(683\) | −4.81312e12 | −0.846319 | −0.423159 | − | 0.906055i | \(-0.639079\pi\) | ||||
−0.423159 | + | 0.906055i | \(0.639079\pi\) | |||||||
\(684\) | −3.09568e11 | −0.0540758 | ||||||||
\(685\) | 7.64434e12 | 1.32658 | ||||||||
\(686\) | 4.43991e12 | 0.765449 | ||||||||
\(687\) | −3.03992e12 | −0.520663 | ||||||||
\(688\) | −1.90482e11 | −0.0324121 | ||||||||
\(689\) | −5.21441e12 | −0.881492 | ||||||||
\(690\) | 1.31817e11 | 0.0221386 | ||||||||
\(691\) | 5.44127e12 | 0.907922 | 0.453961 | − | 0.891021i | \(-0.350010\pi\) | ||||
0.453961 | + | 0.891021i | \(0.350010\pi\) | |||||||
\(692\) | 4.71331e12 | 0.781355 | ||||||||
\(693\) | −2.89764e12 | −0.477249 | ||||||||
\(694\) | −8.46636e12 | −1.38541 | ||||||||
\(695\) | 9.32561e12 | 1.51616 | ||||||||
\(696\) | −6.44744e11 | −0.104147 | ||||||||
\(697\) | −7.60739e12 | −1.22092 | ||||||||
\(698\) | 9.22389e11 | 0.147084 | ||||||||
\(699\) | 4.58030e11 | 0.0725682 | ||||||||
\(700\) | −6.80553e11 | −0.107132 | ||||||||
\(701\) | 9.70124e12 | 1.51739 | 0.758693 | − | 0.651448i | \(-0.225838\pi\) | ||||
0.758693 | + | 0.651448i | \(0.225838\pi\) | |||||||
\(702\) | 2.29316e12 | 0.356383 | ||||||||
\(703\) | 9.32812e9 | 0.00144044 | ||||||||
\(704\) | −1.07691e12 | −0.165236 | ||||||||
\(705\) | −2.36852e12 | −0.361099 | ||||||||
\(706\) | 6.22670e12 | 0.943271 | ||||||||
\(707\) | 5.85021e12 | 0.880610 | ||||||||
\(708\) | 3.60640e12 | 0.539416 | ||||||||
\(709\) | 1.08088e13 | 1.60646 | 0.803231 | − | 0.595668i | \(-0.203113\pi\) | ||||
0.803231 | + | 0.595668i | \(0.203113\pi\) | |||||||
\(710\) | −6.42500e12 | −0.948879 | ||||||||
\(711\) | 2.45153e12 | 0.359769 | ||||||||
\(712\) | −4.40335e12 | −0.642131 | ||||||||
\(713\) | −7.82198e9 | −0.00113348 | ||||||||
\(714\) | −2.49685e12 | −0.359542 | ||||||||
\(715\) | −4.92354e12 | −0.704531 | ||||||||
\(716\) | −4.65972e12 | −0.662599 | ||||||||
\(717\) | −1.59018e12 | −0.224703 | ||||||||
\(718\) | 1.69829e12 | 0.238480 | ||||||||
\(719\) | −1.28259e13 | −1.78981 | −0.894905 | − | 0.446256i | \(-0.852757\pi\) | ||||
−0.894905 | + | 0.446256i | \(0.852757\pi\) | |||||||
\(720\) | 9.61420e11 | 0.133327 | ||||||||
\(721\) | 6.34487e12 | 0.874407 | ||||||||
\(722\) | 2.71737e11 | 0.0372161 | ||||||||
\(723\) | 1.04761e11 | 0.0142587 | ||||||||
\(724\) | 2.84792e12 | 0.385216 | ||||||||
\(725\) | −8.43270e11 | −0.113356 | ||||||||
\(726\) | 2.87604e12 | 0.384220 | ||||||||
\(727\) | −8.26428e12 | −1.09724 | −0.548618 | − | 0.836073i | \(-0.684846\pi\) | ||||
−0.548618 | + | 0.836073i | \(0.684846\pi\) | |||||||
\(728\) | 9.66780e11 | 0.127566 | ||||||||
\(729\) | 7.03215e12 | 0.922176 | ||||||||
\(730\) | −6.45506e11 | −0.0841294 | ||||||||
\(731\) | −9.14037e11 | −0.118396 | ||||||||
\(732\) | −3.19522e12 | −0.411340 | ||||||||
\(733\) | 9.23305e12 | 1.18135 | 0.590673 | − | 0.806911i | \(-0.298862\pi\) | ||||
0.590673 | + | 0.806911i | \(0.298862\pi\) | |||||||
\(734\) | −1.11334e12 | −0.141578 | ||||||||
\(735\) | 2.69072e12 | 0.340075 | ||||||||
\(736\) | −5.35697e10 | −0.00672928 | ||||||||
\(737\) | −4.31970e12 | −0.539324 | ||||||||
\(738\) | 3.59143e12 | 0.445671 | ||||||||
\(739\) | 4.26380e12 | 0.525892 | 0.262946 | − | 0.964811i | \(-0.415306\pi\) | ||||
0.262946 | + | 0.964811i | \(0.415306\pi\) | |||||||
\(740\) | −2.89702e10 | −0.00355147 | ||||||||
\(741\) | −6.44911e11 | −0.0785810 | ||||||||
\(742\) | −8.36609e12 | −1.01322 | ||||||||
\(743\) | −5.50358e12 | −0.662514 | −0.331257 | − | 0.943541i | \(-0.607473\pi\) | ||||
−0.331257 | + | 0.943541i | \(0.607473\pi\) | |||||||
\(744\) | 6.39673e10 | 0.00765385 | ||||||||
\(745\) | 2.60333e12 | 0.309617 | ||||||||
\(746\) | −2.78654e12 | −0.329413 | ||||||||
\(747\) | 6.71854e12 | 0.789464 | ||||||||
\(748\) | −5.16761e12 | −0.603576 | ||||||||
\(749\) | −1.59830e12 | −0.185563 | ||||||||
\(750\) | 3.62953e12 | 0.418865 | ||||||||
\(751\) | 1.00995e13 | 1.15857 | 0.579285 | − | 0.815125i | \(-0.303332\pi\) | ||||
0.579285 | + | 0.815125i | \(0.303332\pi\) | |||||||
\(752\) | 9.62554e11 | 0.109760 | ||||||||
\(753\) | −8.74881e12 | −0.991680 | ||||||||
\(754\) | 1.19793e12 | 0.134977 | ||||||||
\(755\) | 1.92316e12 | 0.215404 | ||||||||
\(756\) | 3.67918e12 | 0.409641 | ||||||||
\(757\) | 1.26401e13 | 1.39900 | 0.699502 | − | 0.714630i | \(-0.253405\pi\) | ||||
0.699502 | + | 0.714630i | \(0.253405\pi\) | |||||||
\(758\) | 1.38380e12 | 0.152251 | ||||||||
\(759\) | 3.34487e11 | 0.0365840 | ||||||||
\(760\) | −8.43930e11 | −0.0917582 | ||||||||
\(761\) | 1.25016e13 | 1.35125 | 0.675625 | − | 0.737245i | \(-0.263874\pi\) | ||||
0.675625 | + | 0.737245i | \(0.263874\pi\) | |||||||
\(762\) | −1.50122e12 | −0.161305 | ||||||||
\(763\) | −6.17428e12 | −0.659517 | ||||||||
\(764\) | −5.71674e12 | −0.607056 | ||||||||
\(765\) | 4.61341e12 | 0.487019 | ||||||||
\(766\) | 1.43010e12 | 0.150085 | ||||||||
\(767\) | −6.70067e12 | −0.699100 | ||||||||
\(768\) | 4.38087e11 | 0.0454396 | ||||||||
\(769\) | −6.06695e12 | −0.625607 | −0.312804 | − | 0.949818i | \(-0.601268\pi\) | ||||
−0.312804 | + | 0.949818i | \(0.601268\pi\) | |||||||
\(770\) | −7.89942e12 | −0.809817 | ||||||||
\(771\) | 2.50515e12 | 0.255323 | ||||||||
\(772\) | 1.11611e12 | 0.113091 | ||||||||
\(773\) | 1.36551e13 | 1.37559 | 0.687794 | − | 0.725906i | \(-0.258579\pi\) | ||||
0.687794 | + | 0.725906i | \(0.258579\pi\) | |||||||
\(774\) | 4.31515e11 | 0.0432177 | ||||||||
\(775\) | 8.36637e10 | 0.00833066 | ||||||||
\(776\) | 4.80555e12 | 0.475736 | ||||||||
\(777\) | −3.55192e10 | −0.00349597 | ||||||||
\(778\) | −6.71609e12 | −0.657216 | ||||||||
\(779\) | −3.15254e12 | −0.306720 | ||||||||
\(780\) | 2.00289e12 | 0.193745 | ||||||||
\(781\) | −1.63035e13 | −1.56802 | ||||||||
\(782\) | −2.57056e11 | −0.0245809 | ||||||||
\(783\) | 4.55886e12 | 0.433439 | ||||||||
\(784\) | −1.09349e12 | −0.103370 | ||||||||
\(785\) | 1.05705e13 | 0.993532 | ||||||||
\(786\) | 3.48224e12 | 0.325429 | ||||||||
\(787\) | −4.83993e11 | −0.0449731 | −0.0224865 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224865 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(788\) | 6.33796e12 | 0.585574 | ||||||||
\(789\) | −7.45542e12 | −0.684898 | ||||||||
\(790\) | 6.68326e12 | 0.610473 | ||||||||
\(791\) | 2.93584e12 | 0.266648 | ||||||||
\(792\) | 2.43962e12 | 0.220322 | ||||||||
\(793\) | 5.93671e12 | 0.533110 | ||||||||
\(794\) | −4.75991e12 | −0.425017 | ||||||||
\(795\) | −1.73321e13 | −1.53886 | ||||||||
\(796\) | 6.58211e12 | 0.581108 | ||||||||
\(797\) | 1.27488e13 | 1.11919 | 0.559597 | − | 0.828765i | \(-0.310956\pi\) | ||||
0.559597 | + | 0.828765i | \(0.310956\pi\) | |||||||
\(798\) | −1.03471e12 | −0.0903243 | ||||||||
\(799\) | 4.61885e12 | 0.400935 | ||||||||
\(800\) | 5.72980e11 | 0.0494577 | ||||||||
\(801\) | 9.97527e12 | 0.856206 | ||||||||
\(802\) | −1.48473e12 | −0.126725 | ||||||||
\(803\) | −1.63798e12 | −0.139024 | ||||||||
\(804\) | 1.75725e12 | 0.148314 | ||||||||
\(805\) | −3.92947e11 | −0.0329801 | ||||||||
\(806\) | −1.18851e11 | −0.00991962 | ||||||||
\(807\) | 6.43628e12 | 0.534200 | ||||||||
\(808\) | −4.92548e12 | −0.406534 | ||||||||
\(809\) | −1.62239e13 | −1.33164 | −0.665821 | − | 0.746112i | \(-0.731918\pi\) | ||||
−0.665821 | + | 0.746112i | \(0.731918\pi\) | |||||||
\(810\) | 3.00218e12 | 0.245050 | ||||||||
\(811\) | 1.64958e11 | 0.0133899 | 0.00669497 | − | 0.999978i | \(-0.497869\pi\) | ||||
0.00669497 | + | 0.999978i | \(0.497869\pi\) | |||||||
\(812\) | 1.92199e12 | 0.155149 | ||||||||
\(813\) | −1.00867e13 | −0.809730 | ||||||||
\(814\) | −7.35123e10 | −0.00586881 | ||||||||
\(815\) | 1.73552e13 | 1.37791 | ||||||||
\(816\) | 2.10218e12 | 0.165983 | ||||||||
\(817\) | −3.78782e11 | −0.0297433 | ||||||||
\(818\) | −1.68203e13 | −1.31354 | ||||||||
\(819\) | −2.19013e12 | −0.170095 | ||||||||
\(820\) | 9.79081e12 | 0.756234 | ||||||||
\(821\) | −6.60429e12 | −0.507320 | −0.253660 | − | 0.967293i | \(-0.581634\pi\) | ||||
−0.253660 | + | 0.967293i | \(0.581634\pi\) | |||||||
\(822\) | −7.89093e12 | −0.602844 | ||||||||
\(823\) | −1.65599e13 | −1.25823 | −0.629113 | − | 0.777314i | \(-0.716582\pi\) | ||||
−0.629113 | + | 0.777314i | \(0.716582\pi\) | |||||||
\(824\) | −5.34195e12 | −0.403671 | ||||||||
\(825\) | −3.57767e12 | −0.268879 | ||||||||
\(826\) | −1.07507e13 | −0.803574 | ||||||||
\(827\) | −8.02404e12 | −0.596511 | −0.298255 | − | 0.954486i | \(-0.596405\pi\) | ||||
−0.298255 | + | 0.954486i | \(0.596405\pi\) | |||||||
\(828\) | 1.21356e11 | 0.00897271 | ||||||||
\(829\) | −2.19013e13 | −1.61055 | −0.805276 | − | 0.592901i | \(-0.797983\pi\) | ||||
−0.805276 | + | 0.592901i | \(0.797983\pi\) | |||||||
\(830\) | 1.83158e13 | 1.33960 | ||||||||
\(831\) | −1.20981e13 | −0.880063 | ||||||||
\(832\) | −8.13963e11 | −0.0588911 | ||||||||
\(833\) | −5.24717e12 | −0.377592 | ||||||||
\(834\) | −9.62643e12 | −0.688998 | ||||||||
\(835\) | −3.34805e12 | −0.238343 | ||||||||
\(836\) | −2.14148e12 | −0.151631 | ||||||||
\(837\) | −4.52300e11 | −0.0318539 | ||||||||
\(838\) | −1.19424e13 | −0.836551 | ||||||||
\(839\) | −3.11694e12 | −0.217170 | −0.108585 | − | 0.994087i | \(-0.534632\pi\) | ||||
−0.108585 | + | 0.994087i | \(0.534632\pi\) | |||||||
\(840\) | 3.21347e12 | 0.222699 | ||||||||
\(841\) | −1.21256e13 | −0.835838 | ||||||||
\(842\) | −1.64274e13 | −1.12632 | ||||||||
\(843\) | 1.97840e13 | 1.34924 | ||||||||
\(844\) | −1.24838e13 | −0.846852 | ||||||||
\(845\) | 1.30444e13 | 0.880172 | ||||||||
\(846\) | −2.18055e12 | −0.146352 | ||||||||
\(847\) | −8.57349e12 | −0.572377 | ||||||||
\(848\) | 7.04368e12 | 0.467755 | ||||||||
\(849\) | 1.13367e13 | 0.748863 | ||||||||
\(850\) | 2.74946e12 | 0.180660 | ||||||||
\(851\) | −3.65678e9 | −0.000239010 0 | ||||||||
\(852\) | 6.63226e12 | 0.431205 | ||||||||
\(853\) | −5.54035e12 | −0.358316 | −0.179158 | − | 0.983820i | \(-0.557337\pi\) | ||||
−0.179158 | + | 0.983820i | \(0.557337\pi\) | |||||||
\(854\) | 9.52497e12 | 0.612778 | ||||||||
\(855\) | 1.91182e12 | 0.122349 | ||||||||
\(856\) | 1.34566e12 | 0.0856651 | ||||||||
\(857\) | −6.97547e12 | −0.441733 | −0.220867 | − | 0.975304i | \(-0.570889\pi\) | ||||
−0.220867 | + | 0.975304i | \(0.570889\pi\) | |||||||
\(858\) | 5.08236e12 | 0.320164 | ||||||||
\(859\) | −4.19926e11 | −0.0263150 | −0.0131575 | − | 0.999913i | \(-0.504188\pi\) | ||||
−0.0131575 | + | 0.999913i | \(0.504188\pi\) | |||||||
\(860\) | 1.17638e12 | 0.0733337 | ||||||||
\(861\) | 1.20041e13 | 0.744416 | ||||||||
\(862\) | 9.62947e12 | 0.594046 | ||||||||
\(863\) | −1.42650e13 | −0.875434 | −0.437717 | − | 0.899113i | \(-0.644213\pi\) | ||||
−0.437717 | + | 0.899113i | \(0.644213\pi\) | |||||||
\(864\) | −3.09762e12 | −0.189111 | ||||||||
\(865\) | −2.91084e13 | −1.76785 | ||||||||
\(866\) | 6.08418e12 | 0.367597 | ||||||||
\(867\) | −2.00859e12 | −0.120727 | ||||||||
\(868\) | −1.90687e11 | −0.0114020 | ||||||||
\(869\) | 1.69589e13 | 1.00881 | ||||||||
\(870\) | 3.98180e12 | 0.235637 | ||||||||
\(871\) | −3.26496e12 | −0.192219 | ||||||||
\(872\) | 5.19833e12 | 0.304466 | ||||||||
\(873\) | −1.08864e13 | −0.634338 | ||||||||
\(874\) | −1.06525e11 | −0.00617521 | ||||||||
\(875\) | −1.08196e13 | −0.623988 | ||||||||
\(876\) | 6.66329e11 | 0.0382314 | ||||||||
\(877\) | 1.63714e12 | 0.0934519 | 0.0467259 | − | 0.998908i | \(-0.485121\pi\) | ||||
0.0467259 | + | 0.998908i | \(0.485121\pi\) | |||||||
\(878\) | 8.83645e12 | 0.501825 | ||||||||
\(879\) | 1.87143e13 | 1.05736 | ||||||||
\(880\) | 6.65078e12 | 0.373853 | ||||||||
\(881\) | −4.20163e11 | −0.0234977 | −0.0117489 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117489 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(882\) | 2.47718e12 | 0.137832 | ||||||||
\(883\) | −2.88540e13 | −1.59729 | −0.798644 | − | 0.601803i | \(-0.794449\pi\) | ||||
−0.798644 | + | 0.601803i | \(0.794449\pi\) | |||||||
\(884\) | −3.90583e12 | −0.215119 | ||||||||
\(885\) | −2.22723e13 | −1.22045 | ||||||||
\(886\) | 2.31359e13 | 1.26135 | ||||||||
\(887\) | 8.99827e12 | 0.488093 | 0.244047 | − | 0.969764i | \(-0.421525\pi\) | ||||
0.244047 | + | 0.969764i | \(0.421525\pi\) | |||||||
\(888\) | 2.99047e10 | 0.00161392 | ||||||||
\(889\) | 4.47515e12 | 0.240298 | ||||||||
\(890\) | 2.71941e13 | 1.45285 | ||||||||
\(891\) | 7.61808e12 | 0.404945 | ||||||||
\(892\) | −5.09985e12 | −0.269722 | ||||||||
\(893\) | 1.91408e12 | 0.100723 | ||||||||
\(894\) | −2.68730e12 | −0.140701 | ||||||||
\(895\) | 2.87774e13 | 1.49916 | ||||||||
\(896\) | −1.30594e12 | −0.0676919 | ||||||||
\(897\) | 2.52816e11 | 0.0130388 | ||||||||
\(898\) | −6.85540e12 | −0.351794 | ||||||||
\(899\) | −2.36279e11 | −0.0120644 | ||||||||
\(900\) | −1.29802e12 | −0.0659461 | ||||||||
\(901\) | 3.37994e13 | 1.70863 | ||||||||
\(902\) | 2.48443e13 | 1.24968 | ||||||||
\(903\) | 1.44231e12 | 0.0721876 | ||||||||
\(904\) | −2.47178e12 | −0.123098 | ||||||||
\(905\) | −1.75881e13 | −0.871567 | ||||||||
\(906\) | −1.98520e12 | −0.0978875 | ||||||||
\(907\) | −2.57709e13 | −1.26444 | −0.632218 | − | 0.774790i | \(-0.717855\pi\) | ||||
−0.632218 | + | 0.774790i | \(0.717855\pi\) | |||||||
\(908\) | 1.61524e13 | 0.788588 | ||||||||
\(909\) | 1.11581e13 | 0.542066 | ||||||||
\(910\) | −5.97062e12 | −0.288625 | ||||||||
\(911\) | −1.30097e12 | −0.0625798 | −0.0312899 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312899 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(912\) | 8.71153e11 | 0.0416982 | ||||||||
\(913\) | 4.64766e13 | 2.21368 | ||||||||
\(914\) | −2.24776e13 | −1.06535 | ||||||||
\(915\) | 1.97330e13 | 0.930675 | ||||||||
\(916\) | −7.62960e12 | −0.358073 | ||||||||
\(917\) | −1.03806e13 | −0.484796 | ||||||||
\(918\) | −1.48641e13 | −0.690789 | ||||||||
\(919\) | −2.22215e13 | −1.02767 | −0.513835 | − | 0.857889i | \(-0.671776\pi\) | ||||
−0.513835 | + | 0.857889i | \(0.671776\pi\) | |||||||
\(920\) | 3.30834e11 | 0.0152253 | ||||||||
\(921\) | −1.06607e13 | −0.488221 | ||||||||
\(922\) | 2.20381e13 | 1.00435 | ||||||||
\(923\) | −1.23227e13 | −0.558854 | ||||||||
\(924\) | 8.15424e12 | 0.368010 | ||||||||
\(925\) | 3.91128e10 | 0.00175663 | ||||||||
\(926\) | 2.16482e13 | 0.967548 | ||||||||
\(927\) | 1.21015e13 | 0.538248 | ||||||||
\(928\) | −1.61818e12 | −0.0716245 | ||||||||
\(929\) | 3.02539e13 | 1.33263 | 0.666316 | − | 0.745670i | \(-0.267870\pi\) | ||||
0.666316 | + | 0.745670i | \(0.267870\pi\) | |||||||
\(930\) | −3.95048e11 | −0.0173172 | ||||||||
\(931\) | −2.17446e12 | −0.0948587 | ||||||||
\(932\) | 1.14956e12 | 0.0499070 | ||||||||
\(933\) | 2.56422e13 | 1.10787 | ||||||||
\(934\) | 1.81660e13 | 0.781084 | ||||||||
\(935\) | 3.19140e13 | 1.36562 | ||||||||
\(936\) | 1.84394e12 | 0.0785244 | ||||||||
\(937\) | −3.10153e13 | −1.31446 | −0.657231 | − | 0.753689i | \(-0.728273\pi\) | ||||
−0.657231 | + | 0.753689i | \(0.728273\pi\) | |||||||
\(938\) | −5.23837e12 | −0.220945 | ||||||||
\(939\) | −6.71807e12 | −0.282000 | ||||||||
\(940\) | −5.94452e12 | −0.248337 | ||||||||
\(941\) | 3.24185e13 | 1.34784 | 0.673922 | − | 0.738803i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738803i | \(0.264608\pi\) | |||||||
\(942\) | −1.09115e13 | −0.451497 | ||||||||
\(943\) | 1.23585e12 | 0.0508936 | ||||||||
\(944\) | 9.05135e12 | 0.370970 | ||||||||
\(945\) | −2.27218e13 | −0.926830 | ||||||||
\(946\) | 2.98508e12 | 0.121184 | ||||||||
\(947\) | −2.07659e13 | −0.839028 | −0.419514 | − | 0.907749i | \(-0.637800\pi\) | ||||
−0.419514 | + | 0.907749i | \(0.637800\pi\) | |||||||
\(948\) | −6.89885e12 | −0.277421 | ||||||||
\(949\) | −1.23804e12 | −0.0495491 | ||||||||
\(950\) | 1.13939e12 | 0.0453855 | ||||||||
\(951\) | 3.11729e13 | 1.23585 | ||||||||
\(952\) | −6.26660e12 | −0.247267 | ||||||||
\(953\) | −3.46692e13 | −1.36153 | −0.680763 | − | 0.732504i | \(-0.738352\pi\) | ||||
−0.680763 | + | 0.732504i | \(0.738352\pi\) | |||||||
\(954\) | −1.59566e13 | −0.623696 | ||||||||
\(955\) | 3.53053e13 | 1.37349 | ||||||||
\(956\) | −3.99103e12 | −0.154534 | ||||||||
\(957\) | 1.01039e13 | 0.389390 | ||||||||
\(958\) | −1.65622e13 | −0.635293 | ||||||||
\(959\) | 2.35229e13 | 0.898064 | ||||||||
\(960\) | −2.70553e12 | −0.102809 | ||||||||
\(961\) | −2.64162e13 | −0.999113 | ||||||||
\(962\) | −5.55629e10 | −0.00209169 | ||||||||
\(963\) | −3.04844e12 | −0.114224 | ||||||||
\(964\) | 2.62930e11 | 0.00980605 | ||||||||
\(965\) | −6.89285e12 | −0.255874 | ||||||||
\(966\) | 4.05622e11 | 0.0149873 | ||||||||
\(967\) | −4.45702e13 | −1.63918 | −0.819589 | − | 0.572952i | \(-0.805798\pi\) | ||||
−0.819589 | + | 0.572952i | \(0.805798\pi\) | |||||||
\(968\) | 7.21830e12 | 0.264238 | ||||||||
\(969\) | 4.18026e12 | 0.152316 | ||||||||
\(970\) | −2.96780e13 | −1.07637 | ||||||||
\(971\) | 4.61615e13 | 1.66645 | 0.833227 | − | 0.552931i | \(-0.186491\pi\) | ||||
0.833227 | + | 0.552931i | \(0.186491\pi\) | |||||||
\(972\) | 1.17864e13 | 0.423527 | ||||||||
\(973\) | 2.86964e13 | 1.02641 | ||||||||
\(974\) | −2.84634e13 | −1.01338 | ||||||||
\(975\) | −2.70411e12 | −0.0958305 | ||||||||
\(976\) | −8.01938e12 | −0.282889 | ||||||||
\(977\) | −1.27596e13 | −0.448036 | −0.224018 | − | 0.974585i | \(-0.571917\pi\) | ||||
−0.224018 | + | 0.974585i | \(0.571917\pi\) | |||||||
\(978\) | −1.79150e13 | −0.626170 | ||||||||
\(979\) | 6.90056e13 | 2.40083 | ||||||||
\(980\) | 6.75317e12 | 0.233879 | ||||||||
\(981\) | −1.17762e13 | −0.405970 | ||||||||
\(982\) | −3.55880e13 | −1.22124 | ||||||||
\(983\) | −2.49925e13 | −0.853725 | −0.426863 | − | 0.904317i | \(-0.640381\pi\) | ||||
−0.426863 | + | 0.904317i | \(0.640381\pi\) | |||||||
\(984\) | −1.01066e13 | −0.343660 | ||||||||
\(985\) | −3.91419e13 | −1.32489 | ||||||||
\(986\) | −7.76491e12 | −0.261632 | ||||||||
\(987\) | −7.28833e12 | −0.244456 | ||||||||
\(988\) | −1.61860e12 | −0.0540422 | ||||||||
\(989\) | 1.48489e11 | 0.00493526 | ||||||||
\(990\) | −1.50665e13 | −0.498489 | ||||||||
\(991\) | 7.39764e12 | 0.243647 | 0.121824 | − | 0.992552i | \(-0.461126\pi\) | ||||
0.121824 | + | 0.992552i | \(0.461126\pi\) | |||||||
\(992\) | 1.60545e11 | 0.00526375 | ||||||||
\(993\) | −1.45252e12 | −0.0474079 | ||||||||
\(994\) | −1.97708e13 | −0.642370 | ||||||||
\(995\) | −4.06497e13 | −1.31478 | ||||||||
\(996\) | −1.89066e13 | −0.608761 | ||||||||
\(997\) | −5.44084e13 | −1.74396 | −0.871982 | − | 0.489537i | \(-0.837166\pi\) | ||||
−0.871982 | + | 0.489537i | \(0.837166\pi\) | |||||||
\(998\) | 3.15679e13 | 1.00730 | ||||||||
\(999\) | −2.11450e11 | −0.00671682 |
(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 | 38.10.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 342.10.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 304.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.10.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
304.10.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
342.10.a.b.1.1 | 1 | 3.2 | odd | 2 |