Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [109,8,Mod(108,109)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(109, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("109.108");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 109 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 109.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(34.0499677778\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 108.58 | ||
Character | \(\chi\) | \(=\) | 109.108 |
Dual form | 109.8.b.a.108.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/109\mathbb{Z}\right)^\times\).
\(n\) | \(6\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.1107i | 1.68916i | 0.535429 | + | 0.844580i | \(0.320150\pi\) | ||||
−0.535429 | + | 0.844580i | \(0.679850\pi\) | |||||||
\(3\) | 70.4891 | 1.50729 | 0.753647 | − | 0.657280i | \(-0.228293\pi\) | ||||
0.753647 | + | 0.657280i | \(0.228293\pi\) | |||||||
\(4\) | −237.218 | −1.85326 | ||||||||
\(5\) | −288.848 | −1.03341 | −0.516707 | − | 0.856162i | \(-0.672842\pi\) | ||||
−0.516707 | + | 0.856162i | \(0.672842\pi\) | |||||||
\(6\) | 1347.09i | 2.54606i | ||||||||
\(7\) | −109.637 | −0.120813 | −0.0604064 | − | 0.998174i | \(-0.519240\pi\) | ||||
−0.0604064 | + | 0.998174i | \(0.519240\pi\) | |||||||
\(8\) | − | 2087.22i | − | 1.44130i | ||||||
\(9\) | 2781.72 | 1.27193 | ||||||||
\(10\) | − | 5520.08i | − | 1.74560i | ||||||
\(11\) | − | 6231.73i | − | 1.41167i | −0.708374 | − | 0.705837i | \(-0.750571\pi\) | ||
0.708374 | − | 0.705837i | \(-0.249429\pi\) | |||||||
\(12\) | −16721.3 | −2.79341 | ||||||||
\(13\) | − | 5635.67i | − | 0.711449i | −0.934591 | − | 0.355725i | \(-0.884234\pi\) | ||
0.934591 | − | 0.355725i | \(-0.115766\pi\) | |||||||
\(14\) | − | 2095.23i | − | 0.204072i | ||||||
\(15\) | −20360.7 | −1.55766 | ||||||||
\(16\) | 9524.34 | 0.581319 | ||||||||
\(17\) | − | 8505.86i | − | 0.419901i | −0.977712 | − | 0.209951i | \(-0.932670\pi\) | ||
0.977712 | − | 0.209951i | \(-0.0673303\pi\) | |||||||
\(18\) | 53160.5i | 2.14850i | ||||||||
\(19\) | − | 15195.3i | − | 0.508245i | −0.967172 | − | 0.254122i | \(-0.918213\pi\) | ||
0.967172 | − | 0.254122i | \(-0.0817866\pi\) | |||||||
\(20\) | 68519.9 | 1.91519 | ||||||||
\(21\) | −7728.20 | −0.182100 | ||||||||
\(22\) | 119093. | 2.38454 | ||||||||
\(23\) | 11730.4i | 0.201032i | 0.994935 | + | 0.100516i | \(0.0320494\pi\) | ||||
−0.994935 | + | 0.100516i | \(0.967951\pi\) | |||||||
\(24\) | − | 147126.i | − | 2.17246i | ||||||
\(25\) | 5308.23 | 0.0679453 | ||||||||
\(26\) | 107701. | 1.20175 | ||||||||
\(27\) | 41921.1 | 0.409883 | ||||||||
\(28\) | 26007.8 | 0.223898 | ||||||||
\(29\) | 11831.9 | 0.0900870 | 0.0450435 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450435 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(30\) | − | 389106.i | − | 2.63113i | ||||||
\(31\) | −85185.7 | −0.513571 | −0.256786 | − | 0.966468i | \(-0.582663\pi\) | ||||
−0.256786 | + | 0.966468i | \(0.582663\pi\) | |||||||
\(32\) | − | 85147.9i | − | 0.459356i | ||||||
\(33\) | − | 439270.i | − | 2.12781i | ||||||
\(34\) | 162553. | 0.709280 | ||||||||
\(35\) | 31668.4 | 0.124850 | ||||||||
\(36\) | −659872. | −2.35723 | ||||||||
\(37\) | − | 90991.7i | − | 0.295322i | −0.989038 | − | 0.147661i | \(-0.952826\pi\) | ||
0.989038 | − | 0.147661i | \(-0.0471744\pi\) | |||||||
\(38\) | 290393. | 0.858507 | ||||||||
\(39\) | − | 397253.i | − | 1.07236i | ||||||
\(40\) | 602890.i | 1.48946i | ||||||||
\(41\) | − | 42050.4i | − | 0.0952854i | −0.998864 | − | 0.0476427i | \(-0.984829\pi\) | ||
0.998864 | − | 0.0476427i | \(-0.0151709\pi\) | |||||||
\(42\) | − | 147691.i | − | 0.307597i | ||||||
\(43\) | 825275. | 1.58292 | 0.791460 | − | 0.611221i | \(-0.209321\pi\) | ||||
0.791460 | + | 0.611221i | \(0.209321\pi\) | |||||||
\(44\) | 1.47828e6i | 2.61620i | ||||||||
\(45\) | −803494. | −1.31443 | ||||||||
\(46\) | −224176. | −0.339575 | ||||||||
\(47\) | − | 470759.i | − | 0.661388i | −0.943738 | − | 0.330694i | \(-0.892717\pi\) | ||
0.943738 | − | 0.330694i | \(-0.107283\pi\) | |||||||
\(48\) | 671362. | 0.876219 | ||||||||
\(49\) | −811523. | −0.985404 | ||||||||
\(50\) | 101444.i | 0.114771i | ||||||||
\(51\) | − | 599571.i | − | 0.632914i | ||||||
\(52\) | 1.33688e6i | 1.31850i | ||||||||
\(53\) | 1.14520e6i | 1.05661i | 0.849055 | + | 0.528305i | \(0.177172\pi\) | ||||
−0.849055 | + | 0.528305i | \(0.822828\pi\) | |||||||
\(54\) | 801140.i | 0.692358i | ||||||||
\(55\) | 1.80002e6i | 1.45884i | ||||||||
\(56\) | 228836.i | 0.174127i | ||||||||
\(57\) | − | 1.07111e6i | − | 0.766074i | ||||||
\(58\) | 226116.i | 0.152171i | ||||||||
\(59\) | − | 1.60549e6i | − | 1.01771i | −0.860852 | − | 0.508856i | \(-0.830069\pi\) | ||
0.860852 | − | 0.508856i | \(-0.169931\pi\) | |||||||
\(60\) | 4.82990e6 | 2.88675 | ||||||||
\(61\) | 1.34053e6 | 0.756173 | 0.378087 | − | 0.925770i | \(-0.376582\pi\) | ||||
0.378087 | + | 0.925770i | \(0.376582\pi\) | |||||||
\(62\) | − | 1.62796e6i | − | 0.867505i | ||||||
\(63\) | −304979. | −0.153666 | ||||||||
\(64\) | 2.84635e6 | 1.35724 | ||||||||
\(65\) | 1.62785e6i | 0.735222i | ||||||||
\(66\) | 8.39473e6 | 3.59421 | ||||||||
\(67\) | − | 1.98728e6i | − | 0.807229i | −0.914929 | − | 0.403614i | \(-0.867754\pi\) | ||
0.914929 | − | 0.403614i | \(-0.132246\pi\) | |||||||
\(68\) | 2.01774e6i | 0.778187i | ||||||||
\(69\) | 826866.i | 0.303014i | ||||||||
\(70\) | 605204.i | 0.210891i | ||||||||
\(71\) | 1.45817e6 | 0.483510 | 0.241755 | − | 0.970337i | \(-0.422277\pi\) | ||||
0.241755 | + | 0.970337i | \(0.422277\pi\) | |||||||
\(72\) | − | 5.80606e6i | − | 1.83323i | ||||||
\(73\) | −2.69579e6 | −0.811064 | −0.405532 | − | 0.914081i | \(-0.632914\pi\) | ||||
−0.405532 | + | 0.914081i | \(0.632914\pi\) | |||||||
\(74\) | 1.73891e6 | 0.498846 | ||||||||
\(75\) | 374172. | 0.102414 | ||||||||
\(76\) | 3.60460e6i | 0.941911i | ||||||||
\(77\) | 683227.i | 0.170548i | ||||||||
\(78\) | 7.59178e6 | 1.81139 | ||||||||
\(79\) | 2.99739e6i | 0.683989i | 0.939702 | + | 0.341994i | \(0.111102\pi\) | ||||
−0.939702 | + | 0.341994i | \(0.888898\pi\) | |||||||
\(80\) | −2.75109e6 | −0.600744 | ||||||||
\(81\) | −3.12863e6 | −0.654119 | ||||||||
\(82\) | 803611. | 0.160952 | ||||||||
\(83\) | −9.05906e6 | −1.73904 | −0.869520 | − | 0.493898i | \(-0.835572\pi\) | ||||
−0.869520 | + | 0.493898i | \(0.835572\pi\) | |||||||
\(84\) | 1.83327e6 | 0.337480 | ||||||||
\(85\) | 2.45690e6i | 0.433932i | ||||||||
\(86\) | 1.57716e7i | 2.67381i | ||||||||
\(87\) | 834022. | 0.135788 | ||||||||
\(88\) | −1.30070e7 | −2.03464 | ||||||||
\(89\) | −5.17372e6 | −0.777925 | −0.388962 | − | 0.921254i | \(-0.627166\pi\) | ||||
−0.388962 | + | 0.921254i | \(0.627166\pi\) | |||||||
\(90\) | − | 1.53553e7i | − | 2.22029i | ||||||
\(91\) | 617877.i | 0.0859522i | ||||||||
\(92\) | − | 2.78266e6i | − | 0.372565i | ||||||
\(93\) | −6.00467e6 | −0.774103 | ||||||||
\(94\) | 8.99653e6 | 1.11719 | ||||||||
\(95\) | 4.38915e6i | 0.525228i | ||||||||
\(96\) | − | 6.00200e6i | − | 0.692384i | ||||||
\(97\) | −1.46853e7 | −1.63374 | −0.816868 | − | 0.576825i | \(-0.804292\pi\) | ||||
−0.816868 | + | 0.576825i | \(0.804292\pi\) | |||||||
\(98\) | − | 1.55087e7i | − | 1.66451i | ||||||
\(99\) | − | 1.73349e7i | − | 1.79556i | ||||||
\(100\) | −1.25920e6 | −0.125920 | ||||||||
\(101\) | − | 1.70701e7i | − | 1.64859i | −0.566164 | − | 0.824293i | \(-0.691573\pi\) | ||
0.566164 | − | 0.824293i | \(-0.308427\pi\) | |||||||
\(102\) | 1.14582e7 | 1.06909 | ||||||||
\(103\) | − | 8.55768e6i | − | 0.771660i | −0.922570 | − | 0.385830i | \(-0.873915\pi\) | ||
0.922570 | − | 0.385830i | \(-0.126085\pi\) | |||||||
\(104\) | −1.17629e7 | −1.02541 | ||||||||
\(105\) | 2.23228e6 | 0.188185 | ||||||||
\(106\) | −2.18855e7 | −1.78478 | ||||||||
\(107\) | 8.17253e6i | 0.644931i | 0.946581 | + | 0.322466i | \(0.104512\pi\) | ||||
−0.946581 | + | 0.322466i | \(0.895488\pi\) | |||||||
\(108\) | −9.94443e6 | −0.759620 | ||||||||
\(109\) | 1.34581e7 | + | 1.29795e6i | 0.995381 | + | 0.0959985i | ||||
\(110\) | −3.43997e7 | −2.46422 | ||||||||
\(111\) | − | 6.41393e6i | − | 0.445137i | ||||||
\(112\) | −1.04422e6 | −0.0702309 | ||||||||
\(113\) | −8.65189e6 | −0.564074 | −0.282037 | − | 0.959403i | \(-0.591010\pi\) | ||||
−0.282037 | + | 0.959403i | \(0.591010\pi\) | |||||||
\(114\) | 2.04696e7 | 1.29402 | ||||||||
\(115\) | − | 3.38830e6i | − | 0.207749i | ||||||
\(116\) | −2.80674e6 | −0.166955 | ||||||||
\(117\) | − | 1.56768e7i | − | 0.904915i | ||||||
\(118\) | 3.06819e7 | 1.71908 | ||||||||
\(119\) | 932555.i | 0.0507295i | ||||||||
\(120\) | 4.24972e7i | 2.24505i | ||||||||
\(121\) | −1.93473e7 | −0.992824 | ||||||||
\(122\) | 2.56184e7i | 1.27730i | ||||||||
\(123\) | − | 2.96409e6i | − | 0.143623i | ||||||
\(124\) | 2.02076e7 | 0.951783 | ||||||||
\(125\) | 2.10330e7 | 0.963199 | ||||||||
\(126\) | − | 5.82835e6i | − | 0.259566i | ||||||
\(127\) | − | 1.62596e7i | − | 0.704362i | −0.935932 | − | 0.352181i | \(-0.885440\pi\) | ||
0.935932 | − | 0.352181i | \(-0.114560\pi\) | |||||||
\(128\) | 4.34967e7i | 1.83325i | ||||||||
\(129\) | 5.81729e7 | 2.38593 | ||||||||
\(130\) | −3.11093e7 | −1.24191 | ||||||||
\(131\) | −1.89113e7 | −0.734974 | −0.367487 | − | 0.930029i | \(-0.619782\pi\) | ||||
−0.367487 | + | 0.930029i | \(0.619782\pi\) | |||||||
\(132\) | 1.04202e8i | 3.94339i | ||||||||
\(133\) | 1.66597e6i | 0.0614025i | ||||||||
\(134\) | 3.79782e7 | 1.36354 | ||||||||
\(135\) | −1.21088e7 | −0.423579 | ||||||||
\(136\) | −1.77536e7 | −0.605202 | ||||||||
\(137\) | −72067.0 | −0.00239450 | −0.00119725 | − | 0.999999i | \(-0.500381\pi\) | ||||
−0.00119725 | + | 0.999999i | \(0.500381\pi\) | |||||||
\(138\) | −1.58020e7 | −0.511840 | ||||||||
\(139\) | − | 5.07596e7i | − | 1.60312i | −0.597913 | − | 0.801561i | \(-0.704003\pi\) | ||
0.597913 | − | 0.801561i | \(-0.295997\pi\) | |||||||
\(140\) | −7.51230e6 | −0.231379 | ||||||||
\(141\) | − | 3.31834e7i | − | 0.996906i | ||||||
\(142\) | 2.78667e7i | 0.816725i | ||||||||
\(143\) | −3.51200e7 | −1.00433 | ||||||||
\(144\) | 2.64940e7 | 0.739399 | ||||||||
\(145\) | −3.41763e6 | −0.0930972 | ||||||||
\(146\) | − | 5.15183e7i | − | 1.37002i | ||||||
\(147\) | −5.72035e7 | −1.48529 | ||||||||
\(148\) | 2.15848e7i | 0.547309i | ||||||||
\(149\) | 1.62383e7i | 0.402151i | 0.979576 | + | 0.201075i | \(0.0644436\pi\) | ||||
−0.979576 | + | 0.201075i | \(0.935556\pi\) | |||||||
\(150\) | 7.15068e6i | 0.172993i | ||||||||
\(151\) | − | 7.16484e7i | − | 1.69351i | −0.531985 | − | 0.846754i | \(-0.678554\pi\) | ||
0.531985 | − | 0.846754i | \(-0.321446\pi\) | |||||||
\(152\) | −3.17160e7 | −0.732532 | ||||||||
\(153\) | − | 2.36609e7i | − | 0.534086i | ||||||
\(154\) | −1.30569e7 | −0.288084 | ||||||||
\(155\) | 2.46057e7 | 0.530732 | ||||||||
\(156\) | 9.42355e7i | 1.98737i | ||||||||
\(157\) | 8.88389e7 | 1.83212 | 0.916061 | − | 0.401039i | \(-0.131351\pi\) | ||||
0.916061 | + | 0.401039i | \(0.131351\pi\) | |||||||
\(158\) | −5.72822e7 | −1.15537 | ||||||||
\(159\) | 8.07239e7i | 1.59262i | ||||||||
\(160\) | 2.45948e7i | 0.474705i | ||||||||
\(161\) | − | 1.28608e6i | − | 0.0242873i | ||||||
\(162\) | − | 5.97903e7i | − | 1.10491i | ||||||
\(163\) | 3.77303e7i | 0.682391i | 0.939992 | + | 0.341196i | \(0.110832\pi\) | ||||
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(164\) | 9.97509e6i | 0.176589i | ||||||||
\(165\) | 1.26882e8i | 2.19891i | ||||||||
\(166\) | − | 1.73125e8i | − | 2.93752i | ||||||
\(167\) | 8.54862e7i | 1.42033i | 0.704037 | + | 0.710164i | \(0.251379\pi\) | ||||
−0.704037 | + | 0.710164i | \(0.748621\pi\) | |||||||
\(168\) | 1.61305e7i | 0.262461i | ||||||||
\(169\) | 3.09877e7 | 0.493840 | ||||||||
\(170\) | −4.69530e7 | −0.732980 | ||||||||
\(171\) | − | 4.22692e7i | − | 0.646453i | ||||||
\(172\) | −1.95770e8 | −2.93357 | ||||||||
\(173\) | −7.69749e7 | −1.13028 | −0.565142 | − | 0.824994i | \(-0.691179\pi\) | ||||
−0.565142 | + | 0.824994i | \(0.691179\pi\) | |||||||
\(174\) | 1.59387e7i | 0.229367i | ||||||||
\(175\) | −581977. | −0.00820867 | ||||||||
\(176\) | − | 5.93531e7i | − | 0.820634i | ||||||
\(177\) | − | 1.13169e8i | − | 1.53399i | ||||||
\(178\) | − | 9.88732e7i | − | 1.31404i | ||||||
\(179\) | 1.16022e8i | 1.51201i | 0.654565 | + | 0.756006i | \(0.272852\pi\) | ||||
−0.654565 | + | 0.756006i | \(0.727148\pi\) | |||||||
\(180\) | 1.90603e8 | 2.43599 | ||||||||
\(181\) | − | 5.42072e7i | − | 0.679488i | −0.940518 | − | 0.339744i | \(-0.889660\pi\) | ||
0.940518 | − | 0.339744i | \(-0.110340\pi\) | |||||||
\(182\) | −1.18080e7 | −0.145187 | ||||||||
\(183\) | 9.44926e7 | 1.13977 | ||||||||
\(184\) | 2.44839e7 | 0.289747 | ||||||||
\(185\) | 2.62828e7i | 0.305190i | ||||||||
\(186\) | − | 1.14753e8i | − | 1.30758i | ||||||
\(187\) | −5.30063e7 | −0.592764 | ||||||||
\(188\) | 1.11672e8i | 1.22573i | ||||||||
\(189\) | −4.59610e6 | −0.0495191 | ||||||||
\(190\) | −8.38795e7 | −0.887194 | ||||||||
\(191\) | −1.07781e8 | −1.11924 | −0.559622 | − | 0.828748i | \(-0.689054\pi\) | ||||
−0.559622 | + | 0.828748i | \(0.689054\pi\) | |||||||
\(192\) | 2.00637e8 | 2.04577 | ||||||||
\(193\) | −1.26358e7 | −0.126518 | −0.0632589 | − | 0.997997i | \(-0.520149\pi\) | ||||
−0.0632589 | + | 0.997997i | \(0.520149\pi\) | |||||||
\(194\) | − | 2.80646e8i | − | 2.75964i | ||||||
\(195\) | 1.14746e8i | 1.10819i | ||||||||
\(196\) | 1.92507e8 | 1.82621 | ||||||||
\(197\) | 1.79992e8 | 1.67734 | 0.838670 | − | 0.544640i | \(-0.183334\pi\) | ||||
0.838670 | + | 0.544640i | \(0.183334\pi\) | |||||||
\(198\) | 3.31282e8 | 3.03298 | ||||||||
\(199\) | − | 1.05569e8i | − | 0.949622i | −0.880088 | − | 0.474811i | \(-0.842516\pi\) | ||
0.880088 | − | 0.474811i | \(-0.157484\pi\) | |||||||
\(200\) | − | 1.10794e7i | − | 0.0979294i | ||||||
\(201\) | − | 1.40081e8i | − | 1.21673i | ||||||
\(202\) | 3.26221e8 | 2.78472 | ||||||||
\(203\) | −1.29721e6 | −0.0108837 | ||||||||
\(204\) | 1.42229e8i | 1.17296i | ||||||||
\(205\) | 1.21462e7i | 0.0984693i | ||||||||
\(206\) | 1.63543e8 | 1.30346 | ||||||||
\(207\) | 3.26307e7i | 0.255699i | ||||||||
\(208\) | − | 5.36760e7i | − | 0.413579i | ||||||
\(209\) | −9.46934e7 | −0.717476 | ||||||||
\(210\) | 4.26603e7i | 0.317875i | ||||||||
\(211\) | −1.23048e8 | −0.901750 | −0.450875 | − | 0.892587i | \(-0.648888\pi\) | ||||
−0.450875 | + | 0.892587i | \(0.648888\pi\) | |||||||
\(212\) | − | 2.71661e8i | − | 1.95818i | ||||||
\(213\) | 1.02785e8 | 0.728791 | ||||||||
\(214\) | −1.56183e8 | −1.08939 | ||||||||
\(215\) | −2.38379e8 | −1.63581 | ||||||||
\(216\) | − | 8.74986e7i | − | 0.590763i | ||||||
\(217\) | 9.33949e6 | 0.0620461 | ||||||||
\(218\) | −2.48046e7 | + | 2.57192e8i | −0.162157 | + | 1.68136i | ||||
\(219\) | −1.90024e8 | −1.22251 | ||||||||
\(220\) | − | 4.26998e8i | − | 2.70362i | ||||||
\(221\) | −4.79362e7 | −0.298738 | ||||||||
\(222\) | 1.22574e8 | 0.751907 | ||||||||
\(223\) | −9.22012e7 | −0.556762 | −0.278381 | − | 0.960471i | \(-0.589798\pi\) | ||||
−0.278381 | + | 0.960471i | \(0.589798\pi\) | |||||||
\(224\) | 9.33534e6i | 0.0554961i | ||||||||
\(225\) | 1.47660e7 | 0.0864219 | ||||||||
\(226\) | − | 1.65343e8i | − | 0.952812i | ||||||
\(227\) | 1.89125e7 | 0.107315 | 0.0536574 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536574 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(228\) | 2.54085e8i | 1.41974i | ||||||||
\(229\) | 3.01779e8i | 1.66060i | 0.557316 | + | 0.830301i | \(0.311831\pi\) | ||||
−0.557316 | + | 0.830301i | \(0.688169\pi\) | |||||||
\(230\) | 6.47527e7 | 0.350922 | ||||||||
\(231\) | 4.81601e7i | 0.257067i | ||||||||
\(232\) | − | 2.46958e7i | − | 0.129842i | ||||||
\(233\) | 2.89056e8 | 1.49705 | 0.748526 | − | 0.663105i | \(-0.230762\pi\) | ||||
0.748526 | + | 0.663105i | \(0.230762\pi\) | |||||||
\(234\) | 2.99595e8 | 1.52855 | ||||||||
\(235\) | 1.35978e8i | 0.683488i | ||||||||
\(236\) | 3.80850e8i | 1.88609i | ||||||||
\(237\) | 2.11284e8i | 1.03097i | ||||||||
\(238\) | −1.78218e7 | −0.0856902 | ||||||||
\(239\) | −8.49929e6 | −0.0402708 | −0.0201354 | − | 0.999797i | \(-0.506410\pi\) | ||||
−0.0201354 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(240\) | −1.93922e8 | −0.905497 | ||||||||
\(241\) | − | 1.54669e8i | − | 0.711777i | −0.934528 | − | 0.355888i | \(-0.884178\pi\) | ||
0.934528 | − | 0.355888i | \(-0.115822\pi\) | |||||||
\(242\) | − | 3.69741e8i | − | 1.67704i | ||||||
\(243\) | −3.12216e8 | −1.39583 | ||||||||
\(244\) | −3.17997e8 | −1.40139 | ||||||||
\(245\) | 2.34407e8 | 1.01833 | ||||||||
\(246\) | 5.66458e7 | 0.242602 | ||||||||
\(247\) | −8.56359e7 | −0.361590 | ||||||||
\(248\) | 1.77801e8i | 0.740209i | ||||||||
\(249\) | −6.38565e8 | −2.62124 | ||||||||
\(250\) | 4.01954e8i | 1.62700i | ||||||||
\(251\) | 1.56014e8i | 0.622739i | 0.950289 | + | 0.311370i | \(0.100788\pi\) | ||||
−0.950289 | + | 0.311370i | \(0.899212\pi\) | |||||||
\(252\) | 7.23463e7 | 0.284783 | ||||||||
\(253\) | 7.31007e7 | 0.283792 | ||||||||
\(254\) | 3.10731e8 | 1.18978 | ||||||||
\(255\) | 1.73185e8i | 0.654063i | ||||||||
\(256\) | −4.66918e8 | −1.73941 | ||||||||
\(257\) | 3.42159e8i | 1.25737i | 0.777661 | + | 0.628683i | \(0.216406\pi\) | ||||
−0.777661 | + | 0.628683i | \(0.783594\pi\) | |||||||
\(258\) | 1.11172e9i | 4.03021i | ||||||||
\(259\) | 9.97604e6i | 0.0356787i | ||||||||
\(260\) | − | 3.86155e8i | − | 1.36256i | ||||||
\(261\) | 3.29131e7 | 0.114585 | ||||||||
\(262\) | − | 3.61408e8i | − | 1.24149i | ||||||
\(263\) | −3.92394e7 | −0.133008 | −0.0665040 | − | 0.997786i | \(-0.521185\pi\) | ||||
−0.0665040 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(264\) | −9.16853e8 | −3.06680 | ||||||||
\(265\) | − | 3.30788e8i | − | 1.09192i | ||||||
\(266\) | −3.18378e7 | −0.103719 | ||||||||
\(267\) | −3.64691e8 | −1.17256 | ||||||||
\(268\) | 4.71417e8i | 1.49601i | ||||||||
\(269\) | 5.32048e8i | 1.66655i | 0.552861 | + | 0.833274i | \(0.313536\pi\) | ||||
−0.552861 | + | 0.833274i | \(0.686464\pi\) | |||||||
\(270\) | − | 2.31408e8i | − | 0.715492i | ||||||
\(271\) | − | 2.71211e8i | − | 0.827779i | −0.910327 | − | 0.413889i | \(-0.864170\pi\) | ||
0.910327 | − | 0.413889i | \(-0.135830\pi\) | |||||||
\(272\) | − | 8.10127e7i | − | 0.244097i | ||||||
\(273\) | 4.35536e7i | 0.129555i | ||||||||
\(274\) | − | 1.37725e6i | − | 0.00404469i | ||||||
\(275\) | − | 3.30795e7i | − | 0.0959167i | ||||||
\(276\) | − | 1.96147e8i | − | 0.561565i | ||||||
\(277\) | − | 6.05389e8i | − | 1.71142i | −0.517459 | − | 0.855708i | \(-0.673122\pi\) | ||
0.517459 | − | 0.855708i | \(-0.326878\pi\) | |||||||
\(278\) | 9.70050e8 | 2.70793 | ||||||||
\(279\) | −2.36963e8 | −0.653228 | ||||||||
\(280\) | − | 6.60989e7i | − | 0.179946i | ||||||
\(281\) | 1.11966e8 | 0.301034 | 0.150517 | − | 0.988607i | \(-0.451906\pi\) | ||||
0.150517 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(282\) | 6.34157e8 | 1.68393 | ||||||||
\(283\) | 1.19684e8i | 0.313895i | 0.987607 | + | 0.156948i | \(0.0501654\pi\) | ||||
−0.987607 | + | 0.156948i | \(0.949835\pi\) | |||||||
\(284\) | −3.45905e8 | −0.896070 | ||||||||
\(285\) | 3.09387e8i | 0.791672i | ||||||||
\(286\) | − | 6.71167e8i | − | 1.69648i | ||||||
\(287\) | 4.61027e6i | 0.0115117i | ||||||||
\(288\) | − | 2.36857e8i | − | 0.584270i | ||||||
\(289\) | 3.37989e8 | 0.823683 | ||||||||
\(290\) | − | 6.53131e7i | − | 0.157256i | ||||||
\(291\) | −1.03515e9 | −2.46252 | ||||||||
\(292\) | 6.39488e8 | 1.50312 | ||||||||
\(293\) | 4.34023e8 | 1.00804 | 0.504018 | − | 0.863693i | \(-0.331854\pi\) | ||||
0.504018 | + | 0.863693i | \(0.331854\pi\) | |||||||
\(294\) | − | 1.09320e9i | − | 2.50890i | ||||||
\(295\) | 4.63742e8i | 1.05172i | ||||||||
\(296\) | −1.89920e8 | −0.425647 | ||||||||
\(297\) | − | 2.61241e8i | − | 0.578621i | ||||||
\(298\) | −3.10325e8 | −0.679297 | ||||||||
\(299\) | 6.61086e7 | 0.143024 | ||||||||
\(300\) | −8.87603e7 | −0.189799 | ||||||||
\(301\) | −9.04805e7 | −0.191237 | ||||||||
\(302\) | 1.36925e9 | 2.86061 | ||||||||
\(303\) | − | 1.20326e9i | − | 2.48490i | ||||||
\(304\) | − | 1.44726e8i | − | 0.295453i | ||||||
\(305\) | −3.87209e8 | −0.781440 | ||||||||
\(306\) | 4.52176e8 | 0.902157 | ||||||||
\(307\) | −1.65036e8 | −0.325533 | −0.162767 | − | 0.986665i | \(-0.552042\pi\) | ||||
−0.162767 | + | 0.986665i | \(0.552042\pi\) | |||||||
\(308\) | − | 1.62074e8i | − | 0.316071i | ||||||
\(309\) | − | 6.03223e8i | − | 1.16312i | ||||||
\(310\) | 4.70232e8i | 0.896492i | ||||||||
\(311\) | 2.39286e7 | 0.0451082 | 0.0225541 | − | 0.999746i | \(-0.492820\pi\) | ||||
0.0225541 | + | 0.999746i | \(0.492820\pi\) | |||||||
\(312\) | −8.29156e8 | −1.54559 | ||||||||
\(313\) | 7.51264e8i | 1.38480i | 0.721514 | + | 0.692400i | \(0.243447\pi\) | ||||
−0.721514 | + | 0.692400i | \(0.756553\pi\) | |||||||
\(314\) | 1.69777e9i | 3.09475i | ||||||||
\(315\) | 8.80925e7 | 0.158801 | ||||||||
\(316\) | − | 7.11034e8i | − | 1.26761i | ||||||
\(317\) | 2.16105e8i | 0.381029i | 0.981684 | + | 0.190514i | \(0.0610156\pi\) | ||||
−0.981684 | + | 0.190514i | \(0.938984\pi\) | |||||||
\(318\) | −1.54269e9 | −2.69019 | ||||||||
\(319\) | − | 7.37334e7i | − | 0.127174i | ||||||
\(320\) | −8.22162e8 | −1.40260 | ||||||||
\(321\) | 5.76075e8i | 0.972101i | ||||||||
\(322\) | 2.45779e7 | 0.0410251 | ||||||||
\(323\) | −1.29249e8 | −0.213413 | ||||||||
\(324\) | 7.42167e8 | 1.21226 | ||||||||
\(325\) | − | 2.99154e7i | − | 0.0483396i | ||||||
\(326\) | −7.21051e8 | −1.15267 | ||||||||
\(327\) | 9.48647e8 | + | 9.14912e7i | 1.50033 | + | 0.144698i | ||||
\(328\) | −8.77684e7 | −0.137335 | ||||||||
\(329\) | 5.16126e7i | 0.0799042i | ||||||||
\(330\) | −2.42480e9 | −3.71431 | ||||||||
\(331\) | 1.07419e8 | 0.162811 | 0.0814056 | − | 0.996681i | \(-0.474059\pi\) | ||||
0.0814056 | + | 0.996681i | \(0.474059\pi\) | |||||||
\(332\) | 2.14897e9 | 3.22290 | ||||||||
\(333\) | − | 2.53113e8i | − | 0.375630i | ||||||
\(334\) | −1.63370e9 | −2.39916 | ||||||||
\(335\) | 5.74021e8i | 0.834202i | ||||||||
\(336\) | −7.36060e7 | −0.105859 | ||||||||
\(337\) | − | 5.32067e8i | − | 0.757289i | −0.925542 | − | 0.378644i | \(-0.876390\pi\) | ||
0.925542 | − | 0.378644i | \(-0.123610\pi\) | |||||||
\(338\) | 5.92196e8i | 0.834175i | ||||||||
\(339\) | −6.09864e8 | −0.850225 | ||||||||
\(340\) | − | 5.82820e8i | − | 0.804190i | ||||||
\(341\) | 5.30855e8i | 0.724996i | ||||||||
\(342\) | 8.07792e8 | 1.09196 | ||||||||
\(343\) | 1.79263e8 | 0.239862 | ||||||||
\(344\) | − | 1.72253e9i | − | 2.28146i | ||||||
\(345\) | − | 2.38839e8i | − | 0.313139i | ||||||
\(346\) | − | 1.47104e9i | − | 1.90923i | ||||||
\(347\) | 1.44182e9 | 1.85249 | 0.926247 | − | 0.376918i | \(-0.123016\pi\) | ||||
0.926247 | + | 0.376918i | \(0.123016\pi\) | |||||||
\(348\) | −1.97845e8 | −0.251650 | ||||||||
\(349\) | 9.53241e8 | 1.20037 | 0.600183 | − | 0.799863i | \(-0.295094\pi\) | ||||
0.600183 | + | 0.799863i | \(0.295094\pi\) | |||||||
\(350\) | − | 1.11220e7i | − | 0.0138658i | ||||||
\(351\) | − | 2.36254e8i | − | 0.291611i | ||||||
\(352\) | −5.30619e8 | −0.648461 | ||||||||
\(353\) | −2.62707e7 | −0.0317877 | −0.0158939 | − | 0.999874i | \(-0.505059\pi\) | ||||
−0.0158939 | + | 0.999874i | \(0.505059\pi\) | |||||||
\(354\) | 2.16274e9 | 2.59115 | ||||||||
\(355\) | −4.21191e8 | −0.499666 | ||||||||
\(356\) | 1.22730e9 | 1.44170 | ||||||||
\(357\) | 6.57350e7i | 0.0764642i | ||||||||
\(358\) | −2.21726e9 | −2.55403 | ||||||||
\(359\) | − | 1.96193e8i | − | 0.223796i | −0.993720 | − | 0.111898i | \(-0.964307\pi\) | ||
0.993720 | − | 0.111898i | \(-0.0356930\pi\) | |||||||
\(360\) | 1.67707e9i | 1.89449i | ||||||||
\(361\) | 6.62973e8 | 0.741687 | ||||||||
\(362\) | 1.03594e9 | 1.14776 | ||||||||
\(363\) | −1.36378e9 | −1.49648 | ||||||||
\(364\) | − | 1.46571e8i | − | 0.159292i | ||||||
\(365\) | 7.78673e8 | 0.838166 | ||||||||
\(366\) | 1.80582e9i | 1.92526i | ||||||||
\(367\) | − | 4.78670e7i | − | 0.0505481i | −0.999681 | − | 0.0252741i | \(-0.991954\pi\) | ||
0.999681 | − | 0.0252741i | \(-0.00804584\pi\) | |||||||
\(368\) | 1.11724e8i | 0.116864i | ||||||||
\(369\) | − | 1.16972e8i | − | 0.121197i | ||||||
\(370\) | −5.02281e8 | −0.515515 | ||||||||
\(371\) | − | 1.25556e8i | − | 0.127652i | ||||||
\(372\) | 1.42441e9 | 1.43462 | ||||||||
\(373\) | −1.03742e9 | −1.03508 | −0.517541 | − | 0.855658i | \(-0.673153\pi\) | ||||
−0.517541 | + | 0.855658i | \(0.673153\pi\) | |||||||
\(374\) | − | 1.01298e9i | − | 1.00127i | ||||||
\(375\) | 1.48260e9 | 1.45182 | ||||||||
\(376\) | −9.82579e8 | −0.953257 | ||||||||
\(377\) | − | 6.66808e7i | − | 0.0640923i | ||||||
\(378\) | − | 8.78345e7i | − | 0.0836457i | ||||||
\(379\) | − | 9.82124e7i | − | 0.0926678i | −0.998926 | − | 0.0463339i | \(-0.985246\pi\) | ||
0.998926 | − | 0.0463339i | \(-0.0147538\pi\) | |||||||
\(380\) | − | 1.04118e9i | − | 0.973385i | ||||||
\(381\) | − | 1.14612e9i | − | 1.06168i | ||||||
\(382\) | − | 2.05976e9i | − | 1.89058i | ||||||
\(383\) | − | 2.75613e8i | − | 0.250671i | −0.992114 | − | 0.125336i | \(-0.959999\pi\) | ||
0.992114 | − | 0.125336i | \(-0.0400007\pi\) | |||||||
\(384\) | 3.06604e9i | 2.76324i | ||||||||
\(385\) | − | 1.97349e8i | − | 0.176247i | ||||||
\(386\) | − | 2.41478e8i | − | 0.213709i | ||||||
\(387\) | 2.29568e9 | 2.01337 | ||||||||
\(388\) | 3.48361e9 | 3.02774 | ||||||||
\(389\) | 2.37877e8i | 0.204894i | 0.994738 | + | 0.102447i | \(0.0326672\pi\) | ||||
−0.994738 | + | 0.102447i | \(0.967333\pi\) | |||||||
\(390\) | −2.19287e9 | −1.87192 | ||||||||
\(391\) | 9.97771e7 | 0.0844136 | ||||||||
\(392\) | 1.69383e9i | 1.42026i | ||||||||
\(393\) | −1.33304e9 | −1.10782 | ||||||||
\(394\) | 3.43977e9i | 2.83330i | ||||||||
\(395\) | − | 8.65791e8i | − | 0.706844i | ||||||
\(396\) | 4.11215e9i | 3.32763i | ||||||||
\(397\) | 1.60162e9i | 1.28467i | 0.766424 | + | 0.642335i | \(0.222034\pi\) | ||||
−0.766424 | + | 0.642335i | \(0.777966\pi\) | |||||||
\(398\) | 2.01749e9 | 1.60406 | ||||||||
\(399\) | 1.17433e8i | 0.0925516i | ||||||||
\(400\) | 5.05573e7 | 0.0394979 | ||||||||
\(401\) | −2.20747e9 | −1.70958 | −0.854790 | − | 0.518974i | \(-0.826314\pi\) | ||||
−0.854790 | + | 0.518974i | \(0.826314\pi\) | |||||||
\(402\) | 2.67705e9 | 2.05525 | ||||||||
\(403\) | 4.80079e8i | 0.365380i | ||||||||
\(404\) | 4.04933e9i | 3.05526i | ||||||||
\(405\) | 9.03700e8 | 0.675976 | ||||||||
\(406\) | − | 2.47906e7i | − | 0.0183843i | ||||||
\(407\) | −5.67036e8 | −0.416898 | ||||||||
\(408\) | −1.25144e9 | −0.912217 | ||||||||
\(409\) | 6.35277e8 | 0.459126 | 0.229563 | − | 0.973294i | \(-0.426270\pi\) | ||||
0.229563 | + | 0.973294i | \(0.426270\pi\) | |||||||
\(410\) | −2.32121e8 | −0.166330 | ||||||||
\(411\) | −5.07994e6 | −0.00360921 | ||||||||
\(412\) | 2.03003e9i | 1.43009i | ||||||||
\(413\) | 1.76020e8i | 0.122953i | ||||||||
\(414\) | −6.23594e8 | −0.431917 | ||||||||
\(415\) | 2.61669e9 | 1.79715 | ||||||||
\(416\) | −4.79865e8 | −0.326808 | ||||||||
\(417\) | − | 3.57800e9i | − | 2.41637i | ||||||
\(418\) | − | 1.80965e9i | − | 1.21193i | ||||||
\(419\) | − | 1.65017e8i | − | 0.109592i | −0.998498 | − | 0.0547960i | \(-0.982549\pi\) | ||
0.998498 | − | 0.0547960i | \(-0.0174508\pi\) | |||||||
\(420\) | −5.29535e8 | −0.348757 | ||||||||
\(421\) | −1.43180e9 | −0.935183 | −0.467591 | − | 0.883945i | \(-0.654878\pi\) | ||||
−0.467591 | + | 0.883945i | \(0.654878\pi\) | |||||||
\(422\) | − | 2.35153e9i | − | 1.52320i | ||||||
\(423\) | − | 1.30952e9i | − | 0.841242i | ||||||
\(424\) | 2.39028e9 | 1.52289 | ||||||||
\(425\) | − | 4.51510e7i | − | 0.0285303i | ||||||
\(426\) | 1.96430e9i | 1.23104i | ||||||||
\(427\) | −1.46971e8 | −0.0913555 | ||||||||
\(428\) | − | 1.93867e9i | − | 1.19523i | ||||||
\(429\) | −2.47558e9 | −1.51383 | ||||||||
\(430\) | − | 4.55558e9i | − | 2.76315i | ||||||
\(431\) | −3.89030e8 | −0.234052 | −0.117026 | − | 0.993129i | \(-0.537336\pi\) | ||||
−0.117026 | + | 0.993129i | \(0.537336\pi\) | |||||||
\(432\) | 3.99271e8 | 0.238273 | ||||||||
\(433\) | 1.66592e9 | 0.986157 | 0.493079 | − | 0.869985i | \(-0.335871\pi\) | ||||
0.493079 | + | 0.869985i | \(0.335871\pi\) | |||||||
\(434\) | 1.78484e8i | 0.104806i | ||||||||
\(435\) | −2.40906e8 | −0.140325 | ||||||||
\(436\) | −3.19249e9 | − | 3.07896e8i | −1.84470 | − | 0.177910i | ||||
\(437\) | 1.78247e8 | 0.102174 | ||||||||
\(438\) | − | 3.63148e9i | − | 2.06502i | ||||||
\(439\) | −8.16250e8 | −0.460466 | −0.230233 | − | 0.973136i | \(-0.573949\pi\) | ||||
−0.230233 | + | 0.973136i | \(0.573949\pi\) | |||||||
\(440\) | 3.75705e9 | 2.10263 | ||||||||
\(441\) | −2.25743e9 | −1.25337 | ||||||||
\(442\) | − | 9.16093e8i | − | 0.504617i | ||||||
\(443\) | −6.67662e8 | −0.364875 | −0.182437 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182437 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(444\) | 1.52150e9i | 0.824955i | ||||||||
\(445\) | 1.49442e9 | 0.803919 | ||||||||
\(446\) | − | 1.76203e9i | − | 0.940460i | ||||||
\(447\) | 1.14462e9i | 0.606159i | ||||||||
\(448\) | −3.12065e8 | −0.163973 | ||||||||
\(449\) | − | 3.01199e9i | − | 1.57033i | −0.619287 | − | 0.785165i | \(-0.712578\pi\) | ||
0.619287 | − | 0.785165i | \(-0.287422\pi\) | |||||||
\(450\) | 2.82188e8i | 0.145980i | ||||||||
\(451\) | −2.62047e8 | −0.134512 | ||||||||
\(452\) | 2.05238e9 | 1.04538 | ||||||||
\(453\) | − | 5.05043e9i | − | 2.55261i | ||||||
\(454\) | 3.61431e8i | 0.181272i | ||||||||
\(455\) | − | 1.78473e8i | − | 0.0888243i | ||||||
\(456\) | −2.23564e9 | −1.10414 | ||||||||
\(457\) | 2.94053e9 | 1.44118 | 0.720591 | − | 0.693361i | \(-0.243871\pi\) | ||||
0.720591 | + | 0.693361i | \(0.243871\pi\) | |||||||
\(458\) | −5.76720e9 | −2.80502 | ||||||||
\(459\) | − | 3.56575e8i | − | 0.172110i | ||||||
\(460\) | 8.03765e8i | 0.385014i | ||||||||
\(461\) | −1.21988e9 | −0.579916 | −0.289958 | − | 0.957039i | \(-0.593641\pi\) | ||||
−0.289958 | + | 0.957039i | \(0.593641\pi\) | |||||||
\(462\) | −9.20372e8 | −0.434227 | ||||||||
\(463\) | 1.25892e9 | 0.589476 | 0.294738 | − | 0.955578i | \(-0.404768\pi\) | ||||
0.294738 | + | 0.955578i | \(0.404768\pi\) | |||||||
\(464\) | 1.12691e8 | 0.0523693 | ||||||||
\(465\) | 1.73444e9 | 0.799969 | ||||||||
\(466\) | 5.52406e9i | 2.52876i | ||||||||
\(467\) | −2.64923e9 | −1.20368 | −0.601840 | − | 0.798617i | \(-0.705565\pi\) | ||||
−0.601840 | + | 0.798617i | \(0.705565\pi\) | |||||||
\(468\) | 3.71882e9i | 1.67705i | ||||||||
\(469\) | 2.17879e8i | 0.0975236i | ||||||||
\(470\) | −2.59863e9 | −1.15452 | ||||||||
\(471\) | 6.26218e9 | 2.76155 | ||||||||
\(472\) | −3.35100e9 | −1.46682 | ||||||||
\(473\) | − | 5.14289e9i | − | 2.23457i | ||||||
\(474\) | −4.03777e9 | −1.74148 | ||||||||
\(475\) | − | 8.06604e7i | − | 0.0345329i | ||||||
\(476\) | − | 2.21219e8i | − | 0.0940150i | ||||||
\(477\) | 3.18561e9i | 1.34394i | ||||||||
\(478\) | − | 1.62427e8i | − | 0.0680238i | ||||||
\(479\) | 2.57179e9 | 1.06921 | 0.534603 | − | 0.845103i | \(-0.320461\pi\) | ||||
0.534603 | + | 0.845103i | \(0.320461\pi\) | |||||||
\(480\) | 1.73367e9i | 0.715519i | ||||||||
\(481\) | −5.12799e8 | −0.210107 | ||||||||
\(482\) | 2.95583e9 | 1.20230 | ||||||||
\(483\) | − | 9.06549e7i | − | 0.0366080i | ||||||
\(484\) | 4.58953e9 | 1.83996 | ||||||||
\(485\) | 4.24182e9 | 1.68833 | ||||||||
\(486\) | − | 5.96666e9i | − | 2.35779i | ||||||
\(487\) | − | 2.30168e8i | − | 0.0903012i | −0.998980 | − | 0.0451506i | \(-0.985623\pi\) | ||
0.998980 | − | 0.0451506i | \(-0.0143768\pi\) | |||||||
\(488\) | − | 2.79798e9i | − | 1.08987i | ||||||
\(489\) | 2.65957e9i | 1.02856i | ||||||||
\(490\) | 4.47967e9i | 1.72012i | ||||||||
\(491\) | − | 1.79156e9i | − | 0.683040i | −0.939874 | − | 0.341520i | \(-0.889058\pi\) | ||
0.939874 | − | 0.341520i | \(-0.110942\pi\) | |||||||
\(492\) | 7.03135e8i | 0.266171i | ||||||||
\(493\) | − | 1.00641e8i | − | 0.0378276i | ||||||
\(494\) | − | 1.63656e9i | − | 0.610784i | ||||||
\(495\) | 5.00716e9i | 1.85555i | ||||||||
\(496\) | −8.11337e8 | −0.298549 | ||||||||
\(497\) | −1.59870e8 | −0.0584142 | ||||||||
\(498\) | − | 1.22034e10i | − | 4.42770i | ||||||
\(499\) | −2.47034e9 | −0.890032 | −0.445016 | − | 0.895523i | \(-0.646802\pi\) | ||||
−0.445016 | + | 0.895523i | \(0.646802\pi\) | |||||||
\(500\) | −4.98939e9 | −1.78506 | ||||||||
\(501\) | 6.02585e9i | 2.14085i | ||||||||
\(502\) | −2.98154e9 | −1.05191 | ||||||||
\(503\) | 4.16423e8i | 0.145897i | 0.997336 | + | 0.0729485i | \(0.0232409\pi\) | ||||
−0.997336 | + | 0.0729485i | \(0.976759\pi\) | |||||||
\(504\) | 6.36558e8i | 0.221478i | ||||||||
\(505\) | 4.93067e9i | 1.70367i | ||||||||
\(506\) | 1.39700e9i | 0.479370i | ||||||||
\(507\) | 2.18430e9 | 0.744362 | ||||||||
\(508\) | 3.85705e9i | 1.30537i | ||||||||
\(509\) | −3.46676e9 | −1.16523 | −0.582615 | − | 0.812748i | \(-0.697970\pi\) | ||||
−0.582615 | + | 0.812748i | \(0.697970\pi\) | |||||||
\(510\) | −3.30968e9 | −1.10482 | ||||||||
\(511\) | 2.95557e8 | 0.0979870 | ||||||||
\(512\) | − | 3.35554e9i | − | 1.10489i | ||||||
\(513\) | − | 6.37006e8i | − | 0.208321i | ||||||
\(514\) | −6.53889e9 | −2.12389 | ||||||||
\(515\) | 2.47187e9i | 0.797444i | ||||||||
\(516\) | −1.37996e10 | −4.42175 | ||||||||
\(517\) | −2.93365e9 | −0.933665 | ||||||||
\(518\) | −1.90649e8 | −0.0602670 | ||||||||
\(519\) | −5.42589e9 | −1.70367 | ||||||||
\(520\) | 3.39769e9 | 1.05967 | ||||||||
\(521\) | 4.01889e9i | 1.24501i | 0.782614 | + | 0.622507i | \(0.213886\pi\) | ||||
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(522\) | 6.28991e8i | 0.193552i | ||||||||
\(523\) | 1.48260e9 | 0.453178 | 0.226589 | − | 0.973990i | \(-0.427243\pi\) | ||||
0.226589 | + | 0.973990i | \(0.427243\pi\) | |||||||
\(524\) | 4.48610e9 | 1.36210 | ||||||||
\(525\) | −4.10231e7 | −0.0123729 | ||||||||
\(526\) | − | 7.49892e8i | − | 0.224672i | ||||||
\(527\) | 7.24578e8i | 0.215649i | ||||||||
\(528\) | − | 4.18375e9i | − | 1.23694i | ||||||
\(529\) | 3.26722e9 | 0.959586 | ||||||||
\(530\) | 6.32158e9 | 1.84442 | ||||||||
\(531\) | − | 4.46601e9i | − | 1.29446i | ||||||
\(532\) | − | 3.95197e8i | − | 0.113795i | ||||||
\(533\) | −2.36982e8 | −0.0677907 | ||||||||
\(534\) | − | 6.96948e9i | − | 1.98064i | ||||||
\(535\) | − | 2.36062e9i | − | 0.666481i | ||||||
\(536\) | −4.14789e9 | −1.16346 | ||||||||
\(537\) | 8.17830e9i | 2.27905i | ||||||||
\(538\) | −1.01678e10 | −2.81507 | ||||||||
\(539\) | 5.05719e9i | 1.39107i | ||||||||
\(540\) | 2.87243e9 | 0.785003 | ||||||||
\(541\) | 3.91359e9 | 1.06264 | 0.531319 | − | 0.847172i | \(-0.321697\pi\) | ||||
0.531319 | + | 0.847172i | \(0.321697\pi\) | |||||||
\(542\) | 5.18302e9 | 1.39825 | ||||||||
\(543\) | − | 3.82102e9i | − | 1.02419i | ||||||
\(544\) | −7.24256e8 | −0.192884 | ||||||||
\(545\) | −3.88733e9 | − | 3.74910e8i | −1.02864 | − | 0.0992062i | ||||
\(546\) | −8.32338e8 | −0.218839 | ||||||||
\(547\) | 4.47999e9i | 1.17037i | 0.810902 | + | 0.585183i | \(0.198977\pi\) | ||||
−0.810902 | + | 0.585183i | \(0.801023\pi\) | |||||||
\(548\) | 1.70956e7 | 0.00443763 | ||||||||
\(549\) | 3.72897e9 | 0.961801 | ||||||||
\(550\) | 6.32171e8 | 0.162019 | ||||||||
\(551\) | − | 1.79790e8i | − | 0.0457863i | ||||||
\(552\) | 1.72585e9 | 0.436734 | ||||||||
\(553\) | − | 3.28625e8i | − | 0.0826346i | ||||||
\(554\) | 1.15694e10 | 2.89086 | ||||||||
\(555\) | 1.85265e9i | 0.460011i | ||||||||
\(556\) | 1.20411e10i | 2.97100i | ||||||||
\(557\) | −2.81429e9 | −0.690042 | −0.345021 | − | 0.938595i | \(-0.612128\pi\) | ||||
−0.345021 | + | 0.938595i | \(0.612128\pi\) | |||||||
\(558\) | − | 4.52851e9i | − | 1.10341i | ||||||
\(559\) | − | 4.65098e9i | − | 1.12617i | ||||||
\(560\) | 3.01620e8 | 0.0725776 | ||||||||
\(561\) | −3.73636e9 | −0.893469 | ||||||||
\(562\) | 2.13975e9i | 0.508494i | ||||||||
\(563\) | − | 6.29803e8i | − | 0.148739i | −0.997231 | − | 0.0743696i | \(-0.976306\pi\) | ||
0.997231 | − | 0.0743696i | \(-0.0236944\pi\) | |||||||
\(564\) | 7.87169e9i | 1.84753i | ||||||||
\(565\) | 2.49908e9 | 0.582923 | ||||||||
\(566\) | −2.28725e9 | −0.530220 | ||||||||
\(567\) | 3.43013e8 | 0.0790261 | ||||||||
\(568\) | − | 3.04353e9i | − | 0.696881i | ||||||
\(569\) | 4.69761e9i | 1.06902i | 0.845164 | + | 0.534508i | \(0.179503\pi\) | ||||
−0.845164 | + | 0.534508i | \(0.820497\pi\) | |||||||
\(570\) | −5.91259e9 | −1.33726 | ||||||||
\(571\) | −4.80983e9 | −1.08119 | −0.540597 | − | 0.841282i | \(-0.681802\pi\) | ||||
−0.540597 | + | 0.841282i | \(0.681802\pi\) | |||||||
\(572\) | 8.33108e9 | 1.86130 | ||||||||
\(573\) | −7.59737e9 | −1.68703 | ||||||||
\(574\) | −8.81053e7 | −0.0194451 | ||||||||
\(575\) | 6.22676e7i | 0.0136592i | ||||||||
\(576\) | 7.91774e9 | 1.72632 | ||||||||
\(577\) | 4.95896e8i | 0.107467i | 0.998555 | + | 0.0537335i | \(0.0171121\pi\) | ||||
−0.998555 | + | 0.0537335i | \(0.982888\pi\) | |||||||
\(578\) | 6.45920e9i | 1.39133i | ||||||||
\(579\) | −8.90685e8 | −0.190699 | ||||||||
\(580\) | 8.10721e8 | 0.172534 | ||||||||
\(581\) | 9.93206e8 | 0.210098 | ||||||||
\(582\) | − | 1.97825e10i | − | 4.15959i | ||||||
\(583\) | 7.13656e9 | 1.49159 | ||||||||
\(584\) | 5.62670e9i | 1.16898i | ||||||||
\(585\) | 4.52823e9i | 0.935153i | ||||||||
\(586\) | 8.29448e9i | 1.70274i | ||||||||
\(587\) | 4.62007e9i | 0.942791i | 0.881922 | + | 0.471396i | \(0.156250\pi\) | ||||
−0.881922 | + | 0.471396i | \(0.843750\pi\) | |||||||
\(588\) | 1.35697e10 | 2.75264 | ||||||||
\(589\) | 1.29443e9i | 0.261020i | ||||||||
\(590\) | −8.86241e9 | −1.77652 | ||||||||
\(591\) | 1.26875e10 | 2.52824 | ||||||||
\(592\) | − | 8.66635e8i | − | 0.171676i | ||||||
\(593\) | 6.28448e9 | 1.23759 | 0.618797 | − | 0.785551i | \(-0.287620\pi\) | ||||
0.618797 | + | 0.785551i | \(0.287620\pi\) | |||||||
\(594\) | 4.99249e9 | 0.977384 | ||||||||
\(595\) | − | 2.69367e8i | − | 0.0524246i | ||||||
\(596\) | − | 3.85201e9i | − | 0.745291i | ||||||
\(597\) | − | 7.44147e9i | − | 1.43136i | ||||||
\(598\) | 1.26338e9i | 0.241591i | ||||||||
\(599\) | − | 2.66782e9i | − | 0.507181i | −0.967312 | − | 0.253591i | \(-0.918388\pi\) | ||
0.967312 | − | 0.253591i | \(-0.0816116\pi\) | |||||||
\(600\) | − | 7.80980e8i | − | 0.147608i | ||||||
\(601\) | − | 6.38397e9i | − | 1.19958i | −0.800157 | − | 0.599791i | \(-0.795250\pi\) | ||
0.800157 | − | 0.599791i | \(-0.204750\pi\) | |||||||
\(602\) | − | 1.72914e9i | − | 0.323030i | ||||||
\(603\) | − | 5.52804e9i | − | 1.02674i | ||||||
\(604\) | 1.69963e10i | 3.13851i | ||||||||
\(605\) | 5.58844e9 | 1.02600 | ||||||||
\(606\) | 2.29950e10 | 4.19740 | ||||||||
\(607\) | 5.66958e9i | 1.02894i | 0.857508 | + | 0.514471i | \(0.172012\pi\) | ||||
−0.857508 | + | 0.514471i | \(0.827988\pi\) | |||||||
\(608\) | −1.29385e9 | −0.233465 | ||||||||
\(609\) | −9.14395e7 | −0.0164049 | ||||||||
\(610\) | − | 7.39982e9i | − | 1.31998i | ||||||
\(611\) | −2.65304e9 | −0.470544 | ||||||||
\(612\) | 5.61278e9i | 0.989802i | ||||||||
\(613\) | − | 5.95866e9i | − | 1.04481i | −0.852698 | − | 0.522404i | \(-0.825035\pi\) | ||
0.852698 | − | 0.522404i | \(-0.174965\pi\) | |||||||
\(614\) | − | 3.15396e9i | − | 0.549878i | ||||||
\(615\) | 8.56173e8i | 0.148422i | ||||||||
\(616\) | 1.42605e9 | 0.245811 | ||||||||
\(617\) | − | 8.65037e9i | − | 1.48264i | −0.671150 | − | 0.741322i | \(-0.734199\pi\) | ||
0.671150 | − | 0.741322i | \(-0.265801\pi\) | |||||||
\(618\) | 1.15280e10 | 1.96469 | ||||||||
\(619\) | 3.20204e9 | 0.542637 | 0.271318 | − | 0.962490i | \(-0.412540\pi\) | ||||
0.271318 | + | 0.962490i | \(0.412540\pi\) | |||||||
\(620\) | −5.83691e9 | −0.983586 | ||||||||
\(621\) | 4.91751e8i | 0.0823996i | ||||||||
\(622\) | 4.57291e8i | 0.0761950i | ||||||||
\(623\) | 5.67230e8 | 0.0939833 | ||||||||
\(624\) | − | 3.78357e9i | − | 0.623385i | ||||||
\(625\) | −6.49004e9 | −1.06333 | ||||||||
\(626\) | −1.43572e10 | −2.33915 | ||||||||
\(627\) | −6.67485e9 | −1.08145 | ||||||||
\(628\) | −2.10742e10 | −3.39540 | ||||||||
\(629\) | −7.73963e8 | −0.124006 | ||||||||
\(630\) | 1.68351e9i | 0.268240i | ||||||||
\(631\) | − | 9.11387e9i | − | 1.44411i | −0.691836 | − | 0.722055i | \(-0.743198\pi\) | ||
0.691836 | − | 0.722055i | \(-0.256802\pi\) | |||||||
\(632\) | 6.25622e9 | 0.985831 | ||||||||
\(633\) | −8.67355e9 | −1.35920 | ||||||||
\(634\) | −4.12991e9 | −0.643618 | ||||||||
\(635\) | 4.69654e9i | 0.727898i | ||||||||
\(636\) | − | 1.91491e10i | − | 2.95154i | ||||||
\(637\) | 4.57347e9i | 0.701065i | ||||||||
\(638\) | 1.40909e9 | 0.214816 | ||||||||
\(639\) | 4.05623e9 | 0.614992 | ||||||||
\(640\) | − | 1.25639e10i | − | 1.89450i | ||||||
\(641\) | − | 2.65939e9i | − | 0.398822i | −0.979916 | − | 0.199411i | \(-0.936097\pi\) | ||
0.979916 | − | 0.199411i | \(-0.0639029\pi\) | |||||||
\(642\) | −1.10092e10 | −1.64203 | ||||||||
\(643\) | − | 5.34520e9i | − | 0.792913i | −0.918054 | − | 0.396457i | \(-0.870240\pi\) | ||
0.918054 | − | 0.396457i | \(-0.129760\pi\) | |||||||
\(644\) | 3.05082e8i | 0.0450107i | ||||||||
\(645\) | −1.68031e10 | −2.46565 | ||||||||
\(646\) | − | 2.47004e9i | − | 0.360488i | ||||||
\(647\) | 1.07598e10 | 1.56185 | 0.780926 | − | 0.624624i | \(-0.214748\pi\) | ||||
0.780926 | + | 0.624624i | \(0.214748\pi\) | |||||||
\(648\) | 6.53015e9i | 0.942780i | ||||||||
\(649\) | −1.00050e10 | −1.43668 | ||||||||
\(650\) | 5.71704e8 | 0.0816534 | ||||||||
\(651\) | 6.58333e8 | 0.0935216 | ||||||||
\(652\) | − | 8.95029e9i | − | 1.26465i | ||||||
\(653\) | 1.38828e10 | 1.95111 | 0.975554 | − | 0.219761i | \(-0.0705279\pi\) | ||||
0.975554 | + | 0.219761i | \(0.0705279\pi\) | |||||||
\(654\) | −1.74846e9 | + | 1.81293e10i | −0.244418 | + | 2.53430i | ||||
\(655\) | 5.46250e9 | 0.759533 | ||||||||
\(656\) | − | 4.00502e8i | − | 0.0553912i | ||||||
\(657\) | −7.49891e9 | −1.03162 | ||||||||
\(658\) | −9.86350e8 | −0.134971 | ||||||||
\(659\) | 7.85491e9 | 1.06916 | 0.534579 | − | 0.845118i | \(-0.320470\pi\) | ||||
0.534579 | + | 0.845118i | \(0.320470\pi\) | |||||||
\(660\) | − | 3.00987e10i | − | 4.07515i | ||||||
\(661\) | −9.70948e9 | −1.30765 | −0.653824 | − | 0.756647i | \(-0.726836\pi\) | ||||
−0.653824 | + | 0.756647i | \(0.726836\pi\) | |||||||
\(662\) | 2.05286e9i | 0.275014i | ||||||||
\(663\) | −3.37898e9 | −0.450286 | ||||||||
\(664\) | 1.89083e10i | 2.50647i | ||||||||
\(665\) | − | 4.81212e8i | − | 0.0634543i | ||||||
\(666\) | 4.83716e9 | 0.634499 | ||||||||
\(667\) | 1.38793e8i | 0.0181104i | ||||||||
\(668\) | − | 2.02788e10i | − | 2.63224i | ||||||
\(669\) | −6.49918e9 | −0.839203 | ||||||||
\(670\) | −1.09699e10 | −1.40910 | ||||||||
\(671\) | − | 8.35381e9i | − | 1.06747i | ||||||
\(672\) | 6.58040e8i | 0.0836489i | ||||||||
\(673\) | 1.48079e10i | 1.87258i | 0.351230 | + | 0.936289i | \(0.385764\pi\) | ||||
−0.351230 | + | 0.936289i | \(0.614236\pi\) | |||||||
\(674\) | 1.01682e10 | 1.27918 | ||||||||
\(675\) | 2.22527e8 | 0.0278496 | ||||||||
\(676\) | −7.35084e9 | −0.915216 | ||||||||
\(677\) | − | 5.04997e8i | − | 0.0625501i | −0.999511 | − | 0.0312751i | \(-0.990043\pi\) | ||
0.999511 | − | 0.0312751i | \(-0.00995678\pi\) | |||||||
\(678\) | − | 1.16549e10i | − | 1.43617i | ||||||
\(679\) | 1.61005e9 | 0.197376 | ||||||||
\(680\) | 5.12810e9 | 0.625425 | ||||||||
\(681\) | 1.33313e9 | 0.161755 | ||||||||
\(682\) | −1.01450e10 | −1.22463 | ||||||||
\(683\) | 1.29185e10 | 1.55146 | 0.775728 | − | 0.631068i | \(-0.217383\pi\) | ||||
0.775728 | + | 0.631068i | \(0.217383\pi\) | |||||||
\(684\) | 1.00270e10i | 1.19805i | ||||||||
\(685\) | 2.08164e7 | 0.00247451 | ||||||||
\(686\) | 3.42584e9i | 0.405166i | ||||||||
\(687\) | 2.12722e10i | 2.50301i | ||||||||
\(688\) | 7.86020e9 | 0.920182 | ||||||||
\(689\) | 6.45395e9 | 0.751724 | ||||||||
\(690\) | 4.56436e9 | 0.528942 | ||||||||
\(691\) | − | 1.23764e10i | − | 1.42699i | −0.700660 | − | 0.713495i | \(-0.747111\pi\) | ||
0.700660 | − | 0.713495i | \(-0.252889\pi\) | |||||||
\(692\) | 1.82598e10 | 2.09471 | ||||||||
\(693\) | 1.90055e9i | 0.216926i | ||||||||
\(694\) | 2.75541e10i | 3.12916i | ||||||||
\(695\) | 1.46618e10i | 1.65669i | ||||||||
\(696\) | − | 1.74079e9i | − | 0.195710i | ||||||
\(697\) | −3.57675e8 | −0.0400104 | ||||||||
\(698\) | 1.82171e10i | 2.02761i | ||||||||
\(699\) | 2.03753e10 | 2.25650 | ||||||||
\(700\) | 1.38055e8 | 0.0152128 | ||||||||
\(701\) | 2.50576e9i | 0.274743i | 0.990520 | + | 0.137371i | \(0.0438654\pi\) | ||||
−0.990520 | + | 0.137371i | \(0.956135\pi\) | |||||||
\(702\) | 4.51496e9 | 0.492577 | ||||||||
\(703\) | −1.38265e9 | −0.150096 | ||||||||
\(704\) | − | 1.77377e10i | − | 1.91599i | ||||||
\(705\) | 9.58497e9i | 1.03022i | ||||||||
\(706\) | − | 5.02050e8i | − | 0.0536946i | ||||||
\(707\) | 1.87151e9i | 0.199170i | ||||||||
\(708\) | 2.68458e10i | 2.84288i | ||||||||
\(709\) | − | 5.25830e9i | − | 0.554094i | −0.960856 | − | 0.277047i | \(-0.910644\pi\) | ||
0.960856 | − | 0.277047i | \(-0.0893557\pi\) | |||||||
\(710\) | − | 8.04924e9i | − | 0.844016i | ||||||
\(711\) | 8.33790e9i | 0.869988i | ||||||||
\(712\) | 1.07987e10i | 1.12122i | ||||||||
\(713\) | − | 9.99262e8i | − | 0.103244i | ||||||
\(714\) | −1.25624e9 | −0.129160 | ||||||||
\(715\) | 1.01443e10 | 1.03789 | ||||||||
\(716\) | − | 2.75225e10i | − | 2.80215i | ||||||
\(717\) | −5.99108e8 | −0.0606999 | ||||||||
\(718\) | 3.74937e9 | 0.378027 | ||||||||
\(719\) | − | 9.50535e9i | − | 0.953711i | −0.878982 | − | 0.476856i | \(-0.841776\pi\) | ||
0.878982 | − | 0.476856i | \(-0.158224\pi\) | |||||||
\(720\) | −7.65274e9 | −0.764106 | ||||||||
\(721\) | 9.38237e8i | 0.0932264i | ||||||||
\(722\) | 1.26699e10i | 1.25283i | ||||||||
\(723\) | − | 1.09025e10i | − | 1.07286i | ||||||
\(724\) | 1.28589e10i | 1.25927i | ||||||||
\(725\) | 6.28065e7 | 0.00612099 | ||||||||
\(726\) | − | 2.60627e10i | − | 2.52779i | ||||||
\(727\) | 3.00737e9 | 0.290280 | 0.145140 | − | 0.989411i | \(-0.453637\pi\) | ||||
0.145140 | + | 0.989411i | \(0.453637\pi\) | |||||||
\(728\) | 1.28965e9 | 0.123883 | ||||||||
\(729\) | −1.51655e10 | −1.44981 | ||||||||
\(730\) | 1.48810e10i | 1.41580i | ||||||||
\(731\) | − | 7.01967e9i | − | 0.664670i | ||||||
\(732\) | −2.24153e10 | −2.11230 | ||||||||
\(733\) | − | 6.74937e9i | − | 0.632993i | −0.948594 | − | 0.316497i | \(-0.897493\pi\) | ||
0.948594 | − | 0.316497i | \(-0.102507\pi\) | |||||||
\(734\) | 9.14770e8 | 0.0853839 | ||||||||
\(735\) | 1.65231e10 | 1.53492 | ||||||||
\(736\) | 9.98819e8 | 0.0923452 | ||||||||
\(737\) | −1.23842e10 | −1.13954 | ||||||||
\(738\) | 2.23542e9 | 0.204721 | ||||||||
\(739\) | − | 1.47005e10i | − | 1.33991i | −0.742401 | − | 0.669956i | \(-0.766313\pi\) | ||
0.742401 | − | 0.669956i | \(-0.233687\pi\) | |||||||
\(740\) | − | 6.23474e9i | − | 0.565597i | ||||||
\(741\) | −6.03640e9 | −0.545023 | ||||||||
\(742\) | 2.39945e9 | 0.215625 | ||||||||
\(743\) | −5.14438e9 | −0.460121 | −0.230061 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230061 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(744\) | 1.25331e10i | 1.11571i | ||||||||
\(745\) | − | 4.69040e9i | − | 0.415588i | ||||||
\(746\) | − | 1.98258e10i | − | 1.74842i | ||||||
\(747\) | −2.51997e10 | −2.21194 | ||||||||
\(748\) | 1.25740e10 | 1.09855 | ||||||||
\(749\) | − | 8.96010e8i | − | 0.0779160i | ||||||
\(750\) | 2.83334e10i | 2.45236i | ||||||||
\(751\) | 5.88362e9 | 0.506879 | 0.253440 | − | 0.967351i | \(-0.418438\pi\) | ||||
0.253440 | + | 0.967351i | \(0.418438\pi\) | |||||||
\(752\) | − | 4.48367e9i | − | 0.384478i | ||||||
\(753\) | 1.09973e10i | 0.938650i | ||||||||
\(754\) | 1.27431e9 | 0.108262 | ||||||||
\(755\) | 2.06955e10i | 1.75010i | ||||||||
\(756\) | 1.09028e9 | 0.0917719 | ||||||||
\(757\) | 4.61667e9i | 0.386806i | 0.981119 | + | 0.193403i | \(0.0619524\pi\) | ||||
−0.981119 | + | 0.193403i | \(0.938048\pi\) | |||||||
\(758\) | 1.87690e9 | 0.156531 | ||||||||
\(759\) | 5.15281e9 | 0.427757 | ||||||||
\(760\) | 9.16112e9 | 0.757009 | ||||||||
\(761\) | − | 1.71644e9i | − | 0.141183i | −0.997505 | − | 0.0705916i | \(-0.977511\pi\) | ||
0.997505 | − | 0.0705916i | \(-0.0224887\pi\) | |||||||
\(762\) | 2.19032e10 | 1.79335 | ||||||||
\(763\) | −1.47550e9 | − | 1.42303e8i | −0.120255 | − | 0.0115979i | ||||
\(764\) | 2.55675e10 | 2.07425 | ||||||||
\(765\) | 6.83441e9i | 0.551932i | ||||||||
\(766\) | 5.26715e9 | 0.423424 | ||||||||
\(767\) | −9.04799e9 | −0.724050 | ||||||||
\(768\) | −3.29126e10 | −2.62179 | ||||||||
\(769\) | − | 1.95456e10i | − | 1.54991i | −0.632016 | − | 0.774956i | \(-0.717772\pi\) | ||
0.632016 | − | 0.774956i | \(-0.282228\pi\) | |||||||
\(770\) | 3.77147e9 | 0.297710 | ||||||||
\(771\) | 2.41185e10i | 1.89522i | ||||||||
\(772\) | 2.99743e9 | 0.234471 | ||||||||
\(773\) | − | 1.69093e10i | − | 1.31673i | −0.752698 | − | 0.658366i | \(-0.771248\pi\) | ||
0.752698 | − | 0.658366i | \(-0.228752\pi\) | |||||||
\(774\) | 4.38720e10i | 3.40090i | ||||||||
\(775\) | −4.52185e8 | −0.0348948 | ||||||||
\(776\) | 3.06515e10i | 2.35470i | ||||||||
\(777\) | 7.03202e8i | 0.0537783i | ||||||||
\(778\) | −4.54599e9 | −0.346099 | ||||||||
\(779\) | −6.38970e8 | −0.0484283 | ||||||||
\(780\) | − | 2.72197e10i | − | 2.05378i | ||||||
\(781\) | − | 9.08695e9i | − | 0.682558i | ||||||
\(782\) | 1.90681e9i | 0.142588i | ||||||||
\(783\) | 4.96007e8 | 0.0369251 | ||||||||
\(784\) | −7.72921e9 | −0.572834 | ||||||||
\(785\) | −2.56609e10 | −1.89334 | ||||||||
\(786\) | − | 2.54753e10i | − | 1.87129i | ||||||
\(787\) | − | 1.86979e10i | − | 1.36735i | −0.729785 | − | 0.683677i | \(-0.760380\pi\) | ||
0.729785 | − | 0.683677i | \(-0.239620\pi\) | |||||||
\(788\) | −4.26973e10 | −3.10855 | ||||||||
\(789\) | −2.76595e9 | −0.200482 | ||||||||
\(790\) | 1.65458e10 | 1.19397 | ||||||||
\(791\) | 9.48565e8 | 0.0681474 | ||||||||
\(792\) | −3.61818e10 | −2.58793 | ||||||||
\(793\) | − | 7.55477e9i | − | 0.537979i | ||||||
\(794\) | −3.06080e10 | −2.17001 | ||||||||
\(795\) | − | 2.33170e10i | − | 1.64584i | ||||||
\(796\) | 2.50428e10i | 1.75990i | ||||||||
\(797\) | −7.07123e8 | −0.0494755 | −0.0247378 | − | 0.999694i | \(-0.507875\pi\) | ||||
−0.0247378 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(798\) | −2.24422e9 | −0.156335 | ||||||||
\(799\) | −4.00421e9 | −0.277718 | ||||||||
\(800\) | − | 4.51984e8i | − | 0.0312111i | ||||||
\(801\) | −1.43918e10 | −0.989468 | ||||||||
\(802\) | − | 4.21862e10i | − | 2.88776i | ||||||
\(803\) | 1.67994e10i | 1.14496i | ||||||||
\(804\) | 3.32298e10i | 2.25492i | ||||||||
\(805\) | 3.71483e8i | 0.0250988i | ||||||||
\(806\) | −9.17462e9 | −0.617185 | ||||||||
\(807\) | 3.75036e10i | 2.51198i | ||||||||
\(808\) | −3.56291e10 | −2.37610 | ||||||||
\(809\) | −1.09048e10 | −0.724097 | −0.362049 | − | 0.932159i | \(-0.617923\pi\) | ||||
−0.362049 | + | 0.932159i | \(0.617923\pi\) | |||||||
\(810\) | 1.72703e10i | 1.14183i | ||||||||
\(811\) | −1.63700e10 | −1.07765 | −0.538823 | − | 0.842419i | \(-0.681131\pi\) | ||||
−0.538823 | + | 0.842419i | \(0.681131\pi\) | |||||||
\(812\) | 3.07722e8 | 0.0201703 | ||||||||
\(813\) | − | 1.91174e10i | − | 1.24771i | ||||||
\(814\) | − | 1.08364e10i | − | 0.704208i | ||||||
\(815\) | − | 1.08983e10i | − | 0.705193i | ||||||
\(816\) | − | 5.71051e9i | − | 0.367925i | ||||||
\(817\) | − | 1.25403e10i | − | 0.804511i | ||||||
\(818\) | 1.21406e10i | 0.775537i | ||||||||
\(819\) | 1.71876e9i | 0.109325i | ||||||||
\(820\) | − | 2.88129e9i | − | 0.182489i | ||||||
\(821\) | 1.67452e10i | 1.05606i | 0.849226 | + | 0.528030i | \(0.177069\pi\) | ||||
−0.849226 | + | 0.528030i | \(0.822931\pi\) | |||||||
\(822\) | − | 9.70810e7i | − | 0.00609653i | ||||||
\(823\) | −2.19243e10 | −1.37096 | −0.685482 | − | 0.728090i | \(-0.740408\pi\) | ||||
−0.685482 | + | 0.728090i | \(0.740408\pi\) | |||||||
\(824\) | −1.78618e10 | −1.11219 | ||||||||
\(825\) | − | 2.33174e9i | − | 0.144575i | ||||||
\(826\) | −3.36387e9 | −0.207687 | ||||||||
\(827\) | 6.87816e9 | 0.422866 | 0.211433 | − | 0.977392i | \(-0.432187\pi\) | ||||
0.211433 | + | 0.977392i | \(0.432187\pi\) | |||||||
\(828\) | − | 7.74056e9i | − | 0.473878i | ||||||
\(829\) | 2.35835e10 | 1.43770 | 0.718848 | − | 0.695167i | \(-0.244670\pi\) | ||||
0.718848 | + | 0.695167i | \(0.244670\pi\) | |||||||
\(830\) | 5.00067e10i | 3.03567i | ||||||||
\(831\) | − | 4.26734e10i | − | 2.57961i | ||||||
\(832\) | − | 1.60411e10i | − | 0.965610i | ||||||
\(833\) | 6.90270e9i | 0.413772i | ||||||||
\(834\) | 6.83780e10 | 4.08164 | ||||||||
\(835\) | − | 2.46925e10i | − | 1.46779i | ||||||
\(836\) | 2.24629e10 | 1.32967 | ||||||||
\(837\) | −3.57108e9 | −0.210504 | ||||||||
\(838\) | 3.15358e9 | 0.185118 | ||||||||
\(839\) | − | 9.12850e9i | − | 0.533621i | −0.963749 | − | 0.266810i | \(-0.914030\pi\) | ||
0.963749 | − | 0.266810i | \(-0.0859697\pi\) | |||||||
\(840\) | − | 4.65926e9i | − | 0.271231i | ||||||
\(841\) | −1.71099e10 | −0.991884 | ||||||||
\(842\) | − | 2.73627e10i | − | 1.57967i | ||||||
\(843\) | 7.89240e9 | 0.453746 | ||||||||
\(844\) | 2.91892e10 | 1.67118 | ||||||||
\(845\) | −8.95075e9 | −0.510342 | ||||||||
\(846\) | 2.50258e10 | 1.42099 | ||||||||
\(847\) | 2.12118e9 | 0.119946 | ||||||||
\(848\) | 1.09072e10i | 0.614228i | ||||||||
\(849\) | 8.43645e9i | 0.473132i | ||||||||
\(850\) | 8.62866e8 | 0.0481923 | ||||||||
\(851\) | 1.06737e9 | 0.0593692 | ||||||||
\(852\) | −2.43825e10 | −1.35064 | ||||||||
\(853\) | − | 2.27462e10i | − | 1.25484i | −0.778683 | − | 0.627418i | \(-0.784112\pi\) | ||
0.778683 | − | 0.627418i | \(-0.215888\pi\) | |||||||
\(854\) | − | 2.80872e9i | − | 0.154314i | ||||||
\(855\) | 1.22094e10i | 0.668054i | ||||||||
\(856\) | 1.70579e10 | 0.929538 | ||||||||
\(857\) | −2.62495e10 | −1.42458 | −0.712292 | − | 0.701883i | \(-0.752343\pi\) | ||||
−0.712292 | + | 0.701883i | \(0.752343\pi\) | |||||||
\(858\) | − | 4.73099e10i | − | 2.55710i | ||||||
\(859\) | − | 1.44031e10i | − | 0.775320i | −0.921802 | − | 0.387660i | \(-0.873283\pi\) | ||
0.921802 | − | 0.387660i | \(-0.126717\pi\) | |||||||
\(860\) | 5.65477e10 | 3.03159 | ||||||||
\(861\) | 3.24974e8i | 0.0173515i | ||||||||
\(862\) | − | 7.43461e9i | − | 0.395351i | ||||||
\(863\) | 1.99980e10 | 1.05913 | 0.529564 | − | 0.848270i | \(-0.322356\pi\) | ||||
0.529564 | + | 0.848270i | \(0.322356\pi\) | |||||||
\(864\) | − | 3.56949e9i | − | 0.188282i | ||||||
\(865\) | 2.22340e10 | 1.16805 | ||||||||
\(866\) | 3.18368e10i | 1.66578i | ||||||||
\(867\) | 2.38246e10 | 1.24153 | ||||||||
\(868\) | −2.21549e9 | −0.114988 | ||||||||
\(869\) | 1.86790e10 | 0.965569 | ||||||||
\(870\) | − | 4.60387e9i | − | 0.237031i | ||||||
\(871\) | −1.11996e10 | −0.574302 | ||||||||
\(872\) | 2.70910e9 | − | 2.80899e10i | 0.138362 | − | 1.43464i | ||||
\(873\) | −4.08504e10 | −2.07800 | ||||||||
\(874\) | 3.40643e9i | 0.172587i | ||||||||
\(875\) | −2.30599e9 | −0.116367 | ||||||||
\(876\) | 4.50769e10 | 2.26564 | ||||||||
\(877\) | 1.01704e10 | 0.509145 | 0.254572 | − | 0.967054i | \(-0.418065\pi\) | ||||
0.254572 | + | 0.967054i | \(0.418065\pi\) | |||||||
\(878\) | − | 1.55991e10i | − | 0.777801i | ||||||
\(879\) | 3.05939e10 | 1.51941 | ||||||||
\(880\) | 1.71440e10i | 0.848054i | ||||||||
\(881\) | −3.45637e10 | −1.70296 | −0.851481 | − | 0.524386i | \(-0.824295\pi\) | ||||
−0.851481 | + | 0.524386i | \(0.824295\pi\) | |||||||
\(882\) | − | 4.31409e10i | − | 2.11714i | ||||||
\(883\) | 1.61470e10i | 0.789275i | 0.918837 | + | 0.394638i | \(0.129130\pi\) | ||||
−0.918837 | + | 0.394638i | \(0.870870\pi\) | |||||||
\(884\) | 1.13713e10 | 0.553640 | ||||||||
\(885\) | 3.26887e10i | 1.58525i | ||||||||
\(886\) | − | 1.27595e10i | − | 0.616332i | ||||||
\(887\) | −2.15373e10 | −1.03624 | −0.518118 | − | 0.855309i | \(-0.673367\pi\) | ||||
−0.518118 | + | 0.855309i | \(0.673367\pi\) | |||||||
\(888\) | −1.33873e10 | −0.641574 | ||||||||
\(889\) | 1.78265e9i | 0.0850960i | ||||||||
\(890\) | 2.85593e10i | 1.35795i | ||||||||
\(891\) | 1.94968e10i | 0.923404i | ||||||||
\(892\) | 2.18717e10 | 1.03183 | ||||||||
\(893\) | −7.15335e9 | −0.336147 | ||||||||
\(894\) | −2.18745e10 | −1.02390 | ||||||||
\(895\) | − | 3.35128e10i | − | 1.56253i | ||||||
\(896\) | − | 4.76884e9i | − | 0.221480i | ||||||
\(897\) | 4.65994e9 | 0.215579 | ||||||||
\(898\) | 5.75611e10 | 2.65254 | ||||||||
\(899\) | −1.00791e9 | −0.0462661 | ||||||||
\(900\) | −3.50275e9 | −0.160162 | ||||||||
\(901\) | 9.74089e9 | 0.443672 | ||||||||
\(902\) | − | 5.00789e9i | − | 0.227212i | ||||||
\(903\) | −6.37789e9 | −0.288251 | ||||||||
\(904\) | 1.80584e10i | 0.812999i | ||||||||
\(905\) | 1.56576e10i | 0.702193i | ||||||||
\(906\) | 9.65171e10 | 4.31177 | ||||||||
\(907\) | −8.78413e9 | −0.390907 | −0.195453 | − | 0.980713i | \(-0.562618\pi\) | ||||
−0.195453 | + | 0.980713i | \(0.562618\pi\) | |||||||
\(908\) | −4.48639e9 | −0.198882 | ||||||||
\(909\) | − | 4.74842e10i | − | 2.09689i | ||||||
\(910\) | 3.41073e9 | 0.150038 | ||||||||
\(911\) | 4.05945e10i | 1.77891i | 0.457026 | + | 0.889454i | \(0.348915\pi\) | ||||
−0.457026 | + | 0.889454i | \(0.651085\pi\) | |||||||
\(912\) | − | 1.02016e10i | − | 0.445334i | ||||||
\(913\) | 5.64536e10i | 2.45496i | ||||||||
\(914\) | 5.61955e10i | 2.43439i | ||||||||
\(915\) | −2.72940e10 | −1.17786 | ||||||||
\(916\) | − | 7.15874e10i | − | 3.07753i | ||||||
\(917\) | 2.07338e9 | 0.0887944 | ||||||||
\(918\) | 6.81439e9 | 0.290722 | ||||||||
\(919\) | − | 4.45729e10i | − | 1.89438i | −0.320677 | − | 0.947189i | \(-0.603911\pi\) | ||
0.320677 | − | 0.947189i | \(-0.396089\pi\) | |||||||
\(920\) | −7.07214e9 | −0.299429 | ||||||||
\(921\) | −1.16333e10 | −0.490674 | ||||||||
\(922\) | − | 2.33128e10i | − | 0.979572i | ||||||
\(923\) | − | 8.21779e9i | − | 0.343993i | ||||||
\(924\) | − | 1.14244e10i | − | 0.476412i | ||||||
\(925\) | − | 4.83005e8i | − | 0.0200657i | ||||||
\(926\) | 2.40589e10i | 0.995719i | ||||||||
\(927\) | − | 2.38050e10i | − | 0.981499i | ||||||
\(928\) | − | 1.00746e9i | − | 0.0413820i | ||||||
\(929\) | 1.34669e10i | 0.551079i | 0.961290 | + | 0.275540i | \(0.0888565\pi\) | ||||
−0.961290 | + | 0.275540i | \(0.911143\pi\) | |||||||
\(930\) | 3.31462e10i | 1.35128i | ||||||||
\(931\) | 1.23314e10i | 0.500827i | ||||||||
\(932\) | −6.85693e10 | −2.77443 | ||||||||
\(933\) | 1.68670e9 | 0.0679913 | ||||||||
\(934\) | − | 5.06286e10i | − | 2.03321i | ||||||
\(935\) | 1.53108e10 | 0.612570 | ||||||||
\(936\) | −3.27210e10 | −1.30425 | ||||||||
\(937\) | 1.03936e10i | 0.412739i | 0.978474 | + | 0.206370i | \(0.0661649\pi\) | ||||
−0.978474 | + | 0.206370i | \(0.933835\pi\) | |||||||
\(938\) | −4.16381e9 | −0.164733 | ||||||||
\(939\) | 5.29559e10i | 2.08730i | ||||||||
\(940\) | − | 3.22564e10i | − | 1.26668i | ||||||
\(941\) | 2.70393e10i | 1.05787i | 0.848663 | + | 0.528934i | \(0.177408\pi\) | ||||
−0.848663 | + | 0.528934i | \(0.822592\pi\) | |||||||
\(942\) | 1.19674e11i | 4.66469i | ||||||||
\(943\) | 4.93268e8 | 0.0191554 | ||||||||
\(944\) | − | 1.52912e10i | − | 0.591615i | ||||||
\(945\) | 1.32757e9 | 0.0511738 | ||||||||
\(946\) | 9.82841e10 | 3.77454 | ||||||||
\(947\) | 1.20985e10 | 0.462921 | 0.231460 | − | 0.972844i | \(-0.425650\pi\) | ||||
0.231460 | + | 0.972844i | \(0.425650\pi\) | |||||||
\(948\) | − | 5.01202e10i | − | 1.91066i | ||||||
\(949\) | 1.51926e10i | 0.577031i | ||||||||
\(950\) | 1.54147e9 | 0.0583315 | ||||||||
\(951\) | 1.52331e10i | 0.574322i | ||||||||
\(952\) | 1.94645e9 | 0.0731162 | ||||||||
\(953\) | 1.99675e10 | 0.747305 | 0.373652 | − | 0.927569i | \(-0.378105\pi\) | ||||
0.373652 | + | 0.927569i | \(0.378105\pi\) | |||||||
\(954\) | −6.08792e10 | −2.27012 | ||||||||
\(955\) | 3.11323e10 | 1.15664 | ||||||||
\(956\) | 2.01618e9 | 0.0746324 | ||||||||
\(957\) | − | 5.19740e9i | − | 0.191688i | ||||||
\(958\) | 4.91486e10i | 1.80606i | ||||||||
\(959\) | 7.90119e6 | 0.000289286 | ||||||||
\(960\) | −5.79535e10 | −2.11412 | ||||||||
\(961\) | −2.02560e10 | −0.736244 | ||||||||
\(962\) | − | 9.79993e9i | − | 0.354904i | ||||||
\(963\) | 2.27337e10i | 0.820309i | ||||||||
\(964\) | 3.66902e10i | 1.31911i | ||||||||
\(965\) | 3.64982e9 | 0.130745 | ||||||||
\(966\) | 1.73248e9 | 0.0618368 | ||||||||
\(967\) | 1.16405e10i | 0.413980i | 0.978343 | + | 0.206990i | \(0.0663668\pi\) | ||||
−0.978343 | + | 0.206990i | \(0.933633\pi\) | |||||||
\(968\) | 4.03822e10i | 1.43095i | ||||||||
\(969\) | −9.11068e9 | −0.321675 | ||||||||
\(970\) | 8.10640e10i | 2.85185i | ||||||||
\(971\) | − | 4.15885e10i | − | 1.45783i | −0.684605 | − | 0.728914i | \(-0.740025\pi\) | ||
0.684605 | − | 0.728914i | \(-0.259975\pi\) | |||||||
\(972\) | 7.40632e10 | 2.58684 | ||||||||
\(973\) | 5.56512e9i | 0.193678i | ||||||||
\(974\) | 4.39866e9 | 0.152533 | ||||||||
\(975\) | − | 2.10871e9i | − | 0.0728620i | ||||||
\(976\) | 1.27676e10 | 0.439578 | ||||||||
\(977\) | −9.03915e9 | −0.310096 | −0.155048 | − | 0.987907i | \(-0.549553\pi\) | ||||
−0.155048 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(978\) | −5.08262e10 | −1.73741 | ||||||||
\(979\) | 3.22412e10i | 1.09818i | ||||||||
\(980\) | −5.56054e10 | −1.88723 | ||||||||
\(981\) | 3.74365e10 | + | 3.61052e9i | 1.26606 | + | 0.122104i | ||||
\(982\) | 3.42379e10 | 1.15376 | ||||||||
\(983\) | − | 1.66615e9i | − | 0.0559469i | −0.999609 | − | 0.0279734i | \(-0.991095\pi\) | ||
0.999609 | − | 0.0279734i | \(-0.00890538\pi\) | |||||||
\(984\) | −6.18672e9 | −0.207003 | ||||||||
\(985\) | −5.19903e10 | −1.73339 | ||||||||
\(986\) | 1.92331e9 | 0.0638969 | ||||||||
\(987\) | 3.63812e9i | 0.120439i | ||||||||
\(988\) | 2.03144e10 | 0.670122 | ||||||||
\(989\) | 9.68080e9i | 0.318218i | ||||||||
\(990\) | −9.56902e10 | −3.13433 | ||||||||
\(991\) | − | 4.06377e10i | − | 1.32639i | −0.748446 | − | 0.663196i | \(-0.769200\pi\) | ||
0.748446 | − | 0.663196i | \(-0.230800\pi\) | |||||||
\(992\) | 7.25339e9i | 0.235912i | ||||||||
\(993\) | 7.57190e9 | 0.245404 | ||||||||
\(994\) | − | 3.05521e9i | − | 0.0986710i | ||||||
\(995\) | 3.04934e10i | 0.981353i | ||||||||
\(996\) | 1.51479e11 | 4.85785 | ||||||||
\(997\) | 2.45217e10 | 0.783642 | 0.391821 | − | 0.920041i | \(-0.371845\pi\) | ||||
0.391821 | + | 0.920041i | \(0.371845\pi\) | |||||||
\(998\) | − | 4.72099e10i | − | 1.50341i | ||||||
\(999\) | − | 3.81447e9i | − | 0.121047i |
(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 | 109.8.b.a.108.58 | yes | 62 | |
109.108 | even | 2 | inner | 109.8.b.a.108.5 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
109.8.b.a.108.5 | ✓ | 62 | 109.108 | even | 2 | inner | |
109.8.b.a.108.58 | yes | 62 | 1.1 | even | 1 | trivial |