Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.2 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 27459.9i | 1.18512i | 0.805525 | + | 0.592562i | \(0.201884\pi\) | ||||
−0.805525 | + | 0.592562i | \(0.798116\pi\) | |||||||
\(3\) | −7.86336e6 | + | 2.60729e6i | −0.949183 | + | 0.314725i | ||||
\(4\) | −2.17175e8 | −0.404521 | ||||||||
\(5\) | −2.60713e10 | −1.91028 | −0.955141 | − | 0.296153i | \(-0.904296\pi\) | ||||
−0.955141 | + | 0.296153i | \(0.904296\pi\) | |||||||
\(6\) | −7.15959e10 | − | 2.15927e11i | −0.372988 | − | 1.12490i | ||||
\(7\) | −1.78867e12 | + | 1.43352e11i | −0.996804 | + | 0.0798881i | ||||
\(8\) | 8.77881e12i | 0.705717i | ||||||||
\(9\) | 5.50345e13 | − | 4.10041e13i | 0.801896 | − | 0.597463i | ||||
\(10\) | − | 7.15915e14i | − | 2.26392i | ||||||
\(11\) | − | 1.84525e15i | − | 1.46508i | −0.680724 | − | 0.732540i | \(-0.738335\pi\) | ||
0.680724 | − | 0.732540i | \(-0.261665\pi\) | |||||||
\(12\) | 1.70773e15 | − | 5.66239e14i | 0.383964 | − | 0.127313i | ||||
\(13\) | 1.93886e14i | 0.0136574i | 0.999977 | + | 0.00682870i | \(0.00217366\pi\) | ||||
−0.999977 | + | 0.00682870i | \(0.997826\pi\) | |||||||
\(14\) | −3.93643e15 | − | 4.91168e16i | −0.0946773 | − | 1.18134i | ||||
\(15\) | 2.05008e17 | − | 6.79754e16i | 1.81321 | − | 0.601213i | ||||
\(16\) | −3.57660e17 | −1.24088 | ||||||||
\(17\) | −8.05269e16 | −0.115993 | −0.0579964 | − | 0.998317i | \(-0.518471\pi\) | ||||
−0.0579964 | + | 0.998317i | \(0.518471\pi\) | |||||||
\(18\) | 1.12597e18 | + | 1.51124e18i | 0.708068 | + | 0.950347i | ||||
\(19\) | 5.95624e18i | 1.71019i | 0.518469 | + | 0.855096i | \(0.326502\pi\) | ||||
−0.518469 | + | 0.855096i | \(0.673498\pi\) | |||||||
\(20\) | 5.66204e18 | 0.772748 | ||||||||
\(21\) | 1.36912e19 | − | 5.79082e18i | 0.921006 | − | 0.389547i | ||||
\(22\) | 5.06704e19 | 1.73630 | ||||||||
\(23\) | − | 6.15339e19i | − | 1.10678i | −0.832922 | − | 0.553390i | \(-0.813334\pi\) | ||
0.832922 | − | 0.553390i | \(-0.186666\pi\) | |||||||
\(24\) | −2.28889e19 | − | 6.90309e19i | −0.222107 | − | 0.669855i | ||||
\(25\) | 4.93447e20 | 2.64917 | ||||||||
\(26\) | −5.32409e18 | −0.0161857 | ||||||||
\(27\) | −3.25846e20 | + | 4.65921e20i | −0.573110 | + | 0.819479i | ||||
\(28\) | 3.88456e20 | − | 3.11325e19i | 0.403228 | − | 0.0323164i | ||||
\(29\) | 9.13257e20i | 0.569931i | 0.958538 | + | 0.284965i | \(0.0919821\pi\) | ||||
−0.958538 | + | 0.284965i | \(0.908018\pi\) | |||||||
\(30\) | 1.86660e21 | + | 5.62950e21i | 0.712513 | + | 2.14888i | ||||
\(31\) | − | 3.13598e21i | − | 0.744096i | −0.928214 | − | 0.372048i | \(-0.878656\pi\) | ||
0.928214 | − | 0.372048i | \(-0.121344\pi\) | |||||||
\(32\) | − | 5.10823e21i | − | 0.764885i | ||||||
\(33\) | 4.81110e21 | + | 1.45099e22i | 0.461097 | + | 1.39063i | ||||
\(34\) | − | 2.21126e21i | − | 0.137466i | ||||||
\(35\) | 4.66330e22 | − | 3.73737e21i | 1.90418 | − | 0.152609i | ||||
\(36\) | −1.19521e22 | + | 8.90508e21i | −0.324384 | + | 0.241686i | ||||
\(37\) | −2.79899e22 | −0.510595 | −0.255298 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255298 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(38\) | −1.63558e23 | −2.02679 | ||||||||
\(39\) | −5.05517e20 | − | 1.52460e21i | −0.00429832 | − | 0.0129634i | ||||
\(40\) | − | 2.28875e23i | − | 1.34812i | ||||||
\(41\) | 2.23493e23 | 0.920232 | 0.460116 | − | 0.887859i | \(-0.347808\pi\) | ||||
0.460116 | + | 0.887859i | \(0.347808\pi\) | |||||||
\(42\) | 1.59015e23 | + | 3.75960e23i | 0.461662 | + | 1.09151i | ||||
\(43\) | 5.48297e23 | 1.13168 | 0.565840 | − | 0.824515i | \(-0.308552\pi\) | ||||
0.565840 | + | 0.824515i | \(0.308552\pi\) | |||||||
\(44\) | 4.00743e23i | 0.592655i | ||||||||
\(45\) | −1.43482e24 | + | 1.06903e24i | −1.53185 | + | 1.14132i | ||||
\(46\) | 1.68972e24 | 1.31167 | ||||||||
\(47\) | −1.11402e24 | −0.633103 | −0.316552 | − | 0.948575i | \(-0.602525\pi\) | ||||
−0.316552 | + | 0.948575i | \(0.602525\pi\) | |||||||
\(48\) | 2.81241e24 | − | 9.32524e23i | 1.17783 | − | 0.390537i | ||||
\(49\) | 3.17881e24 | − | 5.12820e23i | 0.987236 | − | 0.159265i | ||||
\(50\) | 1.35500e25i | 3.13960i | ||||||||
\(51\) | 6.33212e23 | − | 2.09957e23i | 0.110098 | − | 0.0365059i | ||||
\(52\) | − | 4.21073e22i | − | 0.00552470i | ||||||
\(53\) | − | 1.03543e25i | − | 1.03067i | −0.856988 | − | 0.515336i | \(-0.827667\pi\) | ||
0.856988 | − | 0.515336i | \(-0.172333\pi\) | |||||||
\(54\) | −1.27941e25 | − | 8.94770e24i | −0.971184 | − | 0.679207i | ||||
\(55\) | 4.81080e25i | 2.79871i | ||||||||
\(56\) | −1.25846e24 | − | 1.57024e25i | −0.0563784 | − | 0.703462i | ||||
\(57\) | −1.55296e25 | − | 4.68361e25i | −0.538240 | − | 1.62329i | ||||
\(58\) | −2.50780e25 | −0.675439 | ||||||||
\(59\) | −9.54320e24 | −0.200604 | −0.100302 | − | 0.994957i | \(-0.531981\pi\) | ||||
−0.100302 | + | 0.994957i | \(0.531981\pi\) | |||||||
\(60\) | −4.45227e25 | + | 1.47626e25i | −0.733479 | + | 0.243203i | ||||
\(61\) | 8.43183e25i | 1.09305i | 0.837444 | + | 0.546524i | \(0.184049\pi\) | ||||
−0.837444 | + | 0.546524i | \(0.815951\pi\) | |||||||
\(62\) | 8.61137e25 | 0.881846 | ||||||||
\(63\) | −9.25607e25 | + | 8.12323e25i | −0.751603 | + | 0.659615i | ||||
\(64\) | −5.17459e25 | −0.334400 | ||||||||
\(65\) | − | 5.05486e24i | − | 0.0260895i | ||||||
\(66\) | −3.98439e26 | + | 1.32112e26i | −1.64807 | + | 0.546458i | ||||
\(67\) | 2.14590e26 | 0.713716 | 0.356858 | − | 0.934159i | \(-0.383848\pi\) | ||||
0.356858 | + | 0.934159i | \(0.383848\pi\) | |||||||
\(68\) | 1.74884e25 | 0.0469215 | ||||||||
\(69\) | 1.60437e26 | + | 4.83863e26i | 0.348331 | + | 1.05054i | ||||
\(70\) | 1.02628e26 | + | 1.28054e27i | 0.180860 | + | 2.25669i | ||||
\(71\) | − | 7.65917e26i | − | 1.09884i | −0.835545 | − | 0.549422i | \(-0.814848\pi\) | ||
0.835545 | − | 0.549422i | \(-0.185152\pi\) | |||||||
\(72\) | 3.59967e26 | + | 4.83137e26i | 0.421640 | + | 0.565912i | ||||
\(73\) | − | 7.98935e26i | − | 0.766178i | −0.923711 | − | 0.383089i | \(-0.874860\pi\) | ||
0.923711 | − | 0.383089i | \(-0.125140\pi\) | |||||||
\(74\) | − | 7.68601e26i | − | 0.605119i | ||||||
\(75\) | −3.88015e27 | + | 1.28656e27i | −2.51455 | + | 0.833761i | ||||
\(76\) | − | 1.29355e27i | − | 0.691808i | ||||||
\(77\) | 2.64520e26 | + | 3.30055e27i | 0.117042 | + | 1.46040i | ||||
\(78\) | 4.18652e25 | − | 1.38815e25i | 0.0153632 | − | 0.00509405i | ||||
\(79\) | −2.93271e27 | −0.894697 | −0.447349 | − | 0.894360i | \(-0.647632\pi\) | ||||
−0.447349 | + | 0.894360i | \(0.647632\pi\) | |||||||
\(80\) | 9.32466e27 | 2.37044 | ||||||||
\(81\) | 1.34745e27 | − | 4.51328e27i | 0.286076 | − | 0.958207i | ||||
\(82\) | 6.13708e27i | 1.09059i | ||||||||
\(83\) | −5.11580e27 | −0.762573 | −0.381286 | − | 0.924457i | \(-0.624519\pi\) | ||||
−0.381286 | + | 0.924457i | \(0.624519\pi\) | |||||||
\(84\) | −2.97340e27 | + | 1.25762e27i | −0.372566 | + | 0.157580i | ||||
\(85\) | 2.09944e27 | 0.221579 | ||||||||
\(86\) | 1.50562e28i | 1.34118i | ||||||||
\(87\) | −2.38113e27 | − | 7.18127e27i | −0.179371 | − | 0.540969i | ||||
\(88\) | 1.61991e28 | 1.03393 | ||||||||
\(89\) | 2.50441e28 | 1.35691 | 0.678454 | − | 0.734643i | \(-0.262650\pi\) | ||||
0.678454 | + | 0.734643i | \(0.262650\pi\) | |||||||
\(90\) | −2.93555e28 | − | 3.94000e28i | −1.35261 | − | 1.81543i | ||||
\(91\) | −2.77939e25 | − | 3.46799e26i | −0.00109106 | − | 0.0136137i | ||||
\(92\) | 1.33637e28i | 0.447715i | ||||||||
\(93\) | 8.17641e27 | + | 2.46593e28i | 0.234186 | + | 0.706283i | ||||
\(94\) | − | 3.05909e28i | − | 0.750306i | ||||||
\(95\) | − | 1.55287e29i | − | 3.26695i | ||||||
\(96\) | 1.33186e28 | + | 4.01679e28i | 0.240728 | + | 0.726015i | ||||
\(97\) | − | 1.08394e29i | − | 1.68584i | −0.538042 | − | 0.842918i | \(-0.680836\pi\) | ||
0.538042 | − | 0.842918i | \(-0.319164\pi\) | |||||||
\(98\) | 1.40820e28 | + | 8.72897e28i | 0.188749 | + | 1.17000i | ||||
\(99\) | −7.56629e28 | − | 1.01552e29i | −0.875331 | − | 1.17484i | ||||
\(100\) | −1.07165e29 | −1.07165 | ||||||||
\(101\) | −6.79883e28 | −0.588538 | −0.294269 | − | 0.955723i | \(-0.595076\pi\) | ||||
−0.294269 | + | 0.955723i | \(0.595076\pi\) | |||||||
\(102\) | 5.76540e27 | + | 1.73879e28i | 0.0432640 | + | 0.130480i | ||||
\(103\) | − | 1.35130e29i | − | 0.880261i | −0.897934 | − | 0.440130i | \(-0.854932\pi\) | ||
0.897934 | − | 0.440130i | \(-0.145068\pi\) | |||||||
\(104\) | −1.70209e27 | −0.00963826 | ||||||||
\(105\) | −3.56948e29 | + | 1.50974e29i | −1.75938 | + | 0.744145i | ||||
\(106\) | 2.84328e29 | 1.22147 | ||||||||
\(107\) | 2.32027e29i | 0.869908i | 0.900453 | + | 0.434954i | \(0.143235\pi\) | ||||
−0.900453 | + | 0.434954i | \(0.856765\pi\) | |||||||
\(108\) | 7.07657e28 | − | 1.01187e29i | 0.231835 | − | 0.331496i | ||||
\(109\) | 1.37524e29 | 0.394180 | 0.197090 | − | 0.980385i | \(-0.436851\pi\) | ||||
0.197090 | + | 0.980385i | \(0.436851\pi\) | |||||||
\(110\) | −1.32104e30 | −3.31683 | ||||||||
\(111\) | 2.20095e29 | − | 7.29779e28i | 0.484648 | − | 0.160697i | ||||
\(112\) | 6.39738e29 | − | 5.12713e28i | 1.23692 | − | 0.0991318i | ||||
\(113\) | − | 1.01708e29i | − | 0.172869i | −0.996258 | − | 0.0864344i | \(-0.972453\pi\) | ||
0.996258 | − | 0.0864344i | \(-0.0275473\pi\) | |||||||
\(114\) | 1.28611e30 | − | 4.26443e29i | 1.92380 | − | 0.637882i | ||||
\(115\) | 1.60427e30i | 2.11426i | ||||||||
\(116\) | − | 1.98337e29i | − | 0.230549i | ||||||
\(117\) | 7.95013e27 | + | 1.06704e28i | 0.00815979 | + | 0.0109518i | ||||
\(118\) | − | 2.62055e29i | − | 0.237741i | ||||||
\(119\) | 1.44036e29 | − | 1.15437e28i | 0.115622 | − | 0.00926645i | ||||
\(120\) | 5.96743e29 | + | 1.79972e30i | 0.424287 | + | 1.27961i | ||||
\(121\) | −1.81864e30 | −1.14646 | ||||||||
\(122\) | −2.31537e30 | −1.29540 | ||||||||
\(123\) | −1.75740e30 | + | 5.82710e29i | −0.873468 | + | 0.289620i | ||||
\(124\) | 6.81058e29i | 0.301002i | ||||||||
\(125\) | −8.00864e30 | −3.15039 | ||||||||
\(126\) | −2.23063e30 | − | 2.54171e30i | −0.781727 | − | 0.890744i | ||||
\(127\) | −3.24278e30 | −1.01336 | −0.506679 | − | 0.862135i | \(-0.669127\pi\) | ||||
−0.506679 | + | 0.862135i | \(0.669127\pi\) | |||||||
\(128\) | − | 4.16340e30i | − | 1.16119i | ||||||
\(129\) | −4.31146e30 | + | 1.42957e30i | −1.07417 | + | 0.356168i | ||||
\(130\) | 1.38806e29 | 0.0309193 | ||||||||
\(131\) | 2.26554e30 | 0.451583 | 0.225791 | − | 0.974176i | \(-0.427503\pi\) | ||||
0.225791 | + | 0.974176i | \(0.427503\pi\) | |||||||
\(132\) | −1.04485e30 | − | 3.15119e30i | −0.186523 | − | 0.562538i | ||||
\(133\) | −8.53839e29 | − | 1.06538e31i | −0.136624 | − | 1.70473i | ||||
\(134\) | 5.89262e30i | 0.845842i | ||||||||
\(135\) | 8.49522e30 | − | 1.21472e31i | 1.09480 | − | 1.56543i | ||||
\(136\) | − | 7.06930e29i | − | 0.0818582i | ||||||
\(137\) | 8.13564e30i | 0.847117i | 0.905869 | + | 0.423558i | \(0.139219\pi\) | ||||
−0.905869 | + | 0.423558i | \(0.860781\pi\) | |||||||
\(138\) | −1.32868e31 | + | 4.40558e30i | −1.24502 | + | 0.412816i | ||||
\(139\) | − | 8.04462e30i | − | 0.678877i | −0.940628 | − | 0.339438i | \(-0.889763\pi\) | ||
0.940628 | − | 0.339438i | \(-0.110237\pi\) | |||||||
\(140\) | −1.01275e31 | + | 8.11664e29i | −0.770278 | + | 0.0617334i | ||||
\(141\) | 8.75995e30 | − | 2.90458e30i | 0.600931 | − | 0.199253i | ||||
\(142\) | 2.10320e31 | 1.30227 | ||||||||
\(143\) | 3.57768e29 | 0.0200092 | ||||||||
\(144\) | −1.96836e31 | + | 1.46655e31i | −0.995060 | + | 0.741382i | ||||
\(145\) | − | 2.38098e31i | − | 1.08873i | ||||||
\(146\) | 2.19387e31 | 0.908017 | ||||||||
\(147\) | −2.36590e31 | + | 1.23206e31i | −0.886943 | + | 0.461880i | ||||
\(148\) | 6.07872e30 | 0.206546 | ||||||||
\(149\) | − | 2.94023e31i | − | 0.906109i | −0.891483 | − | 0.453054i | \(-0.850334\pi\) | ||
0.891483 | − | 0.453054i | \(-0.149666\pi\) | |||||||
\(150\) | −3.53288e31 | − | 1.06549e32i | −0.988111 | − | 2.98006i | ||||
\(151\) | 1.57029e31 | 0.398855 | 0.199428 | − | 0.979913i | \(-0.436092\pi\) | ||||
0.199428 | + | 0.979913i | \(0.436092\pi\) | |||||||
\(152\) | −5.22887e31 | −1.20691 | ||||||||
\(153\) | −4.43175e30 | + | 3.30193e30i | −0.0930143 | + | 0.0693015i | ||||
\(154\) | −9.06328e31 | + | 7.26370e30i | −1.73075 | + | 0.138710i | ||||
\(155\) | 8.17591e31i | 1.42143i | ||||||||
\(156\) | 1.09786e29 | + | 3.31105e29i | 0.00173876 | + | 0.00524395i | ||||
\(157\) | − | 2.67475e31i | − | 0.386134i | −0.981186 | − | 0.193067i | \(-0.938157\pi\) | ||
0.981186 | − | 0.193067i | \(-0.0618435\pi\) | |||||||
\(158\) | − | 8.05319e31i | − | 1.06033i | ||||||
\(159\) | 2.69966e31 | + | 8.14195e31i | 0.324378 | + | 0.978295i | ||||
\(160\) | 1.33178e32i | 1.46114i | ||||||||
\(161\) | 8.82101e30 | + | 1.10064e32i | 0.0884185 | + | 1.10324i | ||||
\(162\) | 1.23934e32 | + | 3.70009e31i | 1.13559 | + | 0.339035i | ||||
\(163\) | 1.09229e32 | 0.915412 | 0.457706 | − | 0.889104i | \(-0.348671\pi\) | ||||
0.457706 | + | 0.889104i | \(0.348671\pi\) | |||||||
\(164\) | −4.85371e31 | −0.372253 | ||||||||
\(165\) | −1.25432e32 | − | 3.78291e32i | −0.880825 | − | 2.65649i | ||||
\(166\) | − | 1.40479e32i | − | 0.903744i | ||||||
\(167\) | −1.79477e32 | −1.05832 | −0.529162 | − | 0.848521i | \(-0.677494\pi\) | ||||
−0.529162 | + | 0.848521i | \(0.677494\pi\) | |||||||
\(168\) | 5.08365e31 | + | 1.20193e32i | 0.274910 | + | 0.649970i | ||||
\(169\) | 2.01501e32 | 0.999813 | ||||||||
\(170\) | 5.76504e31i | 0.262599i | ||||||||
\(171\) | 2.44230e32 | + | 3.27798e32i | 1.02178 | + | 1.37140i | ||||
\(172\) | −1.19077e32 | −0.457788 | ||||||||
\(173\) | −1.76120e31 | −0.0622502 | −0.0311251 | − | 0.999515i | \(-0.509909\pi\) | ||||
−0.0311251 | + | 0.999515i | \(0.509909\pi\) | |||||||
\(174\) | 1.97197e32 | − | 6.53855e31i | 0.641115 | − | 0.212578i | ||||
\(175\) | −8.82616e32 | + | 7.07366e31i | −2.64071 | + | 0.211637i | ||||
\(176\) | 6.59973e32i | 1.81799i | ||||||||
\(177\) | 7.50416e31 | − | 2.48819e31i | 0.190410 | − | 0.0631352i | ||||
\(178\) | 6.87709e32i | 1.60810i | ||||||||
\(179\) | − | 1.46675e32i | − | 0.316219i | −0.987422 | − | 0.158110i | \(-0.949460\pi\) | ||
0.987422 | − | 0.158110i | \(-0.0505400\pi\) | |||||||
\(180\) | 3.11607e32 | − | 2.32167e32i | 0.619664 | − | 0.461689i | ||||
\(181\) | − | 3.40067e31i | − | 0.0624058i | −0.999513 | − | 0.0312029i | \(-0.990066\pi\) | ||
0.999513 | − | 0.0312029i | \(-0.00993380\pi\) | |||||||
\(182\) | 9.52307e30 | − | 7.63219e29i | 0.0161340 | − | 0.00129305i | ||||
\(183\) | −2.19842e32 | − | 6.63025e32i | −0.344009 | − | 1.03750i | ||||
\(184\) | 5.40195e32 | 0.781073 | ||||||||
\(185\) | 7.29733e32 | 0.975380 | ||||||||
\(186\) | −6.77143e32 | + | 2.24524e32i | −0.837034 | + | 0.277539i | ||||
\(187\) | 1.48592e32i | 0.169939i | ||||||||
\(188\) | 2.41938e32 | 0.256103 | ||||||||
\(189\) | 5.16042e32 | − | 8.80091e32i | 0.505812 | − | 0.862644i | ||||
\(190\) | 4.26416e33 | 3.87174 | ||||||||
\(191\) | 2.40802e32i | 0.202617i | 0.994855 | + | 0.101308i | \(0.0323029\pi\) | ||||
−0.994855 | + | 0.101308i | \(0.967697\pi\) | |||||||
\(192\) | 4.06897e32 | − | 1.34917e32i | 0.317407 | − | 0.105244i | ||||
\(193\) | −1.66406e33 | −1.20389 | −0.601947 | − | 0.798536i | \(-0.705608\pi\) | ||||
−0.601947 | + | 0.798536i | \(0.705608\pi\) | |||||||
\(194\) | 2.97649e33 | 1.99793 | ||||||||
\(195\) | 1.31795e31 | + | 3.97482e31i | 0.00821101 | + | 0.0247637i | ||||
\(196\) | −6.90358e32 | + | 1.11372e32i | −0.399357 | + | 0.0644262i | ||||
\(197\) | 2.90596e33i | 1.56146i | 0.624870 | + | 0.780728i | \(0.285152\pi\) | ||||
−0.624870 | + | 0.780728i | \(0.714848\pi\) | |||||||
\(198\) | 2.78862e33 | − | 2.07769e33i | 1.39233 | − | 1.03738i | ||||
\(199\) | − | 1.38700e33i | − | 0.643732i | −0.946785 | − | 0.321866i | \(-0.895690\pi\) | ||
0.946785 | − | 0.321866i | \(-0.104310\pi\) | |||||||
\(200\) | 4.33188e33i | 1.86957i | ||||||||
\(201\) | −1.68740e33 | + | 5.59499e32i | −0.677447 | + | 0.224624i | ||||
\(202\) | − | 1.86695e33i | − | 0.697490i | ||||||
\(203\) | −1.30917e32 | − | 1.63352e33i | −0.0455307 | − | 0.568109i | ||||
\(204\) | −1.37518e32 | + | 4.55975e31i | −0.0445371 | + | 0.0147674i | ||||
\(205\) | −5.82674e33 | −1.75790 | ||||||||
\(206\) | 3.71065e33 | 1.04322 | ||||||||
\(207\) | −2.52314e33 | − | 3.38649e33i | −0.661260 | − | 0.887522i | ||||
\(208\) | − | 6.93453e31i | − | 0.0169472i | ||||||
\(209\) | 1.09908e34 | 2.50557 | ||||||||
\(210\) | −4.14573e33 | − | 9.80175e33i | −0.881905 | − | 2.08509i | ||||
\(211\) | 3.16343e33 | 0.628148 | 0.314074 | − | 0.949398i | \(-0.398306\pi\) | ||||
0.314074 | + | 0.949398i | \(0.398306\pi\) | |||||||
\(212\) | 2.24870e33i | 0.416928i | ||||||||
\(213\) | 1.99697e33 | + | 6.02268e33i | 0.345833 | + | 1.04300i | ||||
\(214\) | −6.37143e33 | −1.03095 | ||||||||
\(215\) | −1.42948e34 | −2.16183 | ||||||||
\(216\) | −4.09023e33 | − | 2.86054e33i | −0.578320 | − | 0.404454i | ||||
\(217\) | 4.49549e32 | + | 5.60925e33i | 0.0594444 | + | 0.741718i | ||||
\(218\) | 3.77640e33i | 0.467153i | ||||||||
\(219\) | 2.08306e33 | + | 6.28231e33i | 0.241135 | + | 0.727243i | ||||
\(220\) | − | 1.04479e34i | − | 1.13214i | ||||||
\(221\) | − | 1.56130e31i | − | 0.00158416i | ||||||
\(222\) | 2.00396e33 | + | 6.04378e33i | 0.190446 | + | 0.574369i | ||||
\(223\) | 1.87524e34i | 1.66969i | 0.550486 | + | 0.834845i | \(0.314443\pi\) | ||||
−0.550486 | + | 0.834845i | \(0.685557\pi\) | |||||||
\(224\) | 7.32275e32 | + | 9.13696e33i | 0.0611052 | + | 0.762440i | ||||
\(225\) | 2.71566e34 | − | 2.02334e34i | 2.12436 | − | 1.58278i | ||||
\(226\) | 2.79288e33 | 0.204871 | ||||||||
\(227\) | −1.65372e34 | −1.13786 | −0.568929 | − | 0.822387i | \(-0.692642\pi\) | ||||
−0.568929 | + | 0.822387i | \(0.692642\pi\) | |||||||
\(228\) | 3.37266e33 | + | 1.01716e34i | 0.217729 | + | 0.656653i | ||||
\(229\) | 9.33470e33i | 0.565569i | 0.959183 | + | 0.282785i | \(0.0912582\pi\) | ||||
−0.959183 | + | 0.282785i | \(0.908742\pi\) | |||||||
\(230\) | −4.40531e34 | −2.50566 | ||||||||
\(231\) | −1.06855e34 | − | 2.52637e34i | −0.570718 | − | 1.34935i | ||||
\(232\) | −8.01731e33 | −0.402210 | ||||||||
\(233\) | 1.40299e34i | 0.661291i | 0.943755 | + | 0.330645i | \(0.107266\pi\) | ||||
−0.943755 | + | 0.330645i | \(0.892734\pi\) | |||||||
\(234\) | −2.93008e32 | + | 2.18310e32i | −0.0129793 | + | 0.00967037i | ||||
\(235\) | 2.90440e34 | 1.20941 | ||||||||
\(236\) | 2.07255e33 | 0.0811485 | ||||||||
\(237\) | 2.30609e34 | − | 7.64642e33i | 0.849231 | − | 0.281584i | ||||
\(238\) | 3.16988e32 | + | 3.95522e33i | 0.0109819 | + | 0.137027i | ||||
\(239\) | 1.47077e34i | 0.479484i | 0.970837 | + | 0.239742i | \(0.0770628\pi\) | ||||
−0.970837 | + | 0.239742i | \(0.922937\pi\) | |||||||
\(240\) | −7.33232e34 | + | 2.43121e34i | −2.24998 | + | 0.746036i | ||||
\(241\) | 2.73665e33i | 0.0790629i | 0.999218 | + | 0.0395315i | \(0.0125865\pi\) | ||||
−0.999218 | + | 0.0395315i | \(0.987413\pi\) | |||||||
\(242\) | − | 4.99396e34i | − | 1.35870i | ||||||
\(243\) | 1.17192e33 | + | 3.90027e34i | 0.0300335 | + | 0.999549i | ||||
\(244\) | − | 1.83118e34i | − | 0.442160i | ||||||
\(245\) | −8.28755e34 | + | 1.33699e34i | −1.88590 | + | 0.304242i | ||||
\(246\) | −1.60012e34 | − | 4.82581e34i | −0.343236 | − | 1.03517i | ||||
\(247\) | −1.15483e33 | −0.0233568 | ||||||||
\(248\) | 2.75302e34 | 0.525121 | ||||||||
\(249\) | 4.02274e34 | − | 1.33384e34i | 0.723821 | − | 0.240001i | ||||
\(250\) | − | 2.19917e35i | − | 3.73360i | ||||||
\(251\) | 2.11420e34 | 0.338748 | 0.169374 | − | 0.985552i | \(-0.445825\pi\) | ||||
0.169374 | + | 0.985552i | \(0.445825\pi\) | |||||||
\(252\) | 2.01019e34 | − | 1.76417e34i | 0.304039 | − | 0.266828i | ||||
\(253\) | −1.13546e35 | −1.62152 | ||||||||
\(254\) | − | 8.90463e34i | − | 1.20096i | ||||||
\(255\) | −1.65086e34 | + | 5.47384e33i | −0.210319 | + | 0.0697365i | ||||
\(256\) | 8.65457e34 | 1.04176 | ||||||||
\(257\) | −7.36616e34 | −0.837936 | −0.418968 | − | 0.908001i | \(-0.637608\pi\) | ||||
−0.418968 | + | 0.908001i | \(0.637608\pi\) | |||||||
\(258\) | −3.92559e34 | − | 1.18392e35i | −0.422103 | − | 1.27303i | ||||
\(259\) | 5.00649e34 | − | 4.01241e33i | 0.508963 | − | 0.0407905i | ||||
\(260\) | 1.09779e33i | 0.0105537i | ||||||||
\(261\) | 3.74473e34 | + | 5.02606e34i | 0.340513 | + | 0.457026i | ||||
\(262\) | 6.22114e34i | 0.535182i | ||||||||
\(263\) | 2.37182e35i | 1.93074i | 0.260883 | + | 0.965370i | \(0.415986\pi\) | ||||
−0.260883 | + | 0.965370i | \(0.584014\pi\) | |||||||
\(264\) | −1.27379e35 | + | 4.22358e34i | −0.981391 | + | 0.325404i | ||||
\(265\) | 2.69950e35i | 1.96887i | ||||||||
\(266\) | 2.92552e35 | − | 2.34463e34i | 2.02031 | − | 0.161916i | ||||
\(267\) | −1.96931e35 | + | 6.52972e34i | −1.28795 | + | 0.427053i | ||||
\(268\) | −4.66037e34 | −0.288713 | ||||||||
\(269\) | 8.81222e34 | 0.517223 | 0.258611 | − | 0.965981i | \(-0.416735\pi\) | ||||
0.258611 | + | 0.965981i | \(0.416735\pi\) | |||||||
\(270\) | 3.33560e35 | + | 2.33278e35i | 1.85524 | + | 1.29748i | ||||
\(271\) | − | 1.51177e35i | − | 0.796951i | −0.917179 | − | 0.398476i | \(-0.869539\pi\) | ||
0.917179 | − | 0.398476i | \(-0.130461\pi\) | |||||||
\(272\) | 2.88013e34 | 0.143934 | ||||||||
\(273\) | 1.12276e33 | + | 2.65454e33i | 0.00532020 | + | 0.0125785i | ||||
\(274\) | −2.23404e35 | −1.00394 | ||||||||
\(275\) | − | 9.10533e35i | − | 3.88125i | ||||||
\(276\) | −3.48429e34 | − | 1.05083e35i | −0.140907 | − | 0.424964i | ||||
\(277\) | 1.02040e35 | 0.391574 | 0.195787 | − | 0.980646i | \(-0.437274\pi\) | ||||
0.195787 | + | 0.980646i | \(0.437274\pi\) | |||||||
\(278\) | 2.20904e35 | 0.804554 | ||||||||
\(279\) | −1.28588e35 | − | 1.72587e35i | −0.444570 | − | 0.596688i | ||||
\(280\) | 3.28096e34 | + | 4.09382e35i | 0.107699 | + | 1.34381i | ||||
\(281\) | 2.27657e35i | 0.709641i | 0.934934 | + | 0.354821i | \(0.115458\pi\) | ||||
−0.934934 | + | 0.354821i | \(0.884542\pi\) | |||||||
\(282\) | 7.97594e34 | + | 2.40547e35i | 0.236140 | + | 0.712178i | ||||
\(283\) | 1.56973e35i | 0.441490i | 0.975332 | + | 0.220745i | \(0.0708488\pi\) | ||||
−0.975332 | + | 0.220745i | \(0.929151\pi\) | |||||||
\(284\) | 1.66338e35i | 0.444505i | ||||||||
\(285\) | 4.04878e35 | + | 1.22108e36i | 1.02819 | + | 3.10093i | ||||
\(286\) | 9.82428e33i | 0.0237134i | ||||||||
\(287\) | −3.99755e35 | + | 3.20381e34i | −0.917290 | + | 0.0735155i | ||||
\(288\) | −2.09459e35 | − | 2.81129e35i | −0.456990 | − | 0.613358i | ||||
\(289\) | −4.75484e35 | −0.986546 | ||||||||
\(290\) | 6.53815e35 | 1.29028 | ||||||||
\(291\) | 2.82615e35 | + | 8.52342e35i | 0.530575 | + | 1.60017i | ||||
\(292\) | 1.73509e35i | 0.309935i | ||||||||
\(293\) | 3.63411e35 | 0.617758 | 0.308879 | − | 0.951101i | \(-0.400046\pi\) | ||||
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(294\) | −3.38321e35 | − | 6.49675e35i | −0.547385 | − | 1.05114i | ||||
\(295\) | 2.48804e35 | 0.383210 | ||||||||
\(296\) | − | 2.45718e35i | − | 0.360336i | ||||||
\(297\) | 8.59741e35 | + | 6.01267e35i | 1.20060 | + | 0.839652i | ||||
\(298\) | 8.07384e35 | 1.07385 | ||||||||
\(299\) | 1.19306e34 | 0.0151157 | ||||||||
\(300\) | 8.42673e35 | − | 2.79409e35i | 1.01719 | − | 0.337274i | ||||
\(301\) | −9.80726e35 | + | 7.85995e34i | −1.12806 | + | 0.0904077i | ||||
\(302\) | 4.31201e35i | 0.472693i | ||||||||
\(303\) | 5.34616e35 | − | 1.77265e35i | 0.558630 | − | 0.185227i | ||||
\(304\) | − | 2.13031e36i | − | 2.12215i | ||||||
\(305\) | − | 2.19829e36i | − | 2.08803i | ||||||
\(306\) | −9.06708e34 | − | 1.21695e35i | −0.0821309 | − | 0.110234i | ||||
\(307\) | 1.68415e36i | 1.45503i | 0.686090 | + | 0.727517i | \(0.259326\pi\) | ||||
−0.686090 | + | 0.727517i | \(0.740674\pi\) | |||||||
\(308\) | −5.74473e34 | − | 7.16799e35i | −0.0473461 | − | 0.590761i | ||||
\(309\) | 3.52323e35 | + | 1.06257e36i | 0.277040 | + | 0.835528i | ||||
\(310\) | −2.24510e36 | −1.68457 | ||||||||
\(311\) | −2.55264e36 | −1.82795 | −0.913974 | − | 0.405773i | \(-0.867002\pi\) | ||||
−0.913974 | + | 0.405773i | \(0.867002\pi\) | |||||||
\(312\) | 1.33841e34 | − | 4.43784e33i | 0.00914847 | − | 0.00303340i | ||||
\(313\) | − | 1.65771e36i | − | 1.08172i | −0.841112 | − | 0.540862i | \(-0.818098\pi\) | ||
0.841112 | − | 0.540862i | \(-0.181902\pi\) | |||||||
\(314\) | 7.34484e35 | 0.457617 | ||||||||
\(315\) | 2.41318e36 | − | 2.11783e36i | 1.43577 | − | 1.26005i | ||||
\(316\) | 6.36912e35 | 0.361923 | ||||||||
\(317\) | 1.10890e36i | 0.601910i | 0.953638 | + | 0.300955i | \(0.0973054\pi\) | ||||
−0.953638 | + | 0.300955i | \(0.902695\pi\) | |||||||
\(318\) | −2.23577e36 | + | 7.41325e35i | −1.15940 | + | 0.384428i | ||||
\(319\) | 1.68519e36 | 0.834994 | ||||||||
\(320\) | 1.34908e36 | 0.638798 | ||||||||
\(321\) | −6.04961e35 | − | 1.82451e36i | −0.273782 | − | 0.825701i | ||||
\(322\) | −3.02235e36 | + | 2.42224e35i | −1.30748 | + | 0.104787i | ||||
\(323\) | − | 4.79637e35i | − | 0.198370i | ||||||
\(324\) | −2.92634e35 | + | 9.80173e35i | −0.115724 | + | 0.387615i | ||||
\(325\) | 9.56725e34i | 0.0361808i | ||||||||
\(326\) | 2.99941e36i | 1.08488i | ||||||||
\(327\) | −1.08140e36 | + | 3.58565e35i | −0.374149 | + | 0.124058i | ||||
\(328\) | 1.96200e36i | 0.649423i | ||||||||
\(329\) | 1.99262e36 | − | 1.59697e35i | 0.631080 | − | 0.0505774i | ||||
\(330\) | 1.03878e37 | − | 3.44434e36i | 3.14827 | − | 1.04389i | ||||
\(331\) | −4.19132e34 | −0.0121575 | −0.00607876 | − | 0.999982i | \(-0.501935\pi\) | ||||
−0.00607876 | + | 0.999982i | \(0.501935\pi\) | |||||||
\(332\) | 1.11103e36 | 0.308476 | ||||||||
\(333\) | −1.54041e36 | + | 1.14770e36i | −0.409444 | + | 0.305062i | ||||
\(334\) | − | 4.92841e36i | − | 1.25425i | ||||||
\(335\) | −5.59464e36 | −1.36340 | ||||||||
\(336\) | −4.89681e36 | + | 2.07115e36i | −1.14286 | + | 0.483383i | ||||
\(337\) | 2.76289e36 | 0.617631 | 0.308816 | − | 0.951122i | \(-0.400067\pi\) | ||||
0.308816 | + | 0.951122i | \(0.400067\pi\) | |||||||
\(338\) | 5.53319e36i | 1.18490i | ||||||||
\(339\) | 2.65181e35 | + | 7.99764e35i | 0.0544061 | + | 0.164084i | ||||
\(340\) | −4.55946e35 | −0.0896333 | ||||||||
\(341\) | −5.78667e36 | −1.09016 | ||||||||
\(342\) | −9.00131e36 | + | 6.70654e36i | −1.62528 | + | 1.21093i | ||||
\(343\) | −5.61234e36 | + | 1.37296e36i | −0.971357 | + | 0.237625i | ||||
\(344\) | 4.81340e36i | 0.798646i | ||||||||
\(345\) | −4.18279e36 | − | 1.26149e37i | −0.665410 | − | 2.00682i | ||||
\(346\) | − | 4.83625e35i | − | 0.0737743i | ||||||
\(347\) | 6.10380e36i | 0.892941i | 0.894798 | + | 0.446471i | \(0.147319\pi\) | ||||
−0.894798 | + | 0.446471i | \(0.852681\pi\) | |||||||
\(348\) | 5.17122e35 | + | 1.55960e36i | 0.0725595 | + | 0.218833i | ||||
\(349\) | − | 7.10404e36i | − | 0.956174i | −0.878312 | − | 0.478087i | \(-0.841330\pi\) | ||
0.878312 | − | 0.478087i | \(-0.158670\pi\) | |||||||
\(350\) | −1.94242e36 | − | 2.42366e37i | −0.250817 | − | 3.12957i | ||||
\(351\) | −9.03355e34 | − | 6.31770e34i | −0.0111919 | − | 0.00782719i | ||||
\(352\) | −9.42597e36 | −1.12062 | ||||||||
\(353\) | 1.68355e36 | 0.192085 | 0.0960423 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960423 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(354\) | 6.83255e35 | + | 2.06064e36i | 0.0748230 | + | 0.225660i | ||||
\(355\) | 1.99684e37i | 2.09910i | ||||||||
\(356\) | −5.43896e36 | −0.548897 | ||||||||
\(357\) | −1.10251e36 | + | 4.66317e35i | −0.106830 | + | 0.0451847i | ||||
\(358\) | 4.02769e36 | 0.374759 | ||||||||
\(359\) | − | 3.39910e36i | − | 0.303734i | −0.988401 | − | 0.151867i | \(-0.951471\pi\) | ||
0.988401 | − | 0.151867i | \(-0.0485286\pi\) | |||||||
\(360\) | −9.38481e36 | − | 1.25960e37i | −0.805451 | − | 1.08105i | ||||
\(361\) | −2.33470e37 | −1.92476 | ||||||||
\(362\) | 9.33820e35 | 0.0739586 | ||||||||
\(363\) | 1.43006e37 | − | 4.74172e36i | 1.08820 | − | 0.360819i | ||||
\(364\) | 6.03616e33 | + | 7.53162e34i | 0.000441357 | + | 0.00550704i | ||||
\(365\) | 2.08293e37i | 1.46362i | ||||||||
\(366\) | 1.82066e37 | − | 6.03684e36i | 1.22957 | − | 0.407694i | ||||
\(367\) | − | 1.85685e37i | − | 1.20536i | −0.797981 | − | 0.602682i | \(-0.794099\pi\) | ||
0.797981 | − | 0.602682i | \(-0.205901\pi\) | |||||||
\(368\) | 2.20083e37i | 1.37338i | ||||||||
\(369\) | 1.22998e37 | − | 9.16412e36i | 0.737930 | − | 0.549804i | ||||
\(370\) | 2.00384e37i | 1.15595i | ||||||||
\(371\) | 1.48431e36 | + | 1.85204e37i | 0.0823383 | + | 1.02738i | ||||
\(372\) | −1.77572e36 | − | 5.35540e36i | −0.0947329 | − | 0.285706i | ||||
\(373\) | −8.33812e34 | −0.00427848 | −0.00213924 | − | 0.999998i | \(-0.500681\pi\) | ||||
−0.00213924 | + | 0.999998i | \(0.500681\pi\) | |||||||
\(374\) | −4.08033e36 | −0.201399 | ||||||||
\(375\) | 6.29748e37 | − | 2.08809e37i | 2.99029 | − | 0.991505i | ||||
\(376\) | − | 9.77978e36i | − | 0.446792i | ||||||
\(377\) | −1.77068e35 | −0.00778377 | ||||||||
\(378\) | 2.41672e37 | + | 1.41705e37i | 1.02234 | + | 0.599450i | ||||
\(379\) | 1.91804e36 | 0.0780888 | 0.0390444 | − | 0.999237i | \(-0.487569\pi\) | ||||
0.0390444 | + | 0.999237i | \(0.487569\pi\) | |||||||
\(380\) | 3.37245e37i | 1.32155i | ||||||||
\(381\) | 2.54991e37 | − | 8.45486e36i | 0.961863 | − | 0.318929i | ||||
\(382\) | −6.61239e36 | −0.240126 | ||||||||
\(383\) | −3.60082e36 | −0.125898 | −0.0629490 | − | 0.998017i | \(-0.520051\pi\) | ||||
−0.0629490 | + | 0.998017i | \(0.520051\pi\) | |||||||
\(384\) | 1.08552e37 | + | 3.27383e37i | 0.365456 | + | 1.10218i | ||||
\(385\) | −6.89638e36 | − | 8.60496e37i | −0.223584 | − | 2.78977i | ||||
\(386\) | − | 4.56949e37i | − | 1.42676i | ||||||
\(387\) | 3.01752e37 | − | 2.24825e37i | 0.907490 | − | 0.676137i | ||||
\(388\) | 2.35405e37i | 0.681956i | ||||||||
\(389\) | − | 2.94788e37i | − | 0.822699i | −0.911478 | − | 0.411350i | \(-0.865058\pi\) | ||
0.911478 | − | 0.411350i | \(-0.134942\pi\) | |||||||
\(390\) | −1.09148e36 | + | 3.61907e35i | −0.0293480 | + | 0.00973107i | ||||
\(391\) | 4.95513e36i | 0.128379i | ||||||||
\(392\) | 4.50195e36 | + | 2.79061e37i | 0.112396 | + | 0.696709i | ||||
\(393\) | −1.78147e37 | + | 5.90691e36i | −0.428634 | + | 0.142124i | ||||
\(394\) | −7.97975e37 | −1.85052 | ||||||||
\(395\) | 7.64595e37 | 1.70912 | ||||||||
\(396\) | 1.64321e37 | + | 2.20547e37i | 0.354090 | + | 0.475248i | ||||
\(397\) | 2.63789e37i | 0.548018i | 0.961727 | + | 0.274009i | \(0.0883499\pi\) | ||||
−0.961727 | + | 0.274009i | \(0.911650\pi\) | |||||||
\(398\) | 3.80868e37 | 0.762903 | ||||||||
\(399\) | 3.44915e37 | + | 8.15483e37i | 0.666201 | + | 1.57510i | ||||
\(400\) | −1.76486e38 | −3.28732 | ||||||||
\(401\) | − | 3.97992e37i | − | 0.714958i | −0.933921 | − | 0.357479i | \(-0.883636\pi\) | ||
0.933921 | − | 0.357479i | \(-0.116364\pi\) | |||||||
\(402\) | −1.53638e37 | − | 4.63358e37i | −0.266208 | − | 0.802859i | ||||
\(403\) | 6.08023e35 | 0.0101624 | ||||||||
\(404\) | 1.47654e37 | 0.238076 | ||||||||
\(405\) | −3.51298e37 | + | 1.17667e38i | −0.546485 | + | 1.83044i | ||||
\(406\) | 4.48563e37 | − | 3.59497e36i | 0.673280 | − | 0.0539595i | ||||
\(407\) | 5.16484e37i | 0.748063i | ||||||||
\(408\) | 1.84317e36 | + | 5.55884e36i | 0.0257628 | + | 0.0776984i | ||||
\(409\) | 4.93049e37i | 0.665124i | 0.943081 | + | 0.332562i | \(0.107913\pi\) | ||||
−0.943081 | + | 0.332562i | \(0.892087\pi\) | |||||||
\(410\) | − | 1.60002e38i | − | 2.08333i | ||||||
\(411\) | −2.12120e37 | − | 6.39734e37i | −0.266609 | − | 0.804069i | ||||
\(412\) | 2.93469e37i | 0.356084i | ||||||||
\(413\) | 1.70697e37 | − | 1.36804e36i | 0.199963 | − | 0.0160259i | ||||
\(414\) | 9.29926e37 | − | 6.92853e37i | 1.05182 | − | 0.783675i | ||||
\(415\) | 1.33375e38 | 1.45673 | ||||||||
\(416\) | 9.90415e35 | 0.0104463 | ||||||||
\(417\) | 2.09747e37 | + | 6.32577e37i | 0.213659 | + | 0.644378i | ||||
\(418\) | 3.01805e38i | 2.96941i | ||||||||
\(419\) | 6.58531e37 | 0.625854 | 0.312927 | − | 0.949777i | \(-0.398691\pi\) | ||||
0.312927 | + | 0.949777i | \(0.398691\pi\) | |||||||
\(420\) | 7.75203e37 | − | 3.27879e37i | 0.711706 | − | 0.301022i | ||||
\(421\) | −2.19764e38 | −1.94924 | −0.974622 | − | 0.223856i | \(-0.928135\pi\) | ||||
−0.974622 | + | 0.223856i | \(0.928135\pi\) | |||||||
\(422\) | 8.68674e37i | 0.744434i | ||||||||
\(423\) | −6.13095e37 | + | 4.56795e37i | −0.507683 | + | 0.378256i | ||||
\(424\) | 9.08983e37 | 0.727362 | ||||||||
\(425\) | −3.97357e37 | −0.307285 | ||||||||
\(426\) | −1.65382e38 | + | 5.48366e37i | −1.23609 | + | 0.409856i | ||||
\(427\) | −1.20872e37 | − | 1.50818e38i | −0.0873215 | − | 1.08955i | ||||
\(428\) | − | 5.03905e37i | − | 0.351896i | ||||||
\(429\) | −2.81326e36 | + | 9.32806e35i | −0.0189924 | + | 0.00629739i | ||||
\(430\) | − | 3.92534e38i | − | 2.56203i | ||||||
\(431\) | 1.17334e38i | 0.740464i | 0.928939 | + | 0.370232i | \(0.120722\pi\) | ||||
−0.928939 | + | 0.370232i | \(0.879278\pi\) | |||||||
\(432\) | 1.16542e38 | − | 1.66641e38i | 0.711163 | − | 1.01688i | ||||
\(433\) | 2.48867e38i | 1.46856i | 0.678844 | + | 0.734282i | \(0.262481\pi\) | ||||
−0.678844 | + | 0.734282i | \(0.737519\pi\) | |||||||
\(434\) | −1.54029e38 | + | 1.23446e37i | −0.879028 | + | 0.0704490i | ||||
\(435\) | 6.20790e37 | + | 1.87225e38i | 0.342650 | + | 1.03340i | ||||
\(436\) | −2.98669e37 | −0.159454 | ||||||||
\(437\) | 3.66511e38 | 1.89281 | ||||||||
\(438\) | −1.72512e38 | + | 5.72005e37i | −0.861874 | + | 0.285776i | ||||
\(439\) | − | 1.35398e38i | − | 0.654451i | −0.944946 | − | 0.327225i | \(-0.893886\pi\) | ||
0.944946 | − | 0.327225i | \(-0.106114\pi\) | |||||||
\(440\) | −4.22331e38 | −1.97510 | ||||||||
\(441\) | 1.53916e38 | − | 1.58567e38i | 0.696506 | − | 0.717551i | ||||
\(442\) | 4.28732e35 | 0.00187743 | ||||||||
\(443\) | − | 3.89269e38i | − | 1.64967i | −0.565376 | − | 0.824833i | \(-0.691269\pi\) | ||
0.565376 | − | 0.824833i | \(-0.308731\pi\) | |||||||
\(444\) | −4.77992e37 | + | 1.58490e37i | −0.196050 | + | 0.0650053i | ||||
\(445\) | −6.52932e38 | −2.59208 | ||||||||
\(446\) | −5.14938e38 | −1.97879 | ||||||||
\(447\) | 7.66603e37 | + | 2.31201e38i | 0.285175 | + | 0.860063i | ||||
\(448\) | 9.25566e37 | − | 7.41787e36i | 0.333331 | − | 0.0267146i | ||||
\(449\) | − | 3.93055e38i | − | 1.37051i | −0.728304 | − | 0.685254i | \(-0.759691\pi\) | ||
0.728304 | − | 0.685254i | \(-0.240309\pi\) | |||||||
\(450\) | 5.55606e38 | + | 7.45717e38i | 1.87580 | + | 2.51764i | ||||
\(451\) | − | 4.12400e38i | − | 1.34821i | ||||||
\(452\) | 2.20884e37i | 0.0699290i | ||||||||
\(453\) | −1.23478e38 | + | 4.09421e37i | −0.378586 | + | 0.125530i | ||||
\(454\) | − | 4.54111e38i | − | 1.34850i | ||||||
\(455\) | 7.24623e35 | + | 9.04149e36i | 0.00208424 | + | 0.0260061i | ||||
\(456\) | 4.11165e38 | − | 1.36332e38i | 1.14558 | − | 0.379846i | ||||
\(457\) | −4.02004e38 | −1.08504 | −0.542520 | − | 0.840043i | \(-0.682530\pi\) | ||||
−0.542520 | + | 0.840043i | \(0.682530\pi\) | |||||||
\(458\) | −2.56330e38 | −0.670270 | ||||||||
\(459\) | 2.62394e37 | − | 3.75191e37i | 0.0664767 | − | 0.0950537i | ||||
\(460\) | − | 3.48408e38i | − | 0.855262i | ||||||
\(461\) | −1.92578e38 | −0.458081 | −0.229040 | − | 0.973417i | \(-0.573559\pi\) | ||||
−0.229040 | + | 0.973417i | \(0.573559\pi\) | |||||||
\(462\) | 6.93740e38 | − | 2.93423e38i | 1.59915 | − | 0.676372i | ||||
\(463\) | 7.75241e38 | 1.73186 | 0.865929 | − | 0.500166i | \(-0.166728\pi\) | ||||
0.865929 | + | 0.500166i | \(0.166728\pi\) | |||||||
\(464\) | − | 3.26636e38i | − | 0.707218i | ||||||
\(465\) | −2.13170e38 | − | 6.42901e38i | −0.447360 | − | 1.34920i | ||||
\(466\) | −3.85258e38 | −0.783712 | ||||||||
\(467\) | −4.16159e37 | −0.0820663 | −0.0410331 | − | 0.999158i | \(-0.513065\pi\) | ||||
−0.0410331 | + | 0.999158i | \(0.513065\pi\) | |||||||
\(468\) | −1.72657e36 | − | 2.31735e36i | −0.00330080 | − | 0.00443024i | ||||
\(469\) | −3.83832e38 | + | 3.07619e37i | −0.711434 | + | 0.0570174i | ||||
\(470\) | 7.97544e38i | 1.43330i | ||||||||
\(471\) | 6.97385e37 | + | 2.10325e38i | 0.121526 | + | 0.366512i | ||||
\(472\) | − | 8.37780e37i | − | 0.141570i | ||||||
\(473\) | − | 1.01175e39i | − | 1.65800i | ||||||
\(474\) | 2.09970e38 | + | 6.33251e38i | 0.333712 | + | 1.00644i | ||||
\(475\) | 2.93909e39i | 4.53060i | ||||||||
\(476\) | −3.12811e37 | + | 2.50700e36i | −0.0467716 | + | 0.00374847i | ||||
\(477\) | −4.24568e38 | − | 5.69843e38i | −0.615788 | − | 0.826491i | ||||
\(478\) | −4.03871e38 | −0.568248 | ||||||||
\(479\) | 1.11054e39 | 1.51589 | 0.757946 | − | 0.652317i | \(-0.226203\pi\) | ||||
0.757946 | + | 0.652317i | \(0.226203\pi\) | |||||||
\(480\) | −3.47234e38 | − | 1.04723e39i | −0.459859 | − | 1.38689i | ||||
\(481\) | − | 5.42686e36i | − | 0.00697340i | ||||||
\(482\) | −7.51483e37 | −0.0936994 | ||||||||
\(483\) | −3.56332e38 | − | 8.42475e38i | −0.431143 | − | 1.01935i | ||||
\(484\) | 3.94964e38 | 0.463766 | ||||||||
\(485\) | 2.82597e39i | 3.22042i | ||||||||
\(486\) | −1.07101e39 | + | 3.21807e37i | −1.18459 | + | 0.0355935i | ||||
\(487\) | −9.46464e38 | −1.01610 | −0.508048 | − | 0.861329i | \(-0.669633\pi\) | ||||
−0.508048 | + | 0.861329i | \(0.669633\pi\) | |||||||
\(488\) | −7.40214e38 | −0.771383 | ||||||||
\(489\) | −8.58905e38 | + | 2.84791e38i | −0.868893 | + | 0.288103i | ||||
\(490\) | −3.67135e38 | − | 2.27575e39i | −0.360565 | − | 2.23502i | ||||
\(491\) | − | 2.79679e38i | − | 0.266673i | −0.991071 | − | 0.133336i | \(-0.957431\pi\) | ||
0.991071 | − | 0.133336i | \(-0.0425691\pi\) | |||||||
\(492\) | 3.81664e38 | − | 1.26550e38i | 0.353336 | − | 0.117157i | ||||
\(493\) | − | 7.35417e37i | − | 0.0661079i | ||||||
\(494\) | − | 3.17116e37i | − | 0.0276807i | ||||||
\(495\) | 1.97263e39 | + | 2.64760e39i | 1.67213 | + | 2.24428i | ||||
\(496\) | 1.12162e39i | 0.923337i | ||||||||
\(497\) | 1.09796e38 | + | 1.36998e39i | 0.0877845 | + | 1.09533i | ||||
\(498\) | 3.66270e38 | + | 1.10464e39i | 0.284431 | + | 0.857818i | ||||
\(499\) | 2.38891e39 | 1.80195 | 0.900975 | − | 0.433872i | \(-0.142853\pi\) | ||||
0.900975 | + | 0.433872i | \(0.142853\pi\) | |||||||
\(500\) | 1.73928e39 | 1.27440 | ||||||||
\(501\) | 1.41129e39 | − | 4.67947e38i | 1.00454 | − | 0.333081i | ||||
\(502\) | 5.80556e38i | 0.401458i | ||||||||
\(503\) | 2.00686e39 | 1.34828 | 0.674142 | − | 0.738602i | \(-0.264514\pi\) | ||||
0.674142 | + | 0.738602i | \(0.264514\pi\) | |||||||
\(504\) | −7.13123e38 | − | 8.12573e38i | −0.465502 | − | 0.530419i | ||||
\(505\) | 1.77254e39 | 1.12427 | ||||||||
\(506\) | − | 3.11795e39i | − | 1.92170i | ||||||
\(507\) | −1.58447e39 | + | 5.25370e38i | −0.949006 | + | 0.314666i | ||||
\(508\) | 7.04251e38 | 0.409924 | ||||||||
\(509\) | 2.23697e39 | 1.26547 | 0.632737 | − | 0.774367i | \(-0.281932\pi\) | ||||
0.632737 | + | 0.774367i | \(0.281932\pi\) | |||||||
\(510\) | −1.50311e38 | − | 4.53326e38i | −0.0826464 | − | 0.249254i | ||||
\(511\) | 1.14529e38 | + | 1.42903e39i | 0.0612085 | + | 0.763730i | ||||
\(512\) | 1.41328e38i | 0.0734198i | ||||||||
\(513\) | −2.77514e39 | − | 1.94082e39i | −1.40147 | − | 0.980128i | ||||
\(514\) | − | 2.02274e39i | − | 0.993059i | ||||||
\(515\) | 3.52301e39i | 1.68155i | ||||||||
\(516\) | 9.36343e38 | − | 3.10467e38i | 0.434524 | − | 0.144077i | ||||
\(517\) | 2.05565e39i | 0.927547i | ||||||||
\(518\) | 1.10180e38 | + | 1.37478e39i | 0.0483418 | + | 0.603185i | ||||
\(519\) | 1.38490e38 | − | 4.59197e37i | 0.0590869 | − | 0.0195917i | ||||
\(520\) | 4.43756e37 | 0.0184118 | ||||||||
\(521\) | 2.75049e39 | 1.10985 | 0.554923 | − | 0.831901i | \(-0.312748\pi\) | ||||
0.554923 | + | 0.831901i | \(0.312748\pi\) | |||||||
\(522\) | −1.38015e39 | + | 1.02830e39i | −0.541632 | + | 0.403550i | ||||
\(523\) | − | 2.90751e39i | − | 1.10980i | −0.831916 | − | 0.554902i | \(-0.812756\pi\) | ||
0.831916 | − | 0.554902i | \(-0.187244\pi\) | |||||||
\(524\) | −4.92019e38 | −0.182674 | ||||||||
\(525\) | 6.75590e39 | − | 2.85746e39i | 2.43991 | − | 1.03198i | ||||
\(526\) | −6.51300e39 | −2.28817 | ||||||||
\(527\) | 2.52531e38i | 0.0863098i | ||||||||
\(528\) | −1.72074e39 | − | 5.18960e39i | −0.572168 | − | 1.72561i | ||||
\(529\) | −6.95367e38 | −0.224961 | ||||||||
\(530\) | −7.41279e39 | −2.33336 | ||||||||
\(531\) | −5.25205e38 | + | 3.91311e38i | −0.160864 | + | 0.119854i | ||||
\(532\) | 1.85433e38 | + | 2.31374e39i | 0.0552672 | + | 0.689597i | ||||
\(533\) | 4.33321e37i | 0.0125680i | ||||||||
\(534\) | −1.79306e39 | − | 5.40770e39i | −0.506111 | − | 1.52639i | ||||
\(535\) | − | 6.04923e39i | − | 1.66177i | ||||||
\(536\) | 1.88385e39i | 0.503681i | ||||||||
\(537\) | 3.82426e38 | + | 1.15336e39i | 0.0995221 | + | 0.300150i | ||||
\(538\) | 2.41983e39i | 0.612973i | ||||||||
\(539\) | −9.46281e38 | − | 5.86569e39i | −0.233337 | − | 1.44638i | ||||
\(540\) | −1.84495e39 | + | 2.63806e39i | −0.442870 | + | 0.633251i | ||||
\(541\) | 5.32128e39 | 1.24353 | 0.621764 | − | 0.783205i | \(-0.286416\pi\) | ||||
0.621764 | + | 0.783205i | \(0.286416\pi\) | |||||||
\(542\) | 4.15131e39 | 0.944487 | ||||||||
\(543\) | 8.86652e37 | + | 2.67407e38i | 0.0196406 | + | 0.0592345i | ||||
\(544\) | 4.11350e38i | 0.0887212i | ||||||||
\(545\) | −3.58543e39 | −0.752995 | ||||||||
\(546\) | −7.28933e37 | + | 3.08309e37i | −0.0149071 | + | 0.00630510i | ||||
\(547\) | −4.81769e39 | −0.959451 | −0.479726 | − | 0.877419i | \(-0.659264\pi\) | ||||
−0.479726 | + | 0.877419i | \(0.659264\pi\) | |||||||
\(548\) | − | 1.76686e39i | − | 0.342676i | ||||||
\(549\) | 3.45740e39 | + | 4.64041e39i | 0.653056 | + | 0.876511i | ||||
\(550\) | 2.50032e40 | 4.59977 | ||||||||
\(551\) | −5.43958e39 | −0.974692 | ||||||||
\(552\) | −4.24774e39 | + | 1.40844e39i | −0.741382 | + | 0.245823i | ||||
\(553\) | 5.24566e39 | − | 4.20409e38i | 0.891838 | − | 0.0714756i | ||||
\(554\) | 2.80201e39i | 0.464064i | ||||||||
\(555\) | −5.73815e39 | + | 1.90263e39i | −0.925814 | + | 0.306977i | ||||
\(556\) | 1.74709e39i | 0.274620i | ||||||||
\(557\) | 9.50433e39i | 1.45553i | 0.685827 | + | 0.727765i | \(0.259441\pi\) | ||||
−0.685827 | + | 0.727765i | \(0.740559\pi\) | |||||||
\(558\) | 4.73922e39 | − | 3.53102e39i | 0.707150 | − | 0.526871i | ||||
\(559\) | 1.06307e38i | 0.0154558i | ||||||||
\(560\) | −1.66788e40 | + | 1.33671e39i | −2.36286 | + | 0.189370i | ||||
\(561\) | −3.87423e38 | − | 1.16843e39i | −0.0534840 | − | 0.161303i | ||||
\(562\) | −6.25143e39 | −0.841013 | ||||||||
\(563\) | 3.75617e39 | 0.492463 | 0.246231 | − | 0.969211i | \(-0.420808\pi\) | ||||
0.246231 | + | 0.969211i | \(0.420808\pi\) | |||||||
\(564\) | −1.90245e39 | + | 6.30802e38i | −0.243089 | + | 0.0806021i | ||||
\(565\) | 2.65165e39i | 0.330228i | ||||||||
\(566\) | −4.31045e39 | −0.523220 | ||||||||
\(567\) | −1.76317e39 | + | 8.26595e39i | −0.208612 | + | 0.977998i | ||||
\(568\) | 6.72384e39 | 0.775473 | ||||||||
\(569\) | 2.36168e39i | 0.265518i | 0.991148 | + | 0.132759i | \(0.0423836\pi\) | ||||
−0.991148 | + | 0.132759i | \(0.957616\pi\) | |||||||
\(570\) | −3.35306e40 | + | 1.11179e40i | −3.67499 | + | 1.21853i | ||||
\(571\) | −3.21874e39 | −0.343924 | −0.171962 | − | 0.985104i | \(-0.555011\pi\) | ||||
−0.171962 | + | 0.985104i | \(0.555011\pi\) | |||||||
\(572\) | −7.76984e37 | −0.00809412 | ||||||||
\(573\) | −6.27839e38 | − | 1.89351e39i | −0.0637686 | − | 0.192320i | ||||
\(574\) | −8.79763e38 | − | 1.09772e40i | −0.0871251 | − | 1.08710i | ||||
\(575\) | − | 3.03637e40i | − | 2.93205i | ||||||
\(576\) | −2.84781e39 | + | 2.12179e39i | −0.268154 | + | 0.199792i | ||||
\(577\) | 6.93567e39i | 0.636853i | 0.947948 | + | 0.318426i | \(0.103154\pi\) | ||||
−0.947948 | + | 0.318426i | \(0.896846\pi\) | |||||||
\(578\) | − | 1.30567e40i | − | 1.16918i | ||||||
\(579\) | 1.30851e40 | − | 4.33869e39i | 1.14271 | − | 0.378895i | ||||
\(580\) | 5.17090e39i | 0.440413i | ||||||||
\(581\) | 9.15050e39 | − | 7.33360e38i | 0.760135 | − | 0.0609205i | ||||
\(582\) | −2.34052e40 | + | 7.76058e39i | −1.89640 | + | 0.628797i | ||||
\(583\) | −1.91063e40 | −1.51002 | ||||||||
\(584\) | 7.01370e39 | 0.540705 | ||||||||
\(585\) | −2.07270e38 | − | 2.78191e38i | −0.0155875 | − | 0.0209210i | ||||
\(586\) | 9.97924e39i | 0.732120i | ||||||||
\(587\) | 1.82904e40 | 1.30909 | 0.654547 | − | 0.756022i | \(-0.272860\pi\) | ||||
0.654547 | + | 0.756022i | \(0.272860\pi\) | |||||||
\(588\) | 5.13816e39 | − | 2.67572e39i | 0.358787 | − | 0.186840i | ||||
\(589\) | 1.86787e40 | 1.27255 | ||||||||
\(590\) | 6.83212e39i | 0.454152i | ||||||||
\(591\) | −7.57669e39 | − | 2.28506e40i | −0.491429 | − | 1.48211i | ||||
\(592\) | 1.00109e40 | 0.633589 | ||||||||
\(593\) | −2.48997e40 | −1.53781 | −0.768903 | − | 0.639366i | \(-0.779197\pi\) | ||||
−0.768903 | + | 0.639366i | \(0.779197\pi\) | |||||||
\(594\) | −1.65107e40 | + | 2.36084e40i | −0.995092 | + | 1.42286i | ||||
\(595\) | −3.75521e39 | + | 3.00958e38i | −0.220871 | + | 0.0177015i | ||||
\(596\) | 6.38545e39i | 0.366540i | ||||||||
\(597\) | 3.61630e39 | + | 1.09064e40i | 0.202599 | + | 0.611020i | ||||
\(598\) | 3.27612e38i | 0.0179140i | ||||||||
\(599\) | − | 3.33529e39i | − | 0.178010i | −0.996031 | − | 0.0890051i | \(-0.971631\pi\) | ||
0.996031 | − | 0.0890051i | \(-0.0283688\pi\) | |||||||
\(600\) | −1.12945e40 | − | 3.40631e40i | −0.588400 | − | 1.77456i | ||||
\(601\) | − | 2.82826e40i | − | 1.43827i | −0.694873 | − | 0.719133i | \(-0.744539\pi\) | ||
0.694873 | − | 0.719133i | \(-0.255461\pi\) | |||||||
\(602\) | −2.15833e39 | − | 2.69306e40i | −0.107144 | − | 1.33690i | ||||
\(603\) | 1.18099e40 | − | 8.79908e39i | 0.572326 | − | 0.426419i | ||||
\(604\) | −3.41029e39 | −0.161345 | ||||||||
\(605\) | 4.74142e40 | 2.19006 | ||||||||
\(606\) | 4.86769e39 | + | 1.46805e40i | 0.219518 | + | 0.662046i | ||||
\(607\) | 1.30309e40i | 0.573771i | 0.957965 | + | 0.286885i | \(0.0926199\pi\) | ||||
−0.957965 | + | 0.286885i | \(0.907380\pi\) | |||||||
\(608\) | 3.04259e40 | 1.30810 | ||||||||
\(609\) | 5.28851e39 | + | 1.25036e40i | 0.222015 | + | 0.524910i | ||||
\(610\) | 6.03647e40 | 2.47457 | ||||||||
\(611\) | − | 2.15993e38i | − | 0.00864654i | ||||||
\(612\) | 9.62467e38 | − | 7.17098e38i | 0.0376262 | − | 0.0280339i | ||||
\(613\) | −1.11135e40 | −0.424302 | −0.212151 | − | 0.977237i | \(-0.568047\pi\) | ||||
−0.212151 | + | 0.977237i | \(0.568047\pi\) | |||||||
\(614\) | −4.62465e40 | −1.72440 | ||||||||
\(615\) | 4.58177e40 | − | 1.51920e40i | 1.66857 | − | 0.553255i | ||||
\(616\) | −2.89749e40 | + | 2.32217e39i | −1.03063 | + | 0.0825989i | ||||
\(617\) | 5.19429e40i | 1.80464i | 0.431064 | + | 0.902322i | \(0.358138\pi\) | ||||
−0.431064 | + | 0.902322i | \(0.641862\pi\) | |||||||
\(618\) | −2.91782e40 | + | 9.67474e39i | −0.990205 | + | 0.328327i | ||||
\(619\) | 8.01138e39i | 0.265578i | 0.991144 | + | 0.132789i | \(0.0423933\pi\) | ||||
−0.991144 | + | 0.132789i | \(0.957607\pi\) | |||||||
\(620\) | − | 1.77561e40i | − | 0.574999i | ||||||
\(621\) | 2.86699e40 | + | 2.00506e40i | 0.906982 | + | 0.634306i | ||||
\(622\) | − | 7.00952e40i | − | 2.16635i | ||||||
\(623\) | −4.47957e40 | + | 3.59012e39i | −1.35257 | + | 0.108401i | ||||
\(624\) | 1.80803e38 | + | 5.45287e38i | 0.00533372 | + | 0.0160860i | ||||
\(625\) | 1.16884e41 | 3.36895 | ||||||||
\(626\) | 4.55206e40 | 1.28198 | ||||||||
\(627\) | −8.64243e40 | + | 2.86561e40i | −2.37824 | + | 0.788565i | ||||
\(628\) | 5.80890e39i | 0.156199i | ||||||||
\(629\) | 2.25394e39 | 0.0592254 | ||||||||
\(630\) | 5.81554e40 | + | 6.62656e40i | 1.49332 | + | 1.70157i | ||||
\(631\) | −4.96300e40 | −1.24543 | −0.622714 | − | 0.782450i | \(-0.713970\pi\) | ||||
−0.622714 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(632\) | − | 2.57457e40i | − | 0.631403i | ||||||
\(633\) | −2.48752e40 | + | 8.24797e39i | −0.596228 | + | 0.197694i | ||||
\(634\) | −3.04502e40 | −0.713338 | ||||||||
\(635\) | 8.45434e40 | 1.93580 | ||||||||
\(636\) | −5.86300e39 | − | 1.76823e40i | −0.131218 | − | 0.395741i | ||||
\(637\) | 9.94286e37 | + | 6.16326e38i | 0.00217515 | + | 0.0134831i | ||||
\(638\) | 4.62751e40i | 0.989572i | ||||||||
\(639\) | −3.14058e40 | − | 4.21518e40i | −0.656518 | − | 0.881159i | ||||
\(640\) | 1.08545e41i | 2.21820i | ||||||||
\(641\) | − | 6.33546e38i | − | 0.0126572i | −0.999980 | − | 0.00632859i | \(-0.997986\pi\) | ||
0.999980 | − | 0.00632859i | \(-0.00201446\pi\) | |||||||
\(642\) | 5.01008e40 | − | 1.66122e40i | 0.978559 | − | 0.324465i | ||||
\(643\) | 3.01539e40i | 0.575817i | 0.957658 | + | 0.287909i | \(0.0929599\pi\) | ||||
−0.957658 | + | 0.287909i | \(0.907040\pi\) | |||||||
\(644\) | −1.91571e39 | − | 2.39032e40i | −0.0357671 | − | 0.446284i | ||||
\(645\) | 1.12405e41 | − | 3.72707e40i | 2.05197 | − | 0.680381i | ||||
\(646\) | 1.31708e40 | 0.235093 | ||||||||
\(647\) | −8.84082e40 | −1.54305 | −0.771526 | − | 0.636198i | \(-0.780506\pi\) | ||||
−0.771526 | + | 0.636198i | \(0.780506\pi\) | |||||||
\(648\) | 3.96212e40 | + | 1.18290e40i | 0.676223 | + | 0.201889i | ||||
\(649\) | 1.76096e40i | 0.293901i | ||||||||
\(650\) | −2.62716e39 | −0.0428788 | ||||||||
\(651\) | −1.81599e40 | − | 4.29354e40i | −0.289861 | − | 0.685317i | ||||
\(652\) | −2.37218e40 | −0.370303 | ||||||||
\(653\) | − | 6.37221e40i | − | 0.972857i | −0.873720 | − | 0.486428i | \(-0.838299\pi\) | ||
0.873720 | − | 0.486428i | \(-0.161701\pi\) | |||||||
\(654\) | −9.84617e39 | − | 2.96952e40i | −0.147025 | − | 0.443413i | ||||
\(655\) | −5.90654e40 | −0.862650 | ||||||||
\(656\) | −7.99344e40 | −1.14190 | ||||||||
\(657\) | −3.27596e40 | − | 4.39689e40i | −0.457763 | − | 0.614396i | ||||
\(658\) | 4.38527e39 | + | 5.47172e40i | 0.0599405 | + | 0.747908i | ||||
\(659\) | − | 2.02299e39i | − | 0.0270493i | −0.999909 | − | 0.0135246i | \(-0.995695\pi\) | ||
0.999909 | − | 0.0135246i | \(-0.00430516\pi\) | |||||||
\(660\) | 2.72407e40 | + | 8.21554e40i | 0.356312 | + | 1.07461i | ||||
\(661\) | 8.62348e40i | 1.10347i | 0.834019 | + | 0.551736i | \(0.186035\pi\) | ||||
−0.834019 | + | 0.551736i | \(0.813965\pi\) | |||||||
\(662\) | − | 1.15093e39i | − | 0.0144082i | ||||||
\(663\) | 4.07077e37 | + | 1.22771e38i | 0.000498575 | + | 0.00150366i | ||||
\(664\) | − | 4.49106e40i | − | 0.538161i | ||||||
\(665\) | 2.22607e40 | + | 2.77758e41i | 0.260990 | + | 3.25651i | ||||
\(666\) | −3.15158e40 | − | 4.22995e40i | −0.361536 | − | 0.485243i | ||||
\(667\) | 5.61963e40 | 0.630788 | ||||||||
\(668\) | 3.89779e40 | 0.428114 | ||||||||
\(669\) | −4.88929e40 | − | 1.47457e41i | −0.525493 | − | 1.58484i | ||||
\(670\) | − | 1.53628e41i | − | 1.61580i | ||||||
\(671\) | 1.55588e41 | 1.60140 | ||||||||
\(672\) | −2.95809e40 | − | 6.99380e40i | −0.297959 | − | 0.704464i | ||||
\(673\) | −1.47463e41 | −1.45367 | −0.726833 | − | 0.686815i | \(-0.759008\pi\) | ||||
−0.726833 | + | 0.686815i | \(0.759008\pi\) | |||||||
\(674\) | 7.58686e40i | 0.731970i | ||||||||
\(675\) | −1.60788e41 | + | 2.29907e41i | −1.51827 | + | 2.17094i | ||||
\(676\) | −4.37610e40 | −0.404445 | ||||||||
\(677\) | −1.68380e41 | −1.52320 | −0.761598 | − | 0.648050i | \(-0.775585\pi\) | ||||
−0.761598 | + | 0.648050i | \(0.775585\pi\) | |||||||
\(678\) | −2.19614e40 | + | 7.28186e39i | −0.194460 | + | 0.0644780i | ||||
\(679\) | 1.55385e40 | + | 1.93882e41i | 0.134678 | + | 1.68045i | ||||
\(680\) | 1.84306e40i | 0.156372i | ||||||||
\(681\) | 1.30038e41 | − | 4.31174e40i | 1.08003 | − | 0.358112i | ||||
\(682\) | − | 1.58901e41i | − | 1.29198i | ||||||
\(683\) | − | 1.93052e41i | − | 1.53665i | −0.640060 | − | 0.768325i | \(-0.721091\pi\) | ||
0.640060 | − | 0.768325i | \(-0.278909\pi\) | |||||||
\(684\) | −5.30408e40 | − | 7.11898e40i | −0.413330 | − | 0.554759i | ||||
\(685\) | − | 2.12106e41i | − | 1.61823i | ||||||
\(686\) | −3.77012e40 | − | 1.54114e41i | −0.281615 | − | 1.15118i | ||||
\(687\) | −2.43383e40 | − | 7.34021e40i | −0.177999 | − | 0.536829i | ||||
\(688\) | −1.96104e41 | −1.40428 | ||||||||
\(689\) | 2.00755e39 | 0.0140763 | ||||||||
\(690\) | 3.46405e41 | − | 1.14859e41i | 2.37833 | − | 0.788594i | ||||
\(691\) | − | 2.46113e41i | − | 1.65464i | −0.561732 | − | 0.827319i | \(-0.689865\pi\) | ||
0.561732 | − | 0.827319i | \(-0.310135\pi\) | |||||||
\(692\) | 3.82490e39 | 0.0251815 | ||||||||
\(693\) | 1.49894e41 | + | 1.70798e41i | 0.966389 | + | 1.10116i | ||||
\(694\) | −1.67610e41 | −1.05825 | ||||||||
\(695\) | 2.09734e41i | 1.29685i | ||||||||
\(696\) | 6.30430e40 | − | 2.09035e40i | 0.381771 | − | 0.126586i | ||||
\(697\) | −1.79972e40 | −0.106740 | ||||||||
\(698\) | 1.95076e41 | 1.13319 | ||||||||
\(699\) | −3.65799e40 | − | 1.10322e41i | −0.208125 | − | 0.627686i | ||||
\(700\) | 1.91682e41 | − | 1.53622e40i | 1.06822 | − | 0.0856117i | ||||
\(701\) | 1.77281e41i | 0.967725i | 0.875144 | + | 0.483862i | \(0.160766\pi\) | ||||
−0.875144 | + | 0.483862i | \(0.839234\pi\) | |||||||
\(702\) | 1.73483e39 | − | 2.48061e39i | 0.00927619 | − | 0.0132638i | ||||
\(703\) | − | 1.66715e41i | − | 0.873216i | ||||||
\(704\) | 9.54841e40i | 0.489923i | ||||||||
\(705\) | −2.28383e41 | + | 7.57260e40i | −1.14795 | + | 0.380630i | ||||
\(706\) | 4.62301e40i | 0.227644i | ||||||||
\(707\) | 1.21609e41 | − | 9.74625e39i | 0.586657 | − | 0.0470171i | ||||
\(708\) | −1.62972e40 | + | 5.40374e39i | −0.0770248 | + | 0.0255395i | ||||
\(709\) | 1.85949e41 | 0.861039 | 0.430519 | − | 0.902581i | \(-0.358330\pi\) | ||||
0.430519 | + | 0.902581i | \(0.358330\pi\) | |||||||
\(710\) | −5.48332e41 | −2.48770 | ||||||||
\(711\) | −1.61400e41 | + | 1.20253e41i | −0.717454 | + | 0.534549i | ||||
\(712\) | 2.19857e41i | 0.957593i | ||||||||
\(713\) | −1.92969e41 | −0.823550 | ||||||||
\(714\) | −1.28050e40 | − | 3.02749e40i | −0.0535495 | − | 0.126607i | ||||
\(715\) | −9.32747e39 | −0.0382232 | ||||||||
\(716\) | 3.18543e40i | 0.127917i | ||||||||
\(717\) | −3.83471e40 | − | 1.15652e41i | −0.150906 | − | 0.455118i | ||||
\(718\) | 9.33389e40 | 0.359963 | ||||||||
\(719\) | −2.21601e41 | −0.837537 | −0.418768 | − | 0.908093i | \(-0.637538\pi\) | ||||
−0.418768 | + | 0.908093i | \(0.637538\pi\) | |||||||
\(720\) | 5.13178e41 | − | 3.82350e41i | 1.90084 | − | 1.41625i | ||||
\(721\) | 1.93711e40 | + | 2.41703e41i | 0.0703223 | + | 0.877447i | ||||
\(722\) | − | 6.41106e41i | − | 2.28108i | ||||||
\(723\) | −7.13525e39 | − | 2.15193e40i | −0.0248831 | − | 0.0750452i | ||||
\(724\) | 7.38541e39i | 0.0252444i | ||||||||
\(725\) | 4.50644e41i | 1.50985i | ||||||||
\(726\) | 1.30207e41 | + | 3.92693e41i | 0.427616 | + | 1.28965i | ||||
\(727\) | 2.56606e41i | 0.826072i | 0.910715 | + | 0.413036i | \(0.135532\pi\) | ||||
−0.910715 | + | 0.413036i | \(0.864468\pi\) | |||||||
\(728\) | 3.04448e39 | − | 2.43998e38i | 0.00960745 | − | 0.000769982i | ||||
\(729\) | −1.10907e41 | − | 3.03637e41i | −0.343090 | − | 0.939302i | ||||
\(730\) | −5.71969e41 | −1.73457 | ||||||||
\(731\) | −4.41527e40 | −0.131267 | ||||||||
\(732\) | 4.77443e40 | + | 1.43993e41i | 0.139159 | + | 0.419691i | ||||
\(733\) | − | 2.64459e41i | − | 0.755703i | −0.925866 | − | 0.377851i | \(-0.876663\pi\) | ||
0.925866 | − | 0.377851i | \(-0.123337\pi\) | |||||||
\(734\) | 5.09888e41 | 1.42851 | ||||||||
\(735\) | 6.16821e41 | − | 3.21213e41i | 1.69431 | − | 0.882320i | ||||
\(736\) | −3.14330e41 | −0.846559 | ||||||||
\(737\) | − | 3.95973e41i | − | 1.04565i | ||||||
\(738\) | 2.51646e41 | + | 3.37751e41i | 0.651587 | + | 0.874540i | ||||
\(739\) | −5.53934e41 | −1.40642 | −0.703208 | − | 0.710985i | \(-0.748250\pi\) | ||||
−0.703208 | + | 0.710985i | \(0.748250\pi\) | |||||||
\(740\) | −1.58480e41 | −0.394562 | ||||||||
\(741\) | 9.08086e39 | − | 3.01098e39i | 0.0221699 | − | 0.00735096i | ||||
\(742\) | −5.08570e41 | + | 4.07589e40i | −1.21757 | + | 0.0975812i | ||||
\(743\) | − | 4.83025e41i | − | 1.13405i | −0.823701 | − | 0.567024i | \(-0.808094\pi\) | ||
0.823701 | − | 0.567024i | \(-0.191906\pi\) | |||||||
\(744\) | −2.16480e41 | + | 7.17792e40i | −0.498436 | + | 0.165269i | ||||
\(745\) | 7.66555e41i | 1.73092i | ||||||||
\(746\) | − | 2.28964e39i | − | 0.00507054i | ||||||
\(747\) | −2.81545e41 | + | 2.09769e41i | −0.611504 | + | 0.455609i | ||||
\(748\) | − | 3.22706e40i | − | 0.0687438i | ||||||
\(749\) | −3.32615e40 | − | 4.15020e41i | −0.0694952 | − | 0.867127i | ||||
\(750\) | 5.73386e41 | + | 1.72928e42i | 1.17506 | + | 3.54387i | ||||
\(751\) | 1.98960e41 | 0.399933 | 0.199966 | − | 0.979803i | \(-0.435917\pi\) | ||||
0.199966 | + | 0.979803i | \(0.435917\pi\) | |||||||
\(752\) | 3.98441e41 | 0.785607 | ||||||||
\(753\) | −1.66247e41 | + | 5.51232e40i | −0.321533 | + | 0.106612i | ||||
\(754\) | − | 4.86227e39i | − | 0.00922474i | ||||||
\(755\) | −4.09396e41 | −0.761925 | ||||||||
\(756\) | −1.12072e41 | + | 1.91134e41i | −0.204611 | + | 0.348957i | ||||
\(757\) | −1.85018e41 | −0.331378 | −0.165689 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165689 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(758\) | 5.26692e40i | 0.0925450i | ||||||||
\(759\) | 8.92849e41 | − | 2.96046e41i | 1.53912 | − | 0.510333i | ||||
\(760\) | 1.36323e42 | 2.30554 | ||||||||
\(761\) | 4.19703e41 | 0.696409 | 0.348204 | − | 0.937419i | \(-0.386791\pi\) | ||||
0.348204 | + | 0.937419i | \(0.386791\pi\) | |||||||
\(762\) | 2.32170e41 | + | 7.00203e41i | 0.377971 | + | 1.13993i | ||||
\(763\) | −2.45986e41 | + | 1.97143e40i | −0.392920 | + | 0.0314903i | ||||
\(764\) | − | 5.22962e40i | − | 0.0819627i | ||||||
\(765\) | 1.15541e41 | − | 8.60856e40i | 0.177683 | − | 0.132385i | ||||
\(766\) | − | 9.88781e40i | − | 0.149205i | ||||||
\(767\) | − | 1.85029e39i | − | 0.00273973i | ||||||
\(768\) | −6.80540e41 | + | 2.25650e41i | −0.988816 | + | 0.327866i | ||||
\(769\) | − | 2.25526e41i | − | 0.321562i | −0.986990 | − | 0.160781i | \(-0.948599\pi\) | ||
0.986990 | − | 0.160781i | \(-0.0514013\pi\) | |||||||
\(770\) | 2.36291e42 | − | 1.89374e41i | 3.30622 | − | 0.264975i | ||||
\(771\) | 5.79228e41 | − | 1.92057e41i | 0.795355 | − | 0.263719i | ||||
\(772\) | 3.61393e41 | 0.487000 | ||||||||
\(773\) | −4.58104e41 | −0.605845 | −0.302923 | − | 0.953015i | \(-0.597962\pi\) | ||||
−0.302923 | + | 0.953015i | \(0.597962\pi\) | |||||||
\(774\) | 6.17366e41 | + | 8.28609e41i | 0.801307 | + | 1.07549i | ||||
\(775\) | − | 1.54744e42i | − | 1.97124i | ||||||
\(776\) | 9.51571e41 | 1.18972 | ||||||||
\(777\) | −3.83216e41 | + | 1.62085e41i | −0.470261 | + | 0.198901i | ||||
\(778\) | 8.09486e41 | 0.975001 | ||||||||
\(779\) | 1.33118e42i | 1.57377i | ||||||||
\(780\) | −2.86226e39 | − | 8.63232e39i | −0.00332152 | − | 0.0100174i | ||||
\(781\) | −1.41331e42 | −1.60989 | ||||||||
\(782\) | −1.36068e41 | −0.152145 | ||||||||
\(783\) | −4.25506e41 | − | 2.97581e41i | −0.467046 | − | 0.326633i | ||||
\(784\) | −1.13693e42 | + | 1.83415e41i | −1.22504 | + | 0.197630i | ||||
\(785\) | 6.97341e41i | 0.737625i | ||||||||
\(786\) | −1.62203e41 | − | 4.89190e41i | −0.168435 | − | 0.507985i | ||||
\(787\) | − | 5.27423e41i | − | 0.537681i | −0.963185 | − | 0.268841i | \(-0.913359\pi\) | ||
0.963185 | − | 0.268841i | \(-0.0866405\pi\) | |||||||
\(788\) | − | 6.31104e41i | − | 0.631642i | ||||||
\(789\) | −6.18403e41 | − | 1.86505e42i | −0.607652 | − | 1.83263i | ||||
\(790\) | 2.09957e42i | 2.02552i | ||||||||
\(791\) | 1.45800e40 | + | 1.81922e41i | 0.0138101 | + | 0.172316i | ||||
\(792\) | 8.91509e41 | − | 6.64230e41i | 0.829107 | − | 0.617736i | ||||
\(793\) | −1.63481e40 | −0.0149282 | ||||||||
\(794\) | −7.24363e41 | −0.649470 | ||||||||
\(795\) | −7.03837e41 | − | 2.12271e42i | −0.619653 | − | 1.86882i | ||||
\(796\) | 3.01221e41i | 0.260403i | ||||||||
\(797\) | 1.44678e42 | 1.22816 | 0.614082 | − | 0.789242i | \(-0.289526\pi\) | ||||
0.614082 | + | 0.789242i | \(0.289526\pi\) | |||||||
\(798\) | −2.23931e42 | + | 9.47134e41i | −1.86669 | + | 0.789532i | ||||
\(799\) | 8.97086e40 | 0.0734355 | ||||||||
\(800\) | − | 2.52064e42i | − | 2.02631i | ||||||
\(801\) | 1.37829e42 | − | 1.02691e42i | 1.08810 | − | 0.810702i | ||||
\(802\) | 1.09288e42 | 0.847314 | ||||||||
\(803\) | −1.47423e42 | −1.12251 | ||||||||
\(804\) | 3.66462e41 | − | 1.21509e41i | 0.274041 | − | 0.0908651i | ||||
\(805\) | −2.29975e41 | − | 2.86951e42i | −0.168904 | − | 2.10750i | ||||
\(806\) | 1.66963e40i | 0.0120437i | ||||||||
\(807\) | −6.92937e41 | + | 2.29760e41i | −0.490939 | + | 0.162783i | ||||
\(808\) | − | 5.96856e41i | − | 0.415341i | ||||||
\(809\) | − | 6.29459e41i | − | 0.430243i | −0.976587 | − | 0.215121i | \(-0.930985\pi\) | ||
0.976587 | − | 0.215121i | \(-0.0690147\pi\) | |||||||
\(810\) | −3.23112e42 | − | 9.64662e41i | −2.16931 | − | 0.647653i | ||||
\(811\) | 5.18702e41i | 0.342070i | 0.985265 | + | 0.171035i | \(0.0547112\pi\) | ||||
−0.985265 | + | 0.171035i | \(0.945289\pi\) | |||||||
\(812\) | 2.84320e40 | + | 3.54760e41i | 0.0184181 | + | 0.229812i | ||||
\(813\) | 3.94163e41 | + | 1.18876e42i | 0.250820 | + | 0.756453i | ||||
\(814\) | −1.41826e42 | −0.886548 | ||||||||
\(815\) | −2.84773e42 | −1.74869 | ||||||||
\(816\) | −2.26475e41 | + | 7.50933e40i | −0.136619 | + | 0.0452995i | ||||
\(817\) | 3.26579e42i | 1.93539i | ||||||||
\(818\) | −1.35391e42 | −0.788255 | ||||||||
\(819\) | −1.57498e40 | − | 1.79462e40i | −0.00900863 | − | 0.0102649i | ||||
\(820\) | 1.26542e42 | 0.711107 | ||||||||
\(821\) | 8.40658e41i | 0.464134i | 0.972700 | + | 0.232067i | \(0.0745489\pi\) | ||||
−0.972700 | + | 0.232067i | \(0.925451\pi\) | |||||||
\(822\) | 1.75670e42 | − | 5.82479e41i | 0.952922 | − | 0.315965i | ||||
\(823\) | 7.67647e41 | 0.409133 | 0.204566 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204566 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(824\) | 1.18628e42 | 0.621215 | ||||||||
\(825\) | 2.37402e42 | + | 7.15985e42i | 1.22153 | + | 3.68402i | ||||
\(826\) | 3.75662e40 | + | 4.68732e41i | 0.0189927 | + | 0.236981i | ||||
\(827\) | 8.95773e41i | 0.445008i | 0.974932 | + | 0.222504i | \(0.0714231\pi\) | ||||
−0.974932 | + | 0.222504i | \(0.928577\pi\) | |||||||
\(828\) | 5.47965e41 | + | 7.35461e41i | 0.267493 | + | 0.359021i | ||||
\(829\) | − | 3.49904e42i | − | 1.67845i | −0.543786 | − | 0.839224i | \(-0.683010\pi\) | ||
0.543786 | − | 0.839224i | \(-0.316990\pi\) | |||||||
\(830\) | 3.66248e42i | 1.72640i | ||||||||
\(831\) | −8.02376e41 | + | 2.66048e41i | −0.371675 | + | 0.123238i | ||||
\(832\) | − | 1.00328e40i | − | 0.00456703i | ||||||
\(833\) | −2.55979e41 | + | 4.12958e40i | −0.114512 | + | 0.0184737i | ||||
\(834\) | −1.73705e42 | + | 5.75962e41i | −0.763668 | + | 0.253213i | ||||
\(835\) | 4.67918e42 | 2.02170 | ||||||||
\(836\) | −2.38692e42 | −1.01355 | ||||||||
\(837\) | 1.46112e42 | + | 1.02185e42i | 0.609771 | + | 0.426449i | ||||
\(838\) | 1.80832e42i | 0.741715i | ||||||||
\(839\) | −3.78981e42 | −1.52781 | −0.763904 | − | 0.645329i | \(-0.776720\pi\) | ||||
−0.763904 | + | 0.645329i | \(0.776720\pi\) | |||||||
\(840\) | −1.32537e42 | − | 3.13358e42i | −0.525156 | − | 1.24163i | ||||
\(841\) | 1.73365e42 | 0.675179 | ||||||||
\(842\) | − | 6.03470e42i | − | 2.31010i | ||||||
\(843\) | −5.93567e41 | − | 1.79015e42i | −0.223342 | − | 0.673579i | ||||
\(844\) | −6.87018e41 | −0.254099 | ||||||||
\(845\) | −5.25338e42 | −1.90992 | ||||||||
\(846\) | −1.25435e42 | − | 1.68355e42i | −0.448280 | − | 0.601668i | ||||
\(847\) | 3.25295e42 | − | 2.60705e41i | 1.14279 | − | 0.0915884i | ||||
\(848\) | 3.70332e42i | 1.27894i | ||||||||
\(849\) | −4.09273e41 | − | 1.23433e42i | −0.138948 | − | 0.419055i | ||||
\(850\) | − | 1.09114e42i | − | 0.364171i | ||||||
\(851\) | 1.72233e42i | 0.565116i | ||||||||
\(852\) | −4.33692e41 | − | 1.30798e42i | −0.139897 | − | 0.421916i | ||||
\(853\) | − | 1.31506e42i | − | 0.417048i | −0.978017 | − | 0.208524i | \(-0.933134\pi\) | ||
0.978017 | − | 0.208524i | \(-0.0668659\pi\) | |||||||
\(854\) | 4.14145e42 | − | 3.31913e41i | 1.29126 | − | 0.103487i | ||||
\(855\) | −6.36740e42 | − | 8.54613e42i | −1.95188 | − | 2.61975i | ||||
\(856\) | −2.03692e42 | −0.613909 | ||||||||
\(857\) | −2.60807e42 | −0.772854 | −0.386427 | − | 0.922320i | \(-0.626291\pi\) | ||||
−0.386427 | + | 0.922320i | \(0.626291\pi\) | |||||||
\(858\) | −2.56147e40 | − | 7.72518e40i | −0.00746319 | − | 0.0225083i | ||||
\(859\) | 6.29250e42i | 1.80270i | 0.433096 | + | 0.901348i | \(0.357421\pi\) | ||||
−0.433096 | + | 0.901348i | \(0.642579\pi\) | |||||||
\(860\) | 3.10448e42 | 0.874504 | ||||||||
\(861\) | 3.05989e42 | − | 1.29421e42i | 0.847539 | − | 0.358474i | ||||
\(862\) | −3.22198e42 | −0.877542 | ||||||||
\(863\) | 6.65231e42i | 1.78162i | 0.454372 | + | 0.890812i | \(0.349864\pi\) | ||||
−0.454372 | + | 0.890812i | \(0.650136\pi\) | |||||||
\(864\) | 2.38003e42 | + | 1.66450e42i | 0.626807 | + | 0.438363i | ||||
\(865\) | 4.59168e41 | 0.118915 | ||||||||
\(866\) | −6.83387e42 | −1.74043 | ||||||||
\(867\) | 3.73890e42 | − | 1.23972e42i | 0.936412 | − | 0.310491i | ||||
\(868\) | −9.76310e40 | − | 1.21819e42i | −0.0240465 | − | 0.300040i | ||||
\(869\) | 5.41158e42i | 1.31080i | ||||||||
\(870\) | −5.14118e42 | + | 1.70468e42i | −1.22471 | + | 0.406083i | ||||
\(871\) | 4.16060e40i | 0.00974750i | ||||||||
\(872\) | 1.20730e42i | 0.278180i | ||||||||
\(873\) | −4.44460e42 | − | 5.96541e42i | −1.00723 | − | 1.35187i | ||||
\(874\) | 1.00644e43i | 2.24321i | ||||||||
\(875\) | 1.43249e43 | − | 1.14805e42i | 3.14032 | − | 0.251678i | ||||
\(876\) | −4.52388e41 | − | 1.36436e42i | −0.0975443 | − | 0.294185i | ||||
\(877\) | 1.56359e41 | 0.0331610 | 0.0165805 | − | 0.999863i | \(-0.494722\pi\) | ||||
0.0165805 | + | 0.999863i | \(0.494722\pi\) | |||||||
\(878\) | 3.71802e42 | 0.775606 | ||||||||
\(879\) | −2.85763e42 | + | 9.47519e41i | −0.586365 | + | 0.194424i | ||||
\(880\) | − | 1.72063e43i | − | 3.47288i | ||||||
\(881\) | 5.62419e42 | 1.11663 | 0.558315 | − | 0.829629i | \(-0.311448\pi\) | ||||
0.558315 | + | 0.829629i | \(0.311448\pi\) | |||||||
\(882\) | 4.35423e42 | + | 4.22652e42i | 0.850388 | + | 0.825446i | ||||
\(883\) | −7.84637e41 | −0.150743 | −0.0753717 | − | 0.997156i | \(-0.524014\pi\) | ||||
−0.0753717 | + | 0.997156i | \(0.524014\pi\) | |||||||
\(884\) | 3.39077e39i | 0.000640826i | ||||||||
\(885\) | −1.95643e42 | + | 6.48703e41i | −0.363737 | + | 0.120606i | ||||
\(886\) | 1.06893e43 | 1.95506 | ||||||||
\(887\) | 1.60597e42 | 0.288965 | 0.144483 | − | 0.989507i | \(-0.453848\pi\) | ||||
0.144483 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(888\) | 6.40659e41 | + | 1.93217e42i | 0.113407 | + | 0.342025i | ||||
\(889\) | 5.80027e42 | − | 4.64858e41i | 1.01012 | − | 0.0809553i | ||||
\(890\) | − | 1.79294e43i | − | 3.07193i | ||||||
\(891\) | −8.32813e42 | − | 2.48639e42i | −1.40385 | − | 0.419124i | ||||
\(892\) | − | 4.07255e42i | − | 0.675424i | ||||||
\(893\) | − | 6.63538e42i | − | 1.08273i | ||||||
\(894\) | −6.34875e42 | + | 2.10508e42i | −1.01928 | + | 0.337968i | ||||
\(895\) | 3.82402e42i | 0.604068i | ||||||||
\(896\) | 5.96831e41 | + | 7.44696e42i | 0.0927653 | + | 1.15748i | ||||
\(897\) | −9.38144e40 | + | 3.11065e40i | −0.0143476 | + | 0.00475730i | ||||
\(898\) | 1.07933e43 | 1.62422 | ||||||||
\(899\) | 2.86396e42 | 0.424083 | ||||||||
\(900\) | −5.89774e42 | + | 4.39419e42i | −0.859349 | + | 0.640269i | ||||
\(901\) | 8.33798e41i | 0.119551i | ||||||||
\(902\) | 1.13245e43 | 1.59780 | ||||||||
\(903\) | 7.50687e42 | − | 3.17509e42i | 1.04228 | − | 0.440843i | ||||
\(904\) | 8.92872e41 | 0.121996 | ||||||||
\(905\) | 8.86597e41i | 0.119213i | ||||||||
\(906\) | −1.12427e42 | − | 3.39069e42i | −0.148768 | − | 0.448672i | ||||
\(907\) | −6.95849e42 | −0.906169 | −0.453085 | − | 0.891468i | \(-0.649676\pi\) | ||||
−0.453085 | + | 0.891468i | \(0.649676\pi\) | |||||||
\(908\) | 3.59148e42 | 0.460287 | ||||||||
\(909\) | −3.74170e42 | + | 2.78780e42i | −0.471946 | + | 0.351630i | ||||
\(910\) | −2.48279e41 | + | 1.98981e40i | −0.0308204 | + | 0.00247008i | ||||
\(911\) | 6.06042e42i | 0.740433i | 0.928945 | + | 0.370217i | \(0.120717\pi\) | ||||
−0.928945 | + | 0.370217i | \(0.879283\pi\) | |||||||
\(912\) | 5.55434e42 | + | 1.67514e43i | 0.667894 | + | 2.01431i | ||||
\(913\) | 9.43993e42i | 1.11723i | ||||||||
\(914\) | − | 1.10390e43i | − | 1.28591i | ||||||
\(915\) | 5.73157e42 | + | 1.72859e43i | 0.657155 | + | 1.98192i | ||||
\(916\) | − | 2.02727e42i | − | 0.228784i | ||||||
\(917\) | −4.05231e42 | + | 3.24769e41i | −0.450139 | + | 0.0360761i | ||||
\(918\) | 1.03027e42 | + | 7.20530e41i | 0.112650 | + | 0.0787831i | ||||
\(919\) | −1.14023e43 | −1.22720 | −0.613602 | − | 0.789615i | \(-0.710280\pi\) | ||||
−0.613602 | + | 0.789615i | \(0.710280\pi\) | |||||||
\(920\) | −1.40836e43 | −1.49207 | ||||||||
\(921\) | −4.39106e42 | − | 1.32430e43i | −0.457936 | − | 1.38109i | ||||
\(922\) | − | 5.28816e42i | − | 0.542883i | ||||||
\(923\) | 1.48501e41 | 0.0150073 | ||||||||
\(924\) | 2.32063e42 | + | 5.48666e42i | 0.230867 | + | 0.545839i | ||||
\(925\) | −1.38115e43 | −1.35266 | ||||||||
\(926\) | 2.12880e43i | 2.05247i | ||||||||
\(927\) | −5.54088e42 | − | 7.43679e42i | −0.525923 | − | 0.705878i | ||||
\(928\) | 4.66513e42 | 0.435931 | ||||||||
\(929\) | 1.70248e42 | 0.156622 | 0.0783110 | − | 0.996929i | \(-0.475047\pi\) | ||||
0.0783110 | + | 0.996929i | \(0.475047\pi\) | |||||||
\(930\) | 1.76540e43 | − | 5.85362e42i | 1.59897 | − | 0.530178i | ||||
\(931\) | 3.05448e42 | + | 1.89337e43i | 0.272375 | + | 1.68836i | ||||
\(932\) | − | 3.04694e42i | − | 0.267506i | ||||||
\(933\) | 2.00723e43 | − | 6.65547e42i | 1.73506 | − | 0.575301i | ||||
\(934\) | − | 1.14277e42i | − | 0.0972588i | ||||||
\(935\) | − | 3.87399e42i | − | 0.324631i | ||||||
\(936\) | −9.36735e40 | + | 6.97926e40i | −0.00772889 | + | 0.00575850i | ||||
\(937\) | 1.20067e43i | 0.975442i | 0.873000 | + | 0.487721i | \(0.162172\pi\) | ||||
−0.873000 | + | 0.487721i | \(0.837828\pi\) | |||||||
\(938\) | −8.44719e41 | − | 1.05400e43i | −0.0675727 | − | 0.843139i | ||||
\(939\) | 4.32214e42 | + | 1.30352e43i | 0.340445 | + | 1.02675i | ||||
\(940\) | −6.30763e42 | −0.489229 | ||||||||
\(941\) | 1.62705e43 | 1.24266 | 0.621328 | − | 0.783550i | \(-0.286593\pi\) | ||||
0.621328 | + | 0.783550i | \(0.286593\pi\) | |||||||
\(942\) | −5.77551e42 | + | 1.91501e42i | −0.434362 | + | 0.144023i | ||||
\(943\) | − | 1.37524e43i | − | 1.01849i | ||||||
\(944\) | 3.41323e42 | 0.248927 | ||||||||
\(945\) | −1.34539e43 | + | 2.29451e43i | −0.966242 | + | 1.64789i | ||||
\(946\) | 2.77824e43 | 1.96494 | ||||||||
\(947\) | − | 2.22922e43i | − | 1.55266i | −0.630324 | − | 0.776332i | \(-0.717078\pi\) | ||
0.630324 | − | 0.776332i | \(-0.282922\pi\) | |||||||
\(948\) | −5.00827e42 | + | 1.66061e42i | −0.343532 | + | 0.113906i | ||||
\(949\) | 1.54902e41 | 0.0104640 | ||||||||
\(950\) | −8.07071e43 | −5.36932 | ||||||||
\(951\) | −2.89121e42 | − | 8.71965e42i | −0.189436 | − | 0.571323i | ||||
\(952\) | 1.01340e41 | + | 1.26447e42i | 0.00653949 | + | 0.0815966i | ||||
\(953\) | 1.71692e43i | 1.09119i | 0.838047 | + | 0.545597i | \(0.183697\pi\) | ||||
−0.838047 | + | 0.545597i | \(0.816303\pi\) | |||||||
\(954\) | 1.56478e43 | − | 1.16586e43i | 0.979496 | − | 0.729786i | ||||
\(955\) | − | 6.27800e42i | − | 0.387055i | ||||||
\(956\) | − | 3.19414e42i | − | 0.193961i | ||||||
\(957\) | −1.32512e43 | + | 4.39378e42i | −0.792562 | + | 0.262794i | ||||
\(958\) | 3.04952e43i | 1.79652i | ||||||||
\(959\) | −1.16626e42 | − | 1.45520e43i | −0.0676745 | − | 0.844409i | ||||
\(960\) | −1.06083e43 | + | 3.51745e42i | −0.606336 | + | 0.201046i | ||||
\(961\) | 7.92751e42 | 0.446321 | ||||||||
\(962\) | 1.49021e41 | 0.00826435 | ||||||||
\(963\) | 9.51405e42 | + | 1.27695e43i | 0.519738 | + | 0.697576i | ||||
\(964\) | − | 5.94334e41i | − | 0.0319826i | ||||||
\(965\) | 4.33842e43 | 2.29977 | ||||||||
\(966\) | 2.31343e43 | − | 9.78484e42i | 1.20806 | − | 0.510958i | ||||
\(967\) | 1.21025e43 | 0.622576 | 0.311288 | − | 0.950316i | \(-0.399240\pi\) | ||||
0.311288 | + | 0.950316i | \(0.399240\pi\) | |||||||
\(968\) | − | 1.59655e43i | − | 0.809076i | ||||||
\(969\) | 1.25055e42 | + | 3.77156e42i | 0.0624321 | + | 0.188290i | ||||
\(970\) | −7.76009e43 | −3.81660 | ||||||||
\(971\) | −2.09917e43 | −1.01711 | −0.508556 | − | 0.861029i | \(-0.669821\pi\) | ||||
−0.508556 | + | 0.861029i | \(0.669821\pi\) | |||||||
\(972\) | −2.54512e41 | − | 8.47043e42i | −0.0121492 | − | 0.404338i | ||||
\(973\) | 1.15321e42 | + | 1.43892e43i | 0.0542341 | + | 0.676707i | ||||
\(974\) | − | 2.59898e43i | − | 1.20420i | ||||||
\(975\) | −2.49446e41 | − | 7.52307e41i | −0.0113870 | − | 0.0343422i | ||||
\(976\) | − | 3.01573e43i | − | 1.35634i | ||||||
\(977\) | 1.47407e43i | 0.653200i | 0.945163 | + | 0.326600i | \(0.105903\pi\) | ||||
−0.945163 | + | 0.326600i | \(0.894097\pi\) | |||||||
\(978\) | −7.82033e42 | − | 2.35854e43i | −0.341438 | − | 1.02975i | ||||
\(979\) | − | 4.62126e43i | − | 1.98798i | ||||||
\(980\) | 1.79985e43 | − | 2.90361e42i | 0.762885 | − | 0.123072i | ||||
\(981\) | 7.56857e42 | − | 5.63906e42i | 0.316092 | − | 0.235508i | ||||
\(982\) | 7.67997e42 | 0.316041 | ||||||||
\(983\) | −1.75349e43 | −0.711013 | −0.355506 | − | 0.934674i | \(-0.615692\pi\) | ||||
−0.355506 | + | 0.934674i | \(0.615692\pi\) | |||||||
\(984\) | −5.11550e42 | − | 1.54279e43i | −0.204390 | − | 0.616422i | ||||
\(985\) | − | 7.57622e43i | − | 2.98282i | ||||||
\(986\) | 2.01945e42 | 0.0783462 | ||||||||
\(987\) | −1.52523e43 | + | 6.45110e42i | −0.583092 | + | 0.246624i | ||||
\(988\) | 2.50801e41 | 0.00944830 | ||||||||
\(989\) | − | 3.37389e43i | − | 1.25252i | ||||||
\(990\) | −7.27028e43 | + | 5.41682e43i | −2.65975 | + | 1.98168i | ||||
\(991\) | 1.87288e43 | 0.675214 | 0.337607 | − | 0.941287i | \(-0.390383\pi\) | ||||
0.337607 | + | 0.941287i | \(0.390383\pi\) | |||||||
\(992\) | −1.60193e43 | −0.569148 | ||||||||
\(993\) | 3.29579e41 | − | 1.09280e41i | 0.0115397 | − | 0.00382627i | ||||
\(994\) | −3.76194e43 | + | 3.01498e42i | −1.29810 | + | 0.104036i | ||||
\(995\) | 3.61607e43i | 1.22971i | ||||||||
\(996\) | −8.73639e42 | + | 2.89677e42i | −0.292800 | + | 0.0970852i | ||||
\(997\) | 4.04663e43i | 1.33664i | 0.743875 | + | 0.668319i | \(0.232986\pi\) | ||||
−0.743875 | + | 0.668319i | \(0.767014\pi\) | |||||||
\(998\) | 6.55993e43i | 2.13553i | ||||||||
\(999\) | 9.12041e42 | − | 1.30411e43i | 0.292627 | − | 0.418422i |
(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 | 21.30.c.a.20.2 | yes | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.75 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.76 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.1 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.1 | ✓ | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.2 | yes | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.75 | yes | 76 | 3.2 | odd | 2 | inner | |
21.30.c.a.20.76 | yes | 76 | 7.6 | odd | 2 | inner |