Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,32,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 32);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 32 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(60.8771328190\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{337159}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 337159 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-580.654\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32768.0 | −0.707107 | ||||||||
\(3\) | 1.07495e7 | 0.432522 | 0.216261 | − | 0.976336i | \(-0.430614\pi\) | ||||
0.216261 | + | 0.976336i | \(0.430614\pi\) | |||||||
\(4\) | 1.07374e9 | 0.500000 | ||||||||
\(5\) | −3.05176e10 | −0.447214 | ||||||||
\(6\) | −3.52239e11 | −0.305839 | ||||||||
\(7\) | 2.26000e13 | 1.79924 | 0.899620 | − | 0.436674i | \(-0.143844\pi\) | ||||
0.899620 | + | 0.436674i | \(0.143844\pi\) | |||||||
\(8\) | −3.51844e13 | −0.353553 | ||||||||
\(9\) | −5.02122e14 | −0.812925 | ||||||||
\(10\) | 1.00000e15 | 0.316228 | ||||||||
\(11\) | 2.45408e16 | 1.77134 | 0.885671 | − | 0.464313i | \(-0.153699\pi\) | ||||
0.885671 | + | 0.464313i | \(0.153699\pi\) | |||||||
\(12\) | 1.15422e16 | 0.216261 | ||||||||
\(13\) | −1.48420e17 | −0.804211 | −0.402105 | − | 0.915593i | \(-0.631721\pi\) | ||||
−0.402105 | + | 0.915593i | \(0.631721\pi\) | |||||||
\(14\) | −7.40557e17 | −1.27225 | ||||||||
\(15\) | −3.28048e17 | −0.193430 | ||||||||
\(16\) | 1.15292e18 | 0.250000 | ||||||||
\(17\) | 1.16191e19 | 0.984496 | 0.492248 | − | 0.870455i | \(-0.336175\pi\) | ||||
0.492248 | + | 0.870455i | \(0.336175\pi\) | |||||||
\(18\) | 1.64535e19 | 0.574825 | ||||||||
\(19\) | 3.78068e19 | 0.571333 | 0.285667 | − | 0.958329i | \(-0.407785\pi\) | ||||
0.285667 | + | 0.958329i | \(0.407785\pi\) | |||||||
\(20\) | −3.27680e19 | −0.223607 | ||||||||
\(21\) | 2.42938e20 | 0.778211 | ||||||||
\(22\) | −8.04154e20 | −1.25253 | ||||||||
\(23\) | 8.75576e20 | 0.684719 | 0.342359 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342359 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(24\) | −3.78214e20 | −0.152920 | ||||||||
\(25\) | 9.31323e20 | 0.200000 | ||||||||
\(26\) | 4.86342e21 | 0.568663 | ||||||||
\(27\) | −1.20372e22 | −0.784130 | ||||||||
\(28\) | 2.42666e22 | 0.899620 | ||||||||
\(29\) | −8.57580e22 | −1.84546 | −0.922732 | − | 0.385443i | \(-0.874049\pi\) | ||||
−0.922732 | + | 0.385443i | \(0.874049\pi\) | |||||||
\(30\) | 1.07495e22 | 0.136775 | ||||||||
\(31\) | 2.14345e22 | 0.164062 | 0.0820308 | − | 0.996630i | \(-0.473859\pi\) | ||||
0.0820308 | + | 0.996630i | \(0.473859\pi\) | |||||||
\(32\) | −3.77789e22 | −0.176777 | ||||||||
\(33\) | 2.63801e23 | 0.766144 | ||||||||
\(34\) | −3.80734e23 | −0.696143 | ||||||||
\(35\) | −6.89698e23 | −0.804645 | ||||||||
\(36\) | −5.39149e23 | −0.406462 | ||||||||
\(37\) | −2.44667e24 | −1.20628 | −0.603140 | − | 0.797635i | \(-0.706084\pi\) | ||||
−0.603140 | + | 0.797635i | \(0.706084\pi\) | |||||||
\(38\) | −1.23885e24 | −0.403994 | ||||||||
\(39\) | −1.59544e24 | −0.347839 | ||||||||
\(40\) | 1.07374e24 | 0.158114 | ||||||||
\(41\) | 1.07003e25 | 1.07459 | 0.537297 | − | 0.843393i | \(-0.319445\pi\) | ||||
0.537297 | + | 0.843393i | \(0.319445\pi\) | |||||||
\(42\) | −7.96061e24 | −0.550278 | ||||||||
\(43\) | 6.78689e24 | 0.325769 | 0.162884 | − | 0.986645i | \(-0.447920\pi\) | ||||
0.162884 | + | 0.986645i | \(0.447920\pi\) | |||||||
\(44\) | 2.63505e25 | 0.885671 | ||||||||
\(45\) | 1.53235e25 | 0.363551 | ||||||||
\(46\) | −2.86909e25 | −0.484169 | ||||||||
\(47\) | −1.41828e26 | −1.71492 | −0.857460 | − | 0.514551i | \(-0.827959\pi\) | ||||
−0.857460 | + | 0.514551i | \(0.827959\pi\) | |||||||
\(48\) | 1.23933e25 | 0.108130 | ||||||||
\(49\) | 3.52985e26 | 2.23726 | ||||||||
\(50\) | −3.05176e25 | −0.141421 | ||||||||
\(51\) | 1.24899e26 | 0.425816 | ||||||||
\(52\) | −1.59365e26 | −0.402105 | ||||||||
\(53\) | 5.25772e26 | 0.987464 | 0.493732 | − | 0.869614i | \(-0.335632\pi\) | ||||
0.493732 | + | 0.869614i | \(0.335632\pi\) | |||||||
\(54\) | 3.94436e26 | 0.554464 | ||||||||
\(55\) | −7.48926e26 | −0.792168 | ||||||||
\(56\) | −7.95167e26 | −0.636127 | ||||||||
\(57\) | 4.06404e26 | 0.247114 | ||||||||
\(58\) | 2.81012e27 | 1.30494 | ||||||||
\(59\) | 2.03548e27 | 0.725203 | 0.362602 | − | 0.931944i | \(-0.381889\pi\) | ||||
0.362602 | + | 0.931944i | \(0.381889\pi\) | |||||||
\(60\) | −3.52239e26 | −0.0967149 | ||||||||
\(61\) | 6.56027e27 | 1.39415 | 0.697074 | − | 0.716999i | \(-0.254485\pi\) | ||||
0.697074 | + | 0.716999i | \(0.254485\pi\) | |||||||
\(62\) | −7.02366e26 | −0.116009 | ||||||||
\(63\) | −1.13480e28 | −1.46265 | ||||||||
\(64\) | 1.23794e27 | 0.125000 | ||||||||
\(65\) | 4.52941e27 | 0.359654 | ||||||||
\(66\) | −8.64424e27 | −0.541746 | ||||||||
\(67\) | 2.16532e28 | 1.07489 | 0.537444 | − | 0.843299i | \(-0.319390\pi\) | ||||
0.537444 | + | 0.843299i | \(0.319390\pi\) | |||||||
\(68\) | 1.24759e28 | 0.492248 | ||||||||
\(69\) | 9.41199e27 | 0.296156 | ||||||||
\(70\) | 2.26000e28 | 0.568970 | ||||||||
\(71\) | 2.83140e28 | 0.572133 | 0.286066 | − | 0.958210i | \(-0.407652\pi\) | ||||
0.286066 | + | 0.958210i | \(0.407652\pi\) | |||||||
\(72\) | 1.76668e28 | 0.287412 | ||||||||
\(73\) | 2.94533e28 | 0.386928 | 0.193464 | − | 0.981107i | \(-0.438028\pi\) | ||||
0.193464 | + | 0.981107i | \(0.438028\pi\) | |||||||
\(74\) | 8.01724e28 | 0.852969 | ||||||||
\(75\) | 1.00112e28 | 0.0865044 | ||||||||
\(76\) | 4.05948e28 | 0.285667 | ||||||||
\(77\) | 5.54623e29 | 3.18707 | ||||||||
\(78\) | 5.22793e28 | 0.245959 | ||||||||
\(79\) | −2.36152e29 | −0.911951 | −0.455976 | − | 0.889992i | \(-0.650710\pi\) | ||||
−0.455976 | + | 0.889992i | \(0.650710\pi\) | |||||||
\(80\) | −3.51844e28 | −0.111803 | ||||||||
\(81\) | 1.80753e29 | 0.473771 | ||||||||
\(82\) | −3.50626e29 | −0.759853 | ||||||||
\(83\) | 7.97795e29 | 1.43279 | 0.716393 | − | 0.697697i | \(-0.245792\pi\) | ||||
0.716393 | + | 0.697697i | \(0.245792\pi\) | |||||||
\(84\) | 2.60853e29 | 0.389105 | ||||||||
\(85\) | −3.54586e29 | −0.440280 | ||||||||
\(86\) | −2.22393e29 | −0.230353 | ||||||||
\(87\) | −9.21854e29 | −0.798204 | ||||||||
\(88\) | −8.63453e29 | −0.626264 | ||||||||
\(89\) | 1.17539e30 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(90\) | −5.02122e29 | −0.257069 | ||||||||
\(91\) | −3.35429e30 | −1.44697 | ||||||||
\(92\) | 9.40142e29 | 0.342359 | ||||||||
\(93\) | 2.30410e29 | 0.0709603 | ||||||||
\(94\) | 4.64740e30 | 1.21263 | ||||||||
\(95\) | −1.15377e30 | −0.255508 | ||||||||
\(96\) | −4.06104e29 | −0.0764598 | ||||||||
\(97\) | −3.02840e30 | −0.485570 | −0.242785 | − | 0.970080i | \(-0.578061\pi\) | ||||
−0.242785 | + | 0.970080i | \(0.578061\pi\) | |||||||
\(98\) | −1.15666e31 | −1.58198 | ||||||||
\(99\) | −1.23225e31 | −1.43997 | ||||||||
\(100\) | 1.00000e30 | 0.100000 | ||||||||
\(101\) | 1.24493e31 | 1.06699 | 0.533497 | − | 0.845802i | \(-0.320877\pi\) | ||||
0.533497 | + | 0.845802i | \(0.320877\pi\) | |||||||
\(102\) | −4.09270e30 | −0.301097 | ||||||||
\(103\) | 5.50424e30 | 0.348113 | 0.174056 | − | 0.984736i | \(-0.444312\pi\) | ||||
0.174056 | + | 0.984736i | \(0.444312\pi\) | |||||||
\(104\) | 5.22206e30 | 0.284331 | ||||||||
\(105\) | −7.41389e30 | −0.348026 | ||||||||
\(106\) | −1.72285e31 | −0.698242 | ||||||||
\(107\) | 2.87060e31 | 1.00583 | 0.502914 | − | 0.864336i | \(-0.332261\pi\) | ||||
0.502914 | + | 0.864336i | \(0.332261\pi\) | |||||||
\(108\) | −1.29249e31 | −0.392065 | ||||||||
\(109\) | −6.39739e31 | −1.68226 | −0.841128 | − | 0.540837i | \(-0.818108\pi\) | ||||
−0.841128 | + | 0.540837i | \(0.818108\pi\) | |||||||
\(110\) | 2.45408e31 | 0.560148 | ||||||||
\(111\) | −2.63004e31 | −0.521743 | ||||||||
\(112\) | 2.60560e31 | 0.449810 | ||||||||
\(113\) | −5.00616e31 | −0.752990 | −0.376495 | − | 0.926419i | \(-0.622871\pi\) | ||||
−0.376495 | + | 0.926419i | \(0.622871\pi\) | |||||||
\(114\) | −1.33170e31 | −0.174736 | ||||||||
\(115\) | −2.67204e31 | −0.306216 | ||||||||
\(116\) | −9.20819e31 | −0.922732 | ||||||||
\(117\) | 7.45249e31 | 0.653763 | ||||||||
\(118\) | −6.66985e31 | −0.512796 | ||||||||
\(119\) | 2.62592e32 | 1.77134 | ||||||||
\(120\) | 1.15422e31 | 0.0683877 | ||||||||
\(121\) | 4.10309e32 | 2.13765 | ||||||||
\(122\) | −2.14967e32 | −0.985812 | ||||||||
\(123\) | 1.15022e32 | 0.464786 | ||||||||
\(124\) | 2.30151e31 | 0.0820308 | ||||||||
\(125\) | −2.84217e31 | −0.0894427 | ||||||||
\(126\) | 3.71850e32 | 1.03425 | ||||||||
\(127\) | −1.96018e32 | −0.482324 | −0.241162 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241162 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(128\) | −4.05648e31 | −0.0883883 | ||||||||
\(129\) | 7.29555e31 | 0.140902 | ||||||||
\(130\) | −1.48420e32 | −0.254314 | ||||||||
\(131\) | 8.78188e32 | 1.33623 | 0.668117 | − | 0.744056i | \(-0.267101\pi\) | ||||
0.668117 | + | 0.744056i | \(0.267101\pi\) | |||||||
\(132\) | 2.83254e32 | 0.383072 | ||||||||
\(133\) | 8.54435e32 | 1.02797 | ||||||||
\(134\) | −7.09533e32 | −0.760061 | ||||||||
\(135\) | 3.67347e32 | 0.350674 | ||||||||
\(136\) | −4.08810e32 | −0.348072 | ||||||||
\(137\) | 1.58360e33 | 1.20359 | 0.601794 | − | 0.798651i | \(-0.294453\pi\) | ||||
0.601794 | + | 0.798651i | \(0.294453\pi\) | |||||||
\(138\) | −3.08412e32 | −0.209414 | ||||||||
\(139\) | 1.84495e31 | 0.0112009 | 0.00560047 | − | 0.999984i | \(-0.498217\pi\) | ||||
0.00560047 | + | 0.999984i | \(0.498217\pi\) | |||||||
\(140\) | −7.40557e32 | −0.402322 | ||||||||
\(141\) | −1.52457e33 | −0.741740 | ||||||||
\(142\) | −9.27793e32 | −0.404559 | ||||||||
\(143\) | −3.64234e33 | −1.42453 | ||||||||
\(144\) | −5.78907e32 | −0.203231 | ||||||||
\(145\) | 2.61713e33 | 0.825316 | ||||||||
\(146\) | −9.65126e32 | −0.273599 | ||||||||
\(147\) | 3.79441e33 | 0.967666 | ||||||||
\(148\) | −2.62709e33 | −0.603140 | ||||||||
\(149\) | 5.96260e32 | 0.123324 | 0.0616621 | − | 0.998097i | \(-0.480360\pi\) | ||||
0.0616621 | + | 0.998097i | \(0.480360\pi\) | |||||||
\(150\) | −3.28048e32 | −0.0611678 | ||||||||
\(151\) | −8.01584e33 | −1.34836 | −0.674180 | − | 0.738567i | \(-0.735503\pi\) | ||||
−0.674180 | + | 0.738567i | \(0.735503\pi\) | |||||||
\(152\) | −1.33021e33 | −0.201997 | ||||||||
\(153\) | −5.83420e33 | −0.800321 | ||||||||
\(154\) | −1.81739e34 | −2.25360 | ||||||||
\(155\) | −6.54129e32 | −0.0733706 | ||||||||
\(156\) | −1.71309e33 | −0.173919 | ||||||||
\(157\) | 5.03735e33 | 0.463189 | 0.231594 | − | 0.972812i | \(-0.425606\pi\) | ||||
0.231594 | + | 0.972812i | \(0.425606\pi\) | |||||||
\(158\) | 7.73823e33 | 0.644847 | ||||||||
\(159\) | 5.65177e33 | 0.427100 | ||||||||
\(160\) | 1.15292e33 | 0.0790569 | ||||||||
\(161\) | 1.97880e34 | 1.23197 | ||||||||
\(162\) | −5.92293e33 | −0.335007 | ||||||||
\(163\) | 2.60494e34 | 1.33933 | 0.669667 | − | 0.742661i | \(-0.266437\pi\) | ||||
0.669667 | + | 0.742661i | \(0.266437\pi\) | |||||||
\(164\) | 1.14893e34 | 0.537297 | ||||||||
\(165\) | −8.05057e33 | −0.342630 | ||||||||
\(166\) | −2.61422e34 | −1.01313 | ||||||||
\(167\) | 1.50501e34 | 0.531415 | 0.265708 | − | 0.964054i | \(-0.414394\pi\) | ||||
0.265708 | + | 0.964054i | \(0.414394\pi\) | |||||||
\(168\) | −8.54764e33 | −0.275139 | ||||||||
\(169\) | −1.20315e34 | −0.353245 | ||||||||
\(170\) | 1.16191e34 | 0.311325 | ||||||||
\(171\) | −1.89836e34 | −0.464451 | ||||||||
\(172\) | 7.28737e33 | 0.162884 | ||||||||
\(173\) | 2.58953e33 | 0.0529062 | 0.0264531 | − | 0.999650i | \(-0.491579\pi\) | ||||
0.0264531 | + | 0.999650i | \(0.491579\pi\) | |||||||
\(174\) | 3.02073e34 | 0.564415 | ||||||||
\(175\) | 2.10479e34 | 0.359848 | ||||||||
\(176\) | 2.82936e34 | 0.442836 | ||||||||
\(177\) | 2.18803e34 | 0.313666 | ||||||||
\(178\) | −3.85150e34 | −0.505965 | ||||||||
\(179\) | −8.17306e34 | −0.984380 | −0.492190 | − | 0.870488i | \(-0.663803\pi\) | ||||
−0.492190 | + | 0.870488i | \(0.663803\pi\) | |||||||
\(180\) | 1.64535e34 | 0.181775 | ||||||||
\(181\) | 2.40793e34 | 0.244133 | 0.122066 | − | 0.992522i | \(-0.461048\pi\) | ||||
0.122066 | + | 0.992522i | \(0.461048\pi\) | |||||||
\(182\) | 1.09913e35 | 1.02316 | ||||||||
\(183\) | 7.05195e34 | 0.603000 | ||||||||
\(184\) | −3.08066e34 | −0.242085 | ||||||||
\(185\) | 7.46664e34 | 0.539465 | ||||||||
\(186\) | −7.55007e33 | −0.0501765 | ||||||||
\(187\) | 2.85142e35 | 1.74388 | ||||||||
\(188\) | −1.52286e35 | −0.857460 | ||||||||
\(189\) | −2.72041e35 | −1.41084 | ||||||||
\(190\) | 3.78068e34 | 0.180671 | ||||||||
\(191\) | −1.66142e35 | −0.731916 | −0.365958 | − | 0.930631i | \(-0.619259\pi\) | ||||
−0.365958 | + | 0.930631i | \(0.619259\pi\) | |||||||
\(192\) | 1.33072e34 | 0.0540652 | ||||||||
\(193\) | 1.35705e35 | 0.508694 | 0.254347 | − | 0.967113i | \(-0.418140\pi\) | ||||
0.254347 | + | 0.967113i | \(0.418140\pi\) | |||||||
\(194\) | 9.92347e34 | 0.343350 | ||||||||
\(195\) | 4.86889e34 | 0.155558 | ||||||||
\(196\) | 3.79015e35 | 1.11863 | ||||||||
\(197\) | −1.30234e35 | −0.355220 | −0.177610 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177610 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(198\) | 4.03783e35 | 1.01821 | ||||||||
\(199\) | −5.17445e35 | −1.20682 | −0.603409 | − | 0.797432i | \(-0.706191\pi\) | ||||
−0.603409 | + | 0.797432i | \(0.706191\pi\) | |||||||
\(200\) | −3.27680e34 | −0.0707107 | ||||||||
\(201\) | 2.32761e35 | 0.464913 | ||||||||
\(202\) | −4.07937e35 | −0.754479 | ||||||||
\(203\) | −1.93813e36 | −3.32043 | ||||||||
\(204\) | 1.34110e35 | 0.212908 | ||||||||
\(205\) | −3.26546e35 | −0.480573 | ||||||||
\(206\) | −1.80363e35 | −0.246153 | ||||||||
\(207\) | −4.39646e35 | −0.556625 | ||||||||
\(208\) | −1.71116e35 | −0.201053 | ||||||||
\(209\) | 9.27811e35 | 1.01203 | ||||||||
\(210\) | 2.42938e35 | 0.246092 | ||||||||
\(211\) | −1.18735e36 | −1.11738 | −0.558689 | − | 0.829377i | \(-0.688695\pi\) | ||||
−0.558689 | + | 0.829377i | \(0.688695\pi\) | |||||||
\(212\) | 5.64543e35 | 0.493732 | ||||||||
\(213\) | 3.04361e35 | 0.247460 | ||||||||
\(214\) | −9.40638e35 | −0.711228 | ||||||||
\(215\) | −2.07119e35 | −0.145688 | ||||||||
\(216\) | 4.23522e35 | 0.277232 | ||||||||
\(217\) | 4.84420e35 | 0.295186 | ||||||||
\(218\) | 2.09630e36 | 1.18953 | ||||||||
\(219\) | 3.16608e35 | 0.167355 | ||||||||
\(220\) | −8.04154e35 | −0.396084 | ||||||||
\(221\) | −1.72450e36 | −0.791742 | ||||||||
\(222\) | 8.61812e35 | 0.368928 | ||||||||
\(223\) | 2.87825e35 | 0.114922 | 0.0574611 | − | 0.998348i | \(-0.481699\pi\) | ||||
0.0574611 | + | 0.998348i | \(0.481699\pi\) | |||||||
\(224\) | −8.53804e35 | −0.318064 | ||||||||
\(225\) | −4.67638e35 | −0.162585 | ||||||||
\(226\) | 1.64042e36 | 0.532444 | ||||||||
\(227\) | 3.90915e36 | 1.18490 | 0.592450 | − | 0.805607i | \(-0.298161\pi\) | ||||
0.592450 | + | 0.805607i | \(0.298161\pi\) | |||||||
\(228\) | 4.36373e35 | 0.123557 | ||||||||
\(229\) | −9.35252e35 | −0.247445 | −0.123723 | − | 0.992317i | \(-0.539483\pi\) | ||||
−0.123723 | + | 0.992317i | \(0.539483\pi\) | |||||||
\(230\) | 8.75576e35 | 0.216527 | ||||||||
\(231\) | 5.96191e36 | 1.37848 | ||||||||
\(232\) | 3.01734e36 | 0.652470 | ||||||||
\(233\) | 2.81203e36 | 0.568856 | 0.284428 | − | 0.958697i | \(-0.408196\pi\) | ||||
0.284428 | + | 0.958697i | \(0.408196\pi\) | |||||||
\(234\) | −2.44203e36 | −0.462280 | ||||||||
\(235\) | 4.32823e36 | 0.766935 | ||||||||
\(236\) | 2.18558e36 | 0.362602 | ||||||||
\(237\) | −2.53851e36 | −0.394439 | ||||||||
\(238\) | −8.60460e36 | −1.25253 | ||||||||
\(239\) | 9.22821e36 | 1.25878 | 0.629391 | − | 0.777089i | \(-0.283305\pi\) | ||||
0.629391 | + | 0.777089i | \(0.283305\pi\) | |||||||
\(240\) | −3.78214e35 | −0.0483574 | ||||||||
\(241\) | −2.25483e36 | −0.270303 | −0.135151 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135151 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(242\) | −1.34450e37 | −1.51155 | ||||||||
\(243\) | 9.37808e36 | 0.989046 | ||||||||
\(244\) | 7.04403e36 | 0.697074 | ||||||||
\(245\) | −1.07723e37 | −1.00053 | ||||||||
\(246\) | −3.76905e36 | −0.328653 | ||||||||
\(247\) | −5.61128e36 | −0.459472 | ||||||||
\(248\) | −7.54159e35 | −0.0580046 | ||||||||
\(249\) | 8.57589e36 | 0.619711 | ||||||||
\(250\) | 9.31323e35 | 0.0632456 | ||||||||
\(251\) | −1.87833e37 | −1.19903 | −0.599515 | − | 0.800364i | \(-0.704640\pi\) | ||||
−0.599515 | + | 0.800364i | \(0.704640\pi\) | |||||||
\(252\) | −1.21848e37 | −0.731323 | ||||||||
\(253\) | 2.14873e37 | 1.21287 | ||||||||
\(254\) | 6.42312e36 | 0.341054 | ||||||||
\(255\) | −3.81162e36 | −0.190431 | ||||||||
\(256\) | 1.32923e36 | 0.0625000 | ||||||||
\(257\) | −1.96277e37 | −0.868773 | −0.434386 | − | 0.900727i | \(-0.643035\pi\) | ||||
−0.434386 | + | 0.900727i | \(0.643035\pi\) | |||||||
\(258\) | −2.39061e36 | −0.0996329 | ||||||||
\(259\) | −5.52947e37 | −2.17039 | ||||||||
\(260\) | 4.86342e36 | 0.179827 | ||||||||
\(261\) | 4.30610e37 | 1.50022 | ||||||||
\(262\) | −2.87765e37 | −0.944860 | ||||||||
\(263\) | 1.77659e37 | 0.549886 | 0.274943 | − | 0.961461i | \(-0.411341\pi\) | ||||
0.274943 | + | 0.961461i | \(0.411341\pi\) | |||||||
\(264\) | −9.28168e36 | −0.270873 | ||||||||
\(265\) | −1.60453e37 | −0.441607 | ||||||||
\(266\) | −2.79981e37 | −0.726881 | ||||||||
\(267\) | 1.26348e37 | 0.309488 | ||||||||
\(268\) | 2.32500e37 | 0.537444 | ||||||||
\(269\) | 4.11974e37 | 0.898897 | 0.449449 | − | 0.893306i | \(-0.351621\pi\) | ||||
0.449449 | + | 0.893306i | \(0.351621\pi\) | |||||||
\(270\) | −1.20372e37 | −0.247964 | ||||||||
\(271\) | 2.67128e37 | 0.519631 | 0.259816 | − | 0.965658i | \(-0.416338\pi\) | ||||
0.259816 | + | 0.965658i | \(0.416338\pi\) | |||||||
\(272\) | 1.33959e37 | 0.246124 | ||||||||
\(273\) | −3.60569e37 | −0.625846 | ||||||||
\(274\) | −5.18915e37 | −0.851065 | ||||||||
\(275\) | 2.28554e37 | 0.354268 | ||||||||
\(276\) | 1.01060e37 | 0.148078 | ||||||||
\(277\) | −1.71079e37 | −0.237007 | −0.118503 | − | 0.992954i | \(-0.537810\pi\) | ||||
−0.118503 | + | 0.992954i | \(0.537810\pi\) | |||||||
\(278\) | −6.04552e35 | −0.00792025 | ||||||||
\(279\) | −1.07627e37 | −0.133370 | ||||||||
\(280\) | 2.42666e37 | 0.284485 | ||||||||
\(281\) | −8.17662e37 | −0.907038 | −0.453519 | − | 0.891247i | \(-0.649832\pi\) | ||||
−0.453519 | + | 0.891247i | \(0.649832\pi\) | |||||||
\(282\) | 4.99572e37 | 0.524490 | ||||||||
\(283\) | 3.56430e36 | 0.0354229 | 0.0177115 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177115 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(284\) | 3.04019e37 | 0.286066 | ||||||||
\(285\) | −1.24025e37 | −0.110513 | ||||||||
\(286\) | 1.19352e38 | 1.00730 | ||||||||
\(287\) | 2.41826e38 | 1.93345 | ||||||||
\(288\) | 1.89696e37 | 0.143706 | ||||||||
\(289\) | −4.28571e36 | −0.0307685 | ||||||||
\(290\) | −8.57580e37 | −0.583587 | ||||||||
\(291\) | −3.25538e37 | −0.210020 | ||||||||
\(292\) | 3.16253e37 | 0.193464 | ||||||||
\(293\) | 1.72791e38 | 1.00248 | 0.501238 | − | 0.865310i | \(-0.332878\pi\) | ||||
0.501238 | + | 0.865310i | \(0.332878\pi\) | |||||||
\(294\) | −1.24335e38 | −0.684243 | ||||||||
\(295\) | −6.21178e37 | −0.324321 | ||||||||
\(296\) | 8.60844e37 | 0.426484 | ||||||||
\(297\) | −2.95403e38 | −1.38896 | ||||||||
\(298\) | −1.95383e37 | −0.0872034 | ||||||||
\(299\) | −1.29953e38 | −0.550658 | ||||||||
\(300\) | 1.07495e37 | 0.0432522 | ||||||||
\(301\) | 1.53384e38 | 0.586136 | ||||||||
\(302\) | 2.62663e38 | 0.953435 | ||||||||
\(303\) | 1.33823e38 | 0.461499 | ||||||||
\(304\) | 4.35883e37 | 0.142833 | ||||||||
\(305\) | −2.00203e38 | −0.623482 | ||||||||
\(306\) | 1.91175e38 | 0.565912 | ||||||||
\(307\) | −1.39185e38 | −0.391694 | −0.195847 | − | 0.980634i | \(-0.562746\pi\) | ||||
−0.195847 | + | 0.980634i | \(0.562746\pi\) | |||||||
\(308\) | 5.95522e38 | 1.59353 | ||||||||
\(309\) | 5.91677e37 | 0.150567 | ||||||||
\(310\) | 2.14345e37 | 0.0518809 | ||||||||
\(311\) | −7.23579e37 | −0.166610 | −0.0833048 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833048 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(312\) | 5.61344e37 | 0.122980 | ||||||||
\(313\) | −7.16835e38 | −1.49445 | −0.747226 | − | 0.664570i | \(-0.768615\pi\) | ||||
−0.747226 | + | 0.664570i | \(0.768615\pi\) | |||||||
\(314\) | −1.65064e38 | −0.327524 | ||||||||
\(315\) | 3.46312e38 | 0.654115 | ||||||||
\(316\) | −2.53566e38 | −0.455976 | ||||||||
\(317\) | 1.01778e39 | 1.74275 | 0.871373 | − | 0.490620i | \(-0.163230\pi\) | ||||
0.871373 | + | 0.490620i | \(0.163230\pi\) | |||||||
\(318\) | −1.85197e38 | −0.302005 | ||||||||
\(319\) | −2.10457e39 | −3.26895 | ||||||||
\(320\) | −3.77789e37 | −0.0559017 | ||||||||
\(321\) | 3.08575e38 | 0.435043 | ||||||||
\(322\) | −6.48414e38 | −0.871137 | ||||||||
\(323\) | 4.39281e38 | 0.562475 | ||||||||
\(324\) | 1.94083e38 | 0.236886 | ||||||||
\(325\) | −1.38227e38 | −0.160842 | ||||||||
\(326\) | −8.53585e38 | −0.947053 | ||||||||
\(327\) | −6.87686e38 | −0.727612 | ||||||||
\(328\) | −3.76482e38 | −0.379926 | ||||||||
\(329\) | −3.20530e39 | −3.08555 | ||||||||
\(330\) | 2.63801e38 | 0.242276 | ||||||||
\(331\) | 1.30666e39 | 1.14506 | 0.572529 | − | 0.819885i | \(-0.305963\pi\) | ||||
0.572529 | + | 0.819885i | \(0.305963\pi\) | |||||||
\(332\) | 8.56626e38 | 0.716393 | ||||||||
\(333\) | 1.22853e39 | 0.980615 | ||||||||
\(334\) | −4.93161e38 | −0.375767 | ||||||||
\(335\) | −6.60805e38 | −0.480705 | ||||||||
\(336\) | 2.80089e38 | 0.194553 | ||||||||
\(337\) | 1.56627e39 | 1.03897 | 0.519486 | − | 0.854479i | \(-0.326123\pi\) | ||||
0.519486 | + | 0.854479i | \(0.326123\pi\) | |||||||
\(338\) | 3.94248e38 | 0.249782 | ||||||||
\(339\) | −5.38137e38 | −0.325685 | ||||||||
\(340\) | −3.80734e38 | −0.220140 | ||||||||
\(341\) | 5.26020e38 | 0.290609 | ||||||||
\(342\) | 6.22056e38 | 0.328416 | ||||||||
\(343\) | 4.41174e39 | 2.22614 | ||||||||
\(344\) | −2.38792e38 | −0.115177 | ||||||||
\(345\) | −2.87231e38 | −0.132445 | ||||||||
\(346\) | −8.48537e37 | −0.0374103 | ||||||||
\(347\) | −1.53164e39 | −0.645726 | −0.322863 | − | 0.946446i | \(-0.604645\pi\) | ||||
−0.322863 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(348\) | −9.89833e38 | −0.399102 | ||||||||
\(349\) | 2.63344e39 | 1.01562 | 0.507808 | − | 0.861470i | \(-0.330456\pi\) | ||||
0.507808 | + | 0.861470i | \(0.330456\pi\) | |||||||
\(350\) | −6.89698e38 | −0.254451 | ||||||||
\(351\) | 1.78656e39 | 0.630606 | ||||||||
\(352\) | −9.27126e38 | −0.313132 | ||||||||
\(353\) | 4.56209e39 | 1.47454 | 0.737269 | − | 0.675600i | \(-0.236115\pi\) | ||||
0.737269 | + | 0.675600i | \(0.236115\pi\) | |||||||
\(354\) | −7.16974e38 | −0.221796 | ||||||||
\(355\) | −8.64075e38 | −0.255866 | ||||||||
\(356\) | 1.26206e39 | 0.357771 | ||||||||
\(357\) | 2.82272e39 | 0.766145 | ||||||||
\(358\) | 2.67815e39 | 0.696062 | ||||||||
\(359\) | 2.02315e39 | 0.503575 | 0.251787 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251787 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(360\) | −5.39149e38 | −0.128535 | ||||||||
\(361\) | −2.94951e39 | −0.673578 | ||||||||
\(362\) | −7.89031e38 | −0.172628 | ||||||||
\(363\) | 4.41061e39 | 0.924582 | ||||||||
\(364\) | −3.60164e39 | −0.723484 | ||||||||
\(365\) | −8.98844e38 | −0.173039 | ||||||||
\(366\) | −2.31078e39 | −0.426385 | ||||||||
\(367\) | −1.03029e40 | −1.82237 | −0.911185 | − | 0.411998i | \(-0.864831\pi\) | ||||
−0.911185 | + | 0.411998i | \(0.864831\pi\) | |||||||
\(368\) | 1.00947e39 | 0.171180 | ||||||||
\(369\) | −5.37284e39 | −0.873564 | ||||||||
\(370\) | −2.44667e39 | −0.381459 | ||||||||
\(371\) | 1.18824e40 | 1.77668 | ||||||||
\(372\) | 2.47401e38 | 0.0354801 | ||||||||
\(373\) | −4.89843e39 | −0.673860 | −0.336930 | − | 0.941530i | \(-0.609389\pi\) | ||||
−0.336930 | + | 0.941530i | \(0.609389\pi\) | |||||||
\(374\) | −9.34353e39 | −1.23311 | ||||||||
\(375\) | −3.05519e38 | −0.0386859 | ||||||||
\(376\) | 4.99011e39 | 0.606316 | ||||||||
\(377\) | 1.27282e40 | 1.48414 | ||||||||
\(378\) | 8.91425e39 | 0.997613 | ||||||||
\(379\) | −1.32326e40 | −1.42147 | −0.710737 | − | 0.703458i | \(-0.751638\pi\) | ||||
−0.710737 | + | 0.703458i | \(0.751638\pi\) | |||||||
\(380\) | −1.23885e39 | −0.127754 | ||||||||
\(381\) | −2.10709e39 | −0.208616 | ||||||||
\(382\) | 5.44413e39 | 0.517543 | ||||||||
\(383\) | 2.21210e39 | 0.201940 | 0.100970 | − | 0.994889i | \(-0.467805\pi\) | ||||
0.100970 | + | 0.994889i | \(0.467805\pi\) | |||||||
\(384\) | −4.36051e38 | −0.0382299 | ||||||||
\(385\) | −1.69257e40 | −1.42530 | ||||||||
\(386\) | −4.44677e39 | −0.359701 | ||||||||
\(387\) | −3.40785e39 | −0.264826 | ||||||||
\(388\) | −3.25172e39 | −0.242785 | ||||||||
\(389\) | −1.98512e40 | −1.42419 | −0.712096 | − | 0.702082i | \(-0.752254\pi\) | ||||
−0.712096 | + | 0.702082i | \(0.752254\pi\) | |||||||
\(390\) | −1.59544e39 | −0.109996 | ||||||||
\(391\) | 1.01734e40 | 0.674103 | ||||||||
\(392\) | −1.24196e40 | −0.790992 | ||||||||
\(393\) | 9.44007e39 | 0.577950 | ||||||||
\(394\) | 4.26750e39 | 0.251178 | ||||||||
\(395\) | 7.20679e39 | 0.407837 | ||||||||
\(396\) | −1.32312e40 | −0.719984 | ||||||||
\(397\) | 4.66363e39 | 0.244046 | 0.122023 | − | 0.992527i | \(-0.461062\pi\) | ||||
0.122023 | + | 0.992527i | \(0.461062\pi\) | |||||||
\(398\) | 1.69556e40 | 0.853349 | ||||||||
\(399\) | 9.18474e39 | 0.444618 | ||||||||
\(400\) | 1.07374e39 | 0.0500000 | ||||||||
\(401\) | −1.07728e40 | −0.482605 | −0.241303 | − | 0.970450i | \(-0.577575\pi\) | ||||
−0.241303 | + | 0.970450i | \(0.577575\pi\) | |||||||
\(402\) | −7.62712e39 | −0.328743 | ||||||||
\(403\) | −3.18130e39 | −0.131940 | ||||||||
\(404\) | 1.33673e40 | 0.533497 | ||||||||
\(405\) | −5.51616e39 | −0.211877 | ||||||||
\(406\) | 6.35087e40 | 2.34790 | ||||||||
\(407\) | −6.00432e40 | −2.13674 | ||||||||
\(408\) | −4.39450e39 | −0.150549 | ||||||||
\(409\) | −1.59543e40 | −0.526219 | −0.263110 | − | 0.964766i | \(-0.584748\pi\) | ||||
−0.263110 | + | 0.964766i | \(0.584748\pi\) | |||||||
\(410\) | 1.07003e40 | 0.339817 | ||||||||
\(411\) | 1.70229e40 | 0.520578 | ||||||||
\(412\) | 5.91013e39 | 0.174056 | ||||||||
\(413\) | 4.60018e40 | 1.30481 | ||||||||
\(414\) | 1.44063e40 | 0.393593 | ||||||||
\(415\) | −2.43468e40 | −0.640761 | ||||||||
\(416\) | 5.60714e39 | 0.142166 | ||||||||
\(417\) | 1.98322e38 | 0.00484465 | ||||||||
\(418\) | −3.04025e40 | −0.715611 | ||||||||
\(419\) | −5.46661e40 | −1.23994 | −0.619971 | − | 0.784625i | \(-0.712855\pi\) | ||||
−0.619971 | + | 0.784625i | \(0.712855\pi\) | |||||||
\(420\) | −7.96061e39 | −0.174013 | ||||||||
\(421\) | −2.46945e40 | −0.520270 | −0.260135 | − | 0.965572i | \(-0.583767\pi\) | ||||
−0.260135 | + | 0.965572i | \(0.583767\pi\) | |||||||
\(422\) | 3.89070e40 | 0.790105 | ||||||||
\(423\) | 7.12147e40 | 1.39410 | ||||||||
\(424\) | −1.84989e40 | −0.349121 | ||||||||
\(425\) | 1.08211e40 | 0.196899 | ||||||||
\(426\) | −9.97330e39 | −0.174981 | ||||||||
\(427\) | 1.48262e41 | 2.50841 | ||||||||
\(428\) | 3.08228e40 | 0.502914 | ||||||||
\(429\) | −3.91533e40 | −0.616142 | ||||||||
\(430\) | 6.78689e39 | 0.103017 | ||||||||
\(431\) | 4.73716e40 | 0.693618 | 0.346809 | − | 0.937936i | \(-0.387265\pi\) | ||||
0.346809 | + | 0.937936i | \(0.387265\pi\) | |||||||
\(432\) | −1.38780e40 | −0.196032 | ||||||||
\(433\) | −3.30096e38 | −0.00449860 | −0.00224930 | − | 0.999997i | \(-0.500716\pi\) | ||||
−0.00224930 | + | 0.999997i | \(0.500716\pi\) | |||||||
\(434\) | −1.58735e40 | −0.208728 | ||||||||
\(435\) | 2.81327e40 | 0.356967 | ||||||||
\(436\) | −6.86914e40 | −0.841128 | ||||||||
\(437\) | 3.31027e40 | 0.391203 | ||||||||
\(438\) | −1.03746e40 | −0.118338 | ||||||||
\(439\) | −1.10291e39 | −0.0121434 | −0.00607170 | − | 0.999982i | \(-0.501933\pi\) | ||||
−0.00607170 | + | 0.999982i | \(0.501933\pi\) | |||||||
\(440\) | 2.63505e40 | 0.280074 | ||||||||
\(441\) | −1.77242e41 | −1.81873 | ||||||||
\(442\) | 5.65085e40 | 0.559846 | ||||||||
\(443\) | −1.21843e41 | −1.16558 | −0.582791 | − | 0.812622i | \(-0.698039\pi\) | ||||
−0.582791 | + | 0.812622i | \(0.698039\pi\) | |||||||
\(444\) | −2.82399e40 | −0.260871 | ||||||||
\(445\) | −3.58699e40 | −0.320000 | ||||||||
\(446\) | −9.43146e39 | −0.0812622 | ||||||||
\(447\) | 6.40949e39 | 0.0533405 | ||||||||
\(448\) | 2.79775e40 | 0.224905 | ||||||||
\(449\) | 1.34618e41 | 1.04540 | 0.522702 | − | 0.852515i | \(-0.324924\pi\) | ||||
0.522702 | + | 0.852515i | \(0.324924\pi\) | |||||||
\(450\) | 1.53235e40 | 0.114965 | ||||||||
\(451\) | 2.62593e41 | 1.90347 | ||||||||
\(452\) | −5.37533e40 | −0.376495 | ||||||||
\(453\) | −8.61661e40 | −0.583196 | ||||||||
\(454\) | −1.28095e41 | −0.837851 | ||||||||
\(455\) | 1.02365e41 | 0.647104 | ||||||||
\(456\) | −1.42991e40 | −0.0873681 | ||||||||
\(457\) | 6.73134e40 | 0.397558 | 0.198779 | − | 0.980044i | \(-0.436302\pi\) | ||||
0.198779 | + | 0.980044i | \(0.436302\pi\) | |||||||
\(458\) | 3.06463e40 | 0.174970 | ||||||||
\(459\) | −1.39862e41 | −0.771972 | ||||||||
\(460\) | −2.86909e40 | −0.153108 | ||||||||
\(461\) | −3.76769e41 | −1.94407 | −0.972033 | − | 0.234842i | \(-0.924543\pi\) | ||||
−0.972033 | + | 0.234842i | \(0.924543\pi\) | |||||||
\(462\) | −1.95360e41 | −0.974731 | ||||||||
\(463\) | −3.37703e41 | −1.62941 | −0.814704 | − | 0.579877i | \(-0.803100\pi\) | ||||
−0.814704 | + | 0.579877i | \(0.803100\pi\) | |||||||
\(464\) | −9.88722e40 | −0.461366 | ||||||||
\(465\) | −7.03155e39 | −0.0317344 | ||||||||
\(466\) | −9.21445e40 | −0.402242 | ||||||||
\(467\) | −1.12227e41 | −0.473900 | −0.236950 | − | 0.971522i | \(-0.576148\pi\) | ||||
−0.236950 | + | 0.971522i | \(0.576148\pi\) | |||||||
\(468\) | 8.00205e40 | 0.326881 | ||||||||
\(469\) | 4.89364e41 | 1.93398 | ||||||||
\(470\) | −1.41828e41 | −0.542305 | ||||||||
\(471\) | 5.41490e40 | 0.200339 | ||||||||
\(472\) | −7.16169e40 | −0.256398 | ||||||||
\(473\) | 1.66556e41 | 0.577048 | ||||||||
\(474\) | 8.31820e40 | 0.278911 | ||||||||
\(475\) | 3.52104e40 | 0.114267 | ||||||||
\(476\) | 2.81956e41 | 0.885672 | ||||||||
\(477\) | −2.64001e41 | −0.802734 | ||||||||
\(478\) | −3.02390e41 | −0.890093 | ||||||||
\(479\) | 9.96622e40 | 0.284008 | 0.142004 | − | 0.989866i | \(-0.454645\pi\) | ||||
0.142004 | + | 0.989866i | \(0.454645\pi\) | |||||||
\(480\) | 1.23933e40 | 0.0341939 | ||||||||
\(481\) | 3.63134e41 | 0.970104 | ||||||||
\(482\) | 7.38864e40 | 0.191133 | ||||||||
\(483\) | 2.12711e41 | 0.532856 | ||||||||
\(484\) | 4.40565e41 | 1.06883 | ||||||||
\(485\) | 9.24195e40 | 0.217153 | ||||||||
\(486\) | −3.07301e41 | −0.699361 | ||||||||
\(487\) | 1.24135e41 | 0.273650 | 0.136825 | − | 0.990595i | \(-0.456310\pi\) | ||||
0.136825 | + | 0.990595i | \(0.456310\pi\) | |||||||
\(488\) | −2.30819e41 | −0.492906 | ||||||||
\(489\) | 2.80017e41 | 0.579292 | ||||||||
\(490\) | 3.52985e41 | 0.707485 | ||||||||
\(491\) | 2.86826e40 | 0.0557000 | 0.0278500 | − | 0.999612i | \(-0.491134\pi\) | ||||
0.0278500 | + | 0.999612i | \(0.491134\pi\) | |||||||
\(492\) | 1.23504e41 | 0.232393 | ||||||||
\(493\) | −9.96429e41 | −1.81685 | ||||||||
\(494\) | 1.83871e41 | 0.324896 | ||||||||
\(495\) | 3.76052e41 | 0.643973 | ||||||||
\(496\) | 2.47123e40 | 0.0410154 | ||||||||
\(497\) | 6.39897e41 | 1.02940 | ||||||||
\(498\) | −2.81015e41 | −0.438202 | ||||||||
\(499\) | 9.27513e41 | 1.40204 | 0.701022 | − | 0.713140i | \(-0.252728\pi\) | ||||
0.701022 | + | 0.713140i | \(0.252728\pi\) | |||||||
\(500\) | −3.05176e40 | −0.0447214 | ||||||||
\(501\) | 1.61781e41 | 0.229849 | ||||||||
\(502\) | 6.15492e41 | 0.847842 | ||||||||
\(503\) | 2.27661e41 | 0.304078 | 0.152039 | − | 0.988375i | \(-0.451416\pi\) | ||||
0.152039 | + | 0.988375i | \(0.451416\pi\) | |||||||
\(504\) | 3.99271e41 | 0.517124 | ||||||||
\(505\) | −3.79921e41 | −0.477175 | ||||||||
\(506\) | −7.04097e41 | −0.857630 | ||||||||
\(507\) | −1.29332e41 | −0.152786 | ||||||||
\(508\) | −2.10473e41 | −0.241162 | ||||||||
\(509\) | −4.37667e40 | −0.0486427 | −0.0243214 | − | 0.999704i | \(-0.507742\pi\) | ||||
−0.0243214 | + | 0.999704i | \(0.507742\pi\) | |||||||
\(510\) | 1.24899e41 | 0.134655 | ||||||||
\(511\) | 6.65645e41 | 0.696176 | ||||||||
\(512\) | −4.35561e40 | −0.0441942 | ||||||||
\(513\) | −4.55089e41 | −0.447999 | ||||||||
\(514\) | 6.43161e41 | 0.614315 | ||||||||
\(515\) | −1.67976e41 | −0.155681 | ||||||||
\(516\) | 7.83354e40 | 0.0704511 | ||||||||
\(517\) | −3.48056e42 | −3.03771 | ||||||||
\(518\) | 1.81190e42 | 1.53470 | ||||||||
\(519\) | 2.78361e40 | 0.0228831 | ||||||||
\(520\) | −1.59365e41 | −0.127157 | ||||||||
\(521\) | −1.96331e42 | −1.52057 | −0.760283 | − | 0.649592i | \(-0.774940\pi\) | ||||
−0.760283 | + | 0.649592i | \(0.774940\pi\) | |||||||
\(522\) | −1.41102e42 | −1.06082 | ||||||||
\(523\) | −1.34397e42 | −0.980874 | −0.490437 | − | 0.871477i | \(-0.663163\pi\) | ||||
−0.490437 | + | 0.871477i | \(0.663163\pi\) | |||||||
\(524\) | 9.42947e41 | 0.668117 | ||||||||
\(525\) | 2.26254e41 | 0.155642 | ||||||||
\(526\) | −5.82152e41 | −0.388828 | ||||||||
\(527\) | 2.49049e41 | 0.161518 | ||||||||
\(528\) | 3.04142e41 | 0.191536 | ||||||||
\(529\) | −8.68537e41 | −0.531160 | ||||||||
\(530\) | 5.25772e41 | 0.312263 | ||||||||
\(531\) | −1.02206e42 | −0.589536 | ||||||||
\(532\) | 9.17443e41 | 0.513983 | ||||||||
\(533\) | −1.58813e42 | −0.864200 | ||||||||
\(534\) | −4.14017e41 | −0.218841 | ||||||||
\(535\) | −8.76038e41 | −0.449820 | ||||||||
\(536\) | −7.61856e41 | −0.380031 | ||||||||
\(537\) | −8.78562e41 | −0.425766 | ||||||||
\(538\) | −1.34996e42 | −0.635616 | ||||||||
\(539\) | 8.66255e42 | 3.96296 | ||||||||
\(540\) | 3.94436e41 | 0.175337 | ||||||||
\(541\) | −5.23970e40 | −0.0226333 | −0.0113167 | − | 0.999936i | \(-0.503602\pi\) | ||||
−0.0113167 | + | 0.999936i | \(0.503602\pi\) | |||||||
\(542\) | −8.75325e41 | −0.367435 | ||||||||
\(543\) | 2.58840e41 | 0.105593 | ||||||||
\(544\) | −4.38957e41 | −0.174036 | ||||||||
\(545\) | 1.95233e42 | 0.752327 | ||||||||
\(546\) | 1.18151e42 | 0.442540 | ||||||||
\(547\) | 6.69118e41 | 0.243612 | 0.121806 | − | 0.992554i | \(-0.461131\pi\) | ||||
0.121806 | + | 0.992554i | \(0.461131\pi\) | |||||||
\(548\) | 1.70038e42 | 0.601794 | ||||||||
\(549\) | −3.29405e42 | −1.13334 | ||||||||
\(550\) | −7.48926e41 | −0.250506 | ||||||||
\(551\) | −3.24224e42 | −1.05437 | ||||||||
\(552\) | −3.31155e41 | −0.104707 | ||||||||
\(553\) | −5.33704e42 | −1.64082 | ||||||||
\(554\) | 5.60593e41 | 0.167589 | ||||||||
\(555\) | 8.02625e41 | 0.233330 | ||||||||
\(556\) | 1.98099e40 | 0.00560047 | ||||||||
\(557\) | 6.32573e42 | 1.73922 | 0.869612 | − | 0.493736i | \(-0.164369\pi\) | ||||
0.869612 | + | 0.493736i | \(0.164369\pi\) | |||||||
\(558\) | 3.52673e41 | 0.0943067 | ||||||||
\(559\) | −1.00731e42 | −0.261987 | ||||||||
\(560\) | −7.95167e41 | −0.201161 | ||||||||
\(561\) | 3.06513e42 | 0.754266 | ||||||||
\(562\) | 2.67931e42 | 0.641373 | ||||||||
\(563\) | 2.31235e42 | 0.538485 | 0.269242 | − | 0.963072i | \(-0.413227\pi\) | ||||
0.269242 | + | 0.963072i | \(0.413227\pi\) | |||||||
\(564\) | −1.63700e42 | −0.370870 | ||||||||
\(565\) | 1.52776e42 | 0.336747 | ||||||||
\(566\) | −1.16795e41 | −0.0250478 | ||||||||
\(567\) | 4.08503e42 | 0.852428 | ||||||||
\(568\) | −9.96210e41 | −0.202279 | ||||||||
\(569\) | −4.99520e42 | −0.986990 | −0.493495 | − | 0.869749i | \(-0.664281\pi\) | ||||
−0.493495 | + | 0.869749i | \(0.664281\pi\) | |||||||
\(570\) | 4.06404e41 | 0.0781444 | ||||||||
\(571\) | 2.08977e42 | 0.391056 | 0.195528 | − | 0.980698i | \(-0.437358\pi\) | ||||
0.195528 | + | 0.980698i | \(0.437358\pi\) | |||||||
\(572\) | −3.91094e42 | −0.712266 | ||||||||
\(573\) | −1.78594e42 | −0.316570 | ||||||||
\(574\) | −7.92416e42 | −1.36716 | ||||||||
\(575\) | 8.15443e41 | 0.136944 | ||||||||
\(576\) | −6.21597e41 | −0.101616 | ||||||||
\(577\) | −3.85855e42 | −0.614044 | −0.307022 | − | 0.951702i | \(-0.599333\pi\) | ||||
−0.307022 | + | 0.951702i | \(0.599333\pi\) | |||||||
\(578\) | 1.40434e41 | 0.0217566 | ||||||||
\(579\) | 1.45875e42 | 0.220021 | ||||||||
\(580\) | 2.81012e42 | 0.412658 | ||||||||
\(581\) | 1.80302e43 | 2.57792 | ||||||||
\(582\) | 1.06672e42 | 0.148506 | ||||||||
\(583\) | 1.29029e43 | 1.74914 | ||||||||
\(584\) | −1.03630e42 | −0.136800 | ||||||||
\(585\) | −2.27432e42 | −0.292372 | ||||||||
\(586\) | −5.66203e42 | −0.708857 | ||||||||
\(587\) | 9.46507e42 | 1.15407 | 0.577037 | − | 0.816718i | \(-0.304209\pi\) | ||||
0.577037 | + | 0.816718i | \(0.304209\pi\) | |||||||
\(588\) | 4.07422e42 | 0.483833 | ||||||||
\(589\) | 8.10371e41 | 0.0937339 | ||||||||
\(590\) | 2.03548e42 | 0.229329 | ||||||||
\(591\) | −1.39995e42 | −0.153640 | ||||||||
\(592\) | −2.82082e42 | −0.301570 | ||||||||
\(593\) | −1.21956e43 | −1.27015 | −0.635075 | − | 0.772450i | \(-0.719031\pi\) | ||||
−0.635075 | + | 0.772450i | \(0.719031\pi\) | |||||||
\(594\) | 9.67978e42 | 0.982145 | ||||||||
\(595\) | −8.01366e42 | −0.792169 | ||||||||
\(596\) | 6.40229e41 | 0.0616621 | ||||||||
\(597\) | −5.56227e42 | −0.521975 | ||||||||
\(598\) | 4.25829e42 | 0.389374 | ||||||||
\(599\) | 4.86657e42 | 0.433618 | 0.216809 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216809 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(600\) | −3.52239e41 | −0.0305839 | ||||||||
\(601\) | −1.25867e43 | −1.06502 | −0.532508 | − | 0.846425i | \(-0.678750\pi\) | ||||
−0.532508 | + | 0.846425i | \(0.678750\pi\) | |||||||
\(602\) | −5.02608e42 | −0.414461 | ||||||||
\(603\) | −1.08726e43 | −0.873804 | ||||||||
\(604\) | −8.60694e42 | −0.674180 | ||||||||
\(605\) | −1.25216e43 | −0.955988 | ||||||||
\(606\) | −4.38512e42 | −0.326329 | ||||||||
\(607\) | 1.81008e43 | 1.31303 | 0.656513 | − | 0.754315i | \(-0.272031\pi\) | ||||
0.656513 | + | 0.754315i | \(0.272031\pi\) | |||||||
\(608\) | −1.42830e42 | −0.100998 | ||||||||
\(609\) | −2.08339e43 | −1.43616 | ||||||||
\(610\) | 6.56027e42 | 0.440868 | ||||||||
\(611\) | 2.10500e43 | 1.37916 | ||||||||
\(612\) | −6.26442e42 | −0.400160 | ||||||||
\(613\) | 1.34234e43 | 0.836037 | 0.418018 | − | 0.908439i | \(-0.362725\pi\) | ||||
0.418018 | + | 0.908439i | \(0.362725\pi\) | |||||||
\(614\) | 4.56081e42 | 0.276970 | ||||||||
\(615\) | −3.51020e42 | −0.207858 | ||||||||
\(616\) | −1.95141e43 | −1.12680 | ||||||||
\(617\) | −3.23957e42 | −0.182418 | −0.0912089 | − | 0.995832i | \(-0.529073\pi\) | ||||
−0.0912089 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(618\) | −1.93881e42 | −0.106467 | ||||||||
\(619\) | −2.85690e43 | −1.52999 | −0.764997 | − | 0.644034i | \(-0.777260\pi\) | ||||
−0.764997 | + | 0.644034i | \(0.777260\pi\) | |||||||
\(620\) | −7.02366e41 | −0.0366853 | ||||||||
\(621\) | −1.05395e43 | −0.536908 | ||||||||
\(622\) | 2.37102e42 | 0.117811 | ||||||||
\(623\) | 2.65637e43 | 1.28743 | ||||||||
\(624\) | −1.83941e42 | −0.0869597 | ||||||||
\(625\) | 8.67362e41 | 0.0400000 | ||||||||
\(626\) | 2.34893e43 | 1.05674 | ||||||||
\(627\) | 9.97349e42 | 0.437724 | ||||||||
\(628\) | 5.40882e42 | 0.231594 | ||||||||
\(629\) | −2.84280e43 | −1.18758 | ||||||||
\(630\) | −1.13480e43 | −0.462529 | ||||||||
\(631\) | −8.68109e42 | −0.345239 | −0.172619 | − | 0.984989i | \(-0.555223\pi\) | ||||
−0.172619 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(632\) | 8.30886e42 | 0.322424 | ||||||||
\(633\) | −1.27634e43 | −0.483290 | ||||||||
\(634\) | −3.33505e43 | −1.23231 | ||||||||
\(635\) | 5.98200e42 | 0.215702 | ||||||||
\(636\) | 6.06855e42 | 0.213550 | ||||||||
\(637\) | −5.23900e43 | −1.79923 | ||||||||
\(638\) | 6.89626e43 | 2.31150 | ||||||||
\(639\) | −1.42171e43 | −0.465101 | ||||||||
\(640\) | 1.23794e42 | 0.0395285 | ||||||||
\(641\) | 4.01231e43 | 1.25053 | 0.625267 | − | 0.780411i | \(-0.284990\pi\) | ||||
0.625267 | + | 0.780411i | \(0.284990\pi\) | |||||||
\(642\) | −1.01114e43 | −0.307622 | ||||||||
\(643\) | −1.38043e43 | −0.409964 | −0.204982 | − | 0.978766i | \(-0.565714\pi\) | ||||
−0.204982 | + | 0.978766i | \(0.565714\pi\) | |||||||
\(644\) | 2.12472e43 | 0.615987 | ||||||||
\(645\) | −2.22643e42 | −0.0630134 | ||||||||
\(646\) | −1.43944e43 | −0.397730 | ||||||||
\(647\) | 4.95630e43 | 1.33703 | 0.668515 | − | 0.743699i | \(-0.266930\pi\) | ||||
0.668515 | + | 0.743699i | \(0.266930\pi\) | |||||||
\(648\) | −6.35970e42 | −0.167503 | ||||||||
\(649\) | 4.99522e43 | 1.28458 | ||||||||
\(650\) | 4.52941e42 | 0.113733 | ||||||||
\(651\) | 5.20727e42 | 0.127675 | ||||||||
\(652\) | 2.79703e43 | 0.669667 | ||||||||
\(653\) | 8.53813e42 | 0.199622 | 0.0998110 | − | 0.995006i | \(-0.468176\pi\) | ||||
0.0998110 | + | 0.995006i | \(0.468176\pi\) | |||||||
\(654\) | 2.25341e43 | 0.514500 | ||||||||
\(655\) | −2.68002e43 | −0.597582 | ||||||||
\(656\) | 1.23366e43 | 0.268649 | ||||||||
\(657\) | −1.47892e43 | −0.314543 | ||||||||
\(658\) | 1.05031e44 | 2.18181 | ||||||||
\(659\) | 3.89436e43 | 0.790154 | 0.395077 | − | 0.918648i | \(-0.370718\pi\) | ||||
0.395077 | + | 0.918648i | \(0.370718\pi\) | |||||||
\(660\) | −8.64424e42 | −0.171315 | ||||||||
\(661\) | −8.37311e42 | −0.162093 | −0.0810465 | − | 0.996710i | \(-0.525826\pi\) | ||||
−0.0810465 | + | 0.996710i | \(0.525826\pi\) | |||||||
\(662\) | −4.28165e43 | −0.809678 | ||||||||
\(663\) | −1.85375e43 | −0.342446 | ||||||||
\(664\) | −2.80699e43 | −0.506566 | ||||||||
\(665\) | −2.60753e43 | −0.459720 | ||||||||
\(666\) | −4.02563e43 | −0.693399 | ||||||||
\(667\) | −7.50876e43 | −1.26362 | ||||||||
\(668\) | 1.61599e43 | 0.265708 | ||||||||
\(669\) | 3.09398e42 | 0.0497064 | ||||||||
\(670\) | 2.16532e43 | 0.339910 | ||||||||
\(671\) | 1.60994e44 | 2.46951 | ||||||||
\(672\) | −9.17796e42 | −0.137570 | ||||||||
\(673\) | 9.42152e43 | 1.38003 | 0.690013 | − | 0.723797i | \(-0.257605\pi\) | ||||
0.690013 | + | 0.723797i | \(0.257605\pi\) | |||||||
\(674\) | −5.13236e43 | −0.734664 | ||||||||
\(675\) | −1.12105e43 | −0.156826 | ||||||||
\(676\) | −1.29187e43 | −0.176622 | ||||||||
\(677\) | −1.26241e42 | −0.0168685 | −0.00843423 | − | 0.999964i | \(-0.502685\pi\) | ||||
−0.00843423 | + | 0.999964i | \(0.502685\pi\) | |||||||
\(678\) | 1.76337e43 | 0.230294 | ||||||||
\(679\) | −6.84419e43 | −0.873657 | ||||||||
\(680\) | 1.24759e43 | 0.155662 | ||||||||
\(681\) | 4.20213e43 | 0.512495 | ||||||||
\(682\) | −1.72366e43 | −0.205492 | ||||||||
\(683\) | −5.02289e43 | −0.585373 | −0.292686 | − | 0.956209i | \(-0.594549\pi\) | ||||
−0.292686 | + | 0.956209i | \(0.594549\pi\) | |||||||
\(684\) | −2.03835e43 | −0.232225 | ||||||||
\(685\) | −4.83278e43 | −0.538261 | ||||||||
\(686\) | −1.44564e44 | −1.57412 | ||||||||
\(687\) | −1.00535e43 | −0.107025 | ||||||||
\(688\) | 7.82475e42 | 0.0814422 | ||||||||
\(689\) | −7.80349e43 | −0.794129 | ||||||||
\(690\) | 9.41199e42 | 0.0936527 | ||||||||
\(691\) | 5.98132e43 | 0.581952 | 0.290976 | − | 0.956730i | \(-0.406020\pi\) | ||||
0.290976 | + | 0.956730i | \(0.406020\pi\) | |||||||
\(692\) | 2.78049e42 | 0.0264531 | ||||||||
\(693\) | −2.78488e44 | −2.59085 | ||||||||
\(694\) | 5.01886e43 | 0.456597 | ||||||||
\(695\) | −5.63033e41 | −0.00500921 | ||||||||
\(696\) | 3.24348e43 | 0.282208 | ||||||||
\(697\) | 1.24327e44 | 1.05793 | ||||||||
\(698\) | −8.62926e43 | −0.718149 | ||||||||
\(699\) | 3.02278e43 | 0.246043 | ||||||||
\(700\) | 2.26000e43 | 0.179924 | ||||||||
\(701\) | −1.56022e44 | −1.21495 | −0.607473 | − | 0.794340i | \(-0.707817\pi\) | ||||
−0.607473 | + | 0.794340i | \(0.707817\pi\) | |||||||
\(702\) | −5.85421e43 | −0.445906 | ||||||||
\(703\) | −9.25007e43 | −0.689188 | ||||||||
\(704\) | 3.03801e43 | 0.221418 | ||||||||
\(705\) | 4.65263e43 | 0.331716 | ||||||||
\(706\) | −1.49490e44 | −1.04266 | ||||||||
\(707\) | 2.81353e44 | 1.91978 | ||||||||
\(708\) | 2.34938e43 | 0.156833 | ||||||||
\(709\) | −8.54271e43 | −0.557929 | −0.278964 | − | 0.960301i | \(-0.589991\pi\) | ||||
−0.278964 | + | 0.960301i | \(0.589991\pi\) | |||||||
\(710\) | 2.83140e43 | 0.180924 | ||||||||
\(711\) | 1.18577e44 | 0.741348 | ||||||||
\(712\) | −4.13552e43 | −0.252982 | ||||||||
\(713\) | 1.87675e43 | 0.112336 | ||||||||
\(714\) | −9.24950e43 | −0.541746 | ||||||||
\(715\) | 1.11156e44 | 0.637070 | ||||||||
\(716\) | −8.77575e43 | −0.492190 | ||||||||
\(717\) | 9.91985e43 | 0.544450 | ||||||||
\(718\) | −6.62945e43 | −0.356081 | ||||||||
\(719\) | 2.30590e44 | 1.21211 | 0.606057 | − | 0.795421i | \(-0.292750\pi\) | ||||
0.606057 | + | 0.795421i | \(0.292750\pi\) | |||||||
\(720\) | 1.76668e43 | 0.0908877 | ||||||||
\(721\) | 1.24396e44 | 0.626339 | ||||||||
\(722\) | 9.66495e43 | 0.476292 | ||||||||
\(723\) | −2.42383e43 | −0.116912 | ||||||||
\(724\) | 2.58550e43 | 0.122066 | ||||||||
\(725\) | −7.98683e43 | −0.369093 | ||||||||
\(726\) | −1.44527e44 | −0.653778 | ||||||||
\(727\) | −3.33530e44 | −1.47690 | −0.738450 | − | 0.674308i | \(-0.764442\pi\) | ||||
−0.738450 | + | 0.674308i | \(0.764442\pi\) | |||||||
\(728\) | 1.18019e44 | 0.511581 | ||||||||
\(729\) | −1.08371e43 | −0.0459871 | ||||||||
\(730\) | 2.94533e43 | 0.122357 | ||||||||
\(731\) | 7.88574e43 | 0.320718 | ||||||||
\(732\) | 7.57197e43 | 0.301500 | ||||||||
\(733\) | 6.64546e43 | 0.259068 | 0.129534 | − | 0.991575i | \(-0.458652\pi\) | ||||
0.129534 | + | 0.991575i | \(0.458652\pi\) | |||||||
\(734\) | 3.37606e44 | 1.28861 | ||||||||
\(735\) | −1.15796e44 | −0.432753 | ||||||||
\(736\) | −3.30783e43 | −0.121042 | ||||||||
\(737\) | 5.31388e44 | 1.90400 | ||||||||
\(738\) | 1.76057e44 | 0.617703 | ||||||||
\(739\) | 5.13394e43 | 0.176385 | 0.0881926 | − | 0.996103i | \(-0.471891\pi\) | ||||
0.0881926 | + | 0.996103i | \(0.471891\pi\) | |||||||
\(740\) | 8.01724e43 | 0.269732 | ||||||||
\(741\) | −6.03184e43 | −0.198732 | ||||||||
\(742\) | −3.89364e44 | −1.25631 | ||||||||
\(743\) | −5.18614e44 | −1.63877 | −0.819385 | − | 0.573244i | \(-0.805685\pi\) | ||||
−0.819385 | + | 0.573244i | \(0.805685\pi\) | |||||||
\(744\) | −8.10682e42 | −0.0250882 | ||||||||
\(745\) | −1.81964e43 | −0.0551523 | ||||||||
\(746\) | 1.60512e44 | 0.476491 | ||||||||
\(747\) | −4.00591e44 | −1.16475 | ||||||||
\(748\) | 3.06169e44 | 0.871939 | ||||||||
\(749\) | 6.48756e44 | 1.80973 | ||||||||
\(750\) | 1.00112e43 | 0.0273551 | ||||||||
\(751\) | 1.16699e44 | 0.312356 | 0.156178 | − | 0.987729i | \(-0.450083\pi\) | ||||
0.156178 | + | 0.987729i | \(0.450083\pi\) | |||||||
\(752\) | −1.63516e44 | −0.428730 | ||||||||
\(753\) | −2.01911e44 | −0.518607 | ||||||||
\(754\) | −4.17077e44 | −1.04945 | ||||||||
\(755\) | 2.44624e44 | 0.603005 | ||||||||
\(756\) | −2.92102e44 | −0.705419 | ||||||||
\(757\) | 7.15124e44 | 1.69198 | 0.845990 | − | 0.533199i | \(-0.179010\pi\) | ||||
0.845990 | + | 0.533199i | \(0.179010\pi\) | |||||||
\(758\) | 4.33607e44 | 1.00513 | ||||||||
\(759\) | 2.30978e44 | 0.524593 | ||||||||
\(760\) | 4.05948e43 | 0.0903357 | ||||||||
\(761\) | −2.08933e44 | −0.455559 | −0.227779 | − | 0.973713i | \(-0.573146\pi\) | ||||
−0.227779 | + | 0.973713i | \(0.573146\pi\) | |||||||
\(762\) | 6.90453e43 | 0.147514 | ||||||||
\(763\) | −1.44581e45 | −3.02678 | ||||||||
\(764\) | −1.78393e44 | −0.365958 | ||||||||
\(765\) | 1.78046e44 | 0.357914 | ||||||||
\(766\) | −7.24860e43 | −0.142793 | ||||||||
\(767\) | −3.02105e44 | −0.583216 | ||||||||
\(768\) | 1.42885e43 | 0.0270326 | ||||||||
\(769\) | 4.48666e44 | 0.831889 | 0.415944 | − | 0.909390i | \(-0.363451\pi\) | ||||
0.415944 | + | 0.909390i | \(0.363451\pi\) | |||||||
\(770\) | 5.54623e44 | 1.00784 | ||||||||
\(771\) | −2.10988e44 | −0.375763 | ||||||||
\(772\) | 1.45712e44 | 0.254347 | ||||||||
\(773\) | −9.87774e44 | −1.68996 | −0.844978 | − | 0.534800i | \(-0.820387\pi\) | ||||
−0.844978 | + | 0.534800i | \(0.820387\pi\) | |||||||
\(774\) | 1.11668e44 | 0.187260 | ||||||||
\(775\) | 1.99624e43 | 0.0328123 | ||||||||
\(776\) | 1.06552e44 | 0.171675 | ||||||||
\(777\) | −5.94390e44 | −0.938740 | ||||||||
\(778\) | 6.50485e44 | 1.00706 | ||||||||
\(779\) | 4.04543e44 | 0.613952 | ||||||||
\(780\) | 5.22793e43 | 0.0777791 | ||||||||
\(781\) | 6.94849e44 | 1.01344 | ||||||||
\(782\) | −3.33362e44 | −0.476662 | ||||||||
\(783\) | 1.03229e45 | 1.44708 | ||||||||
\(784\) | 4.06964e44 | 0.559316 | ||||||||
\(785\) | −1.53728e44 | −0.207144 | ||||||||
\(786\) | −3.09332e44 | −0.408673 | ||||||||
\(787\) | −8.12711e44 | −1.05276 | −0.526378 | − | 0.850251i | \(-0.676450\pi\) | ||||
−0.526378 | + | 0.850251i | \(0.676450\pi\) | |||||||
\(788\) | −1.39838e44 | −0.177610 | ||||||||
\(789\) | 1.90974e44 | 0.237838 | ||||||||
\(790\) | −2.36152e44 | −0.288384 | ||||||||
\(791\) | −1.13139e45 | −1.35481 | ||||||||
\(792\) | 4.33559e44 | 0.509106 | ||||||||
\(793\) | −9.73673e44 | −1.12119 | ||||||||
\(794\) | −1.52818e44 | −0.172566 | ||||||||
\(795\) | −1.72478e44 | −0.191005 | ||||||||
\(796\) | −5.55603e44 | −0.603409 | ||||||||
\(797\) | 2.32602e44 | 0.247748 | 0.123874 | − | 0.992298i | \(-0.460468\pi\) | ||||
0.123874 | + | 0.992298i | \(0.460468\pi\) | |||||||
\(798\) | −3.00965e44 | −0.314392 | ||||||||
\(799\) | −1.64791e45 | −1.68833 | ||||||||
\(800\) | −3.51844e43 | −0.0353553 | ||||||||
\(801\) | −5.90187e44 | −0.581682 | ||||||||
\(802\) | 3.53004e44 | 0.341253 | ||||||||
\(803\) | 7.22808e44 | 0.685381 | ||||||||
\(804\) | 2.49925e44 | 0.232456 | ||||||||
\(805\) | −6.03882e44 | −0.550955 | ||||||||
\(806\) | 1.04245e44 | 0.0932958 | ||||||||
\(807\) | 4.42851e44 | 0.388793 | ||||||||
\(808\) | −4.38019e44 | −0.377240 | ||||||||
\(809\) | 1.01189e45 | 0.854931 | 0.427466 | − | 0.904032i | \(-0.359407\pi\) | ||||
0.427466 | + | 0.904032i | \(0.359407\pi\) | |||||||
\(810\) | 1.80753e44 | 0.149820 | ||||||||
\(811\) | 7.77255e44 | 0.632034 | 0.316017 | − | 0.948754i | \(-0.397654\pi\) | ||||
0.316017 | + | 0.948754i | \(0.397654\pi\) | |||||||
\(812\) | −2.08105e45 | −1.66022 | ||||||||
\(813\) | 2.87149e44 | 0.224752 | ||||||||
\(814\) | 1.96750e45 | 1.51090 | ||||||||
\(815\) | −7.94963e44 | −0.598969 | ||||||||
\(816\) | 1.43999e44 | 0.106454 | ||||||||
\(817\) | 2.56591e44 | 0.186123 | ||||||||
\(818\) | 5.22791e44 | 0.372093 | ||||||||
\(819\) | 1.68426e45 | 1.17628 | ||||||||
\(820\) | −3.50626e44 | −0.240287 | ||||||||
\(821\) | 2.49289e45 | 1.67642 | 0.838212 | − | 0.545344i | \(-0.183601\pi\) | ||||
0.838212 | + | 0.545344i | \(0.183601\pi\) | |||||||
\(822\) | −5.57807e44 | −0.368104 | ||||||||
\(823\) | −2.55800e45 | −1.65654 | −0.828272 | − | 0.560326i | \(-0.810676\pi\) | ||||
−0.828272 | + | 0.560326i | \(0.810676\pi\) | |||||||
\(824\) | −1.93663e44 | −0.123077 | ||||||||
\(825\) | 2.45684e44 | 0.153229 | ||||||||
\(826\) | −1.50739e45 | −0.922643 | ||||||||
\(827\) | −1.08245e45 | −0.650240 | −0.325120 | − | 0.945673i | \(-0.605405\pi\) | ||||
−0.325120 | + | 0.945673i | \(0.605405\pi\) | |||||||
\(828\) | −4.72066e44 | −0.278312 | ||||||||
\(829\) | 8.46679e43 | 0.0489918 | 0.0244959 | − | 0.999700i | \(-0.492202\pi\) | ||||
0.0244959 | + | 0.999700i | \(0.492202\pi\) | |||||||
\(830\) | 7.97795e44 | 0.453086 | ||||||||
\(831\) | −1.83901e44 | −0.102511 | ||||||||
\(832\) | −1.83735e44 | −0.100526 | ||||||||
\(833\) | 4.10137e45 | 2.20258 | ||||||||
\(834\) | −6.49862e42 | −0.00342568 | ||||||||
\(835\) | −4.59292e44 | −0.237656 | ||||||||
\(836\) | 9.96229e44 | 0.506013 | ||||||||
\(837\) | −2.58012e44 | −0.128646 | ||||||||
\(838\) | 1.79130e45 | 0.876771 | ||||||||
\(839\) | −6.17907e43 | −0.0296902 | −0.0148451 | − | 0.999890i | \(-0.504726\pi\) | ||||
−0.0148451 | + | 0.999890i | \(0.504726\pi\) | |||||||
\(840\) | 2.60853e44 | 0.123046 | ||||||||
\(841\) | 5.19500e45 | 2.40574 | ||||||||
\(842\) | 8.09191e44 | 0.367886 | ||||||||
\(843\) | −8.78944e44 | −0.392314 | ||||||||
\(844\) | −1.27490e45 | −0.558689 | ||||||||
\(845\) | 3.67172e44 | 0.157976 | ||||||||
\(846\) | −2.33356e45 | −0.985778 | ||||||||
\(847\) | 9.27298e45 | 3.84615 | ||||||||
\(848\) | 6.06173e44 | 0.246866 | ||||||||
\(849\) | 3.83144e43 | 0.0153212 | ||||||||
\(850\) | −3.54586e44 | −0.139229 | ||||||||
\(851\) | −2.14224e45 | −0.825963 | ||||||||
\(852\) | 3.26805e44 | 0.123730 | ||||||||
\(853\) | 1.05224e45 | 0.391205 | 0.195602 | − | 0.980683i | \(-0.437334\pi\) | ||||
0.195602 | + | 0.980683i | \(0.437334\pi\) | |||||||
\(854\) | −4.85825e45 | −1.77371 | ||||||||
\(855\) | 5.79335e44 | 0.207709 | ||||||||
\(856\) | −1.01000e45 | −0.355614 | ||||||||
\(857\) | −2.23665e45 | −0.773383 | −0.386692 | − | 0.922209i | \(-0.626382\pi\) | ||||
−0.386692 | + | 0.922209i | \(0.626382\pi\) | |||||||
\(858\) | 1.28298e45 | 0.435678 | ||||||||
\(859\) | −4.60157e45 | −1.53466 | −0.767329 | − | 0.641254i | \(-0.778415\pi\) | ||||
−0.767329 | + | 0.641254i | \(0.778415\pi\) | |||||||
\(860\) | −2.22393e44 | −0.0728441 | ||||||||
\(861\) | 2.59951e45 | 0.836261 | ||||||||
\(862\) | −1.55227e45 | −0.490462 | ||||||||
\(863\) | −4.42805e45 | −1.37419 | −0.687093 | − | 0.726569i | \(-0.741114\pi\) | ||||
−0.687093 | + | 0.726569i | \(0.741114\pi\) | |||||||
\(864\) | 4.54753e44 | 0.138616 | ||||||||
\(865\) | −7.90262e43 | −0.0236604 | ||||||||
\(866\) | 1.08166e43 | 0.00318099 | ||||||||
\(867\) | −4.60692e43 | −0.0133080 | ||||||||
\(868\) | 5.20142e44 | 0.147593 | ||||||||
\(869\) | −5.79536e45 | −1.61538 | ||||||||
\(870\) | −9.21854e44 | −0.252414 | ||||||||
\(871\) | −3.21377e45 | −0.864437 | ||||||||
\(872\) | 2.25088e45 | 0.594767 | ||||||||
\(873\) | 1.52063e45 | 0.394732 | ||||||||
\(874\) | −1.08471e45 | −0.276622 | ||||||||
\(875\) | −6.42331e44 | −0.160929 | ||||||||
\(876\) | 3.39955e44 | 0.0836774 | ||||||||
\(877\) | −5.41361e45 | −1.30916 | −0.654581 | − | 0.755992i | \(-0.727155\pi\) | ||||
−0.654581 | + | 0.755992i | \(0.727155\pi\) | |||||||
\(878\) | 3.61402e43 | 0.00858668 | ||||||||
\(879\) | 1.85742e45 | 0.433593 | ||||||||
\(880\) | −8.63453e44 | −0.198042 | ||||||||
\(881\) | −4.09130e45 | −0.922008 | −0.461004 | − | 0.887398i | \(-0.652511\pi\) | ||||
−0.461004 | + | 0.887398i | \(0.652511\pi\) | |||||||
\(882\) | 5.80785e45 | 1.28603 | ||||||||
\(883\) | 7.61955e45 | 1.65782 | 0.828912 | − | 0.559379i | \(-0.188960\pi\) | ||||
0.828912 | + | 0.559379i | \(0.188960\pi\) | |||||||
\(884\) | −1.85167e45 | −0.395871 | ||||||||
\(885\) | −6.67734e44 | −0.140276 | ||||||||
\(886\) | 3.99255e45 | 0.824190 | ||||||||
\(887\) | −4.92537e45 | −0.999131 | −0.499566 | − | 0.866276i | \(-0.666507\pi\) | ||||
−0.499566 | + | 0.866276i | \(0.666507\pi\) | |||||||
\(888\) | 9.25363e44 | 0.184464 | ||||||||
\(889\) | −4.43001e45 | −0.867816 | ||||||||
\(890\) | 1.17539e45 | 0.226274 | ||||||||
\(891\) | 4.43584e45 | 0.839211 | ||||||||
\(892\) | 3.09050e44 | 0.0574611 | ||||||||
\(893\) | −5.36205e45 | −0.979791 | ||||||||
\(894\) | −2.10026e44 | −0.0377174 | ||||||||
\(895\) | 2.49422e45 | 0.440228 | ||||||||
\(896\) | −9.16765e44 | −0.159032 | ||||||||
\(897\) | −1.39693e45 | −0.238172 | ||||||||
\(898\) | −4.41116e45 | −0.739213 | ||||||||
\(899\) | −1.83818e45 | −0.302770 | ||||||||
\(900\) | −5.02122e44 | −0.0812925 | ||||||||
\(901\) | 6.10899e45 | 0.972154 | ||||||||
\(902\) | −8.60465e45 | −1.34596 | ||||||||
\(903\) | 1.64880e45 | 0.253517 | ||||||||
\(904\) | 1.76139e45 | 0.266222 | ||||||||
\(905\) | −7.34842e44 | −0.109180 | ||||||||
\(906\) | 2.82349e45 | 0.412382 | ||||||||
\(907\) | −2.39988e45 | −0.344570 | −0.172285 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172285 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(908\) | 4.19742e45 | 0.592450 | ||||||||
\(909\) | −6.25105e45 | −0.867386 | ||||||||
\(910\) | −3.35429e45 | −0.457572 | ||||||||
\(911\) | −1.27477e46 | −1.70961 | −0.854805 | − | 0.518949i | \(-0.826324\pi\) | ||||
−0.854805 | + | 0.518949i | \(0.826324\pi\) | |||||||
\(912\) | 4.68552e44 | 0.0617786 | ||||||||
\(913\) | 1.95786e46 | 2.53795 | ||||||||
\(914\) | −2.20573e45 | −0.281116 | ||||||||
\(915\) | −2.15208e45 | −0.269670 | ||||||||
\(916\) | −1.00422e45 | −0.123723 | ||||||||
\(917\) | 1.98471e46 | 2.40420 | ||||||||
\(918\) | 4.58298e45 | 0.545867 | ||||||||
\(919\) | −8.11185e44 | −0.0950013 | −0.0475007 | − | 0.998871i | \(-0.515126\pi\) | ||||
−0.0475007 | + | 0.998871i | \(0.515126\pi\) | |||||||
\(920\) | 9.40142e44 | 0.108264 | ||||||||
\(921\) | −1.49617e45 | −0.169416 | ||||||||
\(922\) | 1.23460e46 | 1.37466 | ||||||||
\(923\) | −4.20236e45 | −0.460115 | ||||||||
\(924\) | 6.40155e45 | 0.689239 | ||||||||
\(925\) | −2.27864e45 | −0.241256 | ||||||||
\(926\) | 1.10659e46 | 1.15217 | ||||||||
\(927\) | −2.76380e45 | −0.282990 | ||||||||
\(928\) | 3.23984e45 | 0.326235 | ||||||||
\(929\) | −8.34797e45 | −0.826680 | −0.413340 | − | 0.910577i | \(-0.635638\pi\) | ||||
−0.413340 | + | 0.910577i | \(0.635638\pi\) | |||||||
\(930\) | 2.30410e44 | 0.0224396 | ||||||||
\(931\) | 1.33453e46 | 1.27822 | ||||||||
\(932\) | 3.01939e45 | 0.284428 | ||||||||
\(933\) | −7.77810e44 | −0.0720623 | ||||||||
\(934\) | 3.67746e45 | 0.335098 | ||||||||
\(935\) | −8.70184e45 | −0.779886 | ||||||||
\(936\) | −2.62211e45 | −0.231140 | ||||||||
\(937\) | 7.08971e45 | 0.614703 | 0.307351 | − | 0.951596i | \(-0.400557\pi\) | ||||
0.307351 | + | 0.951596i | \(0.400557\pi\) | |||||||
\(938\) | −1.60355e46 | −1.36753 | ||||||||
\(939\) | −7.70561e45 | −0.646384 | ||||||||
\(940\) | 4.64740e45 | 0.383468 | ||||||||
\(941\) | −1.27325e46 | −1.03341 | −0.516706 | − | 0.856163i | \(-0.672842\pi\) | ||||
−0.516706 | + | 0.856163i | \(0.672842\pi\) | |||||||
\(942\) | −1.77435e45 | −0.141661 | ||||||||
\(943\) | 9.36889e45 | 0.735795 | ||||||||
\(944\) | 2.34674e45 | 0.181301 | ||||||||
\(945\) | 8.30204e45 | 0.630946 | ||||||||
\(946\) | −5.45770e45 | −0.408035 | ||||||||
\(947\) | 8.84487e45 | 0.650529 | 0.325265 | − | 0.945623i | \(-0.394547\pi\) | ||||
0.325265 | + | 0.945623i | \(0.394547\pi\) | |||||||
\(948\) | −2.72571e45 | −0.197220 | ||||||||
\(949\) | −4.37145e45 | −0.311171 | ||||||||
\(950\) | −1.15377e45 | −0.0807987 | ||||||||
\(951\) | 1.09406e46 | 0.753776 | ||||||||
\(952\) | −9.23912e45 | −0.626265 | ||||||||
\(953\) | 9.38297e44 | 0.0625749 | 0.0312875 | − | 0.999510i | \(-0.490039\pi\) | ||||
0.0312875 | + | 0.999510i | \(0.490039\pi\) | |||||||
\(954\) | 8.65080e45 | 0.567618 | ||||||||
\(955\) | 5.07024e45 | 0.327323 | ||||||||
\(956\) | 9.90872e45 | 0.629391 | ||||||||
\(957\) | −2.26231e46 | −1.41389 | ||||||||
\(958\) | −3.26573e45 | −0.200824 | ||||||||
\(959\) | 3.57895e46 | 2.16554 | ||||||||
\(960\) | −4.06104e44 | −0.0241787 | ||||||||
\(961\) | −1.66097e46 | −0.973084 | ||||||||
\(962\) | −1.18992e46 | −0.685967 | ||||||||
\(963\) | −1.44139e46 | −0.817663 | ||||||||
\(964\) | −2.42111e45 | −0.135151 | ||||||||
\(965\) | −4.14138e45 | −0.227495 | ||||||||
\(966\) | −6.97011e45 | −0.376786 | ||||||||
\(967\) | −1.81981e46 | −0.968092 | −0.484046 | − | 0.875043i | \(-0.660833\pi\) | ||||
−0.484046 | + | 0.875043i | \(0.660833\pi\) | |||||||
\(968\) | −1.44364e46 | −0.755775 | ||||||||
\(969\) | 4.72204e45 | 0.243283 | ||||||||
\(970\) | −3.02840e45 | −0.153551 | ||||||||
\(971\) | −1.52145e46 | −0.759205 | −0.379602 | − | 0.925150i | \(-0.623939\pi\) | ||||
−0.379602 | + | 0.925150i | \(0.623939\pi\) | |||||||
\(972\) | 1.00696e46 | 0.494523 | ||||||||
\(973\) | 4.16958e44 | 0.0201532 | ||||||||
\(974\) | −4.06766e45 | −0.193500 | ||||||||
\(975\) | −1.48587e45 | −0.0695678 | ||||||||
\(976\) | 7.56347e45 | 0.348537 | ||||||||
\(977\) | −1.63297e46 | −0.740650 | −0.370325 | − | 0.928902i | \(-0.620754\pi\) | ||||
−0.370325 | + | 0.928902i | \(0.620754\pi\) | |||||||
\(978\) | −9.17560e45 | −0.409621 | ||||||||
\(979\) | 2.88449e46 | 1.26747 | ||||||||
\(980\) | −1.15666e46 | −0.500267 | ||||||||
\(981\) | 3.21227e46 | 1.36755 | ||||||||
\(982\) | −9.39872e44 | −0.0393859 | ||||||||
\(983\) | 2.28872e46 | 0.944089 | 0.472044 | − | 0.881575i | \(-0.343516\pi\) | ||||
0.472044 | + | 0.881575i | \(0.343516\pi\) | |||||||
\(984\) | −4.04699e45 | −0.164327 | ||||||||
\(985\) | 3.97442e45 | 0.158859 | ||||||||
\(986\) | 3.26510e46 | 1.28471 | ||||||||
\(987\) | −3.44554e46 | −1.33457 | ||||||||
\(988\) | −6.02507e45 | −0.229736 | ||||||||
\(989\) | 5.94243e45 | 0.223060 | ||||||||
\(990\) | −1.23225e46 | −0.455358 | ||||||||
\(991\) | −1.29262e46 | −0.470250 | −0.235125 | − | 0.971965i | \(-0.575550\pi\) | ||||
−0.235125 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(992\) | −8.09773e44 | −0.0290023 | ||||||||
\(993\) | 1.40459e46 | 0.495262 | ||||||||
\(994\) | −2.09681e46 | −0.727898 | ||||||||
\(995\) | 1.57912e46 | 0.539705 | ||||||||
\(996\) | 9.20829e45 | 0.309856 | ||||||||
\(997\) | −7.75877e45 | −0.257050 | −0.128525 | − | 0.991706i | \(-0.541024\pi\) | ||||
−0.128525 | + | 0.991706i | \(0.541024\pi\) | |||||||
\(998\) | −3.03927e46 | −0.991394 | ||||||||
\(999\) | 2.94511e46 | 0.945880 |
(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 | 10.32.a.b.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.32.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |