Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,70,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 70, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 70);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 70 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(90.4544859877\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 14\!\cdots\!28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{51}\cdot 3^{33}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.14909e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.99182e9 | 0.164300 | 0.0821498 | − | 0.996620i | \(-0.473821\pi\) | ||||
0.0821498 | + | 0.996620i | \(0.473821\pi\) | |||||||
\(3\) | −1.66772e16 | −0.577350 | ||||||||
\(4\) | −5.74361e20 | −0.973006 | ||||||||
\(5\) | 2.45458e24 | 1.88587 | 0.942937 | − | 0.332971i | \(-0.108051\pi\) | ||||
0.942937 | + | 0.332971i | \(0.108051\pi\) | |||||||
\(6\) | −6.65724e25 | −0.0948584 | ||||||||
\(7\) | 3.62318e28 | 0.253051 | 0.126526 | − | 0.991963i | \(-0.459617\pi\) | ||||
0.126526 | + | 0.991963i | \(0.459617\pi\) | |||||||
\(8\) | −4.64911e30 | −0.324164 | ||||||||
\(9\) | 2.78128e32 | 0.333333 | ||||||||
\(10\) | 9.79827e33 | 0.309848 | ||||||||
\(11\) | −8.58823e35 | −1.01358 | −0.506788 | − | 0.862071i | \(-0.669167\pi\) | ||||
−0.506788 | + | 0.862071i | \(0.669167\pi\) | |||||||
\(12\) | 9.57873e36 | 0.561765 | ||||||||
\(13\) | 4.20595e37 | 0.155890 | 0.0779450 | − | 0.996958i | \(-0.475164\pi\) | ||||
0.0779450 | + | 0.996958i | \(0.475164\pi\) | |||||||
\(14\) | 1.44631e38 | 0.0415762 | ||||||||
\(15\) | −4.09355e40 | −1.08881 | ||||||||
\(16\) | 3.20485e41 | 0.919746 | ||||||||
\(17\) | −3.41417e42 | −1.21003 | −0.605016 | − | 0.796213i | \(-0.706833\pi\) | ||||
−0.605016 | + | 0.796213i | \(0.706833\pi\) | |||||||
\(18\) | 1.11024e42 | 0.0547665 | ||||||||
\(19\) | −1.21562e44 | −0.928539 | −0.464269 | − | 0.885694i | \(-0.653683\pi\) | ||||
−0.464269 | + | 0.885694i | \(0.653683\pi\) | |||||||
\(20\) | −1.40982e45 | −1.83497 | ||||||||
\(21\) | −6.04245e44 | −0.146099 | ||||||||
\(22\) | −3.42827e45 | −0.166530 | ||||||||
\(23\) | 1.33316e47 | 1.39725 | 0.698623 | − | 0.715490i | \(-0.253797\pi\) | ||||
0.698623 | + | 0.715490i | \(0.253797\pi\) | |||||||
\(24\) | 7.75340e46 | 0.187156 | ||||||||
\(25\) | 4.33092e48 | 2.55652 | ||||||||
\(26\) | 1.67894e47 | 0.0256127 | ||||||||
\(27\) | −4.63840e48 | −0.192450 | ||||||||
\(28\) | −2.08102e49 | −0.246220 | ||||||||
\(29\) | −1.91784e50 | −0.676210 | −0.338105 | − | 0.941108i | \(-0.609786\pi\) | ||||
−0.338105 | + | 0.941108i | \(0.609786\pi\) | |||||||
\(30\) | −1.63407e50 | −0.178891 | ||||||||
\(31\) | 2.32297e51 | 0.820475 | 0.410237 | − | 0.911979i | \(-0.365446\pi\) | ||||
0.410237 | + | 0.911979i | \(0.365446\pi\) | |||||||
\(32\) | 4.02367e51 | 0.475278 | ||||||||
\(33\) | 1.43228e52 | 0.585188 | ||||||||
\(34\) | −1.36288e52 | −0.198808 | ||||||||
\(35\) | 8.89341e52 | 0.477222 | ||||||||
\(36\) | −1.59746e53 | −0.324335 | ||||||||
\(37\) | 1.40508e54 | 1.10852 | 0.554259 | − | 0.832344i | \(-0.313002\pi\) | ||||
0.554259 | + | 0.832344i | \(0.313002\pi\) | |||||||
\(38\) | −4.85256e53 | −0.152559 | ||||||||
\(39\) | −7.01434e53 | −0.0900032 | ||||||||
\(40\) | −1.14116e55 | −0.611333 | ||||||||
\(41\) | −5.81808e55 | −1.32965 | −0.664824 | − | 0.747000i | \(-0.731493\pi\) | ||||
−0.664824 | + | 0.747000i | \(0.731493\pi\) | |||||||
\(42\) | −2.41204e54 | −0.0240040 | ||||||||
\(43\) | −3.25513e55 | −0.143849 | −0.0719244 | − | 0.997410i | \(-0.522914\pi\) | ||||
−0.0719244 | + | 0.997410i | \(0.522914\pi\) | |||||||
\(44\) | 4.93275e56 | 0.986215 | ||||||||
\(45\) | 6.82689e56 | 0.628625 | ||||||||
\(46\) | 5.32175e56 | 0.229567 | ||||||||
\(47\) | −3.00434e57 | −0.617125 | −0.308562 | − | 0.951204i | \(-0.599848\pi\) | ||||
−0.308562 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(48\) | −5.34478e57 | −0.531015 | ||||||||
\(49\) | −1.91878e58 | −0.935965 | ||||||||
\(50\) | 1.72883e58 | 0.420035 | ||||||||
\(51\) | 5.69387e58 | 0.698613 | ||||||||
\(52\) | −2.41573e58 | −0.151682 | ||||||||
\(53\) | 1.16179e59 | 0.378104 | 0.189052 | − | 0.981967i | \(-0.439458\pi\) | ||||
0.189052 | + | 0.981967i | \(0.439458\pi\) | |||||||
\(54\) | −1.85157e58 | −0.0316195 | ||||||||
\(55\) | −2.10805e60 | −1.91148 | ||||||||
\(56\) | −1.68446e59 | −0.0820300 | ||||||||
\(57\) | 2.02732e60 | 0.536092 | ||||||||
\(58\) | −7.65568e59 | −0.111101 | ||||||||
\(59\) | 2.31881e61 | 1.86582 | 0.932911 | − | 0.360106i | \(-0.117260\pi\) | ||||
0.932911 | + | 0.360106i | \(0.117260\pi\) | |||||||
\(60\) | 2.35118e61 | 1.05942 | ||||||||
\(61\) | −7.75450e61 | −1.97549 | −0.987745 | − | 0.156078i | \(-0.950115\pi\) | ||||
−0.987745 | + | 0.156078i | \(0.950115\pi\) | |||||||
\(62\) | 9.27289e60 | 0.134804 | ||||||||
\(63\) | 1.00771e61 | 0.0843503 | ||||||||
\(64\) | −1.73119e62 | −0.841658 | ||||||||
\(65\) | 1.03239e62 | 0.293989 | ||||||||
\(66\) | 5.71739e61 | 0.0961462 | ||||||||
\(67\) | 2.47350e60 | 0.00247589 | 0.00123795 | − | 0.999999i | \(-0.499606\pi\) | ||||
0.00123795 | + | 0.999999i | \(0.499606\pi\) | |||||||
\(68\) | 1.96097e63 | 1.17737 | ||||||||
\(69\) | −2.22334e63 | −0.806700 | ||||||||
\(70\) | 3.55009e62 | 0.0784074 | ||||||||
\(71\) | −2.45908e63 | −0.332935 | −0.166468 | − | 0.986047i | \(-0.553236\pi\) | ||||
−0.166468 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(72\) | −1.29305e63 | −0.108055 | ||||||||
\(73\) | 5.55313e63 | 0.288336 | 0.144168 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144168 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(74\) | 5.60884e63 | 0.182129 | ||||||||
\(75\) | −7.22275e64 | −1.47601 | ||||||||
\(76\) | 6.98207e64 | 0.903473 | ||||||||
\(77\) | −3.11167e64 | −0.256486 | ||||||||
\(78\) | −2.80000e63 | −0.0147875 | ||||||||
\(79\) | −2.90319e65 | −0.987963 | −0.493982 | − | 0.869472i | \(-0.664459\pi\) | ||||
−0.493982 | + | 0.869472i | \(0.664459\pi\) | |||||||
\(80\) | 7.86656e65 | 1.73452 | ||||||||
\(81\) | 7.73554e64 | 0.111111 | ||||||||
\(82\) | −2.32247e65 | −0.218461 | ||||||||
\(83\) | −8.96198e65 | −0.554894 | −0.277447 | − | 0.960741i | \(-0.589488\pi\) | ||||
−0.277447 | + | 0.960741i | \(0.589488\pi\) | |||||||
\(84\) | 3.47055e65 | 0.142155 | ||||||||
\(85\) | −8.38036e66 | −2.28197 | ||||||||
\(86\) | −1.29939e65 | −0.0236343 | ||||||||
\(87\) | 3.19842e66 | 0.390410 | ||||||||
\(88\) | 3.99276e66 | 0.328565 | ||||||||
\(89\) | −1.65103e67 | −0.920023 | −0.460011 | − | 0.887913i | \(-0.652155\pi\) | ||||
−0.460011 | + | 0.887913i | \(0.652155\pi\) | |||||||
\(90\) | 2.72518e66 | 0.103283 | ||||||||
\(91\) | 1.52389e66 | 0.0394481 | ||||||||
\(92\) | −7.65717e67 | −1.35953 | ||||||||
\(93\) | −3.87406e67 | −0.473701 | ||||||||
\(94\) | −1.19928e67 | −0.101393 | ||||||||
\(95\) | −2.98385e68 | −1.75111 | ||||||||
\(96\) | −6.71034e67 | −0.274402 | ||||||||
\(97\) | 3.36704e68 | 0.962993 | 0.481496 | − | 0.876448i | \(-0.340093\pi\) | ||||
0.481496 | + | 0.876448i | \(0.340093\pi\) | |||||||
\(98\) | −7.65942e67 | −0.153779 | ||||||||
\(99\) | −2.38863e68 | −0.337859 | ||||||||
\(100\) | −2.48751e69 | −2.48751 | ||||||||
\(101\) | −1.25892e69 | −0.893118 | −0.446559 | − | 0.894754i | \(-0.647351\pi\) | ||||
−0.446559 | + | 0.894754i | \(0.647351\pi\) | |||||||
\(102\) | 2.27289e68 | 0.114782 | ||||||||
\(103\) | −4.12679e69 | −1.48843 | −0.744214 | − | 0.667941i | \(-0.767176\pi\) | ||||
−0.744214 | + | 0.667941i | \(0.767176\pi\) | |||||||
\(104\) | −1.95539e68 | −0.0505340 | ||||||||
\(105\) | −1.48317e69 | −0.275524 | ||||||||
\(106\) | 4.63768e68 | 0.0621224 | ||||||||
\(107\) | 6.56850e69 | 0.636394 | 0.318197 | − | 0.948025i | \(-0.396923\pi\) | ||||
0.318197 | + | 0.948025i | \(0.396923\pi\) | |||||||
\(108\) | 2.66412e69 | 0.187255 | ||||||||
\(109\) | −3.66549e70 | −1.87464 | −0.937321 | − | 0.348468i | \(-0.886702\pi\) | ||||
−0.937321 | + | 0.348468i | \(0.886702\pi\) | |||||||
\(110\) | −8.41498e69 | −0.314055 | ||||||||
\(111\) | −2.34328e70 | −0.640003 | ||||||||
\(112\) | 1.16117e70 | 0.232743 | ||||||||
\(113\) | −6.51324e70 | −0.960707 | −0.480353 | − | 0.877075i | \(-0.659492\pi\) | ||||
−0.480353 | + | 0.877075i | \(0.659492\pi\) | |||||||
\(114\) | 8.09270e69 | 0.0880797 | ||||||||
\(115\) | 3.27236e71 | 2.63503 | ||||||||
\(116\) | 1.10153e71 | 0.657956 | ||||||||
\(117\) | 1.16979e70 | 0.0519634 | ||||||||
\(118\) | 9.25627e70 | 0.306554 | ||||||||
\(119\) | −1.23702e71 | −0.306200 | ||||||||
\(120\) | 1.90314e71 | 0.352953 | ||||||||
\(121\) | 1.96255e70 | 0.0273354 | ||||||||
\(122\) | −3.09546e71 | −0.324572 | ||||||||
\(123\) | 9.70292e71 | 0.767673 | ||||||||
\(124\) | −1.33422e72 | −0.798326 | ||||||||
\(125\) | 6.47237e72 | 2.93540 | ||||||||
\(126\) | 4.02260e70 | 0.0138587 | ||||||||
\(127\) | 3.25151e72 | 0.852819 | 0.426409 | − | 0.904530i | \(-0.359778\pi\) | ||||
0.426409 | + | 0.904530i | \(0.359778\pi\) | |||||||
\(128\) | −3.06621e72 | −0.613562 | ||||||||
\(129\) | 5.42864e71 | 0.0830512 | ||||||||
\(130\) | 4.12110e71 | 0.0483023 | ||||||||
\(131\) | 6.67900e72 | 0.600969 | 0.300484 | − | 0.953787i | \(-0.402852\pi\) | ||||
0.300484 | + | 0.953787i | \(0.402852\pi\) | |||||||
\(132\) | −8.22643e72 | −0.569391 | ||||||||
\(133\) | −4.40443e72 | −0.234968 | ||||||||
\(134\) | 9.87379e69 | 0.000406788 0 | ||||||||
\(135\) | −1.13853e73 | −0.362937 | ||||||||
\(136\) | 1.58728e73 | 0.392249 | ||||||||
\(137\) | −7.49685e73 | −1.43886 | −0.719431 | − | 0.694564i | \(-0.755598\pi\) | ||||
−0.719431 | + | 0.694564i | \(0.755598\pi\) | |||||||
\(138\) | −8.87518e72 | −0.132541 | ||||||||
\(139\) | −9.78034e73 | −1.13853 | −0.569263 | − | 0.822155i | \(-0.692772\pi\) | ||||
−0.569263 | + | 0.822155i | \(0.692772\pi\) | |||||||
\(140\) | −5.10803e73 | −0.464340 | ||||||||
\(141\) | 5.01039e73 | 0.356297 | ||||||||
\(142\) | −9.81622e72 | −0.0547011 | ||||||||
\(143\) | −3.61217e73 | −0.158006 | ||||||||
\(144\) | 8.91359e73 | 0.306582 | ||||||||
\(145\) | −4.70750e74 | −1.27525 | ||||||||
\(146\) | 2.21671e73 | 0.0473735 | ||||||||
\(147\) | 3.19998e74 | 0.540380 | ||||||||
\(148\) | −8.07025e74 | −1.07859 | ||||||||
\(149\) | −4.01723e74 | −0.425599 | −0.212800 | − | 0.977096i | \(-0.568258\pi\) | ||||
−0.212800 | + | 0.977096i | \(0.568258\pi\) | |||||||
\(150\) | −2.88319e74 | −0.242508 | ||||||||
\(151\) | 2.77648e75 | 1.85691 | 0.928453 | − | 0.371450i | \(-0.121139\pi\) | ||||
0.928453 | + | 0.371450i | \(0.121139\pi\) | |||||||
\(152\) | 5.65156e74 | 0.300999 | ||||||||
\(153\) | −9.49577e74 | −0.403344 | ||||||||
\(154\) | −1.24213e74 | −0.0421406 | ||||||||
\(155\) | 5.70192e75 | 1.54731 | ||||||||
\(156\) | 4.02876e74 | 0.0875736 | ||||||||
\(157\) | 1.47342e75 | 0.256915 | 0.128458 | − | 0.991715i | \(-0.458997\pi\) | ||||
0.128458 | + | 0.991715i | \(0.458997\pi\) | |||||||
\(158\) | −1.15890e75 | −0.162322 | ||||||||
\(159\) | −1.93754e75 | −0.218299 | ||||||||
\(160\) | 9.87642e75 | 0.896314 | ||||||||
\(161\) | 4.83029e75 | 0.353574 | ||||||||
\(162\) | 3.08789e74 | 0.0182555 | ||||||||
\(163\) | −1.36864e76 | −0.654362 | −0.327181 | − | 0.944962i | \(-0.606099\pi\) | ||||
−0.327181 | + | 0.944962i | \(0.606099\pi\) | |||||||
\(164\) | 3.34168e76 | 1.29375 | ||||||||
\(165\) | 3.51564e76 | 1.10359 | ||||||||
\(166\) | −3.57746e75 | −0.0911688 | ||||||||
\(167\) | −7.54924e76 | −1.56381 | −0.781907 | − | 0.623396i | \(-0.785753\pi\) | ||||
−0.781907 | + | 0.623396i | \(0.785753\pi\) | |||||||
\(168\) | 2.80920e75 | 0.0473601 | ||||||||
\(169\) | −7.10243e76 | −0.975698 | ||||||||
\(170\) | −3.34529e76 | −0.374927 | ||||||||
\(171\) | −3.38100e76 | −0.309513 | ||||||||
\(172\) | 1.86962e76 | 0.139966 | ||||||||
\(173\) | 1.16564e74 | 0.000714453 0 | 0.000357227 | − | 1.00000i | \(-0.499886\pi\) | ||||
0.000357227 | 1.00000i | \(0.499886\pi\) | ||||||||
\(174\) | 1.27675e76 | 0.0641442 | ||||||||
\(175\) | 1.56917e77 | 0.646930 | ||||||||
\(176\) | −2.75240e77 | −0.932232 | ||||||||
\(177\) | −3.86712e77 | −1.07723 | ||||||||
\(178\) | −6.59060e76 | −0.151159 | ||||||||
\(179\) | −2.95990e77 | −0.559561 | −0.279780 | − | 0.960064i | \(-0.590262\pi\) | ||||
−0.279780 | + | 0.960064i | \(0.590262\pi\) | |||||||
\(180\) | −3.92110e77 | −0.611655 | ||||||||
\(181\) | −4.99123e77 | −0.643126 | −0.321563 | − | 0.946888i | \(-0.604208\pi\) | ||||
−0.321563 | + | 0.946888i | \(0.604208\pi\) | |||||||
\(182\) | 6.08311e75 | 0.00648131 | ||||||||
\(183\) | 1.29323e78 | 1.14055 | ||||||||
\(184\) | −6.19801e77 | −0.452937 | ||||||||
\(185\) | 3.44890e78 | 2.09052 | ||||||||
\(186\) | −1.54646e77 | −0.0778289 | ||||||||
\(187\) | 2.93217e78 | 1.22646 | ||||||||
\(188\) | 1.72558e78 | 0.600466 | ||||||||
\(189\) | −1.68058e77 | −0.0486997 | ||||||||
\(190\) | −1.19110e78 | −0.287706 | ||||||||
\(191\) | −7.53132e78 | −1.51782 | −0.758909 | − | 0.651197i | \(-0.774267\pi\) | ||||
−0.758909 | + | 0.651197i | \(0.774267\pi\) | |||||||
\(192\) | 2.88714e78 | 0.485931 | ||||||||
\(193\) | 1.51305e78 | 0.212876 | 0.106438 | − | 0.994319i | \(-0.466055\pi\) | ||||
0.106438 | + | 0.994319i | \(0.466055\pi\) | |||||||
\(194\) | 1.34406e78 | 0.158219 | ||||||||
\(195\) | −1.72173e78 | −0.169735 | ||||||||
\(196\) | 1.10207e79 | 0.910699 | ||||||||
\(197\) | 1.05867e79 | 0.733967 | 0.366983 | − | 0.930227i | \(-0.380391\pi\) | ||||
0.366983 | + | 0.930227i | \(0.380391\pi\) | |||||||
\(198\) | −9.53499e77 | −0.0555100 | ||||||||
\(199\) | 2.47010e79 | 1.20860 | 0.604300 | − | 0.796757i | \(-0.293453\pi\) | ||||
0.604300 | + | 0.796757i | \(0.293453\pi\) | |||||||
\(200\) | −2.01349e79 | −0.828732 | ||||||||
\(201\) | −4.12511e76 | −0.00142946 | ||||||||
\(202\) | −5.02537e78 | −0.146739 | ||||||||
\(203\) | −6.94869e78 | −0.171116 | ||||||||
\(204\) | −3.27034e79 | −0.679754 | ||||||||
\(205\) | −1.42810e80 | −2.50755 | ||||||||
\(206\) | −1.64734e79 | −0.244548 | ||||||||
\(207\) | 3.70790e79 | 0.465749 | ||||||||
\(208\) | 1.34794e79 | 0.143379 | ||||||||
\(209\) | 1.04401e80 | 0.941144 | ||||||||
\(210\) | −5.92055e78 | −0.0452686 | ||||||||
\(211\) | −1.98758e80 | −1.28997 | −0.644984 | − | 0.764196i | \(-0.723136\pi\) | ||||
−0.644984 | + | 0.764196i | \(0.723136\pi\) | |||||||
\(212\) | −6.67289e79 | −0.367898 | ||||||||
\(213\) | 4.10105e79 | 0.192220 | ||||||||
\(214\) | 2.62203e79 | 0.104559 | ||||||||
\(215\) | −7.98999e79 | −0.271281 | ||||||||
\(216\) | 2.15644e79 | 0.0623854 | ||||||||
\(217\) | 8.41655e79 | 0.207622 | ||||||||
\(218\) | −1.46320e80 | −0.308003 | ||||||||
\(219\) | −9.26106e79 | −0.166471 | ||||||||
\(220\) | 1.21078e81 | 1.85988 | ||||||||
\(221\) | −1.43598e80 | −0.188632 | ||||||||
\(222\) | −9.35397e79 | −0.105152 | ||||||||
\(223\) | 7.81695e80 | 0.752522 | 0.376261 | − | 0.926514i | \(-0.377210\pi\) | ||||
0.376261 | + | 0.926514i | \(0.377210\pi\) | |||||||
\(224\) | 1.45785e80 | 0.120270 | ||||||||
\(225\) | 1.20455e81 | 0.852174 | ||||||||
\(226\) | −2.59997e80 | −0.157844 | ||||||||
\(227\) | 7.53245e80 | 0.392685 | 0.196343 | − | 0.980535i | \(-0.437094\pi\) | ||||
0.196343 | + | 0.980535i | \(0.437094\pi\) | |||||||
\(228\) | −1.16441e81 | −0.521621 | ||||||||
\(229\) | −1.05540e81 | −0.406532 | −0.203266 | − | 0.979124i | \(-0.565156\pi\) | ||||
−0.203266 | + | 0.979124i | \(0.565156\pi\) | |||||||
\(230\) | 1.30627e81 | 0.432934 | ||||||||
\(231\) | 5.18940e80 | 0.148082 | ||||||||
\(232\) | 8.91624e80 | 0.219203 | ||||||||
\(233\) | 7.14672e81 | 1.51470 | 0.757351 | − | 0.653008i | \(-0.226493\pi\) | ||||
0.757351 | + | 0.653008i | \(0.226493\pi\) | |||||||
\(234\) | 4.66961e79 | 0.00853756 | ||||||||
\(235\) | −7.37441e81 | −1.16382 | ||||||||
\(236\) | −1.33183e82 | −1.81546 | ||||||||
\(237\) | 4.84170e81 | 0.570401 | ||||||||
\(238\) | −4.93795e80 | −0.0503085 | ||||||||
\(239\) | −5.20728e81 | −0.459075 | −0.229537 | − | 0.973300i | \(-0.573721\pi\) | ||||
−0.229537 | + | 0.973300i | \(0.573721\pi\) | |||||||
\(240\) | −1.31192e82 | −1.00143 | ||||||||
\(241\) | −8.58844e81 | −0.567971 | −0.283986 | − | 0.958829i | \(-0.591657\pi\) | ||||
−0.283986 | + | 0.958829i | \(0.591657\pi\) | |||||||
\(242\) | 7.83416e79 | 0.00449120 | ||||||||
\(243\) | −1.29007e81 | −0.0641500 | ||||||||
\(244\) | 4.45389e82 | 1.92216 | ||||||||
\(245\) | −4.70980e82 | −1.76511 | ||||||||
\(246\) | 3.87323e81 | 0.126128 | ||||||||
\(247\) | −5.11285e81 | −0.144750 | ||||||||
\(248\) | −1.07997e82 | −0.265968 | ||||||||
\(249\) | 1.49461e82 | 0.320368 | ||||||||
\(250\) | 2.58366e82 | 0.482286 | ||||||||
\(251\) | 1.36885e82 | 0.222646 | 0.111323 | − | 0.993784i | \(-0.464491\pi\) | ||||
0.111323 | + | 0.993784i | \(0.464491\pi\) | |||||||
\(252\) | −5.78790e81 | −0.0820734 | ||||||||
\(253\) | −1.14495e83 | −1.41621 | ||||||||
\(254\) | 1.29795e82 | 0.140118 | ||||||||
\(255\) | 1.39761e83 | 1.31750 | ||||||||
\(256\) | 8.99516e82 | 0.740850 | ||||||||
\(257\) | 1.35870e83 | 0.978209 | 0.489104 | − | 0.872225i | \(-0.337324\pi\) | ||||
0.489104 | + | 0.872225i | \(0.337324\pi\) | |||||||
\(258\) | 2.16702e81 | 0.0136453 | ||||||||
\(259\) | 5.09088e82 | 0.280511 | ||||||||
\(260\) | −5.92962e82 | −0.286053 | ||||||||
\(261\) | −5.33406e82 | −0.225403 | ||||||||
\(262\) | 2.66614e82 | 0.0987389 | ||||||||
\(263\) | −2.74224e82 | −0.0890495 | −0.0445247 | − | 0.999008i | \(-0.514177\pi\) | ||||
−0.0445247 | + | 0.999008i | \(0.514177\pi\) | |||||||
\(264\) | −6.65880e82 | −0.189697 | ||||||||
\(265\) | 2.85172e83 | 0.713057 | ||||||||
\(266\) | −1.75817e82 | −0.0386051 | ||||||||
\(267\) | 2.75345e83 | 0.531175 | ||||||||
\(268\) | −1.42069e81 | −0.00240906 | ||||||||
\(269\) | −3.09103e83 | −0.460945 | −0.230473 | − | 0.973079i | \(-0.574027\pi\) | ||||
−0.230473 | + | 0.973079i | \(0.574027\pi\) | |||||||
\(270\) | −4.54483e82 | −0.0596303 | ||||||||
\(271\) | 1.04318e84 | 1.20481 | 0.602404 | − | 0.798191i | \(-0.294210\pi\) | ||||
0.602404 | + | 0.798191i | \(0.294210\pi\) | |||||||
\(272\) | −1.09419e84 | −1.11292 | ||||||||
\(273\) | −2.54142e82 | −0.0227754 | ||||||||
\(274\) | −2.99261e83 | −0.236405 | ||||||||
\(275\) | −3.71949e84 | −2.59123 | ||||||||
\(276\) | 1.27700e84 | 0.784924 | ||||||||
\(277\) | −2.70579e84 | −1.46806 | −0.734028 | − | 0.679119i | \(-0.762362\pi\) | ||||
−0.734028 | + | 0.679119i | \(0.762362\pi\) | |||||||
\(278\) | −3.90414e83 | −0.187059 | ||||||||
\(279\) | 6.46084e83 | 0.273492 | ||||||||
\(280\) | −4.13464e83 | −0.154698 | ||||||||
\(281\) | −1.62527e84 | −0.537721 | −0.268861 | − | 0.963179i | \(-0.586647\pi\) | ||||
−0.268861 | + | 0.963179i | \(0.586647\pi\) | |||||||
\(282\) | 2.00006e83 | 0.0585395 | ||||||||
\(283\) | 5.71736e84 | 1.48103 | 0.740514 | − | 0.672041i | \(-0.234582\pi\) | ||||
0.740514 | + | 0.672041i | \(0.234582\pi\) | |||||||
\(284\) | 1.41240e84 | 0.323948 | ||||||||
\(285\) | 4.97622e84 | 1.01100 | ||||||||
\(286\) | −1.44191e83 | −0.0259604 | ||||||||
\(287\) | −2.10800e84 | −0.336469 | ||||||||
\(288\) | 1.11910e84 | 0.158426 | ||||||||
\(289\) | 3.69540e84 | 0.464180 | ||||||||
\(290\) | −1.87915e84 | −0.209523 | ||||||||
\(291\) | −5.61527e84 | −0.555984 | ||||||||
\(292\) | −3.18950e84 | −0.280553 | ||||||||
\(293\) | −1.89352e85 | −1.48025 | −0.740127 | − | 0.672467i | \(-0.765235\pi\) | ||||
−0.740127 | + | 0.672467i | \(0.765235\pi\) | |||||||
\(294\) | 1.27738e84 | 0.0887842 | ||||||||
\(295\) | 5.69171e85 | 3.51871 | ||||||||
\(296\) | −6.53238e84 | −0.359342 | ||||||||
\(297\) | 3.98356e84 | 0.195063 | ||||||||
\(298\) | −1.60361e84 | −0.0699258 | ||||||||
\(299\) | 5.60722e84 | 0.217817 | ||||||||
\(300\) | 4.14847e85 | 1.43616 | ||||||||
\(301\) | −1.17939e84 | −0.0364011 | ||||||||
\(302\) | 1.10832e85 | 0.305089 | ||||||||
\(303\) | 2.09952e85 | 0.515642 | ||||||||
\(304\) | −3.89589e85 | −0.854019 | ||||||||
\(305\) | −1.90341e86 | −3.72552 | ||||||||
\(306\) | −3.79054e84 | −0.0662693 | ||||||||
\(307\) | −6.25855e84 | −0.0977686 | −0.0488843 | − | 0.998804i | \(-0.515567\pi\) | ||||
−0.0488843 | + | 0.998804i | \(0.515567\pi\) | |||||||
\(308\) | 1.78723e85 | 0.249563 | ||||||||
\(309\) | 6.88232e85 | 0.859344 | ||||||||
\(310\) | 2.27611e85 | 0.254223 | ||||||||
\(311\) | −7.80584e85 | −0.780165 | −0.390082 | − | 0.920780i | \(-0.627554\pi\) | ||||
−0.390082 | + | 0.920780i | \(0.627554\pi\) | |||||||
\(312\) | 3.26104e84 | 0.0291758 | ||||||||
\(313\) | −8.60592e85 | −0.689474 | −0.344737 | − | 0.938699i | \(-0.612032\pi\) | ||||
−0.344737 | + | 0.938699i | \(0.612032\pi\) | |||||||
\(314\) | 5.88165e84 | 0.0422110 | ||||||||
\(315\) | 2.47351e85 | 0.159074 | ||||||||
\(316\) | 1.66748e86 | 0.961294 | ||||||||
\(317\) | −2.04537e86 | −1.05737 | −0.528684 | − | 0.848819i | \(-0.677314\pi\) | ||||
−0.528684 | + | 0.848819i | \(0.677314\pi\) | |||||||
\(318\) | −7.73434e84 | −0.0358664 | ||||||||
\(319\) | 1.64709e86 | 0.685390 | ||||||||
\(320\) | −4.24935e86 | −1.58726 | ||||||||
\(321\) | −1.09544e86 | −0.367422 | ||||||||
\(322\) | 1.92817e85 | 0.0580921 | ||||||||
\(323\) | 4.15035e86 | 1.12356 | ||||||||
\(324\) | −4.44299e85 | −0.108112 | ||||||||
\(325\) | 1.82156e86 | 0.398536 | ||||||||
\(326\) | −5.46338e85 | −0.107511 | ||||||||
\(327\) | 6.11301e86 | 1.08232 | ||||||||
\(328\) | 2.70489e86 | 0.431024 | ||||||||
\(329\) | −1.08853e86 | −0.156164 | ||||||||
\(330\) | 1.40338e86 | 0.181320 | ||||||||
\(331\) | 2.28247e86 | 0.265668 | 0.132834 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132834 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(332\) | 5.14741e86 | 0.539915 | ||||||||
\(333\) | 3.90794e86 | 0.369506 | ||||||||
\(334\) | −3.01352e86 | −0.256934 | ||||||||
\(335\) | 6.07143e84 | 0.00466922 | ||||||||
\(336\) | −1.93651e86 | −0.134374 | ||||||||
\(337\) | −1.58037e87 | −0.989754 | −0.494877 | − | 0.868963i | \(-0.664787\pi\) | ||||
−0.494877 | + | 0.868963i | \(0.664787\pi\) | |||||||
\(338\) | −2.83516e86 | −0.160307 | ||||||||
\(339\) | 1.08623e87 | 0.554664 | ||||||||
\(340\) | 4.81336e87 | 2.22037 | ||||||||
\(341\) | −1.99502e87 | −0.831613 | ||||||||
\(342\) | −1.34963e86 | −0.0508528 | ||||||||
\(343\) | −1.43798e87 | −0.489898 | ||||||||
\(344\) | 1.51334e86 | 0.0466306 | ||||||||
\(345\) | −5.45737e87 | −1.52134 | ||||||||
\(346\) | 4.65303e83 | 0.000117384 0 | ||||||||
\(347\) | 1.43275e85 | 0.00327193 | 0.00163597 | − | 0.999999i | \(-0.499479\pi\) | ||||
0.00163597 | + | 0.999999i | \(0.499479\pi\) | |||||||
\(348\) | −1.83705e87 | −0.379871 | ||||||||
\(349\) | −7.98599e87 | −1.49572 | −0.747862 | − | 0.663854i | \(-0.768920\pi\) | ||||
−0.747862 | + | 0.663854i | \(0.768920\pi\) | |||||||
\(350\) | 6.26385e86 | 0.106290 | ||||||||
\(351\) | −1.95089e86 | −0.0300011 | ||||||||
\(352\) | −3.45562e87 | −0.481730 | ||||||||
\(353\) | 4.54672e87 | 0.574740 | 0.287370 | − | 0.957820i | \(-0.407219\pi\) | ||||
0.287370 | + | 0.957820i | \(0.407219\pi\) | |||||||
\(354\) | −1.54369e87 | −0.176989 | ||||||||
\(355\) | −6.03602e87 | −0.627874 | ||||||||
\(356\) | 9.48285e87 | 0.895187 | ||||||||
\(357\) | 2.06299e87 | 0.176785 | ||||||||
\(358\) | −1.18154e87 | −0.0919356 | ||||||||
\(359\) | 1.80684e88 | 1.27691 | 0.638456 | − | 0.769659i | \(-0.279574\pi\) | ||||
0.638456 | + | 0.769659i | \(0.279574\pi\) | |||||||
\(360\) | −3.17390e87 | −0.203778 | ||||||||
\(361\) | −2.36210e87 | −0.137816 | ||||||||
\(362\) | −1.99241e87 | −0.105665 | ||||||||
\(363\) | −3.27298e86 | −0.0157821 | ||||||||
\(364\) | −8.75265e86 | −0.0383833 | ||||||||
\(365\) | 1.36306e88 | 0.543766 | ||||||||
\(366\) | 5.16236e87 | 0.187392 | ||||||||
\(367\) | −7.20654e87 | −0.238094 | −0.119047 | − | 0.992889i | \(-0.537984\pi\) | ||||
−0.119047 | + | 0.992889i | \(0.537984\pi\) | |||||||
\(368\) | 4.27258e88 | 1.28511 | ||||||||
\(369\) | −1.61817e88 | −0.443216 | ||||||||
\(370\) | 1.37674e88 | 0.343472 | ||||||||
\(371\) | 4.20939e87 | 0.0956796 | ||||||||
\(372\) | 2.22511e88 | 0.460914 | ||||||||
\(373\) | 3.41896e88 | 0.645565 | 0.322782 | − | 0.946473i | \(-0.395382\pi\) | ||||
0.322782 | + | 0.946473i | \(0.395382\pi\) | |||||||
\(374\) | 1.17047e88 | 0.201507 | ||||||||
\(375\) | −1.07941e89 | −1.69476 | ||||||||
\(376\) | 1.39675e88 | 0.200050 | ||||||||
\(377\) | −8.06634e87 | −0.105414 | ||||||||
\(378\) | −6.70857e86 | −0.00800134 | ||||||||
\(379\) | −8.74868e88 | −0.952555 | −0.476277 | − | 0.879295i | \(-0.658014\pi\) | ||||
−0.476277 | + | 0.879295i | \(0.658014\pi\) | |||||||
\(380\) | 1.71381e89 | 1.70384 | ||||||||
\(381\) | −5.42260e88 | −0.492375 | ||||||||
\(382\) | −3.00637e88 | −0.249377 | ||||||||
\(383\) | −5.77543e88 | −0.437751 | −0.218875 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218875 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(384\) | 5.11358e88 | 0.354240 | ||||||||
\(385\) | −7.63787e88 | −0.483701 | ||||||||
\(386\) | 6.03984e87 | 0.0349754 | ||||||||
\(387\) | −9.05344e87 | −0.0479496 | ||||||||
\(388\) | −1.93390e89 | −0.936998 | ||||||||
\(389\) | 9.43356e88 | 0.418229 | 0.209115 | − | 0.977891i | \(-0.432942\pi\) | ||||
0.209115 | + | 0.977891i | \(0.432942\pi\) | |||||||
\(390\) | −6.87284e87 | −0.0278873 | ||||||||
\(391\) | −4.55164e89 | −1.69071 | ||||||||
\(392\) | 8.92060e88 | 0.303406 | ||||||||
\(393\) | −1.11387e89 | −0.346969 | ||||||||
\(394\) | 4.22603e88 | 0.120590 | ||||||||
\(395\) | −7.12612e89 | −1.86317 | ||||||||
\(396\) | 1.37194e89 | 0.328738 | ||||||||
\(397\) | 6.06080e89 | 1.33124 | 0.665621 | − | 0.746290i | \(-0.268167\pi\) | ||||
0.665621 | + | 0.746290i | \(0.268167\pi\) | |||||||
\(398\) | 9.86019e88 | 0.198573 | ||||||||
\(399\) | 7.34535e88 | 0.135659 | ||||||||
\(400\) | 1.38799e90 | 2.35135 | ||||||||
\(401\) | −6.19345e88 | −0.0962614 | −0.0481307 | − | 0.998841i | \(-0.515326\pi\) | ||||
−0.0481307 | + | 0.998841i | \(0.515326\pi\) | |||||||
\(402\) | −1.64667e86 | −0.000234859 0 | ||||||||
\(403\) | 9.77030e88 | 0.127904 | ||||||||
\(404\) | 7.23072e89 | 0.869009 | ||||||||
\(405\) | 1.89875e89 | 0.209542 | ||||||||
\(406\) | −2.77379e88 | −0.0281142 | ||||||||
\(407\) | −1.20672e90 | −1.12357 | ||||||||
\(408\) | −2.64714e89 | −0.226465 | ||||||||
\(409\) | −1.19150e90 | −0.936788 | −0.468394 | − | 0.883520i | \(-0.655167\pi\) | ||||
−0.468394 | + | 0.883520i | \(0.655167\pi\) | |||||||
\(410\) | −5.70071e89 | −0.411989 | ||||||||
\(411\) | 1.25026e90 | 0.830728 | ||||||||
\(412\) | 2.37027e90 | 1.44825 | ||||||||
\(413\) | 8.40147e89 | 0.472148 | ||||||||
\(414\) | 1.48013e89 | 0.0765223 | ||||||||
\(415\) | −2.19979e90 | −1.04646 | ||||||||
\(416\) | 1.69233e89 | 0.0740911 | ||||||||
\(417\) | 1.63108e90 | 0.657329 | ||||||||
\(418\) | 4.16749e89 | 0.154630 | ||||||||
\(419\) | 1.29706e90 | 0.443175 | 0.221588 | − | 0.975140i | \(-0.428876\pi\) | ||||
0.221588 | + | 0.975140i | \(0.428876\pi\) | |||||||
\(420\) | 8.51875e89 | 0.268087 | ||||||||
\(421\) | −5.23705e88 | −0.0151829 | −0.00759144 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00759144 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(422\) | −7.93405e89 | −0.211941 | ||||||||
\(423\) | −8.35592e89 | −0.205708 | ||||||||
\(424\) | −5.40130e89 | −0.122568 | ||||||||
\(425\) | −1.47865e91 | −3.09348 | ||||||||
\(426\) | 1.63707e89 | 0.0315817 | ||||||||
\(427\) | −2.80960e90 | −0.499900 | ||||||||
\(428\) | −3.77269e90 | −0.619214 | ||||||||
\(429\) | 6.02408e89 | 0.0912250 | ||||||||
\(430\) | −3.18946e89 | −0.0445713 | ||||||||
\(431\) | −5.57328e90 | −0.718861 | −0.359430 | − | 0.933172i | \(-0.617029\pi\) | ||||
−0.359430 | + | 0.933172i | \(0.617029\pi\) | |||||||
\(432\) | −1.48653e90 | −0.177005 | ||||||||
\(433\) | 1.32658e91 | 1.45848 | 0.729242 | − | 0.684256i | \(-0.239873\pi\) | ||||
0.729242 | + | 0.684256i | \(0.239873\pi\) | |||||||
\(434\) | 3.35974e89 | 0.0341122 | ||||||||
\(435\) | 7.85078e90 | 0.736264 | ||||||||
\(436\) | 2.10532e91 | 1.82404 | ||||||||
\(437\) | −1.62062e91 | −1.29740 | ||||||||
\(438\) | −3.69685e89 | −0.0273511 | ||||||||
\(439\) | −6.30768e90 | −0.431364 | −0.215682 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215682 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(440\) | 9.80056e90 | 0.619632 | ||||||||
\(441\) | −5.33666e90 | −0.311988 | ||||||||
\(442\) | −5.73219e89 | −0.0309922 | ||||||||
\(443\) | 2.35910e91 | 1.17982 | 0.589912 | − | 0.807467i | \(-0.299162\pi\) | ||||
0.589912 | + | 0.807467i | \(0.299162\pi\) | |||||||
\(444\) | 1.34589e91 | 0.622726 | ||||||||
\(445\) | −4.05258e91 | −1.73505 | ||||||||
\(446\) | 3.12039e90 | 0.123639 | ||||||||
\(447\) | 6.69961e90 | 0.245720 | ||||||||
\(448\) | −6.27242e90 | −0.212982 | ||||||||
\(449\) | 2.35122e91 | 0.739257 | 0.369628 | − | 0.929180i | \(-0.379485\pi\) | ||||
0.369628 | + | 0.929180i | \(0.379485\pi\) | |||||||
\(450\) | 4.80835e90 | 0.140012 | ||||||||
\(451\) | 4.99670e91 | 1.34770 | ||||||||
\(452\) | 3.74095e91 | 0.934773 | ||||||||
\(453\) | −4.63039e91 | −1.07209 | ||||||||
\(454\) | 3.00682e90 | 0.0645180 | ||||||||
\(455\) | 3.74052e90 | 0.0743942 | ||||||||
\(456\) | −9.42522e90 | −0.173782 | ||||||||
\(457\) | 4.87186e91 | 0.832887 | 0.416444 | − | 0.909162i | \(-0.363276\pi\) | ||||
0.416444 | + | 0.909162i | \(0.363276\pi\) | |||||||
\(458\) | −4.21298e90 | −0.0667930 | ||||||||
\(459\) | 1.58363e91 | 0.232871 | ||||||||
\(460\) | −1.87952e92 | −2.56390 | ||||||||
\(461\) | −6.07739e91 | −0.769193 | −0.384596 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384596 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(462\) | 2.07152e90 | 0.0243299 | ||||||||
\(463\) | 8.29614e91 | 0.904341 | 0.452170 | − | 0.891932i | \(-0.350650\pi\) | ||||
0.452170 | + | 0.891932i | \(0.350650\pi\) | |||||||
\(464\) | −6.14638e91 | −0.621941 | ||||||||
\(465\) | −9.50920e91 | −0.893341 | ||||||||
\(466\) | 2.85284e91 | 0.248865 | ||||||||
\(467\) | 1.73212e92 | 1.40329 | 0.701644 | − | 0.712528i | \(-0.252450\pi\) | ||||
0.701644 | + | 0.712528i | \(0.252450\pi\) | |||||||
\(468\) | −6.71884e90 | −0.0505606 | ||||||||
\(469\) | 8.96196e88 | 0.000626527 0 | ||||||||
\(470\) | −2.94373e91 | −0.191215 | ||||||||
\(471\) | −2.45725e91 | −0.148330 | ||||||||
\(472\) | −1.07804e92 | −0.604833 | ||||||||
\(473\) | 2.79558e91 | 0.145802 | ||||||||
\(474\) | 1.93272e91 | 0.0937166 | ||||||||
\(475\) | −5.26477e92 | −2.37383 | ||||||||
\(476\) | 7.10494e91 | 0.297934 | ||||||||
\(477\) | 3.23128e91 | 0.126035 | ||||||||
\(478\) | −2.07866e91 | −0.0754258 | ||||||||
\(479\) | 3.66321e92 | 1.23676 | 0.618382 | − | 0.785878i | \(-0.287789\pi\) | ||||
0.618382 | + | 0.785878i | \(0.287789\pi\) | |||||||
\(480\) | −1.64711e92 | −0.517487 | ||||||||
\(481\) | 5.90971e91 | 0.172807 | ||||||||
\(482\) | −3.42835e91 | −0.0933174 | ||||||||
\(483\) | −8.05557e91 | −0.204136 | ||||||||
\(484\) | −1.12721e91 | −0.0265975 | ||||||||
\(485\) | 8.26468e92 | 1.81608 | ||||||||
\(486\) | −5.14973e90 | −0.0105398 | ||||||||
\(487\) | 5.74085e92 | 1.09453 | 0.547264 | − | 0.836960i | \(-0.315669\pi\) | ||||
0.547264 | + | 0.836960i | \(0.315669\pi\) | |||||||
\(488\) | 3.60515e92 | 0.640383 | ||||||||
\(489\) | 2.28251e92 | 0.377796 | ||||||||
\(490\) | −1.88007e92 | −0.290007 | ||||||||
\(491\) | −1.00239e92 | −0.144121 | −0.0720604 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720604 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(492\) | −5.57298e92 | −0.746950 | ||||||||
\(493\) | 6.54783e92 | 0.818236 | ||||||||
\(494\) | −2.04096e91 | −0.0237824 | ||||||||
\(495\) | −5.86310e92 | −0.637159 | ||||||||
\(496\) | 7.44476e92 | 0.754628 | ||||||||
\(497\) | −8.90970e91 | −0.0842496 | ||||||||
\(498\) | 5.96620e91 | 0.0526363 | ||||||||
\(499\) | 5.99629e92 | 0.493644 | 0.246822 | − | 0.969061i | \(-0.420614\pi\) | ||||
0.246822 | + | 0.969061i | \(0.420614\pi\) | |||||||
\(500\) | −3.71748e93 | −2.85617 | ||||||||
\(501\) | 1.25900e93 | 0.902868 | ||||||||
\(502\) | 5.46423e91 | 0.0365806 | ||||||||
\(503\) | 2.62893e93 | 1.64317 | 0.821587 | − | 0.570083i | \(-0.193089\pi\) | ||||
0.821587 | + | 0.570083i | \(0.193089\pi\) | |||||||
\(504\) | −4.68495e91 | −0.0273433 | ||||||||
\(505\) | −3.09011e93 | −1.68431 | ||||||||
\(506\) | −4.57044e92 | −0.232683 | ||||||||
\(507\) | 1.18448e93 | 0.563320 | ||||||||
\(508\) | −1.86754e93 | −0.829797 | ||||||||
\(509\) | −2.27493e93 | −0.944504 | −0.472252 | − | 0.881464i | \(-0.656559\pi\) | ||||
−0.472252 | + | 0.881464i | \(0.656559\pi\) | |||||||
\(510\) | 5.57901e92 | 0.216464 | ||||||||
\(511\) | 2.01200e92 | 0.0729638 | ||||||||
\(512\) | 2.16904e93 | 0.735283 | ||||||||
\(513\) | 5.63855e92 | 0.178697 | ||||||||
\(514\) | 5.42370e92 | 0.160719 | ||||||||
\(515\) | −1.01295e94 | −2.80699 | ||||||||
\(516\) | −3.11800e92 | −0.0808093 | ||||||||
\(517\) | 2.58020e93 | 0.625503 | ||||||||
\(518\) | 2.03219e92 | 0.0460879 | ||||||||
\(519\) | −1.94396e90 | −0.000412490 0 | ||||||||
\(520\) | −4.79967e92 | −0.0953007 | ||||||||
\(521\) | 8.07097e93 | 1.49977 | 0.749884 | − | 0.661569i | \(-0.230109\pi\) | ||||
0.749884 | + | 0.661569i | \(0.230109\pi\) | |||||||
\(522\) | −2.12926e92 | −0.0370337 | ||||||||
\(523\) | 5.06536e93 | 0.824712 | 0.412356 | − | 0.911023i | \(-0.364706\pi\) | ||||
0.412356 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(524\) | −3.83616e93 | −0.584746 | ||||||||
\(525\) | −2.61693e93 | −0.373505 | ||||||||
\(526\) | −1.09465e92 | −0.0146308 | ||||||||
\(527\) | −7.93101e93 | −0.992801 | ||||||||
\(528\) | 4.59022e93 | 0.538224 | ||||||||
\(529\) | 8.66947e93 | 0.952296 | ||||||||
\(530\) | 1.13836e93 | 0.117155 | ||||||||
\(531\) | 6.44926e93 | 0.621941 | ||||||||
\(532\) | 2.52973e93 | 0.228625 | ||||||||
\(533\) | −2.44706e93 | −0.207279 | ||||||||
\(534\) | 1.09913e93 | 0.0872719 | ||||||||
\(535\) | 1.61229e94 | 1.20016 | ||||||||
\(536\) | −1.14996e91 | −0.000802596 0 | ||||||||
\(537\) | 4.93628e93 | 0.323063 | ||||||||
\(538\) | −1.23388e93 | −0.0757332 | ||||||||
\(539\) | 1.64789e94 | 0.948671 | ||||||||
\(540\) | 6.53929e93 | 0.353139 | ||||||||
\(541\) | −1.95910e94 | −0.992546 | −0.496273 | − | 0.868167i | \(-0.665298\pi\) | ||||
−0.496273 | + | 0.868167i | \(0.665298\pi\) | |||||||
\(542\) | 4.16418e93 | 0.197950 | ||||||||
\(543\) | 8.32396e93 | 0.371309 | ||||||||
\(544\) | −1.37375e94 | −0.575102 | ||||||||
\(545\) | −8.99726e94 | −3.53534 | ||||||||
\(546\) | −1.01449e92 | −0.00374199 | ||||||||
\(547\) | −3.66228e92 | −0.0126820 | −0.00634101 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00634101 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(548\) | 4.30590e94 | 1.40002 | ||||||||
\(549\) | −2.15675e94 | −0.658497 | ||||||||
\(550\) | −1.48476e94 | −0.425738 | ||||||||
\(551\) | 2.33137e94 | 0.627887 | ||||||||
\(552\) | 1.03365e94 | 0.261503 | ||||||||
\(553\) | −1.05188e94 | −0.250005 | ||||||||
\(554\) | −1.08011e94 | −0.241201 | ||||||||
\(555\) | −5.75178e94 | −1.20697 | ||||||||
\(556\) | 5.61745e94 | 1.10779 | ||||||||
\(557\) | 4.28418e94 | 0.794078 | 0.397039 | − | 0.917802i | \(-0.370038\pi\) | ||||
0.397039 | + | 0.917802i | \(0.370038\pi\) | |||||||
\(558\) | 2.57905e93 | 0.0449345 | ||||||||
\(559\) | −1.36909e93 | −0.0224246 | ||||||||
\(560\) | 2.85020e94 | 0.438923 | ||||||||
\(561\) | −4.89003e94 | −0.708097 | ||||||||
\(562\) | −6.48778e93 | −0.0883473 | ||||||||
\(563\) | −3.80080e94 | −0.486783 | −0.243391 | − | 0.969928i | \(-0.578260\pi\) | ||||
−0.243391 | + | 0.969928i | \(0.578260\pi\) | |||||||
\(564\) | −2.87777e94 | −0.346679 | ||||||||
\(565\) | −1.59873e95 | −1.81177 | ||||||||
\(566\) | 2.28227e94 | 0.243332 | ||||||||
\(567\) | 2.80273e93 | 0.0281168 | ||||||||
\(568\) | 1.14325e94 | 0.107926 | ||||||||
\(569\) | −1.11959e94 | −0.0994682 | −0.0497341 | − | 0.998762i | \(-0.515837\pi\) | ||||
−0.0497341 | + | 0.998762i | \(0.515837\pi\) | |||||||
\(570\) | 1.98642e94 | 0.166107 | ||||||||
\(571\) | 3.88842e94 | 0.306074 | 0.153037 | − | 0.988220i | \(-0.451095\pi\) | ||||
0.153037 | + | 0.988220i | \(0.451095\pi\) | |||||||
\(572\) | 2.07469e94 | 0.153741 | ||||||||
\(573\) | 1.25601e95 | 0.876313 | ||||||||
\(574\) | −8.41475e93 | −0.0552817 | ||||||||
\(575\) | 5.77382e95 | 3.57209 | ||||||||
\(576\) | −4.81493e94 | −0.280553 | ||||||||
\(577\) | −1.13415e95 | −0.622451 | −0.311226 | − | 0.950336i | \(-0.600739\pi\) | ||||
−0.311226 | + | 0.950336i | \(0.600739\pi\) | |||||||
\(578\) | 1.47514e94 | 0.0762645 | ||||||||
\(579\) | −2.52334e94 | −0.122904 | ||||||||
\(580\) | 2.70380e95 | 1.24082 | ||||||||
\(581\) | −3.24709e94 | −0.140416 | ||||||||
\(582\) | −2.24152e94 | −0.0913480 | ||||||||
\(583\) | −9.97775e94 | −0.383237 | ||||||||
\(584\) | −2.58171e94 | −0.0934682 | ||||||||
\(585\) | 2.87136e94 | 0.0979964 | ||||||||
\(586\) | −7.55859e94 | −0.243205 | ||||||||
\(587\) | −3.85716e95 | −1.17018 | −0.585090 | − | 0.810968i | \(-0.698941\pi\) | ||||
−0.585090 | + | 0.810968i | \(0.698941\pi\) | |||||||
\(588\) | −1.83794e95 | −0.525793 | ||||||||
\(589\) | −2.82386e95 | −0.761842 | ||||||||
\(590\) | 2.27203e95 | 0.578122 | ||||||||
\(591\) | −1.76557e95 | −0.423756 | ||||||||
\(592\) | 4.50308e95 | 1.01955 | ||||||||
\(593\) | 3.26456e95 | 0.697329 | 0.348664 | − | 0.937248i | \(-0.386635\pi\) | ||||
0.348664 | + | 0.937248i | \(0.386635\pi\) | |||||||
\(594\) | 1.59017e94 | 0.0320487 | ||||||||
\(595\) | −3.03636e95 | −0.577455 | ||||||||
\(596\) | 2.30734e95 | 0.414110 | ||||||||
\(597\) | −4.11943e95 | −0.697786 | ||||||||
\(598\) | 2.23830e94 | 0.0357872 | ||||||||
\(599\) | −1.28868e96 | −1.94501 | −0.972504 | − | 0.232887i | \(-0.925183\pi\) | ||||
−0.972504 | + | 0.232887i | \(0.925183\pi\) | |||||||
\(600\) | 3.35793e95 | 0.478469 | ||||||||
\(601\) | 4.73264e95 | 0.636698 | 0.318349 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318349 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(602\) | −4.70793e93 | −0.00598069 | ||||||||
\(603\) | 6.87952e92 | 0.000825298 0 | ||||||||
\(604\) | −1.59470e96 | −1.80678 | ||||||||
\(605\) | 4.81725e94 | 0.0515512 | ||||||||
\(606\) | 8.38090e94 | 0.0847198 | ||||||||
\(607\) | −1.65228e94 | −0.0157788 | −0.00788939 | − | 0.999969i | \(-0.502511\pi\) | ||||
−0.00788939 | + | 0.999969i | \(0.502511\pi\) | |||||||
\(608\) | −4.89126e95 | −0.441314 | ||||||||
\(609\) | 1.15885e95 | 0.0987936 | ||||||||
\(610\) | −7.59807e95 | −0.612102 | ||||||||
\(611\) | −1.26361e95 | −0.0962036 | ||||||||
\(612\) | 5.45400e95 | 0.392456 | ||||||||
\(613\) | 2.85303e96 | 1.94053 | 0.970265 | − | 0.242045i | \(-0.0778181\pi\) | ||||
0.970265 | + | 0.242045i | \(0.0778181\pi\) | |||||||
\(614\) | −2.49830e94 | −0.0160633 | ||||||||
\(615\) | 2.38166e96 | 1.44773 | ||||||||
\(616\) | 1.44665e95 | 0.0831436 | ||||||||
\(617\) | 6.46108e95 | 0.351129 | 0.175564 | − | 0.984468i | \(-0.443825\pi\) | ||||
0.175564 | + | 0.984468i | \(0.443825\pi\) | |||||||
\(618\) | 2.74730e95 | 0.141190 | ||||||||
\(619\) | 6.71691e95 | 0.326469 | 0.163234 | − | 0.986587i | \(-0.447807\pi\) | ||||
0.163234 | + | 0.986587i | \(0.447807\pi\) | |||||||
\(620\) | −3.27496e96 | −1.50554 | ||||||||
\(621\) | −6.18374e95 | −0.268900 | ||||||||
\(622\) | −3.11596e95 | −0.128181 | ||||||||
\(623\) | −5.98197e95 | −0.232813 | ||||||||
\(624\) | −2.24799e95 | −0.0827800 | ||||||||
\(625\) | 8.55012e96 | 2.97928 | ||||||||
\(626\) | −3.43533e95 | −0.113280 | ||||||||
\(627\) | −1.74111e96 | −0.543370 | ||||||||
\(628\) | −8.46277e95 | −0.249980 | ||||||||
\(629\) | −4.79719e96 | −1.34134 | ||||||||
\(630\) | 9.87382e94 | 0.0261358 | ||||||||
\(631\) | −7.92321e95 | −0.198558 | −0.0992792 | − | 0.995060i | \(-0.531654\pi\) | ||||
−0.0992792 | + | 0.995060i | \(0.531654\pi\) | |||||||
\(632\) | 1.34972e96 | 0.320262 | ||||||||
\(633\) | 3.31472e96 | 0.744763 | ||||||||
\(634\) | −8.16474e95 | −0.173725 | ||||||||
\(635\) | 7.98110e96 | 1.60831 | ||||||||
\(636\) | 1.11285e96 | 0.212406 | ||||||||
\(637\) | −8.07028e95 | −0.145908 | ||||||||
\(638\) | 6.57487e95 | 0.112609 | ||||||||
\(639\) | −6.83940e95 | −0.110978 | ||||||||
\(640\) | −7.52628e96 | −1.15710 | ||||||||
\(641\) | −4.54296e96 | −0.661816 | −0.330908 | − | 0.943663i | \(-0.607355\pi\) | ||||
−0.330908 | + | 0.943663i | \(0.607355\pi\) | |||||||
\(642\) | −4.37280e95 | −0.0603673 | ||||||||
\(643\) | −5.85972e96 | −0.766652 | −0.383326 | − | 0.923613i | \(-0.625221\pi\) | ||||
−0.383326 | + | 0.923613i | \(0.625221\pi\) | |||||||
\(644\) | −2.77433e96 | −0.344030 | ||||||||
\(645\) | 1.33250e96 | 0.156624 | ||||||||
\(646\) | 1.65674e96 | 0.184601 | ||||||||
\(647\) | −1.30267e97 | −1.37606 | −0.688031 | − | 0.725681i | \(-0.741525\pi\) | ||||
−0.688031 | + | 0.725681i | \(0.741525\pi\) | |||||||
\(648\) | −3.59633e95 | −0.0360182 | ||||||||
\(649\) | −1.99145e97 | −1.89115 | ||||||||
\(650\) | 7.27135e95 | 0.0654794 | ||||||||
\(651\) | −1.40364e96 | −0.119871 | ||||||||
\(652\) | 7.86095e96 | 0.636698 | ||||||||
\(653\) | 2.42489e97 | 1.86289 | 0.931445 | − | 0.363883i | \(-0.118549\pi\) | ||||
0.931445 | + | 0.363883i | \(0.118549\pi\) | |||||||
\(654\) | 2.44020e96 | 0.177825 | ||||||||
\(655\) | 1.63942e97 | 1.13335 | ||||||||
\(656\) | −1.86460e97 | −1.22294 | ||||||||
\(657\) | 1.54448e96 | 0.0961121 | ||||||||
\(658\) | −4.34521e95 | −0.0256577 | ||||||||
\(659\) | 4.44616e96 | 0.249137 | 0.124568 | − | 0.992211i | \(-0.460245\pi\) | ||||
0.124568 | + | 0.992211i | \(0.460245\pi\) | |||||||
\(660\) | −2.01925e97 | −1.07380 | ||||||||
\(661\) | 2.46337e97 | 1.24331 | 0.621655 | − | 0.783291i | \(-0.286460\pi\) | ||||
0.621655 | + | 0.783291i | \(0.286460\pi\) | |||||||
\(662\) | 9.11123e95 | 0.0436492 | ||||||||
\(663\) | 2.39481e96 | 0.108907 | ||||||||
\(664\) | 4.16652e96 | 0.179877 | ||||||||
\(665\) | −1.08110e97 | −0.443119 | ||||||||
\(666\) | 1.55998e96 | 0.0607097 | ||||||||
\(667\) | −2.55679e97 | −0.944831 | ||||||||
\(668\) | 4.33599e97 | 1.52160 | ||||||||
\(669\) | −1.30365e97 | −0.434469 | ||||||||
\(670\) | 2.42361e94 | 0.000767152 0 | ||||||||
\(671\) | 6.65975e97 | 2.00231 | ||||||||
\(672\) | −2.43128e96 | −0.0694377 | ||||||||
\(673\) | −3.58072e97 | −0.971519 | −0.485759 | − | 0.874093i | \(-0.661457\pi\) | ||||
−0.485759 | + | 0.874093i | \(0.661457\pi\) | |||||||
\(674\) | −6.30856e96 | −0.162616 | ||||||||
\(675\) | −2.00885e97 | −0.492003 | ||||||||
\(676\) | 4.07936e97 | 0.949360 | ||||||||
\(677\) | 2.65612e97 | 0.587407 | 0.293704 | − | 0.955897i | \(-0.405112\pi\) | ||||
0.293704 | + | 0.955897i | \(0.405112\pi\) | |||||||
\(678\) | 4.33602e96 | 0.0911311 | ||||||||
\(679\) | 1.21994e97 | 0.243686 | ||||||||
\(680\) | 3.89612e97 | 0.739733 | ||||||||
\(681\) | −1.25620e97 | −0.226717 | ||||||||
\(682\) | −7.96377e96 | −0.136634 | ||||||||
\(683\) | 2.28473e97 | 0.372667 | 0.186333 | − | 0.982487i | \(-0.440340\pi\) | ||||
0.186333 | + | 0.982487i | \(0.440340\pi\) | |||||||
\(684\) | 1.94191e97 | 0.301158 | ||||||||
\(685\) | −1.84017e98 | −2.71351 | ||||||||
\(686\) | −5.74016e96 | −0.0804900 | ||||||||
\(687\) | 1.76011e97 | 0.234711 | ||||||||
\(688\) | −1.04322e97 | −0.132304 | ||||||||
\(689\) | 4.88645e96 | 0.0589427 | ||||||||
\(690\) | −2.17849e97 | −0.249955 | ||||||||
\(691\) | 6.64879e97 | 0.725688 | 0.362844 | − | 0.931850i | \(-0.381806\pi\) | ||||
0.362844 | + | 0.931850i | \(0.381806\pi\) | |||||||
\(692\) | −6.69498e94 | −0.000695167 0 | ||||||||
\(693\) | −8.65445e96 | −0.0854954 | ||||||||
\(694\) | 5.71930e94 | 0.000537577 0 | ||||||||
\(695\) | −2.40067e98 | −2.14712 | ||||||||
\(696\) | −1.48698e97 | −0.126557 | ||||||||
\(697\) | 1.98639e98 | 1.60892 | ||||||||
\(698\) | −3.18787e97 | −0.245747 | ||||||||
\(699\) | −1.19187e98 | −0.874514 | ||||||||
\(700\) | −9.01271e97 | −0.629467 | ||||||||
\(701\) | −1.82266e98 | −1.21181 | −0.605903 | − | 0.795538i | \(-0.707188\pi\) | ||||
−0.605903 | + | 0.795538i | \(0.707188\pi\) | |||||||
\(702\) | −7.78760e95 | −0.00492916 | ||||||||
\(703\) | −1.70805e98 | −1.02930 | ||||||||
\(704\) | 1.48679e98 | 0.853084 | ||||||||
\(705\) | 1.22984e98 | 0.671932 | ||||||||
\(706\) | 1.81497e97 | 0.0944295 | ||||||||
\(707\) | −4.56128e97 | −0.226005 | ||||||||
\(708\) | 2.22112e98 | 1.04815 | ||||||||
\(709\) | 2.78531e98 | 1.25193 | 0.625963 | − | 0.779853i | \(-0.284706\pi\) | ||||
0.625963 | + | 0.779853i | \(0.284706\pi\) | |||||||
\(710\) | −2.40947e97 | −0.103159 | ||||||||
\(711\) | −8.07460e97 | −0.329321 | ||||||||
\(712\) | 7.67579e97 | 0.298238 | ||||||||
\(713\) | 3.09690e98 | 1.14640 | ||||||||
\(714\) | 8.23511e96 | 0.0290457 | ||||||||
\(715\) | −8.86637e97 | −0.297980 | ||||||||
\(716\) | 1.70005e98 | 0.544456 | ||||||||
\(717\) | 8.68428e97 | 0.265047 | ||||||||
\(718\) | 7.21258e97 | 0.209796 | ||||||||
\(719\) | −1.07858e98 | −0.299023 | −0.149511 | − | 0.988760i | \(-0.547770\pi\) | ||||
−0.149511 | + | 0.988760i | \(0.547770\pi\) | |||||||
\(720\) | 2.18791e98 | 0.578175 | ||||||||
\(721\) | −1.49521e98 | −0.376648 | ||||||||
\(722\) | −9.42907e96 | −0.0226431 | ||||||||
\(723\) | 1.43231e98 | 0.327918 | ||||||||
\(724\) | 2.86677e98 | 0.625766 | ||||||||
\(725\) | −8.30600e98 | −1.72875 | ||||||||
\(726\) | −1.30652e96 | −0.00259300 | ||||||||
\(727\) | −1.83421e98 | −0.347145 | −0.173572 | − | 0.984821i | \(-0.555531\pi\) | ||||
−0.173572 | + | 0.984821i | \(0.555531\pi\) | |||||||
\(728\) | −7.08474e96 | −0.0127877 | ||||||||
\(729\) | 2.15147e97 | 0.0370370 | ||||||||
\(730\) | 5.44111e97 | 0.0893405 | ||||||||
\(731\) | 1.11136e98 | 0.174062 | ||||||||
\(732\) | −7.42783e98 | −1.10976 | ||||||||
\(733\) | 8.73500e98 | 1.24502 | 0.622509 | − | 0.782612i | \(-0.286113\pi\) | ||||
0.622509 | + | 0.782612i | \(0.286113\pi\) | |||||||
\(734\) | −2.87672e97 | −0.0391187 | ||||||||
\(735\) | 7.85462e98 | 1.01909 | ||||||||
\(736\) | 5.36420e98 | 0.664080 | ||||||||
\(737\) | −2.12430e96 | −0.00250951 | ||||||||
\(738\) | −6.45946e97 | −0.0728202 | ||||||||
\(739\) | 6.62422e98 | 0.712692 | 0.356346 | − | 0.934354i | \(-0.384023\pi\) | ||||
0.356346 | + | 0.934354i | \(0.384023\pi\) | |||||||
\(740\) | −1.98091e99 | −2.03409 | ||||||||
\(741\) | 8.52680e97 | 0.0835714 | ||||||||
\(742\) | 1.68032e97 | 0.0157201 | ||||||||
\(743\) | −1.53661e99 | −1.37230 | −0.686150 | − | 0.727460i | \(-0.740701\pi\) | ||||
−0.686150 | + | 0.727460i | \(0.740701\pi\) | |||||||
\(744\) | 1.80109e98 | 0.153557 | ||||||||
\(745\) | −9.86064e98 | −0.802627 | ||||||||
\(746\) | 1.36479e98 | 0.106066 | ||||||||
\(747\) | −2.49258e98 | −0.184965 | ||||||||
\(748\) | −1.68412e99 | −1.19335 | ||||||||
\(749\) | 2.37989e98 | 0.161040 | ||||||||
\(750\) | −4.30881e98 | −0.278448 | ||||||||
\(751\) | −1.21982e99 | −0.752864 | −0.376432 | − | 0.926444i | \(-0.622849\pi\) | ||||
−0.376432 | + | 0.926444i | \(0.622849\pi\) | |||||||
\(752\) | −9.62845e98 | −0.567598 | ||||||||
\(753\) | −2.28286e98 | −0.128544 | ||||||||
\(754\) | −3.21994e97 | −0.0173195 | ||||||||
\(755\) | 6.81510e99 | 3.50189 | ||||||||
\(756\) | 9.65258e97 | 0.0473851 | ||||||||
\(757\) | −1.23583e99 | −0.579629 | −0.289815 | − | 0.957083i | \(-0.593594\pi\) | ||||
−0.289815 | + | 0.957083i | \(0.593594\pi\) | |||||||
\(758\) | −3.49232e98 | −0.156504 | ||||||||
\(759\) | 1.90946e99 | 0.817652 | ||||||||
\(760\) | 1.38722e99 | 0.567646 | ||||||||
\(761\) | −5.18239e98 | −0.202656 | −0.101328 | − | 0.994853i | \(-0.532309\pi\) | ||||
−0.101328 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(762\) | −2.16461e98 | −0.0808970 | ||||||||
\(763\) | −1.32808e99 | −0.474380 | ||||||||
\(764\) | 4.32569e99 | 1.47685 | ||||||||
\(765\) | −2.33082e99 | −0.760657 | ||||||||
\(766\) | −2.30545e98 | −0.0719223 | ||||||||
\(767\) | 9.75279e98 | 0.290863 | ||||||||
\(768\) | −1.50014e99 | −0.427730 | ||||||||
\(769\) | 5.71448e98 | 0.155782 | 0.0778911 | − | 0.996962i | \(-0.475181\pi\) | ||||
0.0778911 | + | 0.996962i | \(0.475181\pi\) | |||||||
\(770\) | −3.04890e98 | −0.0794719 | ||||||||
\(771\) | −2.26593e99 | −0.564769 | ||||||||
\(772\) | −8.69038e98 | −0.207130 | ||||||||
\(773\) | 1.16534e99 | 0.265619 | 0.132809 | − | 0.991142i | \(-0.457600\pi\) | ||||
0.132809 | + | 0.991142i | \(0.457600\pi\) | |||||||
\(774\) | −3.61397e97 | −0.00787810 | ||||||||
\(775\) | 1.00606e100 | 2.09756 | ||||||||
\(776\) | −1.56537e99 | −0.312168 | ||||||||
\(777\) | −8.49015e98 | −0.161953 | ||||||||
\(778\) | 3.76571e98 | 0.0687149 | ||||||||
\(779\) | 7.07260e99 | 1.23463 | ||||||||
\(780\) | 9.88894e98 | 0.165153 | ||||||||
\(781\) | 2.11192e99 | 0.337455 | ||||||||
\(782\) | −1.81694e99 | −0.277784 | ||||||||
\(783\) | 8.89570e98 | 0.130137 | ||||||||
\(784\) | −6.14938e99 | −0.860850 | ||||||||
\(785\) | 3.61664e99 | 0.484509 | ||||||||
\(786\) | −4.44637e98 | −0.0570069 | ||||||||
\(787\) | −1.38928e100 | −1.70475 | −0.852375 | − | 0.522931i | \(-0.824838\pi\) | ||||
−0.852375 | + | 0.522931i | \(0.824838\pi\) | |||||||
\(788\) | −6.08060e99 | −0.714154 | ||||||||
\(789\) | 4.57328e98 | 0.0514127 | ||||||||
\(790\) | −2.84462e99 | −0.306119 | ||||||||
\(791\) | −2.35987e99 | −0.243108 | ||||||||
\(792\) | 1.11050e99 | 0.109522 | ||||||||
\(793\) | −3.26151e99 | −0.307959 | ||||||||
\(794\) | 2.41936e99 | 0.218723 | ||||||||
\(795\) | −4.75587e99 | −0.411684 | ||||||||
\(796\) | −1.41873e100 | −1.17598 | ||||||||
\(797\) | −8.96893e99 | −0.711916 | −0.355958 | − | 0.934502i | \(-0.615845\pi\) | ||||
−0.355958 | + | 0.934502i | \(0.615845\pi\) | |||||||
\(798\) | 2.93213e98 | 0.0222887 | ||||||||
\(799\) | 1.02573e100 | 0.746741 | ||||||||
\(800\) | 1.74262e100 | 1.21506 | ||||||||
\(801\) | −4.59197e99 | −0.306674 | ||||||||
\(802\) | −2.47232e98 | −0.0158157 | ||||||||
\(803\) | −4.76916e99 | −0.292251 | ||||||||
\(804\) | 2.36930e97 | 0.00139087 | ||||||||
\(805\) | 1.18564e100 | 0.666797 | ||||||||
\(806\) | 3.90013e98 | 0.0210146 | ||||||||
\(807\) | 5.15497e99 | 0.266127 | ||||||||
\(808\) | 5.85283e99 | 0.289517 | ||||||||
\(809\) | −1.26179e100 | −0.598087 | −0.299044 | − | 0.954239i | \(-0.596668\pi\) | ||||
−0.299044 | + | 0.954239i | \(0.596668\pi\) | |||||||
\(810\) | 7.57949e98 | 0.0344276 | ||||||||
\(811\) | −2.52772e99 | −0.110030 | −0.0550148 | − | 0.998486i | \(-0.517521\pi\) | ||||
−0.0550148 | + | 0.998486i | \(0.517521\pi\) | |||||||
\(812\) | 3.99106e99 | 0.166496 | ||||||||
\(813\) | −1.73973e100 | −0.695596 | ||||||||
\(814\) | −4.81701e99 | −0.184602 | ||||||||
\(815\) | −3.35945e100 | −1.23404 | ||||||||
\(816\) | 1.82480e100 | 0.642546 | ||||||||
\(817\) | 3.95701e99 | 0.133569 | ||||||||
\(818\) | −4.75627e99 | −0.153914 | ||||||||
\(819\) | 4.23838e98 | 0.0131494 | ||||||||
\(820\) | 8.20243e100 | 2.43986 | ||||||||
\(821\) | 2.15046e100 | 0.613328 | 0.306664 | − | 0.951818i | \(-0.400787\pi\) | ||||
0.306664 | + | 0.951818i | \(0.400787\pi\) | |||||||
\(822\) | 4.99083e99 | 0.136488 | ||||||||
\(823\) | 9.20346e99 | 0.241355 | 0.120678 | − | 0.992692i | \(-0.461493\pi\) | ||||
0.120678 | + | 0.992692i | \(0.461493\pi\) | |||||||
\(824\) | 1.91859e100 | 0.482495 | ||||||||
\(825\) | 6.20306e100 | 1.49605 | ||||||||
\(826\) | 3.35372e99 | 0.0775738 | ||||||||
\(827\) | −7.13320e100 | −1.58250 | −0.791251 | − | 0.611492i | \(-0.790570\pi\) | ||||
−0.791251 | + | 0.611492i | \(0.790570\pi\) | |||||||
\(828\) | −2.12968e100 | −0.453176 | ||||||||
\(829\) | 4.90975e100 | 1.00214 | 0.501070 | − | 0.865407i | \(-0.332940\pi\) | ||||
0.501070 | + | 0.865407i | \(0.332940\pi\) | |||||||
\(830\) | −8.78118e99 | −0.171933 | ||||||||
\(831\) | 4.51250e100 | 0.847583 | ||||||||
\(832\) | −7.28130e99 | −0.131206 | ||||||||
\(833\) | 6.55103e100 | 1.13255 | ||||||||
\(834\) | 6.51100e99 | 0.107999 | ||||||||
\(835\) | −1.85302e101 | −2.94915 | ||||||||
\(836\) | −5.99637e100 | −0.915739 | ||||||||
\(837\) | −1.07749e100 | −0.157900 | ||||||||
\(838\) | 5.17763e99 | 0.0728135 | ||||||||
\(839\) | −4.61585e100 | −0.622965 | −0.311483 | − | 0.950252i | \(-0.600826\pi\) | ||||
−0.311483 | + | 0.950252i | \(0.600826\pi\) | |||||||
\(840\) | 6.89541e99 | 0.0893151 | ||||||||
\(841\) | −4.36570e100 | −0.542740 | ||||||||
\(842\) | −2.09054e98 | −0.00249454 | ||||||||
\(843\) | 2.71049e100 | 0.310453 | ||||||||
\(844\) | 1.14159e101 | 1.25515 | ||||||||
\(845\) | −1.74335e101 | −1.84004 | ||||||||
\(846\) | −3.33554e99 | −0.0337978 | ||||||||
\(847\) | 7.11069e98 | 0.00691726 | ||||||||
\(848\) | 3.72337e100 | 0.347760 | ||||||||
\(849\) | −9.53494e100 | −0.855072 | ||||||||
\(850\) | −5.90250e100 | −0.508257 | ||||||||
\(851\) | 1.87320e101 | 1.54887 | ||||||||
\(852\) | −2.35549e100 | −0.187031 | ||||||||
\(853\) | 1.85595e101 | 1.41522 | 0.707611 | − | 0.706603i | \(-0.249773\pi\) | ||||
0.707611 | + | 0.706603i | \(0.249773\pi\) | |||||||
\(854\) | −1.12154e100 | −0.0821333 | ||||||||
\(855\) | −8.29894e100 | −0.583702 | ||||||||
\(856\) | −3.05376e100 | −0.206296 | ||||||||
\(857\) | −1.43016e101 | −0.927996 | −0.463998 | − | 0.885836i | \(-0.653586\pi\) | ||||
−0.463998 | + | 0.885836i | \(0.653586\pi\) | |||||||
\(858\) | 2.40471e99 | 0.0149882 | ||||||||
\(859\) | −8.89938e100 | −0.532839 | −0.266419 | − | 0.963857i | \(-0.585841\pi\) | ||||
−0.266419 | + | 0.963857i | \(0.585841\pi\) | |||||||
\(860\) | 4.58914e100 | 0.263958 | ||||||||
\(861\) | 3.51555e100 | 0.194260 | ||||||||
\(862\) | −2.22475e100 | −0.118109 | ||||||||
\(863\) | 2.29685e99 | 0.0117155 | 0.00585774 | − | 0.999983i | \(-0.498135\pi\) | ||||
0.00585774 | + | 0.999983i | \(0.498135\pi\) | |||||||
\(864\) | −1.86634e100 | −0.0914673 | ||||||||
\(865\) | 2.86116e98 | 0.00134737 | ||||||||
\(866\) | 5.29548e100 | 0.239628 | ||||||||
\(867\) | −6.16289e100 | −0.267994 | ||||||||
\(868\) | −4.83414e100 | −0.202017 | ||||||||
\(869\) | 2.49333e101 | 1.00138 | ||||||||
\(870\) | 3.13389e100 | 0.120968 | ||||||||
\(871\) | 1.04034e98 | 0.000385967 0 | ||||||||
\(872\) | 1.70413e101 | 0.607691 | ||||||||
\(873\) | 9.36469e100 | 0.320998 | ||||||||
\(874\) | −6.46925e100 | −0.213162 | ||||||||
\(875\) | 2.34506e101 | 0.742807 | ||||||||
\(876\) | 5.31919e100 | 0.161977 | ||||||||
\(877\) | 1.19553e101 | 0.350004 | 0.175002 | − | 0.984568i | \(-0.444007\pi\) | ||||
0.175002 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(878\) | −2.51792e100 | −0.0708729 | ||||||||
\(879\) | 3.15785e101 | 0.854625 | ||||||||
\(880\) | −6.75599e101 | −1.75807 | ||||||||
\(881\) | 1.41431e101 | 0.353896 | 0.176948 | − | 0.984220i | \(-0.443378\pi\) | ||||
0.176948 | + | 0.984220i | \(0.443378\pi\) | |||||||
\(882\) | −2.13030e100 | −0.0512596 | ||||||||
\(883\) | 8.01247e101 | 1.85405 | 0.927027 | − | 0.374995i | \(-0.122356\pi\) | ||||
0.927027 | + | 0.374995i | \(0.122356\pi\) | |||||||
\(884\) | 8.24772e100 | 0.183540 | ||||||||
\(885\) | −9.49217e101 | −2.03153 | ||||||||
\(886\) | 9.41710e100 | 0.193845 | ||||||||
\(887\) | 5.39746e101 | 1.06862 | 0.534311 | − | 0.845288i | \(-0.320571\pi\) | ||||
0.534311 | + | 0.845288i | \(0.320571\pi\) | |||||||
\(888\) | 1.08942e101 | 0.207466 | ||||||||
\(889\) | 1.17808e101 | 0.215807 | ||||||||
\(890\) | −1.61772e101 | −0.285068 | ||||||||
\(891\) | −6.64346e100 | −0.112620 | ||||||||
\(892\) | −4.48975e101 | −0.732209 | ||||||||
\(893\) | 3.65215e101 | 0.573024 | ||||||||
\(894\) | 2.67437e100 | 0.0403717 | ||||||||
\(895\) | −7.26532e101 | −1.05526 | ||||||||
\(896\) | −1.11095e101 | −0.155262 | ||||||||
\(897\) | −9.35126e100 | −0.125757 | ||||||||
\(898\) | 9.38567e100 | 0.121460 | ||||||||
\(899\) | −4.45508e101 | −0.554813 | ||||||||
\(900\) | −6.91847e101 | −0.829170 | ||||||||
\(901\) | −3.96656e101 | −0.457518 | ||||||||
\(902\) | 1.99460e101 | 0.221426 | ||||||||
\(903\) | 1.96690e100 | 0.0210162 | ||||||||
\(904\) | 3.02807e101 | 0.311427 | ||||||||
\(905\) | −1.22514e102 | −1.21286 | ||||||||
\(906\) | −1.84837e101 | −0.176143 | ||||||||
\(907\) | −9.24045e101 | −0.847699 | −0.423850 | − | 0.905733i | \(-0.639322\pi\) | ||||
−0.423850 | + | 0.905733i | \(0.639322\pi\) | |||||||
\(908\) | −4.32635e101 | −0.382085 | ||||||||
\(909\) | −3.50140e101 | −0.297706 | ||||||||
\(910\) | 1.49315e100 | 0.0122229 | ||||||||
\(911\) | 1.06011e102 | 0.835543 | 0.417772 | − | 0.908552i | \(-0.362811\pi\) | ||||
0.417772 | + | 0.908552i | \(0.362811\pi\) | |||||||
\(912\) | 6.49724e101 | 0.493068 | ||||||||
\(913\) | 7.69675e101 | 0.562427 | ||||||||
\(914\) | 1.94476e101 | 0.136843 | ||||||||
\(915\) | 3.17435e102 | 2.15093 | ||||||||
\(916\) | 6.06183e101 | 0.395557 | ||||||||
\(917\) | 2.41992e101 | 0.152076 | ||||||||
\(918\) | 6.32156e100 | 0.0382606 | ||||||||
\(919\) | −2.97590e102 | −1.73474 | −0.867368 | − | 0.497668i | \(-0.834190\pi\) | ||||
−0.867368 | + | 0.497668i | \(0.834190\pi\) | |||||||
\(920\) | −1.52135e102 | −0.854182 | ||||||||
\(921\) | 1.04375e101 | 0.0564467 | ||||||||
\(922\) | −2.42599e101 | −0.126378 | ||||||||
\(923\) | −1.03428e101 | −0.0519013 | ||||||||
\(924\) | −2.98059e101 | −0.144085 | ||||||||
\(925\) | 6.08530e102 | 2.83395 | ||||||||
\(926\) | 3.31167e101 | 0.148583 | ||||||||
\(927\) | −1.14778e102 | −0.496143 | ||||||||
\(928\) | −7.71675e101 | −0.321388 | ||||||||
\(929\) | −3.26208e102 | −1.30904 | −0.654520 | − | 0.756045i | \(-0.727129\pi\) | ||||
−0.654520 | + | 0.756045i | \(0.727129\pi\) | |||||||
\(930\) | −3.79591e101 | −0.146776 | ||||||||
\(931\) | 2.33251e102 | 0.869080 | ||||||||
\(932\) | −4.10480e102 | −1.47381 | ||||||||
\(933\) | 1.30179e102 | 0.450428 | ||||||||
\(934\) | 6.91434e101 | 0.230560 | ||||||||
\(935\) | 7.19725e102 | 2.31295 | ||||||||
\(936\) | −5.43850e100 | −0.0168447 | ||||||||
\(937\) | 4.99948e102 | 1.49248 | 0.746241 | − | 0.665675i | \(-0.231856\pi\) | ||||
0.746241 | + | 0.665675i | \(0.231856\pi\) | |||||||
\(938\) | 3.57746e98 | 0.000102938 0 | ||||||||
\(939\) | 1.43523e102 | 0.398068 | ||||||||
\(940\) | 4.23557e102 | 1.13240 | ||||||||
\(941\) | −6.74589e102 | −1.73859 | −0.869295 | − | 0.494293i | \(-0.835427\pi\) | ||||
−0.869295 | + | 0.494293i | \(0.835427\pi\) | |||||||
\(942\) | −9.80893e100 | −0.0243706 | ||||||||
\(943\) | −7.75645e102 | −1.85784 | ||||||||
\(944\) | 7.43142e102 | 1.71608 | ||||||||
\(945\) | −4.12512e101 | −0.0918415 | ||||||||
\(946\) | 1.11595e101 | 0.0239552 | ||||||||
\(947\) | −6.40994e102 | −1.32672 | −0.663361 | − | 0.748300i | \(-0.730870\pi\) | ||||
−0.663361 | + | 0.748300i | \(0.730870\pi\) | |||||||
\(948\) | −2.78089e102 | −0.555003 | ||||||||
\(949\) | 2.33562e101 | 0.0449488 | ||||||||
\(950\) | −2.10160e102 | −0.390019 | ||||||||
\(951\) | 3.41109e102 | 0.610472 | ||||||||
\(952\) | 5.75102e101 | 0.0992590 | ||||||||
\(953\) | −3.74284e102 | −0.623012 | −0.311506 | − | 0.950244i | \(-0.600833\pi\) | ||||
−0.311506 | + | 0.950244i | \(0.600833\pi\) | |||||||
\(954\) | 1.28987e101 | 0.0207075 | ||||||||
\(955\) | −1.84862e103 | −2.86241 | ||||||||
\(956\) | 2.99086e102 | 0.446682 | ||||||||
\(957\) | −2.74687e102 | −0.395710 | ||||||||
\(958\) | 1.46229e102 | 0.203200 | ||||||||
\(959\) | −2.71625e102 | −0.364106 | ||||||||
\(960\) | 7.08672e102 | 0.916405 | ||||||||
\(961\) | −2.61980e102 | −0.326821 | ||||||||
\(962\) | 2.35905e101 | 0.0283921 | ||||||||
\(963\) | 1.82689e102 | 0.212131 | ||||||||
\(964\) | 4.93287e102 | 0.552639 | ||||||||
\(965\) | 3.71391e102 | 0.401457 | ||||||||
\(966\) | −3.21564e101 | −0.0335395 | ||||||||
\(967\) | 1.14430e103 | 1.15166 | 0.575832 | − | 0.817568i | \(-0.304678\pi\) | ||||
0.575832 | + | 0.817568i | \(0.304678\pi\) | |||||||
\(968\) | −9.12411e100 | −0.00886116 | ||||||||
\(969\) | −6.92161e102 | −0.648689 | ||||||||
\(970\) | 3.29911e102 | 0.298382 | ||||||||
\(971\) | −1.09503e103 | −0.955786 | −0.477893 | − | 0.878418i | \(-0.658599\pi\) | ||||
−0.477893 | + | 0.878418i | \(0.658599\pi\) | |||||||
\(972\) | 7.40966e101 | 0.0624183 | ||||||||
\(973\) | −3.54360e102 | −0.288105 | ||||||||
\(974\) | 2.29165e102 | 0.179831 | ||||||||
\(975\) | −3.03785e102 | −0.230095 | ||||||||
\(976\) | −2.48520e103 | −1.81695 | ||||||||
\(977\) | 6.27156e102 | 0.442602 | 0.221301 | − | 0.975206i | \(-0.428970\pi\) | ||||
0.221301 | + | 0.975206i | \(0.428970\pi\) | |||||||
\(978\) | 9.11138e101 | 0.0620717 | ||||||||
\(979\) | 1.41794e103 | 0.932513 | ||||||||
\(980\) | 2.70513e103 | 1.71746 | ||||||||
\(981\) | −1.01948e103 | −0.624880 | ||||||||
\(982\) | −4.00137e101 | −0.0236790 | ||||||||
\(983\) | 9.29318e102 | 0.530968 | 0.265484 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265484 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(984\) | −4.51099e102 | −0.248852 | ||||||||
\(985\) | 2.59860e103 | 1.38417 | ||||||||
\(986\) | 2.61378e102 | 0.134436 | ||||||||
\(987\) | 1.81536e102 | 0.0901614 | ||||||||
\(988\) | 2.93662e102 | 0.140843 | ||||||||
\(989\) | −4.33962e102 | −0.200992 | ||||||||
\(990\) | −2.34044e102 | −0.104685 | ||||||||
\(991\) | 8.94969e102 | 0.386605 | 0.193302 | − | 0.981139i | \(-0.438080\pi\) | ||||
0.193302 | + | 0.981139i | \(0.438080\pi\) | |||||||
\(992\) | 9.34685e102 | 0.389953 | ||||||||
\(993\) | −3.80652e102 | −0.153384 | ||||||||
\(994\) | −3.55660e101 | −0.0138422 | ||||||||
\(995\) | 6.06306e103 | 2.27927 | ||||||||
\(996\) | −8.58443e102 | −0.311720 | ||||||||
\(997\) | −3.91155e103 | −1.37204 | −0.686019 | − | 0.727583i | \(-0.740643\pi\) | ||||
−0.686019 | + | 0.727583i | \(0.740643\pi\) | |||||||
\(998\) | 2.39361e102 | 0.0811054 | ||||||||
\(999\) | −6.51734e102 | −0.213334 |
(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 | 3.70.a.a.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 9.70.a.d.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.70.a.a.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.70.a.d.1.3 | 6 | 3.2 | odd | 2 |