Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,18,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(42.1410800892\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 327680 x^{12} - 2885829 x^{11} + 40317445636 x^{10} + 536194434472 x^{9} + \cdots + 12\!\cdots\!92 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{33}\cdot 3^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-319.031\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 638.062 | 1.76241 | 0.881206 | − | 0.472732i | \(-0.156732\pi\) | ||||
0.881206 | + | 0.472732i | \(0.156732\pi\) | |||||||
\(3\) | −7193.12 | −0.632975 | −0.316488 | − | 0.948597i | \(-0.602504\pi\) | ||||
−0.316488 | + | 0.948597i | \(0.602504\pi\) | |||||||
\(4\) | 276051. | 2.10610 | ||||||||
\(5\) | 603296. | 0.690693 | 0.345347 | − | 0.938475i | \(-0.387761\pi\) | ||||
0.345347 | + | 0.938475i | \(0.387761\pi\) | |||||||
\(6\) | −4.58966e6 | −1.11556 | ||||||||
\(7\) | −2.24327e7 | −1.47078 | −0.735391 | − | 0.677643i | \(-0.763002\pi\) | ||||
−0.735391 | + | 0.677643i | \(0.763002\pi\) | |||||||
\(8\) | 9.25053e7 | 1.94940 | ||||||||
\(9\) | −7.73991e7 | −0.599342 | ||||||||
\(10\) | 3.84940e8 | 1.21729 | ||||||||
\(11\) | −7.48561e8 | −1.05290 | −0.526452 | − | 0.850205i | \(-0.676478\pi\) | ||||
−0.526452 | + | 0.850205i | \(0.676478\pi\) | |||||||
\(12\) | −1.98567e9 | −1.33311 | ||||||||
\(13\) | −1.54590e9 | −0.525610 | −0.262805 | − | 0.964849i | \(-0.584648\pi\) | ||||
−0.262805 | + | 0.964849i | \(0.584648\pi\) | |||||||
\(14\) | −1.43135e10 | −2.59213 | ||||||||
\(15\) | −4.33958e9 | −0.437192 | ||||||||
\(16\) | 2.28416e10 | 1.32955 | ||||||||
\(17\) | −1.78636e10 | −0.621088 | −0.310544 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310544 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(18\) | −4.93854e10 | −1.05629 | ||||||||
\(19\) | 1.25258e11 | 1.69200 | 0.846002 | − | 0.533180i | \(-0.179003\pi\) | ||||
0.846002 | + | 0.533180i | \(0.179003\pi\) | |||||||
\(20\) | 1.66540e11 | 1.45467 | ||||||||
\(21\) | 1.61361e11 | 0.930969 | ||||||||
\(22\) | −4.77628e11 | −1.85565 | ||||||||
\(23\) | −7.83110e10 | −0.208514 | ||||||||
\(24\) | −6.65402e11 | −1.23392 | ||||||||
\(25\) | −3.98974e11 | −0.522943 | ||||||||
\(26\) | −9.86381e11 | −0.926342 | ||||||||
\(27\) | 1.48566e12 | 1.01234 | ||||||||
\(28\) | −6.19257e12 | −3.09761 | ||||||||
\(29\) | −9.63947e11 | −0.357824 | −0.178912 | − | 0.983865i | \(-0.557258\pi\) | ||||
−0.178912 | + | 0.983865i | \(0.557258\pi\) | |||||||
\(30\) | −2.76892e12 | −0.770513 | ||||||||
\(31\) | −6.60693e12 | −1.39132 | −0.695658 | − | 0.718373i | \(-0.744887\pi\) | ||||
−0.695658 | + | 0.718373i | \(0.744887\pi\) | |||||||
\(32\) | 2.44948e12 | 0.393821 | ||||||||
\(33\) | 5.38449e12 | 0.666463 | ||||||||
\(34\) | −1.13981e13 | −1.09461 | ||||||||
\(35\) | −1.35336e13 | −1.01586 | ||||||||
\(36\) | −2.13661e13 | −1.26227 | ||||||||
\(37\) | −2.57511e13 | −1.20526 | −0.602630 | − | 0.798021i | \(-0.705880\pi\) | ||||
−0.602630 | + | 0.798021i | \(0.705880\pi\) | |||||||
\(38\) | 7.99226e13 | 2.98201 | ||||||||
\(39\) | 1.11199e13 | 0.332698 | ||||||||
\(40\) | 5.58081e13 | 1.34644 | ||||||||
\(41\) | 7.52462e13 | 1.47171 | 0.735854 | − | 0.677140i | \(-0.236781\pi\) | ||||
0.735854 | + | 0.677140i | \(0.236781\pi\) | |||||||
\(42\) | 1.02958e14 | 1.64075 | ||||||||
\(43\) | −2.57319e13 | −0.335730 | −0.167865 | − | 0.985810i | \(-0.553687\pi\) | ||||
−0.167865 | + | 0.985810i | \(0.553687\pi\) | |||||||
\(44\) | −2.06641e14 | −2.21752 | ||||||||
\(45\) | −4.66946e13 | −0.413962 | ||||||||
\(46\) | −4.99672e13 | −0.367488 | ||||||||
\(47\) | −7.41396e13 | −0.454170 | −0.227085 | − | 0.973875i | \(-0.572920\pi\) | ||||
−0.227085 | + | 0.973875i | \(0.572920\pi\) | |||||||
\(48\) | −1.64302e14 | −0.841576 | ||||||||
\(49\) | 2.70596e14 | 1.16320 | ||||||||
\(50\) | −2.54570e14 | −0.921641 | ||||||||
\(51\) | 1.28495e14 | 0.393133 | ||||||||
\(52\) | −4.26747e14 | −1.10699 | ||||||||
\(53\) | −2.95187e14 | −0.651256 | −0.325628 | − | 0.945498i | \(-0.605576\pi\) | ||||
−0.325628 | + | 0.945498i | \(0.605576\pi\) | |||||||
\(54\) | 9.47944e14 | 1.78417 | ||||||||
\(55\) | −4.51603e14 | −0.727234 | ||||||||
\(56\) | −2.07515e15 | −2.86715 | ||||||||
\(57\) | −9.00999e14 | −1.07100 | ||||||||
\(58\) | −6.15057e14 | −0.630634 | ||||||||
\(59\) | 4.75275e14 | 0.421408 | 0.210704 | − | 0.977550i | \(-0.432424\pi\) | ||||
0.210704 | + | 0.977550i | \(0.432424\pi\) | |||||||
\(60\) | −1.19794e15 | −0.920769 | ||||||||
\(61\) | 2.57183e15 | 1.71767 | 0.858834 | − | 0.512255i | \(-0.171190\pi\) | ||||
0.858834 | + | 0.512255i | \(0.171190\pi\) | |||||||
\(62\) | −4.21563e15 | −2.45207 | ||||||||
\(63\) | 1.73627e15 | 0.881502 | ||||||||
\(64\) | −1.43097e15 | −0.635480 | ||||||||
\(65\) | −9.32637e14 | −0.363035 | ||||||||
\(66\) | 3.43564e15 | 1.17458 | ||||||||
\(67\) | −2.44836e14 | −0.0736612 | −0.0368306 | − | 0.999322i | \(-0.511726\pi\) | ||||
−0.0368306 | + | 0.999322i | \(0.511726\pi\) | |||||||
\(68\) | −4.93126e15 | −1.30807 | ||||||||
\(69\) | 5.63301e14 | 0.131984 | ||||||||
\(70\) | −8.63525e15 | −1.79036 | ||||||||
\(71\) | 5.55432e15 | 1.02079 | 0.510393 | − | 0.859941i | \(-0.329500\pi\) | ||||
0.510393 | + | 0.859941i | \(0.329500\pi\) | |||||||
\(72\) | −7.15983e15 | −1.16836 | ||||||||
\(73\) | −1.80186e15 | −0.261503 | −0.130751 | − | 0.991415i | \(-0.541739\pi\) | ||||
−0.130751 | + | 0.991415i | \(0.541739\pi\) | |||||||
\(74\) | −1.64308e16 | −2.12416 | ||||||||
\(75\) | 2.86987e15 | 0.331010 | ||||||||
\(76\) | 3.45777e16 | 3.56353 | ||||||||
\(77\) | 1.67922e16 | 1.54859 | ||||||||
\(78\) | 7.09516e15 | 0.586352 | ||||||||
\(79\) | 1.03672e16 | 0.768829 | 0.384414 | − | 0.923161i | \(-0.374403\pi\) | ||||
0.384414 | + | 0.923161i | \(0.374403\pi\) | |||||||
\(80\) | 1.37802e16 | 0.918315 | ||||||||
\(81\) | −6.91217e14 | −0.0414469 | ||||||||
\(82\) | 4.80117e16 | 2.59376 | ||||||||
\(83\) | −8.33309e15 | −0.406109 | −0.203054 | − | 0.979167i | \(-0.565087\pi\) | ||||
−0.203054 | + | 0.979167i | \(0.565087\pi\) | |||||||
\(84\) | 4.45439e16 | 1.96071 | ||||||||
\(85\) | −1.07770e16 | −0.428981 | ||||||||
\(86\) | −1.64186e16 | −0.591695 | ||||||||
\(87\) | 6.93379e15 | 0.226494 | ||||||||
\(88\) | −6.92458e16 | −2.05254 | ||||||||
\(89\) | −5.37234e16 | −1.44660 | −0.723300 | − | 0.690534i | \(-0.757375\pi\) | ||||
−0.723300 | + | 0.690534i | \(0.757375\pi\) | |||||||
\(90\) | −2.97940e16 | −0.729571 | ||||||||
\(91\) | 3.46788e16 | 0.773058 | ||||||||
\(92\) | −2.16178e16 | −0.439152 | ||||||||
\(93\) | 4.75245e16 | 0.880668 | ||||||||
\(94\) | −4.73056e16 | −0.800435 | ||||||||
\(95\) | 7.55679e16 | 1.16866 | ||||||||
\(96\) | −1.76194e16 | −0.249279 | ||||||||
\(97\) | −1.35423e17 | −1.75442 | −0.877208 | − | 0.480111i | \(-0.840596\pi\) | ||||
−0.877208 | + | 0.480111i | \(0.840596\pi\) | |||||||
\(98\) | 1.72657e17 | 2.05004 | ||||||||
\(99\) | 5.79379e16 | 0.631050 | ||||||||
\(100\) | −1.10137e17 | −1.10137 | ||||||||
\(101\) | 1.10474e17 | 1.01515 | 0.507574 | − | 0.861608i | \(-0.330542\pi\) | ||||
0.507574 | + | 0.861608i | \(0.330542\pi\) | |||||||
\(102\) | 8.19877e16 | 0.692863 | ||||||||
\(103\) | −1.36122e17 | −1.05880 | −0.529399 | − | 0.848373i | \(-0.677582\pi\) | ||||
−0.529399 | + | 0.848373i | \(0.677582\pi\) | |||||||
\(104\) | −1.43004e17 | −1.02463 | ||||||||
\(105\) | 9.73486e16 | 0.643014 | ||||||||
\(106\) | −1.88347e17 | −1.14778 | ||||||||
\(107\) | 1.19785e17 | 0.673968 | 0.336984 | − | 0.941510i | \(-0.390593\pi\) | ||||
0.336984 | + | 0.941510i | \(0.390593\pi\) | |||||||
\(108\) | 4.10118e17 | 2.13210 | ||||||||
\(109\) | 7.32513e16 | 0.352119 | 0.176060 | − | 0.984379i | \(-0.443665\pi\) | ||||
0.176060 | + | 0.984379i | \(0.443665\pi\) | |||||||
\(110\) | −2.88151e17 | −1.28169 | ||||||||
\(111\) | 1.85231e17 | 0.762899 | ||||||||
\(112\) | −5.12399e17 | −1.95549 | ||||||||
\(113\) | 4.21835e17 | 1.49271 | 0.746355 | − | 0.665548i | \(-0.231802\pi\) | ||||
0.746355 | + | 0.665548i | \(0.231802\pi\) | |||||||
\(114\) | −5.74893e17 | −1.88754 | ||||||||
\(115\) | −4.72447e16 | −0.144019 | ||||||||
\(116\) | −2.66098e17 | −0.753614 | ||||||||
\(117\) | 1.19652e17 | 0.315020 | ||||||||
\(118\) | 3.03255e17 | 0.742695 | ||||||||
\(119\) | 4.00729e17 | 0.913485 | ||||||||
\(120\) | −4.01434e17 | −0.852263 | ||||||||
\(121\) | 5.48959e16 | 0.108609 | ||||||||
\(122\) | 1.64099e18 | 3.02724 | ||||||||
\(123\) | −5.41255e17 | −0.931555 | ||||||||
\(124\) | −1.82385e18 | −2.93025 | ||||||||
\(125\) | −7.00977e17 | −1.05189 | ||||||||
\(126\) | 1.10785e18 | 1.55357 | ||||||||
\(127\) | 1.13539e18 | 1.48873 | 0.744363 | − | 0.667776i | \(-0.232753\pi\) | ||||
0.744363 | + | 0.667776i | \(0.232753\pi\) | |||||||
\(128\) | −1.23411e18 | −1.51380 | ||||||||
\(129\) | 1.85093e17 | 0.212509 | ||||||||
\(130\) | −5.95080e17 | −0.639818 | ||||||||
\(131\) | −5.91867e17 | −0.596236 | −0.298118 | − | 0.954529i | \(-0.596359\pi\) | ||||
−0.298118 | + | 0.954529i | \(0.596359\pi\) | |||||||
\(132\) | 1.48639e18 | 1.40364 | ||||||||
\(133\) | −2.80989e18 | −2.48857 | ||||||||
\(134\) | −1.56220e17 | −0.129821 | ||||||||
\(135\) | 8.96294e17 | 0.699219 | ||||||||
\(136\) | −1.65248e18 | −1.21075 | ||||||||
\(137\) | −4.17791e17 | −0.287630 | −0.143815 | − | 0.989605i | \(-0.545937\pi\) | ||||
−0.143815 | + | 0.989605i | \(0.545937\pi\) | |||||||
\(138\) | 3.59420e17 | 0.232611 | ||||||||
\(139\) | 2.06060e18 | 1.25420 | 0.627101 | − | 0.778938i | \(-0.284241\pi\) | ||||
0.627101 | + | 0.778938i | \(0.284241\pi\) | |||||||
\(140\) | −3.73595e18 | −2.13950 | ||||||||
\(141\) | 5.33295e17 | 0.287478 | ||||||||
\(142\) | 3.54400e18 | 1.79905 | ||||||||
\(143\) | 1.15720e18 | 0.553417 | ||||||||
\(144\) | −1.76792e18 | −0.796858 | ||||||||
\(145\) | −5.81545e17 | −0.247147 | ||||||||
\(146\) | −1.14970e18 | −0.460876 | ||||||||
\(147\) | −1.94643e18 | −0.736278 | ||||||||
\(148\) | −7.10860e18 | −2.53840 | ||||||||
\(149\) | −5.30336e18 | −1.78841 | −0.894206 | − | 0.447655i | \(-0.852259\pi\) | ||||
−0.894206 | + | 0.447655i | \(0.852259\pi\) | |||||||
\(150\) | 1.83115e18 | 0.583376 | ||||||||
\(151\) | 4.93874e18 | 1.48700 | 0.743502 | − | 0.668734i | \(-0.233164\pi\) | ||||
0.743502 | + | 0.668734i | \(0.233164\pi\) | |||||||
\(152\) | 1.15871e19 | 3.29840 | ||||||||
\(153\) | 1.38263e18 | 0.372244 | ||||||||
\(154\) | 1.07145e19 | 2.72926 | ||||||||
\(155\) | −3.98594e18 | −0.960972 | ||||||||
\(156\) | 3.06965e18 | 0.700696 | ||||||||
\(157\) | 4.45328e18 | 0.962792 | 0.481396 | − | 0.876503i | \(-0.340130\pi\) | ||||
0.481396 | + | 0.876503i | \(0.340130\pi\) | |||||||
\(158\) | 6.61489e18 | 1.35499 | ||||||||
\(159\) | 2.12332e18 | 0.412229 | ||||||||
\(160\) | 1.47776e18 | 0.272010 | ||||||||
\(161\) | 1.75673e18 | 0.306679 | ||||||||
\(162\) | −4.41039e17 | −0.0730465 | ||||||||
\(163\) | −2.79044e18 | −0.438609 | −0.219304 | − | 0.975656i | \(-0.570379\pi\) | ||||
−0.219304 | + | 0.975656i | \(0.570379\pi\) | |||||||
\(164\) | 2.07718e19 | 3.09956 | ||||||||
\(165\) | 3.24844e18 | 0.460321 | ||||||||
\(166\) | −5.31702e18 | −0.715731 | ||||||||
\(167\) | −4.80740e18 | −0.614922 | −0.307461 | − | 0.951561i | \(-0.599479\pi\) | ||||
−0.307461 | + | 0.951561i | \(0.599479\pi\) | |||||||
\(168\) | 1.49268e19 | 1.81483 | ||||||||
\(169\) | −6.26060e18 | −0.723734 | ||||||||
\(170\) | −6.87641e18 | −0.756042 | ||||||||
\(171\) | −9.69489e18 | −1.01409 | ||||||||
\(172\) | −7.10331e18 | −0.707081 | ||||||||
\(173\) | −1.61296e19 | −1.52838 | −0.764189 | − | 0.644992i | \(-0.776861\pi\) | ||||
−0.764189 | + | 0.644992i | \(0.776861\pi\) | |||||||
\(174\) | 4.42418e18 | 0.399176 | ||||||||
\(175\) | 8.95006e18 | 0.769135 | ||||||||
\(176\) | −1.70983e19 | −1.39989 | ||||||||
\(177\) | −3.41871e18 | −0.266741 | ||||||||
\(178\) | −3.42788e19 | −2.54950 | ||||||||
\(179\) | −3.61435e18 | −0.256318 | −0.128159 | − | 0.991754i | \(-0.540907\pi\) | ||||
−0.128159 | + | 0.991754i | \(0.540907\pi\) | |||||||
\(180\) | −1.28901e19 | −0.871844 | ||||||||
\(181\) | −2.07099e19 | −1.33632 | −0.668159 | − | 0.744019i | \(-0.732917\pi\) | ||||
−0.668159 | + | 0.744019i | \(0.732917\pi\) | |||||||
\(182\) | 2.21272e19 | 1.36245 | ||||||||
\(183\) | −1.84995e19 | −1.08724 | ||||||||
\(184\) | −7.24418e18 | −0.406479 | ||||||||
\(185\) | −1.55355e19 | −0.832464 | ||||||||
\(186\) | 3.03236e19 | 1.55210 | ||||||||
\(187\) | 1.33720e19 | 0.653946 | ||||||||
\(188\) | −2.04663e19 | −0.956527 | ||||||||
\(189\) | −3.33274e19 | −1.48894 | ||||||||
\(190\) | 4.82170e19 | 2.05965 | ||||||||
\(191\) | 6.79091e18 | 0.277424 | 0.138712 | − | 0.990333i | \(-0.455704\pi\) | ||||
0.138712 | + | 0.990333i | \(0.455704\pi\) | |||||||
\(192\) | 1.02932e19 | 0.402243 | ||||||||
\(193\) | 1.65372e19 | 0.618336 | 0.309168 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309168 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(194\) | −8.64082e19 | −3.09200 | ||||||||
\(195\) | 6.70857e18 | 0.229792 | ||||||||
\(196\) | 7.46982e19 | 2.44982 | ||||||||
\(197\) | −1.75462e18 | −0.0551086 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
−0.0275543 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(198\) | 3.69680e19 | 1.11217 | ||||||||
\(199\) | −3.89248e19 | −1.12195 | −0.560977 | − | 0.827831i | \(-0.689575\pi\) | ||||
−0.560977 | + | 0.827831i | \(0.689575\pi\) | |||||||
\(200\) | −3.69072e19 | −1.01943 | ||||||||
\(201\) | 1.76113e18 | 0.0466257 | ||||||||
\(202\) | 7.04894e19 | 1.78911 | ||||||||
\(203\) | 2.16239e19 | 0.526282 | ||||||||
\(204\) | 3.54711e19 | 0.827978 | ||||||||
\(205\) | 4.53957e19 | 1.01650 | ||||||||
\(206\) | −8.68544e19 | −1.86604 | ||||||||
\(207\) | 6.06120e18 | 0.124971 | ||||||||
\(208\) | −3.53109e19 | −0.698828 | ||||||||
\(209\) | −9.37635e19 | −1.78152 | ||||||||
\(210\) | 6.21144e19 | 1.13326 | ||||||||
\(211\) | −1.08560e20 | −1.90226 | −0.951132 | − | 0.308785i | \(-0.900078\pi\) | ||||
−0.951132 | + | 0.308785i | \(0.900078\pi\) | |||||||
\(212\) | −8.14865e19 | −1.37161 | ||||||||
\(213\) | −3.99529e19 | −0.646132 | ||||||||
\(214\) | 7.64300e19 | 1.18781 | ||||||||
\(215\) | −1.55240e19 | −0.231887 | ||||||||
\(216\) | 1.37432e20 | 1.97347 | ||||||||
\(217\) | 1.48211e20 | 2.04632 | ||||||||
\(218\) | 4.67388e19 | 0.620580 | ||||||||
\(219\) | 1.29610e19 | 0.165525 | ||||||||
\(220\) | −1.24665e20 | −1.53163 | ||||||||
\(221\) | 2.76154e19 | 0.326450 | ||||||||
\(222\) | 1.18189e20 | 1.34454 | ||||||||
\(223\) | 7.95082e19 | 0.870604 | 0.435302 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435302 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(224\) | −5.49485e19 | −0.579225 | ||||||||
\(225\) | 3.08802e19 | 0.313422 | ||||||||
\(226\) | 2.69157e20 | 2.63077 | ||||||||
\(227\) | −2.61041e19 | −0.245747 | −0.122874 | − | 0.992422i | \(-0.539211\pi\) | ||||
−0.122874 | + | 0.992422i | \(0.539211\pi\) | |||||||
\(228\) | −2.48721e20 | −2.25563 | ||||||||
\(229\) | 4.16006e19 | 0.363495 | 0.181748 | − | 0.983345i | \(-0.441825\pi\) | ||||
0.181748 | + | 0.983345i | \(0.441825\pi\) | |||||||
\(230\) | −3.01450e19 | −0.253822 | ||||||||
\(231\) | −1.20789e20 | −0.980222 | ||||||||
\(232\) | −8.91702e19 | −0.697544 | ||||||||
\(233\) | −1.61699e20 | −1.21950 | −0.609751 | − | 0.792593i | \(-0.708731\pi\) | ||||
−0.609751 | + | 0.792593i | \(0.708731\pi\) | |||||||
\(234\) | 7.63451e19 | 0.555196 | ||||||||
\(235\) | −4.47281e19 | −0.313692 | ||||||||
\(236\) | 1.31200e20 | 0.887528 | ||||||||
\(237\) | −7.45723e19 | −0.486650 | ||||||||
\(238\) | 2.55690e20 | 1.60994 | ||||||||
\(239\) | 6.66829e19 | 0.405165 | 0.202583 | − | 0.979265i | \(-0.435067\pi\) | ||||
0.202583 | + | 0.979265i | \(0.435067\pi\) | |||||||
\(240\) | −9.91229e19 | −0.581271 | ||||||||
\(241\) | −5.13298e19 | −0.290552 | −0.145276 | − | 0.989391i | \(-0.546407\pi\) | ||||
−0.145276 | + | 0.989391i | \(0.546407\pi\) | |||||||
\(242\) | 3.50270e19 | 0.191413 | ||||||||
\(243\) | −1.86887e20 | −0.986109 | ||||||||
\(244\) | 7.09956e20 | 3.61758 | ||||||||
\(245\) | 1.63250e20 | 0.803415 | ||||||||
\(246\) | −3.45354e20 | −1.64178 | ||||||||
\(247\) | −1.93637e20 | −0.889334 | ||||||||
\(248\) | −6.11177e20 | −2.71224 | ||||||||
\(249\) | 5.99409e19 | 0.257057 | ||||||||
\(250\) | −4.47267e20 | −1.85386 | ||||||||
\(251\) | −1.29684e17 | −0.000519588 0 | −0.000259794 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000259794 | 1.00000i | \(0.500083\pi\) | ||||||||
\(252\) | 4.79299e20 | 1.85653 | ||||||||
\(253\) | 5.86205e19 | 0.219546 | ||||||||
\(254\) | 7.24451e20 | 2.62375 | ||||||||
\(255\) | 7.75205e19 | 0.271535 | ||||||||
\(256\) | −5.99876e20 | −2.03246 | ||||||||
\(257\) | 3.70767e19 | 0.121526 | 0.0607631 | − | 0.998152i | \(-0.480647\pi\) | ||||
0.0607631 | + | 0.998152i | \(0.480647\pi\) | |||||||
\(258\) | 1.18101e20 | 0.374529 | ||||||||
\(259\) | 5.77666e20 | 1.77267 | ||||||||
\(260\) | −2.57455e20 | −0.764589 | ||||||||
\(261\) | 7.46086e19 | 0.214459 | ||||||||
\(262\) | −3.77647e20 | −1.05081 | ||||||||
\(263\) | 3.10619e20 | 0.836767 | 0.418384 | − | 0.908270i | \(-0.362597\pi\) | ||||
0.418384 | + | 0.908270i | \(0.362597\pi\) | |||||||
\(264\) | 4.98094e20 | 1.29921 | ||||||||
\(265\) | −1.78085e20 | −0.449818 | ||||||||
\(266\) | −1.79288e21 | −4.38589 | ||||||||
\(267\) | 3.86439e20 | 0.915662 | ||||||||
\(268\) | −6.75870e19 | −0.155138 | ||||||||
\(269\) | −3.98655e19 | −0.0886550 | −0.0443275 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443275 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(270\) | 5.71891e20 | 1.23231 | ||||||||
\(271\) | 8.92284e20 | 1.86322 | 0.931610 | − | 0.363461i | \(-0.118405\pi\) | ||||
0.931610 | + | 0.363461i | \(0.118405\pi\) | |||||||
\(272\) | −4.08033e20 | −0.825770 | ||||||||
\(273\) | −2.49449e20 | −0.489327 | ||||||||
\(274\) | −2.66577e20 | −0.506923 | ||||||||
\(275\) | 2.98656e20 | 0.550609 | ||||||||
\(276\) | 1.55499e20 | 0.277972 | ||||||||
\(277\) | −3.94414e20 | −0.683713 | −0.341857 | − | 0.939752i | \(-0.611056\pi\) | ||||
−0.341857 | + | 0.939752i | \(0.611056\pi\) | |||||||
\(278\) | 1.31479e21 | 2.21042 | ||||||||
\(279\) | 5.11371e20 | 0.833874 | ||||||||
\(280\) | −1.25193e21 | −1.98032 | ||||||||
\(281\) | −8.69991e20 | −1.33509 | −0.667546 | − | 0.744569i | \(-0.732655\pi\) | ||||
−0.667546 | + | 0.744569i | \(0.732655\pi\) | |||||||
\(282\) | 3.40275e20 | 0.506656 | ||||||||
\(283\) | −8.95374e20 | −1.29366 | −0.646829 | − | 0.762635i | \(-0.723905\pi\) | ||||
−0.646829 | + | 0.762635i | \(0.723905\pi\) | |||||||
\(284\) | 1.53327e21 | 2.14988 | ||||||||
\(285\) | −5.43569e20 | −0.739730 | ||||||||
\(286\) | 7.38366e20 | 0.975350 | ||||||||
\(287\) | −1.68798e21 | −2.16456 | ||||||||
\(288\) | −1.89588e20 | −0.236034 | ||||||||
\(289\) | −5.08132e20 | −0.614250 | ||||||||
\(290\) | −3.71062e20 | −0.435575 | ||||||||
\(291\) | 9.74114e20 | 1.11050 | ||||||||
\(292\) | −4.97404e20 | −0.550751 | ||||||||
\(293\) | −1.34533e21 | −1.44695 | −0.723474 | − | 0.690352i | \(-0.757456\pi\) | ||||
−0.723474 | + | 0.690352i | \(0.757456\pi\) | |||||||
\(294\) | −1.24194e21 | −1.29763 | ||||||||
\(295\) | 2.86731e20 | 0.291064 | ||||||||
\(296\) | −2.38211e21 | −2.34954 | ||||||||
\(297\) | −1.11211e21 | −1.06590 | ||||||||
\(298\) | −3.38387e21 | −3.15192 | ||||||||
\(299\) | 1.21061e20 | 0.109597 | ||||||||
\(300\) | 7.92229e20 | 0.697140 | ||||||||
\(301\) | 5.77237e20 | 0.493786 | ||||||||
\(302\) | 3.15122e21 | 2.62071 | ||||||||
\(303\) | −7.94655e20 | −0.642564 | ||||||||
\(304\) | 2.86110e21 | 2.24961 | ||||||||
\(305\) | 1.55158e21 | 1.18638 | ||||||||
\(306\) | 8.82201e20 | 0.656048 | ||||||||
\(307\) | 3.51894e20 | 0.254528 | 0.127264 | − | 0.991869i | \(-0.459380\pi\) | ||||
0.127264 | + | 0.991869i | \(0.459380\pi\) | |||||||
\(308\) | 4.63551e21 | 3.26149 | ||||||||
\(309\) | 9.79145e20 | 0.670193 | ||||||||
\(310\) | −2.54327e21 | −1.69363 | ||||||||
\(311\) | −2.57095e21 | −1.66583 | −0.832913 | − | 0.553404i | \(-0.813329\pi\) | ||||
−0.832913 | + | 0.553404i | \(0.813329\pi\) | |||||||
\(312\) | 1.02865e21 | 0.648563 | ||||||||
\(313\) | 1.79646e21 | 1.10228 | 0.551139 | − | 0.834413i | \(-0.314193\pi\) | ||||
0.551139 | + | 0.834413i | \(0.314193\pi\) | |||||||
\(314\) | 2.84146e21 | 1.69684 | ||||||||
\(315\) | 1.04749e21 | 0.608847 | ||||||||
\(316\) | 2.86186e21 | 1.61923 | ||||||||
\(317\) | −3.02632e21 | −1.66691 | −0.833453 | − | 0.552590i | \(-0.813639\pi\) | ||||
−0.833453 | + | 0.552590i | \(0.813639\pi\) | |||||||
\(318\) | 1.35481e21 | 0.726518 | ||||||||
\(319\) | 7.21573e20 | 0.376755 | ||||||||
\(320\) | −8.63300e20 | −0.438921 | ||||||||
\(321\) | −8.61626e20 | −0.426605 | ||||||||
\(322\) | 1.12090e21 | 0.540496 | ||||||||
\(323\) | −2.23757e21 | −1.05088 | ||||||||
\(324\) | −1.90811e20 | −0.0872912 | ||||||||
\(325\) | 6.16775e20 | 0.274864 | ||||||||
\(326\) | −1.78047e21 | −0.773010 | ||||||||
\(327\) | −5.26905e20 | −0.222883 | ||||||||
\(328\) | 6.96067e21 | 2.86895 | ||||||||
\(329\) | 1.66315e21 | 0.667985 | ||||||||
\(330\) | 2.07270e21 | 0.811276 | ||||||||
\(331\) | 2.91169e21 | 1.11073 | 0.555364 | − | 0.831607i | \(-0.312579\pi\) | ||||
0.555364 | + | 0.831607i | \(0.312579\pi\) | |||||||
\(332\) | −2.30035e21 | −0.855305 | ||||||||
\(333\) | 1.99311e21 | 0.722363 | ||||||||
\(334\) | −3.06742e21 | −1.08375 | ||||||||
\(335\) | −1.47708e20 | −0.0508773 | ||||||||
\(336\) | 3.68575e21 | 1.23777 | ||||||||
\(337\) | −4.00248e21 | −1.31061 | −0.655307 | − | 0.755363i | \(-0.727461\pi\) | ||||
−0.655307 | + | 0.755363i | \(0.727461\pi\) | |||||||
\(338\) | −3.99465e21 | −1.27552 | ||||||||
\(339\) | −3.03431e21 | −0.944849 | ||||||||
\(340\) | −2.97501e21 | −0.903477 | ||||||||
\(341\) | 4.94569e21 | 1.46492 | ||||||||
\(342\) | −6.18594e21 | −1.78724 | ||||||||
\(343\) | −8.51673e20 | −0.240034 | ||||||||
\(344\) | −2.38034e21 | −0.654474 | ||||||||
\(345\) | 3.39837e20 | 0.0911608 | ||||||||
\(346\) | −1.02917e22 | −2.69363 | ||||||||
\(347\) | 6.03528e21 | 1.54133 | 0.770667 | − | 0.637239i | \(-0.219923\pi\) | ||||
0.770667 | + | 0.637239i | \(0.219923\pi\) | |||||||
\(348\) | 1.91408e21 | 0.477019 | ||||||||
\(349\) | 6.04019e21 | 1.46904 | 0.734522 | − | 0.678585i | \(-0.237406\pi\) | ||||
0.734522 | + | 0.678585i | \(0.237406\pi\) | |||||||
\(350\) | 5.71069e21 | 1.35553 | ||||||||
\(351\) | −2.29669e21 | −0.532098 | ||||||||
\(352\) | −1.83358e21 | −0.414656 | ||||||||
\(353\) | 2.12866e21 | 0.469918 | 0.234959 | − | 0.972005i | \(-0.424504\pi\) | ||||
0.234959 | + | 0.972005i | \(0.424504\pi\) | |||||||
\(354\) | −2.18135e21 | −0.470108 | ||||||||
\(355\) | 3.35090e21 | 0.705050 | ||||||||
\(356\) | −1.48304e22 | −3.04668 | ||||||||
\(357\) | −2.88249e21 | −0.578214 | ||||||||
\(358\) | −2.30618e21 | −0.451739 | ||||||||
\(359\) | 6.87899e20 | 0.131590 | 0.0657949 | − | 0.997833i | \(-0.479042\pi\) | ||||
0.0657949 | + | 0.997833i | \(0.479042\pi\) | |||||||
\(360\) | −4.31950e21 | −0.806978 | ||||||||
\(361\) | 1.02093e22 | 1.86288 | ||||||||
\(362\) | −1.32142e22 | −2.35514 | ||||||||
\(363\) | −3.94873e20 | −0.0687466 | ||||||||
\(364\) | 9.57310e21 | 1.62814 | ||||||||
\(365\) | −1.08705e21 | −0.180618 | ||||||||
\(366\) | −1.18038e22 | −1.91617 | ||||||||
\(367\) | −7.48219e20 | −0.118677 | −0.0593385 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593385 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(368\) | −1.78875e21 | −0.277231 | ||||||||
\(369\) | −5.82399e21 | −0.882057 | ||||||||
\(370\) | −9.91261e21 | −1.46715 | ||||||||
\(371\) | 6.62184e21 | 0.957857 | ||||||||
\(372\) | 1.31192e22 | 1.85478 | ||||||||
\(373\) | −3.97208e21 | −0.548900 | −0.274450 | − | 0.961601i | \(-0.588496\pi\) | ||||
−0.274450 | + | 0.961601i | \(0.588496\pi\) | |||||||
\(374\) | 8.53215e21 | 1.15252 | ||||||||
\(375\) | 5.04222e21 | 0.665818 | ||||||||
\(376\) | −6.85831e21 | −0.885361 | ||||||||
\(377\) | 1.49017e21 | 0.188076 | ||||||||
\(378\) | −2.12650e22 | −2.62412 | ||||||||
\(379\) | −1.20870e22 | −1.45843 | −0.729217 | − | 0.684282i | \(-0.760116\pi\) | ||||
−0.729217 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(380\) | 2.08606e22 | 2.46130 | ||||||||
\(381\) | −8.16702e21 | −0.942326 | ||||||||
\(382\) | 4.33302e21 | 0.488936 | ||||||||
\(383\) | 1.09373e22 | 1.20704 | 0.603519 | − | 0.797348i | \(-0.293765\pi\) | ||||
0.603519 | + | 0.797348i | \(0.293765\pi\) | |||||||
\(384\) | 8.87708e21 | 0.958197 | ||||||||
\(385\) | 1.01307e22 | 1.06960 | ||||||||
\(386\) | 1.05517e22 | 1.08976 | ||||||||
\(387\) | 1.99163e21 | 0.201217 | ||||||||
\(388\) | −3.73836e22 | −3.69497 | ||||||||
\(389\) | −4.29507e21 | −0.415335 | −0.207668 | − | 0.978199i | \(-0.566587\pi\) | ||||
−0.207668 | + | 0.978199i | \(0.566587\pi\) | |||||||
\(390\) | 4.28048e21 | 0.404989 | ||||||||
\(391\) | 1.39892e21 | 0.129506 | ||||||||
\(392\) | 2.50316e22 | 2.26755 | ||||||||
\(393\) | 4.25737e21 | 0.377402 | ||||||||
\(394\) | −1.11955e21 | −0.0971242 | ||||||||
\(395\) | 6.25447e21 | 0.531025 | ||||||||
\(396\) | 1.59938e22 | 1.32905 | ||||||||
\(397\) | −8.75471e21 | −0.712069 | −0.356035 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356035 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(398\) | −2.48364e22 | −1.97735 | ||||||||
\(399\) | 2.02119e22 | 1.57520 | ||||||||
\(400\) | −9.11319e21 | −0.695281 | ||||||||
\(401\) | 7.48858e21 | 0.559335 | 0.279668 | − | 0.960097i | \(-0.409776\pi\) | ||||
0.279668 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(402\) | 1.12371e21 | 0.0821738 | ||||||||
\(403\) | 1.02137e22 | 0.731289 | ||||||||
\(404\) | 3.04965e22 | 2.13800 | ||||||||
\(405\) | −4.17008e20 | −0.0286271 | ||||||||
\(406\) | 1.37974e22 | 0.927526 | ||||||||
\(407\) | 1.92762e22 | 1.26902 | ||||||||
\(408\) | 1.18865e22 | 0.766375 | ||||||||
\(409\) | 1.62989e22 | 1.02923 | 0.514613 | − | 0.857422i | \(-0.327935\pi\) | ||||
0.514613 | + | 0.857422i | \(0.327935\pi\) | |||||||
\(410\) | 2.89653e22 | 1.79149 | ||||||||
\(411\) | 3.00522e21 | 0.182063 | ||||||||
\(412\) | −3.75767e22 | −2.22993 | ||||||||
\(413\) | −1.06617e22 | −0.619800 | ||||||||
\(414\) | 3.86742e21 | 0.220251 | ||||||||
\(415\) | −5.02732e21 | −0.280496 | ||||||||
\(416\) | −3.78666e21 | −0.206996 | ||||||||
\(417\) | −1.48221e22 | −0.793879 | ||||||||
\(418\) | −5.98269e22 | −3.13977 | ||||||||
\(419\) | −3.00022e22 | −1.54289 | −0.771444 | − | 0.636297i | \(-0.780465\pi\) | ||||
−0.771444 | + | 0.636297i | \(0.780465\pi\) | |||||||
\(420\) | 2.68731e22 | 1.35425 | ||||||||
\(421\) | 2.39529e22 | 1.18293 | 0.591465 | − | 0.806330i | \(-0.298550\pi\) | ||||
0.591465 | + | 0.806330i | \(0.298550\pi\) | |||||||
\(422\) | −6.92682e22 | −3.35257 | ||||||||
\(423\) | 5.73834e21 | 0.272203 | ||||||||
\(424\) | −2.73063e22 | −1.26956 | ||||||||
\(425\) | 7.12710e21 | 0.324793 | ||||||||
\(426\) | −2.54924e22 | −1.13875 | ||||||||
\(427\) | −5.76932e22 | −2.52631 | ||||||||
\(428\) | 3.30666e22 | 1.41944 | ||||||||
\(429\) | −8.32390e21 | −0.350300 | ||||||||
\(430\) | −9.90524e21 | −0.408680 | ||||||||
\(431\) | −1.27647e22 | −0.516360 | −0.258180 | − | 0.966097i | \(-0.583123\pi\) | ||||
−0.258180 | + | 0.966097i | \(0.583123\pi\) | |||||||
\(432\) | 3.39349e22 | 1.34597 | ||||||||
\(433\) | −5.10281e22 | −1.98455 | −0.992276 | − | 0.124051i | \(-0.960411\pi\) | ||||
−0.992276 | + | 0.124051i | \(0.960411\pi\) | |||||||
\(434\) | 9.45681e22 | 3.60647 | ||||||||
\(435\) | 4.18312e21 | 0.156438 | ||||||||
\(436\) | 2.02211e22 | 0.741598 | ||||||||
\(437\) | −9.80911e21 | −0.352807 | ||||||||
\(438\) | 8.26991e21 | 0.291723 | ||||||||
\(439\) | 2.55622e22 | 0.884402 | 0.442201 | − | 0.896916i | \(-0.354198\pi\) | ||||
0.442201 | + | 0.896916i | \(0.354198\pi\) | |||||||
\(440\) | −4.17757e22 | −1.41767 | ||||||||
\(441\) | −2.09439e22 | −0.697156 | ||||||||
\(442\) | 1.76203e22 | 0.575340 | ||||||||
\(443\) | 5.61360e22 | 1.79808 | 0.899042 | − | 0.437862i | \(-0.144264\pi\) | ||||
0.899042 | + | 0.437862i | \(0.144264\pi\) | |||||||
\(444\) | 5.11330e22 | 1.60674 | ||||||||
\(445\) | −3.24111e22 | −0.999156 | ||||||||
\(446\) | 5.07311e22 | 1.53436 | ||||||||
\(447\) | 3.81477e22 | 1.13202 | ||||||||
\(448\) | 3.21006e22 | 0.934652 | ||||||||
\(449\) | −1.59468e22 | −0.455595 | −0.227797 | − | 0.973709i | \(-0.573152\pi\) | ||||
−0.227797 | + | 0.973709i | \(0.573152\pi\) | |||||||
\(450\) | 1.97035e22 | 0.552378 | ||||||||
\(451\) | −5.63263e22 | −1.54957 | ||||||||
\(452\) | 1.16448e23 | 3.14380 | ||||||||
\(453\) | −3.55250e22 | −0.941237 | ||||||||
\(454\) | −1.66560e22 | −0.433108 | ||||||||
\(455\) | 2.09216e22 | 0.533946 | ||||||||
\(456\) | −8.33472e22 | −2.08781 | ||||||||
\(457\) | 4.87443e22 | 1.19850 | 0.599248 | − | 0.800564i | \(-0.295466\pi\) | ||||
0.599248 | + | 0.800564i | \(0.295466\pi\) | |||||||
\(458\) | 2.65438e22 | 0.640628 | ||||||||
\(459\) | −2.65393e22 | −0.628755 | ||||||||
\(460\) | −1.30419e22 | −0.303319 | ||||||||
\(461\) | 3.18694e22 | 0.727640 | 0.363820 | − | 0.931469i | \(-0.381472\pi\) | ||||
0.363820 | + | 0.931469i | \(0.381472\pi\) | |||||||
\(462\) | −7.70706e22 | −1.72756 | ||||||||
\(463\) | −4.67460e22 | −1.02874 | −0.514371 | − | 0.857568i | \(-0.671974\pi\) | ||||
−0.514371 | + | 0.857568i | \(0.671974\pi\) | |||||||
\(464\) | −2.20181e22 | −0.475747 | ||||||||
\(465\) | 2.86713e22 | 0.608272 | ||||||||
\(466\) | −1.03174e23 | −2.14927 | ||||||||
\(467\) | −5.85315e22 | −1.19728 | −0.598641 | − | 0.801018i | \(-0.704292\pi\) | ||||
−0.598641 | + | 0.801018i | \(0.704292\pi\) | |||||||
\(468\) | 3.30299e22 | 0.663464 | ||||||||
\(469\) | 5.49233e21 | 0.108340 | ||||||||
\(470\) | −2.85393e22 | −0.552855 | ||||||||
\(471\) | −3.20330e22 | −0.609424 | ||||||||
\(472\) | 4.39655e22 | 0.821495 | ||||||||
\(473\) | 1.92619e22 | 0.353492 | ||||||||
\(474\) | −4.75817e22 | −0.857678 | ||||||||
\(475\) | −4.99748e22 | −0.884821 | ||||||||
\(476\) | 1.10621e23 | 1.92389 | ||||||||
\(477\) | 2.28472e22 | 0.390325 | ||||||||
\(478\) | 4.25478e22 | 0.714068 | ||||||||
\(479\) | −4.41684e22 | −0.728215 | −0.364107 | − | 0.931357i | \(-0.618626\pi\) | ||||
−0.364107 | + | 0.931357i | \(0.618626\pi\) | |||||||
\(480\) | −1.06297e22 | −0.172175 | ||||||||
\(481\) | 3.98086e22 | 0.633496 | ||||||||
\(482\) | −3.27516e22 | −0.512073 | ||||||||
\(483\) | −1.26364e22 | −0.194121 | ||||||||
\(484\) | 1.51541e22 | 0.228741 | ||||||||
\(485\) | −8.17001e22 | −1.21176 | ||||||||
\(486\) | −1.19245e23 | −1.73793 | ||||||||
\(487\) | −6.34578e22 | −0.908842 | −0.454421 | − | 0.890787i | \(-0.650154\pi\) | ||||
−0.454421 | + | 0.890787i | \(0.650154\pi\) | |||||||
\(488\) | 2.37908e23 | 3.34843 | ||||||||
\(489\) | 2.00719e22 | 0.277629 | ||||||||
\(490\) | 1.04163e23 | 1.41595 | ||||||||
\(491\) | −9.45744e22 | −1.26352 | −0.631758 | − | 0.775165i | \(-0.717667\pi\) | ||||
−0.631758 | + | 0.775165i | \(0.717667\pi\) | |||||||
\(492\) | −1.49414e23 | −1.96195 | ||||||||
\(493\) | 1.72196e22 | 0.222240 | ||||||||
\(494\) | −1.23553e23 | −1.56737 | ||||||||
\(495\) | 3.49537e22 | 0.435862 | ||||||||
\(496\) | −1.50913e23 | −1.84983 | ||||||||
\(497\) | −1.24598e23 | −1.50135 | ||||||||
\(498\) | 3.82460e22 | 0.453040 | ||||||||
\(499\) | 6.37196e22 | 0.742025 | 0.371012 | − | 0.928628i | \(-0.379011\pi\) | ||||
0.371012 | + | 0.928628i | \(0.379011\pi\) | |||||||
\(500\) | −1.93505e23 | −2.21538 | ||||||||
\(501\) | 3.45802e22 | 0.389231 | ||||||||
\(502\) | −8.27462e19 | −0.000915728 0 | ||||||||
\(503\) | −6.15421e21 | −0.0669644 | −0.0334822 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334822 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(504\) | 1.60614e23 | 1.71840 | ||||||||
\(505\) | 6.66486e22 | 0.701156 | ||||||||
\(506\) | 3.74035e22 | 0.386930 | ||||||||
\(507\) | 4.50333e22 | 0.458106 | ||||||||
\(508\) | 3.13426e23 | 3.13540 | ||||||||
\(509\) | −5.84358e22 | −0.574881 | −0.287440 | − | 0.957799i | \(-0.592804\pi\) | ||||
−0.287440 | + | 0.957799i | \(0.592804\pi\) | |||||||
\(510\) | 4.94629e22 | 0.478556 | ||||||||
\(511\) | 4.04206e22 | 0.384614 | ||||||||
\(512\) | −2.21001e23 | −2.06823 | ||||||||
\(513\) | 1.86092e23 | 1.71289 | ||||||||
\(514\) | 2.36572e22 | 0.214179 | ||||||||
\(515\) | −8.21220e22 | −0.731304 | ||||||||
\(516\) | 5.10950e22 | 0.447565 | ||||||||
\(517\) | 5.54980e22 | 0.478198 | ||||||||
\(518\) | 3.68587e23 | 3.12418 | ||||||||
\(519\) | 1.16022e23 | 0.967426 | ||||||||
\(520\) | −8.62738e22 | −0.707702 | ||||||||
\(521\) | 8.98353e21 | 0.0724980 | 0.0362490 | − | 0.999343i | \(-0.488459\pi\) | ||||
0.0362490 | + | 0.999343i | \(0.488459\pi\) | |||||||
\(522\) | 4.76049e22 | 0.377966 | ||||||||
\(523\) | −8.47437e22 | −0.661977 | −0.330989 | − | 0.943635i | \(-0.607382\pi\) | ||||
−0.330989 | + | 0.943635i | \(0.607382\pi\) | |||||||
\(524\) | −1.63385e23 | −1.25573 | ||||||||
\(525\) | −6.43789e22 | −0.486844 | ||||||||
\(526\) | 1.98194e23 | 1.47473 | ||||||||
\(527\) | 1.18024e23 | 0.864129 | ||||||||
\(528\) | 1.22990e23 | 0.886099 | ||||||||
\(529\) | 6.13261e21 | 0.0434783 | ||||||||
\(530\) | −1.13629e23 | −0.792766 | ||||||||
\(531\) | −3.67859e22 | −0.252568 | ||||||||
\(532\) | −7.75671e23 | −5.24118 | ||||||||
\(533\) | −1.16323e23 | −0.773545 | ||||||||
\(534\) | 2.46572e23 | 1.61377 | ||||||||
\(535\) | 7.22656e22 | 0.465505 | ||||||||
\(536\) | −2.26486e22 | −0.143595 | ||||||||
\(537\) | 2.59985e22 | 0.162243 | ||||||||
\(538\) | −2.54367e22 | −0.156247 | ||||||||
\(539\) | −2.02558e23 | −1.22474 | ||||||||
\(540\) | 2.47423e23 | 1.47263 | ||||||||
\(541\) | 1.14029e23 | 0.668095 | 0.334047 | − | 0.942556i | \(-0.391585\pi\) | ||||
0.334047 | + | 0.942556i | \(0.391585\pi\) | |||||||
\(542\) | 5.69332e23 | 3.28376 | ||||||||
\(543\) | 1.48969e23 | 0.845856 | ||||||||
\(544\) | −4.37565e22 | −0.244597 | ||||||||
\(545\) | 4.41922e22 | 0.243207 | ||||||||
\(546\) | −1.59164e23 | −0.862396 | ||||||||
\(547\) | 8.65877e22 | 0.461917 | 0.230958 | − | 0.972964i | \(-0.425814\pi\) | ||||
0.230958 | + | 0.972964i | \(0.425814\pi\) | |||||||
\(548\) | −1.15332e23 | −0.605778 | ||||||||
\(549\) | −1.99058e23 | −1.02947 | ||||||||
\(550\) | 1.90561e23 | 0.970401 | ||||||||
\(551\) | −1.20742e23 | −0.605440 | ||||||||
\(552\) | 5.21083e22 | 0.257291 | ||||||||
\(553\) | −2.32564e23 | −1.13078 | ||||||||
\(554\) | −2.51660e23 | −1.20498 | ||||||||
\(555\) | 1.11749e23 | 0.526929 | ||||||||
\(556\) | 5.68829e23 | 2.64147 | ||||||||
\(557\) | 3.90364e23 | 1.78526 | 0.892628 | − | 0.450793i | \(-0.148859\pi\) | ||||
0.892628 | + | 0.450793i | \(0.148859\pi\) | |||||||
\(558\) | 3.26286e23 | 1.46963 | ||||||||
\(559\) | 3.97791e22 | 0.176463 | ||||||||
\(560\) | −3.09128e23 | −1.35064 | ||||||||
\(561\) | −9.61863e22 | −0.413932 | ||||||||
\(562\) | −5.55108e23 | −2.35298 | ||||||||
\(563\) | 2.99806e23 | 1.25175 | 0.625876 | − | 0.779923i | \(-0.284742\pi\) | ||||
0.625876 | + | 0.779923i | \(0.284742\pi\) | |||||||
\(564\) | 1.47216e23 | 0.605458 | ||||||||
\(565\) | 2.54491e23 | 1.03101 | ||||||||
\(566\) | −5.71304e23 | −2.27996 | ||||||||
\(567\) | 1.55059e22 | 0.0609593 | ||||||||
\(568\) | 5.13804e23 | 1.98992 | ||||||||
\(569\) | −6.28850e22 | −0.239935 | −0.119967 | − | 0.992778i | \(-0.538279\pi\) | ||||
−0.119967 | + | 0.992778i | \(0.538279\pi\) | |||||||
\(570\) | −3.46831e23 | −1.30371 | ||||||||
\(571\) | −1.97152e23 | −0.730119 | −0.365059 | − | 0.930984i | \(-0.618951\pi\) | ||||
−0.365059 | + | 0.930984i | \(0.618951\pi\) | |||||||
\(572\) | 3.19446e23 | 1.16555 | ||||||||
\(573\) | −4.88478e22 | −0.175603 | ||||||||
\(574\) | −1.07703e24 | −3.81485 | ||||||||
\(575\) | 3.12440e22 | 0.109041 | ||||||||
\(576\) | 1.10756e23 | 0.380870 | ||||||||
\(577\) | −2.57580e23 | −0.872806 | −0.436403 | − | 0.899751i | \(-0.643748\pi\) | ||||
−0.436403 | + | 0.899751i | \(0.643748\pi\) | |||||||
\(578\) | −3.24220e23 | −1.08256 | ||||||||
\(579\) | −1.18954e23 | −0.391391 | ||||||||
\(580\) | −1.60536e23 | −0.520516 | ||||||||
\(581\) | 1.86934e23 | 0.597297 | ||||||||
\(582\) | 6.21545e23 | 1.95716 | ||||||||
\(583\) | 2.20965e23 | 0.685711 | ||||||||
\(584\) | −1.66682e23 | −0.509775 | ||||||||
\(585\) | 7.21853e22 | 0.217582 | ||||||||
\(586\) | −8.58401e23 | −2.55012 | ||||||||
\(587\) | −4.93333e23 | −1.44450 | −0.722248 | − | 0.691634i | \(-0.756891\pi\) | ||||
−0.722248 | + | 0.691634i | \(0.756891\pi\) | |||||||
\(588\) | −5.37314e23 | −1.55067 | ||||||||
\(589\) | −8.27574e23 | −2.35411 | ||||||||
\(590\) | 1.82952e23 | 0.512975 | ||||||||
\(591\) | 1.26212e22 | 0.0348824 | ||||||||
\(592\) | −5.88195e23 | −1.60246 | ||||||||
\(593\) | 6.66021e23 | 1.78864 | 0.894320 | − | 0.447427i | \(-0.147660\pi\) | ||||
0.894320 | + | 0.447427i | \(0.147660\pi\) | |||||||
\(594\) | −7.09594e23 | −1.87856 | ||||||||
\(595\) | 2.41758e23 | 0.630938 | ||||||||
\(596\) | −1.46400e24 | −3.76657 | ||||||||
\(597\) | 2.79991e23 | 0.710170 | ||||||||
\(598\) | 7.72445e22 | 0.193156 | ||||||||
\(599\) | 6.04611e23 | 1.49055 | 0.745277 | − | 0.666755i | \(-0.232317\pi\) | ||||
0.745277 | + | 0.666755i | \(0.232317\pi\) | |||||||
\(600\) | 2.65478e23 | 0.645272 | ||||||||
\(601\) | −3.04158e22 | −0.0728896 | −0.0364448 | − | 0.999336i | \(-0.511603\pi\) | ||||
−0.0364448 | + | 0.999336i | \(0.511603\pi\) | |||||||
\(602\) | 3.68313e23 | 0.870255 | ||||||||
\(603\) | 1.89501e22 | 0.0441483 | ||||||||
\(604\) | 1.36334e24 | 3.13178 | ||||||||
\(605\) | 3.31185e22 | 0.0750152 | ||||||||
\(606\) | −5.07039e23 | −1.13246 | ||||||||
\(607\) | 5.43871e23 | 1.19782 | 0.598911 | − | 0.800816i | \(-0.295600\pi\) | ||||
0.598911 | + | 0.800816i | \(0.295600\pi\) | |||||||
\(608\) | 3.06818e23 | 0.666347 | ||||||||
\(609\) | −1.55544e23 | −0.333124 | ||||||||
\(610\) | 9.90001e23 | 2.09089 | ||||||||
\(611\) | 1.14613e23 | 0.238716 | ||||||||
\(612\) | 3.81675e23 | 0.783983 | ||||||||
\(613\) | −4.91609e23 | −0.995878 | −0.497939 | − | 0.867212i | \(-0.665910\pi\) | ||||
−0.497939 | + | 0.867212i | \(0.665910\pi\) | |||||||
\(614\) | 2.24530e23 | 0.448584 | ||||||||
\(615\) | −3.26537e23 | −0.643419 | ||||||||
\(616\) | 1.55337e24 | 3.01884 | ||||||||
\(617\) | −9.20397e23 | −1.76421 | −0.882107 | − | 0.471049i | \(-0.843876\pi\) | ||||
−0.882107 | + | 0.471049i | \(0.843876\pi\) | |||||||
\(618\) | 6.24755e23 | 1.18116 | ||||||||
\(619\) | −2.92110e23 | −0.544723 | −0.272362 | − | 0.962195i | \(-0.587805\pi\) | ||||
−0.272362 | + | 0.962195i | \(0.587805\pi\) | |||||||
\(620\) | −1.10032e24 | −2.02390 | ||||||||
\(621\) | −1.16344e23 | −0.211088 | ||||||||
\(622\) | −1.64042e24 | −2.93587 | ||||||||
\(623\) | 1.20516e24 | 2.12763 | ||||||||
\(624\) | 2.53995e23 | 0.442341 | ||||||||
\(625\) | −1.18504e23 | −0.203588 | ||||||||
\(626\) | 1.14625e24 | 1.94267 | ||||||||
\(627\) | 6.74453e23 | 1.12766 | ||||||||
\(628\) | 1.22933e24 | 2.02774 | ||||||||
\(629\) | 4.60006e23 | 0.748572 | ||||||||
\(630\) | 6.68361e23 | 1.07304 | ||||||||
\(631\) | 3.55397e23 | 0.562943 | 0.281471 | − | 0.959570i | \(-0.409178\pi\) | ||||
0.281471 | + | 0.959570i | \(0.409178\pi\) | |||||||
\(632\) | 9.59018e23 | 1.49876 | ||||||||
\(633\) | 7.80889e23 | 1.20409 | ||||||||
\(634\) | −1.93098e24 | −2.93778 | ||||||||
\(635\) | 6.84978e23 | 1.02825 | ||||||||
\(636\) | 5.86143e23 | 0.868196 | ||||||||
\(637\) | −4.18315e23 | −0.611391 | ||||||||
\(638\) | 4.60408e23 | 0.663998 | ||||||||
\(639\) | −4.29899e23 | −0.611800 | ||||||||
\(640\) | −7.44531e23 | −1.04557 | ||||||||
\(641\) | −1.27030e24 | −1.76041 | −0.880203 | − | 0.474598i | \(-0.842594\pi\) | ||||
−0.880203 | + | 0.474598i | \(0.842594\pi\) | |||||||
\(642\) | −5.49770e23 | −0.751854 | ||||||||
\(643\) | 2.06542e23 | 0.278751 | 0.139375 | − | 0.990240i | \(-0.455491\pi\) | ||||
0.139375 | + | 0.990240i | \(0.455491\pi\) | |||||||
\(644\) | 4.84946e23 | 0.645897 | ||||||||
\(645\) | 1.11666e23 | 0.146778 | ||||||||
\(646\) | −1.42770e24 | −1.85209 | ||||||||
\(647\) | 6.63102e20 | 0.000848973 0 | 0.000424486 | − | 1.00000i | \(-0.499865\pi\) | ||||
0.000424486 | 1.00000i | \(0.499865\pi\) | ||||||||
\(648\) | −6.39412e22 | −0.0807967 | ||||||||
\(649\) | −3.55772e23 | −0.443703 | ||||||||
\(650\) | 3.93540e23 | 0.484424 | ||||||||
\(651\) | −1.06610e24 | −1.29527 | ||||||||
\(652\) | −7.70302e23 | −0.923754 | ||||||||
\(653\) | −5.46335e23 | −0.646692 | −0.323346 | − | 0.946281i | \(-0.604808\pi\) | ||||
−0.323346 | + | 0.946281i | \(0.604808\pi\) | |||||||
\(654\) | −3.36198e23 | −0.392812 | ||||||||
\(655\) | −3.57071e23 | −0.411816 | ||||||||
\(656\) | 1.71874e24 | 1.95672 | ||||||||
\(657\) | 1.39462e23 | 0.156730 | ||||||||
\(658\) | 1.06119e24 | 1.17727 | ||||||||
\(659\) | 1.57562e24 | 1.72554 | 0.862771 | − | 0.505594i | \(-0.168727\pi\) | ||||
0.862771 | + | 0.505594i | \(0.168727\pi\) | |||||||
\(660\) | 8.96734e23 | 0.969483 | ||||||||
\(661\) | −1.01783e24 | −1.08633 | −0.543164 | − | 0.839627i | \(-0.682774\pi\) | ||||
−0.543164 | + | 0.839627i | \(0.682774\pi\) | |||||||
\(662\) | 1.85784e24 | 1.95756 | ||||||||
\(663\) | −1.98641e23 | −0.206635 | ||||||||
\(664\) | −7.70855e23 | −0.791670 | ||||||||
\(665\) | −1.69519e24 | −1.71884 | ||||||||
\(666\) | 1.27173e24 | 1.27310 | ||||||||
\(667\) | 7.54876e22 | 0.0746116 | ||||||||
\(668\) | −1.32709e24 | −1.29509 | ||||||||
\(669\) | −5.71912e23 | −0.551071 | ||||||||
\(670\) | −9.42470e22 | −0.0896668 | ||||||||
\(671\) | −1.92517e24 | −1.80854 | ||||||||
\(672\) | 3.95251e23 | 0.366635 | ||||||||
\(673\) | 1.93351e24 | 1.77100 | 0.885501 | − | 0.464637i | \(-0.153815\pi\) | ||||
0.885501 | + | 0.464637i | \(0.153815\pi\) | |||||||
\(674\) | −2.55383e24 | −2.30984 | ||||||||
\(675\) | −5.92740e23 | −0.529398 | ||||||||
\(676\) | −1.72824e24 | −1.52426 | ||||||||
\(677\) | 1.32812e23 | 0.115673 | 0.0578365 | − | 0.998326i | \(-0.481580\pi\) | ||||
0.0578365 | + | 0.998326i | \(0.481580\pi\) | |||||||
\(678\) | −1.93608e24 | −1.66521 | ||||||||
\(679\) | 3.03790e24 | 2.58036 | ||||||||
\(680\) | −9.96932e23 | −0.836257 | ||||||||
\(681\) | 1.87770e23 | 0.155552 | ||||||||
\(682\) | 3.15566e24 | 2.58180 | ||||||||
\(683\) | 2.02529e24 | 1.63648 | 0.818241 | − | 0.574875i | \(-0.194949\pi\) | ||||
0.818241 | + | 0.574875i | \(0.194949\pi\) | |||||||
\(684\) | −2.67628e24 | −2.13577 | ||||||||
\(685\) | −2.52052e23 | −0.198664 | ||||||||
\(686\) | −5.43420e23 | −0.423039 | ||||||||
\(687\) | −2.99239e23 | −0.230083 | ||||||||
\(688\) | −5.87758e23 | −0.446372 | ||||||||
\(689\) | 4.56330e23 | 0.342307 | ||||||||
\(690\) | 2.16837e23 | 0.160663 | ||||||||
\(691\) | 5.47597e23 | 0.400772 | 0.200386 | − | 0.979717i | \(-0.435780\pi\) | ||||
0.200386 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(692\) | −4.45258e24 | −3.21892 | ||||||||
\(693\) | −1.29971e24 | −0.928138 | ||||||||
\(694\) | 3.85088e24 | 2.71647 | ||||||||
\(695\) | 1.24315e24 | 0.866269 | ||||||||
\(696\) | 6.41412e23 | 0.441528 | ||||||||
\(697\) | −1.34417e24 | −0.914060 | ||||||||
\(698\) | 3.85402e24 | 2.58906 | ||||||||
\(699\) | 1.16312e24 | 0.771915 | ||||||||
\(700\) | 2.47067e24 | 1.61988 | ||||||||
\(701\) | −2.55935e23 | −0.165778 | −0.0828889 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828889 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(702\) | −1.46543e24 | −0.937777 | ||||||||
\(703\) | −3.22554e24 | −2.03930 | ||||||||
\(704\) | 1.07117e24 | 0.669099 | ||||||||
\(705\) | 3.21735e23 | 0.198559 | ||||||||
\(706\) | 1.35822e24 | 0.828189 | ||||||||
\(707\) | −2.47824e24 | −1.49306 | ||||||||
\(708\) | −9.43738e23 | −0.561783 | ||||||||
\(709\) | 2.70995e24 | 1.59392 | 0.796962 | − | 0.604030i | \(-0.206439\pi\) | ||||
0.796962 | + | 0.604030i | \(0.206439\pi\) | |||||||
\(710\) | 2.13808e24 | 1.24259 | ||||||||
\(711\) | −8.02410e23 | −0.460792 | ||||||||
\(712\) | −4.96970e24 | −2.82001 | ||||||||
\(713\) | 5.17396e23 | 0.290109 | ||||||||
\(714\) | −1.83921e24 | −1.01905 | ||||||||
\(715\) | 6.98135e23 | 0.382242 | ||||||||
\(716\) | −9.97744e23 | −0.539832 | ||||||||
\(717\) | −4.79658e23 | −0.256460 | ||||||||
\(718\) | 4.38922e23 | 0.231916 | ||||||||
\(719\) | 4.72700e23 | 0.246825 | 0.123413 | − | 0.992355i | \(-0.460616\pi\) | ||||
0.123413 | + | 0.992355i | \(0.460616\pi\) | |||||||
\(720\) | −1.06658e24 | −0.550385 | ||||||||
\(721\) | 3.05359e24 | 1.55726 | ||||||||
\(722\) | 6.51415e24 | 3.28316 | ||||||||
\(723\) | 3.69221e23 | 0.183913 | ||||||||
\(724\) | −5.71698e24 | −2.81442 | ||||||||
\(725\) | 3.84589e23 | 0.187122 | ||||||||
\(726\) | −2.51953e23 | −0.121160 | ||||||||
\(727\) | −2.44509e24 | −1.16212 | −0.581062 | − | 0.813860i | \(-0.697362\pi\) | ||||
−0.581062 | + | 0.813860i | \(0.697362\pi\) | |||||||
\(728\) | 3.20797e24 | 1.50700 | ||||||||
\(729\) | 1.43356e24 | 0.665630 | ||||||||
\(730\) | −6.93607e23 | −0.318324 | ||||||||
\(731\) | 4.59665e23 | 0.208518 | ||||||||
\(732\) | −5.10680e24 | −2.28984 | ||||||||
\(733\) | −1.86965e24 | −0.828660 | −0.414330 | − | 0.910127i | \(-0.635984\pi\) | ||||
−0.414330 | + | 0.910127i | \(0.635984\pi\) | |||||||
\(734\) | −4.77410e23 | −0.209158 | ||||||||
\(735\) | −1.17427e24 | −0.508542 | ||||||||
\(736\) | −1.91821e23 | −0.0821174 | ||||||||
\(737\) | 1.83274e23 | 0.0775582 | ||||||||
\(738\) | −3.71607e24 | −1.55455 | ||||||||
\(739\) | 2.41032e24 | 0.996776 | 0.498388 | − | 0.866954i | \(-0.333926\pi\) | ||||
0.498388 | + | 0.866954i | \(0.333926\pi\) | |||||||
\(740\) | −4.28859e24 | −1.75325 | ||||||||
\(741\) | 1.39286e24 | 0.562927 | ||||||||
\(742\) | 4.22514e24 | 1.68814 | ||||||||
\(743\) | 4.46618e24 | 1.76413 | 0.882067 | − | 0.471124i | \(-0.156152\pi\) | ||||
0.882067 | + | 0.471124i | \(0.156152\pi\) | |||||||
\(744\) | 4.39627e24 | 1.71678 | ||||||||
\(745\) | −3.19949e24 | −1.23524 | ||||||||
\(746\) | −2.53443e24 | −0.967388 | ||||||||
\(747\) | 6.44974e23 | 0.243398 | ||||||||
\(748\) | 3.69134e24 | 1.37728 | ||||||||
\(749\) | −2.68709e24 | −0.991260 | ||||||||
\(750\) | 3.21724e24 | 1.17345 | ||||||||
\(751\) | −4.01373e24 | −1.44747 | −0.723734 | − | 0.690080i | \(-0.757576\pi\) | ||||
−0.723734 | + | 0.690080i | \(0.757576\pi\) | |||||||
\(752\) | −1.69347e24 | −0.603844 | ||||||||
\(753\) | 9.32831e20 | 0.000328886 0 | ||||||||
\(754\) | 9.50819e23 | 0.331468 | ||||||||
\(755\) | 2.97952e24 | 1.02706 | ||||||||
\(756\) | −9.20006e24 | −3.13585 | ||||||||
\(757\) | 3.49186e23 | 0.117691 | 0.0588453 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588453 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(758\) | −7.71228e24 | −2.57036 | ||||||||
\(759\) | −4.21665e23 | −0.138967 | ||||||||
\(760\) | 6.99043e24 | 2.27818 | ||||||||
\(761\) | 1.26963e24 | 0.409175 | 0.204587 | − | 0.978848i | \(-0.434415\pi\) | ||||
0.204587 | + | 0.978848i | \(0.434415\pi\) | |||||||
\(762\) | −5.21106e24 | −1.66077 | ||||||||
\(763\) | −1.64323e24 | −0.517891 | ||||||||
\(764\) | 1.87463e24 | 0.584283 | ||||||||
\(765\) | 8.34133e23 | 0.257106 | ||||||||
\(766\) | 6.97868e24 | 2.12730 | ||||||||
\(767\) | −7.34729e23 | −0.221496 | ||||||||
\(768\) | 4.31498e24 | 1.28650 | ||||||||
\(769\) | 7.04549e23 | 0.207748 | 0.103874 | − | 0.994590i | \(-0.466876\pi\) | ||||
0.103874 | + | 0.994590i | \(0.466876\pi\) | |||||||
\(770\) | 6.46400e24 | 1.88508 | ||||||||
\(771\) | −2.66697e23 | −0.0769231 | ||||||||
\(772\) | 4.56510e24 | 1.30228 | ||||||||
\(773\) | −2.30387e24 | −0.650028 | −0.325014 | − | 0.945709i | \(-0.605369\pi\) | ||||
−0.325014 | + | 0.945709i | \(0.605369\pi\) | |||||||
\(774\) | 1.27078e24 | 0.354628 | ||||||||
\(775\) | 2.63599e24 | 0.727578 | ||||||||
\(776\) | −1.25273e25 | −3.42006 | ||||||||
\(777\) | −4.15522e24 | −1.12206 | ||||||||
\(778\) | −2.74052e24 | −0.731992 | ||||||||
\(779\) | 9.42522e24 | 2.49014 | ||||||||
\(780\) | 1.85191e24 | 0.483966 | ||||||||
\(781\) | −4.15774e24 | −1.07479 | ||||||||
\(782\) | 8.92594e23 | 0.228243 | ||||||||
\(783\) | −1.43210e24 | −0.362242 | ||||||||
\(784\) | 6.18084e24 | 1.54654 | ||||||||
\(785\) | 2.68664e24 | 0.664994 | ||||||||
\(786\) | 2.71646e24 | 0.665139 | ||||||||
\(787\) | 1.70871e23 | 0.0413887 | 0.0206944 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206944 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(788\) | −4.84363e23 | −0.116064 | ||||||||
\(789\) | −2.23432e24 | −0.529653 | ||||||||
\(790\) | 3.99073e24 | 0.935885 | ||||||||
\(791\) | −9.46290e24 | −2.19545 | ||||||||
\(792\) | 5.35957e24 | 1.23017 | ||||||||
\(793\) | −3.97580e24 | −0.902823 | ||||||||
\(794\) | −5.58604e24 | −1.25496 | ||||||||
\(795\) | 1.28099e24 | 0.284724 | ||||||||
\(796\) | −1.07452e25 | −2.36295 | ||||||||
\(797\) | −4.13736e24 | −0.900176 | −0.450088 | − | 0.892984i | \(-0.648607\pi\) | ||||
−0.450088 | + | 0.892984i | \(0.648607\pi\) | |||||||
\(798\) | 1.28964e25 | 2.77616 | ||||||||
\(799\) | 1.32440e24 | 0.282079 | ||||||||
\(800\) | −9.77278e23 | −0.205946 | ||||||||
\(801\) | 4.15814e24 | 0.867008 | ||||||||
\(802\) | 4.77817e24 | 0.985780 | ||||||||
\(803\) | 1.34880e24 | 0.275338 | ||||||||
\(804\) | 4.86162e23 | 0.0981984 | ||||||||
\(805\) | 1.05983e24 | 0.211821 | ||||||||
\(806\) | 6.51696e24 | 1.28883 | ||||||||
\(807\) | 2.86758e23 | 0.0561164 | ||||||||
\(808\) | 1.02195e25 | 1.97893 | ||||||||
\(809\) | 3.28215e24 | 0.628920 | 0.314460 | − | 0.949271i | \(-0.398177\pi\) | ||||
0.314460 | + | 0.949271i | \(0.398177\pi\) | |||||||
\(810\) | −2.66077e23 | −0.0504527 | ||||||||
\(811\) | −8.58930e24 | −1.61169 | −0.805843 | − | 0.592129i | \(-0.798287\pi\) | ||||
−0.805843 | + | 0.592129i | \(0.798287\pi\) | |||||||
\(812\) | 5.96930e24 | 1.10840 | ||||||||
\(813\) | −6.41831e24 | −1.17937 | ||||||||
\(814\) | 1.22994e25 | 2.23654 | ||||||||
\(815\) | −1.68346e24 | −0.302944 | ||||||||
\(816\) | 2.93503e24 | 0.522692 | ||||||||
\(817\) | −3.22314e24 | −0.568057 | ||||||||
\(818\) | 1.03997e25 | 1.81392 | ||||||||
\(819\) | −2.68411e24 | −0.463326 | ||||||||
\(820\) | 1.25315e25 | 2.14085 | ||||||||
\(821\) | 8.31635e23 | 0.140610 | 0.0703050 | − | 0.997526i | \(-0.477603\pi\) | ||||
0.0703050 | + | 0.997526i | \(0.477603\pi\) | |||||||
\(822\) | 1.91752e24 | 0.320870 | ||||||||
\(823\) | 3.24895e24 | 0.538077 | 0.269038 | − | 0.963129i | \(-0.413294\pi\) | ||||
0.269038 | + | 0.963129i | \(0.413294\pi\) | |||||||
\(824\) | −1.25920e25 | −2.06402 | ||||||||
\(825\) | −2.14827e24 | −0.348522 | ||||||||
\(826\) | −6.80283e24 | −1.09234 | ||||||||
\(827\) | 7.68940e24 | 1.22207 | 0.611035 | − | 0.791604i | \(-0.290754\pi\) | ||||
0.611035 | + | 0.791604i | \(0.290754\pi\) | |||||||
\(828\) | 1.67320e24 | 0.263202 | ||||||||
\(829\) | −2.02569e23 | −0.0315398 | −0.0157699 | − | 0.999876i | \(-0.505020\pi\) | ||||
−0.0157699 | + | 0.999876i | \(0.505020\pi\) | |||||||
\(830\) | −3.20774e24 | −0.494351 | ||||||||
\(831\) | 2.83707e24 | 0.432774 | ||||||||
\(832\) | 2.21214e24 | 0.334014 | ||||||||
\(833\) | −4.83382e24 | −0.722450 | ||||||||
\(834\) | −9.45744e24 | −1.39914 | ||||||||
\(835\) | −2.90028e24 | −0.424723 | ||||||||
\(836\) | −2.58835e25 | −3.75206 | ||||||||
\(837\) | −9.81568e24 | −1.40849 | ||||||||
\(838\) | −1.91433e25 | −2.71920 | ||||||||
\(839\) | −2.65888e24 | −0.373871 | −0.186935 | − | 0.982372i | \(-0.559856\pi\) | ||||
−0.186935 | + | 0.982372i | \(0.559856\pi\) | |||||||
\(840\) | 9.00526e24 | 1.25349 | ||||||||
\(841\) | −6.32795e24 | −0.871962 | ||||||||
\(842\) | 1.52834e25 | 2.08481 | ||||||||
\(843\) | 6.25795e24 | 0.845080 | ||||||||
\(844\) | −2.99682e25 | −4.00636 | ||||||||
\(845\) | −3.77699e24 | −0.499878 | ||||||||
\(846\) | 3.66141e24 | 0.479734 | ||||||||
\(847\) | −1.23146e24 | −0.159740 | ||||||||
\(848\) | −6.74253e24 | −0.865881 | ||||||||
\(849\) | 6.44053e24 | 0.818854 | ||||||||
\(850\) | 4.54753e24 | 0.572420 | ||||||||
\(851\) | 2.01659e24 | 0.251314 | ||||||||
\(852\) | −1.10290e25 | −1.36082 | ||||||||
\(853\) | −1.15609e24 | −0.141229 | −0.0706147 | − | 0.997504i | \(-0.522496\pi\) | ||||
−0.0706147 | + | 0.997504i | \(0.522496\pi\) | |||||||
\(854\) | −3.68118e25 | −4.45241 | ||||||||
\(855\) | −5.84889e24 | −0.700425 | ||||||||
\(856\) | 1.10807e25 | 1.31383 | ||||||||
\(857\) | 6.99186e24 | 0.820835 | 0.410417 | − | 0.911898i | \(-0.365383\pi\) | ||||
0.410417 | + | 0.911898i | \(0.365383\pi\) | |||||||
\(858\) | −5.31116e24 | −0.617373 | ||||||||
\(859\) | 7.66436e24 | 0.882133 | 0.441067 | − | 0.897474i | \(-0.354600\pi\) | ||||
0.441067 | + | 0.897474i | \(0.354600\pi\) | |||||||
\(860\) | −4.28540e24 | −0.488376 | ||||||||
\(861\) | 1.21418e25 | 1.37012 | ||||||||
\(862\) | −8.14464e24 | −0.910040 | ||||||||
\(863\) | 4.57890e24 | 0.506605 | 0.253302 | − | 0.967387i | \(-0.418483\pi\) | ||||
0.253302 | + | 0.967387i | \(0.418483\pi\) | |||||||
\(864\) | 3.63910e24 | 0.398683 | ||||||||
\(865\) | −9.73090e24 | −1.05564 | ||||||||
\(866\) | −3.25591e25 | −3.49760 | ||||||||
\(867\) | 3.65506e24 | 0.388805 | ||||||||
\(868\) | 4.09139e25 | 4.30976 | ||||||||
\(869\) | −7.76045e24 | −0.809504 | ||||||||
\(870\) | 2.66909e24 | 0.275708 | ||||||||
\(871\) | 3.78492e23 | 0.0387171 | ||||||||
\(872\) | 6.77613e24 | 0.686423 | ||||||||
\(873\) | 1.04816e25 | 1.05150 | ||||||||
\(874\) | −6.25882e24 | −0.621792 | ||||||||
\(875\) | 1.57248e25 | 1.54710 | ||||||||
\(876\) | 3.57789e24 | 0.348612 | ||||||||
\(877\) | −1.29745e25 | −1.25197 | −0.625983 | − | 0.779837i | \(-0.715302\pi\) | ||||
−0.625983 | + | 0.779837i | \(0.715302\pi\) | |||||||
\(878\) | 1.63103e25 | 1.55868 | ||||||||
\(879\) | 9.67710e24 | 0.915882 | ||||||||
\(880\) | −1.03153e25 | −0.966898 | ||||||||
\(881\) | 8.14729e23 | 0.0756342 | 0.0378171 | − | 0.999285i | \(-0.487960\pi\) | ||||
0.0378171 | + | 0.999285i | \(0.487960\pi\) | |||||||
\(882\) | −1.33635e25 | −1.22868 | ||||||||
\(883\) | 3.28547e24 | 0.299179 | 0.149590 | − | 0.988748i | \(-0.452205\pi\) | ||||
0.149590 | + | 0.988748i | \(0.452205\pi\) | |||||||
\(884\) | 7.62324e24 | 0.687536 | ||||||||
\(885\) | −2.06249e24 | −0.184236 | ||||||||
\(886\) | 3.58183e25 | 3.16897 | ||||||||
\(887\) | 6.08496e24 | 0.533221 | 0.266610 | − | 0.963804i | \(-0.414096\pi\) | ||||
0.266610 | + | 0.963804i | \(0.414096\pi\) | |||||||
\(888\) | 1.71348e25 | 1.48720 | ||||||||
\(889\) | −2.54699e25 | −2.18959 | ||||||||
\(890\) | −2.06803e25 | −1.76093 | ||||||||
\(891\) | 5.17418e23 | 0.0436396 | ||||||||
\(892\) | 2.19483e25 | 1.83358 | ||||||||
\(893\) | −9.28661e24 | −0.768457 | ||||||||
\(894\) | 2.43406e25 | 1.99509 | ||||||||
\(895\) | −2.18052e24 | −0.177037 | ||||||||
\(896\) | 2.76844e25 | 2.22647 | ||||||||
\(897\) | −8.70808e23 | −0.0693724 | ||||||||
\(898\) | −1.01750e25 | −0.802946 | ||||||||
\(899\) | 6.36873e24 | 0.497847 | ||||||||
\(900\) | 8.52451e24 | 0.660097 | ||||||||
\(901\) | 5.27310e24 | 0.404487 | ||||||||
\(902\) | −3.59397e25 | −2.73098 | ||||||||
\(903\) | −4.15214e24 | −0.312554 | ||||||||
\(904\) | 3.90220e25 | 2.90990 | ||||||||
\(905\) | −1.24942e25 | −0.922986 | ||||||||
\(906\) | −2.26671e25 | −1.65885 | ||||||||
\(907\) | 8.70977e23 | 0.0631459 | 0.0315729 | − | 0.999501i | \(-0.489948\pi\) | ||||
0.0315729 | + | 0.999501i | \(0.489948\pi\) | |||||||
\(908\) | −7.20604e24 | −0.517568 | ||||||||
\(909\) | −8.55061e24 | −0.608421 | ||||||||
\(910\) | 1.33493e25 | 0.941033 | ||||||||
\(911\) | 6.53963e24 | 0.456717 | 0.228358 | − | 0.973577i | \(-0.426664\pi\) | ||||
0.228358 | + | 0.973577i | \(0.426664\pi\) | |||||||
\(912\) | −2.05802e25 | −1.42395 | ||||||||
\(913\) | 6.23782e24 | 0.427594 | ||||||||
\(914\) | 3.11019e25 | 2.11224 | ||||||||
\(915\) | −1.11607e25 | −0.750950 | ||||||||
\(916\) | 1.14839e25 | 0.765557 | ||||||||
\(917\) | 1.32772e25 | 0.876933 | ||||||||
\(918\) | −1.69337e25 | −1.10813 | ||||||||
\(919\) | 2.06036e25 | 1.33586 | 0.667930 | − | 0.744224i | \(-0.267180\pi\) | ||||
0.667930 | + | 0.744224i | \(0.267180\pi\) | |||||||
\(920\) | −4.37038e24 | −0.280752 | ||||||||
\(921\) | −2.53122e24 | −0.161110 | ||||||||
\(922\) | 2.03347e25 | 1.28240 | ||||||||
\(923\) | −8.58643e24 | −0.536535 | ||||||||
\(924\) | −3.33438e25 | −2.06444 | ||||||||
\(925\) | 1.02740e25 | 0.630282 | ||||||||
\(926\) | −2.98268e25 | −1.81307 | ||||||||
\(927\) | 1.05358e25 | 0.634582 | ||||||||
\(928\) | −2.36117e24 | −0.140919 | ||||||||
\(929\) | 2.22077e25 | 1.31332 | 0.656658 | − | 0.754188i | \(-0.271969\pi\) | ||||
0.656658 | + | 0.754188i | \(0.271969\pi\) | |||||||
\(930\) | 1.82941e25 | 1.07203 | ||||||||
\(931\) | 3.38945e25 | 1.96814 | ||||||||
\(932\) | −4.46372e25 | −2.56839 | ||||||||
\(933\) | 1.84931e25 | 1.05443 | ||||||||
\(934\) | −3.73467e25 | −2.11010 | ||||||||
\(935\) | 8.06726e24 | 0.451676 | ||||||||
\(936\) | 1.10684e25 | 0.614102 | ||||||||
\(937\) | 1.49369e25 | 0.821246 | 0.410623 | − | 0.911805i | \(-0.365311\pi\) | ||||
0.410623 | + | 0.911805i | \(0.365311\pi\) | |||||||
\(938\) | 3.50444e24 | 0.190939 | ||||||||
\(939\) | −1.29222e25 | −0.697715 | ||||||||
\(940\) | −1.23472e25 | −0.660667 | ||||||||
\(941\) | 1.53792e25 | 0.815498 | 0.407749 | − | 0.913094i | \(-0.366314\pi\) | ||||
0.407749 | + | 0.913094i | \(0.366314\pi\) | |||||||
\(942\) | −2.04390e25 | −1.07406 | ||||||||
\(943\) | −5.89260e24 | −0.306872 | ||||||||
\(944\) | 1.08560e25 | 0.560285 | ||||||||
\(945\) | −2.01063e25 | −1.02840 | ||||||||
\(946\) | 1.22903e25 | 0.622999 | ||||||||
\(947\) | −1.37054e25 | −0.688521 | −0.344260 | − | 0.938874i | \(-0.611870\pi\) | ||||
−0.344260 | + | 0.938874i | \(0.611870\pi\) | |||||||
\(948\) | −2.05857e25 | −1.02493 | ||||||||
\(949\) | 2.78550e24 | 0.137449 | ||||||||
\(950\) | −3.18870e25 | −1.55942 | ||||||||
\(951\) | 2.17687e25 | 1.05511 | ||||||||
\(952\) | 3.70696e25 | 1.78075 | ||||||||
\(953\) | −8.81116e22 | −0.00419511 | −0.00209755 | − | 0.999998i | \(-0.500668\pi\) | ||||
−0.00209755 | + | 0.999998i | \(0.500668\pi\) | |||||||
\(954\) | 1.45779e25 | 0.687915 | ||||||||
\(955\) | 4.09692e24 | 0.191615 | ||||||||
\(956\) | 1.84078e25 | 0.853318 | ||||||||
\(957\) | −5.19036e24 | −0.238477 | ||||||||
\(958\) | −2.81821e25 | −1.28341 | ||||||||
\(959\) | 9.37219e24 | 0.423041 | ||||||||
\(960\) | 6.20982e24 | 0.277826 | ||||||||
\(961\) | 2.11015e25 | 0.935758 | ||||||||
\(962\) | 2.54004e25 | 1.11648 | ||||||||
\(963\) | −9.27123e24 | −0.403937 | ||||||||
\(964\) | −1.41696e25 | −0.611932 | ||||||||
\(965\) | 9.97681e24 | 0.427080 | ||||||||
\(966\) | −8.06278e24 | −0.342120 | ||||||||
\(967\) | 3.24496e24 | 0.136485 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(968\) | 5.07816e24 | 0.211722 | ||||||||
\(969\) | 1.60951e25 | 0.665183 | ||||||||
\(970\) | −5.21297e25 | −2.13563 | ||||||||
\(971\) | 1.10220e24 | 0.0447607 | 0.0223803 | − | 0.999750i | \(-0.492876\pi\) | ||||
0.0223803 | + | 0.999750i | \(0.492876\pi\) | |||||||
\(972\) | −5.15902e25 | −2.07684 | ||||||||
\(973\) | −4.62248e25 | −1.84466 | ||||||||
\(974\) | −4.04900e25 | −1.60176 | ||||||||
\(975\) | −4.43654e24 | −0.173982 | ||||||||
\(976\) | 5.87447e25 | 2.28373 | ||||||||
\(977\) | 2.28152e24 | 0.0879265 | 0.0439633 | − | 0.999033i | \(-0.486002\pi\) | ||||
0.0439633 | + | 0.999033i | \(0.486002\pi\) | |||||||
\(978\) | 1.28071e25 | 0.489296 | ||||||||
\(979\) | 4.02152e25 | 1.52313 | ||||||||
\(980\) | 4.50651e25 | 1.69207 | ||||||||
\(981\) | −5.66959e24 | −0.211040 | ||||||||
\(982\) | −6.03443e25 | −2.22684 | ||||||||
\(983\) | 1.43484e23 | 0.00524927 | 0.00262464 | − | 0.999997i | \(-0.499165\pi\) | ||||
0.00262464 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(984\) | −5.00690e25 | −1.81598 | ||||||||
\(985\) | −1.05855e24 | −0.0380632 | ||||||||
\(986\) | 1.09871e25 | 0.391679 | ||||||||
\(987\) | −1.19633e25 | −0.422818 | ||||||||
\(988\) | −5.34537e25 | −1.87303 | ||||||||
\(989\) | 2.01509e24 | 0.0700046 | ||||||||
\(990\) | 2.23026e25 | 0.768169 | ||||||||
\(991\) | 5.23767e25 | 1.78860 | 0.894298 | − | 0.447472i | \(-0.147675\pi\) | ||||
0.894298 | + | 0.447472i | \(0.147675\pi\) | |||||||
\(992\) | −1.61835e25 | −0.547929 | ||||||||
\(993\) | −2.09442e25 | −0.703064 | ||||||||
\(994\) | −7.95015e25 | −2.64601 | ||||||||
\(995\) | −2.34832e25 | −0.774927 | ||||||||
\(996\) | 1.65467e25 | 0.541387 | ||||||||
\(997\) | 2.03742e25 | 0.660954 | 0.330477 | − | 0.943814i | \(-0.392790\pi\) | ||||
0.330477 | + | 0.943814i | \(0.392790\pi\) | |||||||
\(998\) | 4.06570e25 | 1.30775 | ||||||||
\(999\) | −3.82574e25 | −1.22014 |
(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 | 23.18.a.a.1.14 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.18.a.a.1.14 | ✓ | 14 | 1.1 | even | 1 | trivial |