Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(18.3222087345\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2941}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 735 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-26.6155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 256.000 | 0.707107 | ||||||||
\(3\) | 21829.4 | 1.92093 | 0.960466 | − | 0.278398i | \(-0.0898035\pi\) | ||||
0.960466 | + | 0.278398i | \(0.0898035\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | −390625. | −0.447214 | ||||||||
\(6\) | 5.58834e6 | 1.35830 | ||||||||
\(7\) | 1.53649e7 | 1.00739 | 0.503694 | − | 0.863882i | \(-0.331974\pi\) | ||||
0.503694 | + | 0.863882i | \(0.331974\pi\) | |||||||
\(8\) | 1.67772e7 | 0.353553 | ||||||||
\(9\) | 3.47384e8 | 2.68998 | ||||||||
\(10\) | −1.00000e8 | −0.316228 | ||||||||
\(11\) | −1.15061e9 | −1.61842 | −0.809209 | − | 0.587521i | \(-0.800104\pi\) | ||||
−0.809209 | + | 0.587521i | \(0.800104\pi\) | |||||||
\(12\) | 1.43061e9 | 0.960466 | ||||||||
\(13\) | 4.71918e8 | 0.160453 | 0.0802265 | − | 0.996777i | \(-0.474436\pi\) | ||||
0.0802265 | + | 0.996777i | \(0.474436\pi\) | |||||||
\(14\) | 3.93342e9 | 0.712330 | ||||||||
\(15\) | −8.52712e9 | −0.859067 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | 1.89434e10 | 0.658630 | 0.329315 | − | 0.944220i | \(-0.393182\pi\) | ||||
0.329315 | + | 0.944220i | \(0.393182\pi\) | |||||||
\(18\) | 8.89303e10 | 1.90210 | ||||||||
\(19\) | −7.11086e10 | −0.960542 | −0.480271 | − | 0.877120i | \(-0.659462\pi\) | ||||
−0.480271 | + | 0.877120i | \(0.659462\pi\) | |||||||
\(20\) | −2.56000e10 | −0.223607 | ||||||||
\(21\) | 3.35407e11 | 1.93512 | ||||||||
\(22\) | −2.94556e11 | −1.14439 | ||||||||
\(23\) | −6.03554e10 | −0.160705 | −0.0803525 | − | 0.996767i | \(-0.525605\pi\) | ||||
−0.0803525 | + | 0.996767i | \(0.525605\pi\) | |||||||
\(24\) | 3.66237e11 | 0.679152 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 1.20811e11 | 0.113457 | ||||||||
\(27\) | 4.76414e12 | 3.24633 | ||||||||
\(28\) | 1.00695e12 | 0.503694 | ||||||||
\(29\) | 1.95995e12 | 0.727549 | 0.363775 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363775 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(30\) | −2.18294e12 | −0.607452 | ||||||||
\(31\) | −2.11583e12 | −0.445561 | −0.222780 | − | 0.974869i | \(-0.571513\pi\) | ||||
−0.222780 | + | 0.974869i | \(0.571513\pi\) | |||||||
\(32\) | 1.09951e12 | 0.176777 | ||||||||
\(33\) | −2.51172e13 | −3.10887 | ||||||||
\(34\) | 4.84950e12 | 0.465721 | ||||||||
\(35\) | −6.00192e12 | −0.450517 | ||||||||
\(36\) | 2.27662e13 | 1.34499 | ||||||||
\(37\) | −3.79079e13 | −1.77425 | −0.887126 | − | 0.461526i | \(-0.847302\pi\) | ||||
−0.887126 | + | 0.461526i | \(0.847302\pi\) | |||||||
\(38\) | −1.82038e13 | −0.679206 | ||||||||
\(39\) | 1.03017e13 | 0.308219 | ||||||||
\(40\) | −6.55360e12 | −0.158114 | ||||||||
\(41\) | 7.71153e13 | 1.50827 | 0.754133 | − | 0.656722i | \(-0.228057\pi\) | ||||
0.754133 | + | 0.656722i | \(0.228057\pi\) | |||||||
\(42\) | 8.58642e13 | 1.36834 | ||||||||
\(43\) | −9.99172e13 | −1.30364 | −0.651821 | − | 0.758373i | \(-0.725995\pi\) | ||||
−0.651821 | + | 0.758373i | \(0.725995\pi\) | |||||||
\(44\) | −7.54065e13 | −0.809209 | ||||||||
\(45\) | −1.35697e14 | −1.20299 | ||||||||
\(46\) | −1.54510e13 | −0.113636 | ||||||||
\(47\) | −2.88977e13 | −0.177024 | −0.0885119 | − | 0.996075i | \(-0.528211\pi\) | ||||
−0.0885119 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(48\) | 9.37567e13 | 0.480233 | ||||||||
\(49\) | 3.44976e12 | 0.0148294 | ||||||||
\(50\) | 3.90625e13 | 0.141421 | ||||||||
\(51\) | 4.13523e14 | 1.26518 | ||||||||
\(52\) | 3.09276e13 | 0.0802265 | ||||||||
\(53\) | −1.47516e14 | −0.325458 | −0.162729 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162729 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(54\) | 1.21962e15 | 2.29550 | ||||||||
\(55\) | 4.49458e14 | 0.723779 | ||||||||
\(56\) | 2.57780e14 | 0.356165 | ||||||||
\(57\) | −1.55226e15 | −1.84513 | ||||||||
\(58\) | 5.01748e14 | 0.514455 | ||||||||
\(59\) | −3.95776e14 | −0.350919 | −0.175460 | − | 0.984487i | \(-0.556141\pi\) | ||||
−0.175460 | + | 0.984487i | \(0.556141\pi\) | |||||||
\(60\) | −5.58834e14 | −0.429533 | ||||||||
\(61\) | −2.00041e15 | −1.33603 | −0.668014 | − | 0.744148i | \(-0.732856\pi\) | ||||
−0.668014 | + | 0.744148i | \(0.732856\pi\) | |||||||
\(62\) | −5.41653e14 | −0.315059 | ||||||||
\(63\) | 5.33752e15 | 2.70985 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | −1.84343e14 | −0.0717567 | ||||||||
\(66\) | −6.43000e15 | −2.19830 | ||||||||
\(67\) | −3.33086e15 | −1.00212 | −0.501061 | − | 0.865412i | \(-0.667057\pi\) | ||||
−0.501061 | + | 0.865412i | \(0.667057\pi\) | |||||||
\(68\) | 1.24147e15 | 0.329315 | ||||||||
\(69\) | −1.31752e15 | −0.308703 | ||||||||
\(70\) | −1.53649e15 | −0.318564 | ||||||||
\(71\) | 2.99845e15 | 0.551062 | 0.275531 | − | 0.961292i | \(-0.411146\pi\) | ||||
0.275531 | + | 0.961292i | \(0.411146\pi\) | |||||||
\(72\) | 5.82814e15 | 0.951051 | ||||||||
\(73\) | −1.02670e15 | −0.149004 | −0.0745021 | − | 0.997221i | \(-0.523737\pi\) | ||||
−0.0745021 | + | 0.997221i | \(0.523737\pi\) | |||||||
\(74\) | −9.70443e15 | −1.25459 | ||||||||
\(75\) | 3.33091e15 | 0.384186 | ||||||||
\(76\) | −4.66017e15 | −0.480271 | ||||||||
\(77\) | −1.76790e16 | −1.63037 | ||||||||
\(78\) | 2.63723e15 | 0.217944 | ||||||||
\(79\) | 4.95112e15 | 0.367175 | 0.183587 | − | 0.983003i | \(-0.441229\pi\) | ||||
0.183587 | + | 0.983003i | \(0.441229\pi\) | |||||||
\(80\) | −1.67772e15 | −0.111803 | ||||||||
\(81\) | 5.91373e16 | 3.54600 | ||||||||
\(82\) | 1.97415e16 | 1.06650 | ||||||||
\(83\) | −3.56834e15 | −0.173901 | −0.0869506 | − | 0.996213i | \(-0.527712\pi\) | ||||
−0.0869506 | + | 0.996213i | \(0.527712\pi\) | |||||||
\(84\) | 2.19812e16 | 0.967561 | ||||||||
\(85\) | −7.39975e15 | −0.294548 | ||||||||
\(86\) | −2.55788e16 | −0.921814 | ||||||||
\(87\) | 4.27847e16 | 1.39757 | ||||||||
\(88\) | −1.93041e16 | −0.572197 | ||||||||
\(89\) | −3.06841e16 | −0.826224 | −0.413112 | − | 0.910680i | \(-0.635558\pi\) | ||||
−0.413112 | + | 0.910680i | \(0.635558\pi\) | |||||||
\(90\) | −3.47384e16 | −0.850646 | ||||||||
\(91\) | 7.25097e15 | 0.161638 | ||||||||
\(92\) | −3.95545e15 | −0.0803525 | ||||||||
\(93\) | −4.61874e16 | −0.855892 | ||||||||
\(94\) | −7.39781e15 | −0.125175 | ||||||||
\(95\) | 2.77768e16 | 0.429567 | ||||||||
\(96\) | 2.40017e16 | 0.339576 | ||||||||
\(97\) | 3.74691e16 | 0.485415 | 0.242708 | − | 0.970099i | \(-0.421964\pi\) | ||||
0.242708 | + | 0.970099i | \(0.421964\pi\) | |||||||
\(98\) | 8.83140e14 | 0.0104860 | ||||||||
\(99\) | −3.99704e17 | −4.35351 | ||||||||
\(100\) | 1.00000e16 | 0.100000 | ||||||||
\(101\) | 1.64278e17 | 1.50955 | 0.754774 | − | 0.655985i | \(-0.227746\pi\) | ||||
0.754774 | + | 0.655985i | \(0.227746\pi\) | |||||||
\(102\) | 1.05862e17 | 0.894619 | ||||||||
\(103\) | 2.11450e17 | 1.64472 | 0.822359 | − | 0.568969i | \(-0.192658\pi\) | ||||
0.822359 | + | 0.568969i | \(0.192658\pi\) | |||||||
\(104\) | 7.91746e15 | 0.0567287 | ||||||||
\(105\) | −1.31018e17 | −0.865413 | ||||||||
\(106\) | −3.77642e16 | −0.230134 | ||||||||
\(107\) | −1.95014e17 | −1.09725 | −0.548623 | − | 0.836070i | \(-0.684848\pi\) | ||||
−0.548623 | + | 0.836070i | \(0.684848\pi\) | |||||||
\(108\) | 3.12223e17 | 1.62317 | ||||||||
\(109\) | 1.33790e17 | 0.643129 | 0.321565 | − | 0.946888i | \(-0.395791\pi\) | ||||
0.321565 | + | 0.946888i | \(0.395791\pi\) | |||||||
\(110\) | 1.15061e17 | 0.511789 | ||||||||
\(111\) | −8.27509e17 | −3.40822 | ||||||||
\(112\) | 6.59918e16 | 0.251847 | ||||||||
\(113\) | 2.69841e17 | 0.954864 | 0.477432 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477432 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(114\) | −3.97379e17 | −1.30471 | ||||||||
\(115\) | 2.35763e16 | 0.0718695 | ||||||||
\(116\) | 1.28447e17 | 0.363775 | ||||||||
\(117\) | 1.63937e17 | 0.431615 | ||||||||
\(118\) | −1.01319e17 | −0.248137 | ||||||||
\(119\) | 2.91063e17 | 0.663495 | ||||||||
\(120\) | −1.43061e17 | −0.303726 | ||||||||
\(121\) | 8.18459e17 | 1.61928 | ||||||||
\(122\) | −5.12105e17 | −0.944715 | ||||||||
\(123\) | 1.68338e18 | 2.89727 | ||||||||
\(124\) | −1.38663e17 | −0.222780 | ||||||||
\(125\) | −5.96046e16 | −0.0894427 | ||||||||
\(126\) | 1.36641e18 | 1.91615 | ||||||||
\(127\) | 4.12838e17 | 0.541312 | 0.270656 | − | 0.962676i | \(-0.412759\pi\) | ||||
0.270656 | + | 0.962676i | \(0.412759\pi\) | |||||||
\(128\) | 7.20576e16 | 0.0883883 | ||||||||
\(129\) | −2.18114e18 | −2.50421 | ||||||||
\(130\) | −4.71918e16 | −0.0507397 | ||||||||
\(131\) | 9.36308e16 | 0.0943220 | 0.0471610 | − | 0.998887i | \(-0.484983\pi\) | ||||
0.0471610 | + | 0.998887i | \(0.484983\pi\) | |||||||
\(132\) | −1.64608e18 | −1.55444 | ||||||||
\(133\) | −1.09258e18 | −0.967638 | ||||||||
\(134\) | −8.52701e17 | −0.708608 | ||||||||
\(135\) | −1.86099e18 | −1.45180 | ||||||||
\(136\) | 3.17817e17 | 0.232861 | ||||||||
\(137\) | 1.56947e18 | 1.08051 | 0.540256 | − | 0.841501i | \(-0.318328\pi\) | ||||
0.540256 | + | 0.841501i | \(0.318328\pi\) | |||||||
\(138\) | −3.37286e17 | −0.218286 | ||||||||
\(139\) | 3.76763e17 | 0.229320 | 0.114660 | − | 0.993405i | \(-0.463422\pi\) | ||||
0.114660 | + | 0.993405i | \(0.463422\pi\) | |||||||
\(140\) | −3.93342e17 | −0.225259 | ||||||||
\(141\) | −6.30821e17 | −0.340050 | ||||||||
\(142\) | 7.67602e17 | 0.389659 | ||||||||
\(143\) | −5.42994e17 | −0.259680 | ||||||||
\(144\) | 1.49200e18 | 0.672494 | ||||||||
\(145\) | −7.65606e17 | −0.325370 | ||||||||
\(146\) | −2.62835e17 | −0.105362 | ||||||||
\(147\) | 7.53064e16 | 0.0284862 | ||||||||
\(148\) | −2.48433e18 | −0.887126 | ||||||||
\(149\) | 2.78279e18 | 0.938419 | 0.469210 | − | 0.883087i | \(-0.344539\pi\) | ||||
0.469210 | + | 0.883087i | \(0.344539\pi\) | |||||||
\(150\) | 8.52712e17 | 0.271661 | ||||||||
\(151\) | 2.92545e18 | 0.880822 | 0.440411 | − | 0.897796i | \(-0.354833\pi\) | ||||
0.440411 | + | 0.897796i | \(0.354833\pi\) | |||||||
\(152\) | −1.19300e18 | −0.339603 | ||||||||
\(153\) | 6.58062e18 | 1.77170 | ||||||||
\(154\) | −4.52583e18 | −1.15285 | ||||||||
\(155\) | 8.26497e17 | 0.199261 | ||||||||
\(156\) | 6.75132e17 | 0.154110 | ||||||||
\(157\) | −4.82580e18 | −1.04333 | −0.521665 | − | 0.853150i | \(-0.674689\pi\) | ||||
−0.521665 | + | 0.853150i | \(0.674689\pi\) | |||||||
\(158\) | 1.26749e18 | 0.259632 | ||||||||
\(159\) | −3.22020e18 | −0.625183 | ||||||||
\(160\) | −4.29497e17 | −0.0790569 | ||||||||
\(161\) | −9.27355e17 | −0.161892 | ||||||||
\(162\) | 1.51392e19 | 2.50740 | ||||||||
\(163\) | −4.37304e18 | −0.687367 | −0.343684 | − | 0.939085i | \(-0.611675\pi\) | ||||
−0.343684 | + | 0.939085i | \(0.611675\pi\) | |||||||
\(164\) | 5.05383e18 | 0.754133 | ||||||||
\(165\) | 9.81141e18 | 1.39033 | ||||||||
\(166\) | −9.13495e17 | −0.122967 | ||||||||
\(167\) | −5.59866e15 | −0.000716134 0 | −0.000358067 | − | 1.00000i | \(-0.500114\pi\) | ||||
−0.000358067 | 1.00000i | \(0.500114\pi\) | ||||||||
\(168\) | 5.62720e18 | 0.684169 | ||||||||
\(169\) | −8.42771e18 | −0.974255 | ||||||||
\(170\) | −1.89434e18 | −0.208277 | ||||||||
\(171\) | −2.47020e19 | −2.58384 | ||||||||
\(172\) | −6.54818e18 | −0.651821 | ||||||||
\(173\) | 1.51898e19 | 1.43933 | 0.719664 | − | 0.694323i | \(-0.244296\pi\) | ||||
0.719664 | + | 0.694323i | \(0.244296\pi\) | |||||||
\(174\) | 1.09529e19 | 0.988233 | ||||||||
\(175\) | 2.34450e18 | 0.201477 | ||||||||
\(176\) | −4.94184e18 | −0.404605 | ||||||||
\(177\) | −8.63957e18 | −0.674092 | ||||||||
\(178\) | −7.85512e18 | −0.584229 | ||||||||
\(179\) | −1.47005e19 | −1.04251 | −0.521256 | − | 0.853400i | \(-0.674536\pi\) | ||||
−0.521256 | + | 0.853400i | \(0.674536\pi\) | |||||||
\(180\) | −8.89303e18 | −0.601497 | ||||||||
\(181\) | 1.43306e19 | 0.924690 | 0.462345 | − | 0.886700i | \(-0.347008\pi\) | ||||
0.462345 | + | 0.886700i | \(0.347008\pi\) | |||||||
\(182\) | 1.85625e18 | 0.114296 | ||||||||
\(183\) | −4.36679e19 | −2.56642 | ||||||||
\(184\) | −1.01260e18 | −0.0568178 | ||||||||
\(185\) | 1.48078e19 | 0.793470 | ||||||||
\(186\) | −1.18240e19 | −0.605207 | ||||||||
\(187\) | −2.17964e19 | −1.06594 | ||||||||
\(188\) | −1.89384e18 | −0.0885119 | ||||||||
\(189\) | 7.32006e19 | 3.27031 | ||||||||
\(190\) | 7.11086e18 | 0.303750 | ||||||||
\(191\) | 4.75265e19 | 1.94157 | 0.970783 | − | 0.239957i | \(-0.0771334\pi\) | ||||
0.970783 | + | 0.239957i | \(0.0771334\pi\) | |||||||
\(192\) | 6.14444e18 | 0.240116 | ||||||||
\(193\) | −1.41251e19 | −0.528146 | −0.264073 | − | 0.964503i | \(-0.585066\pi\) | ||||
−0.264073 | + | 0.964503i | \(0.585066\pi\) | |||||||
\(194\) | 9.59209e18 | 0.343240 | ||||||||
\(195\) | −4.02410e18 | −0.137840 | ||||||||
\(196\) | 2.26084e17 | 0.00741469 | ||||||||
\(197\) | 3.44120e19 | 1.08081 | 0.540403 | − | 0.841407i | \(-0.318272\pi\) | ||||
0.540403 | + | 0.841407i | \(0.318272\pi\) | |||||||
\(198\) | −1.02324e20 | −3.07840 | ||||||||
\(199\) | 6.74802e18 | 0.194502 | 0.0972512 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972512 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(200\) | 2.56000e18 | 0.0707107 | ||||||||
\(201\) | −7.27109e19 | −1.92501 | ||||||||
\(202\) | 4.20551e19 | 1.06741 | ||||||||
\(203\) | 3.01145e19 | 0.732924 | ||||||||
\(204\) | 2.71006e19 | 0.632591 | ||||||||
\(205\) | −3.01232e19 | −0.674517 | ||||||||
\(206\) | 5.41312e19 | 1.16299 | ||||||||
\(207\) | −2.09665e19 | −0.432293 | ||||||||
\(208\) | 2.02687e18 | 0.0401132 | ||||||||
\(209\) | 8.18183e19 | 1.55456 | ||||||||
\(210\) | −3.35407e19 | −0.611939 | ||||||||
\(211\) | −4.48247e19 | −0.785447 | −0.392723 | − | 0.919657i | \(-0.628467\pi\) | ||||
−0.392723 | + | 0.919657i | \(0.628467\pi\) | |||||||
\(212\) | −9.66763e18 | −0.162729 | ||||||||
\(213\) | 6.54544e19 | 1.05855 | ||||||||
\(214\) | −4.99236e19 | −0.775870 | ||||||||
\(215\) | 3.90302e19 | 0.583007 | ||||||||
\(216\) | 7.99291e19 | 1.14775 | ||||||||
\(217\) | −3.25096e19 | −0.448852 | ||||||||
\(218\) | 3.42502e19 | 0.454761 | ||||||||
\(219\) | −2.24123e19 | −0.286227 | ||||||||
\(220\) | 2.94556e19 | 0.361889 | ||||||||
\(221\) | 8.93971e18 | 0.105679 | ||||||||
\(222\) | −2.11842e20 | −2.40997 | ||||||||
\(223\) | 1.02752e20 | 1.12512 | 0.562560 | − | 0.826757i | \(-0.309817\pi\) | ||||
0.562560 | + | 0.826757i | \(0.309817\pi\) | |||||||
\(224\) | 1.68939e19 | 0.178083 | ||||||||
\(225\) | 5.30066e19 | 0.537996 | ||||||||
\(226\) | 6.90793e19 | 0.675191 | ||||||||
\(227\) | −4.88230e19 | −0.459626 | −0.229813 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229813 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(228\) | −1.01729e20 | −0.922567 | ||||||||
\(229\) | −1.17440e19 | −0.102616 | −0.0513081 | − | 0.998683i | \(-0.516339\pi\) | ||||
−0.0513081 | + | 0.998683i | \(0.516339\pi\) | |||||||
\(230\) | 6.03554e18 | 0.0508194 | ||||||||
\(231\) | −3.85923e20 | −3.13184 | ||||||||
\(232\) | 3.28825e19 | 0.257228 | ||||||||
\(233\) | −2.34893e20 | −1.77152 | −0.885759 | − | 0.464146i | \(-0.846361\pi\) | ||||
−0.885759 | + | 0.464146i | \(0.846361\pi\) | |||||||
\(234\) | 4.19678e19 | 0.305198 | ||||||||
\(235\) | 1.12882e19 | 0.0791674 | ||||||||
\(236\) | −2.59376e19 | −0.175460 | ||||||||
\(237\) | 1.08080e20 | 0.705318 | ||||||||
\(238\) | 7.45121e19 | 0.469162 | ||||||||
\(239\) | −2.10348e20 | −1.27808 | −0.639038 | − | 0.769175i | \(-0.720667\pi\) | ||||
−0.639038 | + | 0.769175i | \(0.720667\pi\) | |||||||
\(240\) | −3.66237e19 | −0.214767 | ||||||||
\(241\) | −2.95279e20 | −1.67143 | −0.835714 | − | 0.549164i | \(-0.814946\pi\) | ||||
−0.835714 | + | 0.549164i | \(0.814946\pi\) | |||||||
\(242\) | 2.09526e20 | 1.14500 | ||||||||
\(243\) | 6.75692e20 | 3.56530 | ||||||||
\(244\) | −1.31099e20 | −0.668014 | ||||||||
\(245\) | −1.34756e18 | −0.00663190 | ||||||||
\(246\) | 4.30946e20 | 2.04868 | ||||||||
\(247\) | −3.35574e19 | −0.154122 | ||||||||
\(248\) | −3.54978e19 | −0.157530 | ||||||||
\(249\) | −7.78949e19 | −0.334052 | ||||||||
\(250\) | −1.52588e19 | −0.0632456 | ||||||||
\(251\) | 3.61690e20 | 1.44914 | 0.724569 | − | 0.689203i | \(-0.242039\pi\) | ||||
0.724569 | + | 0.689203i | \(0.242039\pi\) | |||||||
\(252\) | 3.49800e20 | 1.35492 | ||||||||
\(253\) | 6.94456e19 | 0.260088 | ||||||||
\(254\) | 1.05687e20 | 0.382766 | ||||||||
\(255\) | −1.61532e20 | −0.565807 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 2.83931e20 | 0.930640 | 0.465320 | − | 0.885143i | \(-0.345939\pi\) | ||||
0.465320 | + | 0.885143i | \(0.345939\pi\) | |||||||
\(258\) | −5.58371e20 | −1.77074 | ||||||||
\(259\) | −5.82452e20 | −1.78736 | ||||||||
\(260\) | −1.20811e19 | −0.0358784 | ||||||||
\(261\) | 6.80856e20 | 1.95709 | ||||||||
\(262\) | 2.39695e19 | 0.0666957 | ||||||||
\(263\) | 1.89218e20 | 0.509728 | 0.254864 | − | 0.966977i | \(-0.417969\pi\) | ||||
0.254864 | + | 0.966977i | \(0.417969\pi\) | |||||||
\(264\) | −4.21397e20 | −1.09915 | ||||||||
\(265\) | 5.76236e19 | 0.145549 | ||||||||
\(266\) | −2.79700e20 | −0.684223 | ||||||||
\(267\) | −6.69816e20 | −1.58712 | ||||||||
\(268\) | −2.18291e20 | −0.501061 | ||||||||
\(269\) | 2.43538e20 | 0.541592 | 0.270796 | − | 0.962637i | \(-0.412713\pi\) | ||||
0.270796 | + | 0.962637i | \(0.412713\pi\) | |||||||
\(270\) | −4.76414e20 | −1.02658 | ||||||||
\(271\) | 4.10787e20 | 0.857784 | 0.428892 | − | 0.903356i | \(-0.358904\pi\) | ||||
0.428892 | + | 0.903356i | \(0.358904\pi\) | |||||||
\(272\) | 8.13611e19 | 0.164657 | ||||||||
\(273\) | 1.58285e20 | 0.310496 | ||||||||
\(274\) | 4.01785e20 | 0.764037 | ||||||||
\(275\) | −1.75569e20 | −0.323684 | ||||||||
\(276\) | −8.63453e19 | −0.154352 | ||||||||
\(277\) | 3.28577e20 | 0.569586 | 0.284793 | − | 0.958589i | \(-0.408075\pi\) | ||||
0.284793 | + | 0.958589i | \(0.408075\pi\) | |||||||
\(278\) | 9.64513e19 | 0.162154 | ||||||||
\(279\) | −7.35007e20 | −1.19855 | ||||||||
\(280\) | −1.00695e20 | −0.159282 | ||||||||
\(281\) | −7.77398e20 | −1.19300 | −0.596499 | − | 0.802614i | \(-0.703442\pi\) | ||||
−0.596499 | + | 0.802614i | \(0.703442\pi\) | |||||||
\(282\) | −1.61490e20 | −0.240452 | ||||||||
\(283\) | −2.99751e20 | −0.433088 | −0.216544 | − | 0.976273i | \(-0.569478\pi\) | ||||
−0.216544 | + | 0.976273i | \(0.569478\pi\) | |||||||
\(284\) | 1.96506e20 | 0.275531 | ||||||||
\(285\) | 6.06351e20 | 0.825169 | ||||||||
\(286\) | −1.39006e20 | −0.183622 | ||||||||
\(287\) | 1.18487e21 | 1.51941 | ||||||||
\(288\) | 3.81953e20 | 0.475525 | ||||||||
\(289\) | −4.68389e20 | −0.566207 | ||||||||
\(290\) | −1.95995e20 | −0.230071 | ||||||||
\(291\) | 8.17929e20 | 0.932449 | ||||||||
\(292\) | −6.72857e19 | −0.0745021 | ||||||||
\(293\) | 2.44316e20 | 0.262771 | 0.131386 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131386 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(294\) | 1.92784e19 | 0.0201428 | ||||||||
\(295\) | 1.54600e20 | 0.156936 | ||||||||
\(296\) | −6.35990e20 | −0.627293 | ||||||||
\(297\) | −5.48168e21 | −5.25392 | ||||||||
\(298\) | 7.12394e20 | 0.663563 | ||||||||
\(299\) | −2.84828e19 | −0.0257856 | ||||||||
\(300\) | 2.18294e20 | 0.192093 | ||||||||
\(301\) | −1.53522e21 | −1.31327 | ||||||||
\(302\) | 7.48914e20 | 0.622835 | ||||||||
\(303\) | 3.58609e21 | 2.89974 | ||||||||
\(304\) | −3.05409e20 | −0.240135 | ||||||||
\(305\) | 7.81411e20 | 0.597490 | ||||||||
\(306\) | 1.68464e21 | 1.25278 | ||||||||
\(307\) | 2.37158e21 | 1.71538 | 0.857692 | − | 0.514164i | \(-0.171898\pi\) | ||||
0.857692 | + | 0.514164i | \(0.171898\pi\) | |||||||
\(308\) | −1.15861e21 | −0.815187 | ||||||||
\(309\) | 4.61583e21 | 3.15939 | ||||||||
\(310\) | 2.11583e20 | 0.140899 | ||||||||
\(311\) | 3.83251e20 | 0.248325 | 0.124162 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124162 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(312\) | 1.72834e20 | 0.108972 | ||||||||
\(313\) | 4.12820e20 | 0.253299 | 0.126650 | − | 0.991948i | \(-0.459578\pi\) | ||||
0.126650 | + | 0.991948i | \(0.459578\pi\) | |||||||
\(314\) | −1.23540e21 | −0.737746 | ||||||||
\(315\) | −2.08497e21 | −1.21188 | ||||||||
\(316\) | 3.24476e20 | 0.183587 | ||||||||
\(317\) | −4.33728e20 | −0.238899 | −0.119449 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119449 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(318\) | −8.24371e20 | −0.442071 | ||||||||
\(319\) | −2.25514e21 | −1.17748 | ||||||||
\(320\) | −1.09951e20 | −0.0559017 | ||||||||
\(321\) | −4.25705e21 | −2.10774 | ||||||||
\(322\) | −2.37403e20 | −0.114475 | ||||||||
\(323\) | −1.34704e21 | −0.632641 | ||||||||
\(324\) | 3.87562e21 | 1.77300 | ||||||||
\(325\) | 7.20089e19 | 0.0320906 | ||||||||
\(326\) | −1.11950e21 | −0.486042 | ||||||||
\(327\) | 2.92056e21 | 1.23541 | ||||||||
\(328\) | 1.29378e21 | 0.533252 | ||||||||
\(329\) | −4.44010e20 | −0.178331 | ||||||||
\(330\) | 2.51172e21 | 0.983111 | ||||||||
\(331\) | 3.49674e20 | 0.133391 | 0.0666953 | − | 0.997773i | \(-0.478754\pi\) | ||||
0.0666953 | + | 0.997773i | \(0.478754\pi\) | |||||||
\(332\) | −2.33855e20 | −0.0869506 | ||||||||
\(333\) | −1.31686e22 | −4.77270 | ||||||||
\(334\) | −1.43326e18 | −0.000506383 0 | ||||||||
\(335\) | 1.30112e21 | 0.448163 | ||||||||
\(336\) | 1.44056e21 | 0.483781 | ||||||||
\(337\) | 5.76519e21 | 1.88782 | 0.943908 | − | 0.330209i | \(-0.107119\pi\) | ||||
0.943908 | + | 0.330209i | \(0.107119\pi\) | |||||||
\(338\) | −2.15749e21 | −0.688902 | ||||||||
\(339\) | 5.89048e21 | 1.83423 | ||||||||
\(340\) | −4.84950e20 | −0.147274 | ||||||||
\(341\) | 2.43450e21 | 0.721104 | ||||||||
\(342\) | −6.32371e21 | −1.82705 | ||||||||
\(343\) | −3.52134e21 | −0.992448 | ||||||||
\(344\) | −1.67633e21 | −0.460907 | ||||||||
\(345\) | 5.14658e20 | 0.138056 | ||||||||
\(346\) | 3.88858e21 | 1.01776 | ||||||||
\(347\) | −4.09086e21 | −1.04475 | −0.522377 | − | 0.852715i | \(-0.674955\pi\) | ||||
−0.522377 | + | 0.852715i | \(0.674955\pi\) | |||||||
\(348\) | 2.80394e21 | 0.698786 | ||||||||
\(349\) | −4.79307e20 | −0.116573 | −0.0582865 | − | 0.998300i | \(-0.518564\pi\) | ||||
−0.0582865 | + | 0.998300i | \(0.518564\pi\) | |||||||
\(350\) | 6.00192e20 | 0.142466 | ||||||||
\(351\) | 2.24828e21 | 0.520883 | ||||||||
\(352\) | −1.26511e21 | −0.286099 | ||||||||
\(353\) | −3.84712e21 | −0.849280 | −0.424640 | − | 0.905362i | \(-0.639599\pi\) | ||||
−0.424640 | + | 0.905362i | \(0.639599\pi\) | |||||||
\(354\) | −2.21173e21 | −0.476655 | ||||||||
\(355\) | −1.17127e21 | −0.246442 | ||||||||
\(356\) | −2.01091e21 | −0.413112 | ||||||||
\(357\) | 6.35374e21 | 1.27453 | ||||||||
\(358\) | −3.76332e21 | −0.737167 | ||||||||
\(359\) | −9.15897e21 | −1.75204 | −0.876019 | − | 0.482276i | \(-0.839810\pi\) | ||||
−0.876019 | + | 0.482276i | \(0.839810\pi\) | |||||||
\(360\) | −2.27662e21 | −0.425323 | ||||||||
\(361\) | −4.23960e20 | −0.0773595 | ||||||||
\(362\) | 3.66863e21 | 0.653854 | ||||||||
\(363\) | 1.78665e22 | 3.11052 | ||||||||
\(364\) | 4.75200e20 | 0.0808191 | ||||||||
\(365\) | 4.01054e20 | 0.0666367 | ||||||||
\(366\) | −1.11790e22 | −1.81473 | ||||||||
\(367\) | 2.75835e21 | 0.437510 | 0.218755 | − | 0.975780i | \(-0.429800\pi\) | ||||
0.218755 | + | 0.975780i | \(0.429800\pi\) | |||||||
\(368\) | −2.59224e20 | −0.0401762 | ||||||||
\(369\) | 2.67886e22 | 4.05720 | ||||||||
\(370\) | 3.79079e21 | 0.561068 | ||||||||
\(371\) | −2.26657e21 | −0.327862 | ||||||||
\(372\) | −3.02694e21 | −0.427946 | ||||||||
\(373\) | −2.71586e21 | −0.375303 | −0.187652 | − | 0.982236i | \(-0.560088\pi\) | ||||
−0.187652 | + | 0.982236i | \(0.560088\pi\) | |||||||
\(374\) | −5.57989e21 | −0.753732 | ||||||||
\(375\) | −1.30114e21 | −0.171813 | ||||||||
\(376\) | −4.84823e20 | −0.0625873 | ||||||||
\(377\) | 9.24936e20 | 0.116737 | ||||||||
\(378\) | 1.87394e22 | 2.31246 | ||||||||
\(379\) | −5.08917e21 | −0.614065 | −0.307032 | − | 0.951699i | \(-0.599336\pi\) | ||||
−0.307032 | + | 0.951699i | \(0.599336\pi\) | |||||||
\(380\) | 1.82038e21 | 0.214784 | ||||||||
\(381\) | 9.01202e21 | 1.03982 | ||||||||
\(382\) | 1.21668e22 | 1.37290 | ||||||||
\(383\) | −7.65783e21 | −0.845116 | −0.422558 | − | 0.906336i | \(-0.638868\pi\) | ||||
−0.422558 | + | 0.906336i | \(0.638868\pi\) | |||||||
\(384\) | 1.57298e21 | 0.169788 | ||||||||
\(385\) | 6.90587e21 | 0.729126 | ||||||||
\(386\) | −3.61603e21 | −0.373456 | ||||||||
\(387\) | −3.47097e22 | −3.50677 | ||||||||
\(388\) | 2.45557e21 | 0.242708 | ||||||||
\(389\) | −1.43205e22 | −1.38480 | −0.692401 | − | 0.721513i | \(-0.743447\pi\) | ||||
−0.692401 | + | 0.721513i | \(0.743447\pi\) | |||||||
\(390\) | −1.03017e21 | −0.0974674 | ||||||||
\(391\) | −1.14333e21 | −0.105845 | ||||||||
\(392\) | 5.78775e19 | 0.00524298 | ||||||||
\(393\) | 2.04391e21 | 0.181186 | ||||||||
\(394\) | 8.80948e21 | 0.764245 | ||||||||
\(395\) | −1.93403e21 | −0.164206 | ||||||||
\(396\) | −2.61950e22 | −2.17675 | ||||||||
\(397\) | −1.12591e22 | −0.915766 | −0.457883 | − | 0.889012i | \(-0.651392\pi\) | ||||
−0.457883 | + | 0.889012i | \(0.651392\pi\) | |||||||
\(398\) | 1.72749e21 | 0.137534 | ||||||||
\(399\) | −2.38503e22 | −1.85877 | ||||||||
\(400\) | 6.55360e20 | 0.0500000 | ||||||||
\(401\) | 7.66443e21 | 0.572470 | 0.286235 | − | 0.958159i | \(-0.407596\pi\) | ||||
0.286235 | + | 0.958159i | \(0.407596\pi\) | |||||||
\(402\) | −1.86140e22 | −1.36119 | ||||||||
\(403\) | −9.98499e20 | −0.0714915 | ||||||||
\(404\) | 1.07661e22 | 0.754774 | ||||||||
\(405\) | −2.31005e22 | −1.58582 | ||||||||
\(406\) | 7.70931e21 | 0.518256 | ||||||||
\(407\) | 4.36173e22 | 2.87148 | ||||||||
\(408\) | 6.93776e21 | 0.447309 | ||||||||
\(409\) | −5.89700e21 | −0.372377 | −0.186189 | − | 0.982514i | \(-0.559614\pi\) | ||||
−0.186189 | + | 0.982514i | \(0.559614\pi\) | |||||||
\(410\) | −7.71153e21 | −0.476955 | ||||||||
\(411\) | 3.42607e22 | 2.07559 | ||||||||
\(412\) | 1.38576e22 | 0.822359 | ||||||||
\(413\) | −6.08106e21 | −0.353512 | ||||||||
\(414\) | −5.36742e21 | −0.305677 | ||||||||
\(415\) | 1.39388e21 | 0.0777710 | ||||||||
\(416\) | 5.18879e20 | 0.0283643 | ||||||||
\(417\) | 8.22452e21 | 0.440508 | ||||||||
\(418\) | 2.09455e22 | 1.09924 | ||||||||
\(419\) | 2.21057e21 | 0.113680 | 0.0568400 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568400 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(420\) | −8.58642e21 | −0.432706 | ||||||||
\(421\) | 3.62617e21 | 0.179081 | 0.0895406 | − | 0.995983i | \(-0.471460\pi\) | ||||
0.0895406 | + | 0.995983i | \(0.471460\pi\) | |||||||
\(422\) | −1.14751e22 | −0.555395 | ||||||||
\(423\) | −1.00386e22 | −0.476190 | ||||||||
\(424\) | −2.47491e21 | −0.115067 | ||||||||
\(425\) | 2.89053e21 | 0.131726 | ||||||||
\(426\) | 1.67563e22 | 0.748509 | ||||||||
\(427\) | −3.07361e22 | −1.34590 | ||||||||
\(428\) | −1.27805e22 | −0.548623 | ||||||||
\(429\) | −1.18532e22 | −0.498828 | ||||||||
\(430\) | 9.99172e21 | 0.412248 | ||||||||
\(431\) | 3.75200e22 | 1.51777 | 0.758885 | − | 0.651225i | \(-0.225744\pi\) | ||||
0.758885 | + | 0.651225i | \(0.225744\pi\) | |||||||
\(432\) | 2.04618e22 | 0.811583 | ||||||||
\(433\) | 1.27233e22 | 0.494828 | 0.247414 | − | 0.968910i | \(-0.420419\pi\) | ||||
0.247414 | + | 0.968910i | \(0.420419\pi\) | |||||||
\(434\) | −8.32245e21 | −0.317386 | ||||||||
\(435\) | −1.67128e22 | −0.625013 | ||||||||
\(436\) | 8.76806e21 | 0.321565 | ||||||||
\(437\) | 4.29178e21 | 0.154364 | ||||||||
\(438\) | −5.73754e21 | −0.202393 | ||||||||
\(439\) | −2.77606e22 | −0.960461 | −0.480231 | − | 0.877142i | \(-0.659447\pi\) | ||||
−0.480231 | + | 0.877142i | \(0.659447\pi\) | |||||||
\(440\) | 7.54065e21 | 0.255894 | ||||||||
\(441\) | 1.19839e21 | 0.0398907 | ||||||||
\(442\) | 2.28856e21 | 0.0747264 | ||||||||
\(443\) | −2.37963e22 | −0.762215 | −0.381107 | − | 0.924531i | \(-0.624457\pi\) | ||||
−0.381107 | + | 0.924531i | \(0.624457\pi\) | |||||||
\(444\) | −5.42316e22 | −1.70411 | ||||||||
\(445\) | 1.19860e22 | 0.369499 | ||||||||
\(446\) | 2.63045e22 | 0.795579 | ||||||||
\(447\) | 6.07467e22 | 1.80264 | ||||||||
\(448\) | 4.32484e21 | 0.125923 | ||||||||
\(449\) | 3.33620e22 | 0.953144 | 0.476572 | − | 0.879135i | \(-0.341879\pi\) | ||||
0.476572 | + | 0.879135i | \(0.341879\pi\) | |||||||
\(450\) | 1.35697e22 | 0.380420 | ||||||||
\(451\) | −8.87297e22 | −2.44100 | ||||||||
\(452\) | 1.76843e22 | 0.477432 | ||||||||
\(453\) | 6.38609e22 | 1.69200 | ||||||||
\(454\) | −1.24987e22 | −0.325005 | ||||||||
\(455\) | −2.83241e21 | −0.0722868 | ||||||||
\(456\) | −2.60426e22 | −0.652354 | ||||||||
\(457\) | 1.34948e22 | 0.331801 | 0.165901 | − | 0.986142i | \(-0.446947\pi\) | ||||
0.165901 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(458\) | −3.00648e21 | −0.0725606 | ||||||||
\(459\) | 9.02489e22 | 2.13813 | ||||||||
\(460\) | 1.54510e21 | 0.0359347 | ||||||||
\(461\) | −1.45529e22 | −0.332271 | −0.166136 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166136 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(462\) | −9.87964e22 | −2.21454 | ||||||||
\(463\) | −5.84077e22 | −1.28538 | −0.642690 | − | 0.766126i | \(-0.722182\pi\) | ||||
−0.642690 | + | 0.766126i | \(0.722182\pi\) | |||||||
\(464\) | 8.41793e21 | 0.181887 | ||||||||
\(465\) | 1.80420e22 | 0.382766 | ||||||||
\(466\) | −6.01327e22 | −1.25265 | ||||||||
\(467\) | 4.47563e22 | 0.915504 | 0.457752 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457752 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(468\) | 1.07438e22 | 0.215807 | ||||||||
\(469\) | −5.11784e22 | −1.00953 | ||||||||
\(470\) | 2.88977e21 | 0.0559798 | ||||||||
\(471\) | −1.05344e23 | −2.00417 | ||||||||
\(472\) | −6.64002e21 | −0.124069 | ||||||||
\(473\) | 1.14966e23 | 2.10984 | ||||||||
\(474\) | 2.76685e22 | 0.498735 | ||||||||
\(475\) | −1.08503e22 | −0.192108 | ||||||||
\(476\) | 1.90751e22 | 0.331748 | ||||||||
\(477\) | −5.12448e22 | −0.875475 | ||||||||
\(478\) | −5.38492e22 | −0.903737 | ||||||||
\(479\) | −3.08295e22 | −0.508293 | −0.254147 | − | 0.967166i | \(-0.581795\pi\) | ||||
−0.254147 | + | 0.967166i | \(0.581795\pi\) | |||||||
\(480\) | −9.37567e21 | −0.151863 | ||||||||
\(481\) | −1.78894e22 | −0.284684 | ||||||||
\(482\) | −7.55915e22 | −1.18188 | ||||||||
\(483\) | −2.02436e22 | −0.310984 | ||||||||
\(484\) | 5.36386e22 | 0.809639 | ||||||||
\(485\) | −1.46364e22 | −0.217084 | ||||||||
\(486\) | 1.72977e23 | 2.52104 | ||||||||
\(487\) | −6.13205e22 | −0.878233 | −0.439116 | − | 0.898430i | \(-0.644708\pi\) | ||||
−0.439116 | + | 0.898430i | \(0.644708\pi\) | |||||||
\(488\) | −3.35613e22 | −0.472358 | ||||||||
\(489\) | −9.54610e22 | −1.32039 | ||||||||
\(490\) | −3.44976e20 | −0.00468946 | ||||||||
\(491\) | 5.21756e22 | 0.697067 | 0.348533 | − | 0.937296i | \(-0.386680\pi\) | ||||
0.348533 | + | 0.937296i | \(0.386680\pi\) | |||||||
\(492\) | 1.10322e23 | 1.44864 | ||||||||
\(493\) | 3.71281e22 | 0.479186 | ||||||||
\(494\) | −8.59069e21 | −0.108981 | ||||||||
\(495\) | 1.56134e23 | 1.94695 | ||||||||
\(496\) | −9.08743e21 | −0.111390 | ||||||||
\(497\) | 4.60708e22 | 0.555133 | ||||||||
\(498\) | −1.99411e22 | −0.236211 | ||||||||
\(499\) | 1.47068e23 | 1.71263 | 0.856314 | − | 0.516455i | \(-0.172749\pi\) | ||||
0.856314 | + | 0.516455i | \(0.172749\pi\) | |||||||
\(500\) | −3.90625e21 | −0.0447214 | ||||||||
\(501\) | −1.22216e20 | −0.00137564 | ||||||||
\(502\) | 9.25926e22 | 1.02469 | ||||||||
\(503\) | −7.90275e22 | −0.859905 | −0.429953 | − | 0.902851i | \(-0.641470\pi\) | ||||
−0.429953 | + | 0.902851i | \(0.641470\pi\) | |||||||
\(504\) | 8.95488e22 | 0.958077 | ||||||||
\(505\) | −6.41710e22 | −0.675090 | ||||||||
\(506\) | 1.77781e22 | 0.183910 | ||||||||
\(507\) | −1.83972e23 | −1.87148 | ||||||||
\(508\) | 2.70557e22 | 0.270656 | ||||||||
\(509\) | 1.37816e23 | 1.35581 | 0.677905 | − | 0.735149i | \(-0.262888\pi\) | ||||
0.677905 | + | 0.735149i | \(0.262888\pi\) | |||||||
\(510\) | −4.13523e22 | −0.400086 | ||||||||
\(511\) | −1.57751e22 | −0.150105 | ||||||||
\(512\) | 4.72237e21 | 0.0441942 | ||||||||
\(513\) | −3.38771e23 | −3.11824 | ||||||||
\(514\) | 7.26864e22 | 0.658062 | ||||||||
\(515\) | −8.25977e22 | −0.735540 | ||||||||
\(516\) | −1.42943e23 | −1.25210 | ||||||||
\(517\) | 3.32500e22 | 0.286499 | ||||||||
\(518\) | −1.49108e23 | −1.26385 | ||||||||
\(519\) | 3.31584e23 | 2.76485 | ||||||||
\(520\) | −3.09276e21 | −0.0253698 | ||||||||
\(521\) | 1.81175e23 | 1.46210 | 0.731051 | − | 0.682323i | \(-0.239030\pi\) | ||||
0.731051 | + | 0.682323i | \(0.239030\pi\) | |||||||
\(522\) | 1.74299e23 | 1.38387 | ||||||||
\(523\) | 8.80774e22 | 0.688019 | 0.344009 | − | 0.938966i | \(-0.388215\pi\) | ||||
0.344009 | + | 0.938966i | \(0.388215\pi\) | |||||||
\(524\) | 6.13619e21 | 0.0471610 | ||||||||
\(525\) | 5.11791e22 | 0.387024 | ||||||||
\(526\) | 4.84398e22 | 0.360432 | ||||||||
\(527\) | −4.00810e22 | −0.293459 | ||||||||
\(528\) | −1.07878e23 | −0.777218 | ||||||||
\(529\) | −1.37407e23 | −0.974174 | ||||||||
\(530\) | 1.47516e22 | 0.102919 | ||||||||
\(531\) | −1.37486e23 | −0.943965 | ||||||||
\(532\) | −7.16031e22 | −0.483819 | ||||||||
\(533\) | 3.63921e22 | 0.242006 | ||||||||
\(534\) | −1.71473e23 | −1.12226 | ||||||||
\(535\) | 7.61774e22 | 0.490704 | ||||||||
\(536\) | −5.58826e22 | −0.354304 | ||||||||
\(537\) | −3.20903e23 | −2.00259 | ||||||||
\(538\) | 6.23457e22 | 0.382963 | ||||||||
\(539\) | −3.96934e21 | −0.0240001 | ||||||||
\(540\) | −1.21962e23 | −0.725902 | ||||||||
\(541\) | 1.23473e23 | 0.723429 | 0.361714 | − | 0.932289i | \(-0.382192\pi\) | ||||
0.361714 | + | 0.932289i | \(0.382192\pi\) | |||||||
\(542\) | 1.05161e23 | 0.606545 | ||||||||
\(543\) | 3.12829e23 | 1.77627 | ||||||||
\(544\) | 2.08284e22 | 0.116430 | ||||||||
\(545\) | −5.22617e22 | −0.287616 | ||||||||
\(546\) | 4.05209e22 | 0.219554 | ||||||||
\(547\) | −2.14828e22 | −0.114604 | −0.0573018 | − | 0.998357i | \(-0.518250\pi\) | ||||
−0.0573018 | + | 0.998357i | \(0.518250\pi\) | |||||||
\(548\) | 1.02857e23 | 0.540256 | ||||||||
\(549\) | −6.94911e23 | −3.59389 | ||||||||
\(550\) | −4.49458e22 | −0.228879 | ||||||||
\(551\) | −1.39369e23 | −0.698842 | ||||||||
\(552\) | −2.21044e22 | −0.109143 | ||||||||
\(553\) | 7.60734e22 | 0.369887 | ||||||||
\(554\) | 8.41158e22 | 0.402758 | ||||||||
\(555\) | 3.23246e23 | 1.52420 | ||||||||
\(556\) | 2.46915e22 | 0.114660 | ||||||||
\(557\) | 3.09249e22 | 0.141429 | 0.0707146 | − | 0.997497i | \(-0.477472\pi\) | ||||
0.0707146 | + | 0.997497i | \(0.477472\pi\) | |||||||
\(558\) | −1.88162e23 | −0.847502 | ||||||||
\(559\) | −4.71527e22 | −0.209173 | ||||||||
\(560\) | −2.57780e22 | −0.112629 | ||||||||
\(561\) | −4.75804e23 | −2.04759 | ||||||||
\(562\) | −1.99014e23 | −0.843577 | ||||||||
\(563\) | −6.71869e22 | −0.280520 | −0.140260 | − | 0.990115i | \(-0.544794\pi\) | ||||
−0.140260 | + | 0.990115i | \(0.544794\pi\) | |||||||
\(564\) | −4.13415e22 | −0.170025 | ||||||||
\(565\) | −1.05407e23 | −0.427028 | ||||||||
\(566\) | −7.67363e22 | −0.306239 | ||||||||
\(567\) | 9.08639e23 | 3.57220 | ||||||||
\(568\) | 5.03056e22 | 0.194830 | ||||||||
\(569\) | 2.77066e23 | 1.05713 | 0.528565 | − | 0.848893i | \(-0.322730\pi\) | ||||
0.528565 | + | 0.848893i | \(0.322730\pi\) | |||||||
\(570\) | 1.55226e23 | 0.583483 | ||||||||
\(571\) | 7.97807e22 | 0.295455 | 0.147727 | − | 0.989028i | \(-0.452804\pi\) | ||||
0.147727 | + | 0.989028i | \(0.452804\pi\) | |||||||
\(572\) | −3.55856e22 | −0.129840 | ||||||||
\(573\) | 1.03748e24 | 3.72962 | ||||||||
\(574\) | 3.03327e23 | 1.07438 | ||||||||
\(575\) | −9.20950e21 | −0.0321410 | ||||||||
\(576\) | 9.77799e22 | 0.336247 | ||||||||
\(577\) | 4.87229e22 | 0.165097 | 0.0825485 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825485 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(578\) | −1.19908e23 | −0.400369 | ||||||||
\(579\) | −3.08343e23 | −1.01453 | ||||||||
\(580\) | −5.01748e22 | −0.162685 | ||||||||
\(581\) | −5.48272e22 | −0.175186 | ||||||||
\(582\) | 2.09390e23 | 0.659341 | ||||||||
\(583\) | 1.69734e23 | 0.526728 | ||||||||
\(584\) | −1.72251e22 | −0.0526810 | ||||||||
\(585\) | −6.40378e22 | −0.193024 | ||||||||
\(586\) | 6.25450e22 | 0.185807 | ||||||||
\(587\) | −4.71668e23 | −1.38106 | −0.690530 | − | 0.723303i | \(-0.742623\pi\) | ||||
−0.690530 | + | 0.723303i | \(0.742623\pi\) | |||||||
\(588\) | 4.93528e21 | 0.0142431 | ||||||||
\(589\) | 1.50454e23 | 0.427980 | ||||||||
\(590\) | 3.95776e22 | 0.110970 | ||||||||
\(591\) | 7.51195e23 | 2.07615 | ||||||||
\(592\) | −1.62813e23 | −0.443563 | ||||||||
\(593\) | −3.16081e23 | −0.848854 | −0.424427 | − | 0.905462i | \(-0.639524\pi\) | ||||
−0.424427 | + | 0.905462i | \(0.639524\pi\) | |||||||
\(594\) | −1.40331e24 | −3.71508 | ||||||||
\(595\) | −1.13696e23 | −0.296724 | ||||||||
\(596\) | 1.82373e23 | 0.469210 | ||||||||
\(597\) | 1.47305e23 | 0.373626 | ||||||||
\(598\) | −7.29159e21 | −0.0182332 | ||||||||
\(599\) | −4.03133e23 | −0.993849 | −0.496924 | − | 0.867794i | \(-0.665537\pi\) | ||||
−0.496924 | + | 0.867794i | \(0.665537\pi\) | |||||||
\(600\) | 5.58834e22 | 0.135830 | ||||||||
\(601\) | −1.75215e23 | −0.419894 | −0.209947 | − | 0.977713i | \(-0.567329\pi\) | ||||
−0.209947 | + | 0.977713i | \(0.567329\pi\) | |||||||
\(602\) | −3.93016e23 | −0.928624 | ||||||||
\(603\) | −1.15709e24 | −2.69569 | ||||||||
\(604\) | 1.91722e23 | 0.440411 | ||||||||
\(605\) | −3.19711e23 | −0.724163 | ||||||||
\(606\) | 9.18039e23 | 2.05042 | ||||||||
\(607\) | −5.38904e23 | −1.18688 | −0.593441 | − | 0.804877i | \(-0.702231\pi\) | ||||
−0.593441 | + | 0.804877i | \(0.702231\pi\) | |||||||
\(608\) | −7.81847e22 | −0.169801 | ||||||||
\(609\) | 6.57382e23 | 1.40790 | ||||||||
\(610\) | 2.00041e23 | 0.422489 | ||||||||
\(611\) | −1.36373e22 | −0.0284040 | ||||||||
\(612\) | 4.31268e23 | 0.885849 | ||||||||
\(613\) | 7.80727e23 | 1.58156 | 0.790779 | − | 0.612102i | \(-0.209676\pi\) | ||||
0.790779 | + | 0.612102i | \(0.209676\pi\) | |||||||
\(614\) | 6.07124e23 | 1.21296 | ||||||||
\(615\) | −6.57572e23 | −1.29570 | ||||||||
\(616\) | −2.96605e23 | −0.576424 | ||||||||
\(617\) | −4.79487e22 | −0.0919079 | −0.0459539 | − | 0.998944i | \(-0.514633\pi\) | ||||
−0.0459539 | + | 0.998944i | \(0.514633\pi\) | |||||||
\(618\) | 1.18165e24 | 2.23403 | ||||||||
\(619\) | −7.24528e23 | −1.35109 | −0.675545 | − | 0.737319i | \(-0.736092\pi\) | ||||
−0.675545 | + | 0.737319i | \(0.736092\pi\) | |||||||
\(620\) | 5.41653e22 | 0.0996304 | ||||||||
\(621\) | −2.87542e23 | −0.521702 | ||||||||
\(622\) | 9.81123e22 | 0.175592 | ||||||||
\(623\) | −4.71458e23 | −0.832328 | ||||||||
\(624\) | 4.42454e22 | 0.0770548 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | 1.05682e23 | 0.179110 | ||||||||
\(627\) | 1.78605e24 | 2.98620 | ||||||||
\(628\) | −3.16263e23 | −0.521665 | ||||||||
\(629\) | −7.18104e23 | −1.16858 | ||||||||
\(630\) | −5.33752e23 | −0.856930 | ||||||||
\(631\) | −5.16806e23 | −0.818613 | −0.409306 | − | 0.912397i | \(-0.634229\pi\) | ||||
−0.409306 | + | 0.912397i | \(0.634229\pi\) | |||||||
\(632\) | 8.30660e22 | 0.129816 | ||||||||
\(633\) | −9.78499e23 | −1.50879 | ||||||||
\(634\) | −1.11034e23 | −0.168927 | ||||||||
\(635\) | −1.61265e23 | −0.242082 | ||||||||
\(636\) | −2.11039e23 | −0.312591 | ||||||||
\(637\) | 1.62800e21 | 0.00237942 | ||||||||
\(638\) | −5.77317e23 | −0.832604 | ||||||||
\(639\) | 1.04161e24 | 1.48234 | ||||||||
\(640\) | −2.81475e22 | −0.0395285 | ||||||||
\(641\) | 8.96049e23 | 1.24176 | 0.620881 | − | 0.783905i | \(-0.286775\pi\) | ||||
0.620881 | + | 0.783905i | \(0.286775\pi\) | |||||||
\(642\) | −1.08981e24 | −1.49039 | ||||||||
\(643\) | 8.53474e23 | 1.15185 | 0.575927 | − | 0.817501i | \(-0.304641\pi\) | ||||
0.575927 | + | 0.817501i | \(0.304641\pi\) | |||||||
\(644\) | −6.07751e22 | −0.0809461 | ||||||||
\(645\) | 8.52007e23 | 1.11992 | ||||||||
\(646\) | −3.44841e23 | −0.447345 | ||||||||
\(647\) | −1.37455e24 | −1.75984 | −0.879921 | − | 0.475119i | \(-0.842405\pi\) | ||||
−0.879921 | + | 0.475119i | \(0.842405\pi\) | |||||||
\(648\) | 9.92160e23 | 1.25370 | ||||||||
\(649\) | 4.55384e23 | 0.567934 | ||||||||
\(650\) | 1.84343e22 | 0.0226915 | ||||||||
\(651\) | −7.09665e23 | −0.862214 | ||||||||
\(652\) | −2.86592e23 | −0.343684 | ||||||||
\(653\) | 9.43977e22 | 0.111738 | 0.0558688 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558688 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(654\) | 7.47663e23 | 0.873565 | ||||||||
\(655\) | −3.65745e22 | −0.0421821 | ||||||||
\(656\) | 3.31208e23 | 0.377066 | ||||||||
\(657\) | −3.56659e23 | −0.400818 | ||||||||
\(658\) | −1.13667e23 | −0.126099 | ||||||||
\(659\) | −4.47186e23 | −0.489736 | −0.244868 | − | 0.969556i | \(-0.578745\pi\) | ||||
−0.244868 | + | 0.969556i | \(0.578745\pi\) | |||||||
\(660\) | 6.43000e23 | 0.695165 | ||||||||
\(661\) | 1.38249e24 | 1.47554 | 0.737769 | − | 0.675054i | \(-0.235879\pi\) | ||||
0.737769 | + | 0.675054i | \(0.235879\pi\) | |||||||
\(662\) | 8.95165e22 | 0.0943214 | ||||||||
\(663\) | 1.95149e23 | 0.203002 | ||||||||
\(664\) | −5.98668e22 | −0.0614834 | ||||||||
\(665\) | 4.26788e23 | 0.432741 | ||||||||
\(666\) | −3.37117e24 | −3.37481 | ||||||||
\(667\) | −1.18294e23 | −0.116921 | ||||||||
\(668\) | −3.66914e20 | −0.000358067 0 | ||||||||
\(669\) | 2.24302e24 | 2.16128 | ||||||||
\(670\) | 3.33086e23 | 0.316899 | ||||||||
\(671\) | 2.30170e24 | 2.16225 | ||||||||
\(672\) | 3.68784e23 | 0.342084 | ||||||||
\(673\) | 5.98224e22 | 0.0547943 | 0.0273972 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273972 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(674\) | 1.47589e24 | 1.33489 | ||||||||
\(675\) | 7.26951e23 | 0.649266 | ||||||||
\(676\) | −5.52318e23 | −0.487127 | ||||||||
\(677\) | −9.03455e23 | −0.786870 | −0.393435 | − | 0.919352i | \(-0.628713\pi\) | ||||
−0.393435 | + | 0.919352i | \(0.628713\pi\) | |||||||
\(678\) | 1.50796e24 | 1.29700 | ||||||||
\(679\) | 5.75709e23 | 0.489001 | ||||||||
\(680\) | −1.24147e23 | −0.104138 | ||||||||
\(681\) | −1.06578e24 | −0.882910 | ||||||||
\(682\) | 6.23232e23 | 0.509897 | ||||||||
\(683\) | 2.90285e23 | 0.234557 | 0.117278 | − | 0.993099i | \(-0.462583\pi\) | ||||
0.117278 | + | 0.993099i | \(0.462583\pi\) | |||||||
\(684\) | −1.61887e24 | −1.29192 | ||||||||
\(685\) | −6.13076e23 | −0.483219 | ||||||||
\(686\) | −9.01463e23 | −0.701767 | ||||||||
\(687\) | −2.56366e23 | −0.197119 | ||||||||
\(688\) | −4.29141e23 | −0.325911 | ||||||||
\(689\) | −6.96156e22 | −0.0522207 | ||||||||
\(690\) | 1.31752e23 | 0.0976206 | ||||||||
\(691\) | −1.83665e24 | −1.34420 | −0.672098 | − | 0.740462i | \(-0.734607\pi\) | ||||
−0.672098 | + | 0.740462i | \(0.734607\pi\) | |||||||
\(692\) | 9.95477e23 | 0.719664 | ||||||||
\(693\) | −6.14142e24 | −4.38567 | ||||||||
\(694\) | −1.04726e24 | −0.738753 | ||||||||
\(695\) | −1.47173e23 | −0.102555 | ||||||||
\(696\) | 7.17807e23 | 0.494117 | ||||||||
\(697\) | 1.46082e24 | 0.993388 | ||||||||
\(698\) | −1.22703e23 | −0.0824295 | ||||||||
\(699\) | −5.12759e24 | −3.40296 | ||||||||
\(700\) | 1.53649e23 | 0.100739 | ||||||||
\(701\) | 2.33493e23 | 0.151241 | 0.0756206 | − | 0.997137i | \(-0.475906\pi\) | ||||
0.0756206 | + | 0.997137i | \(0.475906\pi\) | |||||||
\(702\) | 5.75561e23 | 0.368320 | ||||||||
\(703\) | 2.69558e24 | 1.70424 | ||||||||
\(704\) | −3.23868e23 | −0.202302 | ||||||||
\(705\) | 2.46414e23 | 0.152075 | ||||||||
\(706\) | −9.84863e23 | −0.600532 | ||||||||
\(707\) | 2.52411e24 | 1.52070 | ||||||||
\(708\) | −5.66203e23 | −0.337046 | ||||||||
\(709\) | 3.27467e24 | 1.92608 | 0.963042 | − | 0.269351i | \(-0.0868093\pi\) | ||||
0.963042 | + | 0.269351i | \(0.0868093\pi\) | |||||||
\(710\) | −2.99845e23 | −0.174261 | ||||||||
\(711\) | 1.71994e24 | 0.987692 | ||||||||
\(712\) | −5.14793e23 | −0.292114 | ||||||||
\(713\) | 1.27702e23 | 0.0716038 | ||||||||
\(714\) | 1.62656e24 | 0.901228 | ||||||||
\(715\) | 2.12107e23 | 0.116132 | ||||||||
\(716\) | −9.63411e23 | −0.521256 | ||||||||
\(717\) | −4.59178e24 | −2.45510 | ||||||||
\(718\) | −2.34470e24 | −1.23888 | ||||||||
\(719\) | 3.32629e23 | 0.173686 | 0.0868428 | − | 0.996222i | \(-0.472322\pi\) | ||||
0.0868428 | + | 0.996222i | \(0.472322\pi\) | |||||||
\(720\) | −5.82814e23 | −0.300749 | ||||||||
\(721\) | 3.24891e24 | 1.65687 | ||||||||
\(722\) | −1.08534e23 | −0.0547014 | ||||||||
\(723\) | −6.44578e24 | −3.21070 | ||||||||
\(724\) | 9.39169e23 | 0.462345 | ||||||||
\(725\) | 2.99065e23 | 0.145510 | ||||||||
\(726\) | 4.57383e24 | 2.19947 | ||||||||
\(727\) | 3.34576e24 | 1.59020 | 0.795102 | − | 0.606476i | \(-0.207417\pi\) | ||||
0.795102 | + | 0.606476i | \(0.207417\pi\) | |||||||
\(728\) | 1.21651e23 | 0.0571478 | ||||||||
\(729\) | 7.11298e24 | 3.30269 | ||||||||
\(730\) | 1.02670e23 | 0.0471193 | ||||||||
\(731\) | −1.89277e24 | −0.858617 | ||||||||
\(732\) | −2.86182e24 | −1.28321 | ||||||||
\(733\) | −4.10279e24 | −1.81842 | −0.909212 | − | 0.416333i | \(-0.863315\pi\) | ||||
−0.909212 | + | 0.416333i | \(0.863315\pi\) | |||||||
\(734\) | 7.06138e23 | 0.309366 | ||||||||
\(735\) | −2.94166e22 | −0.0127394 | ||||||||
\(736\) | −6.63614e22 | −0.0284089 | ||||||||
\(737\) | 3.83253e24 | 1.62185 | ||||||||
\(738\) | 6.85789e24 | 2.86887 | ||||||||
\(739\) | −3.64889e24 | −1.50898 | −0.754490 | − | 0.656311i | \(-0.772116\pi\) | ||||
−0.754490 | + | 0.656311i | \(0.772116\pi\) | |||||||
\(740\) | 9.70443e23 | 0.396735 | ||||||||
\(741\) | −7.32539e23 | −0.296057 | ||||||||
\(742\) | −5.80243e23 | −0.231834 | ||||||||
\(743\) | 1.84119e24 | 0.727267 | 0.363634 | − | 0.931542i | \(-0.381536\pi\) | ||||
0.363634 | + | 0.931542i | \(0.381536\pi\) | |||||||
\(744\) | −7.74897e23 | −0.302603 | ||||||||
\(745\) | −1.08703e24 | −0.419674 | ||||||||
\(746\) | −6.95261e23 | −0.265380 | ||||||||
\(747\) | −1.23959e24 | −0.467790 | ||||||||
\(748\) | −1.42845e24 | −0.532969 | ||||||||
\(749\) | −2.99638e24 | −1.10535 | ||||||||
\(750\) | −3.33091e23 | −0.121490 | ||||||||
\(751\) | −4.73106e24 | −1.70616 | −0.853078 | − | 0.521783i | \(-0.825267\pi\) | ||||
−0.853078 | + | 0.521783i | \(0.825267\pi\) | |||||||
\(752\) | −1.24115e23 | −0.0442559 | ||||||||
\(753\) | 7.89548e24 | 2.78369 | ||||||||
\(754\) | 2.36784e23 | 0.0825459 | ||||||||
\(755\) | −1.14275e24 | −0.393916 | ||||||||
\(756\) | 4.79728e24 | 1.63516 | ||||||||
\(757\) | 2.19059e24 | 0.738321 | 0.369160 | − | 0.929366i | \(-0.379645\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379645\pi\) | |||||||
\(758\) | −1.30283e24 | −0.434209 | ||||||||
\(759\) | 1.51596e24 | 0.499611 | ||||||||
\(760\) | 4.66017e23 | 0.151875 | ||||||||
\(761\) | −3.61511e24 | −1.16507 | −0.582534 | − | 0.812806i | \(-0.697939\pi\) | ||||
−0.582534 | + | 0.812806i | \(0.697939\pi\) | |||||||
\(762\) | 2.30708e24 | 0.735267 | ||||||||
\(763\) | 2.05567e24 | 0.647880 | ||||||||
\(764\) | 3.11470e24 | 0.970783 | ||||||||
\(765\) | −2.57056e24 | −0.792328 | ||||||||
\(766\) | −1.96040e24 | −0.597587 | ||||||||
\(767\) | −1.86774e23 | −0.0563061 | ||||||||
\(768\) | 4.02682e23 | 0.120058 | ||||||||
\(769\) | −3.22044e24 | −0.949601 | −0.474800 | − | 0.880093i | \(-0.657480\pi\) | ||||
−0.474800 | + | 0.880093i | \(0.657480\pi\) | |||||||
\(770\) | 1.76790e24 | 0.515570 | ||||||||
\(771\) | 6.19806e24 | 1.78770 | ||||||||
\(772\) | −9.25703e23 | −0.264073 | ||||||||
\(773\) | 4.80504e24 | 1.35573 | 0.677863 | − | 0.735189i | \(-0.262906\pi\) | ||||
0.677863 | + | 0.735189i | \(0.262906\pi\) | |||||||
\(774\) | −8.88567e24 | −2.47966 | ||||||||
\(775\) | −3.22850e23 | −0.0891121 | ||||||||
\(776\) | 6.28627e23 | 0.171620 | ||||||||
\(777\) | −1.27146e25 | −3.43340 | ||||||||
\(778\) | −3.66606e24 | −0.979203 | ||||||||
\(779\) | −5.48356e24 | −1.44875 | ||||||||
\(780\) | −2.63723e23 | −0.0689199 | ||||||||
\(781\) | −3.45004e24 | −0.891848 | ||||||||
\(782\) | −2.92693e23 | −0.0748438 | ||||||||
\(783\) | 9.33749e24 | 2.36187 | ||||||||
\(784\) | 1.48166e22 | 0.00370734 | ||||||||
\(785\) | 1.88508e24 | 0.466592 | ||||||||
\(786\) | 5.23240e23 | 0.128118 | ||||||||
\(787\) | 8.96802e23 | 0.217226 | 0.108613 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108613 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(788\) | 2.25523e24 | 0.540403 | ||||||||
\(789\) | 4.13052e24 | 0.979152 | ||||||||
\(790\) | −4.95112e23 | −0.116111 | ||||||||
\(791\) | 4.14608e24 | 0.961918 | ||||||||
\(792\) | −6.70592e24 | −1.53920 | ||||||||
\(793\) | −9.44030e23 | −0.214370 | ||||||||
\(794\) | −2.88233e24 | −0.647544 | ||||||||
\(795\) | 1.25789e24 | 0.279590 | ||||||||
\(796\) | 4.42238e23 | 0.0972512 | ||||||||
\(797\) | −1.80946e24 | −0.393688 | −0.196844 | − | 0.980435i | \(-0.563069\pi\) | ||||
−0.196844 | + | 0.980435i | \(0.563069\pi\) | |||||||
\(798\) | −6.10568e24 | −1.31435 | ||||||||
\(799\) | −5.47420e23 | −0.116593 | ||||||||
\(800\) | 1.67772e23 | 0.0353553 | ||||||||
\(801\) | −1.06592e25 | −2.22252 | ||||||||
\(802\) | 1.96209e24 | 0.404797 | ||||||||
\(803\) | 1.18133e24 | 0.241151 | ||||||||
\(804\) | −4.76518e24 | −0.962505 | ||||||||
\(805\) | 3.62248e23 | 0.0724004 | ||||||||
\(806\) | −2.55616e23 | −0.0505521 | ||||||||
\(807\) | 5.31630e24 | 1.04036 | ||||||||
\(808\) | 2.75612e24 | 0.533706 | ||||||||
\(809\) | −7.43901e23 | −0.142545 | −0.0712726 | − | 0.997457i | \(-0.522706\pi\) | ||||
−0.0712726 | + | 0.997457i | \(0.522706\pi\) | |||||||
\(810\) | −5.91373e24 | −1.12134 | ||||||||
\(811\) | 1.76744e24 | 0.331640 | 0.165820 | − | 0.986156i | \(-0.446973\pi\) | ||||
0.165820 | + | 0.986156i | \(0.446973\pi\) | |||||||
\(812\) | 1.97358e24 | 0.366462 | ||||||||
\(813\) | 8.96725e24 | 1.64774 | ||||||||
\(814\) | 1.11660e25 | 2.03045 | ||||||||
\(815\) | 1.70822e24 | 0.307400 | ||||||||
\(816\) | 1.77607e24 | 0.316296 | ||||||||
\(817\) | 7.10497e24 | 1.25220 | ||||||||
\(818\) | −1.50963e24 | −0.263310 | ||||||||
\(819\) | 2.51887e24 | 0.434803 | ||||||||
\(820\) | −1.97415e24 | −0.337258 | ||||||||
\(821\) | 4.58049e24 | 0.774453 | 0.387227 | − | 0.921985i | \(-0.373433\pi\) | ||||
0.387227 | + | 0.921985i | \(0.373433\pi\) | |||||||
\(822\) | 8.77075e24 | 1.46766 | ||||||||
\(823\) | −7.92564e24 | −1.31261 | −0.656305 | − | 0.754496i | \(-0.727882\pi\) | ||||
−0.656305 | + | 0.754496i | \(0.727882\pi\) | |||||||
\(824\) | 3.54754e24 | 0.581495 | ||||||||
\(825\) | −3.83258e24 | −0.621774 | ||||||||
\(826\) | −1.55675e24 | −0.249971 | ||||||||
\(827\) | 6.56769e24 | 1.04380 | 0.521898 | − | 0.853008i | \(-0.325224\pi\) | ||||
0.521898 | + | 0.853008i | \(0.325224\pi\) | |||||||
\(828\) | −1.37406e24 | −0.216146 | ||||||||
\(829\) | −1.03161e25 | −1.60621 | −0.803105 | − | 0.595838i | \(-0.796820\pi\) | ||||
−0.803105 | + | 0.595838i | \(0.796820\pi\) | |||||||
\(830\) | 3.56834e23 | 0.0549924 | ||||||||
\(831\) | 7.17266e24 | 1.09414 | ||||||||
\(832\) | 1.32833e23 | 0.0200566 | ||||||||
\(833\) | 6.53501e22 | 0.00976706 | ||||||||
\(834\) | 2.10548e24 | 0.311486 | ||||||||
\(835\) | 2.18698e21 | 0.000320265 0 | ||||||||
\(836\) | 5.36204e24 | 0.777279 | ||||||||
\(837\) | −1.00801e25 | −1.44644 | ||||||||
\(838\) | 5.65905e23 | 0.0803839 | ||||||||
\(839\) | −2.05320e24 | −0.288705 | −0.144353 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144353 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(840\) | −2.19812e24 | −0.305970 | ||||||||
\(841\) | −3.41573e24 | −0.470672 | ||||||||
\(842\) | 9.28299e23 | 0.126630 | ||||||||
\(843\) | −1.69702e25 | −2.29167 | ||||||||
\(844\) | −2.93763e24 | −0.392723 | ||||||||
\(845\) | 3.29207e24 | 0.435700 | ||||||||
\(846\) | −2.56988e24 | −0.336717 | ||||||||
\(847\) | 1.25755e25 | 1.63124 | ||||||||
\(848\) | −6.33578e23 | −0.0813645 | ||||||||
\(849\) | −6.54340e24 | −0.831932 | ||||||||
\(850\) | 7.39975e23 | 0.0931443 | ||||||||
\(851\) | 2.28795e24 | 0.285131 | ||||||||
\(852\) | 4.28962e24 | 0.529276 | ||||||||
\(853\) | −4.58487e24 | −0.560093 | −0.280047 | − | 0.959986i | \(-0.590350\pi\) | ||||
−0.280047 | + | 0.959986i | \(0.590350\pi\) | |||||||
\(854\) | −7.86845e24 | −0.951694 | ||||||||
\(855\) | 9.64921e24 | 1.15553 | ||||||||
\(856\) | −3.27180e24 | −0.387935 | ||||||||
\(857\) | −1.47586e25 | −1.73264 | −0.866322 | − | 0.499485i | \(-0.833522\pi\) | ||||
−0.866322 | + | 0.499485i | \(0.833522\pi\) | |||||||
\(858\) | −3.03443e24 | −0.352724 | ||||||||
\(859\) | 7.38546e24 | 0.850033 | 0.425017 | − | 0.905186i | \(-0.360268\pi\) | ||||
0.425017 | + | 0.905186i | \(0.360268\pi\) | |||||||
\(860\) | 2.55788e24 | 0.291503 | ||||||||
\(861\) | 2.58650e25 | 2.91868 | ||||||||
\(862\) | 9.60512e24 | 1.07323 | ||||||||
\(863\) | 1.21992e24 | 0.134971 | 0.0674856 | − | 0.997720i | \(-0.478502\pi\) | ||||
0.0674856 | + | 0.997720i | \(0.478502\pi\) | |||||||
\(864\) | 5.23823e24 | 0.573876 | ||||||||
\(865\) | −5.93351e24 | −0.643687 | ||||||||
\(866\) | 3.25718e24 | 0.349896 | ||||||||
\(867\) | −1.02247e25 | −1.08765 | ||||||||
\(868\) | −2.13055e24 | −0.224426 | ||||||||
\(869\) | −5.69681e24 | −0.594243 | ||||||||
\(870\) | −4.27847e24 | −0.441951 | ||||||||
\(871\) | −1.57189e24 | −0.160794 | ||||||||
\(872\) | 2.24462e24 | 0.227381 | ||||||||
\(873\) | 1.30162e25 | 1.30576 | ||||||||
\(874\) | 1.09870e24 | 0.109152 | ||||||||
\(875\) | −9.15820e23 | −0.0901035 | ||||||||
\(876\) | −1.46881e24 | −0.143114 | ||||||||
\(877\) | −7.86521e23 | −0.0758951 | −0.0379475 | − | 0.999280i | \(-0.512082\pi\) | ||||
−0.0379475 | + | 0.999280i | \(0.512082\pi\) | |||||||
\(878\) | −7.10670e24 | −0.679149 | ||||||||
\(879\) | 5.33329e24 | 0.504765 | ||||||||
\(880\) | 1.93041e24 | 0.180945 | ||||||||
\(881\) | −1.48916e25 | −1.38244 | −0.691218 | − | 0.722646i | \(-0.742926\pi\) | ||||
−0.691218 | + | 0.722646i | \(0.742926\pi\) | |||||||
\(882\) | 3.06789e23 | 0.0282070 | ||||||||
\(883\) | 2.17779e25 | 1.98313 | 0.991563 | − | 0.129627i | \(-0.0413779\pi\) | ||||
0.991563 | + | 0.129627i | \(0.0413779\pi\) | |||||||
\(884\) | 5.85873e23 | 0.0528395 | ||||||||
\(885\) | 3.37483e24 | 0.301463 | ||||||||
\(886\) | −6.09185e24 | −0.538967 | ||||||||
\(887\) | −1.34341e25 | −1.17722 | −0.588609 | − | 0.808418i | \(-0.700324\pi\) | ||||
−0.588609 | + | 0.808418i | \(0.700324\pi\) | |||||||
\(888\) | −1.38833e25 | −1.20499 | ||||||||
\(889\) | 6.34322e24 | 0.545311 | ||||||||
\(890\) | 3.06841e24 | 0.261275 | ||||||||
\(891\) | −6.80441e25 | −5.73892 | ||||||||
\(892\) | 6.73395e24 | 0.562560 | ||||||||
\(893\) | 2.05487e24 | 0.170039 | ||||||||
\(894\) | 1.55512e25 | 1.27466 | ||||||||
\(895\) | 5.74238e24 | 0.466225 | ||||||||
\(896\) | 1.10716e24 | 0.0890413 | ||||||||
\(897\) | −6.21763e23 | −0.0495324 | ||||||||
\(898\) | 8.54068e24 | 0.673975 | ||||||||
\(899\) | −4.14693e24 | −0.324167 | ||||||||
\(900\) | 3.47384e24 | 0.268998 | ||||||||
\(901\) | −2.79445e24 | −0.214356 | ||||||||
\(902\) | −2.27148e25 | −1.72605 | ||||||||
\(903\) | −3.35130e25 | −2.52271 | ||||||||
\(904\) | 4.52718e24 | 0.337595 | ||||||||
\(905\) | −5.59788e24 | −0.413534 | ||||||||
\(906\) | 1.63484e25 | 1.19642 | ||||||||
\(907\) | −2.23611e25 | −1.62118 | −0.810590 | − | 0.585614i | \(-0.800853\pi\) | ||||
−0.810590 | + | 0.585614i | \(0.800853\pi\) | |||||||
\(908\) | −3.19966e24 | −0.229813 | ||||||||
\(909\) | 5.70675e25 | 4.06065 | ||||||||
\(910\) | −7.25097e23 | −0.0511145 | ||||||||
\(911\) | −2.25949e24 | −0.157799 | −0.0788994 | − | 0.996883i | \(-0.525141\pi\) | ||||
−0.0788994 | + | 0.996883i | \(0.525141\pi\) | |||||||
\(912\) | −6.66691e24 | −0.461284 | ||||||||
\(913\) | 4.10577e24 | 0.281445 | ||||||||
\(914\) | 3.45466e24 | 0.234619 | ||||||||
\(915\) | 1.70578e25 | 1.14774 | ||||||||
\(916\) | −7.69658e23 | −0.0513081 | ||||||||
\(917\) | 1.43863e24 | 0.0950187 | ||||||||
\(918\) | 2.31037e25 | 1.51189 | ||||||||
\(919\) | −1.15664e25 | −0.749923 | −0.374962 | − | 0.927040i | \(-0.622344\pi\) | ||||
−0.374962 | + | 0.927040i | \(0.622344\pi\) | |||||||
\(920\) | 3.95545e23 | 0.0254097 | ||||||||
\(921\) | 5.17702e25 | 3.29513 | ||||||||
\(922\) | −3.72555e24 | −0.234951 | ||||||||
\(923\) | 1.41502e24 | 0.0884195 | ||||||||
\(924\) | −2.52919e25 | −1.56592 | ||||||||
\(925\) | −5.78429e24 | −0.354851 | ||||||||
\(926\) | −1.49524e25 | −0.908901 | ||||||||
\(927\) | 7.34544e25 | 4.42425 | ||||||||
\(928\) | 2.15499e24 | 0.128614 | ||||||||
\(929\) | −3.15273e24 | −0.186446 | −0.0932229 | − | 0.995645i | \(-0.529717\pi\) | ||||
−0.0932229 | + | 0.995645i | \(0.529717\pi\) | |||||||
\(930\) | 4.61874e24 | 0.270657 | ||||||||
\(931\) | −2.45308e23 | −0.0142442 | ||||||||
\(932\) | −1.53940e25 | −0.885759 | ||||||||
\(933\) | 8.36616e24 | 0.477015 | ||||||||
\(934\) | 1.14576e25 | 0.647359 | ||||||||
\(935\) | 8.51424e24 | 0.476702 | ||||||||
\(936\) | 2.75040e24 | 0.152599 | ||||||||
\(937\) | 1.83098e25 | 1.00670 | 0.503348 | − | 0.864084i | \(-0.332102\pi\) | ||||
0.503348 | + | 0.864084i | \(0.332102\pi\) | |||||||
\(938\) | −1.31017e25 | −0.713843 | ||||||||
\(939\) | 9.01163e24 | 0.486570 | ||||||||
\(940\) | 7.39781e23 | 0.0395837 | ||||||||
\(941\) | −7.12799e24 | −0.377968 | −0.188984 | − | 0.981980i | \(-0.560519\pi\) | ||||
−0.188984 | + | 0.981980i | \(0.560519\pi\) | |||||||
\(942\) | −2.69682e25 | −1.41716 | ||||||||
\(943\) | −4.65432e24 | −0.242386 | ||||||||
\(944\) | −1.69984e24 | −0.0877298 | ||||||||
\(945\) | −2.85940e25 | −1.46253 | ||||||||
\(946\) | 2.94313e25 | 1.49188 | ||||||||
\(947\) | 5.41921e24 | 0.272246 | 0.136123 | − | 0.990692i | \(-0.456536\pi\) | ||||
0.136123 | + | 0.990692i | \(0.456536\pi\) | |||||||
\(948\) | 7.08314e24 | 0.352659 | ||||||||
\(949\) | −4.84517e23 | −0.0239082 | ||||||||
\(950\) | −2.77768e24 | −0.135841 | ||||||||
\(951\) | −9.46804e24 | −0.458908 | ||||||||
\(952\) | 4.88323e24 | 0.234581 | ||||||||
\(953\) | 7.60605e24 | 0.362134 | 0.181067 | − | 0.983471i | \(-0.442045\pi\) | ||||
0.181067 | + | 0.983471i | \(0.442045\pi\) | |||||||
\(954\) | −1.31187e25 | −0.619054 | ||||||||
\(955\) | −1.85650e25 | −0.868295 | ||||||||
\(956\) | −1.37854e25 | −0.639038 | ||||||||
\(957\) | −4.92285e25 | −2.26186 | ||||||||
\(958\) | −7.89235e24 | −0.359418 | ||||||||
\(959\) | 2.41148e25 | 1.08849 | ||||||||
\(960\) | −2.40017e24 | −0.107383 | ||||||||
\(961\) | −1.80734e25 | −0.801476 | ||||||||
\(962\) | −4.57969e24 | −0.201302 | ||||||||
\(963\) | −6.77449e25 | −2.95157 | ||||||||
\(964\) | −1.93514e25 | −0.835714 | ||||||||
\(965\) | 5.51762e24 | 0.236194 | ||||||||
\(966\) | −5.18237e24 | −0.219899 | ||||||||
\(967\) | 3.18023e25 | 1.33762 | 0.668811 | − | 0.743433i | \(-0.266804\pi\) | ||||
0.668811 | + | 0.743433i | \(0.266804\pi\) | |||||||
\(968\) | 1.37315e25 | 0.572501 | ||||||||
\(969\) | −2.94050e25 | −1.21526 | ||||||||
\(970\) | −3.74691e24 | −0.153502 | ||||||||
\(971\) | 3.77342e25 | 1.53240 | 0.766198 | − | 0.642604i | \(-0.222146\pi\) | ||||
0.766198 | + | 0.642604i | \(0.222146\pi\) | |||||||
\(972\) | 4.42822e25 | 1.78265 | ||||||||
\(973\) | 5.78892e24 | 0.231014 | ||||||||
\(974\) | −1.56981e25 | −0.621004 | ||||||||
\(975\) | 1.57191e24 | 0.0616438 | ||||||||
\(976\) | −8.59170e24 | −0.334007 | ||||||||
\(977\) | −2.38735e25 | −0.920051 | −0.460025 | − | 0.887906i | \(-0.652160\pi\) | ||||
−0.460025 | + | 0.887906i | \(0.652160\pi\) | |||||||
\(978\) | −2.44380e25 | −0.933654 | ||||||||
\(979\) | 3.53054e25 | 1.33718 | ||||||||
\(980\) | −8.83140e22 | −0.00331595 | ||||||||
\(981\) | 4.64765e25 | 1.73000 | ||||||||
\(982\) | 1.33569e25 | 0.492901 | ||||||||
\(983\) | −1.84561e25 | −0.675202 | −0.337601 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337601 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(984\) | 2.82425e25 | 1.02434 | ||||||||
\(985\) | −1.34422e25 | −0.483351 | ||||||||
\(986\) | 9.50479e24 | 0.338835 | ||||||||
\(987\) | −9.69250e24 | −0.342563 | ||||||||
\(988\) | −2.19922e24 | −0.0770609 | ||||||||
\(989\) | 6.03054e24 | 0.209502 | ||||||||
\(990\) | 3.99704e25 | 1.37670 | ||||||||
\(991\) | −3.80947e25 | −1.30088 | −0.650442 | − | 0.759556i | \(-0.725416\pi\) | ||||
−0.650442 | + | 0.759556i | \(0.725416\pi\) | |||||||
\(992\) | −2.32638e24 | −0.0787648 | ||||||||
\(993\) | 7.63318e24 | 0.256234 | ||||||||
\(994\) | 1.17941e25 | 0.392538 | ||||||||
\(995\) | −2.63594e24 | −0.0869842 | ||||||||
\(996\) | −5.10492e24 | −0.167026 | ||||||||
\(997\) | −3.25991e25 | −1.05754 | −0.528770 | − | 0.848765i | \(-0.677346\pi\) | ||||
−0.528770 | + | 0.848765i | \(0.677346\pi\) | |||||||
\(998\) | 3.76494e25 | 1.21101 | ||||||||
\(999\) | −1.80599e26 | −5.75981 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 10.18.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.18.a.j.1.2 | 2 | |||
4.3 | odd | 2 | 80.18.a.b.1.1 | 2 | |||
5.2 | odd | 4 | 50.18.b.f.49.3 | 4 | |||
5.3 | odd | 4 | 50.18.b.f.49.2 | 4 | |||
5.4 | even | 2 | 50.18.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.18.a.c.1.1 | 2 | 5.4 | even | 2 | |||
50.18.b.f.49.2 | 4 | 5.3 | odd | 4 | |||
50.18.b.f.49.3 | 4 | 5.2 | odd | 4 | |||
80.18.a.b.1.1 | 2 | 4.3 | odd | 2 | |||
90.18.a.j.1.2 | 2 | 3.2 | odd | 2 |