Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,8,Mod(1,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(4.37339035678\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1969}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 492 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(22.6867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −9.37342 | −0.200435 | −0.100217 | − | 0.994966i | \(-0.531954\pi\) | ||||
−0.100217 | + | 0.994966i | \(0.531954\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 462.361 | 1.65419 | 0.827096 | − | 0.562061i | \(-0.189991\pi\) | ||||
0.827096 | + | 0.562061i | \(0.189991\pi\) | |||||||
\(6\) | −74.9873 | −0.141729 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | −2099.14 | −0.959826 | ||||||||
\(10\) | 3698.89 | 1.16969 | ||||||||
\(11\) | 3881.05 | 0.879174 | 0.439587 | − | 0.898200i | \(-0.355125\pi\) | ||||
0.439587 | + | 0.898200i | \(0.355125\pi\) | |||||||
\(12\) | −599.899 | −0.100217 | ||||||||
\(13\) | −11585.6 | −1.46257 | −0.731284 | − | 0.682073i | \(-0.761078\pi\) | ||||
−0.731284 | + | 0.682073i | \(0.761078\pi\) | |||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | −4333.90 | −0.331558 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −15242.4 | −0.752457 | −0.376229 | − | 0.926527i | \(-0.622779\pi\) | ||||
−0.376229 | + | 0.926527i | \(0.622779\pi\) | |||||||
\(18\) | −16793.1 | −0.678699 | ||||||||
\(19\) | −32461.7 | −1.08576 | −0.542880 | − | 0.839810i | \(-0.682666\pi\) | ||||
−0.542880 | + | 0.839810i | \(0.682666\pi\) | |||||||
\(20\) | 29591.1 | 0.827096 | ||||||||
\(21\) | −3215.08 | −0.0757573 | ||||||||
\(22\) | 31048.4 | 0.621670 | ||||||||
\(23\) | 56146.1 | 0.962215 | 0.481108 | − | 0.876662i | \(-0.340235\pi\) | ||||
0.481108 | + | 0.876662i | \(0.340235\pi\) | |||||||
\(24\) | −4799.19 | −0.0708645 | ||||||||
\(25\) | 135652. | 1.73635 | ||||||||
\(26\) | −92684.6 | −1.03419 | ||||||||
\(27\) | 40175.8 | 0.392818 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −26442.0 | −0.201326 | −0.100663 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100663 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(30\) | −34671.2 | −0.234447 | ||||||||
\(31\) | −45448.2 | −0.274000 | −0.137000 | − | 0.990571i | \(-0.543746\pi\) | ||||
−0.137000 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −36378.7 | −0.176217 | ||||||||
\(34\) | −121939. | −0.532068 | ||||||||
\(35\) | 158590. | 0.625226 | ||||||||
\(36\) | −134345. | −0.479913 | ||||||||
\(37\) | −555245. | −1.80210 | −0.901049 | − | 0.433717i | \(-0.857202\pi\) | ||||
−0.901049 | + | 0.433717i | \(0.857202\pi\) | |||||||
\(38\) | −259694. | −0.767749 | ||||||||
\(39\) | 108596. | 0.293150 | ||||||||
\(40\) | 236729. | 0.584845 | ||||||||
\(41\) | 306385. | 0.694264 | 0.347132 | − | 0.937816i | \(-0.387156\pi\) | ||||
0.347132 | + | 0.937816i | \(0.387156\pi\) | |||||||
\(42\) | −25720.7 | −0.0535685 | ||||||||
\(43\) | 780755. | 1.49753 | 0.748765 | − | 0.662836i | \(-0.230647\pi\) | ||||
0.748765 | + | 0.662836i | \(0.230647\pi\) | |||||||
\(44\) | 248387. | 0.439587 | ||||||||
\(45\) | −970559. | −1.58774 | ||||||||
\(46\) | 449169. | 0.680389 | ||||||||
\(47\) | −531243. | −0.746364 | −0.373182 | − | 0.927758i | \(-0.621733\pi\) | ||||
−0.373182 | + | 0.927758i | \(0.621733\pi\) | |||||||
\(48\) | −38393.5 | −0.0501087 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 1.08522e6 | 1.22779 | ||||||||
\(51\) | 142873. | 0.150819 | ||||||||
\(52\) | −741477. | −0.731284 | ||||||||
\(53\) | −363593. | −0.335467 | −0.167733 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167733 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(54\) | 321406. | 0.277764 | ||||||||
\(55\) | 1.79445e6 | 1.45432 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | 304277. | 0.217624 | ||||||||
\(58\) | −211536. | −0.142359 | ||||||||
\(59\) | −2.14095e6 | −1.35714 | −0.678570 | − | 0.734535i | \(-0.737400\pi\) | ||||
−0.678570 | + | 0.734535i | \(0.737400\pi\) | |||||||
\(60\) | −277370. | −0.165779 | ||||||||
\(61\) | 888824. | 0.501373 | 0.250687 | − | 0.968068i | \(-0.419344\pi\) | ||||
0.250687 | + | 0.968068i | \(0.419344\pi\) | |||||||
\(62\) | −363586. | −0.193747 | ||||||||
\(63\) | −720005. | −0.362780 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −5.35672e6 | −2.41937 | ||||||||
\(66\) | −291030. | −0.124604 | ||||||||
\(67\) | 4.34541e6 | 1.76510 | 0.882549 | − | 0.470221i | \(-0.155826\pi\) | ||||
0.882549 | + | 0.470221i | \(0.155826\pi\) | |||||||
\(68\) | −975513. | −0.376229 | ||||||||
\(69\) | −526281. | −0.192862 | ||||||||
\(70\) | 1.26872e6 | 0.442101 | ||||||||
\(71\) | 663207. | 0.219910 | 0.109955 | − | 0.993937i | \(-0.464929\pi\) | ||||
0.109955 | + | 0.993937i | \(0.464929\pi\) | |||||||
\(72\) | −1.07476e6 | −0.339350 | ||||||||
\(73\) | 1.34202e6 | 0.403765 | 0.201882 | − | 0.979410i | \(-0.435294\pi\) | ||||
0.201882 | + | 0.979410i | \(0.435294\pi\) | |||||||
\(74\) | −4.44196e6 | −1.27428 | ||||||||
\(75\) | −1.27153e6 | −0.348026 | ||||||||
\(76\) | −2.07755e6 | −0.542880 | ||||||||
\(77\) | 1.33120e6 | 0.332297 | ||||||||
\(78\) | 868771. | 0.207288 | ||||||||
\(79\) | 7.05834e6 | 1.61067 | 0.805337 | − | 0.592818i | \(-0.201984\pi\) | ||||
0.805337 | + | 0.592818i | \(0.201984\pi\) | |||||||
\(80\) | 1.89383e6 | 0.413548 | ||||||||
\(81\) | 4.21423e6 | 0.881091 | ||||||||
\(82\) | 2.45108e6 | 0.490919 | ||||||||
\(83\) | 6.60874e6 | 1.26866 | 0.634330 | − | 0.773063i | \(-0.281276\pi\) | ||||
0.634330 | + | 0.773063i | \(0.281276\pi\) | |||||||
\(84\) | −205765. | −0.0378786 | ||||||||
\(85\) | −7.04748e6 | −1.24471 | ||||||||
\(86\) | 6.24604e6 | 1.05891 | ||||||||
\(87\) | 247851. | 0.0403528 | ||||||||
\(88\) | 1.98710e6 | 0.310835 | ||||||||
\(89\) | −5.32998e6 | −0.801420 | −0.400710 | − | 0.916205i | \(-0.631237\pi\) | ||||
−0.400710 | + | 0.916205i | \(0.631237\pi\) | |||||||
\(90\) | −7.76448e6 | −1.12270 | ||||||||
\(91\) | −3.97385e6 | −0.552799 | ||||||||
\(92\) | 3.59335e6 | 0.481108 | ||||||||
\(93\) | 426005. | 0.0549192 | ||||||||
\(94\) | −4.24994e6 | −0.527759 | ||||||||
\(95\) | −1.50090e7 | −1.79606 | ||||||||
\(96\) | −307148. | −0.0354322 | ||||||||
\(97\) | −2.09810e6 | −0.233413 | −0.116707 | − | 0.993166i | \(-0.537234\pi\) | ||||
−0.116707 | + | 0.993166i | \(0.537234\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | −8.14686e6 | −0.843854 | ||||||||
\(100\) | 8.68176e6 | 0.868176 | ||||||||
\(101\) | 1.95538e7 | 1.88845 | 0.944227 | − | 0.329294i | \(-0.106811\pi\) | ||||
0.944227 | + | 0.329294i | \(0.106811\pi\) | |||||||
\(102\) | 1.14299e6 | 0.106645 | ||||||||
\(103\) | −8.95093e6 | −0.807119 | −0.403560 | − | 0.914953i | \(-0.632227\pi\) | ||||
−0.403560 | + | 0.914953i | \(0.632227\pi\) | |||||||
\(104\) | −5.93181e6 | −0.517096 | ||||||||
\(105\) | −1.48653e6 | −0.125317 | ||||||||
\(106\) | −2.90874e6 | −0.237211 | ||||||||
\(107\) | −1.39509e7 | −1.10093 | −0.550466 | − | 0.834858i | \(-0.685550\pi\) | ||||
−0.550466 | + | 0.834858i | \(0.685550\pi\) | |||||||
\(108\) | 2.57125e6 | 0.196409 | ||||||||
\(109\) | 5.84295e6 | 0.432155 | 0.216077 | − | 0.976376i | \(-0.430674\pi\) | ||||
0.216077 | + | 0.976376i | \(0.430674\pi\) | |||||||
\(110\) | 1.43556e7 | 1.02836 | ||||||||
\(111\) | 5.20454e6 | 0.361203 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −1.20951e7 | −0.788562 | −0.394281 | − | 0.918990i | \(-0.629006\pi\) | ||||
−0.394281 | + | 0.918990i | \(0.629006\pi\) | |||||||
\(114\) | 2.43422e6 | 0.153884 | ||||||||
\(115\) | 2.59598e7 | 1.59169 | ||||||||
\(116\) | −1.69229e6 | −0.100663 | ||||||||
\(117\) | 2.43197e7 | 1.40381 | ||||||||
\(118\) | −1.71276e7 | −0.959644 | ||||||||
\(119\) | −5.22814e6 | −0.284402 | ||||||||
\(120\) | −2.21896e6 | −0.117223 | ||||||||
\(121\) | −4.42462e6 | −0.227053 | ||||||||
\(122\) | 7.11059e6 | 0.354524 | ||||||||
\(123\) | −2.87188e6 | −0.139155 | ||||||||
\(124\) | −2.90868e6 | −0.137000 | ||||||||
\(125\) | 2.65984e7 | 1.21807 | ||||||||
\(126\) | −5.76004e6 | −0.256524 | ||||||||
\(127\) | −325760. | −0.0141119 | −0.00705594 | − | 0.999975i | \(-0.502246\pi\) | ||||
−0.00705594 | + | 0.999975i | \(0.502246\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −7.31834e6 | −0.300157 | ||||||||
\(130\) | −4.28537e7 | −1.71075 | ||||||||
\(131\) | 6.38049e6 | 0.247973 | 0.123986 | − | 0.992284i | \(-0.460432\pi\) | ||||
0.123986 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(132\) | −2.32824e6 | −0.0881086 | ||||||||
\(133\) | −1.11344e7 | −0.410379 | ||||||||
\(134\) | 3.47633e7 | 1.24811 | ||||||||
\(135\) | 1.85757e7 | 0.649796 | ||||||||
\(136\) | −7.80411e6 | −0.266034 | ||||||||
\(137\) | 4.62324e6 | 0.153612 | 0.0768059 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768059 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(138\) | −4.21025e6 | −0.136374 | ||||||||
\(139\) | −3.55394e7 | −1.12243 | −0.561214 | − | 0.827671i | \(-0.689665\pi\) | ||||
−0.561214 | + | 0.827671i | \(0.689665\pi\) | |||||||
\(140\) | 1.01497e7 | 0.312613 | ||||||||
\(141\) | 4.97956e6 | 0.149597 | ||||||||
\(142\) | 5.30565e6 | 0.155500 | ||||||||
\(143\) | −4.49642e7 | −1.28585 | ||||||||
\(144\) | −8.59807e6 | −0.239956 | ||||||||
\(145\) | −1.22257e7 | −0.333032 | ||||||||
\(146\) | 1.07362e7 | 0.285505 | ||||||||
\(147\) | −1.10277e6 | −0.0286336 | ||||||||
\(148\) | −3.55357e7 | −0.901049 | ||||||||
\(149\) | 1.01708e7 | 0.251885 | 0.125943 | − | 0.992038i | \(-0.459804\pi\) | ||||
0.125943 | + | 0.992038i | \(0.459804\pi\) | |||||||
\(150\) | −1.01722e7 | −0.246091 | ||||||||
\(151\) | 2.45272e7 | 0.579735 | 0.289867 | − | 0.957067i | \(-0.406389\pi\) | ||||
0.289867 | + | 0.957067i | \(0.406389\pi\) | |||||||
\(152\) | −1.66204e7 | −0.383874 | ||||||||
\(153\) | 3.19959e7 | 0.722228 | ||||||||
\(154\) | 1.06496e7 | 0.234969 | ||||||||
\(155\) | −2.10135e7 | −0.453249 | ||||||||
\(156\) | 6.95017e6 | 0.146575 | ||||||||
\(157\) | −1.27379e7 | −0.262693 | −0.131346 | − | 0.991337i | \(-0.541930\pi\) | ||||
−0.131346 | + | 0.991337i | \(0.541930\pi\) | |||||||
\(158\) | 5.64667e7 | 1.13892 | ||||||||
\(159\) | 3.40810e6 | 0.0672393 | ||||||||
\(160\) | 1.51506e7 | 0.292423 | ||||||||
\(161\) | 1.92581e7 | 0.363683 | ||||||||
\(162\) | 3.37139e7 | 0.623026 | ||||||||
\(163\) | −8.51531e7 | −1.54008 | −0.770041 | − | 0.637995i | \(-0.779764\pi\) | ||||
−0.770041 | + | 0.637995i | \(0.779764\pi\) | |||||||
\(164\) | 1.96087e7 | 0.347132 | ||||||||
\(165\) | −1.68201e7 | −0.291497 | ||||||||
\(166\) | 5.28699e7 | 0.897078 | ||||||||
\(167\) | −3.74260e6 | −0.0621822 | −0.0310911 | − | 0.999517i | \(-0.509898\pi\) | ||||
−0.0310911 | + | 0.999517i | \(0.509898\pi\) | |||||||
\(168\) | −1.64612e6 | −0.0267842 | ||||||||
\(169\) | 7.14770e7 | 1.13910 | ||||||||
\(170\) | −5.63799e7 | −0.880142 | ||||||||
\(171\) | 6.81417e7 | 1.04214 | ||||||||
\(172\) | 4.99683e7 | 0.748765 | ||||||||
\(173\) | −7.26865e7 | −1.06731 | −0.533657 | − | 0.845701i | \(-0.679183\pi\) | ||||
−0.533657 | + | 0.845701i | \(0.679183\pi\) | |||||||
\(174\) | 1.98281e6 | 0.0285338 | ||||||||
\(175\) | 4.65288e7 | 0.656279 | ||||||||
\(176\) | 1.58968e7 | 0.219794 | ||||||||
\(177\) | 2.00680e7 | 0.272018 | ||||||||
\(178\) | −4.26398e7 | −0.566690 | ||||||||
\(179\) | 1.02445e8 | 1.33507 | 0.667536 | − | 0.744578i | \(-0.267349\pi\) | ||||
0.667536 | + | 0.744578i | \(0.267349\pi\) | |||||||
\(180\) | −6.21158e7 | −0.793868 | ||||||||
\(181\) | 4.79161e6 | 0.0600630 | 0.0300315 | − | 0.999549i | \(-0.490439\pi\) | ||||
0.0300315 | + | 0.999549i | \(0.490439\pi\) | |||||||
\(182\) | −3.17908e7 | −0.390888 | ||||||||
\(183\) | −8.33131e6 | −0.100493 | ||||||||
\(184\) | 2.87468e7 | 0.340194 | ||||||||
\(185\) | −2.56723e8 | −2.98102 | ||||||||
\(186\) | 3.40804e6 | 0.0388337 | ||||||||
\(187\) | −5.91565e7 | −0.661541 | ||||||||
\(188\) | −3.39996e7 | −0.373182 | ||||||||
\(189\) | 1.37803e7 | 0.148471 | ||||||||
\(190\) | −1.20072e8 | −1.27000 | ||||||||
\(191\) | 2.60173e7 | 0.270175 | 0.135087 | − | 0.990834i | \(-0.456868\pi\) | ||||
0.135087 | + | 0.990834i | \(0.456868\pi\) | |||||||
\(192\) | −2.45718e6 | −0.0250544 | ||||||||
\(193\) | −7.58326e7 | −0.759286 | −0.379643 | − | 0.925133i | \(-0.623953\pi\) | ||||
−0.379643 | + | 0.925133i | \(0.623953\pi\) | |||||||
\(194\) | −1.67848e7 | −0.165048 | ||||||||
\(195\) | 5.02107e7 | 0.484926 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | 1.19192e8 | 1.11075 | 0.555374 | − | 0.831601i | \(-0.312575\pi\) | ||||
0.555374 | + | 0.831601i | \(0.312575\pi\) | |||||||
\(198\) | −6.51749e7 | −0.596695 | ||||||||
\(199\) | 6.72662e7 | 0.605078 | 0.302539 | − | 0.953137i | \(-0.402166\pi\) | ||||
0.302539 | + | 0.953137i | \(0.402166\pi\) | |||||||
\(200\) | 6.94541e7 | 0.613893 | ||||||||
\(201\) | −4.07313e7 | −0.353787 | ||||||||
\(202\) | 1.56430e8 | 1.33534 | ||||||||
\(203\) | −9.06959e6 | −0.0760942 | ||||||||
\(204\) | 9.14389e6 | 0.0754094 | ||||||||
\(205\) | 1.41661e8 | 1.14845 | ||||||||
\(206\) | −7.16074e7 | −0.570720 | ||||||||
\(207\) | −1.17858e8 | −0.923559 | ||||||||
\(208\) | −4.74545e7 | −0.365642 | ||||||||
\(209\) | −1.25986e8 | −0.954573 | ||||||||
\(210\) | −1.18922e7 | −0.0886126 | ||||||||
\(211\) | 2.32421e8 | 1.70328 | 0.851641 | − | 0.524126i | \(-0.175608\pi\) | ||||
0.851641 | + | 0.524126i | \(0.175608\pi\) | |||||||
\(212\) | −2.32699e7 | −0.167733 | ||||||||
\(213\) | −6.21651e6 | −0.0440776 | ||||||||
\(214\) | −1.11608e8 | −0.778476 | ||||||||
\(215\) | 3.60991e8 | 2.47720 | ||||||||
\(216\) | 2.05700e7 | 0.138882 | ||||||||
\(217\) | −1.55887e7 | −0.103562 | ||||||||
\(218\) | 4.67436e7 | 0.305580 | ||||||||
\(219\) | −1.25793e7 | −0.0809286 | ||||||||
\(220\) | 1.14844e8 | 0.727161 | ||||||||
\(221\) | 1.76592e8 | 1.10052 | ||||||||
\(222\) | 4.16363e7 | 0.255409 | ||||||||
\(223\) | −2.53319e8 | −1.52968 | −0.764840 | − | 0.644221i | \(-0.777182\pi\) | ||||
−0.764840 | + | 0.644221i | \(0.777182\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | −2.84753e8 | −1.66659 | ||||||||
\(226\) | −9.67610e7 | −0.557598 | ||||||||
\(227\) | 4.50124e7 | 0.255412 | 0.127706 | − | 0.991812i | \(-0.459239\pi\) | ||||
0.127706 | + | 0.991812i | \(0.459239\pi\) | |||||||
\(228\) | 1.94738e7 | 0.108812 | ||||||||
\(229\) | 1.86973e8 | 1.02886 | 0.514429 | − | 0.857533i | \(-0.328004\pi\) | ||||
0.514429 | + | 0.857533i | \(0.328004\pi\) | |||||||
\(230\) | 2.07678e8 | 1.12549 | ||||||||
\(231\) | −1.24779e7 | −0.0666039 | ||||||||
\(232\) | −1.35383e7 | −0.0711796 | ||||||||
\(233\) | −2.57588e8 | −1.33408 | −0.667038 | − | 0.745024i | \(-0.732438\pi\) | ||||
−0.667038 | + | 0.745024i | \(0.732438\pi\) | |||||||
\(234\) | 1.94558e8 | 0.992644 | ||||||||
\(235\) | −2.45626e8 | −1.23463 | ||||||||
\(236\) | −1.37021e8 | −0.678570 | ||||||||
\(237\) | −6.61607e7 | −0.322835 | ||||||||
\(238\) | −4.18251e7 | −0.201103 | ||||||||
\(239\) | −3.15071e8 | −1.49285 | −0.746425 | − | 0.665469i | \(-0.768231\pi\) | ||||
−0.746425 | + | 0.665469i | \(0.768231\pi\) | |||||||
\(240\) | −1.77517e7 | −0.0828895 | ||||||||
\(241\) | 8.39900e7 | 0.386516 | 0.193258 | − | 0.981148i | \(-0.438095\pi\) | ||||
0.193258 | + | 0.981148i | \(0.438095\pi\) | |||||||
\(242\) | −3.53970e7 | −0.160551 | ||||||||
\(243\) | −1.27366e8 | −0.569419 | ||||||||
\(244\) | 5.68847e7 | 0.250687 | ||||||||
\(245\) | 5.43963e7 | 0.236313 | ||||||||
\(246\) | −2.29750e7 | −0.0983973 | ||||||||
\(247\) | 3.76088e8 | 1.58800 | ||||||||
\(248\) | −2.32695e7 | −0.0968737 | ||||||||
\(249\) | −6.19464e7 | −0.254284 | ||||||||
\(250\) | 2.12787e8 | 0.861303 | ||||||||
\(251\) | −5.33130e6 | −0.0212802 | −0.0106401 | − | 0.999943i | \(-0.503387\pi\) | ||||
−0.0106401 | + | 0.999943i | \(0.503387\pi\) | |||||||
\(252\) | −4.60803e7 | −0.181390 | ||||||||
\(253\) | 2.17906e8 | 0.845955 | ||||||||
\(254\) | −2.60608e6 | −0.00997861 | ||||||||
\(255\) | 6.60590e7 | 0.249483 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.09942e8 | −0.771495 | −0.385747 | − | 0.922604i | \(-0.626056\pi\) | ||||
−0.385747 | + | 0.922604i | \(0.626056\pi\) | |||||||
\(258\) | −5.85467e7 | −0.212243 | ||||||||
\(259\) | −1.90449e8 | −0.681129 | ||||||||
\(260\) | −3.42830e8 | −1.20968 | ||||||||
\(261\) | 5.55053e7 | 0.193238 | ||||||||
\(262\) | 5.10439e7 | 0.175343 | ||||||||
\(263\) | −2.50805e8 | −0.850143 | −0.425071 | − | 0.905160i | \(-0.639751\pi\) | ||||
−0.425071 | + | 0.905160i | \(0.639751\pi\) | |||||||
\(264\) | −1.86259e7 | −0.0623022 | ||||||||
\(265\) | −1.68111e8 | −0.554926 | ||||||||
\(266\) | −8.90750e7 | −0.290182 | ||||||||
\(267\) | 4.99601e7 | 0.160633 | ||||||||
\(268\) | 2.78106e8 | 0.882549 | ||||||||
\(269\) | 3.39197e8 | 1.06248 | 0.531238 | − | 0.847223i | \(-0.321727\pi\) | ||||
0.531238 | + | 0.847223i | \(0.321727\pi\) | |||||||
\(270\) | 1.48606e8 | 0.459475 | ||||||||
\(271\) | 7.59574e7 | 0.231834 | 0.115917 | − | 0.993259i | \(-0.463019\pi\) | ||||
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(272\) | −6.24328e7 | −0.188114 | ||||||||
\(273\) | 3.72486e7 | 0.110800 | ||||||||
\(274\) | 3.69859e7 | 0.108620 | ||||||||
\(275\) | 5.26474e8 | 1.52656 | ||||||||
\(276\) | −3.36820e7 | −0.0964308 | ||||||||
\(277\) | −5.00883e7 | −0.141598 | −0.0707990 | − | 0.997491i | \(-0.522555\pi\) | ||||
−0.0707990 | + | 0.997491i | \(0.522555\pi\) | |||||||
\(278\) | −2.84315e8 | −0.793676 | ||||||||
\(279\) | 9.54021e7 | 0.262992 | ||||||||
\(280\) | 8.11979e7 | 0.221051 | ||||||||
\(281\) | 3.41917e8 | 0.919283 | 0.459641 | − | 0.888105i | \(-0.347978\pi\) | ||||
0.459641 | + | 0.888105i | \(0.347978\pi\) | |||||||
\(282\) | 3.98365e7 | 0.105781 | ||||||||
\(283\) | 3.69077e8 | 0.967977 | 0.483988 | − | 0.875074i | \(-0.339188\pi\) | ||||
0.483988 | + | 0.875074i | \(0.339188\pi\) | |||||||
\(284\) | 4.24452e7 | 0.109955 | ||||||||
\(285\) | 1.40686e8 | 0.359993 | ||||||||
\(286\) | −3.59714e8 | −0.909234 | ||||||||
\(287\) | 1.05090e8 | 0.262407 | ||||||||
\(288\) | −6.87846e7 | −0.169675 | ||||||||
\(289\) | −1.78008e8 | −0.433808 | ||||||||
\(290\) | −9.78058e7 | −0.235489 | ||||||||
\(291\) | 1.96664e7 | 0.0467842 | ||||||||
\(292\) | 8.58892e7 | 0.201882 | ||||||||
\(293\) | 5.92780e8 | 1.37676 | 0.688378 | − | 0.725352i | \(-0.258323\pi\) | ||||
0.688378 | + | 0.725352i | \(0.258323\pi\) | |||||||
\(294\) | −8.82218e6 | −0.0202470 | ||||||||
\(295\) | −9.89892e8 | −2.24497 | ||||||||
\(296\) | −2.84285e8 | −0.637138 | ||||||||
\(297\) | 1.55924e8 | 0.345355 | ||||||||
\(298\) | 8.13663e7 | 0.178110 | ||||||||
\(299\) | −6.50485e8 | −1.40730 | ||||||||
\(300\) | −8.13777e7 | −0.174013 | ||||||||
\(301\) | 2.67799e8 | 0.566013 | ||||||||
\(302\) | 1.96218e8 | 0.409934 | ||||||||
\(303\) | −1.83286e8 | −0.378512 | ||||||||
\(304\) | −1.32963e8 | −0.271440 | ||||||||
\(305\) | 4.10957e8 | 0.829368 | ||||||||
\(306\) | 2.55967e8 | 0.510692 | ||||||||
\(307\) | −9.43846e8 | −1.86173 | −0.930865 | − | 0.365363i | \(-0.880945\pi\) | ||||
−0.930865 | + | 0.365363i | \(0.880945\pi\) | |||||||
\(308\) | 8.51968e7 | 0.166148 | ||||||||
\(309\) | 8.39008e7 | 0.161775 | ||||||||
\(310\) | −1.68108e8 | −0.320495 | ||||||||
\(311\) | −1.64065e8 | −0.309282 | −0.154641 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154641 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(312\) | 5.56014e7 | 0.103644 | ||||||||
\(313\) | 3.46012e8 | 0.637801 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(314\) | −1.01903e8 | −0.185752 | ||||||||
\(315\) | −3.32902e8 | −0.600108 | ||||||||
\(316\) | 4.51734e8 | 0.805337 | ||||||||
\(317\) | −9.53240e8 | −1.68072 | −0.840359 | − | 0.542030i | \(-0.817656\pi\) | ||||
−0.840359 | + | 0.542030i | \(0.817656\pi\) | |||||||
\(318\) | 2.72648e7 | 0.0475453 | ||||||||
\(319\) | −1.02623e8 | −0.177001 | ||||||||
\(320\) | 1.21205e8 | 0.206774 | ||||||||
\(321\) | 1.30768e8 | 0.220665 | ||||||||
\(322\) | 1.54065e8 | 0.257163 | ||||||||
\(323\) | 4.94795e8 | 0.816989 | ||||||||
\(324\) | 2.69711e8 | 0.440546 | ||||||||
\(325\) | −1.57161e9 | −2.53953 | ||||||||
\(326\) | −6.81225e8 | −1.08900 | ||||||||
\(327\) | −5.47684e7 | −0.0866189 | ||||||||
\(328\) | 1.56869e8 | 0.245459 | ||||||||
\(329\) | −1.82216e8 | −0.282099 | ||||||||
\(330\) | −1.34561e8 | −0.206120 | ||||||||
\(331\) | 2.24263e8 | 0.339906 | 0.169953 | − | 0.985452i | \(-0.445638\pi\) | ||||
0.169953 | + | 0.985452i | \(0.445638\pi\) | |||||||
\(332\) | 4.22959e8 | 0.634330 | ||||||||
\(333\) | 1.16554e9 | 1.72970 | ||||||||
\(334\) | −2.99408e7 | −0.0439694 | ||||||||
\(335\) | 2.00915e9 | 2.91981 | ||||||||
\(336\) | −1.31690e7 | −0.0189393 | ||||||||
\(337\) | 3.56750e8 | 0.507761 | 0.253880 | − | 0.967236i | \(-0.418293\pi\) | ||||
0.253880 | + | 0.967236i | \(0.418293\pi\) | |||||||
\(338\) | 5.71816e8 | 0.805468 | ||||||||
\(339\) | 1.13373e8 | 0.158055 | ||||||||
\(340\) | −4.51039e8 | −0.622355 | ||||||||
\(341\) | −1.76387e8 | −0.240894 | ||||||||
\(342\) | 5.45134e8 | 0.736905 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 3.99747e8 | 0.529456 | ||||||||
\(345\) | −2.43332e8 | −0.319030 | ||||||||
\(346\) | −5.81492e8 | −0.754705 | ||||||||
\(347\) | 1.61839e7 | 0.0207936 | 0.0103968 | − | 0.999946i | \(-0.496691\pi\) | ||||
0.0103968 | + | 0.999946i | \(0.496691\pi\) | |||||||
\(348\) | 1.58625e7 | 0.0201764 | ||||||||
\(349\) | 2.07780e8 | 0.261647 | 0.130823 | − | 0.991406i | \(-0.458238\pi\) | ||||
0.130823 | + | 0.991406i | \(0.458238\pi\) | |||||||
\(350\) | 3.72230e8 | 0.464059 | ||||||||
\(351\) | −4.65459e8 | −0.574522 | ||||||||
\(352\) | 1.27174e8 | 0.155417 | ||||||||
\(353\) | −1.31624e9 | −1.59266 | −0.796328 | − | 0.604865i | \(-0.793227\pi\) | ||||
−0.796328 | + | 0.604865i | \(0.793227\pi\) | |||||||
\(354\) | 1.60544e8 | 0.192346 | ||||||||
\(355\) | 3.06641e8 | 0.363773 | ||||||||
\(356\) | −3.41119e8 | −0.400710 | ||||||||
\(357\) | 4.90055e7 | 0.0570041 | ||||||||
\(358\) | 8.19559e8 | 0.944038 | ||||||||
\(359\) | −6.19271e8 | −0.706400 | −0.353200 | − | 0.935548i | \(-0.614906\pi\) | ||||
−0.353200 | + | 0.935548i | \(0.614906\pi\) | |||||||
\(360\) | −4.96926e8 | −0.561350 | ||||||||
\(361\) | 1.59893e8 | 0.178877 | ||||||||
\(362\) | 3.83329e7 | 0.0424709 | ||||||||
\(363\) | 4.14738e7 | 0.0455093 | ||||||||
\(364\) | −2.54327e8 | −0.276399 | ||||||||
\(365\) | 6.20497e8 | 0.667905 | ||||||||
\(366\) | −6.66505e7 | −0.0710591 | ||||||||
\(367\) | 2.78628e8 | 0.294235 | 0.147117 | − | 0.989119i | \(-0.453000\pi\) | ||||
0.147117 | + | 0.989119i | \(0.453000\pi\) | |||||||
\(368\) | 2.29974e8 | 0.240554 | ||||||||
\(369\) | −6.43146e8 | −0.666373 | ||||||||
\(370\) | −2.05379e9 | −2.10790 | ||||||||
\(371\) | −1.24712e8 | −0.126795 | ||||||||
\(372\) | 2.72643e7 | 0.0274596 | ||||||||
\(373\) | −1.65056e8 | −0.164684 | −0.0823420 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823420 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(374\) | −4.73252e8 | −0.467780 | ||||||||
\(375\) | −2.49318e8 | −0.244143 | ||||||||
\(376\) | −2.71996e8 | −0.263880 | ||||||||
\(377\) | 3.06345e8 | 0.294453 | ||||||||
\(378\) | 1.10242e8 | 0.104985 | ||||||||
\(379\) | 4.29433e8 | 0.405190 | 0.202595 | − | 0.979263i | \(-0.435063\pi\) | ||||
0.202595 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(380\) | −9.60578e8 | −0.898029 | ||||||||
\(381\) | 3.05348e6 | 0.00282851 | ||||||||
\(382\) | 2.08138e8 | 0.191043 | ||||||||
\(383\) | 1.34378e9 | 1.22217 | 0.611084 | − | 0.791566i | \(-0.290734\pi\) | ||||
0.611084 | + | 0.791566i | \(0.290734\pi\) | |||||||
\(384\) | −1.96575e7 | −0.0177161 | ||||||||
\(385\) | 6.15495e8 | 0.549682 | ||||||||
\(386\) | −6.06661e8 | −0.536897 | ||||||||
\(387\) | −1.63891e9 | −1.43737 | ||||||||
\(388\) | −1.34279e8 | −0.116707 | ||||||||
\(389\) | −1.07871e8 | −0.0929139 | −0.0464569 | − | 0.998920i | \(-0.514793\pi\) | ||||
−0.0464569 | + | 0.998920i | \(0.514793\pi\) | |||||||
\(390\) | 4.01686e8 | 0.342894 | ||||||||
\(391\) | −8.55801e8 | −0.724026 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | −5.98070e7 | −0.0497024 | ||||||||
\(394\) | 9.53537e8 | 0.785418 | ||||||||
\(395\) | 3.26350e9 | 2.66436 | ||||||||
\(396\) | −5.21399e8 | −0.421927 | ||||||||
\(397\) | −1.86525e9 | −1.49613 | −0.748066 | − | 0.663625i | \(-0.769017\pi\) | ||||
−0.748066 | + | 0.663625i | \(0.769017\pi\) | |||||||
\(398\) | 5.38130e8 | 0.427855 | ||||||||
\(399\) | 1.04367e8 | 0.0822543 | ||||||||
\(400\) | 5.55632e8 | 0.434088 | ||||||||
\(401\) | 9.94724e6 | 0.00770367 | 0.00385183 | − | 0.999993i | \(-0.498774\pi\) | ||||
0.00385183 | + | 0.999993i | \(0.498774\pi\) | |||||||
\(402\) | −3.25850e8 | −0.250165 | ||||||||
\(403\) | 5.26543e8 | 0.400744 | ||||||||
\(404\) | 1.25144e9 | 0.944227 | ||||||||
\(405\) | 1.94850e9 | 1.45749 | ||||||||
\(406\) | −7.25567e7 | −0.0538067 | ||||||||
\(407\) | −2.15493e9 | −1.58436 | ||||||||
\(408\) | 7.31511e7 | 0.0533225 | ||||||||
\(409\) | −8.76376e8 | −0.633372 | −0.316686 | − | 0.948530i | \(-0.602570\pi\) | ||||
−0.316686 | + | 0.948530i | \(0.602570\pi\) | |||||||
\(410\) | 1.13328e9 | 0.812074 | ||||||||
\(411\) | −4.33356e7 | −0.0307892 | ||||||||
\(412\) | −5.72859e8 | −0.403560 | ||||||||
\(413\) | −7.34347e8 | −0.512951 | ||||||||
\(414\) | −9.42868e8 | −0.653055 | ||||||||
\(415\) | 3.05562e9 | 2.09861 | ||||||||
\(416\) | −3.79636e8 | −0.258548 | ||||||||
\(417\) | 3.33126e8 | 0.224974 | ||||||||
\(418\) | −1.00789e9 | −0.674985 | ||||||||
\(419\) | −2.01605e9 | −1.33891 | −0.669457 | − | 0.742851i | \(-0.733473\pi\) | ||||
−0.669457 | + | 0.742851i | \(0.733473\pi\) | |||||||
\(420\) | −9.51378e7 | −0.0626586 | ||||||||
\(421\) | 5.69546e8 | 0.371999 | 0.186000 | − | 0.982550i | \(-0.440448\pi\) | ||||
0.186000 | + | 0.982550i | \(0.440448\pi\) | |||||||
\(422\) | 1.85937e9 | 1.20440 | ||||||||
\(423\) | 1.11515e9 | 0.716380 | ||||||||
\(424\) | −1.86159e8 | −0.118605 | ||||||||
\(425\) | −2.06767e9 | −1.30653 | ||||||||
\(426\) | −4.97321e7 | −0.0311676 | ||||||||
\(427\) | 3.04867e8 | 0.189501 | ||||||||
\(428\) | −8.92860e8 | −0.550466 | ||||||||
\(429\) | 4.21468e8 | 0.257730 | ||||||||
\(430\) | 2.88792e9 | 1.75165 | ||||||||
\(431\) | −7.71940e8 | −0.464422 | −0.232211 | − | 0.972665i | \(-0.574596\pi\) | ||||
−0.232211 | + | 0.972665i | \(0.574596\pi\) | |||||||
\(432\) | 1.64560e8 | 0.0982044 | ||||||||
\(433\) | 1.24002e9 | 0.734043 | 0.367021 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367021 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(434\) | −1.24710e8 | −0.0732296 | ||||||||
\(435\) | 1.14597e8 | 0.0667513 | ||||||||
\(436\) | 3.73949e8 | 0.216077 | ||||||||
\(437\) | −1.82260e9 | −1.04474 | ||||||||
\(438\) | −1.00634e8 | −0.0572252 | ||||||||
\(439\) | 1.90621e9 | 1.07534 | 0.537669 | − | 0.843156i | \(-0.319305\pi\) | ||||
0.537669 | + | 0.843156i | \(0.319305\pi\) | |||||||
\(440\) | 9.18756e8 | 0.514181 | ||||||||
\(441\) | −2.46962e8 | −0.137118 | ||||||||
\(442\) | 1.41274e9 | 0.778185 | ||||||||
\(443\) | −5.04738e8 | −0.275837 | −0.137919 | − | 0.990444i | \(-0.544041\pi\) | ||||
−0.137919 | + | 0.990444i | \(0.544041\pi\) | |||||||
\(444\) | 3.33091e8 | 0.180602 | ||||||||
\(445\) | −2.46437e9 | −1.32570 | ||||||||
\(446\) | −2.02655e9 | −1.08165 | ||||||||
\(447\) | −9.53351e7 | −0.0504866 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −2.02721e9 | −1.05691 | −0.528453 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528453 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(450\) | −2.27803e9 | −1.17846 | ||||||||
\(451\) | 1.18910e9 | 0.610379 | ||||||||
\(452\) | −7.74088e8 | −0.394281 | ||||||||
\(453\) | −2.29904e8 | −0.116199 | ||||||||
\(454\) | 3.60100e8 | 0.180604 | ||||||||
\(455\) | −1.83735e9 | −0.914435 | ||||||||
\(456\) | 1.55790e8 | 0.0769419 | ||||||||
\(457\) | 2.03969e9 | 0.999672 | 0.499836 | − | 0.866120i | \(-0.333394\pi\) | ||||
0.499836 | + | 0.866120i | \(0.333394\pi\) | |||||||
\(458\) | 1.49579e9 | 0.727512 | ||||||||
\(459\) | −6.12375e8 | −0.295579 | ||||||||
\(460\) | 1.66142e9 | 0.795844 | ||||||||
\(461\) | −3.41390e9 | −1.62292 | −0.811461 | − | 0.584406i | \(-0.801327\pi\) | ||||
−0.811461 | + | 0.584406i | \(0.801327\pi\) | |||||||
\(462\) | −9.98231e7 | −0.0470960 | ||||||||
\(463\) | −1.97893e9 | −0.926608 | −0.463304 | − | 0.886199i | \(-0.653336\pi\) | ||||
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(464\) | −1.08306e8 | −0.0503316 | ||||||||
\(465\) | 1.96968e8 | 0.0908469 | ||||||||
\(466\) | −2.06071e9 | −0.943334 | ||||||||
\(467\) | 1.86422e9 | 0.847007 | 0.423504 | − | 0.905894i | \(-0.360800\pi\) | ||||
0.423504 | + | 0.905894i | \(0.360800\pi\) | |||||||
\(468\) | 1.55646e9 | 0.701905 | ||||||||
\(469\) | 1.49047e9 | 0.667144 | ||||||||
\(470\) | −1.96501e9 | −0.873015 | ||||||||
\(471\) | 1.19397e8 | 0.0526528 | ||||||||
\(472\) | −1.09617e9 | −0.479822 | ||||||||
\(473\) | 3.03015e9 | 1.31659 | ||||||||
\(474\) | −5.29286e8 | −0.228279 | ||||||||
\(475\) | −4.40351e9 | −1.88526 | ||||||||
\(476\) | −3.34601e8 | −0.142201 | ||||||||
\(477\) | 7.63231e8 | 0.321990 | ||||||||
\(478\) | −2.52057e9 | −1.05560 | ||||||||
\(479\) | 3.71828e9 | 1.54585 | 0.772926 | − | 0.634496i | \(-0.218792\pi\) | ||||
0.772926 | + | 0.634496i | \(0.218792\pi\) | |||||||
\(480\) | −1.42013e8 | −0.0586117 | ||||||||
\(481\) | 6.43283e9 | 2.63569 | ||||||||
\(482\) | 6.71920e8 | 0.273308 | ||||||||
\(483\) | −1.80514e8 | −0.0728948 | ||||||||
\(484\) | −2.83176e8 | −0.113526 | ||||||||
\(485\) | −9.70080e8 | −0.386110 | ||||||||
\(486\) | −1.01893e9 | −0.402640 | ||||||||
\(487\) | −2.16341e9 | −0.848767 | −0.424383 | − | 0.905483i | \(-0.639509\pi\) | ||||
−0.424383 | + | 0.905483i | \(0.639509\pi\) | |||||||
\(488\) | 4.55078e8 | 0.177262 | ||||||||
\(489\) | 7.98175e8 | 0.308686 | ||||||||
\(490\) | 4.35170e8 | 0.167099 | ||||||||
\(491\) | 2.37608e8 | 0.0905890 | 0.0452945 | − | 0.998974i | \(-0.485577\pi\) | ||||
0.0452945 | + | 0.998974i | \(0.485577\pi\) | |||||||
\(492\) | −1.83800e8 | −0.0695774 | ||||||||
\(493\) | 4.03039e8 | 0.151489 | ||||||||
\(494\) | 3.00870e9 | 1.12288 | ||||||||
\(495\) | −3.76679e9 | −1.39590 | ||||||||
\(496\) | −1.86156e8 | −0.0685000 | ||||||||
\(497\) | 2.27480e8 | 0.0831181 | ||||||||
\(498\) | −4.95571e8 | −0.179806 | ||||||||
\(499\) | 2.65166e9 | 0.955358 | 0.477679 | − | 0.878535i | \(-0.341478\pi\) | ||||
0.477679 | + | 0.878535i | \(0.341478\pi\) | |||||||
\(500\) | 1.70230e9 | 0.609033 | ||||||||
\(501\) | 3.50810e7 | 0.0124635 | ||||||||
\(502\) | −4.26504e7 | −0.0150474 | ||||||||
\(503\) | 2.15865e9 | 0.756300 | 0.378150 | − | 0.925744i | \(-0.376560\pi\) | ||||
0.378150 | + | 0.925744i | \(0.376560\pi\) | |||||||
\(504\) | −3.68642e8 | −0.128262 | ||||||||
\(505\) | 9.04091e9 | 3.12387 | ||||||||
\(506\) | 1.74325e9 | 0.598180 | ||||||||
\(507\) | −6.69984e8 | −0.228316 | ||||||||
\(508\) | −2.08486e7 | −0.00705594 | ||||||||
\(509\) | 2.47831e9 | 0.832998 | 0.416499 | − | 0.909136i | \(-0.363257\pi\) | ||||
0.416499 | + | 0.909136i | \(0.363257\pi\) | |||||||
\(510\) | 5.28472e8 | 0.176411 | ||||||||
\(511\) | 4.60312e8 | 0.152609 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.30418e9 | −0.426506 | ||||||||
\(514\) | −1.67953e9 | −0.545529 | ||||||||
\(515\) | −4.13856e9 | −1.33513 | ||||||||
\(516\) | −4.68374e8 | −0.150079 | ||||||||
\(517\) | −2.06178e9 | −0.656184 | ||||||||
\(518\) | −1.52359e9 | −0.481631 | ||||||||
\(519\) | 6.81321e8 | 0.213927 | ||||||||
\(520\) | −2.74264e9 | −0.855376 | ||||||||
\(521\) | −3.99735e9 | −1.23834 | −0.619170 | − | 0.785257i | \(-0.712531\pi\) | ||||
−0.619170 | + | 0.785257i | \(0.712531\pi\) | |||||||
\(522\) | 4.44043e8 | 0.136640 | ||||||||
\(523\) | −3.93132e9 | −1.20166 | −0.600831 | − | 0.799376i | \(-0.705163\pi\) | ||||
−0.600831 | + | 0.799376i | \(0.705163\pi\) | |||||||
\(524\) | 4.08351e8 | 0.123986 | ||||||||
\(525\) | −4.36134e8 | −0.131541 | ||||||||
\(526\) | −2.00644e9 | −0.601142 | ||||||||
\(527\) | 6.92739e8 | 0.206173 | ||||||||
\(528\) | −1.49007e8 | −0.0440543 | ||||||||
\(529\) | −2.52441e8 | −0.0741421 | ||||||||
\(530\) | −1.34489e9 | −0.392392 | ||||||||
\(531\) | 4.49416e9 | 1.30262 | ||||||||
\(532\) | −7.12600e8 | −0.205190 | ||||||||
\(533\) | −3.54965e9 | −1.01541 | ||||||||
\(534\) | 3.99681e8 | 0.113584 | ||||||||
\(535\) | −6.45037e9 | −1.82115 | ||||||||
\(536\) | 2.22485e9 | 0.624056 | ||||||||
\(537\) | −9.60258e8 | −0.267595 | ||||||||
\(538\) | 2.71358e9 | 0.751284 | ||||||||
\(539\) | 4.56602e8 | 0.125596 | ||||||||
\(540\) | 1.18884e9 | 0.324898 | ||||||||
\(541\) | −2.74766e9 | −0.746057 | −0.373028 | − | 0.927820i | \(-0.621681\pi\) | ||||
−0.373028 | + | 0.927820i | \(0.621681\pi\) | |||||||
\(542\) | 6.07659e8 | 0.163932 | ||||||||
\(543\) | −4.49138e7 | −0.0120387 | ||||||||
\(544\) | −4.99463e8 | −0.133017 | ||||||||
\(545\) | 2.70155e9 | 0.714867 | ||||||||
\(546\) | 2.97989e8 | 0.0783475 | ||||||||
\(547\) | −1.40581e9 | −0.367258 | −0.183629 | − | 0.982996i | \(-0.558784\pi\) | ||||
−0.183629 | + | 0.982996i | \(0.558784\pi\) | |||||||
\(548\) | 2.95887e8 | 0.0768059 | ||||||||
\(549\) | −1.86576e9 | −0.481231 | ||||||||
\(550\) | 4.21179e9 | 1.07944 | ||||||||
\(551\) | 8.58352e8 | 0.218592 | ||||||||
\(552\) | −2.69456e8 | −0.0681869 | ||||||||
\(553\) | 2.42101e9 | 0.608777 | ||||||||
\(554\) | −4.00707e8 | −0.100125 | ||||||||
\(555\) | 2.40637e9 | 0.597500 | ||||||||
\(556\) | −2.27452e9 | −0.561214 | ||||||||
\(557\) | 9.87805e8 | 0.242202 | 0.121101 | − | 0.992640i | \(-0.461357\pi\) | ||||
0.121101 | + | 0.992640i | \(0.461357\pi\) | |||||||
\(558\) | 7.63217e8 | 0.185964 | ||||||||
\(559\) | −9.04550e9 | −2.19024 | ||||||||
\(560\) | 6.49584e8 | 0.156306 | ||||||||
\(561\) | 5.54498e8 | 0.132596 | ||||||||
\(562\) | 2.73534e9 | 0.650031 | ||||||||
\(563\) | 1.88115e9 | 0.444268 | 0.222134 | − | 0.975016i | \(-0.428698\pi\) | ||||
0.222134 | + | 0.975016i | \(0.428698\pi\) | |||||||
\(564\) | 3.18692e8 | 0.0747987 | ||||||||
\(565\) | −5.59231e9 | −1.30443 | ||||||||
\(566\) | 2.95262e9 | 0.684463 | ||||||||
\(567\) | 1.44548e9 | 0.333021 | ||||||||
\(568\) | 3.39562e8 | 0.0777499 | ||||||||
\(569\) | −3.88531e9 | −0.884164 | −0.442082 | − | 0.896975i | \(-0.645760\pi\) | ||||
−0.442082 | + | 0.896975i | \(0.645760\pi\) | |||||||
\(570\) | 1.12549e9 | 0.254553 | ||||||||
\(571\) | 2.44900e9 | 0.550505 | 0.275253 | − | 0.961372i | \(-0.411238\pi\) | ||||
0.275253 | + | 0.961372i | \(0.411238\pi\) | |||||||
\(572\) | −2.87771e9 | −0.642926 | ||||||||
\(573\) | −2.43871e8 | −0.0541525 | ||||||||
\(574\) | 8.40722e8 | 0.185550 | ||||||||
\(575\) | 7.61636e9 | 1.67074 | ||||||||
\(576\) | −5.50277e8 | −0.119978 | ||||||||
\(577\) | 2.88218e9 | 0.624605 | 0.312303 | − | 0.949983i | \(-0.398900\pi\) | ||||
0.312303 | + | 0.949983i | \(0.398900\pi\) | |||||||
\(578\) | −1.42407e9 | −0.306748 | ||||||||
\(579\) | 7.10811e8 | 0.152188 | ||||||||
\(580\) | −7.82446e8 | −0.166516 | ||||||||
\(581\) | 2.26680e9 | 0.479508 | ||||||||
\(582\) | 1.57331e8 | 0.0330814 | ||||||||
\(583\) | −1.41112e9 | −0.294934 | ||||||||
\(584\) | 6.87114e8 | 0.142752 | ||||||||
\(585\) | 1.12445e10 | 2.32217 | ||||||||
\(586\) | 4.74224e9 | 0.973513 | ||||||||
\(587\) | 4.72250e9 | 0.963692 | 0.481846 | − | 0.876256i | \(-0.339966\pi\) | ||||
0.481846 | + | 0.876256i | \(0.339966\pi\) | |||||||
\(588\) | −7.05775e7 | −0.0143168 | ||||||||
\(589\) | 1.47533e9 | 0.297499 | ||||||||
\(590\) | −7.91914e9 | −1.58743 | ||||||||
\(591\) | −1.11724e9 | −0.222633 | ||||||||
\(592\) | −2.27428e9 | −0.450525 | ||||||||
\(593\) | 1.23167e8 | 0.0242550 | 0.0121275 | − | 0.999926i | \(-0.496140\pi\) | ||||
0.0121275 | + | 0.999926i | \(0.496140\pi\) | |||||||
\(594\) | 1.24739e9 | 0.244203 | ||||||||
\(595\) | −2.41729e9 | −0.470456 | ||||||||
\(596\) | 6.50931e8 | 0.125943 | ||||||||
\(597\) | −6.30514e8 | −0.121279 | ||||||||
\(598\) | −5.20388e9 | −0.995115 | ||||||||
\(599\) | 1.35497e9 | 0.257594 | 0.128797 | − | 0.991671i | \(-0.458888\pi\) | ||||
0.128797 | + | 0.991671i | \(0.458888\pi\) | |||||||
\(600\) | −6.51022e8 | −0.123046 | ||||||||
\(601\) | −5.25107e9 | −0.986704 | −0.493352 | − | 0.869830i | \(-0.664228\pi\) | ||||
−0.493352 | + | 0.869830i | \(0.664228\pi\) | |||||||
\(602\) | 2.14239e9 | 0.400231 | ||||||||
\(603\) | −9.12161e9 | −1.69419 | ||||||||
\(604\) | 1.56974e9 | 0.289867 | ||||||||
\(605\) | −2.04577e9 | −0.375589 | ||||||||
\(606\) | −1.46629e9 | −0.267649 | ||||||||
\(607\) | 4.99012e9 | 0.905630 | 0.452815 | − | 0.891605i | \(-0.350420\pi\) | ||||
0.452815 | + | 0.891605i | \(0.350420\pi\) | |||||||
\(608\) | −1.06371e9 | −0.191937 | ||||||||
\(609\) | 8.50130e7 | 0.0152519 | ||||||||
\(610\) | 3.28766e9 | 0.586452 | ||||||||
\(611\) | 6.15476e9 | 1.09161 | ||||||||
\(612\) | 2.04774e9 | 0.361114 | ||||||||
\(613\) | −2.46028e9 | −0.431393 | −0.215696 | − | 0.976460i | \(-0.569202\pi\) | ||||
−0.215696 | + | 0.976460i | \(0.569202\pi\) | |||||||
\(614\) | −7.55077e9 | −1.31644 | ||||||||
\(615\) | −1.32784e9 | −0.230189 | ||||||||
\(616\) | 6.81575e8 | 0.117485 | ||||||||
\(617\) | −1.93223e9 | −0.331178 | −0.165589 | − | 0.986195i | \(-0.552953\pi\) | ||||
−0.165589 | + | 0.986195i | \(0.552953\pi\) | |||||||
\(618\) | 6.71206e8 | 0.114392 | ||||||||
\(619\) | −8.13699e9 | −1.37894 | −0.689472 | − | 0.724313i | \(-0.742157\pi\) | ||||
−0.689472 | + | 0.724313i | \(0.742157\pi\) | |||||||
\(620\) | −1.34486e9 | −0.226624 | ||||||||
\(621\) | 2.25571e9 | 0.377975 | ||||||||
\(622\) | −1.31252e9 | −0.218695 | ||||||||
\(623\) | −1.82818e9 | −0.302908 | ||||||||
\(624\) | 4.44811e8 | 0.0732874 | ||||||||
\(625\) | 1.70022e9 | 0.278565 | ||||||||
\(626\) | 2.76809e9 | 0.450994 | ||||||||
\(627\) | 1.18092e9 | 0.191330 | ||||||||
\(628\) | −8.15223e8 | −0.131346 | ||||||||
\(629\) | 8.46326e9 | 1.35600 | ||||||||
\(630\) | −2.66322e9 | −0.424340 | ||||||||
\(631\) | 8.83737e9 | 1.40030 | 0.700149 | − | 0.713997i | \(-0.253117\pi\) | ||||
0.700149 | + | 0.713997i | \(0.253117\pi\) | |||||||
\(632\) | 3.61387e9 | 0.569459 | ||||||||
\(633\) | −2.17858e9 | −0.341397 | ||||||||
\(634\) | −7.62592e9 | −1.18845 | ||||||||
\(635\) | −1.50619e8 | −0.0233438 | ||||||||
\(636\) | 2.18119e8 | 0.0336196 | ||||||||
\(637\) | −1.36303e9 | −0.208938 | ||||||||
\(638\) | −8.20981e8 | −0.125159 | ||||||||
\(639\) | −1.39216e9 | −0.211075 | ||||||||
\(640\) | 9.69641e8 | 0.146211 | ||||||||
\(641\) | −1.25905e10 | −1.88817 | −0.944086 | − | 0.329700i | \(-0.893052\pi\) | ||||
−0.944086 | + | 0.329700i | \(0.893052\pi\) | |||||||
\(642\) | 1.04614e9 | 0.156034 | ||||||||
\(643\) | 6.47578e9 | 0.960625 | 0.480312 | − | 0.877098i | \(-0.340523\pi\) | ||||
0.480312 | + | 0.877098i | \(0.340523\pi\) | |||||||
\(644\) | 1.23252e9 | 0.181842 | ||||||||
\(645\) | −3.38371e9 | −0.496518 | ||||||||
\(646\) | 3.95836e9 | 0.577698 | ||||||||
\(647\) | 8.69520e9 | 1.26216 | 0.631081 | − | 0.775717i | \(-0.282612\pi\) | ||||
0.631081 | + | 0.775717i | \(0.282612\pi\) | |||||||
\(648\) | 2.15769e9 | 0.311513 | ||||||||
\(649\) | −8.30914e9 | −1.19316 | ||||||||
\(650\) | −1.25729e10 | −1.79572 | ||||||||
\(651\) | 1.46120e8 | 0.0207575 | ||||||||
\(652\) | −5.44980e9 | −0.770041 | ||||||||
\(653\) | −3.87898e9 | −0.545156 | −0.272578 | − | 0.962134i | \(-0.587876\pi\) | ||||
−0.272578 | + | 0.962134i | \(0.587876\pi\) | |||||||
\(654\) | −4.38147e8 | −0.0612488 | ||||||||
\(655\) | 2.95009e9 | 0.410195 | ||||||||
\(656\) | 1.25495e9 | 0.173566 | ||||||||
\(657\) | −2.81708e9 | −0.387544 | ||||||||
\(658\) | −1.45773e9 | −0.199474 | ||||||||
\(659\) | −1.30333e9 | −0.177400 | −0.0887000 | − | 0.996058i | \(-0.528271\pi\) | ||||
−0.0887000 | + | 0.996058i | \(0.528271\pi\) | |||||||
\(660\) | −1.07649e9 | −0.145749 | ||||||||
\(661\) | 6.85888e9 | 0.923736 | 0.461868 | − | 0.886949i | \(-0.347179\pi\) | ||||
0.461868 | + | 0.886949i | \(0.347179\pi\) | |||||||
\(662\) | 1.79410e9 | 0.240350 | ||||||||
\(663\) | −1.65527e9 | −0.220583 | ||||||||
\(664\) | 3.38367e9 | 0.448539 | ||||||||
\(665\) | −5.14810e9 | −0.678846 | ||||||||
\(666\) | 9.32429e9 | 1.22308 | ||||||||
\(667\) | −1.48461e9 | −0.193719 | ||||||||
\(668\) | −2.39527e8 | −0.0310911 | ||||||||
\(669\) | 2.37446e9 | 0.306601 | ||||||||
\(670\) | 1.60732e10 | 2.06462 | ||||||||
\(671\) | 3.44957e9 | 0.440794 | ||||||||
\(672\) | −1.05352e8 | −0.0133921 | ||||||||
\(673\) | −6.44953e9 | −0.815596 | −0.407798 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407798 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(674\) | 2.85400e9 | 0.359041 | ||||||||
\(675\) | 5.44994e9 | 0.682069 | ||||||||
\(676\) | 4.57453e9 | 0.569552 | ||||||||
\(677\) | 3.83027e9 | 0.474426 | 0.237213 | − | 0.971458i | \(-0.423766\pi\) | ||||
0.237213 | + | 0.971458i | \(0.423766\pi\) | |||||||
\(678\) | 9.06981e8 | 0.111762 | ||||||||
\(679\) | −7.19649e8 | −0.0882219 | ||||||||
\(680\) | −3.60831e9 | −0.440071 | ||||||||
\(681\) | −4.21920e8 | −0.0511936 | ||||||||
\(682\) | −1.41109e9 | −0.170338 | ||||||||
\(683\) | −1.97836e9 | −0.237592 | −0.118796 | − | 0.992919i | \(-0.537903\pi\) | ||||
−0.118796 | + | 0.992919i | \(0.537903\pi\) | |||||||
\(684\) | 4.36107e9 | 0.521071 | ||||||||
\(685\) | 2.13761e9 | 0.254103 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | −1.75258e9 | −0.206219 | ||||||||
\(688\) | 3.19797e9 | 0.374382 | ||||||||
\(689\) | 4.21243e9 | 0.490643 | ||||||||
\(690\) | −1.94665e9 | −0.225588 | ||||||||
\(691\) | 1.00255e10 | 1.15593 | 0.577967 | − | 0.816060i | \(-0.303846\pi\) | ||||
0.577967 | + | 0.816060i | \(0.303846\pi\) | |||||||
\(692\) | −4.65193e9 | −0.533657 | ||||||||
\(693\) | −2.79437e9 | −0.318947 | ||||||||
\(694\) | 1.29471e8 | 0.0147033 | ||||||||
\(695\) | −1.64320e10 | −1.85671 | ||||||||
\(696\) | 1.26900e8 | 0.0142669 | ||||||||
\(697\) | −4.67005e9 | −0.522404 | ||||||||
\(698\) | 1.66224e9 | 0.185012 | ||||||||
\(699\) | 2.41448e9 | 0.267395 | ||||||||
\(700\) | 2.97784e9 | 0.328140 | ||||||||
\(701\) | 1.21616e9 | 0.133345 | 0.0666727 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666727 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(702\) | −3.72367e9 | −0.406249 | ||||||||
\(703\) | 1.80242e10 | 1.95665 | ||||||||
\(704\) | 1.01739e9 | 0.109897 | ||||||||
\(705\) | 2.30235e9 | 0.247463 | ||||||||
\(706\) | −1.05299e10 | −1.12618 | ||||||||
\(707\) | 6.70696e9 | 0.713769 | ||||||||
\(708\) | 1.28435e9 | 0.136009 | ||||||||
\(709\) | 1.04706e10 | 1.10334 | 0.551671 | − | 0.834062i | \(-0.313990\pi\) | ||||
0.551671 | + | 0.834062i | \(0.313990\pi\) | |||||||
\(710\) | 2.45313e9 | 0.257226 | ||||||||
\(711\) | −1.48164e10 | −1.54597 | ||||||||
\(712\) | −2.72895e9 | −0.283345 | ||||||||
\(713\) | −2.55174e9 | −0.263647 | ||||||||
\(714\) | 3.92044e8 | 0.0403080 | ||||||||
\(715\) | −2.07897e10 | −2.12705 | ||||||||
\(716\) | 6.55647e9 | 0.667536 | ||||||||
\(717\) | 2.95330e9 | 0.299219 | ||||||||
\(718\) | −4.95417e9 | −0.499500 | ||||||||
\(719\) | −2.99586e9 | −0.300587 | −0.150294 | − | 0.988641i | \(-0.548022\pi\) | ||||
−0.150294 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(720\) | −3.97541e9 | −0.396934 | ||||||||
\(721\) | −3.07017e9 | −0.305062 | ||||||||
\(722\) | 1.27914e9 | 0.126485 | ||||||||
\(723\) | −7.87273e8 | −0.0774714 | ||||||||
\(724\) | 3.06663e8 | 0.0300315 | ||||||||
\(725\) | −3.58692e9 | −0.349573 | ||||||||
\(726\) | 3.31790e8 | 0.0321800 | ||||||||
\(727\) | −6.52469e9 | −0.629781 | −0.314890 | − | 0.949128i | \(-0.601968\pi\) | ||||
−0.314890 | + | 0.949128i | \(0.601968\pi\) | |||||||
\(728\) | −2.03461e9 | −0.195444 | ||||||||
\(729\) | −8.02267e9 | −0.766960 | ||||||||
\(730\) | 4.96397e9 | 0.472280 | ||||||||
\(731\) | −1.19006e10 | −1.12683 | ||||||||
\(732\) | −5.33204e8 | −0.0502464 | ||||||||
\(733\) | −1.19856e10 | −1.12408 | −0.562040 | − | 0.827110i | \(-0.689983\pi\) | ||||
−0.562040 | + | 0.827110i | \(0.689983\pi\) | |||||||
\(734\) | 2.22903e9 | 0.208056 | ||||||||
\(735\) | −5.09879e8 | −0.0473654 | ||||||||
\(736\) | 1.83980e9 | 0.170097 | ||||||||
\(737\) | 1.68647e10 | 1.55183 | ||||||||
\(738\) | −5.14517e9 | −0.471197 | ||||||||
\(739\) | 1.81843e10 | 1.65746 | 0.828728 | − | 0.559651i | \(-0.189065\pi\) | ||||
0.828728 | + | 0.559651i | \(0.189065\pi\) | |||||||
\(740\) | −1.64303e10 | −1.49051 | ||||||||
\(741\) | −3.52523e9 | −0.318290 | ||||||||
\(742\) | −9.97698e8 | −0.0896573 | ||||||||
\(743\) | 6.10111e9 | 0.545692 | 0.272846 | − | 0.962058i | \(-0.412035\pi\) | ||||
0.272846 | + | 0.962058i | \(0.412035\pi\) | |||||||
\(744\) | 2.18114e8 | 0.0194169 | ||||||||
\(745\) | 4.70257e9 | 0.416667 | ||||||||
\(746\) | −1.32045e9 | −0.116449 | ||||||||
\(747\) | −1.38727e10 | −1.21769 | ||||||||
\(748\) | −3.78602e9 | −0.330771 | ||||||||
\(749\) | −4.78517e9 | −0.416113 | ||||||||
\(750\) | −1.99455e9 | −0.172635 | ||||||||
\(751\) | −3.69384e9 | −0.318228 | −0.159114 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159114 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(752\) | −2.17597e9 | −0.186591 | ||||||||
\(753\) | 4.99725e7 | 0.00426529 | ||||||||
\(754\) | 2.45076e9 | 0.208210 | ||||||||
\(755\) | 1.13404e10 | 0.958992 | ||||||||
\(756\) | 8.81938e8 | 0.0742356 | ||||||||
\(757\) | 1.35894e10 | 1.13858 | 0.569292 | − | 0.822135i | \(-0.307217\pi\) | ||||
0.569292 | + | 0.822135i | \(0.307217\pi\) | |||||||
\(758\) | 3.43546e9 | 0.286512 | ||||||||
\(759\) | −2.04252e9 | −0.169559 | ||||||||
\(760\) | −7.68463e9 | −0.635002 | ||||||||
\(761\) | 1.79994e10 | 1.48051 | 0.740255 | − | 0.672326i | \(-0.234705\pi\) | ||||
0.740255 | + | 0.672326i | \(0.234705\pi\) | |||||||
\(762\) | 2.44279e7 | 0.00200006 | ||||||||
\(763\) | 2.00413e9 | 0.163339 | ||||||||
\(764\) | 1.66511e9 | 0.135087 | ||||||||
\(765\) | 1.47936e10 | 1.19470 | ||||||||
\(766\) | 1.07502e10 | 0.864204 | ||||||||
\(767\) | 2.48042e10 | 1.98491 | ||||||||
\(768\) | −1.57260e8 | −0.0125272 | ||||||||
\(769\) | 1.41340e10 | 1.12079 | 0.560394 | − | 0.828226i | \(-0.310650\pi\) | ||||
0.560394 | + | 0.828226i | \(0.310650\pi\) | |||||||
\(770\) | 4.92396e9 | 0.388684 | ||||||||
\(771\) | 1.96787e9 | 0.154634 | ||||||||
\(772\) | −4.85329e9 | −0.379643 | ||||||||
\(773\) | −7.39484e9 | −0.575838 | −0.287919 | − | 0.957655i | \(-0.592963\pi\) | ||||
−0.287919 | + | 0.957655i | \(0.592963\pi\) | |||||||
\(774\) | −1.31113e10 | −1.01637 | ||||||||
\(775\) | −6.16516e9 | −0.475760 | ||||||||
\(776\) | −1.07423e9 | −0.0825241 | ||||||||
\(777\) | 1.78516e9 | 0.136522 | ||||||||
\(778\) | −8.62967e8 | −0.0657000 | ||||||||
\(779\) | −9.94581e9 | −0.753805 | ||||||||
\(780\) | 3.21349e9 | 0.242463 | ||||||||
\(781\) | 2.57394e9 | 0.193339 | ||||||||
\(782\) | −6.84641e9 | −0.511964 | ||||||||
\(783\) | −1.06233e9 | −0.0790845 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −5.88949e9 | −0.434544 | ||||||||
\(786\) | −4.78456e8 | −0.0351449 | ||||||||
\(787\) | −9.49146e9 | −0.694099 | −0.347050 | − | 0.937847i | \(-0.612816\pi\) | ||||
−0.347050 | + | 0.937847i | \(0.612816\pi\) | |||||||
\(788\) | 7.62829e9 | 0.555374 | ||||||||
\(789\) | 2.35090e9 | 0.170398 | ||||||||
\(790\) | 2.61080e10 | 1.88399 | ||||||||
\(791\) | −4.14863e9 | −0.298049 | ||||||||
\(792\) | −4.17119e9 | −0.298347 | ||||||||
\(793\) | −1.02975e10 | −0.733292 | ||||||||
\(794\) | −1.49220e10 | −1.05792 | ||||||||
\(795\) | 1.57577e9 | 0.111227 | ||||||||
\(796\) | 4.30504e9 | 0.302539 | ||||||||
\(797\) | −8.83350e9 | −0.618057 | −0.309029 | − | 0.951053i | \(-0.600004\pi\) | ||||
−0.309029 | + | 0.951053i | \(0.600004\pi\) | |||||||
\(798\) | 8.34937e8 | 0.0581626 | ||||||||
\(799\) | 8.09742e9 | 0.561607 | ||||||||
\(800\) | 4.44506e9 | 0.306946 | ||||||||
\(801\) | 1.11884e10 | 0.769224 | ||||||||
\(802\) | 7.95779e7 | 0.00544731 | ||||||||
\(803\) | 5.20844e9 | 0.354980 | ||||||||
\(804\) | −2.60680e9 | −0.176894 | ||||||||
\(805\) | 8.90420e9 | 0.601602 | ||||||||
\(806\) | 4.21235e9 | 0.283368 | ||||||||
\(807\) | −3.17943e9 | −0.212957 | ||||||||
\(808\) | 1.00116e10 | 0.667670 | ||||||||
\(809\) | 6.15622e9 | 0.408784 | 0.204392 | − | 0.978889i | \(-0.434478\pi\) | ||||
0.204392 | + | 0.978889i | \(0.434478\pi\) | |||||||
\(810\) | 1.55880e10 | 1.03060 | ||||||||
\(811\) | −1.53945e10 | −1.01343 | −0.506715 | − | 0.862114i | \(-0.669140\pi\) | ||||
−0.506715 | + | 0.862114i | \(0.669140\pi\) | |||||||
\(812\) | −5.80454e8 | −0.0380471 | ||||||||
\(813\) | −7.11980e8 | −0.0464677 | ||||||||
\(814\) | −1.72395e10 | −1.12031 | ||||||||
\(815\) | −3.93714e10 | −2.54759 | ||||||||
\(816\) | 5.85209e8 | 0.0377047 | ||||||||
\(817\) | −2.53447e10 | −1.62596 | ||||||||
\(818\) | −7.01101e9 | −0.447862 | ||||||||
\(819\) | 8.34167e9 | 0.530590 | ||||||||
\(820\) | 9.06628e9 | 0.574223 | ||||||||
\(821\) | −2.74907e10 | −1.73374 | −0.866871 | − | 0.498532i | \(-0.833872\pi\) | ||||
−0.866871 | + | 0.498532i | \(0.833872\pi\) | |||||||
\(822\) | −3.46684e8 | −0.0217712 | ||||||||
\(823\) | 1.61300e9 | 0.100864 | 0.0504318 | − | 0.998728i | \(-0.483940\pi\) | ||||
0.0504318 | + | 0.998728i | \(0.483940\pi\) | |||||||
\(824\) | −4.58288e9 | −0.285360 | ||||||||
\(825\) | −4.93486e9 | −0.305975 | ||||||||
\(826\) | −5.87477e9 | −0.362711 | ||||||||
\(827\) | 9.03950e9 | 0.555745 | 0.277872 | − | 0.960618i | \(-0.410371\pi\) | ||||
0.277872 | + | 0.960618i | \(0.410371\pi\) | |||||||
\(828\) | −7.54294e9 | −0.461779 | ||||||||
\(829\) | 2.46326e10 | 1.50165 | 0.750826 | − | 0.660501i | \(-0.229656\pi\) | ||||
0.750826 | + | 0.660501i | \(0.229656\pi\) | |||||||
\(830\) | 2.44450e10 | 1.48394 | ||||||||
\(831\) | 4.69499e8 | 0.0283812 | ||||||||
\(832\) | −3.03709e9 | −0.182821 | ||||||||
\(833\) | −1.79325e9 | −0.107494 | ||||||||
\(834\) | 2.66500e9 | 0.159080 | ||||||||
\(835\) | −1.73043e9 | −0.102861 | ||||||||
\(836\) | −8.06308e9 | −0.477286 | ||||||||
\(837\) | −1.82592e9 | −0.107632 | ||||||||
\(838\) | −1.61284e10 | −0.946755 | ||||||||
\(839\) | −6.84347e9 | −0.400046 | −0.200023 | − | 0.979791i | \(-0.564102\pi\) | ||||
−0.200023 | + | 0.979791i | \(0.564102\pi\) | |||||||
\(840\) | −7.61102e8 | −0.0443063 | ||||||||
\(841\) | −1.65507e10 | −0.959468 | ||||||||
\(842\) | 4.55637e9 | 0.263043 | ||||||||
\(843\) | −3.20493e9 | −0.184256 | ||||||||
\(844\) | 1.48749e10 | 0.851641 | ||||||||
\(845\) | 3.30482e10 | 1.88430 | ||||||||
\(846\) | 8.92123e9 | 0.506557 | ||||||||
\(847\) | −1.51764e9 | −0.0858179 | ||||||||
\(848\) | −1.48928e9 | −0.0838667 | ||||||||
\(849\) | −3.45952e9 | −0.194016 | ||||||||
\(850\) | −1.65413e10 | −0.923857 | ||||||||
\(851\) | −3.11748e10 | −1.73401 | ||||||||
\(852\) | −3.97857e8 | −0.0220388 | ||||||||
\(853\) | 3.54072e10 | 1.95330 | 0.976652 | − | 0.214826i | \(-0.0689185\pi\) | ||||
0.976652 | + | 0.214826i | \(0.0689185\pi\) | |||||||
\(854\) | 2.43893e9 | 0.133998 | ||||||||
\(855\) | 3.15061e10 | 1.72390 | ||||||||
\(856\) | −7.14288e9 | −0.389238 | ||||||||
\(857\) | −1.87299e10 | −1.01649 | −0.508245 | − | 0.861213i | \(-0.669706\pi\) | ||||
−0.508245 | + | 0.861213i | \(0.669706\pi\) | |||||||
\(858\) | 3.37175e9 | 0.182242 | ||||||||
\(859\) | −5.38272e9 | −0.289752 | −0.144876 | − | 0.989450i | \(-0.546278\pi\) | ||||
−0.144876 | + | 0.989450i | \(0.546278\pi\) | |||||||
\(860\) | 2.31034e10 | 1.23860 | ||||||||
\(861\) | −9.85054e8 | −0.0525956 | ||||||||
\(862\) | −6.17552e9 | −0.328396 | ||||||||
\(863\) | 7.29444e9 | 0.386326 | 0.193163 | − | 0.981167i | \(-0.438125\pi\) | ||||
0.193163 | + | 0.981167i | \(0.438125\pi\) | |||||||
\(864\) | 1.31648e9 | 0.0694410 | ||||||||
\(865\) | −3.36074e10 | −1.76554 | ||||||||
\(866\) | 9.92016e9 | 0.519046 | ||||||||
\(867\) | 1.66854e9 | 0.0869503 | ||||||||
\(868\) | −9.97679e8 | −0.0517811 | ||||||||
\(869\) | 2.73938e10 | 1.41606 | ||||||||
\(870\) | 9.16774e8 | 0.0472003 | ||||||||
\(871\) | −5.03440e10 | −2.58157 | ||||||||
\(872\) | 2.99159e9 | 0.152790 | ||||||||
\(873\) | 4.40421e9 | 0.224036 | ||||||||
\(874\) | −1.45808e10 | −0.738740 | ||||||||
\(875\) | 9.12326e9 | 0.460386 | ||||||||
\(876\) | −8.05075e8 | −0.0404643 | ||||||||
\(877\) | 3.05623e10 | 1.52998 | 0.764992 | − | 0.644039i | \(-0.222743\pi\) | ||||
0.764992 | + | 0.644039i | \(0.222743\pi\) | |||||||
\(878\) | 1.52497e10 | 0.760379 | ||||||||
\(879\) | −5.55637e9 | −0.275950 | ||||||||
\(880\) | 7.35005e9 | 0.363581 | ||||||||
\(881\) | −3.10736e10 | −1.53100 | −0.765500 | − | 0.643436i | \(-0.777508\pi\) | ||||
−0.765500 | + | 0.643436i | \(0.777508\pi\) | |||||||
\(882\) | −1.97569e9 | −0.0969571 | ||||||||
\(883\) | 9.10432e9 | 0.445026 | 0.222513 | − | 0.974930i | \(-0.428574\pi\) | ||||
0.222513 | + | 0.974930i | \(0.428574\pi\) | |||||||
\(884\) | 1.13019e10 | 0.550260 | ||||||||
\(885\) | 9.27867e9 | 0.449971 | ||||||||
\(886\) | −4.03790e9 | −0.195046 | ||||||||
\(887\) | −5.03417e8 | −0.0242212 | −0.0121106 | − | 0.999927i | \(-0.503855\pi\) | ||||
−0.0121106 | + | 0.999927i | \(0.503855\pi\) | |||||||
\(888\) | 2.66472e9 | 0.127705 | ||||||||
\(889\) | −1.11736e8 | −0.00533379 | ||||||||
\(890\) | −1.97150e10 | −0.937414 | ||||||||
\(891\) | 1.63557e10 | 0.774633 | ||||||||
\(892\) | −1.62124e10 | −0.764840 | ||||||||
\(893\) | 1.72451e10 | 0.810373 | ||||||||
\(894\) | −7.62680e8 | −0.0356994 | ||||||||
\(895\) | 4.73665e10 | 2.20846 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | 6.09727e9 | 0.282073 | ||||||||
\(898\) | −1.62177e10 | −0.747346 | ||||||||
\(899\) | 1.20174e9 | 0.0551634 | ||||||||
\(900\) | −1.82242e10 | −0.833297 | ||||||||
\(901\) | 5.54202e9 | 0.252424 | ||||||||
\(902\) | 9.51278e9 | 0.431603 | ||||||||
\(903\) | −2.51019e9 | −0.113449 | ||||||||
\(904\) | −6.19271e9 | −0.278799 | ||||||||
\(905\) | 2.21545e9 | 0.0993557 | ||||||||
\(906\) | −1.83923e9 | −0.0821652 | ||||||||
\(907\) | 3.55392e10 | 1.58155 | 0.790774 | − | 0.612108i | \(-0.209678\pi\) | ||||
0.790774 | + | 0.612108i | \(0.209678\pi\) | |||||||
\(908\) | 2.88080e9 | 0.127706 | ||||||||
\(909\) | −4.10462e10 | −1.81259 | ||||||||
\(910\) | −1.46988e10 | −0.646603 | ||||||||
\(911\) | 3.60841e10 | 1.58125 | 0.790627 | − | 0.612299i | \(-0.209755\pi\) | ||||
0.790627 | + | 0.612299i | \(0.209755\pi\) | |||||||
\(912\) | 1.24632e9 | 0.0544061 | ||||||||
\(913\) | 2.56488e10 | 1.11537 | ||||||||
\(914\) | 1.63175e10 | 0.706875 | ||||||||
\(915\) | −3.85207e9 | −0.166234 | ||||||||
\(916\) | 1.19663e10 | 0.514429 | ||||||||
\(917\) | 2.18851e9 | 0.0937250 | ||||||||
\(918\) | −4.89900e9 | −0.209006 | ||||||||
\(919\) | −7.06975e9 | −0.300469 | −0.150235 | − | 0.988650i | \(-0.548003\pi\) | ||||
−0.150235 | + | 0.988650i | \(0.548003\pi\) | |||||||
\(920\) | 1.32914e10 | 0.562747 | ||||||||
\(921\) | 8.84706e9 | 0.373156 | ||||||||
\(922\) | −2.73112e10 | −1.14758 | ||||||||
\(923\) | −7.68363e9 | −0.321633 | ||||||||
\(924\) | −7.98585e8 | −0.0333019 | ||||||||
\(925\) | −7.53203e10 | −3.12908 | ||||||||
\(926\) | −1.58314e10 | −0.655211 | ||||||||
\(927\) | 1.87892e10 | 0.774694 | ||||||||
\(928\) | −8.66450e8 | −0.0355898 | ||||||||
\(929\) | −1.55102e10 | −0.634691 | −0.317345 | − | 0.948310i | \(-0.602791\pi\) | ||||
−0.317345 | + | 0.948310i | \(0.602791\pi\) | |||||||
\(930\) | 1.57574e9 | 0.0642385 | ||||||||
\(931\) | −3.81909e9 | −0.155109 | ||||||||
\(932\) | −1.64856e10 | −0.667038 | ||||||||
\(933\) | 1.53785e9 | 0.0619910 | ||||||||
\(934\) | 1.49137e10 | 0.598925 | ||||||||
\(935\) | −2.73516e10 | −1.09432 | ||||||||
\(936\) | 1.24517e10 | 0.496322 | ||||||||
\(937\) | −3.61814e10 | −1.43680 | −0.718400 | − | 0.695630i | \(-0.755125\pi\) | ||||
−0.718400 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(938\) | 1.19238e10 | 0.471742 | ||||||||
\(939\) | −3.24331e9 | −0.127838 | ||||||||
\(940\) | −1.57201e10 | −0.617315 | ||||||||
\(941\) | 1.86518e10 | 0.729720 | 0.364860 | − | 0.931062i | \(-0.381117\pi\) | ||||
0.364860 | + | 0.931062i | \(0.381117\pi\) | |||||||
\(942\) | 9.55178e8 | 0.0372311 | ||||||||
\(943\) | 1.72023e10 | 0.668031 | ||||||||
\(944\) | −8.76934e9 | −0.339285 | ||||||||
\(945\) | 6.37146e9 | 0.245600 | ||||||||
\(946\) | 2.42412e10 | 0.930969 | ||||||||
\(947\) | 8.55630e9 | 0.327387 | 0.163693 | − | 0.986511i | \(-0.447659\pi\) | ||||
0.163693 | + | 0.986511i | \(0.447659\pi\) | |||||||
\(948\) | −4.23429e9 | −0.161418 | ||||||||
\(949\) | −1.55481e10 | −0.590533 | ||||||||
\(950\) | −3.52281e10 | −1.33308 | ||||||||
\(951\) | 8.93512e9 | 0.336875 | ||||||||
\(952\) | −2.67681e9 | −0.100551 | ||||||||
\(953\) | −5.92820e8 | −0.0221870 | −0.0110935 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110935 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(954\) | 6.10585e9 | 0.227681 | ||||||||
\(955\) | 1.20294e10 | 0.446921 | ||||||||
\(956\) | −2.01646e10 | −0.746425 | ||||||||
\(957\) | 9.61924e8 | 0.0354772 | ||||||||
\(958\) | 2.97462e10 | 1.09308 | ||||||||
\(959\) | 1.58577e9 | 0.0580598 | ||||||||
\(960\) | −1.13611e9 | −0.0414447 | ||||||||
\(961\) | −2.54471e10 | −0.924924 | ||||||||
\(962\) | 5.14626e10 | 1.86371 | ||||||||
\(963\) | 2.92850e10 | 1.05670 | ||||||||
\(964\) | 5.37536e9 | 0.193258 | ||||||||
\(965\) | −3.50620e10 | −1.25601 | ||||||||
\(966\) | −1.44411e9 | −0.0515444 | ||||||||
\(967\) | −5.25393e10 | −1.86849 | −0.934247 | − | 0.356626i | \(-0.883927\pi\) | ||||
−0.934247 | + | 0.356626i | \(0.883927\pi\) | |||||||
\(968\) | −2.26541e9 | −0.0802753 | ||||||||
\(969\) | −4.63792e9 | −0.163753 | ||||||||
\(970\) | −7.76064e9 | −0.273021 | ||||||||
\(971\) | −9.16576e9 | −0.321293 | −0.160647 | − | 0.987012i | \(-0.551358\pi\) | ||||
−0.160647 | + | 0.987012i | \(0.551358\pi\) | |||||||
\(972\) | −8.15143e9 | −0.284710 | ||||||||
\(973\) | −1.21900e10 | −0.424238 | ||||||||
\(974\) | −1.73073e10 | −0.600169 | ||||||||
\(975\) | 1.47314e10 | 0.509011 | ||||||||
\(976\) | 3.64062e9 | 0.125343 | ||||||||
\(977\) | −2.01603e10 | −0.691618 | −0.345809 | − | 0.938305i | \(-0.612396\pi\) | ||||
−0.345809 | + | 0.938305i | \(0.612396\pi\) | |||||||
\(978\) | 6.38540e9 | 0.218274 | ||||||||
\(979\) | −2.06859e10 | −0.704588 | ||||||||
\(980\) | 3.48136e9 | 0.118157 | ||||||||
\(981\) | −1.22652e10 | −0.414793 | ||||||||
\(982\) | 1.90086e9 | 0.0640561 | ||||||||
\(983\) | −1.18989e9 | −0.0399549 | −0.0199775 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199775 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(984\) | −1.47040e9 | −0.0491986 | ||||||||
\(985\) | 5.51097e10 | 1.83739 | ||||||||
\(986\) | 3.22431e9 | 0.107119 | ||||||||
\(987\) | 1.70799e9 | 0.0565425 | ||||||||
\(988\) | 2.40696e10 | 0.793999 | ||||||||
\(989\) | 4.38364e10 | 1.44095 | ||||||||
\(990\) | −3.01343e10 | −0.987048 | ||||||||
\(991\) | 2.09986e10 | 0.685382 | 0.342691 | − | 0.939448i | \(-0.388662\pi\) | ||||
0.342691 | + | 0.939448i | \(0.388662\pi\) | |||||||
\(992\) | −1.48925e9 | −0.0484368 | ||||||||
\(993\) | −2.10211e9 | −0.0681291 | ||||||||
\(994\) | 1.81984e9 | 0.0587734 | ||||||||
\(995\) | 3.11013e10 | 1.00092 | ||||||||
\(996\) | −3.96457e9 | −0.127142 | ||||||||
\(997\) | 3.21657e10 | 1.02792 | 0.513961 | − | 0.857814i | \(-0.328178\pi\) | ||||
0.513961 | + | 0.857814i | \(0.328178\pi\) | |||||||
\(998\) | 2.12133e10 | 0.675540 | ||||||||
\(999\) | −2.23074e10 | −0.707896 |
(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 | 14.8.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 126.8.a.i.1.1 | 2 | |||
4.3 | odd | 2 | 112.8.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 350.8.c.k.99.4 | 4 | |||
5.3 | odd | 4 | 350.8.c.k.99.1 | 4 | |||
5.4 | even | 2 | 350.8.a.j.1.2 | 2 | |||
7.2 | even | 3 | 98.8.c.g.67.2 | 4 | |||
7.3 | odd | 6 | 98.8.c.k.79.1 | 4 | |||
7.4 | even | 3 | 98.8.c.g.79.2 | 4 | |||
7.5 | odd | 6 | 98.8.c.k.67.1 | 4 | |||
7.6 | odd | 2 | 98.8.a.g.1.2 | 2 | |||
8.3 | odd | 2 | 448.8.a.s.1.1 | 2 | |||
8.5 | even | 2 | 448.8.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.8.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
98.8.a.g.1.2 | 2 | 7.6 | odd | 2 | |||
98.8.c.g.67.2 | 4 | 7.2 | even | 3 | |||
98.8.c.g.79.2 | 4 | 7.4 | even | 3 | |||
98.8.c.k.67.1 | 4 | 7.5 | odd | 6 | |||
98.8.c.k.79.1 | 4 | 7.3 | odd | 6 | |||
112.8.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
126.8.a.i.1.1 | 2 | 3.2 | odd | 2 | |||
350.8.a.j.1.2 | 2 | 5.4 | even | 2 | |||
350.8.c.k.99.1 | 4 | 5.3 | odd | 4 | |||
350.8.c.k.99.4 | 4 | 5.2 | odd | 4 | |||
448.8.a.l.1.2 | 2 | 8.5 | even | 2 | |||
448.8.a.s.1.1 | 2 | 8.3 | odd | 2 |