Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,24,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, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
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: | \(33.5204037345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1492261}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 373065 \) |
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 | \(-610.291\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2048.00 | 0.707107 | ||||||||
\(3\) | 247238. | 0.805786 | 0.402893 | − | 0.915247i | \(-0.368005\pi\) | ||||
0.402893 | + | 0.915247i | \(0.368005\pi\) | |||||||
\(4\) | 4.19430e6 | 0.500000 | ||||||||
\(5\) | −4.88281e7 | −0.447214 | ||||||||
\(6\) | 5.06342e8 | 0.569777 | ||||||||
\(7\) | −3.52608e9 | −0.674007 | −0.337004 | − | 0.941503i | \(-0.609413\pi\) | ||||
−0.337004 | + | 0.941503i | \(0.609413\pi\) | |||||||
\(8\) | 8.58993e9 | 0.353553 | ||||||||
\(9\) | −3.30168e10 | −0.350708 | ||||||||
\(10\) | −1.00000e11 | −0.316228 | ||||||||
\(11\) | −6.19384e11 | −0.654552 | −0.327276 | − | 0.944929i | \(-0.606131\pi\) | ||||
−0.327276 | + | 0.944929i | \(0.606131\pi\) | |||||||
\(12\) | 1.03699e12 | 0.402893 | ||||||||
\(13\) | −9.21814e12 | −1.42658 | −0.713288 | − | 0.700871i | \(-0.752795\pi\) | ||||
−0.713288 | + | 0.700871i | \(0.752795\pi\) | |||||||
\(14\) | −7.22141e12 | −0.476595 | ||||||||
\(15\) | −1.20721e13 | −0.360359 | ||||||||
\(16\) | 1.75922e13 | 0.250000 | ||||||||
\(17\) | 2.96454e13 | 0.209795 | 0.104897 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104897 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(18\) | −6.76184e13 | −0.247988 | ||||||||
\(19\) | −3.56432e14 | −0.701957 | −0.350978 | − | 0.936384i | \(-0.614151\pi\) | ||||
−0.350978 | + | 0.936384i | \(0.614151\pi\) | |||||||
\(20\) | −2.04800e14 | −0.223607 | ||||||||
\(21\) | −8.71779e14 | −0.543106 | ||||||||
\(22\) | −1.26850e15 | −0.462838 | ||||||||
\(23\) | 2.73214e15 | 0.597905 | 0.298953 | − | 0.954268i | \(-0.403363\pi\) | ||||
0.298953 | + | 0.954268i | \(0.403363\pi\) | |||||||
\(24\) | 2.12375e15 | 0.284889 | ||||||||
\(25\) | 2.38419e15 | 0.200000 | ||||||||
\(26\) | −1.88788e16 | −1.00874 | ||||||||
\(27\) | −3.14387e16 | −1.08838 | ||||||||
\(28\) | −1.47894e16 | −0.337004 | ||||||||
\(29\) | 5.96584e16 | 0.908018 | 0.454009 | − | 0.890997i | \(-0.349993\pi\) | ||||
0.454009 | + | 0.890997i | \(0.349993\pi\) | |||||||
\(30\) | −2.47238e16 | −0.254812 | ||||||||
\(31\) | 5.61319e16 | 0.396780 | 0.198390 | − | 0.980123i | \(-0.436429\pi\) | ||||
0.198390 | + | 0.980123i | \(0.436429\pi\) | |||||||
\(32\) | 3.60288e16 | 0.176777 | ||||||||
\(33\) | −1.53135e17 | −0.527429 | ||||||||
\(34\) | 6.07138e16 | 0.148347 | ||||||||
\(35\) | 1.72172e17 | 0.301425 | ||||||||
\(36\) | −1.38482e17 | −0.175354 | ||||||||
\(37\) | −1.59225e18 | −1.47127 | −0.735634 | − | 0.677380i | \(-0.763115\pi\) | ||||
−0.735634 | + | 0.677380i | \(0.763115\pi\) | |||||||
\(38\) | −7.29973e17 | −0.496359 | ||||||||
\(39\) | −2.27907e18 | −1.14952 | ||||||||
\(40\) | −4.19430e17 | −0.158114 | ||||||||
\(41\) | −4.81098e18 | −1.36527 | −0.682636 | − | 0.730759i | \(-0.739167\pi\) | ||||
−0.682636 | + | 0.730759i | \(0.739167\pi\) | |||||||
\(42\) | −1.78540e18 | −0.384034 | ||||||||
\(43\) | −7.53412e18 | −1.23636 | −0.618180 | − | 0.786036i | \(-0.712130\pi\) | ||||
−0.618180 | + | 0.786036i | \(0.712130\pi\) | |||||||
\(44\) | −2.59788e18 | −0.327276 | ||||||||
\(45\) | 1.61215e18 | 0.156841 | ||||||||
\(46\) | 5.59542e18 | 0.422783 | ||||||||
\(47\) | 1.70653e18 | 0.100691 | 0.0503454 | − | 0.998732i | \(-0.483968\pi\) | ||||
0.0503454 | + | 0.998732i | \(0.483968\pi\) | |||||||
\(48\) | 4.34945e18 | 0.201447 | ||||||||
\(49\) | −1.49355e19 | −0.545715 | ||||||||
\(50\) | 4.88281e18 | 0.141421 | ||||||||
\(51\) | 7.32946e18 | 0.169050 | ||||||||
\(52\) | −3.86637e19 | −0.713288 | ||||||||
\(53\) | 7.71411e19 | 1.14318 | 0.571589 | − | 0.820540i | \(-0.306327\pi\) | ||||
0.571589 | + | 0.820540i | \(0.306327\pi\) | |||||||
\(54\) | −6.43865e19 | −0.769603 | ||||||||
\(55\) | 3.02434e19 | 0.292725 | ||||||||
\(56\) | −3.02888e19 | −0.238297 | ||||||||
\(57\) | −8.81234e19 | −0.565627 | ||||||||
\(58\) | 1.22180e20 | 0.642066 | ||||||||
\(59\) | 2.22753e20 | 0.961668 | 0.480834 | − | 0.876812i | \(-0.340334\pi\) | ||||
0.480834 | + | 0.876812i | \(0.340334\pi\) | |||||||
\(60\) | −5.06342e19 | −0.180179 | ||||||||
\(61\) | 2.72118e20 | 0.800690 | 0.400345 | − | 0.916364i | \(-0.368890\pi\) | ||||
0.400345 | + | 0.916364i | \(0.368890\pi\) | |||||||
\(62\) | 1.14958e20 | 0.280566 | ||||||||
\(63\) | 1.16420e20 | 0.236380 | ||||||||
\(64\) | 7.37870e19 | 0.125000 | ||||||||
\(65\) | 4.50105e20 | 0.637984 | ||||||||
\(66\) | −3.13620e20 | −0.372949 | ||||||||
\(67\) | 6.39125e20 | 0.639331 | 0.319665 | − | 0.947531i | \(-0.396430\pi\) | ||||
0.319665 | + | 0.947531i | \(0.396430\pi\) | |||||||
\(68\) | 1.24342e20 | 0.104897 | ||||||||
\(69\) | 6.75487e20 | 0.481784 | ||||||||
\(70\) | 3.52608e20 | 0.213140 | ||||||||
\(71\) | −2.68803e21 | −1.38027 | −0.690134 | − | 0.723681i | \(-0.742448\pi\) | ||||
−0.690134 | + | 0.723681i | \(0.742448\pi\) | |||||||
\(72\) | −2.83612e20 | −0.123994 | ||||||||
\(73\) | 4.36224e21 | 1.62741 | 0.813704 | − | 0.581280i | \(-0.197448\pi\) | ||||
0.813704 | + | 0.581280i | \(0.197448\pi\) | |||||||
\(74\) | −3.26093e21 | −1.04034 | ||||||||
\(75\) | 5.89460e20 | 0.161157 | ||||||||
\(76\) | −1.49498e21 | −0.350978 | ||||||||
\(77\) | 2.18400e21 | 0.441173 | ||||||||
\(78\) | −4.66754e21 | −0.812830 | ||||||||
\(79\) | −3.18360e21 | −0.478859 | −0.239429 | − | 0.970914i | \(-0.576960\pi\) | ||||
−0.239429 | + | 0.970914i | \(0.576960\pi\) | |||||||
\(80\) | −8.58993e20 | −0.111803 | ||||||||
\(81\) | −4.66452e21 | −0.526296 | ||||||||
\(82\) | −9.85289e21 | −0.965393 | ||||||||
\(83\) | −2.75933e21 | −0.235183 | −0.117592 | − | 0.993062i | \(-0.537517\pi\) | ||||
−0.117592 | + | 0.993062i | \(0.537517\pi\) | |||||||
\(84\) | −3.65651e21 | −0.271553 | ||||||||
\(85\) | −1.44753e21 | −0.0938231 | ||||||||
\(86\) | −1.54299e22 | −0.874239 | ||||||||
\(87\) | 1.47498e22 | 0.731668 | ||||||||
\(88\) | −5.32047e21 | −0.231419 | ||||||||
\(89\) | −1.40148e22 | −0.535304 | −0.267652 | − | 0.963516i | \(-0.586248\pi\) | ||||
−0.267652 | + | 0.963516i | \(0.586248\pi\) | |||||||
\(90\) | 3.30168e21 | 0.110904 | ||||||||
\(91\) | 3.25039e22 | 0.961522 | ||||||||
\(92\) | 1.14594e22 | 0.298953 | ||||||||
\(93\) | 1.38779e22 | 0.319720 | ||||||||
\(94\) | 3.49498e21 | 0.0711991 | ||||||||
\(95\) | 1.74039e22 | 0.313925 | ||||||||
\(96\) | 8.90767e21 | 0.142444 | ||||||||
\(97\) | 1.12387e23 | 1.59529 | 0.797644 | − | 0.603128i | \(-0.206079\pi\) | ||||
0.797644 | + | 0.603128i | \(0.206079\pi\) | |||||||
\(98\) | −3.05880e22 | −0.385878 | ||||||||
\(99\) | 2.04501e22 | 0.229557 | ||||||||
\(100\) | 1.00000e22 | 0.100000 | ||||||||
\(101\) | 1.15829e23 | 1.03305 | 0.516525 | − | 0.856272i | \(-0.327225\pi\) | ||||
0.516525 | + | 0.856272i | \(0.327225\pi\) | |||||||
\(102\) | 1.50107e22 | 0.119536 | ||||||||
\(103\) | −1.69254e23 | −1.20479 | −0.602394 | − | 0.798199i | \(-0.705786\pi\) | ||||
−0.602394 | + | 0.798199i | \(0.705786\pi\) | |||||||
\(104\) | −7.91832e22 | −0.504371 | ||||||||
\(105\) | 4.25673e22 | 0.242884 | ||||||||
\(106\) | 1.57985e23 | 0.808348 | ||||||||
\(107\) | 1.60256e23 | 0.736041 | 0.368020 | − | 0.929818i | \(-0.380036\pi\) | ||||
0.368020 | + | 0.929818i | \(0.380036\pi\) | |||||||
\(108\) | −1.31864e23 | −0.544191 | ||||||||
\(109\) | −1.24517e23 | −0.462193 | −0.231096 | − | 0.972931i | \(-0.574231\pi\) | ||||
−0.231096 | + | 0.972931i | \(0.574231\pi\) | |||||||
\(110\) | 6.19384e22 | 0.206987 | ||||||||
\(111\) | −3.93664e23 | −1.18553 | ||||||||
\(112\) | −6.20314e22 | −0.168502 | ||||||||
\(113\) | −8.30660e22 | −0.203714 | −0.101857 | − | 0.994799i | \(-0.532478\pi\) | ||||
−0.101857 | + | 0.994799i | \(0.532478\pi\) | |||||||
\(114\) | −1.80477e23 | −0.399959 | ||||||||
\(115\) | −1.33405e23 | −0.267391 | ||||||||
\(116\) | 2.50225e23 | 0.454009 | ||||||||
\(117\) | 3.04353e23 | 0.500312 | ||||||||
\(118\) | 4.56198e23 | 0.680002 | ||||||||
\(119\) | −1.04532e23 | −0.141403 | ||||||||
\(120\) | −1.03699e23 | −0.127406 | ||||||||
\(121\) | −5.11794e23 | −0.571562 | ||||||||
\(122\) | 5.57298e23 | 0.566174 | ||||||||
\(123\) | −1.18945e24 | −1.10012 | ||||||||
\(124\) | 2.35434e23 | 0.198390 | ||||||||
\(125\) | −1.16415e23 | −0.0894427 | ||||||||
\(126\) | 2.38428e23 | 0.167146 | ||||||||
\(127\) | −1.35449e24 | −0.867031 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(128\) | 1.51116e23 | 0.0883883 | ||||||||
\(129\) | −1.86272e24 | −0.996243 | ||||||||
\(130\) | 9.21814e23 | 0.451123 | ||||||||
\(131\) | −3.88681e24 | −1.74170 | −0.870850 | − | 0.491548i | \(-0.836431\pi\) | ||||
−0.870850 | + | 0.491548i | \(0.836431\pi\) | |||||||
\(132\) | −6.42295e23 | −0.263715 | ||||||||
\(133\) | 1.25681e24 | 0.473124 | ||||||||
\(134\) | 1.30893e24 | 0.452075 | ||||||||
\(135\) | 1.53509e24 | 0.486739 | ||||||||
\(136\) | 2.54652e23 | 0.0741737 | ||||||||
\(137\) | 4.74583e24 | 1.27065 | 0.635324 | − | 0.772246i | \(-0.280867\pi\) | ||||
0.635324 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(138\) | 1.38340e24 | 0.340673 | ||||||||
\(139\) | 8.52208e24 | 1.93141 | 0.965707 | − | 0.259633i | \(-0.0836015\pi\) | ||||
0.965707 | + | 0.259633i | \(0.0836015\pi\) | |||||||
\(140\) | 7.22141e23 | 0.150713 | ||||||||
\(141\) | 4.21919e23 | 0.0811352 | ||||||||
\(142\) | −5.50509e24 | −0.975997 | ||||||||
\(143\) | 5.70957e24 | 0.933768 | ||||||||
\(144\) | −5.80837e23 | −0.0876771 | ||||||||
\(145\) | −2.91301e24 | −0.406078 | ||||||||
\(146\) | 8.93386e24 | 1.15075 | ||||||||
\(147\) | −3.69262e24 | −0.439729 | ||||||||
\(148\) | −6.67838e24 | −0.735634 | ||||||||
\(149\) | 4.97391e24 | 0.507056 | 0.253528 | − | 0.967328i | \(-0.418409\pi\) | ||||
0.253528 | + | 0.967328i | \(0.418409\pi\) | |||||||
\(150\) | 1.20721e24 | 0.113955 | ||||||||
\(151\) | 2.56571e24 | 0.224374 | 0.112187 | − | 0.993687i | \(-0.464214\pi\) | ||||
0.112187 | + | 0.993687i | \(0.464214\pi\) | |||||||
\(152\) | −3.06173e24 | −0.248179 | ||||||||
\(153\) | −9.78796e23 | −0.0735768 | ||||||||
\(154\) | 4.47282e24 | 0.311956 | ||||||||
\(155\) | −2.74082e24 | −0.177446 | ||||||||
\(156\) | −9.55911e24 | −0.574758 | ||||||||
\(157\) | −2.22180e25 | −1.24125 | −0.620623 | − | 0.784109i | \(-0.713120\pi\) | ||||
−0.620623 | + | 0.784109i | \(0.713120\pi\) | |||||||
\(158\) | −6.52002e24 | −0.338604 | ||||||||
\(159\) | 1.90722e25 | 0.921157 | ||||||||
\(160\) | −1.75922e24 | −0.0790569 | ||||||||
\(161\) | −9.63373e24 | −0.402992 | ||||||||
\(162\) | −9.55295e24 | −0.372147 | ||||||||
\(163\) | −2.96191e25 | −1.07501 | −0.537507 | − | 0.843259i | \(-0.680634\pi\) | ||||
−0.537507 | + | 0.843259i | \(0.680634\pi\) | |||||||
\(164\) | −2.01787e25 | −0.682636 | ||||||||
\(165\) | 7.47729e24 | 0.235873 | ||||||||
\(166\) | −5.65112e24 | −0.166300 | ||||||||
\(167\) | 1.84259e25 | 0.506044 | 0.253022 | − | 0.967460i | \(-0.418575\pi\) | ||||
0.253022 | + | 0.967460i | \(0.418575\pi\) | |||||||
\(168\) | −7.48852e24 | −0.192017 | ||||||||
\(169\) | 4.32202e25 | 1.03512 | ||||||||
\(170\) | −2.96454e24 | −0.0663430 | ||||||||
\(171\) | 1.17682e25 | 0.246182 | ||||||||
\(172\) | −3.16004e25 | −0.618180 | ||||||||
\(173\) | −9.26470e25 | −1.69551 | −0.847757 | − | 0.530385i | \(-0.822047\pi\) | ||||
−0.847757 | + | 0.530385i | \(0.822047\pi\) | |||||||
\(174\) | 3.02076e25 | 0.517368 | ||||||||
\(175\) | −8.40682e24 | −0.134801 | ||||||||
\(176\) | −1.08963e25 | −0.163638 | ||||||||
\(177\) | 5.50728e25 | 0.774899 | ||||||||
\(178\) | −2.87022e25 | −0.378517 | ||||||||
\(179\) | 1.33235e26 | 1.64744 | 0.823719 | − | 0.566998i | \(-0.191895\pi\) | ||||
0.823719 | + | 0.566998i | \(0.191895\pi\) | |||||||
\(180\) | 6.76184e24 | 0.0784207 | ||||||||
\(181\) | −3.72764e25 | −0.405630 | −0.202815 | − | 0.979217i | \(-0.565009\pi\) | ||||
−0.202815 | + | 0.979217i | \(0.565009\pi\) | |||||||
\(182\) | 6.65680e25 | 0.679899 | ||||||||
\(183\) | 6.72779e25 | 0.645185 | ||||||||
\(184\) | 2.34689e25 | 0.211391 | ||||||||
\(185\) | 7.77466e25 | 0.657971 | ||||||||
\(186\) | 2.84220e25 | 0.226076 | ||||||||
\(187\) | −1.83619e25 | −0.137322 | ||||||||
\(188\) | 7.15772e24 | 0.0503454 | ||||||||
\(189\) | 1.10855e26 | 0.733577 | ||||||||
\(190\) | 3.56432e25 | 0.221978 | ||||||||
\(191\) | −1.74153e26 | −1.02105 | −0.510525 | − | 0.859863i | \(-0.670549\pi\) | ||||
−0.510525 | + | 0.859863i | \(0.670549\pi\) | |||||||
\(192\) | 1.82429e25 | 0.100723 | ||||||||
\(193\) | −2.40877e26 | −1.25281 | −0.626407 | − | 0.779496i | \(-0.715475\pi\) | ||||
−0.626407 | + | 0.779496i | \(0.715475\pi\) | |||||||
\(194\) | 2.30168e26 | 1.12804 | ||||||||
\(195\) | 1.11283e26 | 0.514079 | ||||||||
\(196\) | −6.26441e25 | −0.272857 | ||||||||
\(197\) | −2.32299e26 | −0.954303 | −0.477152 | − | 0.878821i | \(-0.658331\pi\) | ||||
−0.477152 | + | 0.878821i | \(0.658331\pi\) | |||||||
\(198\) | 4.18817e25 | 0.162321 | ||||||||
\(199\) | −3.32534e26 | −1.21626 | −0.608129 | − | 0.793838i | \(-0.708080\pi\) | ||||
−0.608129 | + | 0.793838i | \(0.708080\pi\) | |||||||
\(200\) | 2.04800e25 | 0.0707107 | ||||||||
\(201\) | 1.58016e26 | 0.515164 | ||||||||
\(202\) | 2.37218e26 | 0.730476 | ||||||||
\(203\) | −2.10360e26 | −0.612010 | ||||||||
\(204\) | 3.07420e25 | 0.0845249 | ||||||||
\(205\) | 2.34911e26 | 0.610568 | ||||||||
\(206\) | −3.46632e26 | −0.851913 | ||||||||
\(207\) | −9.02064e25 | −0.209690 | ||||||||
\(208\) | −1.62167e26 | −0.356644 | ||||||||
\(209\) | 2.20768e26 | 0.459467 | ||||||||
\(210\) | 8.71779e25 | 0.171745 | ||||||||
\(211\) | −4.88737e26 | −0.911647 | −0.455823 | − | 0.890070i | \(-0.650655\pi\) | ||||
−0.455823 | + | 0.890070i | \(0.650655\pi\) | |||||||
\(212\) | 3.23553e26 | 0.571589 | ||||||||
\(213\) | −6.64583e26 | −1.11220 | ||||||||
\(214\) | 3.28205e26 | 0.520459 | ||||||||
\(215\) | 3.67877e26 | 0.552917 | ||||||||
\(216\) | −2.70057e26 | −0.384801 | ||||||||
\(217\) | −1.97925e26 | −0.267433 | ||||||||
\(218\) | −2.55010e26 | −0.326820 | ||||||||
\(219\) | 1.07851e27 | 1.31134 | ||||||||
\(220\) | 1.26850e26 | 0.146362 | ||||||||
\(221\) | −2.73276e26 | −0.299288 | ||||||||
\(222\) | −8.06224e26 | −0.838294 | ||||||||
\(223\) | −1.80253e27 | −1.77982 | −0.889909 | − | 0.456138i | \(-0.849232\pi\) | ||||
−0.889909 | + | 0.456138i | \(0.849232\pi\) | |||||||
\(224\) | −1.27040e26 | −0.119149 | ||||||||
\(225\) | −7.87182e25 | −0.0701416 | ||||||||
\(226\) | −1.70119e26 | −0.144048 | ||||||||
\(227\) | 7.37727e26 | 0.593743 | 0.296871 | − | 0.954917i | \(-0.404057\pi\) | ||||
0.296871 | + | 0.954917i | \(0.404057\pi\) | |||||||
\(228\) | −3.69616e26 | −0.282814 | ||||||||
\(229\) | 1.94352e27 | 1.41410 | 0.707052 | − | 0.707162i | \(-0.250025\pi\) | ||||
0.707052 | + | 0.707162i | \(0.250025\pi\) | |||||||
\(230\) | −2.73214e26 | −0.189074 | ||||||||
\(231\) | 5.39966e26 | 0.355491 | ||||||||
\(232\) | 5.12461e26 | 0.321033 | ||||||||
\(233\) | −2.43138e26 | −0.144964 | −0.0724820 | − | 0.997370i | \(-0.523092\pi\) | ||||
−0.0724820 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(234\) | 6.23316e26 | 0.353774 | ||||||||
\(235\) | −8.33269e25 | −0.0450303 | ||||||||
\(236\) | 9.34293e26 | 0.480834 | ||||||||
\(237\) | −7.87106e26 | −0.385858 | ||||||||
\(238\) | −2.14082e26 | −0.0999872 | ||||||||
\(239\) | 3.60889e27 | 1.60619 | 0.803097 | − | 0.595848i | \(-0.203184\pi\) | ||||
0.803097 | + | 0.595848i | \(0.203184\pi\) | |||||||
\(240\) | −2.12375e26 | −0.0900897 | ||||||||
\(241\) | 2.00066e27 | 0.809056 | 0.404528 | − | 0.914526i | \(-0.367436\pi\) | ||||
0.404528 | + | 0.914526i | \(0.367436\pi\) | |||||||
\(242\) | −1.04815e27 | −0.404155 | ||||||||
\(243\) | 1.80649e27 | 0.664301 | ||||||||
\(244\) | 1.14135e27 | 0.400345 | ||||||||
\(245\) | 7.29274e26 | 0.244051 | ||||||||
\(246\) | −2.43600e27 | −0.777901 | ||||||||
\(247\) | 3.28564e27 | 1.00139 | ||||||||
\(248\) | 4.82169e26 | 0.140283 | ||||||||
\(249\) | −6.82211e26 | −0.189507 | ||||||||
\(250\) | −2.38419e26 | −0.0632456 | ||||||||
\(251\) | −1.85132e27 | −0.469065 | −0.234533 | − | 0.972108i | \(-0.575356\pi\) | ||||
−0.234533 | + | 0.972108i | \(0.575356\pi\) | |||||||
\(252\) | 4.88300e26 | 0.118190 | ||||||||
\(253\) | −1.69224e27 | −0.391360 | ||||||||
\(254\) | −2.77400e27 | −0.613083 | ||||||||
\(255\) | −3.57884e26 | −0.0756014 | ||||||||
\(256\) | 3.09485e26 | 0.0625000 | ||||||||
\(257\) | −7.13742e27 | −1.37819 | −0.689097 | − | 0.724669i | \(-0.741992\pi\) | ||||
−0.689097 | + | 0.724669i | \(0.741992\pi\) | |||||||
\(258\) | −3.81484e27 | −0.704450 | ||||||||
\(259\) | 5.61440e27 | 0.991644 | ||||||||
\(260\) | 1.88788e27 | 0.318992 | ||||||||
\(261\) | −1.96973e27 | −0.318449 | ||||||||
\(262\) | −7.96019e27 | −1.23157 | ||||||||
\(263\) | −5.02930e27 | −0.744761 | −0.372380 | − | 0.928080i | \(-0.621458\pi\) | ||||
−0.372380 | + | 0.928080i | \(0.621458\pi\) | |||||||
\(264\) | −1.31542e27 | −0.186474 | ||||||||
\(265\) | −3.76666e27 | −0.511244 | ||||||||
\(266\) | 2.57394e27 | 0.334549 | ||||||||
\(267\) | −3.46497e27 | −0.431341 | ||||||||
\(268\) | 2.68068e27 | 0.319665 | ||||||||
\(269\) | −1.17031e28 | −1.33705 | −0.668527 | − | 0.743688i | \(-0.733075\pi\) | ||||
−0.668527 | + | 0.743688i | \(0.733075\pi\) | |||||||
\(270\) | 3.14387e27 | 0.344177 | ||||||||
\(271\) | −1.49314e27 | −0.156659 | −0.0783294 | − | 0.996928i | \(-0.524959\pi\) | ||||
−0.0783294 | + | 0.996928i | \(0.524959\pi\) | |||||||
\(272\) | 5.21528e26 | 0.0524487 | ||||||||
\(273\) | 8.03618e27 | 0.774781 | ||||||||
\(274\) | 9.71945e27 | 0.898484 | ||||||||
\(275\) | −1.47673e27 | −0.130910 | ||||||||
\(276\) | 2.83320e27 | 0.240892 | ||||||||
\(277\) | 3.00946e27 | 0.245454 | 0.122727 | − | 0.992440i | \(-0.460836\pi\) | ||||
0.122727 | + | 0.992440i | \(0.460836\pi\) | |||||||
\(278\) | 1.74532e28 | 1.36572 | ||||||||
\(279\) | −1.85329e27 | −0.139154 | ||||||||
\(280\) | 1.47894e27 | 0.106570 | ||||||||
\(281\) | −1.97459e28 | −1.36569 | −0.682847 | − | 0.730562i | \(-0.739258\pi\) | ||||
−0.682847 | + | 0.730562i | \(0.739258\pi\) | |||||||
\(282\) | 8.64091e26 | 0.0573713 | ||||||||
\(283\) | 2.06841e28 | 1.31854 | 0.659270 | − | 0.751906i | \(-0.270866\pi\) | ||||
0.659270 | + | 0.751906i | \(0.270866\pi\) | |||||||
\(284\) | −1.12744e28 | −0.690134 | ||||||||
\(285\) | 4.30290e27 | 0.252956 | ||||||||
\(286\) | 1.16932e28 | 0.660274 | ||||||||
\(287\) | 1.69639e28 | 0.920203 | ||||||||
\(288\) | −1.18956e27 | −0.0619970 | ||||||||
\(289\) | −1.90887e28 | −0.955986 | ||||||||
\(290\) | −5.96584e27 | −0.287140 | ||||||||
\(291\) | 2.77862e28 | 1.28546 | ||||||||
\(292\) | 1.82965e28 | 0.813704 | ||||||||
\(293\) | −2.59950e28 | −1.11151 | −0.555754 | − | 0.831347i | \(-0.687570\pi\) | ||||
−0.555754 | + | 0.831347i | \(0.687570\pi\) | |||||||
\(294\) | −7.56249e27 | −0.310936 | ||||||||
\(295\) | −1.08766e28 | −0.430071 | ||||||||
\(296\) | −1.36773e28 | −0.520171 | ||||||||
\(297\) | 1.94726e28 | 0.712403 | ||||||||
\(298\) | 1.01866e28 | 0.358543 | ||||||||
\(299\) | −2.51852e28 | −0.852957 | ||||||||
\(300\) | 2.47238e27 | 0.0805786 | ||||||||
\(301\) | 2.65659e28 | 0.833316 | ||||||||
\(302\) | 5.25458e27 | 0.158657 | ||||||||
\(303\) | 2.86372e28 | 0.832417 | ||||||||
\(304\) | −6.27042e27 | −0.175489 | ||||||||
\(305\) | −1.32870e28 | −0.358080 | ||||||||
\(306\) | −2.00457e27 | −0.0520266 | ||||||||
\(307\) | 5.17015e28 | 1.29245 | 0.646223 | − | 0.763149i | \(-0.276348\pi\) | ||||
0.646223 | + | 0.763149i | \(0.276348\pi\) | |||||||
\(308\) | 9.16034e27 | 0.220586 | ||||||||
\(309\) | −4.18459e28 | −0.970801 | ||||||||
\(310\) | −5.61319e27 | −0.125473 | ||||||||
\(311\) | 2.19009e28 | 0.471756 | 0.235878 | − | 0.971783i | \(-0.424203\pi\) | ||||
0.235878 | + | 0.971783i | \(0.424203\pi\) | |||||||
\(312\) | −1.95771e28 | −0.406415 | ||||||||
\(313\) | −3.44520e28 | −0.689373 | −0.344686 | − | 0.938718i | \(-0.612015\pi\) | ||||
−0.344686 | + | 0.938718i | \(0.612015\pi\) | |||||||
\(314\) | −4.55024e28 | −0.877694 | ||||||||
\(315\) | −5.68456e27 | −0.105712 | ||||||||
\(316\) | −1.33530e28 | −0.239429 | ||||||||
\(317\) | −4.25122e28 | −0.735075 | −0.367538 | − | 0.930009i | \(-0.619799\pi\) | ||||
−0.367538 | + | 0.930009i | \(0.619799\pi\) | |||||||
\(318\) | 3.90598e28 | 0.651356 | ||||||||
\(319\) | −3.69514e28 | −0.594345 | ||||||||
\(320\) | −3.60288e27 | −0.0559017 | ||||||||
\(321\) | 3.96214e28 | 0.593092 | ||||||||
\(322\) | −1.97299e28 | −0.284959 | ||||||||
\(323\) | −1.05666e28 | −0.147267 | ||||||||
\(324\) | −1.95644e28 | −0.263148 | ||||||||
\(325\) | −2.19778e28 | −0.285315 | ||||||||
\(326\) | −6.06599e28 | −0.760150 | ||||||||
\(327\) | −3.07852e28 | −0.372429 | ||||||||
\(328\) | −4.13260e28 | −0.482697 | ||||||||
\(329\) | −6.01737e27 | −0.0678663 | ||||||||
\(330\) | 1.53135e28 | 0.166788 | ||||||||
\(331\) | 1.43295e29 | 1.50733 | 0.753667 | − | 0.657256i | \(-0.228283\pi\) | ||||
0.753667 | + | 0.657256i | \(0.228283\pi\) | |||||||
\(332\) | −1.15735e28 | −0.117592 | ||||||||
\(333\) | 5.25710e28 | 0.515985 | ||||||||
\(334\) | 3.77362e28 | 0.357827 | ||||||||
\(335\) | −3.12073e28 | −0.285917 | ||||||||
\(336\) | −1.53365e28 | −0.135776 | ||||||||
\(337\) | 1.66695e28 | 0.142619 | 0.0713095 | − | 0.997454i | \(-0.477282\pi\) | ||||
0.0713095 | + | 0.997454i | \(0.477282\pi\) | |||||||
\(338\) | 8.85150e28 | 0.731939 | ||||||||
\(339\) | −2.05370e28 | −0.164150 | ||||||||
\(340\) | −6.07138e27 | −0.0469116 | ||||||||
\(341\) | −3.47672e28 | −0.259713 | ||||||||
\(342\) | 2.41014e28 | 0.174077 | ||||||||
\(343\) | 1.49168e29 | 1.04182 | ||||||||
\(344\) | −6.47176e28 | −0.437120 | ||||||||
\(345\) | −3.29827e28 | −0.215460 | ||||||||
\(346\) | −1.89741e29 | −1.19891 | ||||||||
\(347\) | −7.87942e28 | −0.481621 | −0.240811 | − | 0.970572i | \(-0.577413\pi\) | ||||
−0.240811 | + | 0.970572i | \(0.577413\pi\) | |||||||
\(348\) | 6.18651e28 | 0.365834 | ||||||||
\(349\) | −1.45984e29 | −0.835244 | −0.417622 | − | 0.908621i | \(-0.637136\pi\) | ||||
−0.417622 | + | 0.908621i | \(0.637136\pi\) | |||||||
\(350\) | −1.72172e28 | −0.0953190 | ||||||||
\(351\) | 2.89807e29 | 1.55266 | ||||||||
\(352\) | −2.23157e28 | −0.115710 | ||||||||
\(353\) | 5.29769e28 | 0.265875 | 0.132937 | − | 0.991124i | \(-0.457559\pi\) | ||||
0.132937 | + | 0.991124i | \(0.457559\pi\) | |||||||
\(354\) | 1.12789e29 | 0.547936 | ||||||||
\(355\) | 1.31252e29 | 0.617275 | ||||||||
\(356\) | −5.87822e28 | −0.267652 | ||||||||
\(357\) | −2.58442e28 | −0.113941 | ||||||||
\(358\) | 2.72866e29 | 1.16492 | ||||||||
\(359\) | 2.82466e29 | 1.16783 | 0.583915 | − | 0.811815i | \(-0.301520\pi\) | ||||
0.583915 | + | 0.811815i | \(0.301520\pi\) | |||||||
\(360\) | 1.38482e28 | 0.0554518 | ||||||||
\(361\) | −1.30786e29 | −0.507256 | ||||||||
\(362\) | −7.63420e28 | −0.286824 | ||||||||
\(363\) | −1.26535e29 | −0.460557 | ||||||||
\(364\) | 1.36331e29 | 0.480761 | ||||||||
\(365\) | −2.13000e29 | −0.727799 | ||||||||
\(366\) | 1.37785e29 | 0.456215 | ||||||||
\(367\) | 2.59135e29 | 0.831509 | 0.415755 | − | 0.909477i | \(-0.363517\pi\) | ||||
0.415755 | + | 0.909477i | \(0.363517\pi\) | |||||||
\(368\) | 4.80643e28 | 0.149476 | ||||||||
\(369\) | 1.58843e29 | 0.478812 | ||||||||
\(370\) | 1.59225e29 | 0.465255 | ||||||||
\(371\) | −2.72006e29 | −0.770509 | ||||||||
\(372\) | 5.82082e28 | 0.159860 | ||||||||
\(373\) | −6.81722e29 | −1.81533 | −0.907665 | − | 0.419695i | \(-0.862137\pi\) | ||||
−0.907665 | + | 0.419695i | \(0.862137\pi\) | |||||||
\(374\) | −3.76052e28 | −0.0971011 | ||||||||
\(375\) | −2.87822e28 | −0.0720717 | ||||||||
\(376\) | 1.46590e28 | 0.0355996 | ||||||||
\(377\) | −5.49939e29 | −1.29536 | ||||||||
\(378\) | 2.27032e29 | 0.518718 | ||||||||
\(379\) | 8.03139e29 | 1.78008 | 0.890041 | − | 0.455881i | \(-0.150676\pi\) | ||||
0.890041 | + | 0.455881i | \(0.150676\pi\) | |||||||
\(380\) | 7.29973e28 | 0.156962 | ||||||||
\(381\) | −3.34882e29 | −0.698642 | ||||||||
\(382\) | −3.56665e29 | −0.721992 | ||||||||
\(383\) | −9.93629e29 | −1.95181 | −0.975907 | − | 0.218189i | \(-0.929985\pi\) | ||||
−0.975907 | + | 0.218189i | \(0.929985\pi\) | |||||||
\(384\) | 3.73615e28 | 0.0712221 | ||||||||
\(385\) | −1.06640e29 | −0.197298 | ||||||||
\(386\) | −4.93317e29 | −0.885874 | ||||||||
\(387\) | 2.48752e29 | 0.433602 | ||||||||
\(388\) | 4.71383e29 | 0.797644 | ||||||||
\(389\) | −8.33130e29 | −1.36865 | −0.684325 | − | 0.729177i | \(-0.739903\pi\) | ||||
−0.684325 | + | 0.729177i | \(0.739903\pi\) | |||||||
\(390\) | 2.27907e29 | 0.363509 | ||||||||
\(391\) | 8.09953e28 | 0.125437 | ||||||||
\(392\) | −1.28295e29 | −0.192939 | ||||||||
\(393\) | −9.60966e29 | −1.40344 | ||||||||
\(394\) | −4.75749e29 | −0.674794 | ||||||||
\(395\) | 1.55449e29 | 0.214152 | ||||||||
\(396\) | 8.57738e28 | 0.114778 | ||||||||
\(397\) | 6.39815e29 | 0.831694 | 0.415847 | − | 0.909435i | \(-0.363485\pi\) | ||||
0.415847 | + | 0.909435i | \(0.363485\pi\) | |||||||
\(398\) | −6.81030e29 | −0.860025 | ||||||||
\(399\) | 3.10730e29 | 0.381237 | ||||||||
\(400\) | 4.19430e28 | 0.0500000 | ||||||||
\(401\) | 1.37492e30 | 1.59264 | 0.796318 | − | 0.604879i | \(-0.206778\pi\) | ||||
0.796318 | + | 0.604879i | \(0.206778\pi\) | |||||||
\(402\) | 3.23616e29 | 0.364276 | ||||||||
\(403\) | −5.17432e29 | −0.566037 | ||||||||
\(404\) | 4.85821e29 | 0.516525 | ||||||||
\(405\) | 2.27760e29 | 0.235367 | ||||||||
\(406\) | −4.30817e29 | −0.432757 | ||||||||
\(407\) | 9.86214e29 | 0.963021 | ||||||||
\(408\) | 6.29596e28 | 0.0597682 | ||||||||
\(409\) | 2.04005e30 | 1.88288 | 0.941440 | − | 0.337181i | \(-0.109473\pi\) | ||||
0.941440 | + | 0.337181i | \(0.109473\pi\) | |||||||
\(410\) | 4.81098e29 | 0.431737 | ||||||||
\(411\) | 1.17335e30 | 1.02387 | ||||||||
\(412\) | −7.09902e29 | −0.602394 | ||||||||
\(413\) | −7.85444e29 | −0.648171 | ||||||||
\(414\) | −1.84743e29 | −0.148273 | ||||||||
\(415\) | 1.34733e29 | 0.105177 | ||||||||
\(416\) | −3.32119e29 | −0.252185 | ||||||||
\(417\) | 2.10698e30 | 1.55631 | ||||||||
\(418\) | 4.52134e29 | 0.324892 | ||||||||
\(419\) | −5.19038e29 | −0.362859 | −0.181430 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181430 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(420\) | 1.78540e29 | 0.121442 | ||||||||
\(421\) | −1.09510e30 | −0.724787 | −0.362394 | − | 0.932025i | \(-0.618040\pi\) | ||||
−0.362394 | + | 0.932025i | \(0.618040\pi\) | |||||||
\(422\) | −1.00093e30 | −0.644632 | ||||||||
\(423\) | −5.63443e28 | −0.0353131 | ||||||||
\(424\) | 6.62637e29 | 0.404174 | ||||||||
\(425\) | 7.06802e28 | 0.0419590 | ||||||||
\(426\) | −1.36106e30 | −0.786445 | ||||||||
\(427\) | −9.59510e29 | −0.539671 | ||||||||
\(428\) | 6.72164e29 | 0.368020 | ||||||||
\(429\) | 1.41162e30 | 0.752418 | ||||||||
\(430\) | 7.53412e29 | 0.390972 | ||||||||
\(431\) | −1.78506e30 | −0.901911 | −0.450956 | − | 0.892546i | \(-0.648917\pi\) | ||||
−0.450956 | + | 0.892546i | \(0.648917\pi\) | |||||||
\(432\) | −5.53076e29 | −0.272096 | ||||||||
\(433\) | 1.83380e27 | 0.000878501 0 | 0.000439250 | − | 1.00000i | \(-0.499860\pi\) | ||||
0.000439250 | 1.00000i | \(0.499860\pi\) | ||||||||
\(434\) | −4.05351e29 | −0.189104 | ||||||||
\(435\) | −7.20204e29 | −0.327212 | ||||||||
\(436\) | −5.22261e29 | −0.231096 | ||||||||
\(437\) | −9.73821e29 | −0.419704 | ||||||||
\(438\) | 2.20879e30 | 0.927260 | ||||||||
\(439\) | 2.76531e30 | 1.13084 | 0.565420 | − | 0.824803i | \(-0.308714\pi\) | ||||
0.565420 | + | 0.824803i | \(0.308714\pi\) | |||||||
\(440\) | 2.59788e29 | 0.103494 | ||||||||
\(441\) | 4.93123e29 | 0.191387 | ||||||||
\(442\) | −5.59668e29 | −0.211629 | ||||||||
\(443\) | −4.05895e30 | −1.49545 | −0.747724 | − | 0.664010i | \(-0.768853\pi\) | ||||
−0.747724 | + | 0.664010i | \(0.768853\pi\) | |||||||
\(444\) | −1.65115e30 | −0.592764 | ||||||||
\(445\) | 6.84314e29 | 0.239395 | ||||||||
\(446\) | −3.69157e30 | −1.25852 | ||||||||
\(447\) | 1.22974e30 | 0.408579 | ||||||||
\(448\) | −2.60179e29 | −0.0842509 | ||||||||
\(449\) | −2.95251e30 | −0.931876 | −0.465938 | − | 0.884817i | \(-0.654283\pi\) | ||||
−0.465938 | + | 0.884817i | \(0.654283\pi\) | |||||||
\(450\) | −1.61215e29 | −0.0495976 | ||||||||
\(451\) | 2.97984e30 | 0.893641 | ||||||||
\(452\) | −3.48404e29 | −0.101857 | ||||||||
\(453\) | 6.34340e29 | 0.180798 | ||||||||
\(454\) | 1.51086e30 | 0.419840 | ||||||||
\(455\) | −1.58710e30 | −0.430006 | ||||||||
\(456\) | −7.56974e29 | −0.199979 | ||||||||
\(457\) | −7.87636e29 | −0.202903 | −0.101452 | − | 0.994840i | \(-0.532349\pi\) | ||||
−0.101452 | + | 0.994840i | \(0.532349\pi\) | |||||||
\(458\) | 3.98033e30 | 0.999923 | ||||||||
\(459\) | −9.32014e29 | −0.228337 | ||||||||
\(460\) | −5.59542e29 | −0.133696 | ||||||||
\(461\) | 5.04802e30 | 1.17641 | 0.588207 | − | 0.808710i | \(-0.299834\pi\) | ||||
0.588207 | + | 0.808710i | \(0.299834\pi\) | |||||||
\(462\) | 1.10585e30 | 0.251370 | ||||||||
\(463\) | −3.07277e30 | −0.681316 | −0.340658 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340658 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(464\) | 1.04952e30 | 0.227004 | ||||||||
\(465\) | −6.77632e29 | −0.142983 | ||||||||
\(466\) | −4.97947e29 | −0.102505 | ||||||||
\(467\) | −7.91191e30 | −1.58905 | −0.794524 | − | 0.607233i | \(-0.792279\pi\) | ||||
−0.794524 | + | 0.607233i | \(0.792279\pi\) | |||||||
\(468\) | 1.27655e30 | 0.250156 | ||||||||
\(469\) | −2.25360e30 | −0.430913 | ||||||||
\(470\) | −1.70653e29 | −0.0318412 | ||||||||
\(471\) | −5.49311e30 | −1.00018 | ||||||||
\(472\) | 1.91343e30 | 0.340001 | ||||||||
\(473\) | 4.66651e30 | 0.809262 | ||||||||
\(474\) | −1.61199e30 | −0.272843 | ||||||||
\(475\) | −8.49801e29 | −0.140391 | ||||||||
\(476\) | −4.38439e29 | −0.0707016 | ||||||||
\(477\) | −2.54695e30 | −0.400922 | ||||||||
\(478\) | 7.39101e30 | 1.13575 | ||||||||
\(479\) | −1.14342e30 | −0.171533 | −0.0857664 | − | 0.996315i | \(-0.527334\pi\) | ||||
−0.0857664 | + | 0.996315i | \(0.527334\pi\) | |||||||
\(480\) | −4.34945e29 | −0.0637030 | ||||||||
\(481\) | 1.46776e31 | 2.09887 | ||||||||
\(482\) | 4.09736e30 | 0.572089 | ||||||||
\(483\) | −2.38182e30 | −0.324726 | ||||||||
\(484\) | −2.14662e30 | −0.285781 | ||||||||
\(485\) | −5.48762e30 | −0.713435 | ||||||||
\(486\) | 3.69970e30 | 0.469731 | ||||||||
\(487\) | 3.69536e30 | 0.458220 | 0.229110 | − | 0.973401i | \(-0.426419\pi\) | ||||
0.229110 | + | 0.973401i | \(0.426419\pi\) | |||||||
\(488\) | 2.33748e30 | 0.283087 | ||||||||
\(489\) | −7.32295e30 | −0.866232 | ||||||||
\(490\) | 1.49355e30 | 0.172570 | ||||||||
\(491\) | 9.29094e30 | 1.04863 | 0.524315 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524315 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(492\) | −4.98894e30 | −0.550059 | ||||||||
\(493\) | 1.76860e30 | 0.190497 | ||||||||
\(494\) | 6.72900e30 | 0.708093 | ||||||||
\(495\) | −9.98539e29 | −0.102661 | ||||||||
\(496\) | 9.87483e29 | 0.0991951 | ||||||||
\(497\) | 9.47821e30 | 0.930311 | ||||||||
\(498\) | −1.39717e30 | −0.134002 | ||||||||
\(499\) | 3.27584e29 | 0.0307019 | 0.0153510 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153510 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(500\) | −4.88281e29 | −0.0447214 | ||||||||
\(501\) | 4.55557e30 | 0.407764 | ||||||||
\(502\) | −3.79150e30 | −0.331679 | ||||||||
\(503\) | 1.69287e30 | 0.144741 | 0.0723705 | − | 0.997378i | \(-0.476944\pi\) | ||||
0.0723705 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(504\) | 1.00004e30 | 0.0835729 | ||||||||
\(505\) | −5.65571e30 | −0.461994 | ||||||||
\(506\) | −3.46571e30 | −0.276733 | ||||||||
\(507\) | 1.06857e31 | 0.834084 | ||||||||
\(508\) | −5.68116e30 | −0.433515 | ||||||||
\(509\) | −7.45718e30 | −0.556315 | −0.278157 | − | 0.960536i | \(-0.589724\pi\) | ||||
−0.278157 | + | 0.960536i | \(0.589724\pi\) | |||||||
\(510\) | −7.32946e29 | −0.0534583 | ||||||||
\(511\) | −1.53816e31 | −1.09688 | ||||||||
\(512\) | 6.33825e29 | 0.0441942 | ||||||||
\(513\) | 1.12058e31 | 0.763998 | ||||||||
\(514\) | −1.46174e31 | −0.974530 | ||||||||
\(515\) | 8.26435e30 | 0.538797 | ||||||||
\(516\) | −7.81280e30 | −0.498121 | ||||||||
\(517\) | −1.05700e30 | −0.0659073 | ||||||||
\(518\) | 1.14983e31 | 0.701198 | ||||||||
\(519\) | −2.29058e31 | −1.36622 | ||||||||
\(520\) | 3.86637e30 | 0.225561 | ||||||||
\(521\) | 9.54796e30 | 0.544850 | 0.272425 | − | 0.962177i | \(-0.412174\pi\) | ||||
0.272425 | + | 0.962177i | \(0.412174\pi\) | |||||||
\(522\) | −4.03400e30 | −0.225178 | ||||||||
\(523\) | −1.33111e31 | −0.726851 | −0.363425 | − | 0.931623i | \(-0.618393\pi\) | ||||
−0.363425 | + | 0.931623i | \(0.618393\pi\) | |||||||
\(524\) | −1.63025e31 | −0.870850 | ||||||||
\(525\) | −2.07848e30 | −0.108621 | ||||||||
\(526\) | −1.03000e31 | −0.526625 | ||||||||
\(527\) | 1.66405e30 | 0.0832425 | ||||||||
\(528\) | −2.69398e30 | −0.131857 | ||||||||
\(529\) | −1.34159e31 | −0.642509 | ||||||||
\(530\) | −7.71411e30 | −0.361504 | ||||||||
\(531\) | −7.35458e30 | −0.337265 | ||||||||
\(532\) | 5.27143e30 | 0.236562 | ||||||||
\(533\) | 4.43483e31 | 1.94766 | ||||||||
\(534\) | −7.09627e30 | −0.305004 | ||||||||
\(535\) | −7.82502e30 | −0.329167 | ||||||||
\(536\) | 5.49004e30 | 0.226038 | ||||||||
\(537\) | 3.29408e31 | 1.32748 | ||||||||
\(538\) | −2.39679e31 | −0.945440 | ||||||||
\(539\) | 9.25082e30 | 0.357198 | ||||||||
\(540\) | 6.43865e30 | 0.243370 | ||||||||
\(541\) | −2.43916e31 | −0.902551 | −0.451275 | − | 0.892385i | \(-0.649031\pi\) | ||||
−0.451275 | + | 0.892385i | \(0.649031\pi\) | |||||||
\(542\) | −3.05796e30 | −0.110775 | ||||||||
\(543\) | −9.21611e30 | −0.326851 | ||||||||
\(544\) | 1.06809e30 | 0.0370868 | ||||||||
\(545\) | 6.07992e30 | 0.206699 | ||||||||
\(546\) | 1.64581e31 | 0.547853 | ||||||||
\(547\) | −3.76722e31 | −1.22791 | −0.613955 | − | 0.789341i | \(-0.710422\pi\) | ||||
−0.613955 | + | 0.789341i | \(0.710422\pi\) | |||||||
\(548\) | 1.99054e31 | 0.635324 | ||||||||
\(549\) | −8.98447e30 | −0.280809 | ||||||||
\(550\) | −3.02434e30 | −0.0925676 | ||||||||
\(551\) | −2.12642e31 | −0.637389 | ||||||||
\(552\) | 5.80239e30 | 0.170336 | ||||||||
\(553\) | 1.12256e31 | 0.322754 | ||||||||
\(554\) | 6.16337e30 | 0.173563 | ||||||||
\(555\) | 1.92219e31 | 0.530184 | ||||||||
\(556\) | 3.57442e31 | 0.965707 | ||||||||
\(557\) | 6.10400e30 | 0.161540 | 0.0807700 | − | 0.996733i | \(-0.474262\pi\) | ||||
0.0807700 | + | 0.996733i | \(0.474262\pi\) | |||||||
\(558\) | −3.79555e30 | −0.0983968 | ||||||||
\(559\) | 6.94506e31 | 1.76376 | ||||||||
\(560\) | 3.02888e30 | 0.0753563 | ||||||||
\(561\) | −4.53975e30 | −0.110652 | ||||||||
\(562\) | −4.04395e31 | −0.965691 | ||||||||
\(563\) | 1.68208e31 | 0.393549 | 0.196775 | − | 0.980449i | \(-0.436953\pi\) | ||||
0.196775 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(564\) | 1.76966e30 | 0.0405676 | ||||||||
\(565\) | 4.05596e30 | 0.0911038 | ||||||||
\(566\) | 4.23611e31 | 0.932348 | ||||||||
\(567\) | 1.64475e31 | 0.354727 | ||||||||
\(568\) | −2.30900e31 | −0.487999 | ||||||||
\(569\) | 6.94377e31 | 1.43815 | 0.719076 | − | 0.694932i | \(-0.244566\pi\) | ||||
0.719076 | + | 0.694932i | \(0.244566\pi\) | |||||||
\(570\) | 8.81234e30 | 0.178867 | ||||||||
\(571\) | 2.16544e31 | 0.430756 | 0.215378 | − | 0.976531i | \(-0.430902\pi\) | ||||
0.215378 | + | 0.976531i | \(0.430902\pi\) | |||||||
\(572\) | 2.39477e31 | 0.466884 | ||||||||
\(573\) | −4.30572e31 | −0.822749 | ||||||||
\(574\) | 3.47420e31 | 0.650682 | ||||||||
\(575\) | 6.51392e30 | 0.119581 | ||||||||
\(576\) | −2.43621e30 | −0.0438385 | ||||||||
\(577\) | −2.82605e30 | −0.0498492 | −0.0249246 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249246 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(578\) | −3.90937e31 | −0.675984 | ||||||||
\(579\) | −5.95539e31 | −1.00950 | ||||||||
\(580\) | −1.22180e31 | −0.203039 | ||||||||
\(581\) | 9.72963e30 | 0.158515 | ||||||||
\(582\) | 5.69061e31 | 0.908959 | ||||||||
\(583\) | −4.77800e31 | −0.748269 | ||||||||
\(584\) | 3.74713e31 | 0.575376 | ||||||||
\(585\) | −1.48610e31 | −0.223746 | ||||||||
\(586\) | −5.32378e31 | −0.785955 | ||||||||
\(587\) | −8.73921e31 | −1.26513 | −0.632563 | − | 0.774509i | \(-0.717997\pi\) | ||||
−0.632563 | + | 0.774509i | \(0.717997\pi\) | |||||||
\(588\) | −1.54880e31 | −0.219865 | ||||||||
\(589\) | −2.00072e31 | −0.278523 | ||||||||
\(590\) | −2.22753e31 | −0.304106 | ||||||||
\(591\) | −5.74331e31 | −0.768965 | ||||||||
\(592\) | −2.80112e31 | −0.367817 | ||||||||
\(593\) | −7.84285e31 | −1.01005 | −0.505027 | − | 0.863103i | \(-0.668518\pi\) | ||||
−0.505027 | + | 0.863103i | \(0.668518\pi\) | |||||||
\(594\) | 3.98800e31 | 0.503745 | ||||||||
\(595\) | 5.10410e30 | 0.0632374 | ||||||||
\(596\) | 2.08621e31 | 0.253528 | ||||||||
\(597\) | −8.22149e31 | −0.980045 | ||||||||
\(598\) | −5.15793e31 | −0.603132 | ||||||||
\(599\) | 1.13954e32 | 1.30714 | 0.653570 | − | 0.756866i | \(-0.273271\pi\) | ||||
0.653570 | + | 0.756866i | \(0.273271\pi\) | |||||||
\(600\) | 5.06342e30 | 0.0569777 | ||||||||
\(601\) | −1.12055e32 | −1.23701 | −0.618506 | − | 0.785780i | \(-0.712262\pi\) | ||||
−0.618506 | + | 0.785780i | \(0.712262\pi\) | |||||||
\(602\) | 5.44069e31 | 0.589243 | ||||||||
\(603\) | −2.11019e31 | −0.224219 | ||||||||
\(604\) | 1.07614e31 | 0.112187 | ||||||||
\(605\) | 2.49899e31 | 0.255610 | ||||||||
\(606\) | 5.86491e31 | 0.588608 | ||||||||
\(607\) | −2.47121e31 | −0.243355 | −0.121677 | − | 0.992570i | \(-0.538827\pi\) | ||||
−0.121677 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(608\) | −1.28418e31 | −0.124090 | ||||||||
\(609\) | −5.20089e31 | −0.493150 | ||||||||
\(610\) | −2.72118e31 | −0.253201 | ||||||||
\(611\) | −1.57311e31 | −0.143643 | ||||||||
\(612\) | −4.10537e30 | −0.0367884 | ||||||||
\(613\) | 2.06753e32 | 1.81826 | 0.909131 | − | 0.416511i | \(-0.136747\pi\) | ||||
0.909131 | + | 0.416511i | \(0.136747\pi\) | |||||||
\(614\) | 1.05885e32 | 0.913897 | ||||||||
\(615\) | 5.80788e31 | 0.491988 | ||||||||
\(616\) | 1.87604e31 | 0.155978 | ||||||||
\(617\) | −1.21753e32 | −0.993572 | −0.496786 | − | 0.867873i | \(-0.665487\pi\) | ||||
−0.496786 | + | 0.867873i | \(0.665487\pi\) | |||||||
\(618\) | −8.57004e31 | −0.686460 | ||||||||
\(619\) | 2.23981e32 | 1.76104 | 0.880518 | − | 0.474012i | \(-0.157195\pi\) | ||||
0.880518 | + | 0.474012i | \(0.157195\pi\) | |||||||
\(620\) | −1.14958e31 | −0.0887228 | ||||||||
\(621\) | −8.58949e31 | −0.650749 | ||||||||
\(622\) | 4.48530e31 | 0.333582 | ||||||||
\(623\) | 4.94171e31 | 0.360799 | ||||||||
\(624\) | −4.00938e31 | −0.287379 | ||||||||
\(625\) | 5.68434e30 | 0.0400000 | ||||||||
\(626\) | −7.05576e31 | −0.487460 | ||||||||
\(627\) | 5.45822e31 | 0.370233 | ||||||||
\(628\) | −9.31889e31 | −0.620623 | ||||||||
\(629\) | −4.72029e31 | −0.308664 | ||||||||
\(630\) | −1.16420e31 | −0.0747499 | ||||||||
\(631\) | 7.64725e31 | 0.482134 | 0.241067 | − | 0.970508i | \(-0.422503\pi\) | ||||
0.241067 | + | 0.970508i | \(0.422503\pi\) | |||||||
\(632\) | −2.73469e31 | −0.169302 | ||||||||
\(633\) | −1.20834e32 | −0.734593 | ||||||||
\(634\) | −8.70649e31 | −0.519777 | ||||||||
\(635\) | 6.61374e31 | 0.387748 | ||||||||
\(636\) | 7.99945e31 | 0.460578 | ||||||||
\(637\) | 1.37678e32 | 0.778503 | ||||||||
\(638\) | −7.56765e31 | −0.420265 | ||||||||
\(639\) | 8.87502e31 | 0.484071 | ||||||||
\(640\) | −7.37870e30 | −0.0395285 | ||||||||
\(641\) | −5.00356e31 | −0.263276 | −0.131638 | − | 0.991298i | \(-0.542024\pi\) | ||||
−0.131638 | + | 0.991298i | \(0.542024\pi\) | |||||||
\(642\) | 8.11446e31 | 0.419379 | ||||||||
\(643\) | 1.82713e32 | 0.927565 | 0.463783 | − | 0.885949i | \(-0.346492\pi\) | ||||
0.463783 | + | 0.885949i | \(0.346492\pi\) | |||||||
\(644\) | −4.04068e31 | −0.201496 | ||||||||
\(645\) | 9.09530e31 | 0.445533 | ||||||||
\(646\) | −2.16404e31 | −0.104133 | ||||||||
\(647\) | 1.03583e32 | 0.489653 | 0.244826 | − | 0.969567i | \(-0.421269\pi\) | ||||
0.244826 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(648\) | −4.00680e31 | −0.186074 | ||||||||
\(649\) | −1.37970e32 | −0.629461 | ||||||||
\(650\) | −4.50105e31 | −0.201748 | ||||||||
\(651\) | −4.89346e31 | −0.215494 | ||||||||
\(652\) | −1.24231e32 | −0.537507 | ||||||||
\(653\) | 2.79465e32 | 1.18802 | 0.594012 | − | 0.804456i | \(-0.297543\pi\) | ||||
0.594012 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(654\) | −6.30481e31 | −0.263347 | ||||||||
\(655\) | 1.89786e32 | 0.778912 | ||||||||
\(656\) | −8.46357e31 | −0.341318 | ||||||||
\(657\) | −1.44027e32 | −0.570745 | ||||||||
\(658\) | −1.23236e31 | −0.0479887 | ||||||||
\(659\) | 1.29327e32 | 0.494886 | 0.247443 | − | 0.968902i | \(-0.420410\pi\) | ||||
0.247443 | + | 0.968902i | \(0.420410\pi\) | |||||||
\(660\) | 3.13620e31 | 0.117937 | ||||||||
\(661\) | 1.04268e32 | 0.385330 | 0.192665 | − | 0.981265i | \(-0.438287\pi\) | ||||
0.192665 | + | 0.981265i | \(0.438287\pi\) | |||||||
\(662\) | 2.93468e32 | 1.06585 | ||||||||
\(663\) | −6.75640e31 | −0.241162 | ||||||||
\(664\) | −2.37025e31 | −0.0831498 | ||||||||
\(665\) | −6.13676e31 | −0.211587 | ||||||||
\(666\) | 1.07665e32 | 0.364857 | ||||||||
\(667\) | 1.62995e32 | 0.542909 | ||||||||
\(668\) | 7.72837e31 | 0.253022 | ||||||||
\(669\) | −4.45652e32 | −1.43415 | ||||||||
\(670\) | −6.39125e31 | −0.202174 | ||||||||
\(671\) | −1.68546e32 | −0.524093 | ||||||||
\(672\) | −3.14091e31 | −0.0960084 | ||||||||
\(673\) | 9.42317e31 | 0.283155 | 0.141577 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141577 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(674\) | 3.41390e31 | 0.100847 | ||||||||
\(675\) | −7.49557e31 | −0.217676 | ||||||||
\(676\) | 1.81279e32 | 0.517559 | ||||||||
\(677\) | −2.82722e32 | −0.793577 | −0.396789 | − | 0.917910i | \(-0.629875\pi\) | ||||
−0.396789 | + | 0.917910i | \(0.629875\pi\) | |||||||
\(678\) | −4.20599e31 | −0.116072 | ||||||||
\(679\) | −3.96284e32 | −1.07524 | ||||||||
\(680\) | −1.24342e31 | −0.0331715 | ||||||||
\(681\) | 1.82394e32 | 0.478430 | ||||||||
\(682\) | −7.12032e31 | −0.183645 | ||||||||
\(683\) | −6.52604e31 | −0.165505 | −0.0827525 | − | 0.996570i | \(-0.526371\pi\) | ||||
−0.0827525 | + | 0.996570i | \(0.526371\pi\) | |||||||
\(684\) | 4.93596e31 | 0.123091 | ||||||||
\(685\) | −2.31730e32 | −0.568251 | ||||||||
\(686\) | 3.05496e32 | 0.736680 | ||||||||
\(687\) | 4.80512e32 | 1.13947 | ||||||||
\(688\) | −1.32542e32 | −0.309090 | ||||||||
\(689\) | −7.11098e32 | −1.63083 | ||||||||
\(690\) | −6.75487e31 | −0.152353 | ||||||||
\(691\) | −5.18137e31 | −0.114934 | −0.0574668 | − | 0.998347i | \(-0.518302\pi\) | ||||
−0.0574668 | + | 0.998347i | \(0.518302\pi\) | |||||||
\(692\) | −3.88590e32 | −0.847757 | ||||||||
\(693\) | −7.21085e31 | −0.154723 | ||||||||
\(694\) | −1.61371e32 | −0.340558 | ||||||||
\(695\) | −4.16117e32 | −0.863755 | ||||||||
\(696\) | 1.26700e32 | 0.258684 | ||||||||
\(697\) | −1.42623e32 | −0.286427 | ||||||||
\(698\) | −2.98976e32 | −0.590607 | ||||||||
\(699\) | −6.01129e31 | −0.116810 | ||||||||
\(700\) | −3.52608e31 | −0.0674007 | ||||||||
\(701\) | −6.09165e32 | −1.14545 | −0.572727 | − | 0.819746i | \(-0.694114\pi\) | ||||
−0.572727 | + | 0.819746i | \(0.694114\pi\) | |||||||
\(702\) | 5.93524e32 | 1.09790 | ||||||||
\(703\) | 5.67529e32 | 1.03277 | ||||||||
\(704\) | −4.57025e31 | −0.0818190 | ||||||||
\(705\) | −2.06015e31 | −0.0362848 | ||||||||
\(706\) | 1.08497e32 | 0.188002 | ||||||||
\(707\) | −4.08422e32 | −0.696282 | ||||||||
\(708\) | 2.30992e32 | 0.387449 | ||||||||
\(709\) | 8.97201e32 | 1.48067 | 0.740334 | − | 0.672239i | \(-0.234667\pi\) | ||||
0.740334 | + | 0.672239i | \(0.234667\pi\) | |||||||
\(710\) | 2.68803e32 | 0.436479 | ||||||||
\(711\) | 1.05112e32 | 0.167940 | ||||||||
\(712\) | −1.20386e32 | −0.189259 | ||||||||
\(713\) | 1.53360e32 | 0.237237 | ||||||||
\(714\) | −5.29290e31 | −0.0805683 | ||||||||
\(715\) | −2.78788e32 | −0.417594 | ||||||||
\(716\) | 5.58829e32 | 0.823719 | ||||||||
\(717\) | 8.92254e32 | 1.29425 | ||||||||
\(718\) | 5.78490e32 | 0.825780 | ||||||||
\(719\) | −7.87343e32 | −1.10607 | −0.553034 | − | 0.833159i | \(-0.686530\pi\) | ||||
−0.553034 | + | 0.833159i | \(0.686530\pi\) | |||||||
\(720\) | 2.83612e31 | 0.0392104 | ||||||||
\(721\) | 5.96802e32 | 0.812035 | ||||||||
\(722\) | −2.67849e32 | −0.358684 | ||||||||
\(723\) | 4.94639e32 | 0.651926 | ||||||||
\(724\) | −1.56348e32 | −0.202815 | ||||||||
\(725\) | 1.42237e32 | 0.181604 | ||||||||
\(726\) | −2.59143e32 | −0.325663 | ||||||||
\(727\) | −3.15970e32 | −0.390841 | −0.195421 | − | 0.980720i | \(-0.562607\pi\) | ||||
−0.195421 | + | 0.980720i | \(0.562607\pi\) | |||||||
\(728\) | 2.79206e32 | 0.339949 | ||||||||
\(729\) | 8.85767e32 | 1.06158 | ||||||||
\(730\) | −4.36224e32 | −0.514631 | ||||||||
\(731\) | −2.23352e32 | −0.259382 | ||||||||
\(732\) | 2.82184e32 | 0.322593 | ||||||||
\(733\) | 9.47917e31 | 0.106678 | 0.0533389 | − | 0.998576i | \(-0.483014\pi\) | ||||
0.0533389 | + | 0.998576i | \(0.483014\pi\) | |||||||
\(734\) | 5.30709e32 | 0.587966 | ||||||||
\(735\) | 1.80304e32 | 0.196653 | ||||||||
\(736\) | 9.84356e31 | 0.105696 | ||||||||
\(737\) | −3.95864e32 | −0.418475 | ||||||||
\(738\) | 3.25311e32 | 0.338571 | ||||||||
\(739\) | −4.13181e32 | −0.423379 | −0.211689 | − | 0.977337i | \(-0.567897\pi\) | ||||
−0.211689 | + | 0.977337i | \(0.567897\pi\) | |||||||
\(740\) | 3.26093e32 | 0.328985 | ||||||||
\(741\) | 8.12334e32 | 0.806910 | ||||||||
\(742\) | −5.57068e32 | −0.544832 | ||||||||
\(743\) | 2.23848e32 | 0.215566 | 0.107783 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107783 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(744\) | 1.19210e32 | 0.113038 | ||||||||
\(745\) | −2.42867e32 | −0.226763 | ||||||||
\(746\) | −1.39617e33 | −1.28363 | ||||||||
\(747\) | 9.11043e31 | 0.0824807 | ||||||||
\(748\) | −7.70154e31 | −0.0686608 | ||||||||
\(749\) | −5.65076e32 | −0.496097 | ||||||||
\(750\) | −5.89460e31 | −0.0509624 | ||||||||
\(751\) | 1.65408e33 | 1.40831 | 0.704154 | − | 0.710047i | \(-0.251326\pi\) | ||||
0.704154 | + | 0.710047i | \(0.251326\pi\) | |||||||
\(752\) | 3.00217e31 | 0.0251727 | ||||||||
\(753\) | −4.57715e32 | −0.377967 | ||||||||
\(754\) | −1.12628e33 | −0.915955 | ||||||||
\(755\) | −1.25279e32 | −0.100343 | ||||||||
\(756\) | 4.64961e32 | 0.366789 | ||||||||
\(757\) | −6.98662e32 | −0.542831 | −0.271415 | − | 0.962462i | \(-0.587492\pi\) | ||||
−0.271415 | + | 0.962462i | \(0.587492\pi\) | |||||||
\(758\) | 1.64483e33 | 1.25871 | ||||||||
\(759\) | −4.18386e32 | −0.315353 | ||||||||
\(760\) | 1.49498e32 | 0.110989 | ||||||||
\(761\) | −9.28523e32 | −0.678999 | −0.339499 | − | 0.940606i | \(-0.610258\pi\) | ||||
−0.339499 | + | 0.940606i | \(0.610258\pi\) | |||||||
\(762\) | −6.85838e32 | −0.494014 | ||||||||
\(763\) | 4.39056e32 | 0.311521 | ||||||||
\(764\) | −7.30451e32 | −0.510525 | ||||||||
\(765\) | 4.77928e31 | 0.0329045 | ||||||||
\(766\) | −2.03495e33 | −1.38014 | ||||||||
\(767\) | −2.05337e33 | −1.37189 | ||||||||
\(768\) | 7.65163e31 | 0.0503617 | ||||||||
\(769\) | 1.31566e33 | 0.853081 | 0.426540 | − | 0.904469i | \(-0.359732\pi\) | ||||
0.426540 | + | 0.904469i | \(0.359732\pi\) | |||||||
\(770\) | −2.18400e32 | −0.139511 | ||||||||
\(771\) | −1.76464e33 | −1.11053 | ||||||||
\(772\) | −1.01031e33 | −0.626407 | ||||||||
\(773\) | −1.01794e33 | −0.621813 | −0.310906 | − | 0.950441i | \(-0.600633\pi\) | ||||
−0.310906 | + | 0.950441i | \(0.600633\pi\) | |||||||
\(774\) | 5.09445e32 | 0.306603 | ||||||||
\(775\) | 1.33829e32 | 0.0793561 | ||||||||
\(776\) | 9.65393e32 | 0.564020 | ||||||||
\(777\) | 1.38809e33 | 0.799054 | ||||||||
\(778\) | −1.70625e33 | −0.967781 | ||||||||
\(779\) | 1.71479e33 | 0.958362 | ||||||||
\(780\) | 4.66754e32 | 0.257039 | ||||||||
\(781\) | 1.66492e33 | 0.903457 | ||||||||
\(782\) | 1.65878e32 | 0.0886977 | ||||||||
\(783\) | −1.87558e33 | −0.988271 | ||||||||
\(784\) | −2.62749e32 | −0.136429 | ||||||||
\(785\) | 1.08486e33 | 0.555102 | ||||||||
\(786\) | −1.96806e33 | −0.992381 | ||||||||
\(787\) | 3.95568e33 | 1.96567 | 0.982837 | − | 0.184475i | \(-0.0590583\pi\) | ||||
0.982837 | + | 0.184475i | \(0.0590583\pi\) | |||||||
\(788\) | −9.74334e32 | −0.477152 | ||||||||
\(789\) | −1.24343e33 | −0.600118 | ||||||||
\(790\) | 3.18360e32 | 0.151428 | ||||||||
\(791\) | 2.92897e32 | 0.137305 | ||||||||
\(792\) | 1.75665e32 | 0.0811606 | ||||||||
\(793\) | −2.50842e33 | −1.14225 | ||||||||
\(794\) | 1.31034e33 | 0.588097 | ||||||||
\(795\) | −9.31259e32 | −0.411954 | ||||||||
\(796\) | −1.39475e33 | −0.608129 | ||||||||
\(797\) | 2.05790e33 | 0.884408 | 0.442204 | − | 0.896914i | \(-0.354197\pi\) | ||||
0.442204 | + | 0.896914i | \(0.354197\pi\) | |||||||
\(798\) | 6.36375e32 | 0.269575 | ||||||||
\(799\) | 5.05909e31 | 0.0211244 | ||||||||
\(800\) | 8.58993e31 | 0.0353553 | ||||||||
\(801\) | 4.62722e32 | 0.187736 | ||||||||
\(802\) | 2.81583e33 | 1.12616 | ||||||||
\(803\) | −2.70190e33 | −1.06522 | ||||||||
\(804\) | 6.62766e32 | 0.257582 | ||||||||
\(805\) | 4.70397e32 | 0.180224 | ||||||||
\(806\) | −1.05970e33 | −0.400249 | ||||||||
\(807\) | −2.89344e33 | −1.07738 | ||||||||
\(808\) | 9.94962e32 | 0.365238 | ||||||||
\(809\) | 3.34033e33 | 1.20887 | 0.604437 | − | 0.796653i | \(-0.293398\pi\) | ||||
0.604437 | + | 0.796653i | \(0.293398\pi\) | |||||||
\(810\) | 4.66452e32 | 0.166429 | ||||||||
\(811\) | 4.70664e33 | 1.65566 | 0.827830 | − | 0.560980i | \(-0.189575\pi\) | ||||
0.827830 | + | 0.560980i | \(0.189575\pi\) | |||||||
\(812\) | −8.82314e32 | −0.306005 | ||||||||
\(813\) | −3.69161e32 | −0.126234 | ||||||||
\(814\) | 2.01977e33 | 0.680958 | ||||||||
\(815\) | 1.44624e33 | 0.480761 | ||||||||
\(816\) | 1.28941e32 | 0.0422625 | ||||||||
\(817\) | 2.68540e33 | 0.867872 | ||||||||
\(818\) | 4.17802e33 | 1.33140 | ||||||||
\(819\) | −1.07317e33 | −0.337214 | ||||||||
\(820\) | 9.85289e32 | 0.305284 | ||||||||
\(821\) | −1.93945e33 | −0.592561 | −0.296281 | − | 0.955101i | \(-0.595746\pi\) | ||||
−0.296281 | + | 0.955101i | \(0.595746\pi\) | |||||||
\(822\) | 2.40301e33 | 0.723986 | ||||||||
\(823\) | −6.10374e33 | −1.81342 | −0.906709 | − | 0.421756i | \(-0.861414\pi\) | ||||
−0.906709 | + | 0.421756i | \(0.861414\pi\) | |||||||
\(824\) | −1.45388e33 | −0.425957 | ||||||||
\(825\) | −3.65102e32 | −0.105486 | ||||||||
\(826\) | −1.60859e33 | −0.458326 | ||||||||
\(827\) | −2.51659e33 | −0.707129 | −0.353564 | − | 0.935410i | \(-0.615030\pi\) | ||||
−0.353564 | + | 0.935410i | \(0.615030\pi\) | |||||||
\(828\) | −3.78353e32 | −0.104845 | ||||||||
\(829\) | 3.51989e33 | 0.961948 | 0.480974 | − | 0.876735i | \(-0.340283\pi\) | ||||
0.480974 | + | 0.876735i | \(0.340283\pi\) | |||||||
\(830\) | 2.75933e32 | 0.0743714 | ||||||||
\(831\) | 7.44051e32 | 0.197784 | ||||||||
\(832\) | −6.80179e32 | −0.178322 | ||||||||
\(833\) | −4.42770e32 | −0.114488 | ||||||||
\(834\) | 4.31509e33 | 1.10048 | ||||||||
\(835\) | −8.99701e32 | −0.226310 | ||||||||
\(836\) | 9.25970e32 | 0.229734 | ||||||||
\(837\) | −1.76471e33 | −0.431849 | ||||||||
\(838\) | −1.06299e33 | −0.256580 | ||||||||
\(839\) | −2.21395e33 | −0.527116 | −0.263558 | − | 0.964644i | \(-0.584896\pi\) | ||||
−0.263558 | + | 0.964644i | \(0.584896\pi\) | |||||||
\(840\) | 3.65651e32 | 0.0858726 | ||||||||
\(841\) | −7.57601e32 | −0.175504 | ||||||||
\(842\) | −2.24277e33 | −0.512502 | ||||||||
\(843\) | −4.88192e33 | −1.10046 | ||||||||
\(844\) | −2.04991e33 | −0.455823 | ||||||||
\(845\) | −2.11036e33 | −0.462919 | ||||||||
\(846\) | −1.15393e32 | −0.0249701 | ||||||||
\(847\) | 1.80462e33 | 0.385237 | ||||||||
\(848\) | 1.35708e33 | 0.285794 | ||||||||
\(849\) | 5.11389e33 | 1.06246 | ||||||||
\(850\) | 1.44753e32 | 0.0296695 | ||||||||
\(851\) | −4.35025e33 | −0.879678 | ||||||||
\(852\) | −2.78746e33 | −0.556101 | ||||||||
\(853\) | −1.33116e33 | −0.262008 | −0.131004 | − | 0.991382i | \(-0.541820\pi\) | ||||
−0.131004 | + | 0.991382i | \(0.541820\pi\) | |||||||
\(854\) | −1.96508e33 | −0.381605 | ||||||||
\(855\) | −5.74621e32 | −0.110096 | ||||||||
\(856\) | 1.37659e33 | 0.260230 | ||||||||
\(857\) | 2.64308e33 | 0.492982 | 0.246491 | − | 0.969145i | \(-0.420722\pi\) | ||||
0.246491 | + | 0.969145i | \(0.420722\pi\) | |||||||
\(858\) | 2.89100e33 | 0.532040 | ||||||||
\(859\) | −8.59233e32 | −0.156023 | −0.0780117 | − | 0.996952i | \(-0.524857\pi\) | ||||
−0.0780117 | + | 0.996952i | \(0.524857\pi\) | |||||||
\(860\) | 1.54299e33 | 0.276459 | ||||||||
\(861\) | 4.19411e33 | 0.741487 | ||||||||
\(862\) | −3.65580e33 | −0.637748 | ||||||||
\(863\) | 6.91408e33 | 1.19017 | 0.595087 | − | 0.803661i | \(-0.297118\pi\) | ||||
0.595087 | + | 0.803661i | \(0.297118\pi\) | |||||||
\(864\) | −1.13270e33 | −0.192401 | ||||||||
\(865\) | 4.52378e33 | 0.758257 | ||||||||
\(866\) | 3.75563e30 | 0.000621194 0 | ||||||||
\(867\) | −4.71945e33 | −0.770321 | ||||||||
\(868\) | −8.30159e32 | −0.133716 | ||||||||
\(869\) | 1.97187e33 | 0.313438 | ||||||||
\(870\) | −1.47498e33 | −0.231374 | ||||||||
\(871\) | −5.89154e33 | −0.912054 | ||||||||
\(872\) | −1.06959e33 | −0.163410 | ||||||||
\(873\) | −3.71064e33 | −0.559481 | ||||||||
\(874\) | −1.99439e33 | −0.296775 | ||||||||
\(875\) | 4.10489e32 | 0.0602850 | ||||||||
\(876\) | 4.52359e33 | 0.655672 | ||||||||
\(877\) | −8.45783e33 | −1.20994 | −0.604969 | − | 0.796249i | \(-0.706815\pi\) | ||||
−0.604969 | + | 0.796249i | \(0.706815\pi\) | |||||||
\(878\) | 5.66335e33 | 0.799625 | ||||||||
\(879\) | −6.42694e33 | −0.895638 | ||||||||
\(880\) | 5.32047e32 | 0.0731811 | ||||||||
\(881\) | −6.75908e33 | −0.917623 | −0.458812 | − | 0.888534i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888534i | \(0.651725\pi\) | |||||||
\(882\) | 1.00992e33 | 0.135331 | ||||||||
\(883\) | 1.02125e34 | 1.35077 | 0.675386 | − | 0.737464i | \(-0.263977\pi\) | ||||
0.675386 | + | 0.737464i | \(0.263977\pi\) | |||||||
\(884\) | −1.14620e33 | −0.149644 | ||||||||
\(885\) | −2.68910e33 | −0.346545 | ||||||||
\(886\) | −8.31273e33 | −1.05744 | ||||||||
\(887\) | 9.62143e33 | 1.20814 | 0.604071 | − | 0.796931i | \(-0.293544\pi\) | ||||
0.604071 | + | 0.796931i | \(0.293544\pi\) | |||||||
\(888\) | −3.38155e33 | −0.419147 | ||||||||
\(889\) | 4.77605e33 | 0.584385 | ||||||||
\(890\) | 1.40148e33 | 0.169278 | ||||||||
\(891\) | 2.88913e33 | 0.344488 | ||||||||
\(892\) | −7.56034e33 | −0.889909 | ||||||||
\(893\) | −6.08264e32 | −0.0706806 | ||||||||
\(894\) | 2.51850e33 | 0.288909 | ||||||||
\(895\) | −6.50563e33 | −0.736757 | ||||||||
\(896\) | −5.32846e32 | −0.0595744 | ||||||||
\(897\) | −6.22673e33 | −0.687301 | ||||||||
\(898\) | −6.04673e33 | −0.658936 | ||||||||
\(899\) | 3.34874e33 | 0.360284 | ||||||||
\(900\) | −3.30168e32 | −0.0350708 | ||||||||
\(901\) | 2.28688e33 | 0.239833 | ||||||||
\(902\) | 6.10272e33 | 0.631900 | ||||||||
\(903\) | 6.56808e33 | 0.671475 | ||||||||
\(904\) | −7.13532e32 | −0.0720239 | ||||||||
\(905\) | 1.82013e33 | 0.181403 | ||||||||
\(906\) | 1.29913e33 | 0.127843 | ||||||||
\(907\) | 4.24872e33 | 0.412833 | 0.206416 | − | 0.978464i | \(-0.433820\pi\) | ||||
0.206416 | + | 0.978464i | \(0.433820\pi\) | |||||||
\(908\) | 3.09425e33 | 0.296871 | ||||||||
\(909\) | −3.82430e33 | −0.362299 | ||||||||
\(910\) | −3.25039e33 | −0.304060 | ||||||||
\(911\) | 1.36929e34 | 1.26483 | 0.632417 | − | 0.774628i | \(-0.282063\pi\) | ||||
0.632417 | + | 0.774628i | \(0.282063\pi\) | |||||||
\(912\) | −1.55028e33 | −0.141407 | ||||||||
\(913\) | 1.70909e33 | 0.153940 | ||||||||
\(914\) | −1.61308e33 | −0.143474 | ||||||||
\(915\) | −3.28505e33 | −0.288536 | ||||||||
\(916\) | 8.15172e33 | 0.707052 | ||||||||
\(917\) | 1.37052e34 | 1.17392 | ||||||||
\(918\) | −1.90876e33 | −0.161459 | ||||||||
\(919\) | 5.57801e33 | 0.465963 | 0.232981 | − | 0.972481i | \(-0.425152\pi\) | ||||
0.232981 | + | 0.972481i | \(0.425152\pi\) | |||||||
\(920\) | −1.14594e33 | −0.0945371 | ||||||||
\(921\) | 1.27826e34 | 1.04143 | ||||||||
\(922\) | 1.03383e34 | 0.831851 | ||||||||
\(923\) | 2.47787e34 | 1.96906 | ||||||||
\(924\) | 2.26478e33 | 0.177745 | ||||||||
\(925\) | −3.79622e33 | −0.294253 | ||||||||
\(926\) | −6.29304e33 | −0.481763 | ||||||||
\(927\) | 5.58822e33 | 0.422529 | ||||||||
\(928\) | 2.14942e33 | 0.160516 | ||||||||
\(929\) | −1.60947e34 | −1.18714 | −0.593571 | − | 0.804782i | \(-0.702282\pi\) | ||||
−0.593571 | + | 0.804782i | \(0.702282\pi\) | |||||||
\(930\) | −1.38779e33 | −0.101104 | ||||||||
\(931\) | 5.32350e33 | 0.383068 | ||||||||
\(932\) | −1.01980e33 | −0.0724820 | ||||||||
\(933\) | 5.41473e33 | 0.380135 | ||||||||
\(934\) | −1.62036e34 | −1.12363 | ||||||||
\(935\) | 8.96577e32 | 0.0614121 | ||||||||
\(936\) | 2.61438e33 | 0.176887 | ||||||||
\(937\) | 2.39248e33 | 0.159898 | 0.0799489 | − | 0.996799i | \(-0.474524\pi\) | ||||
0.0799489 | + | 0.996799i | \(0.474524\pi\) | |||||||
\(938\) | −4.61538e33 | −0.304702 | ||||||||
\(939\) | −8.51782e33 | −0.555487 | ||||||||
\(940\) | −3.49498e32 | −0.0225151 | ||||||||
\(941\) | −1.12281e34 | −0.714537 | −0.357268 | − | 0.934002i | \(-0.616292\pi\) | ||||
−0.357268 | + | 0.934002i | \(0.616292\pi\) | |||||||
\(942\) | −1.12499e34 | −0.707234 | ||||||||
\(943\) | −1.31443e34 | −0.816303 | ||||||||
\(944\) | 3.91871e33 | 0.240417 | ||||||||
\(945\) | −5.41286e33 | −0.328066 | ||||||||
\(946\) | 9.55702e33 | 0.572235 | ||||||||
\(947\) | −4.28978e33 | −0.253752 | −0.126876 | − | 0.991919i | \(-0.540495\pi\) | ||||
−0.126876 | + | 0.991919i | \(0.540495\pi\) | |||||||
\(948\) | −3.30136e33 | −0.192929 | ||||||||
\(949\) | −4.02117e34 | −2.32162 | ||||||||
\(950\) | −1.74039e33 | −0.0992717 | ||||||||
\(951\) | −1.05106e34 | −0.592314 | ||||||||
\(952\) | −8.97923e32 | −0.0499936 | ||||||||
\(953\) | 3.92575e33 | 0.215951 | 0.107975 | − | 0.994154i | \(-0.465563\pi\) | ||||
0.107975 | + | 0.994154i | \(0.465563\pi\) | |||||||
\(954\) | −5.21616e33 | −0.283494 | ||||||||
\(955\) | 8.50357e33 | 0.456628 | ||||||||
\(956\) | 1.51368e34 | 0.803097 | ||||||||
\(957\) | −9.13578e33 | −0.478915 | ||||||||
\(958\) | −2.34172e33 | −0.121292 | ||||||||
\(959\) | −1.67341e34 | −0.856426 | ||||||||
\(960\) | −8.90767e32 | −0.0450448 | ||||||||
\(961\) | −1.68625e34 | −0.842565 | ||||||||
\(962\) | 3.00597e34 | 1.48413 | ||||||||
\(963\) | −5.29115e33 | −0.258136 | ||||||||
\(964\) | 8.39140e33 | 0.404528 | ||||||||
\(965\) | 1.17616e34 | 0.560276 | ||||||||
\(966\) | −4.87796e33 | −0.229616 | ||||||||
\(967\) | −2.44005e33 | −0.113500 | −0.0567498 | − | 0.998388i | \(-0.518074\pi\) | ||||
−0.0567498 | + | 0.998388i | \(0.518074\pi\) | |||||||
\(968\) | −4.39627e33 | −0.202078 | ||||||||
\(969\) | −2.61245e33 | −0.118666 | ||||||||
\(970\) | −1.12387e34 | −0.504475 | ||||||||
\(971\) | 1.61207e34 | 0.715094 | 0.357547 | − | 0.933895i | \(-0.383613\pi\) | ||||
0.357547 | + | 0.933895i | \(0.383613\pi\) | |||||||
\(972\) | 7.57699e33 | 0.332150 | ||||||||
\(973\) | −3.00495e34 | −1.30179 | ||||||||
\(974\) | 7.56810e33 | 0.324010 | ||||||||
\(975\) | −5.43373e33 | −0.229903 | ||||||||
\(976\) | 4.78716e33 | 0.200173 | ||||||||
\(977\) | −3.11737e34 | −1.28825 | −0.644126 | − | 0.764920i | \(-0.722779\pi\) | ||||
−0.644126 | + | 0.764920i | \(0.722779\pi\) | |||||||
\(978\) | −1.49974e34 | −0.612519 | ||||||||
\(979\) | 8.68052e33 | 0.350384 | ||||||||
\(980\) | 3.05880e33 | 0.122025 | ||||||||
\(981\) | 4.11114e33 | 0.162095 | ||||||||
\(982\) | 1.90278e34 | 0.741494 | ||||||||
\(983\) | 3.16423e34 | 1.21872 | 0.609358 | − | 0.792895i | \(-0.291427\pi\) | ||||
0.609358 | + | 0.792895i | \(0.291427\pi\) | |||||||
\(984\) | −1.02173e34 | −0.388950 | ||||||||
\(985\) | 1.13427e34 | 0.426777 | ||||||||
\(986\) | 3.62209e33 | 0.134702 | ||||||||
\(987\) | −1.48772e33 | −0.0546857 | ||||||||
\(988\) | 1.37810e34 | 0.500697 | ||||||||
\(989\) | −2.05842e34 | −0.739227 | ||||||||
\(990\) | −2.04501e33 | −0.0725922 | ||||||||
\(991\) | −2.83514e34 | −0.994779 | −0.497390 | − | 0.867527i | \(-0.665708\pi\) | ||||
−0.497390 | + | 0.867527i | \(0.665708\pi\) | |||||||
\(992\) | 2.02236e33 | 0.0701415 | ||||||||
\(993\) | 3.54279e34 | 1.21459 | ||||||||
\(994\) | 1.94114e34 | 0.657829 | ||||||||
\(995\) | 1.62370e34 | 0.543927 | ||||||||
\(996\) | −2.86140e33 | −0.0947537 | ||||||||
\(997\) | 1.22327e34 | 0.400430 | 0.200215 | − | 0.979752i | \(-0.435836\pi\) | ||||
0.200215 | + | 0.979752i | \(0.435836\pi\) | |||||||
\(998\) | 6.70891e32 | 0.0217096 | ||||||||
\(999\) | 5.00583e34 | 1.60130 |
(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 | 10.24.a.c.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.24.b.c.49.3 | 4 | |||
5.3 | odd | 4 | 50.24.b.c.49.2 | 4 | |||
5.4 | even | 2 | 50.24.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.24.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.24.a.b.1.1 | 2 | 5.4 | even | 2 | |||
50.24.b.c.49.2 | 4 | 5.3 | odd | 4 | |||
50.24.b.c.49.3 | 4 | 5.2 | odd | 4 |