Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,7,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.37");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(8.74205517755\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 5050x^{8} + 7354489x^{6} + 2475755792x^{4} + 232626987584x^{2} + 2900002611200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(11.5377i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.7.b.a.37.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.65685i | − | 0.707107i | ||||||
\(3\) | 14.3661i | 0.532078i | 0.963962 | + | 0.266039i | \(0.0857151\pi\) | ||||
−0.963962 | + | 0.266039i | \(0.914285\pi\) | |||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | −88.1981 | −0.705585 | −0.352792 | − | 0.935702i | \(-0.614768\pi\) | ||||
−0.352792 | + | 0.935702i | \(0.614768\pi\) | |||||||
\(6\) | 81.2670 | 0.376236 | ||||||||
\(7\) | 443.109 | 1.29186 | 0.645931 | − | 0.763396i | \(-0.276469\pi\) | ||||
0.645931 | + | 0.763396i | \(0.276469\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 522.615 | 0.716893 | ||||||||
\(10\) | 498.924i | 0.498924i | ||||||||
\(11\) | 843.338 | 0.633612 | 0.316806 | − | 0.948490i | \(-0.397390\pi\) | ||||
0.316806 | + | 0.948490i | \(0.397390\pi\) | |||||||
\(12\) | − | 459.716i | − | 0.266039i | ||||||
\(13\) | 2248.44i | 1.02342i | 0.859159 | + | 0.511708i | \(0.170987\pi\) | ||||
−0.859159 | + | 0.511708i | \(0.829013\pi\) | |||||||
\(14\) | − | 2506.60i | − | 0.913485i | ||||||
\(15\) | − | 1267.06i | − | 0.375426i | ||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 8662.52 | 1.76318 | 0.881592 | − | 0.472012i | \(-0.156472\pi\) | ||||
0.881592 | + | 0.472012i | \(0.156472\pi\) | |||||||
\(18\) | − | 2956.36i | − | 0.506920i | ||||||
\(19\) | 993.652 | − | 6786.64i | 0.144868 | − | 0.989451i | ||||
\(20\) | 2822.34 | 0.352792 | ||||||||
\(21\) | 6365.75i | 0.687372i | ||||||||
\(22\) | − | 4770.64i | − | 0.448032i | ||||||
\(23\) | −4047.37 | −0.332651 | −0.166326 | − | 0.986071i | \(-0.553190\pi\) | ||||
−0.166326 | + | 0.986071i | \(0.553190\pi\) | |||||||
\(24\) | −2600.54 | −0.188118 | ||||||||
\(25\) | −7846.10 | −0.502150 | ||||||||
\(26\) | 12719.1 | 0.723664 | ||||||||
\(27\) | 17980.8i | 0.913521i | ||||||||
\(28\) | −14179.5 | −0.645931 | ||||||||
\(29\) | 12069.5i | 0.494875i | 0.968904 | + | 0.247437i | \(0.0795884\pi\) | ||||
−0.968904 | + | 0.247437i | \(0.920412\pi\) | |||||||
\(30\) | −7167.60 | −0.265466 | ||||||||
\(31\) | 22921.6i | 0.769415i | 0.923039 | + | 0.384708i | \(0.125698\pi\) | ||||
−0.923039 | + | 0.384708i | \(0.874302\pi\) | |||||||
\(32\) | − | 5792.62i | − | 0.176777i | ||||||
\(33\) | 12115.5i | 0.337131i | ||||||||
\(34\) | − | 49002.6i | − | 1.24676i | ||||||
\(35\) | −39081.3 | −0.911518 | ||||||||
\(36\) | −16723.7 | −0.358446 | ||||||||
\(37\) | 71411.8i | 1.40982i | 0.709294 | + | 0.704912i | \(0.249014\pi\) | ||||
−0.709294 | + | 0.704912i | \(0.750986\pi\) | |||||||
\(38\) | −38391.1 | − | 5620.95i | −0.699647 | − | 0.102437i | ||||
\(39\) | −32301.4 | −0.544537 | ||||||||
\(40\) | − | 15965.6i | − | 0.249462i | ||||||
\(41\) | − | 134921.i | − | 1.95762i | −0.204766 | − | 0.978811i | \(-0.565643\pi\) | ||
0.204766 | − | 0.978811i | \(-0.434357\pi\) | |||||||
\(42\) | 36010.1 | 0.486045 | ||||||||
\(43\) | 28498.1 | 0.358435 | 0.179217 | − | 0.983810i | \(-0.442643\pi\) | ||||
0.179217 | + | 0.983810i | \(0.442643\pi\) | |||||||
\(44\) | −26986.8 | −0.316806 | ||||||||
\(45\) | −46093.6 | −0.505828 | ||||||||
\(46\) | 22895.4i | 0.235220i | ||||||||
\(47\) | 40848.6 | 0.393445 | 0.196723 | − | 0.980459i | \(-0.436970\pi\) | ||||
0.196723 | + | 0.980459i | \(0.436970\pi\) | |||||||
\(48\) | 14710.9i | 0.133020i | ||||||||
\(49\) | 78696.4 | 0.668908 | ||||||||
\(50\) | 44384.2i | 0.355074i | ||||||||
\(51\) | 124447.i | 0.938152i | ||||||||
\(52\) | − | 71950.2i | − | 0.511708i | ||||||
\(53\) | − | 153651.i | − | 1.03207i | −0.856568 | − | 0.516034i | \(-0.827408\pi\) | ||
0.856568 | − | 0.516034i | \(-0.172592\pi\) | |||||||
\(54\) | 101715. | 0.645957 | ||||||||
\(55\) | −74380.8 | −0.447067 | ||||||||
\(56\) | 80211.3i | 0.456742i | ||||||||
\(57\) | 97497.7 | + | 14274.9i | 0.526465 | + | 0.0770814i | ||||
\(58\) | 68275.4 | 0.349929 | ||||||||
\(59\) | 187198.i | 0.911477i | 0.890114 | + | 0.455739i | \(0.150625\pi\) | ||||
−0.890114 | + | 0.455739i | \(0.849375\pi\) | |||||||
\(60\) | 40546.0i | 0.187713i | ||||||||
\(61\) | 162214. | 0.714658 | 0.357329 | − | 0.933979i | \(-0.383688\pi\) | ||||
0.357329 | + | 0.933979i | \(0.383688\pi\) | |||||||
\(62\) | 129664. | 0.544059 | ||||||||
\(63\) | 231575. | 0.926127 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | − | 198308.i | − | 0.722106i | ||||||
\(66\) | 68535.6 | 0.238388 | ||||||||
\(67\) | − | 51055.2i | − | 0.169752i | −0.996392 | − | 0.0848761i | \(-0.972951\pi\) | ||
0.996392 | − | 0.0848761i | \(-0.0270494\pi\) | |||||||
\(68\) | −277201. | −0.881592 | ||||||||
\(69\) | − | 58145.0i | − | 0.176997i | ||||||
\(70\) | 221077.i | 0.644541i | ||||||||
\(71\) | − | 485892.i | − | 1.35758i | −0.734334 | − | 0.678788i | \(-0.762505\pi\) | ||
0.734334 | − | 0.678788i | \(-0.237495\pi\) | |||||||
\(72\) | 94603.4i | 0.253460i | ||||||||
\(73\) | −705653. | −1.81394 | −0.906969 | − | 0.421197i | \(-0.861610\pi\) | ||||
−0.906969 | + | 0.421197i | \(0.861610\pi\) | |||||||
\(74\) | 403966. | 0.996897 | ||||||||
\(75\) | − | 112718.i | − | 0.267183i | ||||||
\(76\) | −31796.9 | + | 217173.i | −0.0724342 | + | 0.494725i | ||||
\(77\) | 373690. | 0.818540 | ||||||||
\(78\) | 182724.i | 0.385046i | ||||||||
\(79\) | − | 57963.0i | − | 0.117563i | −0.998271 | − | 0.0587814i | \(-0.981279\pi\) | ||
0.998271 | − | 0.0587814i | \(-0.0187215\pi\) | |||||||
\(80\) | −90314.8 | −0.176396 | ||||||||
\(81\) | 122671. | 0.230828 | ||||||||
\(82\) | −763230. | −1.38425 | ||||||||
\(83\) | −174244. | −0.304735 | −0.152368 | − | 0.988324i | \(-0.548690\pi\) | ||||
−0.152368 | + | 0.988324i | \(0.548690\pi\) | |||||||
\(84\) | − | 203704.i | − | 0.343686i | ||||||
\(85\) | −764018. | −1.24408 | ||||||||
\(86\) | − | 161209.i | − | 0.253452i | ||||||
\(87\) | −173392. | −0.263312 | ||||||||
\(88\) | 152660.i | 0.224016i | ||||||||
\(89\) | − | 446408.i | − | 0.633231i | −0.948554 | − | 0.316615i | \(-0.897454\pi\) | ||
0.948554 | − | 0.316615i | \(-0.102546\pi\) | |||||||
\(90\) | 260745.i | 0.357675i | ||||||||
\(91\) | 996306.i | 1.32211i | ||||||||
\(92\) | 129516. | 0.166326 | ||||||||
\(93\) | −329295. | −0.409389 | ||||||||
\(94\) | − | 231075.i | − | 0.278208i | ||||||
\(95\) | −87638.2 | + | 598569.i | −0.102217 | + | 0.698141i | ||||
\(96\) | 83217.4 | 0.0940591 | ||||||||
\(97\) | − | 503915.i | − | 0.552131i | −0.961139 | − | 0.276066i | \(-0.910969\pi\) | ||
0.961139 | − | 0.276066i | \(-0.0890307\pi\) | |||||||
\(98\) | − | 445174.i | − | 0.472990i | ||||||
\(99\) | 440741. | 0.454232 | ||||||||
\(100\) | 251075. | 0.251075 | ||||||||
\(101\) | 274413. | 0.266342 | 0.133171 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133171 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(102\) | 703977. | 0.663374 | ||||||||
\(103\) | 372124.i | 0.340546i | 0.985397 | + | 0.170273i | \(0.0544650\pi\) | ||||
−0.985397 | + | 0.170273i | \(0.945535\pi\) | |||||||
\(104\) | −407012. | −0.361832 | ||||||||
\(105\) | − | 561447.i | − | 0.484999i | ||||||
\(106\) | −869182. | −0.729782 | ||||||||
\(107\) | 2.01674e6i | 1.64626i | 0.567850 | + | 0.823132i | \(0.307775\pi\) | ||||
−0.567850 | + | 0.823132i | \(0.692225\pi\) | |||||||
\(108\) | − | 575387.i | − | 0.456761i | ||||||
\(109\) | 60863.7i | 0.0469979i | 0.999724 | + | 0.0234990i | \(0.00748064\pi\) | ||||
−0.999724 | + | 0.0234990i | \(0.992519\pi\) | |||||||
\(110\) | 420761.i | 0.316124i | ||||||||
\(111\) | −1.02591e6 | −0.750137 | ||||||||
\(112\) | 453743. | 0.322966 | ||||||||
\(113\) | − | 1.63566e6i | − | 1.13360i | −0.823857 | − | 0.566798i | \(-0.808182\pi\) | ||
0.823857 | − | 0.566798i | \(-0.191818\pi\) | |||||||
\(114\) | 80751.2 | − | 551530.i | 0.0545047 | − | 0.372267i | ||||
\(115\) | 356970. | 0.234714 | ||||||||
\(116\) | − | 386224.i | − | 0.247437i | ||||||
\(117\) | 1.17507e6i | 0.733679i | ||||||||
\(118\) | 1.05895e6 | 0.644512 | ||||||||
\(119\) | 3.83844e6 | 2.27779 | ||||||||
\(120\) | 229363. | 0.132733 | ||||||||
\(121\) | −1.06034e6 | −0.598535 | ||||||||
\(122\) | − | 917619.i | − | 0.505339i | ||||||
\(123\) | 1.93829e6 | 1.04161 | ||||||||
\(124\) | − | 733493.i | − | 0.384708i | ||||||
\(125\) | 2.07011e6 | 1.05989 | ||||||||
\(126\) | − | 1.30999e6i | − | 0.654870i | ||||||
\(127\) | 1.92623e6i | 0.940368i | 0.882568 | + | 0.470184i | \(0.155812\pi\) | ||||
−0.882568 | + | 0.470184i | \(0.844188\pi\) | |||||||
\(128\) | 185364.i | 0.0883883i | ||||||||
\(129\) | 409407.i | 0.190715i | ||||||||
\(130\) | −1.12180e6 | −0.510606 | ||||||||
\(131\) | −1.95713e6 | −0.870572 | −0.435286 | − | 0.900292i | \(-0.643353\pi\) | ||||
−0.435286 | + | 0.900292i | \(0.643353\pi\) | |||||||
\(132\) | − | 387696.i | − | 0.168566i | ||||||
\(133\) | 440296. | − | 3.00722e6i | 0.187150 | − | 1.27823i | ||||
\(134\) | −288812. | −0.120033 | ||||||||
\(135\) | − | 1.58588e6i | − | 0.644567i | ||||||
\(136\) | 1.56808e6i | 0.623380i | ||||||||
\(137\) | 897719. | 0.349123 | 0.174562 | − | 0.984646i | \(-0.444149\pi\) | ||||
0.174562 | + | 0.984646i | \(0.444149\pi\) | |||||||
\(138\) | −328918. | −0.125155 | ||||||||
\(139\) | −3.75579e6 | −1.39848 | −0.699240 | − | 0.714887i | \(-0.746478\pi\) | ||||
−0.699240 | + | 0.714887i | \(0.746478\pi\) | |||||||
\(140\) | 1.25060e6 | 0.455759 | ||||||||
\(141\) | 586836.i | 0.209344i | ||||||||
\(142\) | −2.74862e6 | −0.959952 | ||||||||
\(143\) | 1.89620e6i | 0.648449i | ||||||||
\(144\) | 535157. | 0.179223 | ||||||||
\(145\) | − | 1.06451e6i | − | 0.349176i | ||||||
\(146\) | 3.99178e6i | 1.28265i | ||||||||
\(147\) | 1.13056e6i | 0.355912i | ||||||||
\(148\) | − | 2.28518e6i | − | 0.704912i | ||||||
\(149\) | −4.44414e6 | −1.34347 | −0.671736 | − | 0.740790i | \(-0.734451\pi\) | ||||
−0.671736 | + | 0.740790i | \(0.734451\pi\) | |||||||
\(150\) | −637629. | −0.188927 | ||||||||
\(151\) | 4.71415e6i | 1.36922i | 0.728910 | + | 0.684610i | \(0.240027\pi\) | ||||
−0.728910 | + | 0.684610i | \(0.759973\pi\) | |||||||
\(152\) | 1.22851e6 | + | 179870.i | 0.349824 | + | 0.0512187i | ||||
\(153\) | 4.52716e6 | 1.26401 | ||||||||
\(154\) | − | 2.11391e6i | − | 0.578795i | ||||||
\(155\) | − | 2.02164e6i | − | 0.542887i | ||||||
\(156\) | 1.03365e6 | 0.272269 | ||||||||
\(157\) | −2.23912e6 | −0.578599 | −0.289300 | − | 0.957239i | \(-0.593422\pi\) | ||||
−0.289300 | + | 0.957239i | \(0.593422\pi\) | |||||||
\(158\) | −327888. | −0.0831294 | ||||||||
\(159\) | 2.20737e6 | 0.549141 | ||||||||
\(160\) | 510898.i | 0.124731i | ||||||||
\(161\) | −1.79342e6 | −0.429740 | ||||||||
\(162\) | − | 693933.i | − | 0.163220i | ||||||
\(163\) | −6.99610e6 | −1.61545 | −0.807725 | − | 0.589560i | \(-0.799301\pi\) | ||||
−0.807725 | + | 0.589560i | \(0.799301\pi\) | |||||||
\(164\) | 4.31748e6i | 0.978811i | ||||||||
\(165\) | − | 1.06856e6i | − | 0.237875i | ||||||
\(166\) | 985671.i | 0.215480i | ||||||||
\(167\) | 1.64432e6i | 0.353050i | 0.984296 | + | 0.176525i | \(0.0564857\pi\) | ||||
−0.984296 | + | 0.176525i | \(0.943514\pi\) | |||||||
\(168\) | −1.15232e6 | −0.243023 | ||||||||
\(169\) | −228694. | −0.0473801 | ||||||||
\(170\) | 4.32194e6i | 0.879694i | ||||||||
\(171\) | 519297. | − | 3.54680e6i | 0.103855 | − | 0.709330i | ||||
\(172\) | −911938. | −0.179217 | ||||||||
\(173\) | − | 7.04201e6i | − | 1.36006i | −0.733184 | − | 0.680031i | \(-0.761966\pi\) | ||
0.733184 | − | 0.680031i | \(-0.238034\pi\) | |||||||
\(174\) | 980852.i | 0.186190i | ||||||||
\(175\) | −3.47668e6 | −0.648709 | ||||||||
\(176\) | 863578. | 0.158403 | ||||||||
\(177\) | −2.68931e6 | −0.484977 | ||||||||
\(178\) | −2.52527e6 | −0.447762 | ||||||||
\(179\) | − | 2.49268e6i | − | 0.434618i | −0.976103 | − | 0.217309i | \(-0.930272\pi\) | ||
0.976103 | − | 0.217309i | \(-0.0697279\pi\) | |||||||
\(180\) | 1.47500e6 | 0.252914 | ||||||||
\(181\) | − | 8.52372e6i | − | 1.43745i | −0.695293 | − | 0.718726i | \(-0.744725\pi\) | ||
0.695293 | − | 0.718726i | \(-0.255275\pi\) | |||||||
\(182\) | 5.63596e6 | 0.934875 | ||||||||
\(183\) | 2.33038e6i | 0.380254i | ||||||||
\(184\) | − | 732652.i | − | 0.117610i | ||||||
\(185\) | − | 6.29839e6i | − | 0.994751i | ||||||
\(186\) | 1.86277e6i | 0.289482i | ||||||||
\(187\) | 7.30543e6 | 1.11718 | ||||||||
\(188\) | −1.30716e6 | −0.196723 | ||||||||
\(189\) | 7.96747e6i | 1.18014i | ||||||||
\(190\) | 3.38602e6 | + | 495757.i | 0.493660 | + | 0.0722783i | ||||
\(191\) | 7.28172e6 | 1.04504 | 0.522521 | − | 0.852626i | \(-0.324992\pi\) | ||||
0.522521 | + | 0.852626i | \(0.324992\pi\) | |||||||
\(192\) | − | 470749.i | − | 0.0665098i | ||||||
\(193\) | − | 881891.i | − | 0.122671i | −0.998117 | − | 0.0613357i | \(-0.980464\pi\) | ||
0.998117 | − | 0.0613357i | \(-0.0195360\pi\) | |||||||
\(194\) | −2.85057e6 | −0.390416 | ||||||||
\(195\) | 2.84892e6 | 0.384217 | ||||||||
\(196\) | −2.51828e6 | −0.334454 | ||||||||
\(197\) | 1.06316e7 | 1.39059 | 0.695297 | − | 0.718723i | \(-0.255273\pi\) | ||||
0.695297 | + | 0.718723i | \(0.255273\pi\) | |||||||
\(198\) | − | 2.49321e6i | − | 0.321191i | ||||||
\(199\) | −227906. | −0.0289199 | −0.0144600 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144600 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(200\) | − | 1.42030e6i | − | 0.177537i | ||||||
\(201\) | 733464. | 0.0903214 | ||||||||
\(202\) | − | 1.55231e6i | − | 0.188332i | ||||||
\(203\) | 5.34810e6i | 0.639310i | ||||||||
\(204\) | − | 3.98230e6i | − | 0.469076i | ||||||
\(205\) | 1.18998e7i | 1.38127i | ||||||||
\(206\) | 2.10505e6 | 0.240803 | ||||||||
\(207\) | −2.11521e6 | −0.238475 | ||||||||
\(208\) | 2.30241e6i | 0.255854i | ||||||||
\(209\) | 837985. | − | 5.72344e6i | 0.0917904 | − | 0.626928i | ||||
\(210\) | −3.17602e6 | −0.342946 | ||||||||
\(211\) | 4.71940e6i | 0.502389i | 0.967937 | + | 0.251194i | \(0.0808233\pi\) | ||||
−0.967937 | + | 0.251194i | \(0.919177\pi\) | |||||||
\(212\) | 4.91684e6i | 0.516034i | ||||||||
\(213\) | 6.98038e6 | 0.722337 | ||||||||
\(214\) | 1.14084e7 | 1.16408 | ||||||||
\(215\) | −2.51347e6 | −0.252906 | ||||||||
\(216\) | −3.25488e6 | −0.322979 | ||||||||
\(217\) | 1.01568e7i | 0.993978i | ||||||||
\(218\) | 344297. | 0.0332325 | ||||||||
\(219\) | − | 1.01375e7i | − | 0.965157i | ||||||
\(220\) | 2.38019e6 | 0.223534 | ||||||||
\(221\) | 1.94772e7i | 1.80447i | ||||||||
\(222\) | 5.80343e6i | 0.530427i | ||||||||
\(223\) | − | 2.20494e7i | − | 1.98830i | −0.108021 | − | 0.994149i | \(-0.534451\pi\) | ||
0.108021 | − | 0.994149i | \(-0.465549\pi\) | |||||||
\(224\) | − | 2.56676e6i | − | 0.228371i | ||||||
\(225\) | −4.10049e6 | −0.359988 | ||||||||
\(226\) | −9.25270e6 | −0.801573 | ||||||||
\(227\) | − | 1.32001e7i | − | 1.12849i | −0.825606 | − | 0.564246i | \(-0.809167\pi\) | ||
0.825606 | − | 0.564246i | \(-0.190833\pi\) | |||||||
\(228\) | −3.11993e6 | − | 456798.i | −0.263233 | − | 0.0385407i | ||||
\(229\) | −1.05934e7 | −0.882121 | −0.441060 | − | 0.897477i | \(-0.645398\pi\) | ||||
−0.441060 | + | 0.897477i | \(0.645398\pi\) | |||||||
\(230\) | − | 2.01933e6i | − | 0.165968i | ||||||
\(231\) | 5.36848e6i | 0.435527i | ||||||||
\(232\) | −2.18481e6 | −0.174965 | ||||||||
\(233\) | −8.02445e6 | −0.634377 | −0.317189 | − | 0.948362i | \(-0.602739\pi\) | ||||
−0.317189 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(234\) | 6.64720e6 | 0.518790 | ||||||||
\(235\) | −3.60277e6 | −0.277609 | ||||||||
\(236\) | − | 5.99035e6i | − | 0.455739i | ||||||
\(237\) | 832703. | 0.0625526 | ||||||||
\(238\) | − | 2.17135e7i | − | 1.61064i | ||||||
\(239\) | −2.23585e6 | −0.163776 | −0.0818878 | − | 0.996642i | \(-0.526095\pi\) | ||||
−0.0818878 | + | 0.996642i | \(0.526095\pi\) | |||||||
\(240\) | − | 1.29747e6i | − | 0.0938566i | ||||||
\(241\) | 1.51033e7i | 1.07900i | 0.841987 | + | 0.539498i | \(0.181386\pi\) | ||||
−0.841987 | + | 0.539498i | \(0.818614\pi\) | |||||||
\(242\) | 5.99820e6i | 0.423228i | ||||||||
\(243\) | 1.48703e7i | 1.03634i | ||||||||
\(244\) | −5.19084e6 | −0.357329 | ||||||||
\(245\) | −6.94087e6 | −0.471971 | ||||||||
\(246\) | − | 1.09646e7i | − | 0.736528i | ||||||
\(247\) | 1.52594e7 | + | 2.23417e6i | 1.01262 | + | 0.148261i | ||||
\(248\) | −4.14926e6 | −0.272029 | ||||||||
\(249\) | − | 2.50320e6i | − | 0.162143i | ||||||
\(250\) | − | 1.17103e7i | − | 0.749458i | ||||||
\(251\) | −2.60236e7 | −1.64568 | −0.822841 | − | 0.568271i | \(-0.807612\pi\) | ||||
−0.822841 | + | 0.568271i | \(0.807612\pi\) | |||||||
\(252\) | −7.41041e6 | −0.463063 | ||||||||
\(253\) | −3.41330e6 | −0.210772 | ||||||||
\(254\) | 1.08964e7 | 0.664941 | ||||||||
\(255\) | − | 1.09760e7i | − | 0.661946i | ||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | − | 2.37806e7i | − | 1.40095i | −0.713675 | − | 0.700477i | \(-0.752971\pi\) | ||
0.713675 | − | 0.700477i | \(-0.247029\pi\) | |||||||
\(258\) | 2.31595e6 | 0.134856 | ||||||||
\(259\) | 3.16432e7i | 1.82130i | ||||||||
\(260\) | 6.34587e6i | 0.361053i | ||||||||
\(261\) | 6.30770e6i | 0.354772i | ||||||||
\(262\) | 1.10712e7i | 0.615588i | ||||||||
\(263\) | 1.51982e7 | 0.835459 | 0.417729 | − | 0.908571i | \(-0.362826\pi\) | ||||
0.417729 | + | 0.908571i | \(0.362826\pi\) | |||||||
\(264\) | −2.19314e6 | −0.119194 | ||||||||
\(265\) | 1.35517e7i | 0.728211i | ||||||||
\(266\) | −1.70114e7 | − | 2.49069e6i | −0.903848 | − | 0.132335i | ||||
\(267\) | 6.41315e6 | 0.336928 | ||||||||
\(268\) | 1.63377e6i | 0.0848761i | ||||||||
\(269\) | 3.09109e6i | 0.158802i | 0.996843 | + | 0.0794009i | \(0.0253007\pi\) | ||||
−0.996843 | + | 0.0794009i | \(0.974699\pi\) | |||||||
\(270\) | −8.97107e6 | −0.455777 | ||||||||
\(271\) | −2.30217e7 | −1.15672 | −0.578362 | − | 0.815780i | \(-0.696308\pi\) | ||||
−0.578362 | + | 0.815780i | \(0.696308\pi\) | |||||||
\(272\) | 8.87042e6 | 0.440796 | ||||||||
\(273\) | −1.43130e7 | −0.703467 | ||||||||
\(274\) | − | 5.07826e6i | − | 0.246867i | ||||||
\(275\) | −6.61691e6 | −0.318169 | ||||||||
\(276\) | 1.86064e6i | 0.0884983i | ||||||||
\(277\) | 1.85846e7 | 0.874409 | 0.437205 | − | 0.899362i | \(-0.355969\pi\) | ||||
0.437205 | + | 0.899362i | \(0.355969\pi\) | |||||||
\(278\) | 2.12459e7i | 0.988875i | ||||||||
\(279\) | 1.19792e7i | 0.551588i | ||||||||
\(280\) | − | 7.07448e6i | − | 0.322270i | ||||||
\(281\) | 5.09402e6i | 0.229584i | 0.993390 | + | 0.114792i | \(0.0366202\pi\) | ||||
−0.993390 | + | 0.114792i | \(0.963380\pi\) | |||||||
\(282\) | 3.31965e6 | 0.148028 | ||||||||
\(283\) | 3.57694e7 | 1.57817 | 0.789083 | − | 0.614286i | \(-0.210556\pi\) | ||||
0.789083 | + | 0.614286i | \(0.210556\pi\) | |||||||
\(284\) | 1.55485e7i | 0.678788i | ||||||||
\(285\) | −8.59911e6 | − | 1.25902e6i | −0.371466 | − | 0.0543874i | ||||
\(286\) | 1.07265e7 | 0.458523 | ||||||||
\(287\) | − | 5.97848e7i | − | 2.52898i | ||||||
\(288\) | − | 3.02731e6i | − | 0.126730i | ||||||
\(289\) | 5.09017e7 | 2.10882 | ||||||||
\(290\) | −6.02176e6 | −0.246905 | ||||||||
\(291\) | 7.23930e6 | 0.293777 | ||||||||
\(292\) | 2.25809e7 | 0.906969 | ||||||||
\(293\) | − | 8.47647e6i | − | 0.336986i | −0.985703 | − | 0.168493i | \(-0.946110\pi\) | ||
0.985703 | − | 0.168493i | \(-0.0538901\pi\) | |||||||
\(294\) | 6.39542e6 | 0.251668 | ||||||||
\(295\) | − | 1.65105e7i | − | 0.643124i | ||||||
\(296\) | −1.29269e7 | −0.498448 | ||||||||
\(297\) | 1.51639e7i | 0.578818i | ||||||||
\(298\) | 2.51399e7i | 0.949979i | ||||||||
\(299\) | − | 9.10028e6i | − | 0.340441i | ||||||
\(300\) | 3.60698e6i | 0.133592i | ||||||||
\(301\) | 1.26277e7 | 0.463048 | ||||||||
\(302\) | 2.66673e7 | 0.968184 | ||||||||
\(303\) | 3.94225e6i | 0.141715i | ||||||||
\(304\) | 1.01750e6 | − | 6.94952e6i | 0.0362171 | − | 0.247363i | ||||
\(305\) | −1.43069e7 | −0.504251 | ||||||||
\(306\) | − | 2.56095e7i | − | 0.893792i | ||||||
\(307\) | − | 3.21243e7i | − | 1.11024i | −0.831769 | − | 0.555122i | \(-0.812672\pi\) | ||
0.831769 | − | 0.555122i | \(-0.187328\pi\) | |||||||
\(308\) | −1.19581e7 | −0.409270 | ||||||||
\(309\) | −5.34598e6 | −0.181197 | ||||||||
\(310\) | −1.14362e7 | −0.383879 | ||||||||
\(311\) | −3.20291e7 | −1.06479 | −0.532395 | − | 0.846496i | \(-0.678708\pi\) | ||||
−0.532395 | + | 0.846496i | \(0.678708\pi\) | |||||||
\(312\) | − | 5.84718e6i | − | 0.192523i | ||||||
\(313\) | 3.71743e7 | 1.21230 | 0.606150 | − | 0.795350i | \(-0.292713\pi\) | ||||
0.606150 | + | 0.795350i | \(0.292713\pi\) | |||||||
\(314\) | 1.26664e7i | 0.409132i | ||||||||
\(315\) | −2.04245e7 | −0.653461 | ||||||||
\(316\) | 1.85482e6i | 0.0587814i | ||||||||
\(317\) | 4.65424e7i | 1.46107i | 0.682875 | + | 0.730535i | \(0.260729\pi\) | ||||
−0.682875 | + | 0.730535i | \(0.739271\pi\) | |||||||
\(318\) | − | 1.24868e7i | − | 0.388301i | ||||||
\(319\) | 1.01787e7i | 0.313559i | ||||||||
\(320\) | 2.89007e6 | 0.0881981 | ||||||||
\(321\) | −2.89728e7 | −0.875941 | ||||||||
\(322\) | 1.01451e7i | 0.303872i | ||||||||
\(323\) | 8.60754e6 | − | 5.87895e7i | 0.255430 | − | 1.74458i | ||||
\(324\) | −3.92548e6 | −0.115414 | ||||||||
\(325\) | − | 1.76415e7i | − | 0.513909i | ||||||
\(326\) | 3.95759e7i | 1.14230i | ||||||||
\(327\) | −874375. | −0.0250066 | ||||||||
\(328\) | 2.44234e7 | 0.692124 | ||||||||
\(329\) | 1.81004e7 | 0.508277 | ||||||||
\(330\) | −6.04471e6 | −0.168203 | ||||||||
\(331\) | − | 9.73822e6i | − | 0.268532i | −0.990945 | − | 0.134266i | \(-0.957132\pi\) | ||
0.990945 | − | 0.134266i | \(-0.0428676\pi\) | |||||||
\(332\) | 5.57580e6 | 0.152368 | ||||||||
\(333\) | 3.73209e7i | 1.01069i | ||||||||
\(334\) | 9.30167e6 | 0.249644 | ||||||||
\(335\) | 4.50297e6i | 0.119774i | ||||||||
\(336\) | 6.51853e6i | 0.171843i | ||||||||
\(337\) | − | 5.43094e7i | − | 1.41901i | −0.704701 | − | 0.709505i | \(-0.748919\pi\) | ||
0.704701 | − | 0.709505i | \(-0.251081\pi\) | |||||||
\(338\) | 1.29369e6i | 0.0335028i | ||||||||
\(339\) | 2.34981e7 | 0.603161 | ||||||||
\(340\) | 2.44486e7 | 0.622038 | ||||||||
\(341\) | 1.93307e7i | 0.487511i | ||||||||
\(342\) | −2.00637e7 | − | 2.93759e6i | −0.501572 | − | 0.0734366i | ||||
\(343\) | −1.72602e7 | −0.427725 | ||||||||
\(344\) | 5.15870e6i | 0.126726i | ||||||||
\(345\) | 5.12827e6i | 0.124886i | ||||||||
\(346\) | −3.98356e7 | −0.961709 | ||||||||
\(347\) | −2.27844e7 | −0.545318 | −0.272659 | − | 0.962111i | \(-0.587903\pi\) | ||||
−0.272659 | + | 0.962111i | \(0.587903\pi\) | |||||||
\(348\) | 5.54854e6 | 0.131656 | ||||||||
\(349\) | −4.88429e7 | −1.14901 | −0.574507 | − | 0.818500i | \(-0.694806\pi\) | ||||
−0.574507 | + | 0.818500i | \(0.694806\pi\) | |||||||
\(350\) | 1.96670e7i | 0.458707i | ||||||||
\(351\) | −4.04289e7 | −0.934912 | ||||||||
\(352\) | − | 4.88514e6i | − | 0.112008i | ||||||
\(353\) | −9.20565e6 | −0.209281 | −0.104641 | − | 0.994510i | \(-0.533369\pi\) | ||||
−0.104641 | + | 0.994510i | \(0.533369\pi\) | |||||||
\(354\) | 1.52130e7i | 0.342931i | ||||||||
\(355\) | 4.28547e7i | 0.957885i | ||||||||
\(356\) | 1.42851e7i | 0.316615i | ||||||||
\(357\) | 5.51435e7i | 1.21196i | ||||||||
\(358\) | −1.41007e7 | −0.307321 | ||||||||
\(359\) | −4.65298e7 | −1.00565 | −0.502826 | − | 0.864388i | \(-0.667706\pi\) | ||||
−0.502826 | + | 0.864388i | \(0.667706\pi\) | |||||||
\(360\) | − | 8.34383e6i | − | 0.178837i | ||||||
\(361\) | −4.50712e7 | − | 1.34871e7i | −0.958026 | − | 0.286680i | ||||
\(362\) | −4.82175e7 | −1.01643 | ||||||||
\(363\) | − | 1.52330e7i | − | 0.318468i | ||||||
\(364\) | − | 3.18818e7i | − | 0.661056i | ||||||
\(365\) | 6.22372e7 | 1.27989 | ||||||||
\(366\) | 1.31826e7 | 0.268880 | ||||||||
\(367\) | 9.72438e7 | 1.96727 | 0.983635 | − | 0.180173i | \(-0.0576658\pi\) | ||||
0.983635 | + | 0.180173i | \(0.0576658\pi\) | |||||||
\(368\) | −4.14450e6 | −0.0831628 | ||||||||
\(369\) | − | 7.05118e7i | − | 1.40340i | ||||||
\(370\) | −3.56291e7 | −0.703395 | ||||||||
\(371\) | − | 6.80842e7i | − | 1.33329i | ||||||
\(372\) | 1.05374e7 | 0.204695 | ||||||||
\(373\) | 5.95500e7i | 1.14751i | 0.819028 | + | 0.573753i | \(0.194513\pi\) | ||||
−0.819028 | + | 0.573753i | \(0.805487\pi\) | |||||||
\(374\) | − | 4.13258e7i | − | 0.789962i | ||||||
\(375\) | 2.97394e7i | 0.563947i | ||||||||
\(376\) | 7.39439e6i | 0.139104i | ||||||||
\(377\) | −2.71376e7 | −0.506463 | ||||||||
\(378\) | 4.50708e7 | 0.834488 | ||||||||
\(379\) | 7.91278e7i | 1.45349i | 0.686909 | + | 0.726744i | \(0.258967\pi\) | ||||
−0.686909 | + | 0.726744i | \(0.741033\pi\) | |||||||
\(380\) | 2.80442e6 | − | 1.91542e7i | 0.0511085 | − | 0.349071i | ||||
\(381\) | −2.76725e7 | −0.500349 | ||||||||
\(382\) | − | 4.11916e7i | − | 0.738956i | ||||||
\(383\) | 6.73426e7i | 1.19865i | 0.800505 | + | 0.599327i | \(0.204565\pi\) | ||||
−0.800505 | + | 0.599327i | \(0.795435\pi\) | |||||||
\(384\) | −2.66296e6 | −0.0470295 | ||||||||
\(385\) | −3.29588e7 | −0.577549 | ||||||||
\(386\) | −4.98873e6 | −0.0867418 | ||||||||
\(387\) | 1.48935e7 | 0.256959 | ||||||||
\(388\) | 1.61253e7i | 0.276066i | ||||||||
\(389\) | 6.05262e7 | 1.02824 | 0.514120 | − | 0.857718i | \(-0.328119\pi\) | ||||
0.514120 | + | 0.857718i | \(0.328119\pi\) | |||||||
\(390\) | − | 1.61159e7i | − | 0.271683i | ||||||
\(391\) | −3.50604e7 | −0.586525 | ||||||||
\(392\) | 1.42456e7i | 0.236495i | ||||||||
\(393\) | − | 2.81163e7i | − | 0.463213i | ||||||
\(394\) | − | 6.01415e7i | − | 0.983298i | ||||||
\(395\) | 5.11222e6i | 0.0829504i | ||||||||
\(396\) | −1.41037e7 | −0.227116 | ||||||||
\(397\) | 8.45812e7 | 1.35177 | 0.675885 | − | 0.737007i | \(-0.263762\pi\) | ||||
0.675885 | + | 0.737007i | \(0.263762\pi\) | |||||||
\(398\) | 1.28923e6i | 0.0204495i | ||||||||
\(399\) | 4.32021e7 | + | 6.32535e6i | 0.680121 | + | 0.0995785i | ||||
\(400\) | −8.03441e6 | −0.125538 | ||||||||
\(401\) | − | 4.02141e7i | − | 0.623656i | −0.950139 | − | 0.311828i | \(-0.899059\pi\) | ||
0.950139 | − | 0.311828i | \(-0.100941\pi\) | |||||||
\(402\) | − | 4.14910e6i | − | 0.0638669i | ||||||
\(403\) | −5.15381e7 | −0.787432 | ||||||||
\(404\) | −8.78121e6 | −0.133171 | ||||||||
\(405\) | −1.08194e7 | −0.162868 | ||||||||
\(406\) | 3.02534e7 | 0.452060 | ||||||||
\(407\) | 6.02243e7i | 0.893282i | ||||||||
\(408\) | −2.25273e7 | −0.331687 | ||||||||
\(409\) | − | 1.25079e8i | − | 1.82816i | −0.405529 | − | 0.914082i | \(-0.632913\pi\) | ||
0.405529 | − | 0.914082i | \(-0.367087\pi\) | |||||||
\(410\) | 6.73154e7 | 0.976704 | ||||||||
\(411\) | 1.28967e7i | 0.185761i | ||||||||
\(412\) | − | 1.19080e7i | − | 0.170273i | ||||||
\(413\) | 8.29492e7i | 1.17750i | ||||||||
\(414\) | 1.19655e7i | 0.168627i | ||||||||
\(415\) | 1.53680e7 | 0.215016 | ||||||||
\(416\) | 1.30244e7 | 0.180916 | ||||||||
\(417\) | − | 5.39560e7i | − | 0.744101i | ||||||
\(418\) | −3.23766e7 | − | 4.74036e6i | −0.443305 | − | 0.0649056i | ||||
\(419\) | 1.43907e8 | 1.95631 | 0.978157 | − | 0.207867i | \(-0.0666523\pi\) | ||||
0.978157 | + | 0.207867i | \(0.0666523\pi\) | |||||||
\(420\) | 1.79663e7i | 0.242500i | ||||||||
\(421\) | − | 2.37670e6i | − | 0.0318514i | −0.999873 | − | 0.0159257i | \(-0.994930\pi\) | ||
0.999873 | − | 0.0159257i | \(-0.00506952\pi\) | |||||||
\(422\) | 2.66970e7 | 0.355242 | ||||||||
\(423\) | 2.13481e7 | 0.282058 | ||||||||
\(424\) | 2.78138e7 | 0.364891 | ||||||||
\(425\) | −6.79670e7 | −0.885383 | ||||||||
\(426\) | − | 3.94870e7i | − | 0.510770i | ||||||
\(427\) | 7.18783e7 | 0.923239 | ||||||||
\(428\) | − | 6.45358e7i | − | 0.823132i | ||||||
\(429\) | −2.72410e7 | −0.345026 | ||||||||
\(430\) | 1.42184e7i | 0.178832i | ||||||||
\(431\) | 5.20048e7i | 0.649548i | 0.945792 | + | 0.324774i | \(0.105288\pi\) | ||||
−0.945792 | + | 0.324774i | \(0.894712\pi\) | |||||||
\(432\) | 1.84124e7i | 0.228380i | ||||||||
\(433\) | − | 2.80831e7i | − | 0.345925i | −0.984928 | − | 0.172962i | \(-0.944666\pi\) | ||
0.984928 | − | 0.172962i | \(-0.0553339\pi\) | |||||||
\(434\) | 5.74554e7 | 0.702849 | ||||||||
\(435\) | 1.52928e7 | 0.185789 | ||||||||
\(436\) | − | 1.94764e6i | − | 0.0234990i | ||||||
\(437\) | −4.02168e6 | + | 2.74680e7i | −0.0481907 | + | 0.329142i | ||||
\(438\) | −5.73463e7 | −0.682469 | ||||||||
\(439\) | 1.34570e8i | 1.59058i | 0.606228 | + | 0.795291i | \(0.292682\pi\) | ||||
−0.606228 | + | 0.795291i | \(0.707318\pi\) | |||||||
\(440\) | − | 1.34644e7i | − | 0.158062i | ||||||
\(441\) | 4.11279e7 | 0.479535 | ||||||||
\(442\) | 1.10180e8 | 1.27595 | ||||||||
\(443\) | −8.52003e7 | −0.980009 | −0.490005 | − | 0.871720i | \(-0.663005\pi\) | ||||
−0.490005 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(444\) | 3.28292e7 | 0.375069 | ||||||||
\(445\) | 3.93723e7i | 0.446798i | ||||||||
\(446\) | −1.24730e8 | −1.40594 | ||||||||
\(447\) | − | 6.38450e7i | − | 0.714833i | ||||||
\(448\) | −1.45198e7 | −0.161483 | ||||||||
\(449\) | − | 1.98487e6i | − | 0.0219277i | −0.999940 | − | 0.0109639i | \(-0.996510\pi\) | ||
0.999940 | − | 0.0109639i | \(-0.00348998\pi\) | |||||||
\(450\) | 2.31959e7i | 0.254550i | ||||||||
\(451\) | − | 1.13784e8i | − | 1.24037i | ||||||
\(452\) | 5.23412e7i | 0.566798i | ||||||||
\(453\) | −6.77241e7 | −0.728532 | ||||||||
\(454\) | −7.46709e7 | −0.797965 | ||||||||
\(455\) | − | 8.78722e7i | − | 0.932862i | ||||||
\(456\) | −2.58404e6 | + | 1.76490e7i | −0.0272524 | + | 0.186134i | ||||
\(457\) | 1.17624e8 | 1.23238 | 0.616192 | − | 0.787596i | \(-0.288674\pi\) | ||||
0.616192 | + | 0.787596i | \(0.288674\pi\) | |||||||
\(458\) | 5.99252e7i | 0.623753i | ||||||||
\(459\) | 1.55759e8i | 1.61071i | ||||||||
\(460\) | −1.14230e7 | −0.117357 | ||||||||
\(461\) | −9.91086e7 | −1.01160 | −0.505800 | − | 0.862651i | \(-0.668803\pi\) | ||||
−0.505800 | + | 0.862651i | \(0.668803\pi\) | |||||||
\(462\) | 3.03687e7 | 0.307964 | ||||||||
\(463\) | −2.50690e7 | −0.252577 | −0.126288 | − | 0.991994i | \(-0.540306\pi\) | ||||
−0.126288 | + | 0.991994i | \(0.540306\pi\) | |||||||
\(464\) | 1.23592e7i | 0.123719i | ||||||||
\(465\) | 2.90432e7 | 0.288859 | ||||||||
\(466\) | 4.53932e7i | 0.448572i | ||||||||
\(467\) | −9.78891e7 | −0.961133 | −0.480567 | − | 0.876958i | \(-0.659569\pi\) | ||||
−0.480567 | + | 0.876958i | \(0.659569\pi\) | |||||||
\(468\) | − | 3.76022e7i | − | 0.366840i | ||||||
\(469\) | − | 2.26230e7i | − | 0.219296i | ||||||
\(470\) | 2.03804e7i | 0.196299i | ||||||||
\(471\) | − | 3.21674e7i | − | 0.307860i | ||||||
\(472\) | −3.38865e7 | −0.322256 | ||||||||
\(473\) | 2.40335e7 | 0.227109 | ||||||||
\(474\) | − | 4.71048e6i | − | 0.0442314i | ||||||
\(475\) | −7.79630e6 | + | 5.32487e7i | −0.0727457 | + | 0.496853i | ||||
\(476\) | −1.22830e8 | −1.13890 | ||||||||
\(477\) | − | 8.03003e7i | − | 0.739882i | ||||||
\(478\) | 1.26479e7i | 0.115807i | ||||||||
\(479\) | −960933. | −0.00874352 | −0.00437176 | − | 0.999990i | \(-0.501392\pi\) | ||||
−0.00437176 | + | 0.999990i | \(0.501392\pi\) | |||||||
\(480\) | −7.33962e6 | −0.0663666 | ||||||||
\(481\) | −1.60566e8 | −1.44284 | ||||||||
\(482\) | 8.54370e7 | 0.762965 | ||||||||
\(483\) | − | 2.57645e7i | − | 0.228655i | ||||||
\(484\) | 3.39309e7 | 0.299268 | ||||||||
\(485\) | 4.44443e7i | 0.389575i | ||||||||
\(486\) | 8.41194e7 | 0.732803 | ||||||||
\(487\) | − | 1.11694e8i | − | 0.967039i | −0.875334 | − | 0.483520i | \(-0.839358\pi\) | ||
0.875334 | − | 0.483520i | \(-0.160642\pi\) | |||||||
\(488\) | 2.93638e7i | 0.252670i | ||||||||
\(489\) | − | 1.00507e8i | − | 0.859546i | ||||||
\(490\) | 3.92635e7i | 0.333734i | ||||||||
\(491\) | 1.22509e8 | 1.03496 | 0.517481 | − | 0.855694i | \(-0.326870\pi\) | ||||
0.517481 | + | 0.855694i | \(0.326870\pi\) | |||||||
\(492\) | −6.20254e7 | −0.520804 | ||||||||
\(493\) | 1.04552e8i | 0.872555i | ||||||||
\(494\) | 1.26384e7 | − | 8.63202e7i | 0.104836 | − | 0.716030i | ||||
\(495\) | −3.88725e7 | −0.320499 | ||||||||
\(496\) | 2.34718e7i | 0.192354i | ||||||||
\(497\) | − | 2.15303e8i | − | 1.75380i | ||||||
\(498\) | −1.41603e7 | −0.114652 | ||||||||
\(499\) | −1.28023e8 | −1.03035 | −0.515176 | − | 0.857084i | \(-0.672274\pi\) | ||||
−0.515176 | + | 0.857084i | \(0.672274\pi\) | |||||||
\(500\) | −6.62434e7 | −0.529947 | ||||||||
\(501\) | −2.36225e7 | −0.187850 | ||||||||
\(502\) | 1.47212e8i | 1.16367i | ||||||||
\(503\) | 6.43740e7 | 0.505832 | 0.252916 | − | 0.967488i | \(-0.418610\pi\) | ||||
0.252916 | + | 0.967488i | \(0.418610\pi\) | |||||||
\(504\) | 4.19196e7i | 0.327435i | ||||||||
\(505\) | −2.42027e7 | −0.187927 | ||||||||
\(506\) | 1.93085e7i | 0.149038i | ||||||||
\(507\) | − | 3.28545e6i | − | 0.0252099i | ||||||
\(508\) | − | 6.16395e7i | − | 0.470184i | ||||||
\(509\) | − | 9.29852e7i | − | 0.705116i | −0.935790 | − | 0.352558i | \(-0.885312\pi\) | ||
0.935790 | − | 0.352558i | \(-0.114688\pi\) | |||||||
\(510\) | −6.20895e7 | −0.468066 | ||||||||
\(511\) | −3.12681e8 | −2.34336 | ||||||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | 1.22030e8 | + | 1.78667e7i | 0.903885 | + | 0.132340i | ||||
\(514\) | −1.34524e8 | −0.990624 | ||||||||
\(515\) | − | 3.28206e7i | − | 0.240284i | ||||||
\(516\) | − | 1.31010e7i | − | 0.0953577i | ||||||
\(517\) | 3.44492e7 | 0.249292 | ||||||||
\(518\) | 1.79001e8 | 1.28785 | ||||||||
\(519\) | 1.01166e8 | 0.723659 | ||||||||
\(520\) | 3.58977e7 | 0.255303 | ||||||||
\(521\) | − | 7.12432e7i | − | 0.503767i | −0.967758 | − | 0.251884i | \(-0.918950\pi\) | ||
0.967758 | − | 0.251884i | \(-0.0810500\pi\) | |||||||
\(522\) | 3.56817e7 | 0.250862 | ||||||||
\(523\) | 1.96941e8i | 1.37668i | 0.725390 | + | 0.688338i | \(0.241659\pi\) | ||||
−0.725390 | + | 0.688338i | \(0.758341\pi\) | |||||||
\(524\) | 6.26280e7 | 0.435286 | ||||||||
\(525\) | − | 4.99463e7i | − | 0.345164i | ||||||
\(526\) | − | 8.59740e7i | − | 0.590759i | ||||||
\(527\) | 1.98559e8i | 1.35662i | ||||||||
\(528\) | 1.24063e7i | 0.0842829i | ||||||||
\(529\) | −1.31655e8 | −0.889343 | ||||||||
\(530\) | 7.66602e7 | 0.514923 | ||||||||
\(531\) | 9.78326e7i | 0.653431i | ||||||||
\(532\) | −1.40895e7 | + | 9.62311e7i | −0.0935750 | + | 0.639117i | ||||
\(533\) | 3.03363e8 | 2.00346 | ||||||||
\(534\) | − | 3.62783e7i | − | 0.238244i | ||||||
\(535\) | − | 1.77873e8i | − | 1.16158i | ||||||
\(536\) | 9.24197e6 | 0.0600164 | ||||||||
\(537\) | 3.58101e7 | 0.231251 | ||||||||
\(538\) | 1.74859e7 | 0.112290 | ||||||||
\(539\) | 6.63677e7 | 0.423829 | ||||||||
\(540\) | 5.07480e7i | 0.322283i | ||||||||
\(541\) | −1.91247e8 | −1.20782 | −0.603909 | − | 0.797053i | \(-0.706391\pi\) | ||||
−0.603909 | + | 0.797053i | \(0.706391\pi\) | |||||||
\(542\) | 1.30231e8i | 0.817928i | ||||||||
\(543\) | 1.22453e8 | 0.764838 | ||||||||
\(544\) | − | 5.01787e7i | − | 0.311690i | ||||||
\(545\) | − | 5.36806e6i | − | 0.0331610i | ||||||
\(546\) | 8.09668e7i | 0.497427i | ||||||||
\(547\) | 1.37101e7i | 0.0837682i | 0.999122 | + | 0.0418841i | \(0.0133360\pi\) | ||||
−0.999122 | + | 0.0418841i | \(0.986664\pi\) | |||||||
\(548\) | −2.87270e7 | −0.174562 | ||||||||
\(549\) | 8.47753e7 | 0.512333 | ||||||||
\(550\) | 3.74309e7i | 0.224979i | ||||||||
\(551\) | 8.19114e7 | + | 1.19929e7i | 0.489654 | + | 0.0716917i | ||||
\(552\) | 1.05254e7 | 0.0625777 | ||||||||
\(553\) | − | 2.56839e7i | − | 0.151875i | ||||||
\(554\) | − | 1.05131e8i | − | 0.618301i | ||||||
\(555\) | 9.04834e7 | 0.529285 | ||||||||
\(556\) | 1.20185e8 | 0.699240 | ||||||||
\(557\) | 2.61178e7 | 0.151137 | 0.0755686 | − | 0.997141i | \(-0.475923\pi\) | ||||
0.0755686 | + | 0.997141i | \(0.475923\pi\) | |||||||
\(558\) | 6.77645e7 | 0.390032 | ||||||||
\(559\) | 6.40763e7i | 0.366828i | ||||||||
\(560\) | −4.00193e7 | −0.227880 | ||||||||
\(561\) | 1.04951e8i | 0.594425i | ||||||||
\(562\) | 2.88161e7 | 0.162341 | ||||||||
\(563\) | 8.77820e6i | 0.0491904i | 0.999697 | + | 0.0245952i | \(0.00782968\pi\) | ||||
−0.999697 | + | 0.0245952i | \(0.992170\pi\) | |||||||
\(564\) | − | 1.87788e7i | − | 0.104672i | ||||||
\(565\) | 1.44262e8i | 0.799847i | ||||||||
\(566\) | − | 2.02343e8i | − | 1.11593i | ||||||
\(567\) | 5.43567e7 | 0.298197 | ||||||||
\(568\) | 8.79558e7 | 0.479976 | ||||||||
\(569\) | − | 1.21946e8i | − | 0.661959i | −0.943638 | − | 0.330980i | \(-0.892621\pi\) | ||
0.943638 | − | 0.330980i | \(-0.107379\pi\) | |||||||
\(570\) | −7.12210e6 | + | 4.86439e7i | −0.0384577 | + | 0.262666i | ||||
\(571\) | 2.03510e8 | 1.09314 | 0.546572 | − | 0.837412i | \(-0.315932\pi\) | ||||
0.546572 | + | 0.837412i | \(0.315932\pi\) | |||||||
\(572\) | − | 6.06784e7i | − | 0.324224i | ||||||
\(573\) | 1.04610e8i | 0.556044i | ||||||||
\(574\) | −3.38194e8 | −1.78826 | ||||||||
\(575\) | 3.17561e7 | 0.167041 | ||||||||
\(576\) | −1.71250e7 | −0.0896116 | ||||||||
\(577\) | 1.06556e8 | 0.554688 | 0.277344 | − | 0.960771i | \(-0.410546\pi\) | ||||
0.277344 | + | 0.960771i | \(0.410546\pi\) | |||||||
\(578\) | − | 2.87944e8i | − | 1.49116i | ||||||
\(579\) | 1.26694e7 | 0.0652708 | ||||||||
\(580\) | 3.40642e7i | 0.174588i | ||||||||
\(581\) | −7.72089e7 | −0.393676 | ||||||||
\(582\) | − | 4.09517e7i | − | 0.207732i | ||||||
\(583\) | − | 1.29580e8i | − | 0.653931i | ||||||
\(584\) | − | 1.27737e8i | − | 0.641324i | ||||||
\(585\) | − | 1.03639e8i | − | 0.517673i | ||||||
\(586\) | −4.79501e7 | −0.238285 | ||||||||
\(587\) | −2.13383e8 | −1.05498 | −0.527492 | − | 0.849560i | \(-0.676867\pi\) | ||||
−0.527492 | + | 0.849560i | \(0.676867\pi\) | |||||||
\(588\) | − | 3.61780e7i | − | 0.177956i | ||||||
\(589\) | 1.55561e8 | + | 2.27761e7i | 0.761299 | + | 0.111464i | ||||
\(590\) | −9.33977e7 | −0.454758 | ||||||||
\(591\) | 1.52735e8i | 0.739905i | ||||||||
\(592\) | 7.31257e7i | 0.352456i | ||||||||
\(593\) | −8.55599e7 | −0.410304 | −0.205152 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205152 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(594\) | 8.57801e7 | 0.409286 | ||||||||
\(595\) | −3.38543e8 | −1.60717 | ||||||||
\(596\) | 1.42212e8 | 0.671736 | ||||||||
\(597\) | − | 3.27413e6i | − | 0.0153877i | ||||||
\(598\) | −5.14790e7 | −0.240728 | ||||||||
\(599\) | 3.85400e8i | 1.79321i | 0.442831 | + | 0.896605i | \(0.353974\pi\) | ||||
−0.442831 | + | 0.896605i | \(0.646026\pi\) | |||||||
\(600\) | 2.04041e7 | 0.0944636 | ||||||||
\(601\) | − | 1.89176e8i | − | 0.871449i | −0.900080 | − | 0.435725i | \(-0.856492\pi\) | ||
0.900080 | − | 0.435725i | \(-0.143508\pi\) | |||||||
\(602\) | − | 7.14333e7i | − | 0.327425i | ||||||
\(603\) | − | 2.66822e7i | − | 0.121694i | ||||||
\(604\) | − | 1.50853e8i | − | 0.684610i | ||||||
\(605\) | 9.35201e7 | 0.422317 | ||||||||
\(606\) | 2.23007e7 | 0.100208 | ||||||||
\(607\) | − | 2.73759e8i | − | 1.22406i | −0.790836 | − | 0.612028i | \(-0.790354\pi\) | ||
0.790836 | − | 0.612028i | \(-0.209646\pi\) | |||||||
\(608\) | −3.93124e7 | − | 5.75585e6i | −0.174912 | − | 0.0256094i | ||||
\(609\) | −7.68314e7 | −0.340163 | ||||||||
\(610\) | 8.09323e7i | 0.356560i | ||||||||
\(611\) | 9.18459e7i | 0.402658i | ||||||||
\(612\) | −1.44869e8 | −0.632007 | ||||||||
\(613\) | −1.29168e8 | −0.560758 | −0.280379 | − | 0.959889i | \(-0.590460\pi\) | ||||
−0.280379 | + | 0.959889i | \(0.590460\pi\) | |||||||
\(614\) | −1.81722e8 | −0.785061 | ||||||||
\(615\) | −1.70954e8 | −0.734943 | ||||||||
\(616\) | 6.76452e7i | 0.289398i | ||||||||
\(617\) | 7.84207e7 | 0.333868 | 0.166934 | − | 0.985968i | \(-0.446613\pi\) | ||||
0.166934 | + | 0.985968i | \(0.446613\pi\) | |||||||
\(618\) | 3.02414e7i | 0.128126i | ||||||||
\(619\) | −1.21305e8 | −0.511456 | −0.255728 | − | 0.966749i | \(-0.582315\pi\) | ||||
−0.255728 | + | 0.966749i | \(0.582315\pi\) | |||||||
\(620\) | 6.46926e7i | 0.271444i | ||||||||
\(621\) | − | 7.27751e7i | − | 0.303884i | ||||||
\(622\) | 1.81184e8i | 0.752920i | ||||||||
\(623\) | − | 1.97807e8i | − | 0.818047i | ||||||
\(624\) | −3.30767e7 | −0.136134 | ||||||||
\(625\) | −5.99840e7 | −0.245695 | ||||||||
\(626\) | − | 2.10290e8i | − | 0.857225i | ||||||
\(627\) | 8.22235e7 | + | 1.20386e7i | 0.333575 | + | 0.0488397i | ||||
\(628\) | 7.16518e7 | 0.289300 | ||||||||
\(629\) | 6.18607e8i | 2.48578i | ||||||||
\(630\) | 1.15538e8i | 0.462066i | ||||||||
\(631\) | 3.52334e8 | 1.40238 | 0.701191 | − | 0.712973i | \(-0.252652\pi\) | ||||
0.701191 | + | 0.712973i | \(0.252652\pi\) | |||||||
\(632\) | 1.04924e7 | 0.0415647 | ||||||||
\(633\) | −6.77995e7 | −0.267310 | ||||||||
\(634\) | 2.63284e8 | 1.03313 | ||||||||
\(635\) | − | 1.69890e8i | − | 0.663509i | ||||||
\(636\) | −7.06358e7 | −0.274570 | ||||||||
\(637\) | 1.76944e8i | 0.684571i | ||||||||
\(638\) | 5.75792e7 | 0.221719 | ||||||||
\(639\) | − | 2.53934e8i | − | 0.973237i | ||||||
\(640\) | − | 1.63487e7i | − | 0.0623655i | ||||||
\(641\) | 4.58136e8i | 1.73948i | 0.493507 | + | 0.869742i | \(0.335715\pi\) | ||||
−0.493507 | + | 0.869742i | \(0.664285\pi\) | |||||||
\(642\) | 1.63895e8i | 0.619384i | ||||||||
\(643\) | −5.78444e7 | −0.217585 | −0.108792 | − | 0.994064i | \(-0.534698\pi\) | ||||
−0.108792 | + | 0.994064i | \(0.534698\pi\) | |||||||
\(644\) | 5.73896e7 | 0.214870 | ||||||||
\(645\) | − | 3.61089e7i | − | 0.134566i | ||||||
\(646\) | −3.32563e8 | − | 4.86916e7i | −1.23361 | − | 0.180616i | ||||
\(647\) | −7.21979e7 | −0.266570 | −0.133285 | − | 0.991078i | \(-0.542553\pi\) | ||||
−0.133285 | + | 0.991078i | \(0.542553\pi\) | |||||||
\(648\) | 2.22059e7i | 0.0816099i | ||||||||
\(649\) | 1.57871e8i | 0.577523i | ||||||||
\(650\) | −9.97955e7 | −0.363388 | ||||||||
\(651\) | −1.45914e8 | −0.528874 | ||||||||
\(652\) | 2.23875e8 | 0.807725 | ||||||||
\(653\) | −4.68602e8 | −1.68293 | −0.841463 | − | 0.540316i | \(-0.818305\pi\) | ||||
−0.841463 | + | 0.540316i | \(0.818305\pi\) | |||||||
\(654\) | 4.94621e6i | 0.0176823i | ||||||||
\(655\) | 1.72615e8 | 0.614262 | ||||||||
\(656\) | − | 1.38159e8i | − | 0.489405i | ||||||
\(657\) | −3.68785e8 | −1.30040 | ||||||||
\(658\) | − | 1.02391e8i | − | 0.359406i | ||||||
\(659\) | − | 1.19637e8i | − | 0.418032i | −0.977912 | − | 0.209016i | \(-0.932974\pi\) | ||
0.977912 | − | 0.209016i | \(-0.0670261\pi\) | |||||||
\(660\) | 3.41940e7i | 0.118937i | ||||||||
\(661\) | 7.97327e7i | 0.276078i | 0.990427 | + | 0.138039i | \(0.0440799\pi\) | ||||
−0.990427 | + | 0.138039i | \(0.955920\pi\) | |||||||
\(662\) | −5.50877e7 | −0.189881 | ||||||||
\(663\) | −2.79812e8 | −0.960120 | ||||||||
\(664\) | − | 3.15415e7i | − | 0.107740i | ||||||
\(665\) | −3.88333e7 | + | 2.65231e8i | −0.132050 | + | 0.901902i | ||||
\(666\) | 2.11119e8 | 0.714668 | ||||||||
\(667\) | − | 4.88497e7i | − | 0.164621i | ||||||
\(668\) | − | 5.26182e7i | − | 0.176525i | ||||||
\(669\) | 3.16764e8 | 1.05793 | ||||||||
\(670\) | 2.54726e7 | 0.0846934 | ||||||||
\(671\) | 1.36801e8 | 0.452816 | ||||||||
\(672\) | 3.68744e7 | 0.121511 | ||||||||
\(673\) | 2.04103e8i | 0.669584i | 0.942292 | + | 0.334792i | \(0.108666\pi\) | ||||
−0.942292 | + | 0.334792i | \(0.891334\pi\) | |||||||
\(674\) | −3.07220e8 | −1.00339 | ||||||||
\(675\) | − | 1.41079e8i | − | 0.458725i | ||||||
\(676\) | 7.31822e6 | 0.0236900 | ||||||||
\(677\) | 1.53931e7i | 0.0496090i | 0.999692 | + | 0.0248045i | \(0.00789633\pi\) | ||||
−0.999692 | + | 0.0248045i | \(0.992104\pi\) | |||||||
\(678\) | − | 1.32925e8i | − | 0.426500i | ||||||
\(679\) | − | 2.23289e8i | − | 0.713277i | ||||||
\(680\) | − | 1.38302e8i | − | 0.439847i | ||||||
\(681\) | 1.89634e8 | 0.600447 | ||||||||
\(682\) | 1.09351e8 | 0.344722 | ||||||||
\(683\) | − | 3.74454e8i | − | 1.17527i | −0.809127 | − | 0.587633i | \(-0.800060\pi\) | ||
0.809127 | − | 0.587633i | \(-0.199940\pi\) | |||||||
\(684\) | −1.66175e7 | + | 1.13498e8i | −0.0519275 | + | 0.354665i | ||||
\(685\) | −7.91771e7 | −0.246336 | ||||||||
\(686\) | 9.76387e7i | 0.302447i | ||||||||
\(687\) | − | 1.52186e8i | − | 0.469357i | ||||||
\(688\) | 2.91820e7 | 0.0896087 | ||||||||
\(689\) | 3.45476e8 | 1.05623 | ||||||||
\(690\) | 2.90099e7 | 0.0883078 | ||||||||
\(691\) | 2.10626e7 | 0.0638377 | 0.0319189 | − | 0.999490i | \(-0.489838\pi\) | ||||
0.0319189 | + | 0.999490i | \(0.489838\pi\) | |||||||
\(692\) | 2.25344e8i | 0.680031i | ||||||||
\(693\) | 1.95296e8 | 0.586805 | ||||||||
\(694\) | 1.28888e8i | 0.385598i | ||||||||
\(695\) | 3.31253e8 | 0.986746 | ||||||||
\(696\) | − | 3.13873e7i | − | 0.0930949i | ||||||
\(697\) | − | 1.16876e9i | − | 3.45165i | ||||||
\(698\) | 2.76297e8i | 0.812475i | ||||||||
\(699\) | − | 1.15280e8i | − | 0.337538i | ||||||
\(700\) | 1.11254e8 | 0.324355 | ||||||||
\(701\) | 4.79784e7 | 0.139281 | 0.0696405 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696405 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(702\) | 2.28701e8i | 0.661083i | ||||||||
\(703\) | 4.84647e8 | + | 7.09586e7i | 1.39495 | + | 0.204239i | ||||
\(704\) | −2.76345e7 | −0.0792015 | ||||||||
\(705\) | − | 5.17578e7i | − | 0.147710i | ||||||
\(706\) | 5.20750e7i | 0.147984i | ||||||||
\(707\) | 1.21595e8 | 0.344078 | ||||||||
\(708\) | 8.60580e7 | 0.242489 | ||||||||
\(709\) | 2.94752e8 | 0.827023 | 0.413511 | − | 0.910499i | \(-0.364302\pi\) | ||||
0.413511 | + | 0.910499i | \(0.364302\pi\) | |||||||
\(710\) | 2.42423e8 | 0.677327 | ||||||||
\(711\) | − | 3.02923e7i | − | 0.0842798i | ||||||
\(712\) | 8.08085e7 | 0.223881 | ||||||||
\(713\) | − | 9.27723e7i | − | 0.255947i | ||||||
\(714\) | 3.11939e8 | 0.856987 | ||||||||
\(715\) | − | 1.67241e8i | − | 0.457536i | ||||||
\(716\) | 7.97658e7i | 0.217309i | ||||||||
\(717\) | − | 3.21205e7i | − | 0.0871415i | ||||||
\(718\) | 2.63212e8i | 0.711103i | ||||||||
\(719\) | −4.44179e8 | −1.19501 | −0.597505 | − | 0.801865i | \(-0.703841\pi\) | ||||
−0.597505 | + | 0.801865i | \(0.703841\pi\) | |||||||
\(720\) | −4.71999e7 | −0.126457 | ||||||||
\(721\) | 1.64891e8i | 0.439939i | ||||||||
\(722\) | −7.62947e7 | + | 2.54961e8i | −0.202714 | + | 0.677427i | ||||
\(723\) | −2.16975e8 | −0.574110 | ||||||||
\(724\) | 2.72759e8i | 0.718726i | ||||||||
\(725\) | − | 9.46985e7i | − | 0.248502i | ||||||
\(726\) | −8.61708e7 | −0.225191 | ||||||||
\(727\) | −5.00461e8 | −1.30247 | −0.651234 | − | 0.758877i | \(-0.725748\pi\) | ||||
−0.651234 | + | 0.758877i | \(0.725748\pi\) | |||||||
\(728\) | −1.80351e8 | −0.467437 | ||||||||
\(729\) | −1.24202e8 | −0.320586 | ||||||||
\(730\) | − | 3.52067e8i | − | 0.905017i | ||||||
\(731\) | 2.46865e8 | 0.631986 | ||||||||
\(732\) | − | 7.45722e7i | − | 0.190127i | ||||||
\(733\) | −3.49394e8 | −0.887163 | −0.443581 | − | 0.896234i | \(-0.646292\pi\) | ||||
−0.443581 | + | 0.896234i | \(0.646292\pi\) | |||||||
\(734\) | − | 5.50094e8i | − | 1.39107i | ||||||
\(735\) | − | 9.97133e7i | − | 0.251126i | ||||||
\(736\) | 2.34449e7i | 0.0588050i | ||||||||
\(737\) | − | 4.30568e7i | − | 0.107557i | ||||||
\(738\) | −3.98875e8 | −0.992357 | ||||||||
\(739\) | 6.49894e8 | 1.61031 | 0.805154 | − | 0.593065i | \(-0.202082\pi\) | ||||
0.805154 | + | 0.593065i | \(0.202082\pi\) | |||||||
\(740\) | 2.01548e8i | 0.497375i | ||||||||
\(741\) | −3.20964e7 | + | 2.19218e8i | −0.0788863 | + | 0.538793i | ||||
\(742\) | −3.85142e8 | −0.942778 | ||||||||
\(743\) | 3.83317e8i | 0.934525i | 0.884119 | + | 0.467263i | \(0.154760\pi\) | ||||
−0.884119 | + | 0.467263i | \(0.845240\pi\) | |||||||
\(744\) | − | 5.96088e7i | − | 0.144741i | ||||||
\(745\) | 3.91965e8 | 0.947934 | ||||||||
\(746\) | 3.36866e8 | 0.811410 | ||||||||
\(747\) | −9.10623e7 | −0.218462 | ||||||||
\(748\) | −2.33774e8 | −0.558588 | ||||||||
\(749\) | 8.93637e8i | 2.12675i | ||||||||
\(750\) | 1.68231e8 | 0.398771 | ||||||||
\(751\) | 6.34895e8i | 1.49893i | 0.662043 | + | 0.749466i | \(0.269690\pi\) | ||||
−0.662043 | + | 0.749466i | \(0.730310\pi\) | |||||||
\(752\) | 4.18290e7 | 0.0983613 | ||||||||
\(753\) | − | 3.73858e8i | − | 0.875632i | ||||||
\(754\) | 1.53513e8i | 0.358123i | ||||||||
\(755\) | − | 4.15779e8i | − | 0.966100i | ||||||
\(756\) | − | 2.54959e8i | − | 0.590072i | ||||||
\(757\) | 4.31098e8 | 0.993775 | 0.496888 | − | 0.867815i | \(-0.334476\pi\) | ||||
0.496888 | + | 0.867815i | \(0.334476\pi\) | |||||||
\(758\) | 4.47614e8 | 1.02777 | ||||||||
\(759\) | − | 4.90359e7i | − | 0.112147i | ||||||
\(760\) | −1.08353e8 | − | 1.58642e7i | −0.246830 | − | 0.0361391i | ||||
\(761\) | 4.43879e8 | 1.00719 | 0.503594 | − | 0.863940i | \(-0.332011\pi\) | ||||
0.503594 | + | 0.863940i | \(0.332011\pi\) | |||||||
\(762\) | 1.56539e8i | 0.353801i | ||||||||
\(763\) | 2.69692e7i | 0.0607148i | ||||||||
\(764\) | −2.33015e8 | −0.522521 | ||||||||
\(765\) | −3.99287e8 | −0.891868 | ||||||||
\(766\) | 3.80947e8 | 0.847576 | ||||||||
\(767\) | −4.20905e8 | −0.932820 | ||||||||
\(768\) | 1.50640e7i | 0.0332549i | ||||||||
\(769\) | −4.67263e8 | −1.02750 | −0.513751 | − | 0.857939i | \(-0.671745\pi\) | ||||
−0.513751 | + | 0.857939i | \(0.671745\pi\) | |||||||
\(770\) | 1.86443e8i | 0.408389i | ||||||||
\(771\) | 3.41635e8 | 0.745417 | ||||||||
\(772\) | 2.82205e7i | 0.0613357i | ||||||||
\(773\) | 1.87256e8i | 0.405413i | 0.979240 | + | 0.202706i | \(0.0649737\pi\) | ||||
−0.979240 | + | 0.202706i | \(0.935026\pi\) | |||||||
\(774\) | − | 8.42504e7i | − | 0.181698i | ||||||
\(775\) | − | 1.79846e8i | − | 0.386362i | ||||||
\(776\) | 9.12184e7 | 0.195208 | ||||||||
\(777\) | −4.54590e8 | −0.969074 | ||||||||
\(778\) | − | 3.42388e8i | − | 0.727075i | ||||||
\(779\) | −9.15662e8 | − | 1.34065e8i | −1.93697 | − | 0.283598i | ||||
\(780\) | −9.11655e7 | −0.192109 | ||||||||
\(781\) | − | 4.09771e8i | − | 0.860178i | ||||||
\(782\) | 1.98332e8i | 0.414736i | ||||||||
\(783\) | −2.17020e8 | −0.452079 | ||||||||
\(784\) | 8.05851e7 | 0.167227 | ||||||||
\(785\) | 1.97486e8 | 0.408251 | ||||||||
\(786\) | −1.59050e8 | −0.327541 | ||||||||
\(787\) | 2.29826e8i | 0.471492i | 0.971815 | + | 0.235746i | \(0.0757533\pi\) | ||||
−0.971815 | + | 0.235746i | \(0.924247\pi\) | |||||||
\(788\) | −3.40211e8 | −0.695297 | ||||||||
\(789\) | 2.18339e8i | 0.444530i | ||||||||
\(790\) | 2.89191e7 | 0.0586548 | ||||||||
\(791\) | − | 7.24776e8i | − | 1.46445i | ||||||
\(792\) | 7.97826e7i | 0.160595i | ||||||||
\(793\) | 3.64729e8i | 0.731392i | ||||||||
\(794\) | − | 4.78464e8i | − | 0.955845i | ||||||
\(795\) | −1.94686e8 | −0.387465 | ||||||||
\(796\) | 7.29300e6 | 0.0144600 | ||||||||
\(797\) | 7.30396e8i | 1.44273i | 0.692558 | + | 0.721363i | \(0.256484\pi\) | ||||
−0.692558 | + | 0.721363i | \(0.743516\pi\) | |||||||
\(798\) | 3.57816e7 | − | 2.44388e8i | 0.0704126 | − | 0.480918i | ||||
\(799\) | 3.53852e8 | 0.693716 | ||||||||
\(800\) | 4.54495e7i | 0.0887685i | ||||||||
\(801\) | − | 2.33299e8i | − | 0.453958i | ||||||
\(802\) | −2.27485e8 | −0.440992 | ||||||||
\(803\) | −5.95104e8 | −1.14933 | ||||||||
\(804\) | −2.34709e7 | −0.0451607 | ||||||||
\(805\) | 1.58177e8 | 0.303218 | ||||||||
\(806\) | 2.91543e8i | 0.556798i | ||||||||
\(807\) | −4.44070e7 | −0.0844950 | ||||||||
\(808\) | 4.96740e7i | 0.0941662i | ||||||||
\(809\) | −7.36585e8 | −1.39116 | −0.695580 | − | 0.718448i | \(-0.744853\pi\) | ||||
−0.695580 | + | 0.718448i | \(0.744853\pi\) | |||||||
\(810\) | 6.12036e7i | 0.115165i | ||||||||
\(811\) | 5.64694e8i | 1.05865i | 0.848421 | + | 0.529323i | \(0.177554\pi\) | ||||
−0.848421 | + | 0.529323i | \(0.822446\pi\) | |||||||
\(812\) | − | 1.71139e8i | − | 0.319655i | ||||||
\(813\) | − | 3.30733e8i | − | 0.615468i | ||||||
\(814\) | 3.40680e8 | 0.631646 | ||||||||
\(815\) | 6.17043e8 | 1.13984 | ||||||||
\(816\) | 1.27434e8i | 0.234538i | ||||||||
\(817\) | 2.83172e7 | − | 1.93406e8i | 0.0519259 | − | 0.354654i | ||||
\(818\) | −7.07555e8 | −1.29271 | ||||||||
\(819\) | 5.20684e8i | 0.947813i | ||||||||
\(820\) | − | 3.80793e8i | − | 0.690634i | ||||||
\(821\) | −4.47879e8 | −0.809340 | −0.404670 | − | 0.914463i | \(-0.632614\pi\) | ||||
−0.404670 | + | 0.914463i | \(0.632614\pi\) | |||||||
\(822\) | 7.29549e7 | 0.131353 | ||||||||
\(823\) | 6.68232e7 | 0.119875 | 0.0599374 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599374 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(824\) | −6.73617e7 | −0.120401 | ||||||||
\(825\) | − | 9.50594e7i | − | 0.169291i | ||||||
\(826\) | 4.69232e8 | 0.832620 | ||||||||
\(827\) | − | 3.98025e8i | − | 0.703710i | −0.936055 | − | 0.351855i | \(-0.885551\pi\) | ||
0.936055 | − | 0.351855i | \(-0.114449\pi\) | |||||||
\(828\) | 6.76868e7 | 0.119238 | ||||||||
\(829\) | − | 1.22758e8i | − | 0.215469i | −0.994180 | − | 0.107735i | \(-0.965640\pi\) | ||
0.994180 | − | 0.107735i | \(-0.0343597\pi\) | |||||||
\(830\) | − | 8.69343e7i | − | 0.152040i | ||||||
\(831\) | 2.66989e8i | 0.465254i | ||||||||
\(832\) | − | 7.36770e7i | − | 0.127927i | ||||||
\(833\) | 6.81709e8 | 1.17941 | ||||||||
\(834\) | −3.05222e8 | −0.526159 | ||||||||
\(835\) | − | 1.45026e8i | − | 0.249107i | ||||||
\(836\) | −2.68155e7 | + | 1.83150e8i | −0.0458952 | + | 0.313464i | ||||
\(837\) | −4.12151e8 | −0.702877 | ||||||||
\(838\) | − | 8.14059e8i | − | 1.38332i | ||||||
\(839\) | 3.01242e8i | 0.510071i | 0.966932 | + | 0.255035i | \(0.0820871\pi\) | ||||
−0.966932 | + | 0.255035i | \(0.917913\pi\) | |||||||
\(840\) | 1.01633e8 | 0.171473 | ||||||||
\(841\) | 4.49151e8 | 0.755099 | ||||||||
\(842\) | −1.34446e7 | −0.0225223 | ||||||||
\(843\) | −7.31813e7 | −0.122157 | ||||||||
\(844\) | − | 1.51021e8i | − | 0.251194i | ||||||
\(845\) | 2.01704e7 | 0.0334306 | ||||||||
\(846\) | − | 1.20763e8i | − | 0.199445i | ||||||
\(847\) | −4.69847e8 | −0.773225 | ||||||||
\(848\) | − | 1.57339e8i | − | 0.258017i | ||||||
\(849\) | 5.13868e8i | 0.839708i | ||||||||
\(850\) | 3.84480e8i | 0.626061i | ||||||||
\(851\) | − | 2.89030e8i | − | 0.468980i | ||||||
\(852\) | −2.23372e8 | −0.361169 | ||||||||
\(853\) | 5.69751e8 | 0.917991 | 0.458995 | − | 0.888439i | \(-0.348209\pi\) | ||||
0.458995 | + | 0.888439i | \(0.348209\pi\) | |||||||
\(854\) | − | 4.06605e8i | − | 0.652829i | ||||||
\(855\) | −4.58010e7 | + | 3.12821e8i | −0.0732786 | + | 0.500492i | ||||
\(856\) | −3.65070e8 | −0.582042 | ||||||||
\(857\) | − | 3.43485e7i | − | 0.0545714i | −0.999628 | − | 0.0272857i | \(-0.991314\pi\) | ||
0.999628 | − | 0.0272857i | \(-0.00868639\pi\) | |||||||
\(858\) | 1.54098e8i | 0.243970i | ||||||||
\(859\) | 2.02023e8 | 0.318729 | 0.159365 | − | 0.987220i | \(-0.449055\pi\) | ||||
0.159365 | + | 0.987220i | \(0.449055\pi\) | |||||||
\(860\) | 8.04312e7 | 0.126453 | ||||||||
\(861\) | 8.58875e8 | 1.34561 | ||||||||
\(862\) | 2.94183e8 | 0.459300 | ||||||||
\(863\) | 1.48089e8i | 0.230404i | 0.993342 | + | 0.115202i | \(0.0367515\pi\) | ||||
−0.993342 | + | 0.115202i | \(0.963249\pi\) | |||||||
\(864\) | 1.04156e8 | 0.161489 | ||||||||
\(865\) | 6.21092e8i | 0.959638i | ||||||||
\(866\) | −1.58862e8 | −0.244606 | ||||||||
\(867\) | 7.31260e8i | 1.12206i | ||||||||
\(868\) | − | 3.25017e8i | − | 0.496989i | ||||||
\(869\) | − | 4.88824e7i | − | 0.0744892i | ||||||
\(870\) | − | 8.65093e7i | − | 0.131373i | ||||||
\(871\) | 1.14795e8 | 0.173727 | ||||||||
\(872\) | −1.10175e7 | −0.0166163 | ||||||||
\(873\) | − | 2.63353e8i | − | 0.395819i | ||||||
\(874\) | 1.55383e8 | + | 2.27500e7i | 0.232739 | + | 0.0340759i | ||||
\(875\) | 9.17282e8 | 1.36924 | ||||||||
\(876\) | 3.24400e8i | 0.482579i | ||||||||
\(877\) | − | 8.48597e8i | − | 1.25806i | −0.777379 | − | 0.629032i | \(-0.783451\pi\) | ||
0.777379 | − | 0.629032i | \(-0.216549\pi\) | |||||||
\(878\) | 7.61245e8 | 1.12471 | ||||||||
\(879\) | 1.21774e8 | 0.179303 | ||||||||
\(880\) | −7.61659e7 | −0.111767 | ||||||||
\(881\) | −2.29592e8 | −0.335760 | −0.167880 | − | 0.985807i | \(-0.553692\pi\) | ||||
−0.167880 | + | 0.985807i | \(0.553692\pi\) | |||||||
\(882\) | − | 2.32654e8i | − | 0.339083i | ||||||
\(883\) | 6.05960e8 | 0.880160 | 0.440080 | − | 0.897958i | \(-0.354950\pi\) | ||||
0.440080 | + | 0.897958i | \(0.354950\pi\) | |||||||
\(884\) | − | 6.23270e8i | − | 0.902235i | ||||||
\(885\) | 2.37192e8 | 0.342193 | ||||||||
\(886\) | 4.81966e8i | 0.692971i | ||||||||
\(887\) | − | 1.01673e9i | − | 1.45692i | −0.685086 | − | 0.728462i | \(-0.740235\pi\) | ||
0.685086 | − | 0.728462i | \(-0.259765\pi\) | |||||||
\(888\) | − | 1.85710e8i | − | 0.265214i | ||||||
\(889\) | 8.53531e8i | 1.21483i | ||||||||
\(890\) | 2.22724e8 | 0.315934 | ||||||||
\(891\) | 1.03453e8 | 0.146255 | ||||||||
\(892\) | 7.05579e8i | 0.994149i | ||||||||
\(893\) | 4.05894e7 | − | 2.77225e8i | 0.0569978 | − | 0.389295i | ||||
\(894\) | −3.61162e8 | −0.505463 | ||||||||
\(895\) | 2.19850e8i | 0.306660i | ||||||||
\(896\) | 8.21363e7i | 0.114186i | ||||||||
\(897\) | 1.30736e8 | 0.181141 | ||||||||
\(898\) | −1.12281e7 | −0.0155053 | ||||||||
\(899\) | −2.76653e8 | −0.380764 | ||||||||
\(900\) | 1.31216e8 | 0.179994 | ||||||||
\(901\) | − | 1.33101e9i | − | 1.81972i | ||||||
\(902\) | −6.43661e8 | −0.877076 | ||||||||
\(903\) | 1.81412e8i | 0.246378i | ||||||||
\(904\) | 2.96086e8 | 0.400786 | ||||||||
\(905\) | 7.51776e8i | 1.01424i | ||||||||
\(906\) | 3.83105e8i | 0.515150i | ||||||||
\(907\) | 9.83840e8i | 1.31857i | 0.751894 | + | 0.659284i | \(0.229141\pi\) | ||||
−0.751894 | + | 0.659284i | \(0.770859\pi\) | |||||||
\(908\) | 4.22402e8i | 0.564246i | ||||||||
\(909\) | 1.43412e8 | 0.190939 | ||||||||
\(910\) | −4.97080e8 | −0.659633 | ||||||||
\(911\) | 1.30290e7i | 0.0172328i | 0.999963 | + | 0.00861641i | \(0.00274272\pi\) | ||||
−0.999963 | + | 0.00861641i | \(0.997257\pi\) | |||||||
\(912\) | 9.98377e7 | + | 1.46175e7i | 0.131616 | + | 0.0192703i | ||||
\(913\) | −1.46946e8 | −0.193084 | ||||||||
\(914\) | − | 6.65380e8i | − | 0.871428i | ||||||
\(915\) | − | 2.05535e8i | − | 0.268301i | ||||||
\(916\) | 3.38988e8 | 0.441060 | ||||||||
\(917\) | −8.67220e8 | −1.12466 | ||||||||
\(918\) | 8.81108e8 | 1.13894 | ||||||||
\(919\) | −2.98731e8 | −0.384888 | −0.192444 | − | 0.981308i | \(-0.561641\pi\) | ||||
−0.192444 | + | 0.981308i | \(0.561641\pi\) | |||||||
\(920\) | 6.46185e7i | 0.0829838i | ||||||||
\(921\) | 4.61501e8 | 0.590737 | ||||||||
\(922\) | 5.60643e8i | 0.715309i | ||||||||
\(923\) | 1.09250e9 | 1.38937 | ||||||||
\(924\) | − | 1.71791e8i | − | 0.217764i | ||||||
\(925\) | − | 5.60305e8i | − | 0.707944i | ||||||
\(926\) | 1.41812e8i | 0.178599i | ||||||||
\(927\) | 1.94478e8i | 0.244135i | ||||||||
\(928\) | 6.99140e7 | 0.0874823 | ||||||||
\(929\) | −9.87802e8 | −1.23203 | −0.616017 | − | 0.787733i | \(-0.711255\pi\) | ||||
−0.616017 | + | 0.787733i | \(0.711255\pi\) | |||||||
\(930\) | − | 1.64293e8i | − | 0.204254i | ||||||
\(931\) | 7.81969e7 | − | 5.34084e8i | 0.0969037 | − | 0.661852i | ||||
\(932\) | 2.56782e8 | 0.317189 | ||||||||
\(933\) | − | 4.60134e8i | − | 0.566552i | ||||||
\(934\) | 5.53744e8i | 0.679624i | ||||||||
\(935\) | −6.44325e8 | −0.788261 | ||||||||
\(936\) | −2.12710e8 | −0.259395 | ||||||||
\(937\) | −8.49634e8 | −1.03279 | −0.516396 | − | 0.856350i | \(-0.672727\pi\) | ||||
−0.516396 | + | 0.856350i | \(0.672727\pi\) | |||||||
\(938\) | −1.27975e8 | −0.155066 | ||||||||
\(939\) | 5.34051e8i | 0.645039i | ||||||||
\(940\) | 1.15289e8 | 0.138804 | ||||||||
\(941\) | − | 8.83763e8i | − | 1.06064i | −0.847798 | − | 0.530319i | \(-0.822072\pi\) | ||
0.847798 | − | 0.530319i | \(-0.177928\pi\) | |||||||
\(942\) | −1.81966e8 | −0.217690 | ||||||||
\(943\) | 5.46076e8i | 0.651205i | ||||||||
\(944\) | 1.91691e8i | 0.227869i | ||||||||
\(945\) | − | 7.02715e8i | − | 0.832691i | ||||||
\(946\) | − | 1.35954e8i | − | 0.160590i | ||||||
\(947\) | 1.85948e8 | 0.218948 | 0.109474 | − | 0.993990i | \(-0.465083\pi\) | ||||
0.109474 | + | 0.993990i | \(0.465083\pi\) | |||||||
\(948\) | −2.66465e7 | −0.0312763 | ||||||||
\(949\) | − | 1.58662e9i | − | 1.85641i | ||||||
\(950\) | 3.01220e8 | + | 4.41025e7i | 0.351328 | + | 0.0514390i | ||||
\(951\) | −6.68634e8 | −0.777404 | ||||||||
\(952\) | 6.94832e8i | 0.805321i | ||||||||
\(953\) | 9.07378e8i | 1.04836i | 0.851608 | + | 0.524179i | \(0.175628\pi\) | ||||
−0.851608 | + | 0.524179i | \(0.824372\pi\) | |||||||
\(954\) | −4.54247e8 | −0.523175 | ||||||||
\(955\) | −6.42233e8 | −0.737366 | ||||||||
\(956\) | 7.15473e7 | 0.0818878 | ||||||||
\(957\) | −1.46228e8 | −0.166838 | ||||||||
\(958\) | 5.43586e6i | 0.00618260i | ||||||||
\(959\) | 3.97787e8 | 0.451019 | ||||||||
\(960\) | 4.15191e7i | 0.0469283i | ||||||||
\(961\) | 3.62102e8 | 0.408000 | ||||||||
\(962\) | 9.08296e8i | 1.02024i | ||||||||
\(963\) | 1.05398e9i | 1.18019i | ||||||||
\(964\) | − | 4.83304e8i | − | 0.539498i | ||||||
\(965\) | 7.77811e7i | 0.0865550i | ||||||||
\(966\) | −1.45746e8 | −0.161684 | ||||||||
\(967\) | 4.77936e8 | 0.528555 | 0.264277 | − | 0.964447i | \(-0.414867\pi\) | ||||
0.264277 | + | 0.964447i | \(0.414867\pi\) | |||||||
\(968\) | − | 1.91942e8i | − | 0.211614i | ||||||
\(969\) | 8.44576e8 | + | 1.23657e8i | 0.928255 | + | 0.135909i | ||||
\(970\) | 2.51415e8 | 0.275471 | ||||||||
\(971\) | − | 6.23290e8i | − | 0.680820i | −0.940277 | − | 0.340410i | \(-0.889434\pi\) | ||
0.940277 | − | 0.340410i | \(-0.110566\pi\) | |||||||
\(972\) | − | 4.75851e8i | − | 0.518170i | ||||||
\(973\) | −1.66422e9 | −1.80664 | ||||||||
\(974\) | −6.31838e8 | −0.683800 | ||||||||
\(975\) | 2.53440e8 | 0.273440 | ||||||||
\(976\) | 1.66107e8 | 0.178664 | ||||||||
\(977\) | − | 1.47715e9i | − | 1.58395i | −0.610554 | − | 0.791975i | \(-0.709053\pi\) | ||
0.610554 | − | 0.791975i | \(-0.290947\pi\) | |||||||
\(978\) | −5.68553e8 | −0.607791 | ||||||||
\(979\) | − | 3.76473e8i | − | 0.401223i | ||||||
\(980\) | 2.22108e8 | 0.235986 | ||||||||
\(981\) | 3.18082e7i | 0.0336925i | ||||||||
\(982\) | − | 6.93018e8i | − | 0.731829i | ||||||
\(983\) | − | 1.78294e9i | − | 1.87705i | −0.345206 | − | 0.938527i | \(-0.612191\pi\) | ||
0.345206 | − | 0.938527i | \(-0.387809\pi\) | |||||||
\(984\) | 3.50869e8i | 0.368264i | ||||||||
\(985\) | −9.37687e8 | −0.981182 | ||||||||
\(986\) | 5.91437e8 | 0.616990 | ||||||||
\(987\) | 2.60032e8i | 0.270443i | ||||||||
\(988\) | −4.88301e8 | − | 7.14935e7i | −0.506310 | − | 0.0741303i | ||||
\(989\) | −1.15342e8 | −0.119234 | ||||||||
\(990\) | 2.19896e8i | 0.226627i | ||||||||
\(991\) | 1.44206e9i | 1.48171i | 0.671668 | + | 0.740853i | \(0.265578\pi\) | ||||
−0.671668 | + | 0.740853i | \(0.734422\pi\) | |||||||
\(992\) | 1.32776e8 | 0.136015 | ||||||||
\(993\) | 1.39900e8 | 0.142880 | ||||||||
\(994\) | −1.21794e9 | −1.24013 | ||||||||
\(995\) | 2.01009e7 | 0.0204054 | ||||||||
\(996\) | 8.01025e7i | 0.0810715i | ||||||||
\(997\) | −6.78975e8 | −0.685123 | −0.342561 | − | 0.939495i | \(-0.611294\pi\) | ||||
−0.342561 | + | 0.939495i | \(0.611294\pi\) | |||||||
\(998\) | 7.24207e8i | 0.728570i | ||||||||
\(999\) | −1.28405e9 | −1.28791 |
(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 | 38.7.b.a.37.4 | ✓ | 10 | |
3.2 | odd | 2 | 342.7.d.a.37.9 | 10 | |||
4.3 | odd | 2 | 304.7.e.e.113.3 | 10 | |||
19.18 | odd | 2 | inner | 38.7.b.a.37.7 | yes | 10 | |
57.56 | even | 2 | 342.7.d.a.37.4 | 10 | |||
76.75 | even | 2 | 304.7.e.e.113.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.7.b.a.37.4 | ✓ | 10 | 1.1 | even | 1 | trivial | |
38.7.b.a.37.7 | yes | 10 | 19.18 | odd | 2 | inner | |
304.7.e.e.113.3 | 10 | 4.3 | odd | 2 | |||
304.7.e.e.113.8 | 10 | 76.75 | even | 2 | |||
342.7.d.a.37.4 | 10 | 57.56 | even | 2 | |||
342.7.d.a.37.9 | 10 | 3.2 | odd | 2 |