Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(65.2743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 62.2743 | 1.37608 | 0.688041 | − | 0.725672i | \(-0.258471\pi\) | ||||
0.688041 | + | 0.725672i | \(0.258471\pi\) | |||||||
\(3\) | −384.675 | −0.913959 | −0.456979 | − | 0.889477i | \(-0.651069\pi\) | ||||
−0.456979 | + | 0.889477i | \(0.651069\pi\) | |||||||
\(4\) | 1830.09 | 0.893600 | ||||||||
\(5\) | 1377.47 | 0.197127 | 0.0985635 | − | 0.995131i | \(-0.468575\pi\) | ||||
0.0985635 | + | 0.995131i | \(0.468575\pi\) | |||||||
\(6\) | −23955.4 | −1.25768 | ||||||||
\(7\) | 33050.3 | 0.743252 | 0.371626 | − | 0.928383i | \(-0.378800\pi\) | ||||
0.371626 | + | 0.928383i | \(0.378800\pi\) | |||||||
\(8\) | −13570.0 | −0.146415 | ||||||||
\(9\) | −29172.4 | −0.164679 | ||||||||
\(10\) | 85780.8 | 0.271263 | ||||||||
\(11\) | −800438. | −1.49854 | −0.749270 | − | 0.662265i | \(-0.769595\pi\) | ||||
−0.749270 | + | 0.662265i | \(0.769595\pi\) | |||||||
\(12\) | −703990. | −0.816714 | ||||||||
\(13\) | 1.48554e6 | 1.10968 | 0.554839 | − | 0.831958i | \(-0.312780\pi\) | ||||
0.554839 | + | 0.831958i | \(0.312780\pi\) | |||||||
\(14\) | 2.05818e6 | 1.02277 | ||||||||
\(15\) | −529877. | −0.180166 | ||||||||
\(16\) | −4.59309e6 | −1.09508 | ||||||||
\(17\) | −1.13043e7 | −1.93097 | −0.965485 | − | 0.260457i | \(-0.916127\pi\) | ||||
−0.965485 | + | 0.260457i | \(0.916127\pi\) | |||||||
\(18\) | −1.81669e6 | −0.226612 | ||||||||
\(19\) | −9.78812e6 | −0.906890 | −0.453445 | − | 0.891284i | \(-0.649805\pi\) | ||||
−0.453445 | + | 0.891284i | \(0.649805\pi\) | |||||||
\(20\) | 2.52089e6 | 0.176153 | ||||||||
\(21\) | −1.27136e7 | −0.679302 | ||||||||
\(22\) | −4.98468e7 | −2.06211 | ||||||||
\(23\) | 546284. | 0.0176977 | 0.00884883 | − | 0.999961i | \(-0.497183\pi\) | ||||
0.00884883 | + | 0.999961i | \(0.497183\pi\) | |||||||
\(24\) | 5.22005e6 | 0.133818 | ||||||||
\(25\) | −4.69307e7 | −0.961141 | ||||||||
\(26\) | 9.25112e7 | 1.52701 | ||||||||
\(27\) | 7.93659e7 | 1.06447 | ||||||||
\(28\) | 6.04851e7 | 0.664170 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | −3.29977e7 | −0.247923 | ||||||||
\(31\) | 4.17817e6 | 0.0262118 | 0.0131059 | − | 0.999914i | \(-0.495828\pi\) | ||||
0.0131059 | + | 0.999914i | \(0.495828\pi\) | |||||||
\(32\) | −2.58240e8 | −1.36050 | ||||||||
\(33\) | 3.07908e8 | 1.36960 | ||||||||
\(34\) | −7.03969e8 | −2.65717 | ||||||||
\(35\) | 4.55257e7 | 0.146515 | ||||||||
\(36\) | −5.33882e7 | −0.147157 | ||||||||
\(37\) | 3.50598e8 | 0.831190 | 0.415595 | − | 0.909550i | \(-0.363573\pi\) | ||||
0.415595 | + | 0.909550i | \(0.363573\pi\) | |||||||
\(38\) | −6.09549e8 | −1.24795 | ||||||||
\(39\) | −5.71451e8 | −1.01420 | ||||||||
\(40\) | −1.86923e7 | −0.0288624 | ||||||||
\(41\) | 7.34075e8 | 0.989531 | 0.494765 | − | 0.869027i | \(-0.335254\pi\) | ||||
0.494765 | + | 0.869027i | \(0.335254\pi\) | |||||||
\(42\) | −7.91731e8 | −0.934774 | ||||||||
\(43\) | −1.74203e9 | −1.80709 | −0.903545 | − | 0.428494i | \(-0.859044\pi\) | ||||
−0.903545 | + | 0.428494i | \(0.859044\pi\) | |||||||
\(44\) | −1.46488e9 | −1.33909 | ||||||||
\(45\) | −4.01841e7 | −0.0324627 | ||||||||
\(46\) | 3.40195e7 | 0.0243534 | ||||||||
\(47\) | 1.70223e9 | 1.08263 | 0.541315 | − | 0.840820i | \(-0.317927\pi\) | ||||
0.541315 | + | 0.840820i | \(0.317927\pi\) | |||||||
\(48\) | 1.76685e9 | 1.00086 | ||||||||
\(49\) | −8.85005e8 | −0.447577 | ||||||||
\(50\) | −2.92258e9 | −1.32261 | ||||||||
\(51\) | 4.34849e9 | 1.76483 | ||||||||
\(52\) | 2.71868e9 | 0.991608 | ||||||||
\(53\) | 2.30025e9 | 0.755539 | 0.377770 | − | 0.925900i | \(-0.376691\pi\) | ||||
0.377770 | + | 0.925900i | \(0.376691\pi\) | |||||||
\(54\) | 4.94246e9 | 1.46480 | ||||||||
\(55\) | −1.10258e9 | −0.295403 | ||||||||
\(56\) | −4.48494e8 | −0.108823 | ||||||||
\(57\) | 3.76524e9 | 0.828860 | ||||||||
\(58\) | 1.27732e9 | 0.255532 | ||||||||
\(59\) | −2.84523e8 | −0.0518121 | −0.0259060 | − | 0.999664i | \(-0.508247\pi\) | ||||
−0.0259060 | + | 0.999664i | \(0.508247\pi\) | |||||||
\(60\) | −9.69723e8 | −0.160996 | ||||||||
\(61\) | 5.13866e9 | 0.778997 | 0.389499 | − | 0.921027i | \(-0.372648\pi\) | ||||
0.389499 | + | 0.921027i | \(0.372648\pi\) | |||||||
\(62\) | 2.60193e8 | 0.0360696 | ||||||||
\(63\) | −9.64157e8 | −0.122398 | ||||||||
\(64\) | −6.67509e9 | −0.777083 | ||||||||
\(65\) | 2.04629e9 | 0.218747 | ||||||||
\(66\) | 1.91748e10 | 1.88469 | ||||||||
\(67\) | −3.85315e9 | −0.348662 | −0.174331 | − | 0.984687i | \(-0.555776\pi\) | ||||
−0.174331 | + | 0.984687i | \(0.555776\pi\) | |||||||
\(68\) | −2.06880e10 | −1.72552 | ||||||||
\(69\) | −2.10142e8 | −0.0161749 | ||||||||
\(70\) | 2.83508e9 | 0.201617 | ||||||||
\(71\) | 2.82041e10 | 1.85520 | 0.927602 | − | 0.373570i | \(-0.121867\pi\) | ||||
0.927602 | + | 0.373570i | \(0.121867\pi\) | |||||||
\(72\) | 3.95871e8 | 0.0241115 | ||||||||
\(73\) | −1.81192e10 | −1.02297 | −0.511484 | − | 0.859293i | \(-0.670904\pi\) | ||||
−0.511484 | + | 0.859293i | \(0.670904\pi\) | |||||||
\(74\) | 2.18333e10 | 1.14378 | ||||||||
\(75\) | 1.80531e10 | 0.878443 | ||||||||
\(76\) | −1.79132e10 | −0.810396 | ||||||||
\(77\) | −2.64547e10 | −1.11379 | ||||||||
\(78\) | −3.55867e10 | −1.39562 | ||||||||
\(79\) | −3.94609e10 | −1.44284 | −0.721419 | − | 0.692499i | \(-0.756510\pi\) | ||||
−0.721419 | + | 0.692499i | \(0.756510\pi\) | |||||||
\(80\) | −6.32684e9 | −0.215870 | ||||||||
\(81\) | −2.53622e10 | −0.808202 | ||||||||
\(82\) | 4.57140e10 | 1.36168 | ||||||||
\(83\) | 1.27885e10 | 0.356362 | 0.178181 | − | 0.983998i | \(-0.442979\pi\) | ||||
0.178181 | + | 0.983998i | \(0.442979\pi\) | |||||||
\(84\) | −2.32671e10 | −0.607024 | ||||||||
\(85\) | −1.55713e10 | −0.380646 | ||||||||
\(86\) | −1.08484e11 | −2.48670 | ||||||||
\(87\) | −7.89012e9 | −0.169718 | ||||||||
\(88\) | 1.08620e10 | 0.219409 | ||||||||
\(89\) | 4.46844e10 | 0.848225 | 0.424112 | − | 0.905610i | \(-0.360586\pi\) | ||||
0.424112 | + | 0.905610i | \(0.360586\pi\) | |||||||
\(90\) | −2.50244e9 | −0.0446714 | ||||||||
\(91\) | 4.90976e10 | 0.824770 | ||||||||
\(92\) | 9.99751e8 | 0.0158146 | ||||||||
\(93\) | −1.60724e9 | −0.0239565 | ||||||||
\(94\) | 1.06005e11 | 1.48979 | ||||||||
\(95\) | −1.34828e10 | −0.178772 | ||||||||
\(96\) | 9.93386e10 | 1.24344 | ||||||||
\(97\) | −7.40280e10 | −0.875289 | −0.437644 | − | 0.899148i | \(-0.644187\pi\) | ||||
−0.437644 | + | 0.899148i | \(0.644187\pi\) | |||||||
\(98\) | −5.51131e10 | −0.615902 | ||||||||
\(99\) | 2.33507e10 | 0.246778 | ||||||||
\(100\) | −8.58875e10 | −0.858875 | ||||||||
\(101\) | −8.70065e10 | −0.823728 | −0.411864 | − | 0.911245i | \(-0.635122\pi\) | ||||
−0.411864 | + | 0.911245i | \(0.635122\pi\) | |||||||
\(102\) | 2.70799e11 | 2.42855 | ||||||||
\(103\) | −2.00277e11 | −1.70227 | −0.851133 | − | 0.524951i | \(-0.824084\pi\) | ||||
−0.851133 | + | 0.524951i | \(0.824084\pi\) | |||||||
\(104\) | −2.01589e10 | −0.162474 | ||||||||
\(105\) | −1.75126e10 | −0.133909 | ||||||||
\(106\) | 1.43246e11 | 1.03968 | ||||||||
\(107\) | −6.27684e10 | −0.432644 | −0.216322 | − | 0.976322i | \(-0.569406\pi\) | ||||
−0.216322 | + | 0.976322i | \(0.569406\pi\) | |||||||
\(108\) | 1.45247e11 | 0.951209 | ||||||||
\(109\) | 1.65628e11 | 1.03107 | 0.515535 | − | 0.856868i | \(-0.327593\pi\) | ||||
0.515535 | + | 0.856868i | \(0.327593\pi\) | |||||||
\(110\) | −6.86623e10 | −0.406498 | ||||||||
\(111\) | −1.34866e11 | −0.759673 | ||||||||
\(112\) | −1.51803e11 | −0.813920 | ||||||||
\(113\) | 1.11390e11 | 0.568741 | 0.284370 | − | 0.958714i | \(-0.408215\pi\) | ||||
0.284370 | + | 0.958714i | \(0.408215\pi\) | |||||||
\(114\) | 2.34478e11 | 1.14058 | ||||||||
\(115\) | 7.52489e8 | 0.00348869 | ||||||||
\(116\) | 3.75373e10 | 0.165937 | ||||||||
\(117\) | −4.33369e10 | −0.182741 | ||||||||
\(118\) | −1.77185e10 | −0.0712977 | ||||||||
\(119\) | −3.73611e11 | −1.43520 | ||||||||
\(120\) | 7.19045e9 | 0.0263790 | ||||||||
\(121\) | 3.55390e11 | 1.24562 | ||||||||
\(122\) | 3.20007e11 | 1.07196 | ||||||||
\(123\) | −2.82380e11 | −0.904391 | ||||||||
\(124\) | 7.64644e9 | 0.0234229 | ||||||||
\(125\) | −1.31905e11 | −0.386594 | ||||||||
\(126\) | −6.00422e10 | −0.168430 | ||||||||
\(127\) | −4.11525e11 | −1.10529 | −0.552644 | − | 0.833417i | \(-0.686381\pi\) | ||||
−0.552644 | + | 0.833417i | \(0.686381\pi\) | |||||||
\(128\) | 1.13189e11 | 0.291173 | ||||||||
\(129\) | 6.70115e11 | 1.65161 | ||||||||
\(130\) | 1.27431e11 | 0.301014 | ||||||||
\(131\) | −9.62047e10 | −0.217873 | −0.108937 | − | 0.994049i | \(-0.534745\pi\) | ||||
−0.108937 | + | 0.994049i | \(0.534745\pi\) | |||||||
\(132\) | 5.63501e11 | 1.22388 | ||||||||
\(133\) | −3.23500e11 | −0.674047 | ||||||||
\(134\) | −2.39952e11 | −0.479787 | ||||||||
\(135\) | 1.09324e11 | 0.209836 | ||||||||
\(136\) | 1.53400e11 | 0.282724 | ||||||||
\(137\) | −3.08367e11 | −0.545890 | −0.272945 | − | 0.962030i | \(-0.587998\pi\) | ||||
−0.272945 | + | 0.962030i | \(0.587998\pi\) | |||||||
\(138\) | −1.30864e10 | −0.0222580 | ||||||||
\(139\) | 6.03606e11 | 0.986671 | 0.493336 | − | 0.869839i | \(-0.335777\pi\) | ||||
0.493336 | + | 0.869839i | \(0.335777\pi\) | |||||||
\(140\) | 8.33162e10 | 0.130926 | ||||||||
\(141\) | −6.54804e11 | −0.989479 | ||||||||
\(142\) | 1.75639e12 | 2.55291 | ||||||||
\(143\) | −1.18909e12 | −1.66290 | ||||||||
\(144\) | 1.33992e11 | 0.180337 | ||||||||
\(145\) | 2.82534e10 | 0.0366056 | ||||||||
\(146\) | −1.12836e12 | −1.40769 | ||||||||
\(147\) | 3.40439e11 | 0.409067 | ||||||||
\(148\) | 6.41627e11 | 0.742751 | ||||||||
\(149\) | −1.18808e12 | −1.32532 | −0.662660 | − | 0.748920i | \(-0.730573\pi\) | ||||
−0.662660 | + | 0.748920i | \(0.730573\pi\) | |||||||
\(150\) | 1.12424e12 | 1.20881 | ||||||||
\(151\) | 4.61543e11 | 0.478453 | 0.239226 | − | 0.970964i | \(-0.423106\pi\) | ||||
0.239226 | + | 0.970964i | \(0.423106\pi\) | |||||||
\(152\) | 1.32825e11 | 0.132782 | ||||||||
\(153\) | 3.29775e11 | 0.317991 | ||||||||
\(154\) | −1.64745e12 | −1.53267 | ||||||||
\(155\) | 5.75529e9 | 0.00516706 | ||||||||
\(156\) | −1.04581e12 | −0.906289 | ||||||||
\(157\) | 4.49681e11 | 0.376232 | 0.188116 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188116 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(158\) | −2.45740e12 | −1.98546 | ||||||||
\(159\) | −8.84846e11 | −0.690532 | ||||||||
\(160\) | −3.55718e11 | −0.268192 | ||||||||
\(161\) | 1.80549e10 | 0.0131538 | ||||||||
\(162\) | −1.57942e12 | −1.11215 | ||||||||
\(163\) | −1.77931e12 | −1.21121 | −0.605604 | − | 0.795766i | \(-0.707068\pi\) | ||||
−0.605604 | + | 0.795766i | \(0.707068\pi\) | |||||||
\(164\) | 1.34343e12 | 0.884245 | ||||||||
\(165\) | 4.24134e11 | 0.269986 | ||||||||
\(166\) | 7.96398e11 | 0.490383 | ||||||||
\(167\) | 5.68373e11 | 0.338604 | 0.169302 | − | 0.985564i | \(-0.445849\pi\) | ||||
0.169302 | + | 0.985564i | \(0.445849\pi\) | |||||||
\(168\) | 1.72524e11 | 0.0994601 | ||||||||
\(169\) | 4.14679e11 | 0.231385 | ||||||||
\(170\) | −9.69695e11 | −0.523801 | ||||||||
\(171\) | 2.85543e11 | 0.149346 | ||||||||
\(172\) | −3.18808e12 | −1.61481 | ||||||||
\(173\) | −3.46675e11 | −0.170086 | −0.0850430 | − | 0.996377i | \(-0.527103\pi\) | ||||
−0.0850430 | + | 0.996377i | \(0.527103\pi\) | |||||||
\(174\) | −4.91352e11 | −0.233546 | ||||||||
\(175\) | −1.55107e12 | −0.714370 | ||||||||
\(176\) | 3.67649e12 | 1.64102 | ||||||||
\(177\) | 1.09449e11 | 0.0473541 | ||||||||
\(178\) | 2.78269e12 | 1.16723 | ||||||||
\(179\) | −1.84659e12 | −0.751068 | −0.375534 | − | 0.926809i | \(-0.622541\pi\) | ||||
−0.375534 | + | 0.926809i | \(0.622541\pi\) | |||||||
\(180\) | −7.35405e10 | −0.0290087 | ||||||||
\(181\) | 1.69842e12 | 0.649849 | 0.324925 | − | 0.945740i | \(-0.394661\pi\) | ||||
0.324925 | + | 0.945740i | \(0.394661\pi\) | |||||||
\(182\) | 3.05752e12 | 1.13495 | ||||||||
\(183\) | −1.97671e12 | −0.711971 | ||||||||
\(184\) | −7.41310e9 | −0.00259121 | ||||||||
\(185\) | 4.82938e11 | 0.163850 | ||||||||
\(186\) | −1.00090e11 | −0.0329661 | ||||||||
\(187\) | 9.04842e12 | 2.89364 | ||||||||
\(188\) | 3.11524e12 | 0.967437 | ||||||||
\(189\) | 2.62306e12 | 0.791168 | ||||||||
\(190\) | −8.39633e11 | −0.246005 | ||||||||
\(191\) | 6.53577e12 | 1.86043 | 0.930215 | − | 0.367016i | \(-0.119621\pi\) | ||||
0.930215 | + | 0.367016i | \(0.119621\pi\) | |||||||
\(192\) | 2.56774e12 | 0.710222 | ||||||||
\(193\) | 2.24825e12 | 0.604338 | 0.302169 | − | 0.953254i | \(-0.402289\pi\) | ||||
0.302169 | + | 0.953254i | \(0.402289\pi\) | |||||||
\(194\) | −4.61004e12 | −1.20447 | ||||||||
\(195\) | −7.87155e11 | −0.199926 | ||||||||
\(196\) | −1.61964e12 | −0.399955 | ||||||||
\(197\) | 4.50505e12 | 1.08177 | 0.540885 | − | 0.841097i | \(-0.318089\pi\) | ||||
0.540885 | + | 0.841097i | \(0.318089\pi\) | |||||||
\(198\) | 1.45415e12 | 0.339587 | ||||||||
\(199\) | −4.83401e12 | −1.09803 | −0.549017 | − | 0.835811i | \(-0.684998\pi\) | ||||
−0.549017 | + | 0.835811i | \(0.684998\pi\) | |||||||
\(200\) | 6.36852e11 | 0.140726 | ||||||||
\(201\) | 1.48221e12 | 0.318662 | ||||||||
\(202\) | −5.41827e12 | −1.13352 | ||||||||
\(203\) | 6.77899e11 | 0.138018 | ||||||||
\(204\) | 7.95814e12 | 1.57705 | ||||||||
\(205\) | 1.01116e12 | 0.195063 | ||||||||
\(206\) | −1.24721e13 | −2.34246 | ||||||||
\(207\) | −1.59364e10 | −0.00291444 | ||||||||
\(208\) | −6.82324e12 | −1.21519 | ||||||||
\(209\) | 7.83479e12 | 1.35901 | ||||||||
\(210\) | −1.09058e12 | −0.184269 | ||||||||
\(211\) | −1.10099e13 | −1.81229 | −0.906146 | − | 0.422964i | \(-0.860990\pi\) | ||||
−0.906146 | + | 0.422964i | \(0.860990\pi\) | |||||||
\(212\) | 4.20966e12 | 0.675150 | ||||||||
\(213\) | −1.08494e13 | −1.69558 | ||||||||
\(214\) | −3.90886e12 | −0.595353 | ||||||||
\(215\) | −2.39959e12 | −0.356226 | ||||||||
\(216\) | −1.07700e12 | −0.155854 | ||||||||
\(217\) | 1.38090e11 | 0.0194820 | ||||||||
\(218\) | 1.03144e13 | 1.41884 | ||||||||
\(219\) | 6.96998e12 | 0.934951 | ||||||||
\(220\) | −2.01782e12 | −0.263972 | ||||||||
\(221\) | −1.67931e13 | −2.14276 | ||||||||
\(222\) | −8.39871e12 | −1.04537 | ||||||||
\(223\) | −5.53451e12 | −0.672051 | −0.336026 | − | 0.941853i | \(-0.609083\pi\) | ||||
−0.336026 | + | 0.941853i | \(0.609083\pi\) | |||||||
\(224\) | −8.53492e12 | −1.01120 | ||||||||
\(225\) | 1.36908e12 | 0.158280 | ||||||||
\(226\) | 6.93673e12 | 0.782634 | ||||||||
\(227\) | −4.70942e12 | −0.518592 | −0.259296 | − | 0.965798i | \(-0.583490\pi\) | ||||
−0.259296 | + | 0.965798i | \(0.583490\pi\) | |||||||
\(228\) | 6.89074e12 | 0.740669 | ||||||||
\(229\) | −4.06336e12 | −0.426374 | −0.213187 | − | 0.977011i | \(-0.568384\pi\) | ||||
−0.213187 | + | 0.977011i | \(0.568384\pi\) | |||||||
\(230\) | 4.68607e10 | 0.00480072 | ||||||||
\(231\) | 1.01765e13 | 1.01796 | ||||||||
\(232\) | −2.78337e11 | −0.0271886 | ||||||||
\(233\) | 1.96315e13 | 1.87282 | 0.936411 | − | 0.350906i | \(-0.114126\pi\) | ||||
0.936411 | + | 0.350906i | \(0.114126\pi\) | |||||||
\(234\) | −2.69878e12 | −0.251466 | ||||||||
\(235\) | 2.34476e12 | 0.213415 | ||||||||
\(236\) | −5.20703e11 | −0.0462993 | ||||||||
\(237\) | 1.51796e13 | 1.31869 | ||||||||
\(238\) | −2.32664e13 | −1.97495 | ||||||||
\(239\) | 1.39900e13 | 1.16046 | 0.580231 | − | 0.814452i | \(-0.302962\pi\) | ||||
0.580231 | + | 0.814452i | \(0.302962\pi\) | |||||||
\(240\) | 2.43377e12 | 0.197296 | ||||||||
\(241\) | −1.44074e13 | −1.14154 | −0.570772 | − | 0.821109i | \(-0.693356\pi\) | ||||
−0.570772 | + | 0.821109i | \(0.693356\pi\) | |||||||
\(242\) | 2.21317e13 | 1.71408 | ||||||||
\(243\) | −4.30322e12 | −0.325806 | ||||||||
\(244\) | 9.40423e12 | 0.696112 | ||||||||
\(245\) | −1.21907e12 | −0.0882295 | ||||||||
\(246\) | −1.75850e13 | −1.24451 | ||||||||
\(247\) | −1.45407e13 | −1.00636 | ||||||||
\(248\) | −5.66980e10 | −0.00383781 | ||||||||
\(249\) | −4.91943e12 | −0.325700 | ||||||||
\(250\) | −8.21427e12 | −0.531985 | ||||||||
\(251\) | −2.15745e13 | −1.36689 | −0.683446 | − | 0.730001i | \(-0.739520\pi\) | ||||
−0.683446 | + | 0.730001i | \(0.739520\pi\) | |||||||
\(252\) | −1.76450e12 | −0.109375 | ||||||||
\(253\) | −4.37267e11 | −0.0265206 | ||||||||
\(254\) | −2.56274e13 | −1.52097 | ||||||||
\(255\) | 5.98990e12 | 0.347895 | ||||||||
\(256\) | 2.07194e13 | 1.17776 | ||||||||
\(257\) | 2.02393e13 | 1.12607 | 0.563034 | − | 0.826434i | \(-0.309634\pi\) | ||||
0.563034 | + | 0.826434i | \(0.309634\pi\) | |||||||
\(258\) | 4.17310e13 | 2.27274 | ||||||||
\(259\) | 1.15874e13 | 0.617783 | ||||||||
\(260\) | 3.74489e12 | 0.195473 | ||||||||
\(261\) | −5.98360e11 | −0.0305802 | ||||||||
\(262\) | −5.99108e12 | −0.299811 | ||||||||
\(263\) | 1.12028e13 | 0.548997 | 0.274499 | − | 0.961587i | \(-0.411488\pi\) | ||||
0.274499 | + | 0.961587i | \(0.411488\pi\) | |||||||
\(264\) | −4.17833e12 | −0.200531 | ||||||||
\(265\) | 3.16851e12 | 0.148937 | ||||||||
\(266\) | −2.01458e13 | −0.927544 | ||||||||
\(267\) | −1.71890e13 | −0.775242 | ||||||||
\(268\) | −7.05162e12 | −0.311564 | ||||||||
\(269\) | −1.31186e13 | −0.567871 | −0.283935 | − | 0.958843i | \(-0.591640\pi\) | ||||
−0.283935 | + | 0.958843i | \(0.591640\pi\) | |||||||
\(270\) | 6.80807e12 | 0.288751 | ||||||||
\(271\) | −1.61271e13 | −0.670232 | −0.335116 | − | 0.942177i | \(-0.608775\pi\) | ||||
−0.335116 | + | 0.942177i | \(0.608775\pi\) | |||||||
\(272\) | 5.19219e13 | 2.11457 | ||||||||
\(273\) | −1.88866e13 | −0.753806 | ||||||||
\(274\) | −1.92034e13 | −0.751189 | ||||||||
\(275\) | 3.75651e13 | 1.44031 | ||||||||
\(276\) | −3.84579e11 | −0.0144539 | ||||||||
\(277\) | 3.78738e13 | 1.39540 | 0.697702 | − | 0.716388i | \(-0.254206\pi\) | ||||
0.697702 | + | 0.716388i | \(0.254206\pi\) | |||||||
\(278\) | 3.75892e13 | 1.35774 | ||||||||
\(279\) | −1.21887e11 | −0.00431654 | ||||||||
\(280\) | −6.17785e11 | −0.0214520 | ||||||||
\(281\) | −5.07029e12 | −0.172643 | −0.0863214 | − | 0.996267i | \(-0.527511\pi\) | ||||
−0.0863214 | + | 0.996267i | \(0.527511\pi\) | |||||||
\(282\) | −4.07775e13 | −1.36160 | ||||||||
\(283\) | −5.45868e13 | −1.78757 | −0.893783 | − | 0.448500i | \(-0.851958\pi\) | ||||
−0.893783 | + | 0.448500i | \(0.851958\pi\) | |||||||
\(284\) | 5.16161e13 | 1.65781 | ||||||||
\(285\) | 5.18649e12 | 0.163391 | ||||||||
\(286\) | −7.40495e13 | −2.28828 | ||||||||
\(287\) | 2.42614e13 | 0.735471 | ||||||||
\(288\) | 7.53350e12 | 0.224047 | ||||||||
\(289\) | 9.35159e13 | 2.72865 | ||||||||
\(290\) | 1.75946e12 | 0.0503722 | ||||||||
\(291\) | 2.84767e13 | 0.799978 | ||||||||
\(292\) | −3.31597e13 | −0.914125 | ||||||||
\(293\) | −3.12899e13 | −0.846511 | −0.423256 | − | 0.906010i | \(-0.639113\pi\) | ||||
−0.423256 | + | 0.906010i | \(0.639113\pi\) | |||||||
\(294\) | 2.12006e13 | 0.562909 | ||||||||
\(295\) | −3.91921e11 | −0.0102136 | ||||||||
\(296\) | −4.75763e12 | −0.121699 | ||||||||
\(297\) | −6.35275e13 | −1.59515 | ||||||||
\(298\) | −7.39869e13 | −1.82375 | ||||||||
\(299\) | 8.11529e11 | 0.0196387 | ||||||||
\(300\) | 3.30388e13 | 0.784977 | ||||||||
\(301\) | −5.75746e13 | −1.34312 | ||||||||
\(302\) | 2.87423e13 | 0.658390 | ||||||||
\(303\) | 3.34692e13 | 0.752854 | ||||||||
\(304\) | 4.49578e13 | 0.993116 | ||||||||
\(305\) | 7.07834e12 | 0.153561 | ||||||||
\(306\) | 2.05365e13 | 0.437581 | ||||||||
\(307\) | −2.08032e12 | −0.0435381 | −0.0217691 | − | 0.999763i | \(-0.506930\pi\) | ||||
−0.0217691 | + | 0.999763i | \(0.506930\pi\) | |||||||
\(308\) | −4.84146e13 | −0.995285 | ||||||||
\(309\) | 7.70416e13 | 1.55580 | ||||||||
\(310\) | 3.58407e11 | 0.00711029 | ||||||||
\(311\) | 3.53426e13 | 0.688837 | 0.344418 | − | 0.938816i | \(-0.388076\pi\) | ||||
0.344418 | + | 0.938816i | \(0.388076\pi\) | |||||||
\(312\) | 7.75461e12 | 0.148494 | ||||||||
\(313\) | 2.98830e13 | 0.562252 | 0.281126 | − | 0.959671i | \(-0.409292\pi\) | ||||
0.281126 | + | 0.959671i | \(0.409292\pi\) | |||||||
\(314\) | 2.80036e13 | 0.517726 | ||||||||
\(315\) | −1.32809e12 | −0.0241280 | ||||||||
\(316\) | −7.22170e13 | −1.28932 | ||||||||
\(317\) | −4.25262e13 | −0.746157 | −0.373079 | − | 0.927800i | \(-0.621698\pi\) | ||||
−0.373079 | + | 0.927800i | \(0.621698\pi\) | |||||||
\(318\) | −5.51032e13 | −0.950228 | ||||||||
\(319\) | −1.64179e13 | −0.278272 | ||||||||
\(320\) | −9.19472e12 | −0.153184 | ||||||||
\(321\) | 2.41454e13 | 0.395418 | ||||||||
\(322\) | 1.12435e12 | 0.0181007 | ||||||||
\(323\) | 1.10648e14 | 1.75118 | ||||||||
\(324\) | −4.64152e13 | −0.722209 | ||||||||
\(325\) | −6.97176e13 | −1.06656 | ||||||||
\(326\) | −1.10805e14 | −1.66672 | ||||||||
\(327\) | −6.37129e13 | −0.942356 | ||||||||
\(328\) | −9.96143e12 | −0.144882 | ||||||||
\(329\) | 5.62592e13 | 0.804666 | ||||||||
\(330\) | 2.64126e13 | 0.371522 | ||||||||
\(331\) | 3.15763e12 | 0.0436825 | 0.0218412 | − | 0.999761i | \(-0.493047\pi\) | ||||
0.0218412 | + | 0.999761i | \(0.493047\pi\) | |||||||
\(332\) | 2.34042e13 | 0.318445 | ||||||||
\(333\) | −1.02278e13 | −0.136880 | ||||||||
\(334\) | 3.53950e13 | 0.465947 | ||||||||
\(335\) | −5.30758e12 | −0.0687307 | ||||||||
\(336\) | 5.83948e13 | 0.743889 | ||||||||
\(337\) | −6.97371e13 | −0.873976 | −0.436988 | − | 0.899467i | \(-0.643955\pi\) | ||||
−0.436988 | + | 0.899467i | \(0.643955\pi\) | |||||||
\(338\) | 2.58239e13 | 0.318405 | ||||||||
\(339\) | −4.28489e13 | −0.519806 | ||||||||
\(340\) | −2.84970e13 | −0.340146 | ||||||||
\(341\) | −3.34437e12 | −0.0392794 | ||||||||
\(342\) | 1.77820e13 | 0.205512 | ||||||||
\(343\) | −9.46009e13 | −1.07591 | ||||||||
\(344\) | 2.36394e13 | 0.264585 | ||||||||
\(345\) | −2.89463e11 | −0.00318852 | ||||||||
\(346\) | −2.15889e13 | −0.234052 | ||||||||
\(347\) | −1.18515e14 | −1.26462 | −0.632309 | − | 0.774716i | \(-0.717893\pi\) | ||||
−0.632309 | + | 0.774716i | \(0.717893\pi\) | |||||||
\(348\) | −1.44396e13 | −0.151660 | ||||||||
\(349\) | −3.54876e13 | −0.366890 | −0.183445 | − | 0.983030i | \(-0.558725\pi\) | ||||
−0.183445 | + | 0.983030i | \(0.558725\pi\) | |||||||
\(350\) | −9.65921e13 | −0.983031 | ||||||||
\(351\) | 1.17901e14 | 1.18122 | ||||||||
\(352\) | 2.06706e14 | 2.03877 | ||||||||
\(353\) | −1.48557e14 | −1.44256 | −0.721278 | − | 0.692645i | \(-0.756445\pi\) | ||||
−0.721278 | + | 0.692645i | \(0.756445\pi\) | |||||||
\(354\) | 6.81585e12 | 0.0651631 | ||||||||
\(355\) | 3.88502e13 | 0.365711 | ||||||||
\(356\) | 8.17766e13 | 0.757973 | ||||||||
\(357\) | 1.43719e14 | 1.31171 | ||||||||
\(358\) | −1.14995e14 | −1.03353 | ||||||||
\(359\) | −1.39595e14 | −1.23552 | −0.617760 | − | 0.786367i | \(-0.711960\pi\) | ||||
−0.617760 | + | 0.786367i | \(0.711960\pi\) | |||||||
\(360\) | 5.45299e11 | 0.00475304 | ||||||||
\(361\) | −2.06830e13 | −0.177551 | ||||||||
\(362\) | 1.05768e14 | 0.894246 | ||||||||
\(363\) | −1.36710e14 | −1.13845 | ||||||||
\(364\) | 8.98532e13 | 0.737014 | ||||||||
\(365\) | −2.49585e13 | −0.201655 | ||||||||
\(366\) | −1.23098e14 | −0.979731 | ||||||||
\(367\) | −2.38895e14 | −1.87303 | −0.936514 | − | 0.350631i | \(-0.885967\pi\) | ||||
−0.936514 | + | 0.350631i | \(0.885967\pi\) | |||||||
\(368\) | −2.50914e12 | −0.0193803 | ||||||||
\(369\) | −2.14148e13 | −0.162955 | ||||||||
\(370\) | 3.00746e13 | 0.225471 | ||||||||
\(371\) | 7.60238e13 | 0.561556 | ||||||||
\(372\) | −2.94139e12 | −0.0214075 | ||||||||
\(373\) | −3.21648e13 | −0.230665 | −0.115333 | − | 0.993327i | \(-0.536793\pi\) | ||||
−0.115333 | + | 0.993327i | \(0.536793\pi\) | |||||||
\(374\) | 5.63484e14 | 3.98188 | ||||||||
\(375\) | 5.07404e13 | 0.353331 | ||||||||
\(376\) | −2.30993e13 | −0.158513 | ||||||||
\(377\) | 3.04702e13 | 0.206062 | ||||||||
\(378\) | 1.63350e14 | 1.08871 | ||||||||
\(379\) | 1.37788e14 | 0.905099 | 0.452550 | − | 0.891739i | \(-0.350515\pi\) | ||||
0.452550 | + | 0.891739i | \(0.350515\pi\) | |||||||
\(380\) | −2.46748e13 | −0.159751 | ||||||||
\(381\) | 1.58303e14 | 1.01019 | ||||||||
\(382\) | 4.07011e14 | 2.56010 | ||||||||
\(383\) | −1.73711e14 | −1.07704 | −0.538522 | − | 0.842611i | \(-0.681017\pi\) | ||||
−0.538522 | + | 0.842611i | \(0.681017\pi\) | |||||||
\(384\) | −4.35411e13 | −0.266120 | ||||||||
\(385\) | −3.64405e13 | −0.219559 | ||||||||
\(386\) | 1.40008e14 | 0.831618 | ||||||||
\(387\) | 5.08193e13 | 0.297590 | ||||||||
\(388\) | −1.35478e14 | −0.782158 | ||||||||
\(389\) | 2.34150e14 | 1.33282 | 0.666411 | − | 0.745585i | \(-0.267830\pi\) | ||||
0.666411 | + | 0.745585i | \(0.267830\pi\) | |||||||
\(390\) | −4.90195e13 | −0.275115 | ||||||||
\(391\) | −6.17538e12 | −0.0341737 | ||||||||
\(392\) | 1.20096e13 | 0.0655321 | ||||||||
\(393\) | 3.70075e13 | 0.199127 | ||||||||
\(394\) | 2.80549e14 | 1.48860 | ||||||||
\(395\) | −5.43560e13 | −0.284422 | ||||||||
\(396\) | 4.27340e13 | 0.220521 | ||||||||
\(397\) | −1.79333e14 | −0.912669 | −0.456334 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456334 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(398\) | −3.01035e14 | −1.51098 | ||||||||
\(399\) | 1.24442e14 | 0.616051 | ||||||||
\(400\) | 2.15557e14 | 1.05253 | ||||||||
\(401\) | −3.03065e14 | −1.45963 | −0.729813 | − | 0.683646i | \(-0.760393\pi\) | ||||
−0.729813 | + | 0.683646i | \(0.760393\pi\) | |||||||
\(402\) | 9.23035e13 | 0.438506 | ||||||||
\(403\) | 6.20686e12 | 0.0290867 | ||||||||
\(404\) | −1.59230e14 | −0.736083 | ||||||||
\(405\) | −3.49356e13 | −0.159318 | ||||||||
\(406\) | 4.22157e13 | 0.189925 | ||||||||
\(407\) | −2.80632e14 | −1.24557 | ||||||||
\(408\) | −5.90092e13 | −0.258398 | ||||||||
\(409\) | 1.52684e14 | 0.659651 | 0.329825 | − | 0.944042i | \(-0.393010\pi\) | ||||
0.329825 | + | 0.944042i | \(0.393010\pi\) | |||||||
\(410\) | 6.29696e13 | 0.268423 | ||||||||
\(411\) | 1.18621e14 | 0.498921 | ||||||||
\(412\) | −3.66526e14 | −1.52114 | ||||||||
\(413\) | −9.40356e12 | −0.0385094 | ||||||||
\(414\) | −9.92432e11 | −0.00401050 | ||||||||
\(415\) | 1.76158e13 | 0.0702486 | ||||||||
\(416\) | −3.83627e14 | −1.50972 | ||||||||
\(417\) | −2.32192e14 | −0.901777 | ||||||||
\(418\) | 4.87906e14 | 1.87011 | ||||||||
\(419\) | −2.74751e14 | −1.03935 | −0.519676 | − | 0.854363i | \(-0.673947\pi\) | ||||
−0.519676 | + | 0.854363i | \(0.673947\pi\) | |||||||
\(420\) | −3.20496e13 | −0.119661 | ||||||||
\(421\) | −9.97837e13 | −0.367712 | −0.183856 | − | 0.982953i | \(-0.558858\pi\) | ||||
−0.183856 | + | 0.982953i | \(0.558858\pi\) | |||||||
\(422\) | −6.85632e14 | −2.49386 | ||||||||
\(423\) | −4.96582e13 | −0.178287 | ||||||||
\(424\) | −3.12144e13 | −0.110622 | ||||||||
\(425\) | 5.30520e14 | 1.85593 | ||||||||
\(426\) | −6.75640e14 | −2.33326 | ||||||||
\(427\) | 1.69834e14 | 0.578991 | ||||||||
\(428\) | −1.14872e14 | −0.386610 | ||||||||
\(429\) | 4.57411e14 | 1.51982 | ||||||||
\(430\) | −1.49433e14 | −0.490196 | ||||||||
\(431\) | −9.82326e13 | −0.318149 | −0.159075 | − | 0.987267i | \(-0.550851\pi\) | ||||
−0.159075 | + | 0.987267i | \(0.550851\pi\) | |||||||
\(432\) | −3.64535e14 | −1.16568 | ||||||||
\(433\) | 1.34165e14 | 0.423601 | 0.211800 | − | 0.977313i | \(-0.432067\pi\) | ||||
0.211800 | + | 0.977313i | \(0.432067\pi\) | |||||||
\(434\) | 8.59945e12 | 0.0268088 | ||||||||
\(435\) | −1.08684e13 | −0.0334560 | ||||||||
\(436\) | 3.03115e14 | 0.921364 | ||||||||
\(437\) | −5.34710e12 | −0.0160498 | ||||||||
\(438\) | 4.34051e14 | 1.28657 | ||||||||
\(439\) | 1.46616e14 | 0.429168 | 0.214584 | − | 0.976705i | \(-0.431160\pi\) | ||||
0.214584 | + | 0.976705i | \(0.431160\pi\) | |||||||
\(440\) | 1.49620e13 | 0.0432514 | ||||||||
\(441\) | 2.58178e13 | 0.0737066 | ||||||||
\(442\) | −1.04578e15 | −2.94861 | ||||||||
\(443\) | −1.21156e13 | −0.0337385 | −0.0168693 | − | 0.999858i | \(-0.505370\pi\) | ||||
−0.0168693 | + | 0.999858i | \(0.505370\pi\) | |||||||
\(444\) | −2.46818e14 | −0.678844 | ||||||||
\(445\) | 6.15513e13 | 0.167208 | ||||||||
\(446\) | −3.44658e14 | −0.924797 | ||||||||
\(447\) | 4.57024e14 | 1.21129 | ||||||||
\(448\) | −2.20614e14 | −0.577569 | ||||||||
\(449\) | 4.14075e14 | 1.07084 | 0.535419 | − | 0.844586i | \(-0.320154\pi\) | ||||
0.535419 | + | 0.844586i | \(0.320154\pi\) | |||||||
\(450\) | 8.52587e13 | 0.217806 | ||||||||
\(451\) | −5.87582e14 | −1.48285 | ||||||||
\(452\) | 2.03854e14 | 0.508227 | ||||||||
\(453\) | −1.77544e14 | −0.437286 | ||||||||
\(454\) | −2.93276e14 | −0.713624 | ||||||||
\(455\) | 6.76304e13 | 0.162584 | ||||||||
\(456\) | −5.10945e13 | −0.121358 | ||||||||
\(457\) | 6.86418e14 | 1.61083 | 0.805415 | − | 0.592711i | \(-0.201942\pi\) | ||||
0.805415 | + | 0.592711i | \(0.201942\pi\) | |||||||
\(458\) | −2.53043e14 | −0.586725 | ||||||||
\(459\) | −8.97178e14 | −2.05546 | ||||||||
\(460\) | 1.37712e12 | 0.00311749 | ||||||||
\(461\) | 8.82601e14 | 1.97428 | 0.987142 | − | 0.159848i | \(-0.0511003\pi\) | ||||
0.987142 | + | 0.159848i | \(0.0511003\pi\) | |||||||
\(462\) | 6.33732e14 | 1.40080 | ||||||||
\(463\) | −3.93909e14 | −0.860399 | −0.430200 | − | 0.902734i | \(-0.641557\pi\) | ||||
−0.430200 | + | 0.902734i | \(0.641557\pi\) | |||||||
\(464\) | −9.42097e13 | −0.203351 | ||||||||
\(465\) | −2.21392e12 | −0.00472248 | ||||||||
\(466\) | 1.22254e15 | 2.57715 | ||||||||
\(467\) | −4.51731e13 | −0.0941102 | −0.0470551 | − | 0.998892i | \(-0.514984\pi\) | ||||
−0.0470551 | + | 0.998892i | \(0.514984\pi\) | |||||||
\(468\) | −7.93106e13 | −0.163297 | ||||||||
\(469\) | −1.27348e14 | −0.259143 | ||||||||
\(470\) | 1.46019e14 | 0.293677 | ||||||||
\(471\) | −1.72981e14 | −0.343861 | ||||||||
\(472\) | 3.86099e12 | 0.00758608 | ||||||||
\(473\) | 1.39439e15 | 2.70799 | ||||||||
\(474\) | 9.45299e14 | 1.81463 | ||||||||
\(475\) | 4.59363e14 | 0.871649 | ||||||||
\(476\) | −6.83743e14 | −1.28249 | ||||||||
\(477\) | −6.71038e13 | −0.124422 | ||||||||
\(478\) | 8.71221e14 | 1.59689 | ||||||||
\(479\) | −4.93799e14 | −0.894756 | −0.447378 | − | 0.894345i | \(-0.647642\pi\) | ||||
−0.447378 | + | 0.894345i | \(0.647642\pi\) | |||||||
\(480\) | 1.36836e14 | 0.245116 | ||||||||
\(481\) | 5.20829e14 | 0.922353 | ||||||||
\(482\) | −8.97213e14 | −1.57086 | ||||||||
\(483\) | −6.94525e12 | −0.0120220 | ||||||||
\(484\) | 6.50397e14 | 1.11309 | ||||||||
\(485\) | −1.01971e14 | −0.172543 | ||||||||
\(486\) | −2.67980e14 | −0.448336 | ||||||||
\(487\) | 5.62413e14 | 0.930350 | 0.465175 | − | 0.885219i | \(-0.345991\pi\) | ||||
0.465175 | + | 0.885219i | \(0.345991\pi\) | |||||||
\(488\) | −6.97319e13 | −0.114057 | ||||||||
\(489\) | 6.84454e14 | 1.10699 | ||||||||
\(490\) | −7.59165e13 | −0.121411 | ||||||||
\(491\) | −6.06349e14 | −0.958902 | −0.479451 | − | 0.877569i | \(-0.659164\pi\) | ||||
−0.479451 | + | 0.877569i | \(0.659164\pi\) | |||||||
\(492\) | −5.16782e14 | −0.808163 | ||||||||
\(493\) | −2.31865e14 | −0.358572 | ||||||||
\(494\) | −9.05511e14 | −1.38483 | ||||||||
\(495\) | 3.21649e13 | 0.0486467 | ||||||||
\(496\) | −1.91907e13 | −0.0287040 | ||||||||
\(497\) | 9.32154e14 | 1.37888 | ||||||||
\(498\) | −3.06354e14 | −0.448190 | ||||||||
\(499\) | −9.66448e14 | −1.39838 | −0.699191 | − | 0.714935i | \(-0.746456\pi\) | ||||
−0.699191 | + | 0.714935i | \(0.746456\pi\) | |||||||
\(500\) | −2.41398e14 | −0.345460 | ||||||||
\(501\) | −2.18639e14 | −0.309470 | ||||||||
\(502\) | −1.34353e15 | −1.88095 | ||||||||
\(503\) | 5.10073e14 | 0.706331 | 0.353166 | − | 0.935561i | \(-0.385105\pi\) | ||||
0.353166 | + | 0.935561i | \(0.385105\pi\) | |||||||
\(504\) | 1.30837e13 | 0.0179210 | ||||||||
\(505\) | −1.19849e14 | −0.162379 | ||||||||
\(506\) | −2.72305e13 | −0.0364946 | ||||||||
\(507\) | −1.59517e14 | −0.211476 | ||||||||
\(508\) | −7.53128e14 | −0.987685 | ||||||||
\(509\) | −5.21410e12 | −0.00676443 | −0.00338222 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338222 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(510\) | 3.73017e14 | 0.478732 | ||||||||
\(511\) | −5.98843e14 | −0.760323 | ||||||||
\(512\) | 1.05847e15 | 1.32952 | ||||||||
\(513\) | −7.76842e14 | −0.965356 | ||||||||
\(514\) | 1.26039e15 | 1.54956 | ||||||||
\(515\) | −2.75876e14 | −0.335562 | ||||||||
\(516\) | 1.22637e15 | 1.47587 | ||||||||
\(517\) | −1.36253e15 | −1.62236 | ||||||||
\(518\) | 7.21596e14 | 0.850120 | ||||||||
\(519\) | 1.33357e14 | 0.155452 | ||||||||
\(520\) | −2.77682e13 | −0.0320280 | ||||||||
\(521\) | 4.21554e14 | 0.481112 | 0.240556 | − | 0.970635i | \(-0.422670\pi\) | ||||
0.240556 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(522\) | −3.72625e13 | −0.0420808 | ||||||||
\(523\) | 8.60935e14 | 0.962080 | 0.481040 | − | 0.876699i | \(-0.340259\pi\) | ||||
0.481040 | + | 0.876699i | \(0.340259\pi\) | |||||||
\(524\) | −1.76064e14 | −0.194692 | ||||||||
\(525\) | 5.96659e14 | 0.652905 | ||||||||
\(526\) | 6.97648e14 | 0.755465 | ||||||||
\(527\) | −4.72314e13 | −0.0506142 | ||||||||
\(528\) | −1.41425e15 | −1.49982 | ||||||||
\(529\) | −9.52511e14 | −0.999687 | ||||||||
\(530\) | 1.97317e14 | 0.204950 | ||||||||
\(531\) | 8.30022e12 | 0.00853238 | ||||||||
\(532\) | −5.92035e14 | −0.602329 | ||||||||
\(533\) | 1.09050e15 | 1.09806 | ||||||||
\(534\) | −1.07043e15 | −1.06680 | ||||||||
\(535\) | −8.64614e13 | −0.0852858 | ||||||||
\(536\) | 5.22874e13 | 0.0510494 | ||||||||
\(537\) | 7.10337e14 | 0.686446 | ||||||||
\(538\) | −8.16951e14 | −0.781436 | ||||||||
\(539\) | 7.08392e14 | 0.670711 | ||||||||
\(540\) | 2.00073e14 | 0.187509 | ||||||||
\(541\) | −2.89790e14 | −0.268842 | −0.134421 | − | 0.990924i | \(-0.542918\pi\) | ||||
−0.134421 | + | 0.990924i | \(0.542918\pi\) | |||||||
\(542\) | −1.00430e15 | −0.922293 | ||||||||
\(543\) | −6.53339e14 | −0.593936 | ||||||||
\(544\) | 2.91923e15 | 2.62709 | ||||||||
\(545\) | 2.28147e14 | 0.203252 | ||||||||
\(546\) | −1.17615e15 | −1.03730 | ||||||||
\(547\) | 2.01239e15 | 1.75704 | 0.878520 | − | 0.477705i | \(-0.158531\pi\) | ||||
0.878520 | + | 0.477705i | \(0.158531\pi\) | |||||||
\(548\) | −5.64340e14 | −0.487807 | ||||||||
\(549\) | −1.49907e14 | −0.128285 | ||||||||
\(550\) | 2.33934e15 | 1.98198 | ||||||||
\(551\) | −2.00766e14 | −0.168405 | ||||||||
\(552\) | 2.85163e12 | 0.00236826 | ||||||||
\(553\) | −1.30419e15 | −1.07239 | ||||||||
\(554\) | 2.35857e15 | 1.92019 | ||||||||
\(555\) | −1.85774e14 | −0.149752 | ||||||||
\(556\) | 1.10466e15 | 0.881689 | ||||||||
\(557\) | 1.45243e15 | 1.14787 | 0.573933 | − | 0.818902i | \(-0.305417\pi\) | ||||
0.573933 | + | 0.818902i | \(0.305417\pi\) | |||||||
\(558\) | −7.59046e12 | −0.00593991 | ||||||||
\(559\) | −2.58786e15 | −2.00529 | ||||||||
\(560\) | −2.09104e14 | −0.160446 | ||||||||
\(561\) | −3.48070e15 | −2.64466 | ||||||||
\(562\) | −3.15749e14 | −0.237571 | ||||||||
\(563\) | −1.90166e15 | −1.41689 | −0.708447 | − | 0.705764i | \(-0.750604\pi\) | ||||
−0.708447 | + | 0.705764i | \(0.750604\pi\) | |||||||
\(564\) | −1.19835e15 | −0.884198 | ||||||||
\(565\) | 1.53436e14 | 0.112114 | ||||||||
\(566\) | −3.39935e15 | −2.45984 | ||||||||
\(567\) | −8.38229e14 | −0.600697 | ||||||||
\(568\) | −3.82731e14 | −0.271630 | ||||||||
\(569\) | 1.27765e15 | 0.898041 | 0.449020 | − | 0.893522i | \(-0.351773\pi\) | ||||
0.449020 | + | 0.893522i | \(0.351773\pi\) | |||||||
\(570\) | 3.22985e14 | 0.224839 | ||||||||
\(571\) | 8.73926e14 | 0.602527 | 0.301263 | − | 0.953541i | \(-0.402592\pi\) | ||||
0.301263 | + | 0.953541i | \(0.402592\pi\) | |||||||
\(572\) | −2.17614e15 | −1.48596 | ||||||||
\(573\) | −2.51414e15 | −1.70036 | ||||||||
\(574\) | 1.51086e15 | 1.01207 | ||||||||
\(575\) | −2.56375e13 | −0.0170099 | ||||||||
\(576\) | 1.94729e14 | 0.127969 | ||||||||
\(577\) | 1.90100e15 | 1.23741 | 0.618706 | − | 0.785623i | \(-0.287657\pi\) | ||||
0.618706 | + | 0.785623i | \(0.287657\pi\) | |||||||
\(578\) | 5.82364e15 | 3.75484 | ||||||||
\(579\) | −8.64846e14 | −0.552340 | ||||||||
\(580\) | 5.17064e13 | 0.0327107 | ||||||||
\(581\) | 4.22665e14 | 0.264867 | ||||||||
\(582\) | 1.77337e15 | 1.10083 | ||||||||
\(583\) | −1.84121e15 | −1.13221 | ||||||||
\(584\) | 2.45878e14 | 0.149778 | ||||||||
\(585\) | −5.96952e13 | −0.0360232 | ||||||||
\(586\) | −1.94856e15 | −1.16487 | ||||||||
\(587\) | −5.70371e14 | −0.337791 | −0.168895 | − | 0.985634i | \(-0.554020\pi\) | ||||
−0.168895 | + | 0.985634i | \(0.554020\pi\) | |||||||
\(588\) | 6.23035e14 | 0.365542 | ||||||||
\(589\) | −4.08964e13 | −0.0237712 | ||||||||
\(590\) | −2.44066e13 | −0.0140547 | ||||||||
\(591\) | −1.73298e15 | −0.988693 | ||||||||
\(592\) | −1.61033e15 | −0.910219 | ||||||||
\(593\) | 6.76252e14 | 0.378711 | 0.189355 | − | 0.981909i | \(-0.439360\pi\) | ||||
0.189355 | + | 0.981909i | \(0.439360\pi\) | |||||||
\(594\) | −3.95613e15 | −2.19505 | ||||||||
\(595\) | −5.14637e14 | −0.282916 | ||||||||
\(596\) | −2.17430e15 | −1.18431 | ||||||||
\(597\) | 1.85952e15 | 1.00356 | ||||||||
\(598\) | 5.05375e13 | 0.0270244 | ||||||||
\(599\) | −5.41473e14 | −0.286899 | −0.143449 | − | 0.989658i | \(-0.545819\pi\) | ||||
−0.143449 | + | 0.989658i | \(0.545819\pi\) | |||||||
\(600\) | −2.44981e14 | −0.128617 | ||||||||
\(601\) | 2.86332e15 | 1.48957 | 0.744785 | − | 0.667305i | \(-0.232552\pi\) | ||||
0.744785 | + | 0.667305i | \(0.232552\pi\) | |||||||
\(602\) | −3.58542e15 | −1.84825 | ||||||||
\(603\) | 1.12406e14 | 0.0574174 | ||||||||
\(604\) | 8.44666e14 | 0.427545 | ||||||||
\(605\) | 4.89538e14 | 0.245545 | ||||||||
\(606\) | 2.08427e15 | 1.03599 | ||||||||
\(607\) | 2.24665e15 | 1.10662 | 0.553310 | − | 0.832976i | \(-0.313365\pi\) | ||||
0.553310 | + | 0.832976i | \(0.313365\pi\) | |||||||
\(608\) | 2.52769e15 | 1.23383 | ||||||||
\(609\) | −2.60771e14 | −0.126143 | ||||||||
\(610\) | 4.40799e14 | 0.211313 | ||||||||
\(611\) | 2.52874e15 | 1.20137 | ||||||||
\(612\) | 6.03518e14 | 0.284157 | ||||||||
\(613\) | −1.37966e15 | −0.643783 | −0.321891 | − | 0.946777i | \(-0.604319\pi\) | ||||
−0.321891 | + | 0.946777i | \(0.604319\pi\) | |||||||
\(614\) | −1.29551e14 | −0.0599120 | ||||||||
\(615\) | −3.88969e14 | −0.178280 | ||||||||
\(616\) | 3.58992e14 | 0.163076 | ||||||||
\(617\) | −1.77458e15 | −0.798966 | −0.399483 | − | 0.916741i | \(-0.630810\pi\) | ||||
−0.399483 | + | 0.916741i | \(0.630810\pi\) | |||||||
\(618\) | 4.79772e15 | 2.14091 | ||||||||
\(619\) | −6.71770e14 | −0.297113 | −0.148557 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148557 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(620\) | 1.05327e13 | 0.00461728 | ||||||||
\(621\) | 4.33563e13 | 0.0188386 | ||||||||
\(622\) | 2.20094e15 | 0.947895 | ||||||||
\(623\) | 1.47683e15 | 0.630445 | ||||||||
\(624\) | 2.62473e15 | 1.11063 | ||||||||
\(625\) | 2.10984e15 | 0.884933 | ||||||||
\(626\) | 1.86095e15 | 0.773705 | ||||||||
\(627\) | −3.01384e15 | −1.24208 | ||||||||
\(628\) | 8.22957e14 | 0.336201 | ||||||||
\(629\) | −3.96328e15 | −1.60500 | ||||||||
\(630\) | −8.27062e13 | −0.0332021 | ||||||||
\(631\) | 3.94122e15 | 1.56845 | 0.784223 | − | 0.620479i | \(-0.213062\pi\) | ||||
0.784223 | + | 0.620479i | \(0.213062\pi\) | |||||||
\(632\) | 5.35486e14 | 0.211253 | ||||||||
\(633\) | 4.23521e15 | 1.65636 | ||||||||
\(634\) | −2.64829e15 | −1.02677 | ||||||||
\(635\) | −5.66862e14 | −0.217882 | ||||||||
\(636\) | −1.61935e15 | −0.617059 | ||||||||
\(637\) | −1.31471e15 | −0.496666 | ||||||||
\(638\) | −1.02241e15 | −0.382925 | ||||||||
\(639\) | −8.22783e14 | −0.305514 | ||||||||
\(640\) | 1.55915e14 | 0.0573980 | ||||||||
\(641\) | −2.71163e15 | −0.989716 | −0.494858 | − | 0.868974i | \(-0.664780\pi\) | ||||
−0.494858 | + | 0.868974i | \(0.664780\pi\) | |||||||
\(642\) | 1.50364e15 | 0.544128 | ||||||||
\(643\) | 1.11976e15 | 0.401757 | 0.200879 | − | 0.979616i | \(-0.435620\pi\) | ||||
0.200879 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(644\) | 3.30421e13 | 0.0117542 | ||||||||
\(645\) | 9.23062e14 | 0.325576 | ||||||||
\(646\) | 6.89054e15 | 2.40976 | ||||||||
\(647\) | −5.20369e14 | −0.180442 | −0.0902210 | − | 0.995922i | \(-0.528757\pi\) | ||||
−0.0902210 | + | 0.995922i | \(0.528757\pi\) | |||||||
\(648\) | 3.44166e14 | 0.118333 | ||||||||
\(649\) | 2.27743e14 | 0.0776425 | ||||||||
\(650\) | −4.34162e15 | −1.46767 | ||||||||
\(651\) | −5.31196e13 | −0.0178057 | ||||||||
\(652\) | −3.25629e15 | −1.08234 | ||||||||
\(653\) | 6.45444e14 | 0.212734 | 0.106367 | − | 0.994327i | \(-0.466078\pi\) | ||||
0.106367 | + | 0.994327i | \(0.466078\pi\) | |||||||
\(654\) | −3.96768e15 | −1.29676 | ||||||||
\(655\) | −1.32519e14 | −0.0429487 | ||||||||
\(656\) | −3.37168e15 | −1.08361 | ||||||||
\(657\) | 5.28580e14 | 0.168462 | ||||||||
\(658\) | 3.50350e15 | 1.10729 | ||||||||
\(659\) | −4.90862e14 | −0.153847 | −0.0769236 | − | 0.997037i | \(-0.524510\pi\) | ||||
−0.0769236 | + | 0.997037i | \(0.524510\pi\) | |||||||
\(660\) | 7.76204e14 | 0.241259 | ||||||||
\(661\) | −1.13195e15 | −0.348915 | −0.174458 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174458 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(662\) | 1.96639e14 | 0.0601106 | ||||||||
\(663\) | 6.45987e15 | 1.95839 | ||||||||
\(664\) | −1.73541e14 | −0.0521768 | ||||||||
\(665\) | −4.45611e14 | −0.132873 | ||||||||
\(666\) | −6.36930e14 | −0.188358 | ||||||||
\(667\) | 1.12049e13 | 0.00328637 | ||||||||
\(668\) | 1.04017e15 | 0.302577 | ||||||||
\(669\) | 2.12899e15 | 0.614227 | ||||||||
\(670\) | −3.30526e14 | −0.0945790 | ||||||||
\(671\) | −4.11318e15 | −1.16736 | ||||||||
\(672\) | 3.28317e15 | 0.924192 | ||||||||
\(673\) | −1.66789e15 | −0.465676 | −0.232838 | − | 0.972516i | \(-0.574801\pi\) | ||||
−0.232838 | + | 0.972516i | \(0.574801\pi\) | |||||||
\(674\) | −4.34283e15 | −1.20266 | ||||||||
\(675\) | −3.72470e15 | −1.02310 | ||||||||
\(676\) | 7.58901e14 | 0.206766 | ||||||||
\(677\) | 3.40687e15 | 0.920699 | 0.460349 | − | 0.887738i | \(-0.347724\pi\) | ||||
0.460349 | + | 0.887738i | \(0.347724\pi\) | |||||||
\(678\) | −2.66839e15 | −0.715295 | ||||||||
\(679\) | −2.44665e15 | −0.650560 | ||||||||
\(680\) | 2.11304e14 | 0.0557324 | ||||||||
\(681\) | 1.81160e15 | 0.473971 | ||||||||
\(682\) | −2.08268e14 | −0.0540517 | ||||||||
\(683\) | 1.01334e15 | 0.260882 | 0.130441 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130441 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(684\) | 5.22570e14 | 0.133455 | ||||||||
\(685\) | −4.24765e14 | −0.107610 | ||||||||
\(686\) | −5.89121e15 | −1.48055 | ||||||||
\(687\) | 1.56307e15 | 0.389688 | ||||||||
\(688\) | 8.00132e15 | 1.97891 | ||||||||
\(689\) | 3.41712e15 | 0.838405 | ||||||||
\(690\) | −1.80261e13 | −0.00438766 | ||||||||
\(691\) | −3.43978e15 | −0.830618 | −0.415309 | − | 0.909680i | \(-0.636327\pi\) | ||||
−0.415309 | + | 0.909680i | \(0.636327\pi\) | |||||||
\(692\) | −6.34447e14 | −0.151989 | ||||||||
\(693\) | 7.71748e14 | 0.183418 | ||||||||
\(694\) | −7.38041e15 | −1.74022 | ||||||||
\(695\) | 8.31448e14 | 0.194500 | ||||||||
\(696\) | 1.07069e14 | 0.0248493 | ||||||||
\(697\) | −8.29823e15 | −1.91076 | ||||||||
\(698\) | −2.20996e15 | −0.504871 | ||||||||
\(699\) | −7.55175e15 | −1.71168 | ||||||||
\(700\) | −2.83861e15 | −0.638361 | ||||||||
\(701\) | −1.06049e15 | −0.236622 | −0.118311 | − | 0.992977i | \(-0.537748\pi\) | ||||
−0.118311 | + | 0.992977i | \(0.537748\pi\) | |||||||
\(702\) | 7.34223e15 | 1.62545 | ||||||||
\(703\) | −3.43170e15 | −0.753797 | ||||||||
\(704\) | 5.34300e15 | 1.16449 | ||||||||
\(705\) | −9.01971e14 | −0.195053 | ||||||||
\(706\) | −9.25130e15 | −1.98507 | ||||||||
\(707\) | −2.87559e15 | −0.612237 | ||||||||
\(708\) | 2.00301e14 | 0.0423156 | ||||||||
\(709\) | 2.55303e15 | 0.535181 | 0.267591 | − | 0.963533i | \(-0.413773\pi\) | ||||
0.267591 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(710\) | 2.41937e15 | 0.503248 | ||||||||
\(711\) | 1.15117e15 | 0.237605 | ||||||||
\(712\) | −6.06369e14 | −0.124193 | ||||||||
\(713\) | 2.28247e12 | 0.000463888 0 | ||||||||
\(714\) | 8.94999e15 | 1.80502 | ||||||||
\(715\) | −1.63793e15 | −0.327802 | ||||||||
\(716\) | −3.37944e15 | −0.671155 | ||||||||
\(717\) | −5.38161e15 | −1.06061 | ||||||||
\(718\) | −8.69317e15 | −1.70018 | ||||||||
\(719\) | 2.96226e15 | 0.574929 | 0.287464 | − | 0.957791i | \(-0.407188\pi\) | ||||
0.287464 | + | 0.957791i | \(0.407188\pi\) | |||||||
\(720\) | 1.84569e14 | 0.0355493 | ||||||||
\(721\) | −6.61923e15 | −1.26521 | ||||||||
\(722\) | −1.28802e15 | −0.244325 | ||||||||
\(723\) | 5.54217e15 | 1.04332 | ||||||||
\(724\) | 3.10826e15 | 0.580705 | ||||||||
\(725\) | −9.62603e14 | −0.178479 | ||||||||
\(726\) | −8.51350e15 | −1.56659 | ||||||||
\(727\) | 1.27741e15 | 0.233287 | 0.116643 | − | 0.993174i | \(-0.462787\pi\) | ||||
0.116643 | + | 0.993174i | \(0.462787\pi\) | |||||||
\(728\) | −6.66257e14 | −0.120759 | ||||||||
\(729\) | 6.14818e15 | 1.10597 | ||||||||
\(730\) | −1.55428e15 | −0.277493 | ||||||||
\(731\) | 1.96925e16 | 3.48944 | ||||||||
\(732\) | −3.61757e15 | −0.636218 | ||||||||
\(733\) | 7.57379e15 | 1.32203 | 0.661015 | − | 0.750372i | \(-0.270126\pi\) | ||||
0.661015 | + | 0.750372i | \(0.270126\pi\) | |||||||
\(734\) | −1.48770e16 | −2.57744 | ||||||||
\(735\) | 4.68944e14 | 0.0806381 | ||||||||
\(736\) | −1.41073e14 | −0.0240777 | ||||||||
\(737\) | 3.08421e15 | 0.522483 | ||||||||
\(738\) | −1.33359e15 | −0.224240 | ||||||||
\(739\) | −3.67278e15 | −0.612986 | −0.306493 | − | 0.951873i | \(-0.599156\pi\) | ||||
−0.306493 | + | 0.951873i | \(0.599156\pi\) | |||||||
\(740\) | 8.83820e14 | 0.146416 | ||||||||
\(741\) | 5.59343e15 | 0.919767 | ||||||||
\(742\) | 4.73433e15 | 0.772747 | ||||||||
\(743\) | 7.23474e15 | 1.17215 | 0.586077 | − | 0.810256i | \(-0.300672\pi\) | ||||
0.586077 | + | 0.810256i | \(0.300672\pi\) | |||||||
\(744\) | 2.18103e13 | 0.00350760 | ||||||||
\(745\) | −1.63654e15 | −0.261257 | ||||||||
\(746\) | −2.00304e15 | −0.317414 | ||||||||
\(747\) | −3.73073e14 | −0.0586854 | ||||||||
\(748\) | 1.65594e16 | 2.58575 | ||||||||
\(749\) | −2.07451e15 | −0.321563 | ||||||||
\(750\) | 3.15982e15 | 0.486212 | ||||||||
\(751\) | −2.47237e15 | −0.377654 | −0.188827 | − | 0.982010i | \(-0.560469\pi\) | ||||
−0.188827 | + | 0.982010i | \(0.560469\pi\) | |||||||
\(752\) | −7.81850e15 | −1.18556 | ||||||||
\(753\) | 8.29914e15 | 1.24928 | ||||||||
\(754\) | 1.89751e15 | 0.283558 | ||||||||
\(755\) | 6.35760e14 | 0.0943159 | ||||||||
\(756\) | 4.80045e15 | 0.706988 | ||||||||
\(757\) | 1.07908e15 | 0.157771 | 0.0788854 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788854 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(758\) | 8.58066e15 | 1.24549 | ||||||||
\(759\) | 1.68206e14 | 0.0242388 | ||||||||
\(760\) | 1.82962e14 | 0.0261750 | ||||||||
\(761\) | 8.35973e15 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(762\) | 9.85822e15 | 1.39010 | ||||||||
\(763\) | 5.47406e15 | 0.766345 | ||||||||
\(764\) | 1.19611e16 | 1.66248 | ||||||||
\(765\) | 4.54254e14 | 0.0626846 | ||||||||
\(766\) | −1.08177e16 | −1.48210 | ||||||||
\(767\) | −4.22671e14 | −0.0574947 | ||||||||
\(768\) | −7.97022e15 | −1.07643 | ||||||||
\(769\) | 8.47458e15 | 1.13638 | 0.568190 | − | 0.822898i | \(-0.307644\pi\) | ||||
0.568190 | + | 0.822898i | \(0.307644\pi\) | |||||||
\(770\) | −2.26931e15 | −0.302130 | ||||||||
\(771\) | −7.78556e15 | −1.02918 | ||||||||
\(772\) | 4.11451e15 | 0.540036 | ||||||||
\(773\) | −1.35997e16 | −1.77232 | −0.886159 | − | 0.463381i | \(-0.846636\pi\) | ||||
−0.886159 | + | 0.463381i | \(0.846636\pi\) | |||||||
\(774\) | 3.16474e15 | 0.409508 | ||||||||
\(775\) | −1.96085e14 | −0.0251932 | ||||||||
\(776\) | 1.00456e15 | 0.128156 | ||||||||
\(777\) | −4.45737e15 | −0.564629 | ||||||||
\(778\) | 1.45816e16 | 1.83407 | ||||||||
\(779\) | −7.18522e15 | −0.897395 | ||||||||
\(780\) | −1.44057e15 | −0.178654 | ||||||||
\(781\) | −2.25757e16 | −2.78010 | ||||||||
\(782\) | −3.84568e14 | −0.0470257 | ||||||||
\(783\) | 1.62788e15 | 0.197667 | ||||||||
\(784\) | 4.06491e15 | 0.490132 | ||||||||
\(785\) | 6.19420e14 | 0.0741655 | ||||||||
\(786\) | 2.30462e15 | 0.274015 | ||||||||
\(787\) | 6.33252e15 | 0.747680 | 0.373840 | − | 0.927493i | \(-0.378041\pi\) | ||||
0.373840 | + | 0.927493i | \(0.378041\pi\) | |||||||
\(788\) | 8.24465e15 | 0.966670 | ||||||||
\(789\) | −4.30944e15 | −0.501761 | ||||||||
\(790\) | −3.38499e15 | −0.391388 | ||||||||
\(791\) | 3.68147e15 | 0.422718 | ||||||||
\(792\) | −3.16870e14 | −0.0361321 | ||||||||
\(793\) | 7.63370e15 | 0.864436 | ||||||||
\(794\) | −1.11679e16 | −1.25591 | ||||||||
\(795\) | −1.21885e15 | −0.136122 | ||||||||
\(796\) | −8.84669e15 | −0.981203 | ||||||||
\(797\) | −1.53574e16 | −1.69159 | −0.845796 | − | 0.533507i | \(-0.820874\pi\) | ||||
−0.845796 | + | 0.533507i | \(0.820874\pi\) | |||||||
\(798\) | 7.74956e15 | 0.847737 | ||||||||
\(799\) | −1.92426e16 | −2.09053 | ||||||||
\(800\) | 1.21194e16 | 1.30763 | ||||||||
\(801\) | −1.30355e15 | −0.139685 | ||||||||
\(802\) | −1.88732e16 | −2.00857 | ||||||||
\(803\) | 1.45033e16 | 1.53296 | ||||||||
\(804\) | 2.71258e15 | 0.284757 | ||||||||
\(805\) | 2.48700e13 | 0.00259297 | ||||||||
\(806\) | 3.86528e14 | 0.0400256 | ||||||||
\(807\) | 5.04639e15 | 0.519010 | ||||||||
\(808\) | 1.18068e15 | 0.120606 | ||||||||
\(809\) | −8.68168e15 | −0.880819 | −0.440410 | − | 0.897797i | \(-0.645167\pi\) | ||||
−0.440410 | + | 0.897797i | \(0.645167\pi\) | |||||||
\(810\) | −2.17559e15 | −0.219235 | ||||||||
\(811\) | −1.24520e16 | −1.24630 | −0.623151 | − | 0.782102i | \(-0.714148\pi\) | ||||
−0.623151 | + | 0.782102i | \(0.714148\pi\) | |||||||
\(812\) | 1.24062e15 | 0.123333 | ||||||||
\(813\) | 6.20368e15 | 0.612564 | ||||||||
\(814\) | −1.74762e16 | −1.71401 | ||||||||
\(815\) | −2.45093e15 | −0.238762 | ||||||||
\(816\) | −1.99730e16 | −1.93263 | ||||||||
\(817\) | 1.70512e16 | 1.63883 | ||||||||
\(818\) | 9.50827e15 | 0.907733 | ||||||||
\(819\) | −1.43230e15 | −0.135823 | ||||||||
\(820\) | 1.85052e15 | 0.174309 | ||||||||
\(821\) | 1.60834e16 | 1.50484 | 0.752420 | − | 0.658684i | \(-0.228887\pi\) | ||||
0.752420 | + | 0.658684i | \(0.228887\pi\) | |||||||
\(822\) | 7.38704e15 | 0.686555 | ||||||||
\(823\) | 9.49861e15 | 0.876922 | 0.438461 | − | 0.898750i | \(-0.355524\pi\) | ||||
0.438461 | + | 0.898750i | \(0.355524\pi\) | |||||||
\(824\) | 2.71777e15 | 0.249238 | ||||||||
\(825\) | −1.44504e16 | −1.31638 | ||||||||
\(826\) | −5.85601e14 | −0.0529921 | ||||||||
\(827\) | 2.12819e15 | 0.191306 | 0.0956532 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956532 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(828\) | −2.91652e13 | −0.00260434 | ||||||||
\(829\) | −1.90510e15 | −0.168993 | −0.0844965 | − | 0.996424i | \(-0.526928\pi\) | ||||
−0.0844965 | + | 0.996424i | \(0.526928\pi\) | |||||||
\(830\) | 1.09701e15 | 0.0966678 | ||||||||
\(831\) | −1.45691e16 | −1.27534 | ||||||||
\(832\) | −9.91614e15 | −0.862312 | ||||||||
\(833\) | 1.00044e16 | 0.864258 | ||||||||
\(834\) | −1.44596e16 | −1.24092 | ||||||||
\(835\) | 7.82914e14 | 0.0667481 | ||||||||
\(836\) | 1.43384e16 | 1.21441 | ||||||||
\(837\) | 3.31604e14 | 0.0279017 | ||||||||
\(838\) | −1.71100e16 | −1.43023 | ||||||||
\(839\) | 2.03621e15 | 0.169095 | 0.0845477 | − | 0.996419i | \(-0.473055\pi\) | ||||
0.0845477 | + | 0.996419i | \(0.473055\pi\) | |||||||
\(840\) | 2.37646e14 | 0.0196063 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | −6.21396e15 | −0.506002 | ||||||||
\(843\) | 1.95041e15 | 0.157788 | ||||||||
\(844\) | −2.01491e16 | −1.61946 | ||||||||
\(845\) | 5.71207e14 | 0.0456122 | ||||||||
\(846\) | −3.09243e15 | −0.245337 | ||||||||
\(847\) | 1.17457e16 | 0.925810 | ||||||||
\(848\) | −1.05652e16 | −0.827375 | ||||||||
\(849\) | 2.09981e16 | 1.63376 | ||||||||
\(850\) | 3.30378e16 | 2.55392 | ||||||||
\(851\) | 1.91526e14 | 0.0147101 | ||||||||
\(852\) | −1.98554e16 | −1.51517 | ||||||||
\(853\) | −1.08461e16 | −0.822343 | −0.411172 | − | 0.911558i | \(-0.634880\pi\) | ||||
−0.411172 | + | 0.911558i | \(0.634880\pi\) | |||||||
\(854\) | 1.05763e16 | 0.796739 | ||||||||
\(855\) | 3.93326e14 | 0.0294401 | ||||||||
\(856\) | 8.51770e14 | 0.0633456 | ||||||||
\(857\) | 2.23715e16 | 1.65311 | 0.826553 | − | 0.562859i | \(-0.190299\pi\) | ||||
0.826553 | + | 0.562859i | \(0.190299\pi\) | |||||||
\(858\) | 2.84850e16 | 2.09139 | ||||||||
\(859\) | 1.15245e16 | 0.840738 | 0.420369 | − | 0.907353i | \(-0.361901\pi\) | ||||
0.420369 | + | 0.907353i | \(0.361901\pi\) | |||||||
\(860\) | −4.39147e15 | −0.318324 | ||||||||
\(861\) | −9.33274e15 | −0.672190 | ||||||||
\(862\) | −6.11737e15 | −0.437799 | ||||||||
\(863\) | −6.38998e15 | −0.454402 | −0.227201 | − | 0.973848i | \(-0.572957\pi\) | ||||
−0.227201 | + | 0.973848i | \(0.572957\pi\) | |||||||
\(864\) | −2.04955e16 | −1.44821 | ||||||||
\(865\) | −4.77533e14 | −0.0335286 | ||||||||
\(866\) | 8.35505e15 | 0.582909 | ||||||||
\(867\) | −3.59732e16 | −2.49387 | ||||||||
\(868\) | 2.52717e14 | 0.0174091 | ||||||||
\(869\) | 3.15860e16 | 2.16215 | ||||||||
\(870\) | −6.76821e14 | −0.0460382 | ||||||||
\(871\) | −5.72402e15 | −0.386902 | ||||||||
\(872\) | −2.24758e15 | −0.150964 | ||||||||
\(873\) | 2.15958e15 | 0.144142 | ||||||||
\(874\) | −3.32987e14 | −0.0220859 | ||||||||
\(875\) | −4.35949e15 | −0.287337 | ||||||||
\(876\) | 1.27557e16 | 0.835472 | ||||||||
\(877\) | −1.02607e16 | −0.667849 | −0.333924 | − | 0.942600i | \(-0.608373\pi\) | ||||
−0.333924 | + | 0.942600i | \(0.608373\pi\) | |||||||
\(878\) | 9.13044e15 | 0.590571 | ||||||||
\(879\) | 1.20364e16 | 0.773676 | ||||||||
\(880\) | 5.06424e15 | 0.323489 | ||||||||
\(881\) | −7.21654e15 | −0.458101 | −0.229051 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229051 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(882\) | 1.60778e15 | 0.101426 | ||||||||
\(883\) | 8.51122e15 | 0.533591 | 0.266795 | − | 0.963753i | \(-0.414035\pi\) | ||||
0.266795 | + | 0.963753i | \(0.414035\pi\) | |||||||
\(884\) | −3.07329e16 | −1.91477 | ||||||||
\(885\) | 1.50762e14 | 0.00933478 | ||||||||
\(886\) | −7.54494e14 | −0.0464269 | ||||||||
\(887\) | −1.37601e16 | −0.841477 | −0.420739 | − | 0.907182i | \(-0.638229\pi\) | ||||
−0.420739 | + | 0.907182i | \(0.638229\pi\) | |||||||
\(888\) | 1.83014e15 | 0.111228 | ||||||||
\(889\) | −1.36010e16 | −0.821507 | ||||||||
\(890\) | 3.83307e15 | 0.230092 | ||||||||
\(891\) | 2.03009e16 | 1.21112 | ||||||||
\(892\) | −1.01287e16 | −0.600545 | ||||||||
\(893\) | −1.66616e16 | −0.981825 | ||||||||
\(894\) | 2.84609e16 | 1.66683 | ||||||||
\(895\) | −2.54362e15 | −0.148056 | ||||||||
\(896\) | 3.74094e15 | 0.216415 | ||||||||
\(897\) | −3.12175e14 | −0.0179490 | ||||||||
\(898\) | 2.57862e16 | 1.47356 | ||||||||
\(899\) | 8.56991e13 | 0.00486741 | ||||||||
\(900\) | 2.50555e15 | 0.141439 | ||||||||
\(901\) | −2.60027e16 | −1.45892 | ||||||||
\(902\) | −3.65913e16 | −2.04052 | ||||||||
\(903\) | 2.21475e16 | 1.22756 | ||||||||
\(904\) | −1.51157e15 | −0.0832723 | ||||||||
\(905\) | 2.33952e15 | 0.128103 | ||||||||
\(906\) | −1.10564e16 | −0.601741 | ||||||||
\(907\) | −1.86017e15 | −0.100626 | −0.0503132 | − | 0.998733i | \(-0.516022\pi\) | ||||
−0.0503132 | + | 0.998733i | \(0.516022\pi\) | |||||||
\(908\) | −8.61868e15 | −0.463413 | ||||||||
\(909\) | 2.53819e15 | 0.135651 | ||||||||
\(910\) | 4.21164e15 | 0.223729 | ||||||||
\(911\) | 1.78581e15 | 0.0942939 | 0.0471469 | − | 0.998888i | \(-0.484987\pi\) | ||||
0.0471469 | + | 0.998888i | \(0.484987\pi\) | |||||||
\(912\) | −1.72941e16 | −0.907667 | ||||||||
\(913\) | −1.02364e16 | −0.534023 | ||||||||
\(914\) | 4.27462e16 | 2.21663 | ||||||||
\(915\) | −2.72286e15 | −0.140349 | ||||||||
\(916\) | −7.43633e15 | −0.381008 | ||||||||
\(917\) | −3.17959e15 | −0.161935 | ||||||||
\(918\) | −5.58711e16 | −2.82848 | ||||||||
\(919\) | −1.41640e15 | −0.0712770 | −0.0356385 | − | 0.999365i | \(-0.511346\pi\) | ||||
−0.0356385 | + | 0.999365i | \(0.511346\pi\) | |||||||
\(920\) | −1.02113e13 | −0.000510797 0 | ||||||||
\(921\) | 8.00247e14 | 0.0397920 | ||||||||
\(922\) | 5.49634e16 | 2.71677 | ||||||||
\(923\) | 4.18984e16 | 2.05868 | ||||||||
\(924\) | 1.86239e16 | 0.909649 | ||||||||
\(925\) | −1.64538e16 | −0.798891 | ||||||||
\(926\) | −2.45304e16 | −1.18398 | ||||||||
\(927\) | 5.84258e15 | 0.280328 | ||||||||
\(928\) | −5.29681e15 | −0.252639 | ||||||||
\(929\) | −3.39995e16 | −1.61208 | −0.806039 | − | 0.591862i | \(-0.798393\pi\) | ||||
−0.806039 | + | 0.591862i | \(0.798393\pi\) | |||||||
\(930\) | −1.37870e14 | −0.00649851 | ||||||||
\(931\) | 8.66254e15 | 0.405903 | ||||||||
\(932\) | 3.59275e16 | 1.67355 | ||||||||
\(933\) | −1.35954e16 | −0.629568 | ||||||||
\(934\) | −2.81312e15 | −0.129503 | ||||||||
\(935\) | 1.24639e16 | 0.570414 | ||||||||
\(936\) | 5.88084e14 | 0.0267561 | ||||||||
\(937\) | −7.34935e14 | −0.0332415 | −0.0166208 | − | 0.999862i | \(-0.505291\pi\) | ||||
−0.0166208 | + | 0.999862i | \(0.505291\pi\) | |||||||
\(938\) | −7.93049e15 | −0.356603 | ||||||||
\(939\) | −1.14953e16 | −0.513875 | ||||||||
\(940\) | 4.29114e15 | 0.190708 | ||||||||
\(941\) | −3.19965e16 | −1.41371 | −0.706854 | − | 0.707360i | \(-0.749886\pi\) | ||||
−0.706854 | + | 0.707360i | \(0.749886\pi\) | |||||||
\(942\) | −1.07723e16 | −0.473180 | ||||||||
\(943\) | 4.01014e14 | 0.0175124 | ||||||||
\(944\) | 1.30684e15 | 0.0567383 | ||||||||
\(945\) | 3.61318e15 | 0.155961 | ||||||||
\(946\) | 8.68347e16 | 3.72642 | ||||||||
\(947\) | 3.54537e16 | 1.51264 | 0.756321 | − | 0.654201i | \(-0.226995\pi\) | ||||
0.756321 | + | 0.654201i | \(0.226995\pi\) | |||||||
\(948\) | 2.77801e16 | 1.17839 | ||||||||
\(949\) | −2.69168e16 | −1.13517 | ||||||||
\(950\) | 2.86065e16 | 1.19946 | ||||||||
\(951\) | 1.63587e16 | 0.681957 | ||||||||
\(952\) | 5.06992e15 | 0.210135 | ||||||||
\(953\) | 1.61742e16 | 0.666519 | 0.333260 | − | 0.942835i | \(-0.391851\pi\) | ||||
0.333260 | + | 0.942835i | \(0.391851\pi\) | |||||||
\(954\) | −4.17884e15 | −0.171214 | ||||||||
\(955\) | 9.00281e15 | 0.366741 | ||||||||
\(956\) | 2.56031e16 | 1.03699 | ||||||||
\(957\) | 6.31555e15 | 0.254329 | ||||||||
\(958\) | −3.07510e16 | −1.23126 | ||||||||
\(959\) | −1.01916e16 | −0.405733 | ||||||||
\(960\) | 3.53698e15 | 0.140004 | ||||||||
\(961\) | −2.53910e16 | −0.999313 | ||||||||
\(962\) | 3.24343e16 | 1.26923 | ||||||||
\(963\) | 1.83111e15 | 0.0712474 | ||||||||
\(964\) | −2.63669e16 | −1.02008 | ||||||||
\(965\) | 3.09689e15 | 0.119131 | ||||||||
\(966\) | −4.32511e14 | −0.0165433 | ||||||||
\(967\) | 2.66442e16 | 1.01335 | 0.506673 | − | 0.862138i | \(-0.330875\pi\) | ||||
0.506673 | + | 0.862138i | \(0.330875\pi\) | |||||||
\(968\) | −4.82266e15 | −0.182378 | ||||||||
\(969\) | −4.25635e16 | −1.60050 | ||||||||
\(970\) | −6.35018e15 | −0.237433 | ||||||||
\(971\) | −3.55781e16 | −1.32275 | −0.661374 | − | 0.750056i | \(-0.730026\pi\) | ||||
−0.661374 | + | 0.750056i | \(0.730026\pi\) | |||||||
\(972\) | −7.87529e15 | −0.291140 | ||||||||
\(973\) | 1.99494e16 | 0.733345 | ||||||||
\(974\) | 3.50239e16 | 1.28024 | ||||||||
\(975\) | 2.68186e16 | 0.974789 | ||||||||
\(976\) | −2.36024e16 | −0.853064 | ||||||||
\(977\) | 8.11999e15 | 0.291834 | 0.145917 | − | 0.989297i | \(-0.453387\pi\) | ||||
0.145917 | + | 0.989297i | \(0.453387\pi\) | |||||||
\(978\) | 4.26239e16 | 1.52331 | ||||||||
\(979\) | −3.57671e16 | −1.27110 | ||||||||
\(980\) | −2.23100e15 | −0.0788418 | ||||||||
\(981\) | −4.83177e15 | −0.169796 | ||||||||
\(982\) | −3.77600e16 | −1.31953 | ||||||||
\(983\) | 1.07762e15 | 0.0374472 | 0.0187236 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187236 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(984\) | 3.83191e15 | 0.132417 | ||||||||
\(985\) | 6.20555e15 | 0.213246 | ||||||||
\(986\) | −1.44392e16 | −0.493425 | ||||||||
\(987\) | −2.16415e16 | −0.735432 | ||||||||
\(988\) | −2.66108e16 | −0.899279 | ||||||||
\(989\) | −9.51645e14 | −0.0319812 | ||||||||
\(990\) | 2.00305e15 | 0.0669418 | ||||||||
\(991\) | 1.71972e16 | 0.571547 | 0.285773 | − | 0.958297i | \(-0.407750\pi\) | ||||
0.285773 | + | 0.958297i | \(0.407750\pi\) | |||||||
\(992\) | −1.07897e15 | −0.0356612 | ||||||||
\(993\) | −1.21466e15 | −0.0399240 | ||||||||
\(994\) | 5.80493e16 | 1.89746 | ||||||||
\(995\) | −6.65869e15 | −0.216452 | ||||||||
\(996\) | −9.00301e15 | −0.291046 | ||||||||
\(997\) | 3.20573e16 | 1.03063 | 0.515316 | − | 0.857000i | \(-0.327674\pi\) | ||||
0.515316 | + | 0.857000i | \(0.327674\pi\) | |||||||
\(998\) | −6.01849e16 | −1.92429 | ||||||||
\(999\) | 2.78255e16 | 0.884776 |
(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 | 29.12.a.a.1.10 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.2 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.2 | 11 | 3.2 | odd | 2 |