Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −55.7627 | −0.616096 | −0.308048 | − | 0.951371i | \(-0.599676\pi\) | ||||
−0.308048 | + | 0.951371i | \(0.599676\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −5082.53 | −0.620425 | ||||||||
\(5\) | 35389.9 | 1.01292 | 0.506460 | − | 0.862264i | \(-0.330954\pi\) | ||||
0.506460 | + | 0.862264i | \(0.330954\pi\) | |||||||
\(6\) | −40651.0 | −0.355703 | ||||||||
\(7\) | 112882. | 0.362650 | 0.181325 | − | 0.983423i | \(-0.441961\pi\) | ||||
0.181325 | + | 0.983423i | \(0.441961\pi\) | |||||||
\(8\) | 740223. | 0.998338 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −1.97344e6 | −0.624056 | ||||||||
\(11\) | −7.74091e6 | −1.31747 | −0.658733 | − | 0.752377i | \(-0.728907\pi\) | ||||
−0.658733 | + | 0.752377i | \(0.728907\pi\) | |||||||
\(12\) | −3.70516e6 | −0.358203 | ||||||||
\(13\) | −2.59034e7 | −1.48842 | −0.744209 | − | 0.667947i | \(-0.767173\pi\) | ||||
−0.744209 | + | 0.667947i | \(0.767173\pi\) | |||||||
\(14\) | −6.29460e6 | −0.223427 | ||||||||
\(15\) | 2.57993e7 | 0.584809 | ||||||||
\(16\) | 359253. | 0.00535329 | ||||||||
\(17\) | −1.29900e8 | −1.30524 | −0.652620 | − | 0.757685i | \(-0.726330\pi\) | ||||
−0.652620 | + | 0.757685i | \(0.726330\pi\) | |||||||
\(18\) | −2.96346e7 | −0.205365 | ||||||||
\(19\) | −3.90885e8 | −1.90612 | −0.953062 | − | 0.302776i | \(-0.902087\pi\) | ||||
−0.953062 | + | 0.302776i | \(0.902087\pi\) | |||||||
\(20\) | −1.79870e8 | −0.628441 | ||||||||
\(21\) | 8.22910e7 | 0.209376 | ||||||||
\(22\) | 4.31654e8 | 0.811686 | ||||||||
\(23\) | −7.02596e8 | −0.989634 | −0.494817 | − | 0.868997i | \(-0.664765\pi\) | ||||
−0.494817 | + | 0.868997i | \(0.664765\pi\) | |||||||
\(24\) | 5.39622e8 | 0.576391 | ||||||||
\(25\) | 3.17454e7 | 0.0260058 | ||||||||
\(26\) | 1.44444e9 | 0.917009 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −5.73726e8 | −0.224997 | ||||||||
\(29\) | 4.55351e9 | 1.42154 | 0.710770 | − | 0.703425i | \(-0.248347\pi\) | ||||
0.710770 | + | 0.703425i | \(0.248347\pi\) | |||||||
\(30\) | −1.43864e9 | −0.360299 | ||||||||
\(31\) | −7.21548e8 | −0.146021 | −0.0730103 | − | 0.997331i | \(-0.523261\pi\) | ||||
−0.0730103 | + | 0.997331i | \(0.523261\pi\) | |||||||
\(32\) | −6.08394e9 | −1.00164 | ||||||||
\(33\) | −5.64312e9 | −0.760639 | ||||||||
\(34\) | 7.24356e9 | 0.804153 | ||||||||
\(35\) | 3.99489e9 | 0.367335 | ||||||||
\(36\) | −2.70106e9 | −0.206808 | ||||||||
\(37\) | 1.70177e10 | 1.09041 | 0.545204 | − | 0.838303i | \(-0.316452\pi\) | ||||
0.545204 | + | 0.838303i | \(0.316452\pi\) | |||||||
\(38\) | 2.17968e10 | 1.17436 | ||||||||
\(39\) | −1.88836e10 | −0.859339 | ||||||||
\(40\) | 2.61964e10 | 1.01124 | ||||||||
\(41\) | 1.42424e10 | 0.468262 | 0.234131 | − | 0.972205i | \(-0.424776\pi\) | ||||
0.234131 | + | 0.972205i | \(0.424776\pi\) | |||||||
\(42\) | −4.58877e9 | −0.128996 | ||||||||
\(43\) | 8.71016e9 | 0.210127 | 0.105063 | − | 0.994466i | \(-0.466495\pi\) | ||||
0.105063 | + | 0.994466i | \(0.466495\pi\) | |||||||
\(44\) | 3.93434e10 | 0.817390 | ||||||||
\(45\) | 1.88077e10 | 0.337640 | ||||||||
\(46\) | 3.91786e10 | 0.609710 | ||||||||
\(47\) | 6.41381e10 | 0.867921 | 0.433960 | − | 0.900932i | \(-0.357116\pi\) | ||||
0.433960 | + | 0.900932i | \(0.357116\pi\) | |||||||
\(48\) | 2.61896e8 | 0.00309072 | ||||||||
\(49\) | −8.41466e10 | −0.868485 | ||||||||
\(50\) | −1.77021e9 | −0.0160221 | ||||||||
\(51\) | −9.46969e10 | −0.753581 | ||||||||
\(52\) | 1.31655e11 | 0.923453 | ||||||||
\(53\) | −2.07313e11 | −1.28479 | −0.642396 | − | 0.766373i | \(-0.722059\pi\) | ||||
−0.642396 | + | 0.766373i | \(0.722059\pi\) | |||||||
\(54\) | −2.16036e10 | −0.118568 | ||||||||
\(55\) | −2.73950e11 | −1.33449 | ||||||||
\(56\) | 8.35579e10 | 0.362047 | ||||||||
\(57\) | −2.84955e11 | −1.10050 | ||||||||
\(58\) | −2.53916e11 | −0.875805 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −1.31125e11 | −0.362831 | ||||||||
\(61\) | 7.37636e11 | 1.83315 | 0.916575 | − | 0.399863i | \(-0.130942\pi\) | ||||
0.916575 | + | 0.399863i | \(0.130942\pi\) | |||||||
\(62\) | 4.02354e10 | 0.0899628 | ||||||||
\(63\) | 5.99902e10 | 0.120883 | ||||||||
\(64\) | 3.36314e11 | 0.611751 | ||||||||
\(65\) | −9.16720e11 | −1.50765 | ||||||||
\(66\) | 3.14675e11 | 0.468627 | ||||||||
\(67\) | −9.39581e11 | −1.26896 | −0.634480 | − | 0.772939i | \(-0.718786\pi\) | ||||
−0.634480 | + | 0.772939i | \(0.718786\pi\) | |||||||
\(68\) | 6.60219e11 | 0.809804 | ||||||||
\(69\) | −5.12192e11 | −0.571365 | ||||||||
\(70\) | −2.22766e11 | −0.226314 | ||||||||
\(71\) | 7.47914e11 | 0.692903 | 0.346452 | − | 0.938068i | \(-0.387386\pi\) | ||||
0.346452 | + | 0.938068i | \(0.387386\pi\) | |||||||
\(72\) | 3.93385e11 | 0.332779 | ||||||||
\(73\) | 2.15376e12 | 1.66571 | 0.832853 | − | 0.553495i | \(-0.186706\pi\) | ||||
0.832853 | + | 0.553495i | \(0.186706\pi\) | |||||||
\(74\) | −9.48952e11 | −0.671797 | ||||||||
\(75\) | 2.31424e10 | 0.0150145 | ||||||||
\(76\) | 1.98669e12 | 1.18261 | ||||||||
\(77\) | −8.73810e11 | −0.477779 | ||||||||
\(78\) | 1.05300e12 | 0.529435 | ||||||||
\(79\) | 2.70570e12 | 1.25229 | 0.626144 | − | 0.779707i | \(-0.284632\pi\) | ||||
0.626144 | + | 0.779707i | \(0.284632\pi\) | |||||||
\(80\) | 1.27140e10 | 0.00542245 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −7.94195e11 | −0.288494 | ||||||||
\(83\) | 7.98844e11 | 0.268197 | 0.134099 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134099 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(84\) | −4.18246e11 | −0.129902 | ||||||||
\(85\) | −4.59715e12 | −1.32210 | ||||||||
\(86\) | −4.85701e11 | −0.129458 | ||||||||
\(87\) | 3.31951e12 | 0.820726 | ||||||||
\(88\) | −5.73000e12 | −1.31528 | ||||||||
\(89\) | 1.42309e12 | 0.303528 | 0.151764 | − | 0.988417i | \(-0.451505\pi\) | ||||
0.151764 | + | 0.988417i | \(0.451505\pi\) | |||||||
\(90\) | −1.04877e12 | −0.208019 | ||||||||
\(91\) | −2.92403e12 | −0.539775 | ||||||||
\(92\) | 3.57096e12 | 0.613994 | ||||||||
\(93\) | −5.26008e11 | −0.0843050 | ||||||||
\(94\) | −3.57651e12 | −0.534723 | ||||||||
\(95\) | −1.38334e13 | −1.93075 | ||||||||
\(96\) | −4.43519e12 | −0.578295 | ||||||||
\(97\) | 5.33688e12 | 0.650536 | 0.325268 | − | 0.945622i | \(-0.394545\pi\) | ||||
0.325268 | + | 0.945622i | \(0.394545\pi\) | |||||||
\(98\) | 4.69224e12 | 0.535070 | ||||||||
\(99\) | −4.11384e12 | −0.439155 | ||||||||
\(100\) | −1.61347e11 | −0.0161347 | ||||||||
\(101\) | 1.92748e12 | 0.180676 | 0.0903379 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903379 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(102\) | 5.28055e12 | 0.464278 | ||||||||
\(103\) | 2.16694e13 | 1.78816 | 0.894078 | − | 0.447910i | \(-0.147832\pi\) | ||||
0.894078 | + | 0.447910i | \(0.147832\pi\) | |||||||
\(104\) | −1.91743e13 | −1.48594 | ||||||||
\(105\) | 2.91228e12 | 0.212081 | ||||||||
\(106\) | 1.15603e13 | 0.791555 | ||||||||
\(107\) | 8.12374e12 | 0.523313 | 0.261656 | − | 0.965161i | \(-0.415731\pi\) | ||||
0.261656 | + | 0.965161i | \(0.415731\pi\) | |||||||
\(108\) | −1.96907e12 | −0.119401 | ||||||||
\(109\) | −2.43955e13 | −1.39328 | −0.696638 | − | 0.717423i | \(-0.745321\pi\) | ||||
−0.696638 | + | 0.717423i | \(0.745321\pi\) | |||||||
\(110\) | 1.52762e13 | 0.822172 | ||||||||
\(111\) | 1.24059e13 | 0.629548 | ||||||||
\(112\) | 4.05533e10 | 0.00194137 | ||||||||
\(113\) | −1.50096e13 | −0.678201 | −0.339100 | − | 0.940750i | \(-0.610123\pi\) | ||||
−0.339100 | + | 0.940750i | \(0.610123\pi\) | |||||||
\(114\) | 1.58899e13 | 0.678014 | ||||||||
\(115\) | −2.48648e13 | −1.00242 | ||||||||
\(116\) | −2.31433e13 | −0.881959 | ||||||||
\(117\) | −1.37661e13 | −0.496139 | ||||||||
\(118\) | 2.35210e12 | 0.0802089 | ||||||||
\(119\) | −1.46634e13 | −0.473345 | ||||||||
\(120\) | 1.90972e13 | 0.583837 | ||||||||
\(121\) | 2.53989e13 | 0.735717 | ||||||||
\(122\) | −4.11325e13 | −1.12940 | ||||||||
\(123\) | 1.03827e13 | 0.270351 | ||||||||
\(124\) | 3.66729e12 | 0.0905949 | ||||||||
\(125\) | −4.20772e13 | −0.986578 | ||||||||
\(126\) | −3.34521e12 | −0.0744758 | ||||||||
\(127\) | 8.13608e13 | 1.72064 | 0.860322 | − | 0.509751i | \(-0.170262\pi\) | ||||
0.860322 | + | 0.509751i | \(0.170262\pi\) | |||||||
\(128\) | 3.10859e13 | 0.624739 | ||||||||
\(129\) | 6.34970e12 | 0.121317 | ||||||||
\(130\) | 5.11188e13 | 0.928856 | ||||||||
\(131\) | −3.74993e13 | −0.648276 | −0.324138 | − | 0.946010i | \(-0.605074\pi\) | ||||
−0.324138 | + | 0.946010i | \(0.605074\pi\) | |||||||
\(132\) | 2.86813e13 | 0.471920 | ||||||||
\(133\) | −4.41240e13 | −0.691256 | ||||||||
\(134\) | 5.23935e13 | 0.781802 | ||||||||
\(135\) | 1.37108e13 | 0.194936 | ||||||||
\(136\) | −9.61548e13 | −1.30307 | ||||||||
\(137\) | −8.77589e12 | −0.113399 | −0.0566993 | − | 0.998391i | \(-0.518058\pi\) | ||||
−0.0566993 | + | 0.998391i | \(0.518058\pi\) | |||||||
\(138\) | 2.85612e13 | 0.352016 | ||||||||
\(139\) | −6.68002e13 | −0.785564 | −0.392782 | − | 0.919632i | \(-0.628487\pi\) | ||||
−0.392782 | + | 0.919632i | \(0.628487\pi\) | |||||||
\(140\) | −2.03041e13 | −0.227904 | ||||||||
\(141\) | 4.67567e13 | 0.501094 | ||||||||
\(142\) | −4.17057e13 | −0.426895 | ||||||||
\(143\) | 2.00516e14 | 1.96094 | ||||||||
\(144\) | 1.90922e11 | 0.00178443 | ||||||||
\(145\) | 1.61148e14 | 1.43991 | ||||||||
\(146\) | −1.20099e14 | −1.02623 | ||||||||
\(147\) | −6.13429e13 | −0.501420 | ||||||||
\(148\) | −8.64928e13 | −0.676518 | ||||||||
\(149\) | 1.38447e14 | 1.03651 | 0.518254 | − | 0.855227i | \(-0.326582\pi\) | ||||
0.518254 | + | 0.855227i | \(0.326582\pi\) | |||||||
\(150\) | −1.29048e12 | −0.00925036 | ||||||||
\(151\) | 1.57694e14 | 1.08259 | 0.541295 | − | 0.840833i | \(-0.317934\pi\) | ||||
0.541295 | + | 0.840833i | \(0.317934\pi\) | |||||||
\(152\) | −2.89342e14 | −1.90296 | ||||||||
\(153\) | −6.90341e13 | −0.435080 | ||||||||
\(154\) | 4.87260e13 | 0.294358 | ||||||||
\(155\) | −2.55355e13 | −0.147907 | ||||||||
\(156\) | 9.59763e13 | 0.533156 | ||||||||
\(157\) | −2.83769e14 | −1.51223 | −0.756113 | − | 0.654441i | \(-0.772904\pi\) | ||||
−0.756113 | + | 0.654441i | \(0.772904\pi\) | |||||||
\(158\) | −1.50877e14 | −0.771530 | ||||||||
\(159\) | −1.51131e14 | −0.741775 | ||||||||
\(160\) | −2.15310e14 | −1.01458 | ||||||||
\(161\) | −7.93105e13 | −0.358891 | ||||||||
\(162\) | −1.57490e13 | −0.0684551 | ||||||||
\(163\) | 4.30080e14 | 1.79610 | 0.898049 | − | 0.439896i | \(-0.144985\pi\) | ||||
0.898049 | + | 0.439896i | \(0.144985\pi\) | |||||||
\(164\) | −7.23875e13 | −0.290522 | ||||||||
\(165\) | −1.99710e14 | −0.770466 | ||||||||
\(166\) | −4.45456e13 | −0.165235 | ||||||||
\(167\) | −2.72981e14 | −0.973812 | −0.486906 | − | 0.873454i | \(-0.661875\pi\) | ||||
−0.486906 | + | 0.873454i | \(0.661875\pi\) | |||||||
\(168\) | 6.09137e13 | 0.209028 | ||||||||
\(169\) | 3.68111e14 | 1.21539 | ||||||||
\(170\) | 2.56349e14 | 0.814543 | ||||||||
\(171\) | −2.07733e14 | −0.635375 | ||||||||
\(172\) | −4.42696e13 | −0.130368 | ||||||||
\(173\) | −6.11310e14 | −1.73365 | −0.866825 | − | 0.498612i | \(-0.833843\pi\) | ||||
−0.866825 | + | 0.498612i | \(0.833843\pi\) | |||||||
\(174\) | −1.85104e14 | −0.505646 | ||||||||
\(175\) | 3.58349e12 | 0.00943101 | ||||||||
\(176\) | −2.78095e12 | −0.00705278 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | −7.93555e13 | −0.187002 | ||||||||
\(179\) | 1.01687e14 | 0.231058 | 0.115529 | − | 0.993304i | \(-0.463144\pi\) | ||||
0.115529 | + | 0.993304i | \(0.463144\pi\) | |||||||
\(180\) | −9.55905e13 | −0.209480 | ||||||||
\(181\) | −3.26880e14 | −0.691000 | −0.345500 | − | 0.938419i | \(-0.612291\pi\) | ||||
−0.345500 | + | 0.938419i | \(0.612291\pi\) | |||||||
\(182\) | 1.63052e14 | 0.332553 | ||||||||
\(183\) | 5.37736e14 | 1.05837 | ||||||||
\(184\) | −5.20077e14 | −0.987989 | ||||||||
\(185\) | 6.02255e14 | 1.10450 | ||||||||
\(186\) | 2.93316e13 | 0.0519400 | ||||||||
\(187\) | 1.00554e15 | 1.71961 | ||||||||
\(188\) | −3.25984e14 | −0.538480 | ||||||||
\(189\) | 4.37328e13 | 0.0697920 | ||||||||
\(190\) | 7.71388e14 | 1.18953 | ||||||||
\(191\) | −1.58373e14 | −0.236028 | −0.118014 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118014 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(192\) | 2.45173e14 | 0.353195 | ||||||||
\(193\) | −4.12134e14 | −0.574006 | −0.287003 | − | 0.957930i | \(-0.592659\pi\) | ||||
−0.287003 | + | 0.957930i | \(0.592659\pi\) | |||||||
\(194\) | −2.97599e14 | −0.400793 | ||||||||
\(195\) | −6.68289e14 | −0.870441 | ||||||||
\(196\) | 4.27677e14 | 0.538830 | ||||||||
\(197\) | 1.49525e15 | 1.82257 | 0.911285 | − | 0.411775i | \(-0.135091\pi\) | ||||
0.911285 | + | 0.411775i | \(0.135091\pi\) | |||||||
\(198\) | 2.29398e14 | 0.270562 | ||||||||
\(199\) | 1.60159e15 | 1.82813 | 0.914063 | − | 0.405572i | \(-0.132928\pi\) | ||||
0.914063 | + | 0.405572i | \(0.132928\pi\) | |||||||
\(200\) | 2.34987e13 | 0.0259626 | ||||||||
\(201\) | −6.84955e14 | −0.732635 | ||||||||
\(202\) | −1.07481e14 | −0.111314 | ||||||||
\(203\) | 5.14009e14 | 0.515521 | ||||||||
\(204\) | 4.81300e14 | 0.467541 | ||||||||
\(205\) | 5.04038e14 | 0.474311 | ||||||||
\(206\) | −1.20835e15 | −1.10168 | ||||||||
\(207\) | −3.73388e14 | −0.329878 | ||||||||
\(208\) | −9.30588e12 | −0.00796794 | ||||||||
\(209\) | 3.02581e15 | 2.51125 | ||||||||
\(210\) | −1.62396e14 | −0.130662 | ||||||||
\(211\) | −4.16709e14 | −0.325085 | −0.162543 | − | 0.986702i | \(-0.551970\pi\) | ||||
−0.162543 | + | 0.986702i | \(0.551970\pi\) | |||||||
\(212\) | 1.05367e15 | 0.797117 | ||||||||
\(213\) | 5.45230e14 | 0.400048 | ||||||||
\(214\) | −4.53001e14 | −0.322411 | ||||||||
\(215\) | 3.08252e14 | 0.212841 | ||||||||
\(216\) | 2.86778e14 | 0.192130 | ||||||||
\(217\) | −8.14498e13 | −0.0529544 | ||||||||
\(218\) | 1.36036e15 | 0.858391 | ||||||||
\(219\) | 1.57009e15 | 0.961695 | ||||||||
\(220\) | 1.39236e15 | 0.827950 | ||||||||
\(221\) | 3.36485e15 | 1.94274 | ||||||||
\(222\) | −6.91786e14 | −0.387862 | ||||||||
\(223\) | 1.26649e15 | 0.689639 | 0.344819 | − | 0.938669i | \(-0.387940\pi\) | ||||
0.344819 | + | 0.938669i | \(0.387940\pi\) | |||||||
\(224\) | −6.86768e14 | −0.363243 | ||||||||
\(225\) | 1.68708e13 | 0.00866861 | ||||||||
\(226\) | 8.36973e14 | 0.417837 | ||||||||
\(227\) | −1.16866e15 | −0.566919 | −0.283459 | − | 0.958984i | \(-0.591482\pi\) | ||||
−0.283459 | + | 0.958984i | \(0.591482\pi\) | |||||||
\(228\) | 1.44829e15 | 0.682779 | ||||||||
\(229\) | −1.37038e15 | −0.627930 | −0.313965 | − | 0.949435i | \(-0.601657\pi\) | ||||
−0.313965 | + | 0.949435i | \(0.601657\pi\) | |||||||
\(230\) | 1.38653e15 | 0.617587 | ||||||||
\(231\) | −6.37007e14 | −0.275846 | ||||||||
\(232\) | 3.37061e15 | 1.41918 | ||||||||
\(233\) | −7.05044e14 | −0.288671 | −0.144335 | − | 0.989529i | \(-0.546104\pi\) | ||||
−0.144335 | + | 0.989529i | \(0.546104\pi\) | |||||||
\(234\) | 7.67636e14 | 0.305670 | ||||||||
\(235\) | 2.26984e15 | 0.879134 | ||||||||
\(236\) | 2.14384e14 | 0.0807725 | ||||||||
\(237\) | 1.97246e15 | 0.723009 | ||||||||
\(238\) | 8.17668e14 | 0.291626 | ||||||||
\(239\) | −4.82720e15 | −1.67536 | −0.837682 | − | 0.546158i | \(-0.816090\pi\) | ||||
−0.837682 | + | 0.546158i | \(0.816090\pi\) | |||||||
\(240\) | 9.26847e12 | 0.00313065 | ||||||||
\(241\) | 4.23734e15 | 1.39310 | 0.696550 | − | 0.717508i | \(-0.254718\pi\) | ||||
0.696550 | + | 0.717508i | \(0.254718\pi\) | |||||||
\(242\) | −1.41631e15 | −0.453272 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −3.74905e15 | −1.13733 | ||||||||
\(245\) | −2.97795e15 | −0.879705 | ||||||||
\(246\) | −5.78968e14 | −0.166562 | ||||||||
\(247\) | 1.01253e16 | 2.83711 | ||||||||
\(248\) | −5.34106e14 | −0.145778 | ||||||||
\(249\) | 5.82357e14 | 0.154844 | ||||||||
\(250\) | 2.34633e15 | 0.607827 | ||||||||
\(251\) | 3.47724e15 | 0.877718 | 0.438859 | − | 0.898556i | \(-0.355383\pi\) | ||||
0.438859 | + | 0.898556i | \(0.355383\pi\) | |||||||
\(252\) | −3.04902e14 | −0.0749991 | ||||||||
\(253\) | 5.43873e15 | 1.30381 | ||||||||
\(254\) | −4.53690e15 | −1.06008 | ||||||||
\(255\) | −3.35132e15 | −0.763316 | ||||||||
\(256\) | −4.48851e15 | −0.996650 | ||||||||
\(257\) | 6.61181e15 | 1.43138 | 0.715690 | − | 0.698418i | \(-0.246112\pi\) | ||||
0.715690 | + | 0.698418i | \(0.246112\pi\) | |||||||
\(258\) | −3.54076e14 | −0.0747427 | ||||||||
\(259\) | 1.92099e15 | 0.395437 | ||||||||
\(260\) | 4.65925e15 | 0.935383 | ||||||||
\(261\) | 2.41992e15 | 0.473847 | ||||||||
\(262\) | 2.09106e15 | 0.399400 | ||||||||
\(263\) | 6.55505e15 | 1.22142 | 0.610708 | − | 0.791856i | \(-0.290885\pi\) | ||||
0.610708 | + | 0.791856i | \(0.290885\pi\) | |||||||
\(264\) | −4.17717e15 | −0.759375 | ||||||||
\(265\) | −7.33678e15 | −1.30139 | ||||||||
\(266\) | 2.46047e15 | 0.425880 | ||||||||
\(267\) | 1.03744e15 | 0.175242 | ||||||||
\(268\) | 4.77545e15 | 0.787295 | ||||||||
\(269\) | 1.58276e15 | 0.254699 | 0.127349 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127349 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(270\) | −7.64550e14 | −0.120100 | ||||||||
\(271\) | −1.19736e16 | −1.83622 | −0.918108 | − | 0.396331i | \(-0.870283\pi\) | ||||
−0.918108 | + | 0.396331i | \(0.870283\pi\) | |||||||
\(272\) | −4.66669e13 | −0.00698733 | ||||||||
\(273\) | −2.13162e15 | −0.311639 | ||||||||
\(274\) | 4.89367e14 | 0.0698644 | ||||||||
\(275\) | −2.45738e14 | −0.0342618 | ||||||||
\(276\) | 2.60323e15 | 0.354490 | ||||||||
\(277\) | −1.16282e16 | −1.54666 | −0.773329 | − | 0.634005i | \(-0.781410\pi\) | ||||
−0.773329 | + | 0.634005i | \(0.781410\pi\) | |||||||
\(278\) | 3.72496e15 | 0.483983 | ||||||||
\(279\) | −3.83460e14 | −0.0486735 | ||||||||
\(280\) | 2.95711e15 | 0.366725 | ||||||||
\(281\) | −3.27561e15 | −0.396918 | −0.198459 | − | 0.980109i | \(-0.563594\pi\) | ||||
−0.198459 | + | 0.980109i | \(0.563594\pi\) | |||||||
\(282\) | −2.60728e15 | −0.308722 | ||||||||
\(283\) | 3.41648e13 | 0.00395336 | 0.00197668 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197668 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(284\) | −3.80129e15 | −0.429895 | ||||||||
\(285\) | −1.00846e16 | −1.11472 | ||||||||
\(286\) | −1.11813e16 | −1.20813 | ||||||||
\(287\) | 1.60771e15 | 0.169815 | ||||||||
\(288\) | −3.23325e15 | −0.333879 | ||||||||
\(289\) | 6.96937e15 | 0.703651 | ||||||||
\(290\) | −8.98606e15 | −0.887120 | ||||||||
\(291\) | 3.89059e15 | 0.375587 | ||||||||
\(292\) | −1.09465e16 | −1.03345 | ||||||||
\(293\) | 1.29046e16 | 1.19153 | 0.595767 | − | 0.803158i | \(-0.296848\pi\) | ||||
0.595767 | + | 0.803158i | \(0.296848\pi\) | |||||||
\(294\) | 3.42064e15 | 0.308923 | ||||||||
\(295\) | −1.49277e15 | −0.131871 | ||||||||
\(296\) | 1.25969e16 | 1.08860 | ||||||||
\(297\) | −2.99899e15 | −0.253546 | ||||||||
\(298\) | −7.72017e15 | −0.638589 | ||||||||
\(299\) | 1.81996e16 | 1.47299 | ||||||||
\(300\) | −1.17622e14 | −0.00931536 | ||||||||
\(301\) | 9.83220e14 | 0.0762024 | ||||||||
\(302\) | −8.79342e15 | −0.666980 | ||||||||
\(303\) | 1.40513e15 | 0.104313 | ||||||||
\(304\) | −1.40427e14 | −0.0102040 | ||||||||
\(305\) | 2.61049e16 | 1.85683 | ||||||||
\(306\) | 3.84952e15 | 0.268051 | ||||||||
\(307\) | −8.62429e15 | −0.587928 | −0.293964 | − | 0.955817i | \(-0.594975\pi\) | ||||
−0.293964 | + | 0.955817i | \(0.594975\pi\) | |||||||
\(308\) | 4.44116e15 | 0.296426 | ||||||||
\(309\) | 1.57970e16 | 1.03239 | ||||||||
\(310\) | 1.42393e15 | 0.0911250 | ||||||||
\(311\) | 6.60329e15 | 0.413826 | 0.206913 | − | 0.978359i | \(-0.433658\pi\) | ||||
0.206913 | + | 0.978359i | \(0.433658\pi\) | |||||||
\(312\) | −1.39781e16 | −0.857910 | ||||||||
\(313\) | 2.88885e16 | 1.73655 | 0.868273 | − | 0.496086i | \(-0.165230\pi\) | ||||
0.868273 | + | 0.496086i | \(0.165230\pi\) | |||||||
\(314\) | 1.58237e16 | 0.931677 | ||||||||
\(315\) | 2.12305e15 | 0.122445 | ||||||||
\(316\) | −1.37518e16 | −0.776951 | ||||||||
\(317\) | 1.22993e16 | 0.680764 | 0.340382 | − | 0.940287i | \(-0.389444\pi\) | ||||
0.340382 | + | 0.940287i | \(0.389444\pi\) | |||||||
\(318\) | 8.42746e15 | 0.457004 | ||||||||
\(319\) | −3.52483e16 | −1.87283 | ||||||||
\(320\) | 1.19021e16 | 0.619654 | ||||||||
\(321\) | 5.92220e15 | 0.302135 | ||||||||
\(322\) | 4.42256e15 | 0.221111 | ||||||||
\(323\) | 5.07759e16 | 2.48795 | ||||||||
\(324\) | −1.43546e15 | −0.0689362 | ||||||||
\(325\) | −8.22314e14 | −0.0387075 | ||||||||
\(326\) | −2.39824e16 | −1.10657 | ||||||||
\(327\) | −1.77843e16 | −0.804408 | ||||||||
\(328\) | 1.05426e16 | 0.467483 | ||||||||
\(329\) | 7.24004e15 | 0.314752 | ||||||||
\(330\) | 1.11363e16 | 0.474681 | ||||||||
\(331\) | −2.55496e16 | −1.06783 | −0.533914 | − | 0.845539i | \(-0.679279\pi\) | ||||
−0.533914 | + | 0.845539i | \(0.679279\pi\) | |||||||
\(332\) | −4.06014e15 | −0.166396 | ||||||||
\(333\) | 9.04390e15 | 0.363470 | ||||||||
\(334\) | 1.52221e16 | 0.599962 | ||||||||
\(335\) | −3.32517e16 | −1.28535 | ||||||||
\(336\) | 2.95633e13 | 0.00112085 | ||||||||
\(337\) | −6.15670e15 | −0.228957 | −0.114478 | − | 0.993426i | \(-0.536520\pi\) | ||||
−0.114478 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(338\) | −2.05269e16 | −0.748797 | ||||||||
\(339\) | −1.09420e16 | −0.391559 | ||||||||
\(340\) | 2.33651e16 | 0.820266 | ||||||||
\(341\) | 5.58544e15 | 0.192377 | ||||||||
\(342\) | 1.15837e16 | 0.391452 | ||||||||
\(343\) | −2.04357e16 | −0.677606 | ||||||||
\(344\) | 6.44746e15 | 0.209777 | ||||||||
\(345\) | −1.81265e16 | −0.578747 | ||||||||
\(346\) | 3.40883e16 | 1.06810 | ||||||||
\(347\) | 1.84981e16 | 0.568835 | 0.284418 | − | 0.958700i | \(-0.408200\pi\) | ||||
0.284418 | + | 0.958700i | \(0.408200\pi\) | |||||||
\(348\) | −1.68715e16 | −0.509200 | ||||||||
\(349\) | −3.31225e16 | −0.981201 | −0.490600 | − | 0.871385i | \(-0.663223\pi\) | ||||
−0.490600 | + | 0.871385i | \(0.663223\pi\) | |||||||
\(350\) | −1.99825e14 | −0.00581041 | ||||||||
\(351\) | −1.00355e16 | −0.286446 | ||||||||
\(352\) | 4.70952e16 | 1.31962 | ||||||||
\(353\) | −5.18852e16 | −1.42728 | −0.713638 | − | 0.700515i | \(-0.752954\pi\) | ||||
−0.713638 | + | 0.700515i | \(0.752954\pi\) | |||||||
\(354\) | 1.71468e15 | 0.0463086 | ||||||||
\(355\) | 2.64686e16 | 0.701855 | ||||||||
\(356\) | −7.23291e15 | −0.188316 | ||||||||
\(357\) | −1.06896e16 | −0.273286 | ||||||||
\(358\) | −5.67034e15 | −0.142354 | ||||||||
\(359\) | −9.40818e15 | −0.231949 | −0.115974 | − | 0.993252i | \(-0.536999\pi\) | ||||
−0.115974 | + | 0.993252i | \(0.536999\pi\) | |||||||
\(360\) | 1.39219e16 | 0.337079 | ||||||||
\(361\) | 1.10738e17 | 2.63331 | ||||||||
\(362\) | 1.82277e16 | 0.425722 | ||||||||
\(363\) | 1.85158e16 | 0.424766 | ||||||||
\(364\) | 1.48615e16 | 0.334890 | ||||||||
\(365\) | 7.62213e16 | 1.68723 | ||||||||
\(366\) | −2.99856e16 | −0.652058 | ||||||||
\(367\) | −4.62025e16 | −0.987043 | −0.493522 | − | 0.869734i | \(-0.664291\pi\) | ||||
−0.493522 | + | 0.869734i | \(0.664291\pi\) | |||||||
\(368\) | −2.52410e14 | −0.00529780 | ||||||||
\(369\) | 7.56901e15 | 0.156087 | ||||||||
\(370\) | −3.35834e16 | −0.680476 | ||||||||
\(371\) | −2.34019e16 | −0.465930 | ||||||||
\(372\) | 2.67345e15 | 0.0523050 | ||||||||
\(373\) | −5.25352e16 | −1.01005 | −0.505025 | − | 0.863105i | \(-0.668517\pi\) | ||||
−0.505025 | + | 0.863105i | \(0.668517\pi\) | |||||||
\(374\) | −5.60717e16 | −1.05944 | ||||||||
\(375\) | −3.06742e16 | −0.569601 | ||||||||
\(376\) | 4.74765e16 | 0.866478 | ||||||||
\(377\) | −1.17951e17 | −2.11585 | ||||||||
\(378\) | −2.43866e15 | −0.0429986 | ||||||||
\(379\) | −7.83601e16 | −1.35813 | −0.679063 | − | 0.734080i | \(-0.737614\pi\) | ||||
−0.679063 | + | 0.734080i | \(0.737614\pi\) | |||||||
\(380\) | 7.03087e16 | 1.19789 | ||||||||
\(381\) | 5.93120e16 | 0.993414 | ||||||||
\(382\) | 8.83127e15 | 0.145416 | ||||||||
\(383\) | 7.07693e16 | 1.14565 | 0.572826 | − | 0.819677i | \(-0.305847\pi\) | ||||
0.572826 | + | 0.819677i | \(0.305847\pi\) | |||||||
\(384\) | 2.26616e16 | 0.360693 | ||||||||
\(385\) | −3.09241e16 | −0.483952 | ||||||||
\(386\) | 2.29817e16 | 0.353643 | ||||||||
\(387\) | 4.62893e15 | 0.0700422 | ||||||||
\(388\) | −2.71248e16 | −0.403609 | ||||||||
\(389\) | −4.03950e16 | −0.591092 | −0.295546 | − | 0.955329i | \(-0.595502\pi\) | ||||
−0.295546 | + | 0.955329i | \(0.595502\pi\) | |||||||
\(390\) | 3.72656e16 | 0.536275 | ||||||||
\(391\) | 9.12670e16 | 1.29171 | ||||||||
\(392\) | −6.22873e16 | −0.867041 | ||||||||
\(393\) | −2.73370e16 | −0.374282 | ||||||||
\(394\) | −8.33793e16 | −1.12288 | ||||||||
\(395\) | 9.57547e16 | 1.26847 | ||||||||
\(396\) | 2.09087e16 | 0.272463 | ||||||||
\(397\) | −1.70754e16 | −0.218893 | −0.109446 | − | 0.993993i | \(-0.534908\pi\) | ||||
−0.109446 | + | 0.993993i | \(0.534908\pi\) | |||||||
\(398\) | −8.93089e16 | −1.12630 | ||||||||
\(399\) | −3.21664e16 | −0.399097 | ||||||||
\(400\) | 1.14046e13 | 0.000139217 0 | ||||||||
\(401\) | −5.15982e16 | −0.619721 | −0.309860 | − | 0.950782i | \(-0.600282\pi\) | ||||
−0.309860 | + | 0.950782i | \(0.600282\pi\) | |||||||
\(402\) | 3.81949e16 | 0.451373 | ||||||||
\(403\) | 1.86905e16 | 0.217340 | ||||||||
\(404\) | −9.79644e15 | −0.112096 | ||||||||
\(405\) | 9.99517e15 | 0.112547 | ||||||||
\(406\) | −2.86625e16 | −0.317611 | ||||||||
\(407\) | −1.31732e17 | −1.43658 | ||||||||
\(408\) | −7.00968e16 | −0.752328 | ||||||||
\(409\) | 3.80753e16 | 0.402200 | 0.201100 | − | 0.979571i | \(-0.435548\pi\) | ||||
0.201100 | + | 0.979571i | \(0.435548\pi\) | |||||||
\(410\) | −2.81065e16 | −0.292221 | ||||||||
\(411\) | −6.39762e15 | −0.0654707 | ||||||||
\(412\) | −1.10135e17 | −1.10942 | ||||||||
\(413\) | −4.76143e15 | −0.0472130 | ||||||||
\(414\) | 2.08211e16 | 0.203237 | ||||||||
\(415\) | 2.82710e16 | 0.271662 | ||||||||
\(416\) | 1.57595e17 | 1.49085 | ||||||||
\(417\) | −4.86973e16 | −0.453546 | ||||||||
\(418\) | −1.68727e17 | −1.54717 | ||||||||
\(419\) | 4.30196e16 | 0.388396 | 0.194198 | − | 0.980962i | \(-0.437790\pi\) | ||||
0.194198 | + | 0.980962i | \(0.437790\pi\) | |||||||
\(420\) | −1.48017e16 | −0.131581 | ||||||||
\(421\) | −2.04885e16 | −0.179340 | −0.0896698 | − | 0.995972i | \(-0.528581\pi\) | ||||
−0.0896698 | + | 0.995972i | \(0.528581\pi\) | |||||||
\(422\) | 2.32368e16 | 0.200284 | ||||||||
\(423\) | 3.40856e16 | 0.289307 | ||||||||
\(424\) | −1.53458e17 | −1.28266 | ||||||||
\(425\) | −4.12372e15 | −0.0339438 | ||||||||
\(426\) | −3.04034e16 | −0.246468 | ||||||||
\(427\) | 8.32659e16 | 0.664792 | ||||||||
\(428\) | −4.12891e16 | −0.324677 | ||||||||
\(429\) | 1.46176e17 | 1.13215 | ||||||||
\(430\) | −1.71889e16 | −0.131131 | ||||||||
\(431\) | 5.41548e16 | 0.406944 | 0.203472 | − | 0.979081i | \(-0.434777\pi\) | ||||
0.203472 | + | 0.979081i | \(0.434777\pi\) | |||||||
\(432\) | 1.39182e14 | 0.00103024 | ||||||||
\(433\) | −2.45592e17 | −1.79078 | −0.895390 | − | 0.445283i | \(-0.853103\pi\) | ||||
−0.895390 | + | 0.445283i | \(0.853103\pi\) | |||||||
\(434\) | 4.54186e15 | 0.0326250 | ||||||||
\(435\) | 1.17477e17 | 0.831330 | ||||||||
\(436\) | 1.23991e17 | 0.864423 | ||||||||
\(437\) | 2.74634e17 | 1.88636 | ||||||||
\(438\) | −8.75523e16 | −0.592497 | ||||||||
\(439\) | 1.12802e17 | 0.752135 | 0.376068 | − | 0.926592i | \(-0.377276\pi\) | ||||
0.376068 | + | 0.926592i | \(0.377276\pi\) | |||||||
\(440\) | −2.02784e17 | −1.33227 | ||||||||
\(441\) | −4.47190e16 | −0.289495 | ||||||||
\(442\) | −1.87633e17 | −1.19692 | ||||||||
\(443\) | 7.60744e16 | 0.478205 | 0.239103 | − | 0.970994i | \(-0.423147\pi\) | ||||
0.239103 | + | 0.970994i | \(0.423147\pi\) | |||||||
\(444\) | −6.30533e16 | −0.390588 | ||||||||
\(445\) | 5.03632e16 | 0.307449 | ||||||||
\(446\) | −7.06231e16 | −0.424884 | ||||||||
\(447\) | 1.00928e17 | 0.598428 | ||||||||
\(448\) | 3.79638e16 | 0.221851 | ||||||||
\(449\) | 3.03944e14 | 0.00175062 | 0.000875310 | − | 1.00000i | \(-0.499721\pi\) | ||||
0.000875310 | 1.00000i | \(0.499721\pi\) | ||||||||
\(450\) | −9.40761e14 | −0.00534070 | ||||||||
\(451\) | −1.10249e17 | −0.616919 | ||||||||
\(452\) | 7.62865e16 | 0.420773 | ||||||||
\(453\) | 1.14959e17 | 0.625034 | ||||||||
\(454\) | 6.51677e16 | 0.349276 | ||||||||
\(455\) | −1.03481e17 | −0.546749 | ||||||||
\(456\) | −2.10931e17 | −1.09867 | ||||||||
\(457\) | −6.41357e16 | −0.329340 | −0.164670 | − | 0.986349i | \(-0.552656\pi\) | ||||
−0.164670 | + | 0.986349i | \(0.552656\pi\) | |||||||
\(458\) | 7.64162e16 | 0.386865 | ||||||||
\(459\) | −5.03258e16 | −0.251194 | ||||||||
\(460\) | 1.26376e17 | 0.621927 | ||||||||
\(461\) | −2.60089e17 | −1.26202 | −0.631011 | − | 0.775774i | \(-0.717360\pi\) | ||||
−0.631011 | + | 0.775774i | \(0.717360\pi\) | |||||||
\(462\) | 3.55212e16 | 0.169948 | ||||||||
\(463\) | 1.55350e17 | 0.732884 | 0.366442 | − | 0.930441i | \(-0.380576\pi\) | ||||
0.366442 | + | 0.930441i | \(0.380576\pi\) | |||||||
\(464\) | 1.63586e15 | 0.00760992 | ||||||||
\(465\) | −1.86154e16 | −0.0853942 | ||||||||
\(466\) | 3.93151e16 | 0.177849 | ||||||||
\(467\) | 3.24764e17 | 1.44880 | 0.724401 | − | 0.689379i | \(-0.242117\pi\) | ||||
0.724401 | + | 0.689379i | \(0.242117\pi\) | |||||||
\(468\) | 6.99667e16 | 0.307818 | ||||||||
\(469\) | −1.06062e17 | −0.460189 | ||||||||
\(470\) | −1.26573e17 | −0.541631 | ||||||||
\(471\) | −2.06867e17 | −0.873084 | ||||||||
\(472\) | −3.12230e16 | −0.129973 | ||||||||
\(473\) | −6.74245e16 | −0.276835 | ||||||||
\(474\) | −1.09990e17 | −0.445443 | ||||||||
\(475\) | −1.24088e16 | −0.0495703 | ||||||||
\(476\) | 7.45269e16 | 0.293676 | ||||||||
\(477\) | −1.10174e17 | −0.428264 | ||||||||
\(478\) | 2.69178e17 | 1.03219 | ||||||||
\(479\) | 1.41061e17 | 0.533611 | 0.266806 | − | 0.963750i | \(-0.414032\pi\) | ||||
0.266806 | + | 0.963750i | \(0.414032\pi\) | |||||||
\(480\) | −1.56961e17 | −0.585766 | ||||||||
\(481\) | −4.40816e17 | −1.62298 | ||||||||
\(482\) | −2.36285e17 | −0.858283 | ||||||||
\(483\) | −5.78173e16 | −0.207206 | ||||||||
\(484\) | −1.29091e17 | −0.456457 | ||||||||
\(485\) | 1.88872e17 | 0.658941 | ||||||||
\(486\) | −1.14810e16 | −0.0395226 | ||||||||
\(487\) | 2.40411e17 | 0.816612 | 0.408306 | − | 0.912845i | \(-0.366120\pi\) | ||||
0.408306 | + | 0.912845i | \(0.366120\pi\) | |||||||
\(488\) | 5.46015e17 | 1.83010 | ||||||||
\(489\) | 3.13528e17 | 1.03698 | ||||||||
\(490\) | 1.66058e17 | 0.541983 | ||||||||
\(491\) | −1.88402e17 | −0.606815 | −0.303407 | − | 0.952861i | \(-0.598124\pi\) | ||||
−0.303407 | + | 0.952861i | \(0.598124\pi\) | |||||||
\(492\) | −5.27705e16 | −0.167733 | ||||||||
\(493\) | −5.91499e17 | −1.85545 | ||||||||
\(494\) | −5.64612e17 | −1.74793 | ||||||||
\(495\) | −1.45588e17 | −0.444829 | ||||||||
\(496\) | −2.59218e14 | −0.000781691 0 | ||||||||
\(497\) | 8.44261e16 | 0.251281 | ||||||||
\(498\) | −3.24738e16 | −0.0953986 | ||||||||
\(499\) | 3.96915e17 | 1.15092 | 0.575458 | − | 0.817831i | \(-0.304824\pi\) | ||||
0.575458 | + | 0.817831i | \(0.304824\pi\) | |||||||
\(500\) | 2.13858e17 | 0.612098 | ||||||||
\(501\) | −1.99003e17 | −0.562230 | ||||||||
\(502\) | −1.93900e17 | −0.540759 | ||||||||
\(503\) | 1.41417e17 | 0.389322 | 0.194661 | − | 0.980871i | \(-0.437639\pi\) | ||||
0.194661 | + | 0.980871i | \(0.437639\pi\) | |||||||
\(504\) | 4.44061e16 | 0.120682 | ||||||||
\(505\) | 6.82133e16 | 0.183010 | ||||||||
\(506\) | −3.03278e17 | −0.803272 | ||||||||
\(507\) | 2.68353e17 | 0.701705 | ||||||||
\(508\) | −4.13518e17 | −1.06753 | ||||||||
\(509\) | −4.87285e17 | −1.24199 | −0.620994 | − | 0.783815i | \(-0.713271\pi\) | ||||
−0.620994 | + | 0.783815i | \(0.713271\pi\) | |||||||
\(510\) | 1.86878e17 | 0.470276 | ||||||||
\(511\) | 2.43121e17 | 0.604068 | ||||||||
\(512\) | −4.36415e15 | −0.0107064 | ||||||||
\(513\) | −1.51437e17 | −0.366834 | ||||||||
\(514\) | −3.68692e17 | −0.881867 | ||||||||
\(515\) | 7.66880e17 | 1.81126 | ||||||||
\(516\) | −3.22725e16 | −0.0752679 | ||||||||
\(517\) | −4.96487e17 | −1.14346 | ||||||||
\(518\) | −1.07120e17 | −0.243627 | ||||||||
\(519\) | −4.45645e17 | −1.00092 | ||||||||
\(520\) | −6.78577e17 | −1.50514 | ||||||||
\(521\) | 8.76008e16 | 0.191895 | 0.0959473 | − | 0.995386i | \(-0.469412\pi\) | ||||
0.0959473 | + | 0.995386i | \(0.469412\pi\) | |||||||
\(522\) | −1.34941e17 | −0.291935 | ||||||||
\(523\) | −6.91313e17 | −1.47711 | −0.738557 | − | 0.674191i | \(-0.764492\pi\) | ||||
−0.738557 | + | 0.674191i | \(0.764492\pi\) | |||||||
\(524\) | 1.90591e17 | 0.402207 | ||||||||
\(525\) | 2.61236e15 | 0.00544500 | ||||||||
\(526\) | −3.65527e17 | −0.752510 | ||||||||
\(527\) | 9.37289e16 | 0.190592 | ||||||||
\(528\) | −2.02731e15 | −0.00407192 | ||||||||
\(529\) | −1.03957e16 | −0.0206249 | ||||||||
\(530\) | 4.09119e17 | 0.801781 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 2.24261e17 | 0.428873 | ||||||||
\(533\) | −3.68927e17 | −0.696969 | ||||||||
\(534\) | −5.78501e16 | −0.107966 | ||||||||
\(535\) | 2.87499e17 | 0.530074 | ||||||||
\(536\) | −6.95500e17 | −1.26685 | ||||||||
\(537\) | 7.41298e16 | 0.133401 | ||||||||
\(538\) | −8.82592e16 | −0.156919 | ||||||||
\(539\) | 6.51371e17 | 1.14420 | ||||||||
\(540\) | −6.96854e16 | −0.120944 | ||||||||
\(541\) | 4.44253e17 | 0.761813 | 0.380906 | − | 0.924614i | \(-0.375612\pi\) | ||||
0.380906 | + | 0.924614i | \(0.375612\pi\) | |||||||
\(542\) | 6.67679e17 | 1.13129 | ||||||||
\(543\) | −2.38296e17 | −0.398949 | ||||||||
\(544\) | 7.90302e17 | 1.30738 | ||||||||
\(545\) | −8.63354e17 | −1.41128 | ||||||||
\(546\) | 1.18865e17 | 0.192000 | ||||||||
\(547\) | −5.72288e17 | −0.913476 | −0.456738 | − | 0.889601i | \(-0.650982\pi\) | ||||
−0.456738 | + | 0.889601i | \(0.650982\pi\) | |||||||
\(548\) | 4.46037e16 | 0.0703553 | ||||||||
\(549\) | 3.92010e17 | 0.611050 | ||||||||
\(550\) | 1.37030e16 | 0.0211086 | ||||||||
\(551\) | −1.77990e18 | −2.70963 | ||||||||
\(552\) | −3.79136e17 | −0.570416 | ||||||||
\(553\) | 3.05426e17 | 0.454142 | ||||||||
\(554\) | 6.48420e17 | 0.952890 | ||||||||
\(555\) | 4.39044e17 | 0.637681 | ||||||||
\(556\) | 3.39514e17 | 0.487384 | ||||||||
\(557\) | 1.09323e18 | 1.55115 | 0.775575 | − | 0.631255i | \(-0.217460\pi\) | ||||
0.775575 | + | 0.631255i | \(0.217460\pi\) | |||||||
\(558\) | 2.13828e16 | 0.0299876 | ||||||||
\(559\) | −2.25623e17 | −0.312756 | ||||||||
\(560\) | 1.43518e15 | 0.00196645 | ||||||||
\(561\) | 7.33040e17 | 0.992817 | ||||||||
\(562\) | 1.82656e17 | 0.244540 | ||||||||
\(563\) | −3.86699e17 | −0.511763 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(564\) | −2.37642e17 | −0.310892 | ||||||||
\(565\) | −5.31188e17 | −0.686963 | ||||||||
\(566\) | −1.90512e15 | −0.00243565 | ||||||||
\(567\) | 3.18812e16 | 0.0402944 | ||||||||
\(568\) | 5.53623e17 | 0.691752 | ||||||||
\(569\) | 1.07796e18 | 1.33160 | 0.665799 | − | 0.746131i | \(-0.268091\pi\) | ||||
0.665799 | + | 0.746131i | \(0.268091\pi\) | |||||||
\(570\) | 5.62342e17 | 0.686774 | ||||||||
\(571\) | −3.64277e17 | −0.439843 | −0.219921 | − | 0.975518i | \(-0.570580\pi\) | ||||
−0.219921 | + | 0.975518i | \(0.570580\pi\) | |||||||
\(572\) | −1.01913e18 | −1.21662 | ||||||||
\(573\) | −1.15454e17 | −0.136271 | ||||||||
\(574\) | −8.96504e16 | −0.104622 | ||||||||
\(575\) | −2.23042e16 | −0.0257362 | ||||||||
\(576\) | 1.78731e17 | 0.203917 | ||||||||
\(577\) | 8.86790e16 | 0.100041 | 0.0500205 | − | 0.998748i | \(-0.484071\pi\) | ||||
0.0500205 | + | 0.998748i | \(0.484071\pi\) | |||||||
\(578\) | −3.88631e17 | −0.433517 | ||||||||
\(579\) | −3.00446e17 | −0.331402 | ||||||||
\(580\) | −8.19041e17 | −0.893354 | ||||||||
\(581\) | 9.01751e16 | 0.0972617 | ||||||||
\(582\) | −2.16950e17 | −0.231398 | ||||||||
\(583\) | 1.60479e18 | 1.69267 | ||||||||
\(584\) | 1.59426e18 | 1.66294 | ||||||||
\(585\) | −4.87183e17 | −0.502549 | ||||||||
\(586\) | −7.19597e17 | −0.734099 | ||||||||
\(587\) | 1.16655e18 | 1.17694 | 0.588471 | − | 0.808519i | \(-0.299730\pi\) | ||||
0.588471 | + | 0.808519i | \(0.299730\pi\) | |||||||
\(588\) | 3.11777e17 | 0.311094 | ||||||||
\(589\) | 2.82043e17 | 0.278333 | ||||||||
\(590\) | 8.32407e16 | 0.0812451 | ||||||||
\(591\) | 1.09004e18 | 1.05226 | ||||||||
\(592\) | 6.11366e15 | 0.00583728 | ||||||||
\(593\) | −1.23991e18 | −1.17094 | −0.585470 | − | 0.810694i | \(-0.699090\pi\) | ||||
−0.585470 | + | 0.810694i | \(0.699090\pi\) | |||||||
\(594\) | 1.67231e17 | 0.156209 | ||||||||
\(595\) | −5.18935e17 | −0.479461 | ||||||||
\(596\) | −7.03660e17 | −0.643076 | ||||||||
\(597\) | 1.16756e18 | 1.05547 | ||||||||
\(598\) | −1.01486e18 | −0.907503 | ||||||||
\(599\) | 2.98890e17 | 0.264385 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(600\) | 1.71305e16 | 0.0149895 | ||||||||
\(601\) | 1.47417e18 | 1.27604 | 0.638020 | − | 0.770020i | \(-0.279754\pi\) | ||||
0.638020 | + | 0.770020i | \(0.279754\pi\) | |||||||
\(602\) | −5.48270e16 | −0.0469480 | ||||||||
\(603\) | −4.99332e17 | −0.422987 | ||||||||
\(604\) | −8.01482e17 | −0.671667 | ||||||||
\(605\) | 8.98867e17 | 0.745222 | ||||||||
\(606\) | −7.83538e16 | −0.0642670 | ||||||||
\(607\) | 2.55738e17 | 0.207524 | 0.103762 | − | 0.994602i | \(-0.466912\pi\) | ||||
0.103762 | + | 0.994602i | \(0.466912\pi\) | |||||||
\(608\) | 2.37812e18 | 1.90924 | ||||||||
\(609\) | 3.74713e17 | 0.297636 | ||||||||
\(610\) | −1.45568e18 | −1.14399 | ||||||||
\(611\) | −1.66140e18 | −1.29183 | ||||||||
\(612\) | 3.50867e17 | 0.269935 | ||||||||
\(613\) | −1.27632e18 | −0.971556 | −0.485778 | − | 0.874082i | \(-0.661464\pi\) | ||||
−0.485778 | + | 0.874082i | \(0.661464\pi\) | |||||||
\(614\) | 4.80913e17 | 0.362220 | ||||||||
\(615\) | 3.67444e17 | 0.273844 | ||||||||
\(616\) | −6.46814e17 | −0.476985 | ||||||||
\(617\) | −1.98750e18 | −1.45029 | −0.725143 | − | 0.688599i | \(-0.758226\pi\) | ||||
−0.725143 | + | 0.688599i | \(0.758226\pi\) | |||||||
\(618\) | −8.80884e17 | −0.636053 | ||||||||
\(619\) | 1.46096e18 | 1.04388 | 0.521939 | − | 0.852983i | \(-0.325209\pi\) | ||||
0.521939 | + | 0.852983i | \(0.325209\pi\) | |||||||
\(620\) | 1.29785e17 | 0.0917654 | ||||||||
\(621\) | −2.72200e17 | −0.190455 | ||||||||
\(622\) | −3.68217e17 | −0.254956 | ||||||||
\(623\) | 1.60642e17 | 0.110074 | ||||||||
\(624\) | −6.78399e15 | −0.00460029 | ||||||||
\(625\) | −1.52786e18 | −1.02533 | ||||||||
\(626\) | −1.61090e18 | −1.06988 | ||||||||
\(627\) | 2.20581e18 | 1.44987 | ||||||||
\(628\) | 1.44226e18 | 0.938224 | ||||||||
\(629\) | −2.21059e18 | −1.42325 | ||||||||
\(630\) | −1.18387e17 | −0.0754380 | ||||||||
\(631\) | −5.87590e17 | −0.370582 | −0.185291 | − | 0.982684i | \(-0.559323\pi\) | ||||
−0.185291 | + | 0.982684i | \(0.559323\pi\) | |||||||
\(632\) | 2.00282e18 | 1.25021 | ||||||||
\(633\) | −3.03781e17 | −0.187688 | ||||||||
\(634\) | −6.85844e17 | −0.419416 | ||||||||
\(635\) | 2.87935e18 | 1.74287 | ||||||||
\(636\) | 7.68127e17 | 0.460216 | ||||||||
\(637\) | 2.17968e18 | 1.29267 | ||||||||
\(638\) | 1.96554e18 | 1.15384 | ||||||||
\(639\) | 3.97472e17 | 0.230968 | ||||||||
\(640\) | 1.10013e18 | 0.632810 | ||||||||
\(641\) | 2.74499e18 | 1.56301 | 0.781507 | − | 0.623897i | \(-0.214451\pi\) | ||||
0.781507 | + | 0.623897i | \(0.214451\pi\) | |||||||
\(642\) | −3.30238e17 | −0.186144 | ||||||||
\(643\) | 3.08333e18 | 1.72048 | 0.860238 | − | 0.509892i | \(-0.170315\pi\) | ||||
0.860238 | + | 0.509892i | \(0.170315\pi\) | |||||||
\(644\) | 4.03097e17 | 0.222665 | ||||||||
\(645\) | 2.24716e17 | 0.122884 | ||||||||
\(646\) | −2.83140e18 | −1.53282 | ||||||||
\(647\) | −3.89479e17 | −0.208740 | −0.104370 | − | 0.994539i | \(-0.533283\pi\) | ||||
−0.104370 | + | 0.994539i | \(0.533283\pi\) | |||||||
\(648\) | 2.09061e17 | 0.110926 | ||||||||
\(649\) | 3.26516e17 | 0.171519 | ||||||||
\(650\) | 4.58544e16 | 0.0238476 | ||||||||
\(651\) | −5.93769e16 | −0.0305732 | ||||||||
\(652\) | −2.18589e18 | −1.11434 | ||||||||
\(653\) | −3.66726e18 | −1.85100 | −0.925500 | − | 0.378749i | \(-0.876354\pi\) | ||||
−0.925500 | + | 0.378749i | \(0.876354\pi\) | |||||||
\(654\) | 9.91700e17 | 0.495593 | ||||||||
\(655\) | −1.32710e18 | −0.656651 | ||||||||
\(656\) | 5.11664e15 | 0.00250674 | ||||||||
\(657\) | 1.14459e18 | 0.555235 | ||||||||
\(658\) | −4.03724e17 | −0.193917 | ||||||||
\(659\) | 1.66169e18 | 0.790303 | 0.395152 | − | 0.918616i | \(-0.370692\pi\) | ||||
0.395152 | + | 0.918616i | \(0.370692\pi\) | |||||||
\(660\) | 1.01503e18 | 0.478017 | ||||||||
\(661\) | 3.38080e18 | 1.57656 | 0.788279 | − | 0.615318i | \(-0.210972\pi\) | ||||
0.788279 | + | 0.615318i | \(0.210972\pi\) | |||||||
\(662\) | 1.42471e18 | 0.657885 | ||||||||
\(663\) | 2.45297e18 | 1.12164 | ||||||||
\(664\) | 5.91322e17 | 0.267751 | ||||||||
\(665\) | −1.56154e18 | −0.700187 | ||||||||
\(666\) | −5.04312e17 | −0.223932 | ||||||||
\(667\) | −3.19927e18 | −1.40680 | ||||||||
\(668\) | 1.38743e18 | 0.604178 | ||||||||
\(669\) | 9.23275e17 | 0.398163 | ||||||||
\(670\) | 1.85421e18 | 0.791902 | ||||||||
\(671\) | −5.70997e18 | −2.41511 | ||||||||
\(672\) | −5.00654e17 | −0.209719 | ||||||||
\(673\) | 1.31123e18 | 0.543979 | 0.271990 | − | 0.962300i | \(-0.412318\pi\) | ||||
0.271990 | + | 0.962300i | \(0.412318\pi\) | |||||||
\(674\) | 3.43314e17 | 0.141059 | ||||||||
\(675\) | 1.22988e16 | 0.00500482 | ||||||||
\(676\) | −1.87093e18 | −0.754058 | ||||||||
\(677\) | 4.09276e18 | 1.63377 | 0.816883 | − | 0.576804i | \(-0.195700\pi\) | ||||
0.816883 | + | 0.576804i | \(0.195700\pi\) | |||||||
\(678\) | 6.10154e17 | 0.241238 | ||||||||
\(679\) | 6.02438e17 | 0.235917 | ||||||||
\(680\) | −3.40291e18 | −1.31991 | ||||||||
\(681\) | −8.51954e17 | −0.327311 | ||||||||
\(682\) | −3.11459e17 | −0.118523 | ||||||||
\(683\) | −1.85693e18 | −0.699939 | −0.349970 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349970 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(684\) | 1.05581e18 | 0.394203 | ||||||||
\(685\) | −3.10578e17 | −0.114864 | ||||||||
\(686\) | 1.13955e18 | 0.417471 | ||||||||
\(687\) | −9.99009e17 | −0.362535 | ||||||||
\(688\) | 3.12915e15 | 0.00112487 | ||||||||
\(689\) | 5.37010e18 | 1.91231 | ||||||||
\(690\) | 1.01078e18 | 0.356564 | ||||||||
\(691\) | 2.65304e18 | 0.927120 | 0.463560 | − | 0.886066i | \(-0.346572\pi\) | ||||
0.463560 | + | 0.886066i | \(0.346572\pi\) | |||||||
\(692\) | 3.10700e18 | 1.07560 | ||||||||
\(693\) | −4.64378e17 | −0.159260 | ||||||||
\(694\) | −1.03151e18 | −0.350457 | ||||||||
\(695\) | −2.36406e18 | −0.795713 | ||||||||
\(696\) | 2.45717e18 | 0.819362 | ||||||||
\(697\) | −1.85009e18 | −0.611194 | ||||||||
\(698\) | 1.84700e18 | 0.604514 | ||||||||
\(699\) | −5.13977e17 | −0.166664 | ||||||||
\(700\) | −1.82132e16 | −0.00585124 | ||||||||
\(701\) | 2.05507e18 | 0.654123 | 0.327062 | − | 0.945003i | \(-0.393942\pi\) | ||||
0.327062 | + | 0.945003i | \(0.393942\pi\) | |||||||
\(702\) | 5.59607e17 | 0.176478 | ||||||||
\(703\) | −6.65197e18 | −2.07845 | ||||||||
\(704\) | −2.60337e18 | −0.805961 | ||||||||
\(705\) | 1.65472e18 | 0.507568 | ||||||||
\(706\) | 2.89326e18 | 0.879339 | ||||||||
\(707\) | 2.17577e17 | 0.0655221 | ||||||||
\(708\) | 1.56286e17 | 0.0466340 | ||||||||
\(709\) | 5.06643e18 | 1.49796 | 0.748982 | − | 0.662591i | \(-0.230543\pi\) | ||||
0.748982 | + | 0.662591i | \(0.230543\pi\) | |||||||
\(710\) | −1.47596e18 | −0.432410 | ||||||||
\(711\) | 1.43792e18 | 0.417429 | ||||||||
\(712\) | 1.05341e18 | 0.303023 | ||||||||
\(713\) | 5.06956e17 | 0.144507 | ||||||||
\(714\) | 5.96080e17 | 0.168370 | ||||||||
\(715\) | 7.09625e18 | 1.98627 | ||||||||
\(716\) | −5.16827e17 | −0.143354 | ||||||||
\(717\) | −3.51903e18 | −0.967272 | ||||||||
\(718\) | 5.24625e17 | 0.142903 | ||||||||
\(719\) | −2.40099e18 | −0.648116 | −0.324058 | − | 0.946037i | \(-0.605047\pi\) | ||||
−0.324058 | + | 0.946037i | \(0.605047\pi\) | |||||||
\(720\) | 6.75672e15 | 0.00180748 | ||||||||
\(721\) | 2.44609e18 | 0.648475 | ||||||||
\(722\) | −6.17507e18 | −1.62237 | ||||||||
\(723\) | 3.08902e18 | 0.804306 | ||||||||
\(724\) | 1.66138e18 | 0.428714 | ||||||||
\(725\) | 1.44553e17 | 0.0369683 | ||||||||
\(726\) | −1.03249e18 | −0.261697 | ||||||||
\(727\) | −3.72909e18 | −0.936762 | −0.468381 | − | 0.883526i | \(-0.655163\pi\) | ||||
−0.468381 | + | 0.883526i | \(0.655163\pi\) | |||||||
\(728\) | −2.16443e18 | −0.538878 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −4.25031e18 | −1.03949 | ||||||||
\(731\) | −1.13145e18 | −0.274266 | ||||||||
\(732\) | −2.73306e18 | −0.656640 | ||||||||
\(733\) | −5.51789e18 | −1.31401 | −0.657003 | − | 0.753888i | \(-0.728176\pi\) | ||||
−0.657003 | + | 0.753888i | \(0.728176\pi\) | |||||||
\(734\) | 2.57638e18 | 0.608114 | ||||||||
\(735\) | −2.17092e18 | −0.507898 | ||||||||
\(736\) | 4.27455e18 | 0.991253 | ||||||||
\(737\) | 7.27321e18 | 1.67181 | ||||||||
\(738\) | −4.22068e17 | −0.0961648 | ||||||||
\(739\) | −2.12651e18 | −0.480262 | −0.240131 | − | 0.970741i | \(-0.577190\pi\) | ||||
−0.240131 | + | 0.970741i | \(0.577190\pi\) | |||||||
\(740\) | −3.06098e18 | −0.685258 | ||||||||
\(741\) | 7.38132e18 | 1.63801 | ||||||||
\(742\) | 1.30495e18 | 0.287057 | ||||||||
\(743\) | 7.02153e18 | 1.53110 | 0.765551 | − | 0.643375i | \(-0.222466\pi\) | ||||
0.765551 | + | 0.643375i | \(0.222466\pi\) | |||||||
\(744\) | −3.89364e17 | −0.0841649 | ||||||||
\(745\) | 4.89963e18 | 1.04990 | ||||||||
\(746\) | 2.92950e18 | 0.622288 | ||||||||
\(747\) | 4.24538e17 | 0.0893990 | ||||||||
\(748\) | −5.11069e18 | −1.06689 | ||||||||
\(749\) | 9.17024e17 | 0.189779 | ||||||||
\(750\) | 1.71048e18 | 0.350929 | ||||||||
\(751\) | −4.88108e18 | −0.992788 | −0.496394 | − | 0.868097i | \(-0.665343\pi\) | ||||
−0.496394 | + | 0.868097i | \(0.665343\pi\) | |||||||
\(752\) | 2.30418e16 | 0.00464623 | ||||||||
\(753\) | 2.53491e18 | 0.506751 | ||||||||
\(754\) | 6.57728e18 | 1.30356 | ||||||||
\(755\) | 5.58077e18 | 1.09658 | ||||||||
\(756\) | −2.22273e17 | −0.0433008 | ||||||||
\(757\) | −3.89271e18 | −0.751845 | −0.375923 | − | 0.926651i | \(-0.622674\pi\) | ||||
−0.375923 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(758\) | 4.36957e18 | 0.836737 | ||||||||
\(759\) | 3.96483e18 | 0.752754 | ||||||||
\(760\) | −1.02398e19 | −1.92754 | ||||||||
\(761\) | 7.13340e18 | 1.33136 | 0.665681 | − | 0.746237i | \(-0.268141\pi\) | ||||
0.665681 | + | 0.746237i | \(0.268141\pi\) | |||||||
\(762\) | −3.30740e18 | −0.612039 | ||||||||
\(763\) | −2.75381e18 | −0.505271 | ||||||||
\(764\) | 8.04932e17 | 0.146438 | ||||||||
\(765\) | −2.44311e18 | −0.440701 | ||||||||
\(766\) | −3.94628e18 | −0.705832 | ||||||||
\(767\) | 1.09262e18 | 0.193776 | ||||||||
\(768\) | −3.27213e18 | −0.575416 | ||||||||
\(769\) | −1.33412e18 | −0.232635 | −0.116317 | − | 0.993212i | \(-0.537109\pi\) | ||||
−0.116317 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(770\) | 1.72441e18 | 0.298161 | ||||||||
\(771\) | 4.82001e18 | 0.826407 | ||||||||
\(772\) | 2.09468e18 | 0.356128 | ||||||||
\(773\) | 2.34497e18 | 0.395339 | 0.197670 | − | 0.980269i | \(-0.436663\pi\) | ||||
0.197670 | + | 0.980269i | \(0.436663\pi\) | |||||||
\(774\) | −2.58122e17 | −0.0431527 | ||||||||
\(775\) | −2.29058e16 | −0.00379739 | ||||||||
\(776\) | 3.95048e18 | 0.649455 | ||||||||
\(777\) | 1.40040e18 | 0.228306 | ||||||||
\(778\) | 2.25253e18 | 0.364169 | ||||||||
\(779\) | −5.56715e18 | −0.892565 | ||||||||
\(780\) | 3.39660e18 | 0.540044 | ||||||||
\(781\) | −5.78954e18 | −0.912876 | ||||||||
\(782\) | −5.08929e18 | −0.795817 | ||||||||
\(783\) | 1.76412e18 | 0.273575 | ||||||||
\(784\) | −3.02300e16 | −0.00464925 | ||||||||
\(785\) | −1.00426e19 | −1.53176 | ||||||||
\(786\) | 1.52438e18 | 0.230594 | ||||||||
\(787\) | −1.04240e18 | −0.156387 | −0.0781935 | − | 0.996938i | \(-0.524915\pi\) | ||||
−0.0781935 | + | 0.996938i | \(0.524915\pi\) | |||||||
\(788\) | −7.59967e18 | −1.13077 | ||||||||
\(789\) | 4.77863e18 | 0.705185 | ||||||||
\(790\) | −5.33954e18 | −0.781498 | ||||||||
\(791\) | −1.69431e18 | −0.245950 | ||||||||
\(792\) | −3.04516e18 | −0.438425 | ||||||||
\(793\) | −1.91073e19 | −2.72849 | ||||||||
\(794\) | 9.52168e17 | 0.134859 | ||||||||
\(795\) | −5.34851e18 | −0.751358 | ||||||||
\(796\) | −8.14012e18 | −1.13422 | ||||||||
\(797\) | −8.26338e18 | −1.14203 | −0.571017 | − | 0.820938i | \(-0.693451\pi\) | ||||
−0.571017 | + | 0.820938i | \(0.693451\pi\) | |||||||
\(798\) | 1.79368e18 | 0.245882 | ||||||||
\(799\) | −8.33153e18 | −1.13284 | ||||||||
\(800\) | −1.93137e17 | −0.0260484 | ||||||||
\(801\) | 7.56290e17 | 0.101176 | ||||||||
\(802\) | 2.87725e18 | 0.381808 | ||||||||
\(803\) | −1.66720e19 | −2.19451 | ||||||||
\(804\) | 3.48130e18 | 0.454545 | ||||||||
\(805\) | −2.80679e18 | −0.363527 | ||||||||
\(806\) | −1.04223e18 | −0.133902 | ||||||||
\(807\) | 1.15384e18 | 0.147050 | ||||||||
\(808\) | 1.42676e18 | 0.180375 | ||||||||
\(809\) | 9.98180e18 | 1.25182 | 0.625912 | − | 0.779894i | \(-0.284727\pi\) | ||||
0.625912 | + | 0.779894i | \(0.284727\pi\) | |||||||
\(810\) | −5.57357e17 | −0.0693395 | ||||||||
\(811\) | 6.13636e18 | 0.757312 | 0.378656 | − | 0.925537i | \(-0.376386\pi\) | ||||
0.378656 | + | 0.925537i | \(0.376386\pi\) | |||||||
\(812\) | −2.61247e18 | −0.319843 | ||||||||
\(813\) | −8.72874e18 | −1.06014 | ||||||||
\(814\) | 7.34575e18 | 0.885069 | ||||||||
\(815\) | 1.52205e19 | 1.81930 | ||||||||
\(816\) | −3.40202e16 | −0.00403414 | ||||||||
\(817\) | −3.40467e18 | −0.400527 | ||||||||
\(818\) | −2.12318e18 | −0.247794 | ||||||||
\(819\) | −1.55395e18 | −0.179925 | ||||||||
\(820\) | −2.56179e18 | −0.294275 | ||||||||
\(821\) | 9.34465e18 | 1.06496 | 0.532479 | − | 0.846443i | \(-0.321261\pi\) | ||||
0.532479 | + | 0.846443i | \(0.321261\pi\) | |||||||
\(822\) | 3.56748e17 | 0.0403362 | ||||||||
\(823\) | 2.28720e18 | 0.256570 | 0.128285 | − | 0.991737i | \(-0.459053\pi\) | ||||
0.128285 | + | 0.991737i | \(0.459053\pi\) | |||||||
\(824\) | 1.60402e19 | 1.78518 | ||||||||
\(825\) | −1.79143e17 | −0.0197811 | ||||||||
\(826\) | 2.65510e17 | 0.0290878 | ||||||||
\(827\) | 7.13544e18 | 0.775595 | 0.387798 | − | 0.921745i | \(-0.373236\pi\) | ||||
0.387798 | + | 0.921745i | \(0.373236\pi\) | |||||||
\(828\) | 1.89775e18 | 0.204665 | ||||||||
\(829\) | −6.78150e18 | −0.725640 | −0.362820 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362820 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(830\) | −1.57647e18 | −0.167370 | ||||||||
\(831\) | −8.47696e18 | −0.892964 | ||||||||
\(832\) | −8.71167e18 | −0.910541 | ||||||||
\(833\) | 1.09306e19 | 1.13358 | ||||||||
\(834\) | 2.71549e18 | 0.279428 | ||||||||
\(835\) | −9.66078e18 | −0.986393 | ||||||||
\(836\) | −1.53787e19 | −1.55805 | ||||||||
\(837\) | −2.79542e17 | −0.0281017 | ||||||||
\(838\) | −2.39889e18 | −0.239289 | ||||||||
\(839\) | −1.39131e18 | −0.137711 | −0.0688557 | − | 0.997627i | \(-0.521935\pi\) | ||||
−0.0688557 | + | 0.997627i | \(0.521935\pi\) | |||||||
\(840\) | 2.15573e18 | 0.211729 | ||||||||
\(841\) | 1.04738e19 | 1.02077 | ||||||||
\(842\) | 1.14249e18 | 0.110490 | ||||||||
\(843\) | −2.38792e18 | −0.229161 | ||||||||
\(844\) | 2.11794e18 | 0.201691 | ||||||||
\(845\) | 1.30274e19 | 1.23109 | ||||||||
\(846\) | −1.90071e18 | −0.178241 | ||||||||
\(847\) | 2.86708e18 | 0.266808 | ||||||||
\(848\) | −7.44777e16 | −0.00687786 | ||||||||
\(849\) | 2.49061e16 | 0.00228248 | ||||||||
\(850\) | 2.29950e17 | 0.0209127 | ||||||||
\(851\) | −1.19566e19 | −1.07911 | ||||||||
\(852\) | −2.77114e18 | −0.248200 | ||||||||
\(853\) | −1.30566e19 | −1.16055 | −0.580273 | − | 0.814422i | \(-0.697054\pi\) | ||||
−0.580273 | + | 0.814422i | \(0.697054\pi\) | |||||||
\(854\) | −4.64313e18 | −0.409576 | ||||||||
\(855\) | −7.35164e18 | −0.643583 | ||||||||
\(856\) | 6.01338e18 | 0.522443 | ||||||||
\(857\) | −8.27918e18 | −0.713859 | −0.356929 | − | 0.934131i | \(-0.616176\pi\) | ||||
−0.356929 | + | 0.934131i | \(0.616176\pi\) | |||||||
\(858\) | −8.15117e18 | −0.697513 | ||||||||
\(859\) | 7.43253e18 | 0.631220 | 0.315610 | − | 0.948889i | \(-0.397791\pi\) | ||||
0.315610 | + | 0.948889i | \(0.397791\pi\) | |||||||
\(860\) | −1.56670e18 | −0.132052 | ||||||||
\(861\) | 1.17202e18 | 0.0980428 | ||||||||
\(862\) | −3.01982e18 | −0.250717 | ||||||||
\(863\) | 1.64542e19 | 1.35583 | 0.677917 | − | 0.735138i | \(-0.262883\pi\) | ||||
0.677917 | + | 0.735138i | \(0.262883\pi\) | |||||||
\(864\) | −2.35704e18 | −0.192765 | ||||||||
\(865\) | −2.16342e19 | −1.75605 | ||||||||
\(866\) | 1.36948e19 | 1.10329 | ||||||||
\(867\) | 5.08067e18 | 0.406253 | ||||||||
\(868\) | 4.13971e17 | 0.0328543 | ||||||||
\(869\) | −2.09446e19 | −1.64985 | ||||||||
\(870\) | −6.55084e18 | −0.512179 | ||||||||
\(871\) | 2.43383e19 | 1.88874 | ||||||||
\(872\) | −1.80581e19 | −1.39096 | ||||||||
\(873\) | 2.83624e18 | 0.216845 | ||||||||
\(874\) | −1.53143e19 | −1.16218 | ||||||||
\(875\) | −4.74976e18 | −0.357782 | ||||||||
\(876\) | −7.98002e18 | −0.596660 | ||||||||
\(877\) | −6.72310e18 | −0.498968 | −0.249484 | − | 0.968379i | \(-0.580261\pi\) | ||||
−0.249484 | + | 0.968379i | \(0.580261\pi\) | |||||||
\(878\) | −6.29012e18 | −0.463388 | ||||||||
\(879\) | 9.40748e18 | 0.687932 | ||||||||
\(880\) | −9.84176e16 | −0.00714390 | ||||||||
\(881\) | −1.22874e19 | −0.885355 | −0.442677 | − | 0.896681i | \(-0.645971\pi\) | ||||
−0.442677 | + | 0.896681i | \(0.645971\pi\) | |||||||
\(882\) | 2.49365e18 | 0.178357 | ||||||||
\(883\) | −1.76396e19 | −1.25241 | −0.626203 | − | 0.779660i | \(-0.715392\pi\) | ||||
−0.626203 | + | 0.779660i | \(0.715392\pi\) | |||||||
\(884\) | −1.71019e19 | −1.20533 | ||||||||
\(885\) | −1.08823e18 | −0.0761357 | ||||||||
\(886\) | −4.24211e18 | −0.294621 | ||||||||
\(887\) | 2.09206e19 | 1.44235 | 0.721174 | − | 0.692754i | \(-0.243603\pi\) | ||||
0.721174 | + | 0.692754i | \(0.243603\pi\) | |||||||
\(888\) | 9.18313e18 | 0.628502 | ||||||||
\(889\) | 9.18418e18 | 0.623992 | ||||||||
\(890\) | −2.80839e18 | −0.189418 | ||||||||
\(891\) | −2.18626e18 | −0.146385 | ||||||||
\(892\) | −6.43699e18 | −0.427870 | ||||||||
\(893\) | −2.50707e19 | −1.65436 | ||||||||
\(894\) | −5.62800e18 | −0.368689 | ||||||||
\(895\) | 3.59870e18 | 0.234043 | ||||||||
\(896\) | 3.50904e18 | 0.226562 | ||||||||
\(897\) | 1.32675e19 | 0.850431 | ||||||||
\(898\) | −1.69487e16 | −0.00107855 | ||||||||
\(899\) | −3.28557e18 | −0.207574 | ||||||||
\(900\) | −8.57463e16 | −0.00537823 | ||||||||
\(901\) | 2.69299e19 | 1.67696 | ||||||||
\(902\) | 6.14779e18 | 0.380081 | ||||||||
\(903\) | 7.16768e17 | 0.0439955 | ||||||||
\(904\) | −1.11104e19 | −0.677074 | ||||||||
\(905\) | −1.15683e19 | −0.699927 | ||||||||
\(906\) | −6.41040e18 | −0.385081 | ||||||||
\(907\) | 4.88579e17 | 0.0291399 | 0.0145699 | − | 0.999894i | \(-0.495362\pi\) | ||||
0.0145699 | + | 0.999894i | \(0.495362\pi\) | |||||||
\(908\) | 5.93975e18 | 0.351731 | ||||||||
\(909\) | 1.02434e18 | 0.0602253 | ||||||||
\(910\) | 5.77039e18 | 0.336850 | ||||||||
\(911\) | 2.29445e18 | 0.132987 | 0.0664934 | − | 0.997787i | \(-0.478819\pi\) | ||||
0.0664934 | + | 0.997787i | \(0.478819\pi\) | |||||||
\(912\) | −1.02371e17 | −0.00589130 | ||||||||
\(913\) | −6.18377e18 | −0.353341 | ||||||||
\(914\) | 3.57638e18 | 0.202905 | ||||||||
\(915\) | 1.90305e19 | 1.07204 | ||||||||
\(916\) | 6.96500e18 | 0.389584 | ||||||||
\(917\) | −4.23300e18 | −0.235097 | ||||||||
\(918\) | 2.80630e18 | 0.154759 | ||||||||
\(919\) | −1.90274e19 | −1.04191 | −0.520954 | − | 0.853585i | \(-0.674424\pi\) | ||||
−0.520954 | + | 0.853585i | \(0.674424\pi\) | |||||||
\(920\) | −1.84055e19 | −1.00075 | ||||||||
\(921\) | −6.28711e18 | −0.339440 | ||||||||
\(922\) | 1.45033e19 | 0.777527 | ||||||||
\(923\) | −1.93735e19 | −1.03133 | ||||||||
\(924\) | 3.23761e18 | 0.171142 | ||||||||
\(925\) | 5.40233e17 | 0.0283570 | ||||||||
\(926\) | −8.66274e18 | −0.451527 | ||||||||
\(927\) | 1.15160e19 | 0.596052 | ||||||||
\(928\) | −2.77033e19 | −1.42387 | ||||||||
\(929\) | −2.53179e18 | −0.129219 | −0.0646094 | − | 0.997911i | \(-0.520580\pi\) | ||||
−0.0646094 | + | 0.997911i | \(0.520580\pi\) | |||||||
\(930\) | 1.03804e18 | 0.0526111 | ||||||||
\(931\) | 3.28917e19 | 1.65544 | ||||||||
\(932\) | 3.58341e18 | 0.179099 | ||||||||
\(933\) | 4.81380e18 | 0.238922 | ||||||||
\(934\) | −1.81097e19 | −0.892601 | ||||||||
\(935\) | 3.55861e19 | 1.74183 | ||||||||
\(936\) | −1.01900e19 | −0.495315 | ||||||||
\(937\) | 1.08706e19 | 0.524744 | 0.262372 | − | 0.964967i | \(-0.415495\pi\) | ||||
0.262372 | + | 0.964967i | \(0.415495\pi\) | |||||||
\(938\) | 5.91429e18 | 0.283520 | ||||||||
\(939\) | 2.10597e19 | 1.00260 | ||||||||
\(940\) | −1.15365e19 | −0.545437 | ||||||||
\(941\) | −3.07512e19 | −1.44388 | −0.721938 | − | 0.691958i | \(-0.756748\pi\) | ||||
−0.721938 | + | 0.691958i | \(0.756748\pi\) | |||||||
\(942\) | 1.15355e19 | 0.537904 | ||||||||
\(943\) | −1.00067e19 | −0.463408 | ||||||||
\(944\) | −1.51535e16 | −0.000696939 0 | ||||||||
\(945\) | 1.54770e18 | 0.0706937 | ||||||||
\(946\) | 3.75977e18 | 0.170557 | ||||||||
\(947\) | 2.33777e19 | 1.05324 | 0.526620 | − | 0.850101i | \(-0.323459\pi\) | ||||
0.526620 | + | 0.850101i | \(0.323459\pi\) | |||||||
\(948\) | −1.00251e19 | −0.448573 | ||||||||
\(949\) | −5.57896e19 | −2.47927 | ||||||||
\(950\) | 6.91948e17 | 0.0305401 | ||||||||
\(951\) | 8.96622e18 | 0.393039 | ||||||||
\(952\) | −1.08542e19 | −0.472559 | ||||||||
\(953\) | 3.92221e19 | 1.69600 | 0.848002 | − | 0.529992i | \(-0.177805\pi\) | ||||
0.848002 | + | 0.529992i | \(0.177805\pi\) | |||||||
\(954\) | 6.14362e18 | 0.263852 | ||||||||
\(955\) | −5.60480e18 | −0.239077 | ||||||||
\(956\) | 2.45344e19 | 1.03944 | ||||||||
\(957\) | −2.56960e19 | −1.08128 | ||||||||
\(958\) | −7.86591e18 | −0.328756 | ||||||||
\(959\) | −9.90640e17 | −0.0411240 | ||||||||
\(960\) | 8.67665e18 | 0.357758 | ||||||||
\(961\) | −2.38969e19 | −0.978678 | ||||||||
\(962\) | 2.45811e19 | 0.999915 | ||||||||
\(963\) | 4.31729e18 | 0.174438 | ||||||||
\(964\) | −2.15364e19 | −0.864315 | ||||||||
\(965\) | −1.45854e19 | −0.581422 | ||||||||
\(966\) | 3.22405e18 | 0.127659 | ||||||||
\(967\) | −5.29017e18 | −0.208064 | −0.104032 | − | 0.994574i | \(-0.533174\pi\) | ||||
−0.104032 | + | 0.994574i | \(0.533174\pi\) | |||||||
\(968\) | 1.88009e19 | 0.734494 | ||||||||
\(969\) | 3.70156e19 | 1.43642 | ||||||||
\(970\) | −1.05320e19 | −0.405971 | ||||||||
\(971\) | 4.26955e18 | 0.163477 | 0.0817387 | − | 0.996654i | \(-0.473953\pi\) | ||||
0.0817387 | + | 0.996654i | \(0.473953\pi\) | |||||||
\(972\) | −1.04645e18 | −0.0398003 | ||||||||
\(973\) | −7.54055e18 | −0.284885 | ||||||||
\(974\) | −1.34059e19 | −0.503111 | ||||||||
\(975\) | −5.99467e17 | −0.0223478 | ||||||||
\(976\) | 2.64998e17 | 0.00981339 | ||||||||
\(977\) | 4.80164e19 | 1.76634 | 0.883172 | − | 0.469049i | \(-0.155403\pi\) | ||||
0.883172 | + | 0.469049i | \(0.155403\pi\) | |||||||
\(978\) | −1.74832e19 | −0.638878 | ||||||||
\(979\) | −1.10160e19 | −0.399887 | ||||||||
\(980\) | 1.51355e19 | 0.545792 | ||||||||
\(981\) | −1.29648e19 | −0.464425 | ||||||||
\(982\) | 1.05058e19 | 0.373856 | ||||||||
\(983\) | 1.28512e19 | 0.454302 | 0.227151 | − | 0.973859i | \(-0.427059\pi\) | ||||
0.227151 | + | 0.973859i | \(0.427059\pi\) | |||||||
\(984\) | 7.68553e18 | 0.269902 | ||||||||
\(985\) | 5.29170e19 | 1.84612 | ||||||||
\(986\) | 3.29836e19 | 1.14314 | ||||||||
\(987\) | 5.27799e18 | 0.181722 | ||||||||
\(988\) | −5.14619e19 | −1.76022 | ||||||||
\(989\) | −6.11972e18 | −0.207948 | ||||||||
\(990\) | 8.11840e18 | 0.274057 | ||||||||
\(991\) | 3.43466e19 | 1.15187 | 0.575937 | − | 0.817494i | \(-0.304637\pi\) | ||||
0.575937 | + | 0.817494i | \(0.304637\pi\) | |||||||
\(992\) | 4.38985e18 | 0.146260 | ||||||||
\(993\) | −1.86256e19 | −0.616511 | ||||||||
\(994\) | −4.70782e18 | −0.154813 | ||||||||
\(995\) | 5.66802e19 | 1.85174 | ||||||||
\(996\) | −2.95984e18 | −0.0960690 | ||||||||
\(997\) | 2.00453e19 | 0.646389 | 0.323195 | − | 0.946333i | \(-0.395243\pi\) | ||||
0.323195 | + | 0.946333i | \(0.395243\pi\) | |||||||
\(998\) | −2.21330e19 | −0.709075 | ||||||||
\(999\) | 6.59300e18 | 0.209849 |
(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 | 177.14.a.c.1.12 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.12 | ✓ | 31 | 1.1 | even | 1 | trivial |