Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, 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("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −66.4070 | −1.46740 | −0.733700 | − | 0.679473i | \(-0.762208\pi\) | ||||
−0.733700 | + | 0.679473i | \(0.762208\pi\) | |||||||
\(3\) | −356.598 | −0.847251 | −0.423626 | − | 0.905837i | \(-0.639243\pi\) | ||||
−0.423626 | + | 0.905837i | \(0.639243\pi\) | |||||||
\(4\) | 2361.89 | 1.15326 | ||||||||
\(5\) | −8882.65 | −1.27118 | −0.635591 | − | 0.772026i | \(-0.719243\pi\) | ||||
−0.635591 | + | 0.772026i | \(0.719243\pi\) | |||||||
\(6\) | 23680.6 | 1.24326 | ||||||||
\(7\) | −71949.2 | −1.61803 | −0.809015 | − | 0.587788i | \(-0.799999\pi\) | ||||
−0.809015 | + | 0.587788i | \(0.799999\pi\) | |||||||
\(8\) | −20844.3 | −0.224901 | ||||||||
\(9\) | −49984.8 | −0.282166 | ||||||||
\(10\) | 589870. | 1.86533 | ||||||||
\(11\) | 734093. | 1.37433 | 0.687166 | − | 0.726501i | \(-0.258855\pi\) | ||||
0.687166 | + | 0.726501i | \(0.258855\pi\) | |||||||
\(12\) | −842244. | −0.977105 | ||||||||
\(13\) | −172292. | −0.128700 | −0.0643499 | − | 0.997927i | \(-0.520497\pi\) | ||||
−0.0643499 | + | 0.997927i | \(0.520497\pi\) | |||||||
\(14\) | 4.77793e6 | 2.37430 | ||||||||
\(15\) | 3.16754e6 | 1.07701 | ||||||||
\(16\) | −3.45294e6 | −0.823245 | ||||||||
\(17\) | 1.81711e6 | 0.310393 | 0.155196 | − | 0.987884i | \(-0.450399\pi\) | ||||
0.155196 | + | 0.987884i | \(0.450399\pi\) | |||||||
\(18\) | 3.31934e6 | 0.414050 | ||||||||
\(19\) | 8.19267e6 | 0.759068 | 0.379534 | − | 0.925178i | \(-0.376084\pi\) | ||||
0.379534 | + | 0.925178i | \(0.376084\pi\) | |||||||
\(20\) | −2.09798e7 | −1.46601 | ||||||||
\(21\) | 2.56569e7 | 1.37088 | ||||||||
\(22\) | −4.87489e7 | −2.01670 | ||||||||
\(23\) | 4.88503e7 | 1.58258 | 0.791288 | − | 0.611444i | \(-0.209411\pi\) | ||||
0.791288 | + | 0.611444i | \(0.209411\pi\) | |||||||
\(24\) | 7.43302e6 | 0.190548 | ||||||||
\(25\) | 3.00734e7 | 0.615903 | ||||||||
\(26\) | 1.14414e7 | 0.188854 | ||||||||
\(27\) | 8.09948e7 | 1.08632 | ||||||||
\(28\) | −1.69936e8 | −1.86602 | ||||||||
\(29\) | −5.68080e7 | −0.514305 | −0.257152 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257152 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(30\) | −2.10347e8 | −1.58041 | ||||||||
\(31\) | −2.22367e8 | −1.39502 | −0.697510 | − | 0.716575i | \(-0.745709\pi\) | ||||
−0.697510 | + | 0.716575i | \(0.745709\pi\) | |||||||
\(32\) | 2.71988e8 | 1.43293 | ||||||||
\(33\) | −2.61776e8 | −1.16440 | ||||||||
\(34\) | −1.20669e8 | −0.455471 | ||||||||
\(35\) | 6.39100e8 | 2.05681 | ||||||||
\(36\) | −1.18058e8 | −0.325412 | ||||||||
\(37\) | −5.85250e8 | −1.38750 | −0.693748 | − | 0.720218i | \(-0.744042\pi\) | ||||
−0.693748 | + | 0.720218i | \(0.744042\pi\) | |||||||
\(38\) | −5.44051e8 | −1.11386 | ||||||||
\(39\) | 6.14392e7 | 0.109041 | ||||||||
\(40\) | 1.85152e8 | 0.285890 | ||||||||
\(41\) | 9.16053e8 | 1.23484 | 0.617418 | − | 0.786635i | \(-0.288179\pi\) | ||||
0.617418 | + | 0.786635i | \(0.288179\pi\) | |||||||
\(42\) | −1.70380e9 | −2.01163 | ||||||||
\(43\) | 8.11149e8 | 0.841442 | 0.420721 | − | 0.907190i | \(-0.361777\pi\) | ||||
0.420721 | + | 0.907190i | \(0.361777\pi\) | |||||||
\(44\) | 1.73385e9 | 1.58497 | ||||||||
\(45\) | 4.43998e8 | 0.358684 | ||||||||
\(46\) | −3.24400e9 | −2.32227 | ||||||||
\(47\) | 1.78873e9 | 1.13764 | 0.568821 | − | 0.822461i | \(-0.307400\pi\) | ||||
0.568821 | + | 0.822461i | \(0.307400\pi\) | |||||||
\(48\) | 1.23131e9 | 0.697495 | ||||||||
\(49\) | 3.19936e9 | 1.61802 | ||||||||
\(50\) | −1.99708e9 | −0.903777 | ||||||||
\(51\) | −6.47977e8 | −0.262981 | ||||||||
\(52\) | −4.06935e8 | −0.148425 | ||||||||
\(53\) | 1.17129e9 | 0.384722 | 0.192361 | − | 0.981324i | \(-0.438386\pi\) | ||||
0.192361 | + | 0.981324i | \(0.438386\pi\) | |||||||
\(54\) | −5.37862e9 | −1.59406 | ||||||||
\(55\) | −6.52070e9 | −1.74703 | ||||||||
\(56\) | 1.49973e9 | 0.363897 | ||||||||
\(57\) | −2.92149e9 | −0.643121 | ||||||||
\(58\) | 3.77245e9 | 0.754691 | ||||||||
\(59\) | 2.25620e8 | 0.0410859 | 0.0205429 | − | 0.999789i | \(-0.493461\pi\) | ||||
0.0205429 | + | 0.999789i | \(0.493461\pi\) | |||||||
\(60\) | 7.48136e9 | 1.24208 | ||||||||
\(61\) | 4.05728e9 | 0.615064 | 0.307532 | − | 0.951538i | \(-0.400497\pi\) | ||||
0.307532 | + | 0.951538i | \(0.400497\pi\) | |||||||
\(62\) | 1.47667e10 | 2.04705 | ||||||||
\(63\) | 3.59637e9 | 0.456553 | ||||||||
\(64\) | −1.09903e10 | −1.27944 | ||||||||
\(65\) | 1.53041e9 | 0.163601 | ||||||||
\(66\) | 1.73838e10 | 1.70865 | ||||||||
\(67\) | −2.93192e9 | −0.265302 | −0.132651 | − | 0.991163i | \(-0.542349\pi\) | ||||
−0.132651 | + | 0.991163i | \(0.542349\pi\) | |||||||
\(68\) | 4.29180e9 | 0.357965 | ||||||||
\(69\) | −1.74199e10 | −1.34084 | ||||||||
\(70\) | −4.24407e10 | −3.01817 | ||||||||
\(71\) | −1.34111e10 | −0.882150 | −0.441075 | − | 0.897470i | \(-0.645403\pi\) | ||||
−0.441075 | + | 0.897470i | \(0.645403\pi\) | |||||||
\(72\) | 1.04190e9 | 0.0634594 | ||||||||
\(73\) | −1.27365e10 | −0.719076 | −0.359538 | − | 0.933130i | \(-0.617066\pi\) | ||||
−0.359538 | + | 0.933130i | \(0.617066\pi\) | |||||||
\(74\) | 3.88647e10 | 2.03601 | ||||||||
\(75\) | −1.07241e10 | −0.521825 | ||||||||
\(76\) | 1.93502e10 | 0.875407 | ||||||||
\(77\) | −5.28174e10 | −2.22371 | ||||||||
\(78\) | −4.07999e9 | −0.160007 | ||||||||
\(79\) | −4.82571e10 | −1.76446 | −0.882230 | − | 0.470818i | \(-0.843959\pi\) | ||||
−0.882230 | + | 0.470818i | \(0.843959\pi\) | |||||||
\(80\) | 3.06713e10 | 1.04649 | ||||||||
\(81\) | −2.00279e10 | −0.638217 | ||||||||
\(82\) | −6.08323e10 | −1.81200 | ||||||||
\(83\) | −5.57621e10 | −1.55385 | −0.776926 | − | 0.629591i | \(-0.783222\pi\) | ||||
−0.776926 | + | 0.629591i | \(0.783222\pi\) | |||||||
\(84\) | 6.05988e10 | 1.58099 | ||||||||
\(85\) | −1.61407e10 | −0.394566 | ||||||||
\(86\) | −5.38660e10 | −1.23473 | ||||||||
\(87\) | 2.02576e10 | 0.435745 | ||||||||
\(88\) | −1.53016e10 | −0.309089 | ||||||||
\(89\) | 7.86518e9 | 0.149301 | 0.0746506 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746506 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(90\) | −2.94845e10 | −0.526333 | ||||||||
\(91\) | 1.23963e10 | 0.208240 | ||||||||
\(92\) | 1.15379e11 | 1.82513 | ||||||||
\(93\) | 7.92956e10 | 1.18193 | ||||||||
\(94\) | −1.18784e11 | −1.66938 | ||||||||
\(95\) | −7.27727e10 | −0.964914 | ||||||||
\(96\) | −9.69905e10 | −1.21405 | ||||||||
\(97\) | 9.81092e10 | 1.16002 | 0.580009 | − | 0.814610i | \(-0.303049\pi\) | ||||
0.580009 | + | 0.814610i | \(0.303049\pi\) | |||||||
\(98\) | −2.12460e11 | −2.37429 | ||||||||
\(99\) | −3.66935e10 | −0.387789 | ||||||||
\(100\) | 7.10300e10 | 0.710300 | ||||||||
\(101\) | 5.20646e10 | 0.492918 | 0.246459 | − | 0.969153i | \(-0.420733\pi\) | ||||
0.246459 | + | 0.969153i | \(0.420733\pi\) | |||||||
\(102\) | 4.30302e10 | 0.385898 | ||||||||
\(103\) | −7.05612e10 | −0.599737 | −0.299869 | − | 0.953981i | \(-0.596943\pi\) | ||||
−0.299869 | + | 0.953981i | \(0.596943\pi\) | |||||||
\(104\) | 3.59131e9 | 0.0289447 | ||||||||
\(105\) | −2.27902e11 | −1.74264 | ||||||||
\(106\) | −7.77818e10 | −0.564541 | ||||||||
\(107\) | −1.52894e11 | −1.05385 | −0.526927 | − | 0.849910i | \(-0.676656\pi\) | ||||
−0.526927 | + | 0.849910i | \(0.676656\pi\) | |||||||
\(108\) | 1.91300e11 | 1.25281 | ||||||||
\(109\) | 5.35156e10 | 0.333146 | 0.166573 | − | 0.986029i | \(-0.446730\pi\) | ||||
0.166573 | + | 0.986029i | \(0.446730\pi\) | |||||||
\(110\) | 4.33020e11 | 2.56359 | ||||||||
\(111\) | 2.08699e11 | 1.17556 | ||||||||
\(112\) | 2.48436e11 | 1.33204 | ||||||||
\(113\) | −1.31645e11 | −0.672163 | −0.336081 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336081 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(114\) | 1.94007e11 | 0.943717 | ||||||||
\(115\) | −4.33921e11 | −2.01174 | ||||||||
\(116\) | −1.34174e11 | −0.593129 | ||||||||
\(117\) | 8.61201e9 | 0.0363147 | ||||||||
\(118\) | −1.49828e10 | −0.0602894 | ||||||||
\(119\) | −1.30739e11 | −0.502225 | ||||||||
\(120\) | −6.60250e10 | −0.242221 | ||||||||
\(121\) | 2.53581e11 | 0.888787 | ||||||||
\(122\) | −2.69432e11 | −0.902546 | ||||||||
\(123\) | −3.26663e11 | −1.04622 | ||||||||
\(124\) | −5.25205e11 | −1.60883 | ||||||||
\(125\) | 1.66592e11 | 0.488257 | ||||||||
\(126\) | −2.38824e11 | −0.669946 | ||||||||
\(127\) | −5.31958e10 | −0.142875 | −0.0714376 | − | 0.997445i | \(-0.522759\pi\) | ||||
−0.0714376 | + | 0.997445i | \(0.522759\pi\) | |||||||
\(128\) | 1.72801e11 | 0.444519 | ||||||||
\(129\) | −2.89254e11 | −0.712913 | ||||||||
\(130\) | −1.01630e11 | −0.240068 | ||||||||
\(131\) | −6.83862e11 | −1.54873 | −0.774366 | − | 0.632737i | \(-0.781931\pi\) | ||||
−0.774366 | + | 0.632737i | \(0.781931\pi\) | |||||||
\(132\) | −6.18286e11 | −1.34287 | ||||||||
\(133\) | −5.89456e11 | −1.22820 | ||||||||
\(134\) | 1.94700e11 | 0.389305 | ||||||||
\(135\) | −7.19448e11 | −1.38091 | ||||||||
\(136\) | −3.78763e10 | −0.0698077 | ||||||||
\(137\) | −3.11681e9 | −0.00551755 | −0.00275878 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275878 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(138\) | 1.15681e12 | 1.96755 | ||||||||
\(139\) | −3.81730e10 | −0.0623985 | −0.0311993 | − | 0.999513i | \(-0.509933\pi\) | ||||
−0.0311993 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(140\) | 1.50948e12 | 2.37205 | ||||||||
\(141\) | −6.37856e11 | −0.963868 | ||||||||
\(142\) | 8.90589e11 | 1.29447 | ||||||||
\(143\) | −1.26479e11 | −0.176876 | ||||||||
\(144\) | 1.72594e11 | 0.232291 | ||||||||
\(145\) | 5.04606e11 | 0.653775 | ||||||||
\(146\) | 8.45794e11 | 1.05517 | ||||||||
\(147\) | −1.14089e12 | −1.37087 | ||||||||
\(148\) | −1.38229e12 | −1.60015 | ||||||||
\(149\) | 1.34519e12 | 1.50058 | 0.750289 | − | 0.661110i | \(-0.229914\pi\) | ||||
0.750289 | + | 0.661110i | \(0.229914\pi\) | |||||||
\(150\) | 7.12156e11 | 0.765726 | ||||||||
\(151\) | −4.77753e11 | −0.495257 | −0.247628 | − | 0.968855i | \(-0.579651\pi\) | ||||
−0.247628 | + | 0.968855i | \(0.579651\pi\) | |||||||
\(152\) | −1.70770e11 | −0.170715 | ||||||||
\(153\) | −9.08278e10 | −0.0875822 | ||||||||
\(154\) | 3.50745e12 | 3.26307 | ||||||||
\(155\) | 1.97521e12 | 1.77333 | ||||||||
\(156\) | 1.45112e11 | 0.125753 | ||||||||
\(157\) | 1.42016e12 | 1.18820 | 0.594098 | − | 0.804393i | \(-0.297509\pi\) | ||||
0.594098 | + | 0.804393i | \(0.297509\pi\) | |||||||
\(158\) | 3.20461e12 | 2.58917 | ||||||||
\(159\) | −4.17679e11 | −0.325956 | ||||||||
\(160\) | −2.41598e12 | −1.82152 | ||||||||
\(161\) | −3.51474e12 | −2.56066 | ||||||||
\(162\) | 1.32999e12 | 0.936520 | ||||||||
\(163\) | 2.17044e12 | 1.47746 | 0.738730 | − | 0.674002i | \(-0.235426\pi\) | ||||
0.738730 | + | 0.674002i | \(0.235426\pi\) | |||||||
\(164\) | 2.16361e12 | 1.42409 | ||||||||
\(165\) | 2.32527e12 | 1.48017 | ||||||||
\(166\) | 3.70300e12 | 2.28013 | ||||||||
\(167\) | 1.30933e12 | 0.780027 | 0.390014 | − | 0.920809i | \(-0.372470\pi\) | ||||
0.390014 | + | 0.920809i | \(0.372470\pi\) | |||||||
\(168\) | −5.34800e11 | −0.308312 | ||||||||
\(169\) | −1.76248e12 | −0.983436 | ||||||||
\(170\) | 1.07186e12 | 0.578986 | ||||||||
\(171\) | −4.09509e11 | −0.214183 | ||||||||
\(172\) | 1.91584e12 | 0.970406 | ||||||||
\(173\) | −8.80885e10 | −0.0432181 | −0.0216091 | − | 0.999766i | \(-0.506879\pi\) | ||||
−0.0216091 | + | 0.999766i | \(0.506879\pi\) | |||||||
\(174\) | −1.34525e12 | −0.639413 | ||||||||
\(175\) | −2.16376e12 | −0.996550 | ||||||||
\(176\) | −2.53478e12 | −1.13141 | ||||||||
\(177\) | −8.04558e10 | −0.0348100 | ||||||||
\(178\) | −5.22303e11 | −0.219085 | ||||||||
\(179\) | 3.56060e12 | 1.44821 | 0.724105 | − | 0.689690i | \(-0.242253\pi\) | ||||
0.724105 | + | 0.689690i | \(0.242253\pi\) | |||||||
\(180\) | 1.04867e12 | 0.413658 | ||||||||
\(181\) | −3.46272e12 | −1.32491 | −0.662453 | − | 0.749104i | \(-0.730485\pi\) | ||||
−0.662453 | + | 0.749104i | \(0.730485\pi\) | |||||||
\(182\) | −8.23201e11 | −0.305572 | ||||||||
\(183\) | −1.44682e12 | −0.521114 | ||||||||
\(184\) | −1.01825e12 | −0.355923 | ||||||||
\(185\) | 5.19857e12 | 1.76376 | ||||||||
\(186\) | −5.26578e12 | −1.73437 | ||||||||
\(187\) | 1.33393e12 | 0.426583 | ||||||||
\(188\) | 4.22477e12 | 1.31200 | ||||||||
\(189\) | −5.82751e12 | −1.75769 | ||||||||
\(190\) | 4.83261e12 | 1.41592 | ||||||||
\(191\) | 1.01997e11 | 0.0290337 | 0.0145169 | − | 0.999895i | \(-0.495379\pi\) | ||||
0.0145169 | + | 0.999895i | \(0.495379\pi\) | |||||||
\(192\) | 3.91912e12 | 1.08401 | ||||||||
\(193\) | 5.38994e11 | 0.144884 | 0.0724418 | − | 0.997373i | \(-0.476921\pi\) | ||||
0.0724418 | + | 0.997373i | \(0.476921\pi\) | |||||||
\(194\) | −6.51513e12 | −1.70221 | ||||||||
\(195\) | −5.45743e11 | −0.138611 | ||||||||
\(196\) | 7.55652e12 | 1.86601 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | 2.43670e12 | 0.569042 | ||||||||
\(199\) | 1.42363e11 | 0.0323375 | 0.0161687 | − | 0.999869i | \(-0.494853\pi\) | ||||
0.0161687 | + | 0.999869i | \(0.494853\pi\) | |||||||
\(200\) | −6.26858e11 | −0.138517 | ||||||||
\(201\) | 1.04552e12 | 0.224778 | ||||||||
\(202\) | −3.45745e12 | −0.723308 | ||||||||
\(203\) | 4.08729e12 | 0.832160 | ||||||||
\(204\) | −1.53045e12 | −0.303286 | ||||||||
\(205\) | −8.13698e12 | −1.56970 | ||||||||
\(206\) | 4.68575e12 | 0.880055 | ||||||||
\(207\) | −2.44177e12 | −0.446548 | ||||||||
\(208\) | 5.94916e11 | 0.105951 | ||||||||
\(209\) | 6.01419e12 | 1.04321 | ||||||||
\(210\) | 1.51343e13 | 2.55714 | ||||||||
\(211\) | 2.22628e12 | 0.366461 | 0.183230 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183230 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(212\) | 2.76645e12 | 0.443686 | ||||||||
\(213\) | 4.78236e12 | 0.747403 | ||||||||
\(214\) | 1.01533e13 | 1.54643 | ||||||||
\(215\) | −7.20516e12 | −1.06963 | ||||||||
\(216\) | −1.68828e12 | −0.244314 | ||||||||
\(217\) | 1.59991e13 | 2.25719 | ||||||||
\(218\) | −3.55381e12 | −0.488859 | ||||||||
\(219\) | 4.54182e12 | 0.609238 | ||||||||
\(220\) | −1.54011e13 | −2.01478 | ||||||||
\(221\) | −3.13074e11 | −0.0399475 | ||||||||
\(222\) | −1.38591e13 | −1.72501 | ||||||||
\(223\) | −6.37378e11 | −0.0773964 | −0.0386982 | − | 0.999251i | \(-0.512321\pi\) | ||||
−0.0386982 | + | 0.999251i | \(0.512321\pi\) | |||||||
\(224\) | −1.95693e13 | −2.31853 | ||||||||
\(225\) | −1.50321e12 | −0.173787 | ||||||||
\(226\) | 8.74218e12 | 0.986332 | ||||||||
\(227\) | −1.20060e13 | −1.32208 | −0.661038 | − | 0.750353i | \(-0.729884\pi\) | ||||
−0.661038 | + | 0.750353i | \(0.729884\pi\) | |||||||
\(228\) | −6.90023e12 | −0.741689 | ||||||||
\(229\) | −8.77847e12 | −0.921136 | −0.460568 | − | 0.887624i | \(-0.652354\pi\) | ||||
−0.460568 | + | 0.887624i | \(0.652354\pi\) | |||||||
\(230\) | 2.88154e13 | 2.95203 | ||||||||
\(231\) | 1.88346e13 | 1.88404 | ||||||||
\(232\) | 1.18412e12 | 0.115668 | ||||||||
\(233\) | 1.49151e13 | 1.42288 | 0.711440 | − | 0.702747i | \(-0.248043\pi\) | ||||
0.711440 | + | 0.702747i | \(0.248043\pi\) | |||||||
\(234\) | −5.71897e11 | −0.0532882 | ||||||||
\(235\) | −1.58886e13 | −1.44615 | ||||||||
\(236\) | 5.32890e11 | 0.0473829 | ||||||||
\(237\) | 1.72084e13 | 1.49494 | ||||||||
\(238\) | 8.68201e12 | 0.736965 | ||||||||
\(239\) | −6.38408e12 | −0.529554 | −0.264777 | − | 0.964310i | \(-0.585298\pi\) | ||||
−0.264777 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(240\) | −1.09373e13 | −0.886643 | ||||||||
\(241\) | −3.26533e12 | −0.258722 | −0.129361 | − | 0.991598i | \(-0.541293\pi\) | ||||
−0.129361 | + | 0.991598i | \(0.541293\pi\) | |||||||
\(242\) | −1.68396e13 | −1.30421 | ||||||||
\(243\) | −7.20606e12 | −0.545586 | ||||||||
\(244\) | 9.58283e12 | 0.709332 | ||||||||
\(245\) | −2.84188e13 | −2.05680 | ||||||||
\(246\) | 2.16927e13 | 1.53522 | ||||||||
\(247\) | −1.41154e12 | −0.0976919 | ||||||||
\(248\) | 4.63507e12 | 0.313742 | ||||||||
\(249\) | 1.98847e13 | 1.31650 | ||||||||
\(250\) | −1.10628e13 | −0.716468 | ||||||||
\(251\) | −1.19506e13 | −0.757154 | −0.378577 | − | 0.925570i | \(-0.623586\pi\) | ||||
−0.378577 | + | 0.925570i | \(0.623586\pi\) | |||||||
\(252\) | 8.49421e12 | 0.526526 | ||||||||
\(253\) | 3.58607e13 | 2.17498 | ||||||||
\(254\) | 3.53257e12 | 0.209655 | ||||||||
\(255\) | 5.75576e12 | 0.334296 | ||||||||
\(256\) | 1.10330e13 | 0.627152 | ||||||||
\(257\) | 1.75239e13 | 0.974985 | 0.487492 | − | 0.873127i | \(-0.337912\pi\) | ||||
0.487492 | + | 0.873127i | \(0.337912\pi\) | |||||||
\(258\) | 1.92085e13 | 1.04613 | ||||||||
\(259\) | 4.21083e13 | 2.24501 | ||||||||
\(260\) | 3.61467e12 | 0.188675 | ||||||||
\(261\) | 2.83954e12 | 0.145119 | ||||||||
\(262\) | 4.54132e13 | 2.27261 | ||||||||
\(263\) | −1.51987e13 | −0.744815 | −0.372408 | − | 0.928069i | \(-0.621468\pi\) | ||||
−0.372408 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(264\) | 5.45653e12 | 0.261876 | ||||||||
\(265\) | −1.04042e13 | −0.489051 | ||||||||
\(266\) | 3.91440e13 | 1.80225 | ||||||||
\(267\) | −2.80471e12 | −0.126496 | ||||||||
\(268\) | −6.92486e12 | −0.305964 | ||||||||
\(269\) | 2.12488e12 | 0.0919808 | 0.0459904 | − | 0.998942i | \(-0.485356\pi\) | ||||
0.0459904 | + | 0.998942i | \(0.485356\pi\) | |||||||
\(270\) | 4.77764e13 | 2.02634 | ||||||||
\(271\) | 3.13855e12 | 0.130436 | 0.0652180 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652180 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(272\) | −6.27436e12 | −0.255529 | ||||||||
\(273\) | −4.42050e12 | −0.176432 | ||||||||
\(274\) | 2.06978e11 | 0.00809646 | ||||||||
\(275\) | 2.20767e13 | 0.846455 | ||||||||
\(276\) | −4.11439e13 | −1.54634 | ||||||||
\(277\) | 3.38406e13 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(278\) | 2.53495e12 | 0.0915637 | ||||||||
\(279\) | 1.11150e13 | 0.393627 | ||||||||
\(280\) | −1.33216e13 | −0.462579 | ||||||||
\(281\) | 2.80480e13 | 0.955029 | 0.477515 | − | 0.878624i | \(-0.341538\pi\) | ||||
0.477515 | + | 0.878624i | \(0.341538\pi\) | |||||||
\(282\) | 4.23581e13 | 1.41438 | ||||||||
\(283\) | 1.83797e13 | 0.601883 | 0.300941 | − | 0.953643i | \(-0.402699\pi\) | ||||
0.300941 | + | 0.953643i | \(0.402699\pi\) | |||||||
\(284\) | −3.16754e13 | −1.01735 | ||||||||
\(285\) | 2.59506e13 | 0.817524 | ||||||||
\(286\) | 8.39907e12 | 0.259548 | ||||||||
\(287\) | −6.59092e13 | −1.99800 | ||||||||
\(288\) | −1.35953e13 | −0.404324 | ||||||||
\(289\) | −3.09700e13 | −0.903656 | ||||||||
\(290\) | −3.35093e13 | −0.959349 | ||||||||
\(291\) | −3.49855e13 | −0.982827 | ||||||||
\(292\) | −3.00822e13 | −0.829285 | ||||||||
\(293\) | −4.97511e13 | −1.34595 | −0.672977 | − | 0.739663i | \(-0.734985\pi\) | ||||
−0.672977 | + | 0.739663i | \(0.734985\pi\) | |||||||
\(294\) | 7.57627e13 | 2.01162 | ||||||||
\(295\) | −2.00411e12 | −0.0522276 | ||||||||
\(296\) | 1.21991e13 | 0.312050 | ||||||||
\(297\) | 5.94577e13 | 1.49296 | ||||||||
\(298\) | −8.93299e13 | −2.20195 | ||||||||
\(299\) | −8.41655e12 | −0.203677 | ||||||||
\(300\) | −2.53292e13 | −0.601802 | ||||||||
\(301\) | −5.83615e13 | −1.36148 | ||||||||
\(302\) | 3.17261e13 | 0.726740 | ||||||||
\(303\) | −1.85661e13 | −0.417625 | ||||||||
\(304\) | −2.82888e13 | −0.624899 | ||||||||
\(305\) | −3.60394e13 | −0.781859 | ||||||||
\(306\) | 6.03160e12 | 0.128518 | ||||||||
\(307\) | 2.79635e13 | 0.585235 | 0.292617 | − | 0.956230i | \(-0.405474\pi\) | ||||
0.292617 | + | 0.956230i | \(0.405474\pi\) | |||||||
\(308\) | −1.24749e14 | −2.56453 | ||||||||
\(309\) | 2.51620e13 | 0.508128 | ||||||||
\(310\) | −1.31168e14 | −2.60218 | ||||||||
\(311\) | −1.43131e13 | −0.278967 | −0.139483 | − | 0.990224i | \(-0.544544\pi\) | ||||
−0.139483 | + | 0.990224i | \(0.544544\pi\) | |||||||
\(312\) | −1.28065e12 | −0.0245235 | ||||||||
\(313\) | −7.01132e13 | −1.31919 | −0.659593 | − | 0.751623i | \(-0.729271\pi\) | ||||
−0.659593 | + | 0.751623i | \(0.729271\pi\) | |||||||
\(314\) | −9.43083e13 | −1.74356 | ||||||||
\(315\) | −3.19453e13 | −0.580361 | ||||||||
\(316\) | −1.13978e14 | −2.03489 | ||||||||
\(317\) | 2.33871e13 | 0.410346 | 0.205173 | − | 0.978726i | \(-0.434224\pi\) | ||||
0.205173 | + | 0.978726i | \(0.434224\pi\) | |||||||
\(318\) | 2.77368e13 | 0.478308 | ||||||||
\(319\) | −4.17024e13 | −0.706825 | ||||||||
\(320\) | 9.76230e13 | 1.62640 | ||||||||
\(321\) | 5.45218e13 | 0.892879 | ||||||||
\(322\) | 2.33403e14 | 3.75751 | ||||||||
\(323\) | 1.48870e13 | 0.235609 | ||||||||
\(324\) | −4.73037e13 | −0.736033 | ||||||||
\(325\) | −5.18142e12 | −0.0792666 | ||||||||
\(326\) | −1.44132e14 | −2.16803 | ||||||||
\(327\) | −1.90836e13 | −0.282258 | ||||||||
\(328\) | −1.90944e13 | −0.277716 | ||||||||
\(329\) | −1.28697e14 | −1.84074 | ||||||||
\(330\) | −1.54414e14 | −2.17200 | ||||||||
\(331\) | −5.65661e13 | −0.782532 | −0.391266 | − | 0.920278i | \(-0.627963\pi\) | ||||
−0.391266 | + | 0.920278i | \(0.627963\pi\) | |||||||
\(332\) | −1.31704e14 | −1.79200 | ||||||||
\(333\) | 2.92536e13 | 0.391504 | ||||||||
\(334\) | −8.69489e13 | −1.14461 | ||||||||
\(335\) | 2.60432e13 | 0.337247 | ||||||||
\(336\) | −8.85919e13 | −1.12857 | ||||||||
\(337\) | 8.25902e13 | 1.03506 | 0.517528 | − | 0.855666i | \(-0.326852\pi\) | ||||
0.517528 | + | 0.855666i | \(0.326852\pi\) | |||||||
\(338\) | 1.17041e14 | 1.44310 | ||||||||
\(339\) | 4.69445e13 | 0.569490 | ||||||||
\(340\) | −3.81226e13 | −0.455039 | ||||||||
\(341\) | −1.63238e14 | −1.91722 | ||||||||
\(342\) | 2.71943e13 | 0.314292 | ||||||||
\(343\) | −8.79242e13 | −0.999979 | ||||||||
\(344\) | −1.69078e13 | −0.189241 | ||||||||
\(345\) | 1.54735e14 | 1.70445 | ||||||||
\(346\) | 5.84969e12 | 0.0634183 | ||||||||
\(347\) | 9.88266e13 | 1.05454 | 0.527268 | − | 0.849699i | \(-0.323216\pi\) | ||||
0.527268 | + | 0.849699i | \(0.323216\pi\) | |||||||
\(348\) | 4.78462e13 | 0.502530 | ||||||||
\(349\) | 3.55192e13 | 0.367218 | 0.183609 | − | 0.982999i | \(-0.441222\pi\) | ||||
0.183609 | + | 0.982999i | \(0.441222\pi\) | |||||||
\(350\) | 1.43689e14 | 1.46234 | ||||||||
\(351\) | −1.39548e13 | −0.139809 | ||||||||
\(352\) | 1.99665e14 | 1.96932 | ||||||||
\(353\) | −2.96980e13 | −0.288381 | −0.144190 | − | 0.989550i | \(-0.546058\pi\) | ||||
−0.144190 | + | 0.989550i | \(0.546058\pi\) | |||||||
\(354\) | 5.34283e12 | 0.0510803 | ||||||||
\(355\) | 1.19126e14 | 1.12137 | ||||||||
\(356\) | 1.85767e13 | 0.172184 | ||||||||
\(357\) | 4.66214e13 | 0.425511 | ||||||||
\(358\) | −2.36449e14 | −2.12510 | ||||||||
\(359\) | −7.96347e13 | −0.704827 | −0.352414 | − | 0.935844i | \(-0.614639\pi\) | ||||
−0.352414 | + | 0.935844i | \(0.614639\pi\) | |||||||
\(360\) | −9.25480e12 | −0.0806684 | ||||||||
\(361\) | −4.93704e13 | −0.423815 | ||||||||
\(362\) | 2.29949e14 | 1.94417 | ||||||||
\(363\) | −9.04266e13 | −0.753026 | ||||||||
\(364\) | 2.92787e13 | 0.240156 | ||||||||
\(365\) | 1.13134e14 | 0.914077 | ||||||||
\(366\) | 9.60788e13 | 0.764683 | ||||||||
\(367\) | 2.17763e14 | 1.70734 | 0.853672 | − | 0.520810i | \(-0.174370\pi\) | ||||
0.853672 | + | 0.520810i | \(0.174370\pi\) | |||||||
\(368\) | −1.68677e14 | −1.30285 | ||||||||
\(369\) | −4.57887e13 | −0.348428 | ||||||||
\(370\) | −3.45222e14 | −2.58814 | ||||||||
\(371\) | −8.42733e13 | −0.622492 | ||||||||
\(372\) | 1.87287e14 | 1.36308 | ||||||||
\(373\) | −8.76633e13 | −0.628665 | −0.314333 | − | 0.949313i | \(-0.601781\pi\) | ||||
−0.314333 | + | 0.949313i | \(0.601781\pi\) | |||||||
\(374\) | −8.85820e13 | −0.625968 | ||||||||
\(375\) | −5.94063e13 | −0.413676 | ||||||||
\(376\) | −3.72847e13 | −0.255857 | ||||||||
\(377\) | 9.78759e12 | 0.0661909 | ||||||||
\(378\) | 3.86987e14 | 2.57924 | ||||||||
\(379\) | −3.46120e11 | −0.00227359 | −0.00113679 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113679 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(380\) | −1.71881e14 | −1.11280 | ||||||||
\(381\) | 1.89695e13 | 0.121051 | ||||||||
\(382\) | −6.77329e12 | −0.0426041 | ||||||||
\(383\) | 3.19451e14 | 1.98067 | 0.990334 | − | 0.138704i | \(-0.0442937\pi\) | ||||
0.990334 | + | 0.138704i | \(0.0442937\pi\) | |||||||
\(384\) | −6.16204e13 | −0.376619 | ||||||||
\(385\) | 4.69159e14 | 2.82674 | ||||||||
\(386\) | −3.57930e13 | −0.212602 | ||||||||
\(387\) | −4.05451e13 | −0.237426 | ||||||||
\(388\) | 2.31723e14 | 1.33781 | ||||||||
\(389\) | −1.34834e14 | −0.767497 | −0.383749 | − | 0.923438i | \(-0.625367\pi\) | ||||
−0.383749 | + | 0.923438i | \(0.625367\pi\) | |||||||
\(390\) | 3.62411e13 | 0.203398 | ||||||||
\(391\) | 8.87663e13 | 0.491220 | ||||||||
\(392\) | −6.66883e13 | −0.363895 | ||||||||
\(393\) | 2.43864e14 | 1.31217 | ||||||||
\(394\) | 1.97036e13 | 0.104548 | ||||||||
\(395\) | 4.28651e14 | 2.24295 | ||||||||
\(396\) | −8.66659e13 | −0.447224 | ||||||||
\(397\) | −3.35806e14 | −1.70900 | −0.854498 | − | 0.519454i | \(-0.826135\pi\) | ||||
−0.854498 | + | 0.519454i | \(0.826135\pi\) | |||||||
\(398\) | −9.45391e12 | −0.0474520 | ||||||||
\(399\) | 2.10199e14 | 1.04059 | ||||||||
\(400\) | −1.03842e14 | −0.507039 | ||||||||
\(401\) | 2.68768e14 | 1.29444 | 0.647222 | − | 0.762302i | \(-0.275931\pi\) | ||||
0.647222 | + | 0.762302i | \(0.275931\pi\) | |||||||
\(402\) | −6.94297e13 | −0.329839 | ||||||||
\(403\) | 3.83121e13 | 0.179539 | ||||||||
\(404\) | 1.22971e14 | 0.568465 | ||||||||
\(405\) | 1.77901e14 | 0.811290 | ||||||||
\(406\) | −2.71424e14 | −1.22111 | ||||||||
\(407\) | −4.29628e14 | −1.90688 | ||||||||
\(408\) | 1.35066e13 | 0.0591446 | ||||||||
\(409\) | −2.43368e14 | −1.05144 | −0.525720 | − | 0.850657i | \(-0.676204\pi\) | ||||
−0.525720 | + | 0.850657i | \(0.676204\pi\) | |||||||
\(410\) | 5.40352e14 | 2.30338 | ||||||||
\(411\) | 1.11145e12 | 0.00467475 | ||||||||
\(412\) | −1.66657e14 | −0.691656 | ||||||||
\(413\) | −1.62332e13 | −0.0664782 | ||||||||
\(414\) | 1.62151e14 | 0.655266 | ||||||||
\(415\) | 4.95316e14 | 1.97523 | ||||||||
\(416\) | −4.68615e13 | −0.184418 | ||||||||
\(417\) | 1.36124e13 | 0.0528672 | ||||||||
\(418\) | −3.99384e14 | −1.53081 | ||||||||
\(419\) | −4.62562e14 | −1.74982 | −0.874909 | − | 0.484287i | \(-0.839079\pi\) | ||||
−0.874909 | + | 0.484287i | \(0.839079\pi\) | |||||||
\(420\) | −5.38278e14 | −2.00972 | ||||||||
\(421\) | −2.85905e14 | −1.05359 | −0.526793 | − | 0.849993i | \(-0.676606\pi\) | ||||
−0.526793 | + | 0.849993i | \(0.676606\pi\) | |||||||
\(422\) | −1.47841e14 | −0.537744 | ||||||||
\(423\) | −8.94091e13 | −0.321003 | ||||||||
\(424\) | −2.44147e13 | −0.0865244 | ||||||||
\(425\) | 5.46466e13 | 0.191172 | ||||||||
\(426\) | −3.17582e14 | −1.09674 | ||||||||
\(427\) | −2.91918e14 | −0.995193 | ||||||||
\(428\) | −3.61119e14 | −1.21537 | ||||||||
\(429\) | 4.51021e13 | 0.149859 | ||||||||
\(430\) | 4.78473e14 | 1.56957 | ||||||||
\(431\) | 4.07553e14 | 1.31996 | 0.659978 | − | 0.751285i | \(-0.270565\pi\) | ||||
0.659978 | + | 0.751285i | \(0.270565\pi\) | |||||||
\(432\) | −2.79670e14 | −0.894304 | ||||||||
\(433\) | −1.22761e13 | −0.0387594 | −0.0193797 | − | 0.999812i | \(-0.506169\pi\) | ||||
−0.0193797 | + | 0.999812i | \(0.506169\pi\) | |||||||
\(434\) | −1.06245e15 | −3.31220 | ||||||||
\(435\) | −1.79941e14 | −0.553911 | ||||||||
\(436\) | 1.26398e14 | 0.384206 | ||||||||
\(437\) | 4.00215e14 | 1.20128 | ||||||||
\(438\) | −3.01608e14 | −0.893996 | ||||||||
\(439\) | 3.05170e14 | 0.893279 | 0.446640 | − | 0.894714i | \(-0.352621\pi\) | ||||
0.446640 | + | 0.894714i | \(0.352621\pi\) | |||||||
\(440\) | 1.35919e14 | 0.392908 | ||||||||
\(441\) | −1.59919e14 | −0.456550 | ||||||||
\(442\) | 2.07903e13 | 0.0586190 | ||||||||
\(443\) | 6.65281e12 | 0.0185261 | 0.00926307 | − | 0.999957i | \(-0.497051\pi\) | ||||
0.00926307 | + | 0.999957i | \(0.497051\pi\) | |||||||
\(444\) | 4.92923e14 | 1.35573 | ||||||||
\(445\) | −6.98637e13 | −0.189789 | ||||||||
\(446\) | 4.23264e13 | 0.113572 | ||||||||
\(447\) | −4.79692e14 | −1.27137 | ||||||||
\(448\) | 7.90743e14 | 2.07017 | ||||||||
\(449\) | −2.05736e14 | −0.532054 | −0.266027 | − | 0.963966i | \(-0.585711\pi\) | ||||
−0.266027 | + | 0.963966i | \(0.585711\pi\) | |||||||
\(450\) | 9.98238e13 | 0.255015 | ||||||||
\(451\) | 6.72468e14 | 1.69707 | ||||||||
\(452\) | −3.10932e14 | −0.775182 | ||||||||
\(453\) | 1.70366e14 | 0.419607 | ||||||||
\(454\) | 7.97282e14 | 1.94001 | ||||||||
\(455\) | −1.10112e14 | −0.264711 | ||||||||
\(456\) | 6.08963e13 | 0.144639 | ||||||||
\(457\) | 7.22802e14 | 1.69621 | 0.848106 | − | 0.529826i | \(-0.177743\pi\) | ||||
0.848106 | + | 0.529826i | \(0.177743\pi\) | |||||||
\(458\) | 5.82952e14 | 1.35168 | ||||||||
\(459\) | 1.47176e14 | 0.337185 | ||||||||
\(460\) | −1.02487e15 | −2.32007 | ||||||||
\(461\) | −7.93708e14 | −1.77544 | −0.887719 | − | 0.460385i | \(-0.847711\pi\) | ||||
−0.887719 | + | 0.460385i | \(0.847711\pi\) | |||||||
\(462\) | −1.25075e15 | −2.76464 | ||||||||
\(463\) | −7.95113e14 | −1.73673 | −0.868367 | − | 0.495922i | \(-0.834830\pi\) | ||||
−0.868367 | + | 0.495922i | \(0.834830\pi\) | |||||||
\(464\) | 1.96155e14 | 0.423399 | ||||||||
\(465\) | −7.04355e14 | −1.50245 | ||||||||
\(466\) | −9.90466e14 | −2.08794 | ||||||||
\(467\) | −1.28045e14 | −0.266759 | −0.133379 | − | 0.991065i | \(-0.542583\pi\) | ||||
−0.133379 | + | 0.991065i | \(0.542583\pi\) | |||||||
\(468\) | 2.03406e13 | 0.0418804 | ||||||||
\(469\) | 2.10949e14 | 0.429267 | ||||||||
\(470\) | 1.05512e15 | 2.12208 | ||||||||
\(471\) | −5.06425e14 | −1.00670 | ||||||||
\(472\) | −4.70289e12 | −0.00924026 | ||||||||
\(473\) | 5.95459e14 | 1.15642 | ||||||||
\(474\) | −1.14276e15 | −2.19368 | ||||||||
\(475\) | 2.46382e14 | 0.467513 | ||||||||
\(476\) | −3.08792e14 | −0.579198 | ||||||||
\(477\) | −5.85467e13 | −0.108555 | ||||||||
\(478\) | 4.23947e14 | 0.777067 | ||||||||
\(479\) | −5.78121e14 | −1.04755 | −0.523773 | − | 0.851858i | \(-0.675476\pi\) | ||||
−0.523773 | + | 0.851858i | \(0.675476\pi\) | |||||||
\(480\) | 8.61533e14 | 1.54328 | ||||||||
\(481\) | 1.00834e14 | 0.178571 | ||||||||
\(482\) | 2.16841e14 | 0.379649 | ||||||||
\(483\) | 1.25335e15 | 2.16952 | ||||||||
\(484\) | 5.98930e14 | 1.02501 | ||||||||
\(485\) | −8.71470e14 | −1.47460 | ||||||||
\(486\) | 4.78533e14 | 0.800594 | ||||||||
\(487\) | 6.73661e14 | 1.11438 | 0.557189 | − | 0.830386i | \(-0.311880\pi\) | ||||
0.557189 | + | 0.830386i | \(0.311880\pi\) | |||||||
\(488\) | −8.45710e13 | −0.138329 | ||||||||
\(489\) | −7.73974e14 | −1.25178 | ||||||||
\(490\) | 1.88721e15 | 3.01815 | ||||||||
\(491\) | −1.01698e15 | −1.60828 | −0.804141 | − | 0.594439i | \(-0.797374\pi\) | ||||
−0.804141 | + | 0.594439i | \(0.797374\pi\) | |||||||
\(492\) | −7.71540e14 | −1.20656 | ||||||||
\(493\) | −1.03226e14 | −0.159636 | ||||||||
\(494\) | 9.37358e13 | 0.143353 | ||||||||
\(495\) | 3.25936e14 | 0.492951 | ||||||||
\(496\) | 7.67819e14 | 1.14844 | ||||||||
\(497\) | 9.64916e14 | 1.42735 | ||||||||
\(498\) | −1.32048e15 | −1.93184 | ||||||||
\(499\) | 1.31409e15 | 1.90139 | 0.950694 | − | 0.310129i | \(-0.100372\pi\) | ||||
0.950694 | + | 0.310129i | \(0.100372\pi\) | |||||||
\(500\) | 3.93471e14 | 0.563089 | ||||||||
\(501\) | −4.66906e14 | −0.660879 | ||||||||
\(502\) | 7.93603e14 | 1.11105 | ||||||||
\(503\) | −7.64595e14 | −1.05878 | −0.529392 | − | 0.848377i | \(-0.677580\pi\) | ||||
−0.529392 | + | 0.848377i | \(0.677580\pi\) | |||||||
\(504\) | −7.49636e13 | −0.102679 | ||||||||
\(505\) | −4.62472e14 | −0.626589 | ||||||||
\(506\) | −2.38140e15 | −3.19157 | ||||||||
\(507\) | 6.28495e14 | 0.833217 | ||||||||
\(508\) | −1.25642e14 | −0.164773 | ||||||||
\(509\) | −1.33935e15 | −1.73759 | −0.868793 | − | 0.495175i | \(-0.835104\pi\) | ||||
−0.868793 | + | 0.495175i | \(0.835104\pi\) | |||||||
\(510\) | −3.82222e14 | −0.490547 | ||||||||
\(511\) | 9.16382e14 | 1.16349 | ||||||||
\(512\) | −1.08656e15 | −1.36480 | ||||||||
\(513\) | 6.63564e14 | 0.824588 | ||||||||
\(514\) | −1.16371e15 | −1.43069 | ||||||||
\(515\) | 6.26770e14 | 0.762375 | ||||||||
\(516\) | −6.83186e14 | −0.822177 | ||||||||
\(517\) | 1.31309e15 | 1.56350 | ||||||||
\(518\) | −2.79628e15 | −3.29433 | ||||||||
\(519\) | 3.14122e13 | 0.0366166 | ||||||||
\(520\) | −3.19004e13 | −0.0367940 | ||||||||
\(521\) | 5.20356e13 | 0.0593873 | 0.0296936 | − | 0.999559i | \(-0.490547\pi\) | ||||
0.0296936 | + | 0.999559i | \(0.490547\pi\) | |||||||
\(522\) | −1.88565e14 | −0.212948 | ||||||||
\(523\) | 1.09851e15 | 1.22756 | 0.613780 | − | 0.789477i | \(-0.289648\pi\) | ||||
0.613780 | + | 0.789477i | \(0.289648\pi\) | |||||||
\(524\) | −1.61521e15 | −1.78610 | ||||||||
\(525\) | 7.71592e14 | 0.844328 | ||||||||
\(526\) | 1.00930e15 | 1.09294 | ||||||||
\(527\) | −4.04065e14 | −0.433004 | ||||||||
\(528\) | 9.03898e14 | 0.958590 | ||||||||
\(529\) | 1.43355e15 | 1.50455 | ||||||||
\(530\) | 6.90909e14 | 0.717634 | ||||||||
\(531\) | −1.12776e13 | −0.0115930 | ||||||||
\(532\) | −1.39223e15 | −1.41643 | ||||||||
\(533\) | −1.57829e14 | −0.158923 | ||||||||
\(534\) | 1.86252e14 | 0.185620 | ||||||||
\(535\) | 1.35811e15 | 1.33964 | ||||||||
\(536\) | 6.11137e13 | 0.0596668 | ||||||||
\(537\) | −1.26970e15 | −1.22700 | ||||||||
\(538\) | −1.41107e14 | −0.134973 | ||||||||
\(539\) | 2.34863e15 | 2.22370 | ||||||||
\(540\) | −1.69926e15 | −1.59255 | ||||||||
\(541\) | −7.41170e14 | −0.687595 | −0.343798 | − | 0.939044i | \(-0.611713\pi\) | ||||
−0.343798 | + | 0.939044i | \(0.611713\pi\) | |||||||
\(542\) | −2.08421e14 | −0.191402 | ||||||||
\(543\) | 1.23480e15 | 1.12253 | ||||||||
\(544\) | 4.94232e14 | 0.444772 | ||||||||
\(545\) | −4.75360e14 | −0.423489 | ||||||||
\(546\) | 2.93552e14 | 0.258896 | ||||||||
\(547\) | −6.86045e13 | −0.0598994 | −0.0299497 | − | 0.999551i | \(-0.509535\pi\) | ||||
−0.0299497 | + | 0.999551i | \(0.509535\pi\) | |||||||
\(548\) | −7.36154e12 | −0.00636320 | ||||||||
\(549\) | −2.02802e14 | −0.173550 | ||||||||
\(550\) | −1.46605e15 | −1.24209 | ||||||||
\(551\) | −4.65409e14 | −0.390392 | ||||||||
\(552\) | 3.63106e14 | 0.301556 | ||||||||
\(553\) | 3.47206e15 | 2.85495 | ||||||||
\(554\) | −2.24725e15 | −1.82957 | ||||||||
\(555\) | −1.85380e15 | −1.49435 | ||||||||
\(556\) | −9.01602e13 | −0.0719620 | ||||||||
\(557\) | 1.97526e15 | 1.56107 | 0.780533 | − | 0.625114i | \(-0.214948\pi\) | ||||
0.780533 | + | 0.625114i | \(0.214948\pi\) | |||||||
\(558\) | −7.38111e14 | −0.577609 | ||||||||
\(559\) | −1.39755e14 | −0.108293 | ||||||||
\(560\) | −2.20677e15 | −1.69326 | ||||||||
\(561\) | −4.75676e14 | −0.361423 | ||||||||
\(562\) | −1.86258e15 | −1.40141 | ||||||||
\(563\) | −1.95018e15 | −1.45304 | −0.726521 | − | 0.687144i | \(-0.758864\pi\) | ||||
−0.726521 | + | 0.687144i | \(0.758864\pi\) | |||||||
\(564\) | −1.50654e15 | −1.11160 | ||||||||
\(565\) | 1.16936e15 | 0.854441 | ||||||||
\(566\) | −1.22054e15 | −0.883203 | ||||||||
\(567\) | 1.44099e15 | 1.03265 | ||||||||
\(568\) | 2.79544e14 | 0.198397 | ||||||||
\(569\) | 9.04698e13 | 0.0635896 | 0.0317948 | − | 0.999494i | \(-0.489878\pi\) | ||||
0.0317948 | + | 0.999494i | \(0.489878\pi\) | |||||||
\(570\) | −1.72330e15 | −1.19964 | ||||||||
\(571\) | −1.35852e15 | −0.936631 | −0.468315 | − | 0.883561i | \(-0.655139\pi\) | ||||
−0.468315 | + | 0.883561i | \(0.655139\pi\) | |||||||
\(572\) | −2.98728e14 | −0.203985 | ||||||||
\(573\) | −3.63718e13 | −0.0245988 | ||||||||
\(574\) | 4.37683e15 | 2.93187 | ||||||||
\(575\) | 1.46910e15 | 0.974714 | ||||||||
\(576\) | 5.49348e14 | 0.361014 | ||||||||
\(577\) | −2.70905e15 | −1.76340 | −0.881699 | − | 0.471812i | \(-0.843600\pi\) | ||||
−0.881699 | + | 0.471812i | \(0.843600\pi\) | |||||||
\(578\) | 2.05663e15 | 1.32603 | ||||||||
\(579\) | −1.92204e14 | −0.122753 | ||||||||
\(580\) | 1.19182e15 | 0.753975 | ||||||||
\(581\) | 4.01204e15 | 2.51418 | ||||||||
\(582\) | 2.32328e15 | 1.44220 | ||||||||
\(583\) | 8.59836e14 | 0.528735 | ||||||||
\(584\) | 2.65483e14 | 0.161721 | ||||||||
\(585\) | −7.64975e13 | −0.0461625 | ||||||||
\(586\) | 3.30382e15 | 1.97505 | ||||||||
\(587\) | 2.40206e15 | 1.42257 | 0.711286 | − | 0.702903i | \(-0.248113\pi\) | ||||
0.711286 | + | 0.702903i | \(0.248113\pi\) | |||||||
\(588\) | −2.69464e15 | −1.58098 | ||||||||
\(589\) | −1.82178e15 | −1.05892 | ||||||||
\(590\) | 1.33087e14 | 0.0766388 | ||||||||
\(591\) | 1.05806e14 | 0.0603641 | ||||||||
\(592\) | 2.02083e15 | 1.14225 | ||||||||
\(593\) | 9.94972e14 | 0.557199 | 0.278599 | − | 0.960407i | \(-0.410130\pi\) | ||||
0.278599 | + | 0.960407i | \(0.410130\pi\) | |||||||
\(594\) | −3.94841e15 | −2.19077 | ||||||||
\(595\) | 1.16131e15 | 0.638419 | ||||||||
\(596\) | 3.17718e15 | 1.73056 | ||||||||
\(597\) | −5.07665e13 | −0.0273980 | ||||||||
\(598\) | 5.58917e14 | 0.298876 | ||||||||
\(599\) | 7.03886e14 | 0.372954 | 0.186477 | − | 0.982459i | \(-0.440293\pi\) | ||||
0.186477 | + | 0.982459i | \(0.440293\pi\) | |||||||
\(600\) | 2.23536e14 | 0.117359 | ||||||||
\(601\) | −6.08696e14 | −0.316658 | −0.158329 | − | 0.987386i | \(-0.550611\pi\) | ||||
−0.158329 | + | 0.987386i | \(0.550611\pi\) | |||||||
\(602\) | 3.87561e15 | 1.99784 | ||||||||
\(603\) | 1.46551e14 | 0.0748592 | ||||||||
\(604\) | −1.12840e15 | −0.571162 | ||||||||
\(605\) | −2.25248e15 | −1.12981 | ||||||||
\(606\) | 1.23292e15 | 0.612824 | ||||||||
\(607\) | 1.96266e15 | 0.966737 | 0.483368 | − | 0.875417i | \(-0.339413\pi\) | ||||
0.483368 | + | 0.875417i | \(0.339413\pi\) | |||||||
\(608\) | 2.22831e15 | 1.08769 | ||||||||
\(609\) | −1.45752e15 | −0.705049 | ||||||||
\(610\) | 2.39327e15 | 1.14730 | ||||||||
\(611\) | −3.08184e14 | −0.146414 | ||||||||
\(612\) | −2.14525e14 | −0.101005 | ||||||||
\(613\) | −3.41572e15 | −1.59386 | −0.796928 | − | 0.604074i | \(-0.793543\pi\) | ||||
−0.796928 | + | 0.604074i | \(0.793543\pi\) | |||||||
\(614\) | −1.85697e15 | −0.858774 | ||||||||
\(615\) | 2.90163e15 | 1.32993 | ||||||||
\(616\) | 1.10094e15 | 0.500115 | ||||||||
\(617\) | −1.86989e15 | −0.841873 | −0.420936 | − | 0.907090i | \(-0.638298\pi\) | ||||
−0.420936 | + | 0.907090i | \(0.638298\pi\) | |||||||
\(618\) | −1.67093e15 | −0.745627 | ||||||||
\(619\) | −1.77723e15 | −0.786042 | −0.393021 | − | 0.919530i | \(-0.628570\pi\) | ||||
−0.393021 | + | 0.919530i | \(0.628570\pi\) | |||||||
\(620\) | 4.66522e15 | 2.04511 | ||||||||
\(621\) | 3.95662e15 | 1.71918 | ||||||||
\(622\) | 9.50492e14 | 0.409356 | ||||||||
\(623\) | −5.65893e14 | −0.241574 | ||||||||
\(624\) | −2.12146e14 | −0.0897675 | ||||||||
\(625\) | −2.94820e15 | −1.23657 | ||||||||
\(626\) | 4.65601e15 | 1.93577 | ||||||||
\(627\) | −2.14465e15 | −0.883862 | ||||||||
\(628\) | 3.35425e15 | 1.37030 | ||||||||
\(629\) | −1.06346e15 | −0.430669 | ||||||||
\(630\) | 2.12139e15 | 0.851623 | ||||||||
\(631\) | −2.17086e14 | −0.0863914 | −0.0431957 | − | 0.999067i | \(-0.513754\pi\) | ||||
−0.0431957 | + | 0.999067i | \(0.513754\pi\) | |||||||
\(632\) | 1.00588e15 | 0.396829 | ||||||||
\(633\) | −7.93889e14 | −0.310484 | ||||||||
\(634\) | −1.55307e15 | −0.602142 | ||||||||
\(635\) | 4.72520e14 | 0.181620 | ||||||||
\(636\) | −9.86512e14 | −0.375914 | ||||||||
\(637\) | −5.51225e14 | −0.208239 | ||||||||
\(638\) | 2.76933e15 | 1.03720 | ||||||||
\(639\) | 6.70350e14 | 0.248913 | ||||||||
\(640\) | −1.53493e15 | −0.565065 | ||||||||
\(641\) | 4.44521e15 | 1.62246 | 0.811229 | − | 0.584729i | \(-0.198799\pi\) | ||||
0.811229 | + | 0.584729i | \(0.198799\pi\) | |||||||
\(642\) | −3.62063e15 | −1.31021 | ||||||||
\(643\) | 1.01635e15 | 0.364654 | 0.182327 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182327 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(644\) | −8.30142e15 | −2.95311 | ||||||||
\(645\) | 2.56935e15 | 0.906242 | ||||||||
\(646\) | −9.88599e14 | −0.345733 | ||||||||
\(647\) | 1.97785e15 | 0.685834 | 0.342917 | − | 0.939366i | \(-0.388585\pi\) | ||||
0.342917 | + | 0.939366i | \(0.388585\pi\) | |||||||
\(648\) | 4.17467e14 | 0.143536 | ||||||||
\(649\) | 1.65626e14 | 0.0564656 | ||||||||
\(650\) | 3.44083e14 | 0.116316 | ||||||||
\(651\) | −5.70525e15 | −1.91240 | ||||||||
\(652\) | 5.12633e15 | 1.70390 | ||||||||
\(653\) | −5.36920e14 | −0.176965 | −0.0884825 | − | 0.996078i | \(-0.528202\pi\) | ||||
−0.0884825 | + | 0.996078i | \(0.528202\pi\) | |||||||
\(654\) | 1.26728e15 | 0.414186 | ||||||||
\(655\) | 6.07451e15 | 1.96872 | ||||||||
\(656\) | −3.16307e15 | −1.01657 | ||||||||
\(657\) | 6.36632e14 | 0.202899 | ||||||||
\(658\) | 8.54640e15 | 2.70110 | ||||||||
\(659\) | −5.49096e15 | −1.72099 | −0.860496 | − | 0.509457i | \(-0.829846\pi\) | ||||
−0.860496 | + | 0.509457i | \(0.829846\pi\) | |||||||
\(660\) | 5.49202e15 | 1.70703 | ||||||||
\(661\) | −1.02732e15 | −0.316665 | −0.158332 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158332 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(662\) | 3.75638e15 | 1.14829 | ||||||||
\(663\) | 1.11642e14 | 0.0338456 | ||||||||
\(664\) | 1.16232e15 | 0.349463 | ||||||||
\(665\) | 5.23593e15 | 1.56126 | ||||||||
\(666\) | −1.94264e15 | −0.574493 | ||||||||
\(667\) | −2.77509e15 | −0.813926 | ||||||||
\(668\) | 3.09250e15 | 0.899578 | ||||||||
\(669\) | 2.27288e14 | 0.0655742 | ||||||||
\(670\) | −1.72945e15 | −0.494877 | ||||||||
\(671\) | 2.97842e15 | 0.845302 | ||||||||
\(672\) | 6.97839e15 | 1.96437 | ||||||||
\(673\) | −4.63405e15 | −1.29383 | −0.646916 | − | 0.762561i | \(-0.723941\pi\) | ||||
−0.646916 | + | 0.762561i | \(0.723941\pi\) | |||||||
\(674\) | −5.48456e15 | −1.51884 | ||||||||
\(675\) | 2.43579e15 | 0.669066 | ||||||||
\(676\) | −4.16277e15 | −1.13416 | ||||||||
\(677\) | 6.36284e15 | 1.71954 | 0.859772 | − | 0.510677i | \(-0.170605\pi\) | ||||
0.859772 | + | 0.510677i | \(0.170605\pi\) | |||||||
\(678\) | −3.11744e15 | −0.835671 | ||||||||
\(679\) | −7.05888e15 | −1.87695 | ||||||||
\(680\) | 3.36442e14 | 0.0887383 | ||||||||
\(681\) | 4.28132e15 | 1.12013 | ||||||||
\(682\) | 1.08401e16 | 2.81333 | ||||||||
\(683\) | 8.32427e14 | 0.214305 | 0.107153 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107153 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(684\) | −9.67214e14 | −0.247010 | ||||||||
\(685\) | 2.76855e13 | 0.00701381 | ||||||||
\(686\) | 5.83878e15 | 1.46737 | ||||||||
\(687\) | 3.13039e15 | 0.780434 | ||||||||
\(688\) | −2.80085e15 | −0.692713 | ||||||||
\(689\) | −2.01804e14 | −0.0495136 | ||||||||
\(690\) | −1.02755e16 | −2.50111 | ||||||||
\(691\) | 8.61434e14 | 0.208014 | 0.104007 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104007 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(692\) | −2.08055e14 | −0.0498419 | ||||||||
\(693\) | 2.64007e15 | 0.627455 | ||||||||
\(694\) | −6.56277e15 | −1.54743 | ||||||||
\(695\) | 3.39077e14 | 0.0793199 | ||||||||
\(696\) | −4.22255e14 | −0.0979996 | ||||||||
\(697\) | 1.66457e15 | 0.383284 | ||||||||
\(698\) | −2.35872e15 | −0.538855 | ||||||||
\(699\) | −5.31869e15 | −1.20554 | ||||||||
\(700\) | −5.11055e15 | −1.14929 | ||||||||
\(701\) | −6.61418e15 | −1.47580 | −0.737899 | − | 0.674911i | \(-0.764182\pi\) | ||||
−0.737899 | + | 0.674911i | \(0.764182\pi\) | |||||||
\(702\) | 9.26695e14 | 0.205155 | ||||||||
\(703\) | −4.79476e15 | −1.05320 | ||||||||
\(704\) | −8.06791e15 | −1.75837 | ||||||||
\(705\) | 5.66586e15 | 1.22525 | ||||||||
\(706\) | 1.97215e15 | 0.423170 | ||||||||
\(707\) | −3.74600e15 | −0.797556 | ||||||||
\(708\) | −1.90028e14 | −0.0401452 | ||||||||
\(709\) | 4.90188e15 | 1.02756 | 0.513781 | − | 0.857921i | \(-0.328244\pi\) | ||||
0.513781 | + | 0.857921i | \(0.328244\pi\) | |||||||
\(710\) | −7.91079e15 | −1.64550 | ||||||||
\(711\) | 2.41212e15 | 0.497870 | ||||||||
\(712\) | −1.63944e14 | −0.0335780 | ||||||||
\(713\) | −1.08627e16 | −2.20773 | ||||||||
\(714\) | −3.09599e15 | −0.624395 | ||||||||
\(715\) | 1.12347e15 | 0.224842 | ||||||||
\(716\) | 8.40973e15 | 1.67017 | ||||||||
\(717\) | 2.27655e15 | 0.448665 | ||||||||
\(718\) | 5.28830e15 | 1.03426 | ||||||||
\(719\) | −8.02162e15 | −1.55687 | −0.778436 | − | 0.627724i | \(-0.783987\pi\) | ||||
−0.778436 | + | 0.627724i | \(0.783987\pi\) | |||||||
\(720\) | −1.53310e15 | −0.295285 | ||||||||
\(721\) | 5.07682e15 | 0.970393 | ||||||||
\(722\) | 3.27854e15 | 0.621907 | ||||||||
\(723\) | 1.16441e15 | 0.219202 | ||||||||
\(724\) | −8.17855e15 | −1.52797 | ||||||||
\(725\) | −1.70841e15 | −0.316762 | ||||||||
\(726\) | 6.00496e15 | 1.10499 | ||||||||
\(727\) | −7.48240e15 | −1.36647 | −0.683237 | − | 0.730196i | \(-0.739429\pi\) | ||||
−0.683237 | + | 0.730196i | \(0.739429\pi\) | |||||||
\(728\) | −2.58392e14 | −0.0468334 | ||||||||
\(729\) | 6.11755e15 | 1.10047 | ||||||||
\(730\) | −7.51289e15 | −1.34132 | ||||||||
\(731\) | 1.47395e15 | 0.261178 | ||||||||
\(732\) | −3.41722e15 | −0.600983 | ||||||||
\(733\) | −3.43264e15 | −0.599180 | −0.299590 | − | 0.954068i | \(-0.596850\pi\) | ||||
−0.299590 | + | 0.954068i | \(0.596850\pi\) | |||||||
\(734\) | −1.44610e16 | −2.50536 | ||||||||
\(735\) | 1.01341e16 | 1.74263 | ||||||||
\(736\) | 1.32867e16 | 2.26772 | ||||||||
\(737\) | −2.15230e15 | −0.364613 | ||||||||
\(738\) | 3.04069e15 | 0.511284 | ||||||||
\(739\) | 3.78300e15 | 0.631381 | 0.315690 | − | 0.948862i | \(-0.397764\pi\) | ||||
0.315690 | + | 0.948862i | \(0.397764\pi\) | |||||||
\(740\) | 1.22784e16 | 2.03408 | ||||||||
\(741\) | 5.03351e14 | 0.0827696 | ||||||||
\(742\) | 5.59634e15 | 0.913445 | ||||||||
\(743\) | 3.18850e14 | 0.0516592 | 0.0258296 | − | 0.999666i | \(-0.491777\pi\) | ||||
0.0258296 | + | 0.999666i | \(0.491777\pi\) | |||||||
\(744\) | −1.65286e15 | −0.265818 | ||||||||
\(745\) | −1.19488e16 | −1.90751 | ||||||||
\(746\) | 5.82146e15 | 0.922504 | ||||||||
\(747\) | 2.78726e15 | 0.438444 | ||||||||
\(748\) | 3.15058e15 | 0.491963 | ||||||||
\(749\) | 1.10006e16 | 1.70517 | ||||||||
\(750\) | 3.94499e15 | 0.607028 | ||||||||
\(751\) | −1.92402e15 | −0.293893 | −0.146947 | − | 0.989144i | \(-0.546945\pi\) | ||||
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(752\) | −6.17636e15 | −0.936558 | ||||||||
\(753\) | 4.26156e15 | 0.641499 | ||||||||
\(754\) | −6.49964e14 | −0.0971286 | ||||||||
\(755\) | 4.24372e15 | 0.629561 | ||||||||
\(756\) | −1.37639e16 | −2.02709 | ||||||||
\(757\) | −6.83677e15 | −0.999594 | −0.499797 | − | 0.866142i | \(-0.666592\pi\) | ||||
−0.499797 | + | 0.866142i | \(0.666592\pi\) | |||||||
\(758\) | 2.29848e13 | 0.00333626 | ||||||||
\(759\) | −1.27879e16 | −1.84276 | ||||||||
\(760\) | 1.51689e15 | 0.217010 | ||||||||
\(761\) | 1.15743e16 | 1.64391 | 0.821956 | − | 0.569550i | \(-0.192883\pi\) | ||||
0.821956 | + | 0.569550i | \(0.192883\pi\) | |||||||
\(762\) | −1.25971e15 | −0.177630 | ||||||||
\(763\) | −3.85040e15 | −0.539040 | ||||||||
\(764\) | 2.40905e14 | 0.0334836 | ||||||||
\(765\) | 8.06792e14 | 0.111333 | ||||||||
\(766\) | −2.12138e16 | −2.90643 | ||||||||
\(767\) | −3.88727e13 | −0.00528774 | ||||||||
\(768\) | −3.93434e15 | −0.531355 | ||||||||
\(769\) | 2.61757e15 | 0.350997 | 0.175498 | − | 0.984480i | \(-0.443846\pi\) | ||||
0.175498 | + | 0.984480i | \(0.443846\pi\) | |||||||
\(770\) | −3.11554e16 | −4.14796 | ||||||||
\(771\) | −6.24898e15 | −0.826057 | ||||||||
\(772\) | 1.27304e15 | 0.167089 | ||||||||
\(773\) | 1.23256e16 | 1.60628 | 0.803140 | − | 0.595790i | \(-0.203161\pi\) | ||||
0.803140 | + | 0.595790i | \(0.203161\pi\) | |||||||
\(774\) | 2.69248e15 | 0.348399 | ||||||||
\(775\) | −6.68733e15 | −0.859198 | ||||||||
\(776\) | −2.04501e15 | −0.260890 | ||||||||
\(777\) | −1.50157e16 | −1.90209 | ||||||||
\(778\) | 8.95392e15 | 1.12623 | ||||||||
\(779\) | 7.50492e15 | 0.937325 | ||||||||
\(780\) | −1.28898e15 | −0.159855 | ||||||||
\(781\) | −9.84498e15 | −1.21237 | ||||||||
\(782\) | −5.89470e15 | −0.720817 | ||||||||
\(783\) | −4.60115e15 | −0.558697 | ||||||||
\(784\) | −1.10472e16 | −1.33203 | ||||||||
\(785\) | −1.26148e16 | −1.51041 | ||||||||
\(786\) | −1.61943e16 | −1.92547 | ||||||||
\(787\) | 9.78875e15 | 1.15576 | 0.577878 | − | 0.816123i | \(-0.303881\pi\) | ||||
0.577878 | + | 0.816123i | \(0.303881\pi\) | |||||||
\(788\) | −7.00794e14 | −0.0821667 | ||||||||
\(789\) | 5.41981e15 | 0.631045 | ||||||||
\(790\) | −2.84654e16 | −3.29131 | ||||||||
\(791\) | 9.47178e15 | 1.08758 | ||||||||
\(792\) | 7.64849e14 | 0.0872142 | ||||||||
\(793\) | −6.99038e14 | −0.0791587 | ||||||||
\(794\) | 2.22999e16 | 2.50778 | ||||||||
\(795\) | 3.71010e15 | 0.414349 | ||||||||
\(796\) | 3.36246e14 | 0.0372937 | ||||||||
\(797\) | 4.21477e15 | 0.464251 | 0.232126 | − | 0.972686i | \(-0.425432\pi\) | ||||
0.232126 | + | 0.972686i | \(0.425432\pi\) | |||||||
\(798\) | −1.39587e16 | −1.52696 | ||||||||
\(799\) | 3.25031e15 | 0.353116 | ||||||||
\(800\) | 8.17961e15 | 0.882547 | ||||||||
\(801\) | −3.93139e14 | −0.0421277 | ||||||||
\(802\) | −1.78481e16 | −1.89947 | ||||||||
\(803\) | −9.34979e15 | −0.988249 | ||||||||
\(804\) | 2.46939e15 | 0.259228 | ||||||||
\(805\) | 3.12202e16 | 3.25506 | ||||||||
\(806\) | −2.54419e15 | −0.263456 | ||||||||
\(807\) | −7.57728e14 | −0.0779308 | ||||||||
\(808\) | −1.08525e15 | −0.110858 | ||||||||
\(809\) | −1.55258e16 | −1.57521 | −0.787605 | − | 0.616181i | \(-0.788679\pi\) | ||||
−0.787605 | + | 0.616181i | \(0.788679\pi\) | |||||||
\(810\) | −1.18139e16 | −1.19049 | ||||||||
\(811\) | 1.95871e16 | 1.96045 | 0.980226 | − | 0.197882i | \(-0.0634064\pi\) | ||||
0.980226 | + | 0.197882i | \(0.0634064\pi\) | |||||||
\(812\) | 9.65371e15 | 0.959702 | ||||||||
\(813\) | −1.11920e15 | −0.110512 | ||||||||
\(814\) | 2.85303e16 | 2.79816 | ||||||||
\(815\) | −1.92793e16 | −1.87812 | ||||||||
\(816\) | 2.23743e15 | 0.216497 | ||||||||
\(817\) | 6.64548e15 | 0.638712 | ||||||||
\(818\) | 1.61613e16 | 1.54289 | ||||||||
\(819\) | −6.19627e14 | −0.0587582 | ||||||||
\(820\) | −1.92186e16 | −1.81028 | ||||||||
\(821\) | −9.61396e15 | −0.899528 | −0.449764 | − | 0.893147i | \(-0.648492\pi\) | ||||
−0.449764 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(822\) | −7.38078e13 | −0.00685974 | ||||||||
\(823\) | −5.95315e15 | −0.549601 | −0.274801 | − | 0.961501i | \(-0.588612\pi\) | ||||
−0.274801 | + | 0.961501i | \(0.588612\pi\) | |||||||
\(824\) | 1.47080e15 | 0.134882 | ||||||||
\(825\) | −7.87250e15 | −0.717160 | ||||||||
\(826\) | 1.07800e15 | 0.0975501 | ||||||||
\(827\) | −1.45871e16 | −1.31126 | −0.655628 | − | 0.755084i | \(-0.727596\pi\) | ||||
−0.655628 | + | 0.755084i | \(0.727596\pi\) | |||||||
\(828\) | −5.76719e15 | −0.514989 | ||||||||
\(829\) | 5.22485e15 | 0.463472 | 0.231736 | − | 0.972779i | \(-0.425559\pi\) | ||||
0.231736 | + | 0.972779i | \(0.425559\pi\) | |||||||
\(830\) | −3.28924e16 | −2.89845 | ||||||||
\(831\) | −1.20675e16 | −1.05636 | ||||||||
\(832\) | 1.89355e15 | 0.164664 | ||||||||
\(833\) | 5.81358e15 | 0.502222 | ||||||||
\(834\) | −9.03959e14 | −0.0775774 | ||||||||
\(835\) | −1.16304e16 | −0.991557 | ||||||||
\(836\) | 1.42048e16 | 1.20310 | ||||||||
\(837\) | −1.80106e16 | −1.51543 | ||||||||
\(838\) | 3.07173e16 | 2.56768 | ||||||||
\(839\) | 2.06112e16 | 1.71164 | 0.855820 | − | 0.517275i | \(-0.173053\pi\) | ||||
0.855820 | + | 0.517275i | \(0.173053\pi\) | |||||||
\(840\) | 4.75044e15 | 0.391921 | ||||||||
\(841\) | −8.97336e15 | −0.735491 | ||||||||
\(842\) | 1.89861e16 | 1.54603 | ||||||||
\(843\) | −1.00019e16 | −0.809150 | ||||||||
\(844\) | 5.25823e15 | 0.422626 | ||||||||
\(845\) | 1.56555e16 | 1.25013 | ||||||||
\(846\) | 5.93739e15 | 0.471041 | ||||||||
\(847\) | −1.82450e16 | −1.43808 | ||||||||
\(848\) | −4.04439e15 | −0.316720 | ||||||||
\(849\) | −6.55415e15 | −0.509946 | ||||||||
\(850\) | −3.62892e15 | −0.280526 | ||||||||
\(851\) | −2.85897e16 | −2.19582 | ||||||||
\(852\) | 1.12954e16 | 0.861953 | ||||||||
\(853\) | −1.51561e16 | −1.14913 | −0.574565 | − | 0.818459i | \(-0.694829\pi\) | ||||
−0.574565 | + | 0.818459i | \(0.694829\pi\) | |||||||
\(854\) | 1.93854e16 | 1.46035 | ||||||||
\(855\) | 3.63753e15 | 0.272266 | ||||||||
\(856\) | 3.18697e15 | 0.237013 | ||||||||
\(857\) | −3.46162e15 | −0.255791 | −0.127895 | − | 0.991788i | \(-0.540822\pi\) | ||||
−0.127895 | + | 0.991788i | \(0.540822\pi\) | |||||||
\(858\) | −2.99509e15 | −0.219903 | ||||||||
\(859\) | 4.22500e15 | 0.308223 | 0.154111 | − | 0.988053i | \(-0.450749\pi\) | ||||
0.154111 | + | 0.988053i | \(0.450749\pi\) | |||||||
\(860\) | −1.70178e16 | −1.23356 | ||||||||
\(861\) | 2.35031e16 | 1.69281 | ||||||||
\(862\) | −2.70644e16 | −1.93691 | ||||||||
\(863\) | −1.05088e15 | −0.0747297 | −0.0373649 | − | 0.999302i | \(-0.511896\pi\) | ||||
−0.0373649 | + | 0.999302i | \(0.511896\pi\) | |||||||
\(864\) | 2.20296e16 | 1.55662 | ||||||||
\(865\) | 7.82460e14 | 0.0549381 | ||||||||
\(866\) | 8.15218e14 | 0.0568755 | ||||||||
\(867\) | 1.10438e16 | 0.765624 | ||||||||
\(868\) | 3.77881e16 | 2.60313 | ||||||||
\(869\) | −3.54252e16 | −2.42495 | ||||||||
\(870\) | 1.19494e16 | 0.812810 | ||||||||
\(871\) | 5.05148e14 | 0.0341443 | ||||||||
\(872\) | −1.11549e15 | −0.0749249 | ||||||||
\(873\) | −4.90397e15 | −0.327318 | ||||||||
\(874\) | −2.65771e16 | −1.76276 | ||||||||
\(875\) | −1.19861e16 | −0.790014 | ||||||||
\(876\) | 1.07273e16 | 0.702613 | ||||||||
\(877\) | −2.10513e16 | −1.37019 | −0.685096 | − | 0.728453i | \(-0.740240\pi\) | ||||
−0.685096 | + | 0.728453i | \(0.740240\pi\) | |||||||
\(878\) | −2.02654e16 | −1.31080 | ||||||||
\(879\) | 1.77411e16 | 1.14036 | ||||||||
\(880\) | 2.25156e16 | 1.43823 | ||||||||
\(881\) | −1.47479e16 | −0.936186 | −0.468093 | − | 0.883679i | \(-0.655059\pi\) | ||||
−0.468093 | + | 0.883679i | \(0.655059\pi\) | |||||||
\(882\) | 1.06198e16 | 0.669942 | ||||||||
\(883\) | 6.44188e15 | 0.403858 | 0.201929 | − | 0.979400i | \(-0.435279\pi\) | ||||
0.201929 | + | 0.979400i | \(0.435279\pi\) | |||||||
\(884\) | −7.39445e14 | −0.0460700 | ||||||||
\(885\) | 7.14661e14 | 0.0442499 | ||||||||
\(886\) | −4.41793e14 | −0.0271853 | ||||||||
\(887\) | 2.27071e16 | 1.38861 | 0.694306 | − | 0.719680i | \(-0.255711\pi\) | ||||
0.694306 | + | 0.719680i | \(0.255711\pi\) | |||||||
\(888\) | −4.35018e15 | −0.264384 | ||||||||
\(889\) | 3.82739e15 | 0.231176 | ||||||||
\(890\) | 4.63943e15 | 0.278497 | ||||||||
\(891\) | −1.47024e16 | −0.877122 | ||||||||
\(892\) | −1.50542e15 | −0.0892585 | ||||||||
\(893\) | 1.46544e16 | 0.863548 | ||||||||
\(894\) | 3.18549e16 | 1.86560 | ||||||||
\(895\) | −3.16276e16 | −1.84094 | ||||||||
\(896\) | −1.24329e16 | −0.719246 | ||||||||
\(897\) | 3.00132e15 | 0.172566 | ||||||||
\(898\) | 1.36623e16 | 0.780737 | ||||||||
\(899\) | 1.26322e16 | 0.717466 | ||||||||
\(900\) | −3.55042e15 | −0.200422 | ||||||||
\(901\) | 2.12836e15 | 0.119415 | ||||||||
\(902\) | −4.46566e16 | −2.49029 | ||||||||
\(903\) | 2.08116e16 | 1.15351 | ||||||||
\(904\) | 2.74405e15 | 0.151170 | ||||||||
\(905\) | 3.07581e16 | 1.68420 | ||||||||
\(906\) | −1.13135e16 | −0.615731 | ||||||||
\(907\) | −8.91834e15 | −0.482440 | −0.241220 | − | 0.970470i | \(-0.577548\pi\) | ||||
−0.241220 | + | 0.970470i | \(0.577548\pi\) | |||||||
\(908\) | −2.83568e16 | −1.52470 | ||||||||
\(909\) | −2.60244e15 | −0.139085 | ||||||||
\(910\) | 7.31221e15 | 0.388437 | ||||||||
\(911\) | −4.70880e15 | −0.248633 | −0.124317 | − | 0.992243i | \(-0.539674\pi\) | ||||
−0.124317 | + | 0.992243i | \(0.539674\pi\) | |||||||
\(912\) | 1.00877e16 | 0.529446 | ||||||||
\(913\) | −4.09346e16 | −2.13551 | ||||||||
\(914\) | −4.79991e16 | −2.48902 | ||||||||
\(915\) | 1.28516e16 | 0.662431 | ||||||||
\(916\) | −2.07338e16 | −1.06231 | ||||||||
\(917\) | 4.92033e16 | 2.50590 | ||||||||
\(918\) | −9.77353e15 | −0.494785 | ||||||||
\(919\) | −1.36883e16 | −0.688832 | −0.344416 | − | 0.938817i | \(-0.611923\pi\) | ||||
−0.344416 | + | 0.938817i | \(0.611923\pi\) | |||||||
\(920\) | 9.04475e15 | 0.452443 | ||||||||
\(921\) | −9.97172e15 | −0.495841 | ||||||||
\(922\) | 5.27078e16 | 2.60528 | ||||||||
\(923\) | 2.31063e15 | 0.113533 | ||||||||
\(924\) | 4.44852e16 | 2.17280 | ||||||||
\(925\) | −1.76005e16 | −0.854564 | ||||||||
\(926\) | 5.28010e16 | 2.54848 | ||||||||
\(927\) | 3.52699e15 | 0.169225 | ||||||||
\(928\) | −1.54511e16 | −0.736963 | ||||||||
\(929\) | 3.10992e16 | 1.47456 | 0.737282 | − | 0.675586i | \(-0.236109\pi\) | ||||
0.737282 | + | 0.675586i | \(0.236109\pi\) | |||||||
\(930\) | 4.67741e16 | 2.20470 | ||||||||
\(931\) | 2.62113e16 | 1.22819 | ||||||||
\(932\) | 3.52278e16 | 1.64096 | ||||||||
\(933\) | 5.10403e15 | 0.236355 | ||||||||
\(934\) | 8.50305e15 | 0.391442 | ||||||||
\(935\) | −1.18488e16 | −0.542264 | ||||||||
\(936\) | −1.79511e14 | −0.00816721 | ||||||||
\(937\) | −3.02952e15 | −0.137027 | −0.0685134 | − | 0.997650i | \(-0.521826\pi\) | ||||
−0.0685134 | + | 0.997650i | \(0.521826\pi\) | |||||||
\(938\) | −1.40085e16 | −0.629907 | ||||||||
\(939\) | 2.50022e16 | 1.11768 | ||||||||
\(940\) | −3.75272e16 | −1.66779 | ||||||||
\(941\) | −7.94534e15 | −0.351050 | −0.175525 | − | 0.984475i | \(-0.556162\pi\) | ||||
−0.175525 | + | 0.984475i | \(0.556162\pi\) | |||||||
\(942\) | 3.36302e16 | 1.47723 | ||||||||
\(943\) | 4.47495e16 | 1.95422 | ||||||||
\(944\) | −7.79054e14 | −0.0338237 | ||||||||
\(945\) | 5.17637e16 | 2.23435 | ||||||||
\(946\) | −3.95426e16 | −1.69693 | ||||||||
\(947\) | −7.96212e15 | −0.339706 | −0.169853 | − | 0.985469i | \(-0.554329\pi\) | ||||
−0.169853 | + | 0.985469i | \(0.554329\pi\) | |||||||
\(948\) | 4.06442e16 | 1.72406 | ||||||||
\(949\) | 2.19441e15 | 0.0925450 | ||||||||
\(950\) | −1.63615e16 | −0.686028 | ||||||||
\(951\) | −8.33979e15 | −0.347666 | ||||||||
\(952\) | 2.72517e15 | 0.112951 | ||||||||
\(953\) | 4.41331e16 | 1.81867 | 0.909334 | − | 0.416067i | \(-0.136592\pi\) | ||||
0.909334 | + | 0.416067i | \(0.136592\pi\) | |||||||
\(954\) | 3.88791e15 | 0.159294 | ||||||||
\(955\) | −9.06001e14 | −0.0369071 | ||||||||
\(956\) | −1.50785e16 | −0.610716 | ||||||||
\(957\) | 1.48710e16 | 0.598858 | ||||||||
\(958\) | 3.83913e16 | 1.53717 | ||||||||
\(959\) | 2.24252e14 | 0.00892757 | ||||||||
\(960\) | −3.48122e16 | −1.37797 | ||||||||
\(961\) | 2.40385e16 | 0.946083 | ||||||||
\(962\) | −6.69609e15 | −0.262035 | ||||||||
\(963\) | 7.64239e15 | 0.297362 | ||||||||
\(964\) | −7.71234e15 | −0.298375 | ||||||||
\(965\) | −4.78770e15 | −0.184173 | ||||||||
\(966\) | −8.32312e16 | −3.18355 | ||||||||
\(967\) | −2.96400e16 | −1.12728 | −0.563640 | − | 0.826020i | \(-0.690600\pi\) | ||||
−0.563640 | + | 0.826020i | \(0.690600\pi\) | |||||||
\(968\) | −5.28572e15 | −0.199889 | ||||||||
\(969\) | −5.30867e15 | −0.199620 | ||||||||
\(970\) | 5.78717e16 | 2.16382 | ||||||||
\(971\) | −3.43704e16 | −1.27785 | −0.638924 | − | 0.769270i | \(-0.720620\pi\) | ||||
−0.638924 | + | 0.769270i | \(0.720620\pi\) | |||||||
\(972\) | −1.70199e16 | −0.629206 | ||||||||
\(973\) | 2.74651e15 | 0.100963 | ||||||||
\(974\) | −4.47358e16 | −1.63524 | ||||||||
\(975\) | 1.84769e15 | 0.0671587 | ||||||||
\(976\) | −1.40095e16 | −0.506349 | ||||||||
\(977\) | −1.79823e16 | −0.646285 | −0.323142 | − | 0.946350i | \(-0.604739\pi\) | ||||
−0.323142 | + | 0.946350i | \(0.604739\pi\) | |||||||
\(978\) | 5.13973e16 | 1.83686 | ||||||||
\(979\) | 5.77378e15 | 0.205189 | ||||||||
\(980\) | −6.71220e16 | −2.37204 | ||||||||
\(981\) | −2.67497e15 | −0.0940024 | ||||||||
\(982\) | 6.75342e16 | 2.35999 | ||||||||
\(983\) | −2.24970e16 | −0.781773 | −0.390886 | − | 0.920439i | \(-0.627831\pi\) | ||||
−0.390886 | + | 0.920439i | \(0.627831\pi\) | |||||||
\(984\) | 6.80904e15 | 0.235295 | ||||||||
\(985\) | 2.63557e15 | 0.0905680 | ||||||||
\(986\) | 6.85494e15 | 0.234251 | ||||||||
\(987\) | 4.58932e16 | 1.55957 | ||||||||
\(988\) | −3.33389e15 | −0.112665 | ||||||||
\(989\) | 3.96249e16 | 1.33165 | ||||||||
\(990\) | −2.16444e16 | −0.723356 | ||||||||
\(991\) | 1.43578e16 | 0.477182 | 0.238591 | − | 0.971120i | \(-0.423314\pi\) | ||||
0.238591 | + | 0.971120i | \(0.423314\pi\) | |||||||
\(992\) | −6.04812e16 | −1.99897 | ||||||||
\(993\) | 2.01713e16 | 0.663001 | ||||||||
\(994\) | −6.40771e16 | −2.09449 | ||||||||
\(995\) | −1.26456e15 | −0.0411068 | ||||||||
\(996\) | 4.69653e16 | 1.51828 | ||||||||
\(997\) | 1.14056e16 | 0.366687 | 0.183343 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183343 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(998\) | −8.72645e16 | −2.79010 | ||||||||
\(999\) | −4.74022e16 | −1.50726 |
(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 | 197.12.a.b.1.15 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.15 | ✓ | 92 | 1.1 | even | 1 | trivial |