Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(7.01814\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.01814 | 0.443545 | 0.221773 | − | 0.975098i | \(-0.428816\pi\) | ||||
0.221773 | + | 0.975098i | \(0.428816\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | −102.818 | −0.803268 | ||||||||
\(5\) | −77.5687 | −0.277518 | −0.138759 | − | 0.990326i | \(-0.544311\pi\) | ||||
−0.138759 | + | 0.990326i | \(0.544311\pi\) | |||||||
\(6\) | 135.490 | 0.256081 | ||||||||
\(7\) | −216.829 | −0.238932 | −0.119466 | − | 0.992838i | \(-0.538118\pi\) | ||||
−0.119466 | + | 0.992838i | \(0.538118\pi\) | |||||||
\(8\) | −1158.28 | −0.799831 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −389.251 | −0.123092 | ||||||||
\(11\) | 3376.21 | 0.764813 | 0.382407 | − | 0.923994i | \(-0.375095\pi\) | ||||
0.382407 | + | 0.923994i | \(0.375095\pi\) | |||||||
\(12\) | −2776.09 | −0.463767 | ||||||||
\(13\) | 12448.6 | 1.57151 | 0.785756 | − | 0.618536i | \(-0.212274\pi\) | ||||
0.785756 | + | 0.618536i | \(0.212274\pi\) | |||||||
\(14\) | −1088.08 | −0.105977 | ||||||||
\(15\) | −2094.36 | −0.160225 | ||||||||
\(16\) | 7348.33 | 0.448506 | ||||||||
\(17\) | −26362.1 | −1.30139 | −0.650696 | − | 0.759338i | \(-0.725523\pi\) | ||||
−0.650696 | + | 0.759338i | \(0.725523\pi\) | |||||||
\(18\) | 3658.23 | 0.147848 | ||||||||
\(19\) | 41401.4 | 1.38477 | 0.692384 | − | 0.721529i | \(-0.256560\pi\) | ||||
0.692384 | + | 0.721529i | \(0.256560\pi\) | |||||||
\(20\) | 7975.48 | 0.222921 | ||||||||
\(21\) | −5854.37 | −0.137947 | ||||||||
\(22\) | 16942.3 | 0.339229 | ||||||||
\(23\) | −42118.5 | −0.721815 | −0.360907 | − | 0.932602i | \(-0.617533\pi\) | ||||
−0.360907 | + | 0.932602i | \(0.617533\pi\) | |||||||
\(24\) | −31273.5 | −0.461783 | ||||||||
\(25\) | −72108.1 | −0.922984 | ||||||||
\(26\) | 62468.7 | 0.697037 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 22293.9 | 0.191926 | ||||||||
\(29\) | −151717. | −1.15516 | −0.577580 | − | 0.816334i | \(-0.696003\pi\) | ||||
−0.577580 | + | 0.816334i | \(0.696003\pi\) | |||||||
\(30\) | −10509.8 | −0.0710672 | ||||||||
\(31\) | −239434. | −1.44351 | −0.721754 | − | 0.692149i | \(-0.756664\pi\) | ||||
−0.721754 | + | 0.692149i | \(0.756664\pi\) | |||||||
\(32\) | 185135. | 0.998764 | ||||||||
\(33\) | 91157.8 | 0.441565 | ||||||||
\(34\) | −132289. | −0.577226 | ||||||||
\(35\) | 16819.1 | 0.0663079 | ||||||||
\(36\) | −74954.5 | −0.267756 | ||||||||
\(37\) | −411153. | −1.33444 | −0.667218 | − | 0.744863i | \(-0.732515\pi\) | ||||
−0.667218 | + | 0.744863i | \(0.732515\pi\) | |||||||
\(38\) | 207758. | 0.614208 | ||||||||
\(39\) | 336111. | 0.907313 | ||||||||
\(40\) | 89846.2 | 0.221968 | ||||||||
\(41\) | −536752. | −1.21627 | −0.608135 | − | 0.793834i | \(-0.708082\pi\) | ||||
−0.608135 | + | 0.793834i | \(0.708082\pi\) | |||||||
\(42\) | −29378.1 | −0.0611858 | ||||||||
\(43\) | 583229. | 1.11866 | 0.559331 | − | 0.828944i | \(-0.311058\pi\) | ||||
0.559331 | + | 0.828944i | \(0.311058\pi\) | |||||||
\(44\) | −347136. | −0.614350 | ||||||||
\(45\) | −56547.6 | −0.0925061 | ||||||||
\(46\) | −211357. | −0.320158 | ||||||||
\(47\) | −587465. | −0.825353 | −0.412677 | − | 0.910878i | \(-0.635406\pi\) | ||||
−0.412677 | + | 0.910878i | \(0.635406\pi\) | |||||||
\(48\) | 198405. | 0.258945 | ||||||||
\(49\) | −776528. | −0.942912 | ||||||||
\(50\) | −361849. | −0.409385 | ||||||||
\(51\) | −711776. | −0.751359 | ||||||||
\(52\) | −1.27994e6 | −1.26234 | ||||||||
\(53\) | −267710. | −0.247001 | −0.123501 | − | 0.992344i | \(-0.539412\pi\) | ||||
−0.123501 | + | 0.992344i | \(0.539412\pi\) | |||||||
\(54\) | 98772.1 | 0.0853603 | ||||||||
\(55\) | −261889. | −0.212250 | ||||||||
\(56\) | 251148. | 0.191105 | ||||||||
\(57\) | 1.11784e6 | 0.799496 | ||||||||
\(58\) | −761339. | −0.512366 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 215338. | 0.128704 | ||||||||
\(61\) | −498824. | −0.281380 | −0.140690 | − | 0.990054i | \(-0.544932\pi\) | ||||
−0.140690 | + | 0.990054i | \(0.544932\pi\) | |||||||
\(62\) | −1.20151e6 | −0.640261 | ||||||||
\(63\) | −158068. | −0.0796439 | ||||||||
\(64\) | −11553.8 | −0.00550929 | ||||||||
\(65\) | −965620. | −0.436124 | ||||||||
\(66\) | 457443. | 0.195854 | ||||||||
\(67\) | 2.87144e6 | 1.16637 | 0.583187 | − | 0.812338i | \(-0.301805\pi\) | ||||
0.583187 | + | 0.812338i | \(0.301805\pi\) | |||||||
\(68\) | 2.71050e6 | 1.04537 | ||||||||
\(69\) | −1.13720e6 | −0.416740 | ||||||||
\(70\) | 84400.8 | 0.0294106 | ||||||||
\(71\) | 1.08176e6 | 0.358697 | 0.179349 | − | 0.983786i | \(-0.442601\pi\) | ||||
0.179349 | + | 0.983786i | \(0.442601\pi\) | |||||||
\(72\) | −844385. | −0.266610 | ||||||||
\(73\) | −4746.50 | −0.00142805 | −0.000714025 | − | 1.00000i | \(-0.500227\pi\) | ||||
−0.000714025 | 1.00000i | \(0.500227\pi\) | ||||||||
\(74\) | −2.06322e6 | −0.591883 | ||||||||
\(75\) | −1.94692e6 | −0.532885 | ||||||||
\(76\) | −4.25682e6 | −1.11234 | ||||||||
\(77\) | −732060. | −0.182738 | ||||||||
\(78\) | 1.68666e6 | 0.402435 | ||||||||
\(79\) | −1.41454e6 | −0.322791 | −0.161396 | − | 0.986890i | \(-0.551600\pi\) | ||||
−0.161396 | + | 0.986890i | \(0.551600\pi\) | |||||||
\(80\) | −570000. | −0.124469 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −2.69350e6 | −0.539471 | ||||||||
\(83\) | 3.72243e6 | 0.714583 | 0.357292 | − | 0.933993i | \(-0.383700\pi\) | ||||
0.357292 | + | 0.933993i | \(0.383700\pi\) | |||||||
\(84\) | 601936. | 0.110809 | ||||||||
\(85\) | 2.04487e6 | 0.361160 | ||||||||
\(86\) | 2.92672e6 | 0.496178 | ||||||||
\(87\) | −4.09637e6 | −0.666932 | ||||||||
\(88\) | −3.91060e6 | −0.611721 | ||||||||
\(89\) | 1.04746e7 | 1.57497 | 0.787484 | − | 0.616336i | \(-0.211384\pi\) | ||||
0.787484 | + | 0.616336i | \(0.211384\pi\) | |||||||
\(90\) | −283764. | −0.0410307 | ||||||||
\(91\) | −2.69921e6 | −0.375484 | ||||||||
\(92\) | 4.33055e6 | 0.579810 | ||||||||
\(93\) | −6.46471e6 | −0.833410 | ||||||||
\(94\) | −2.94798e6 | −0.366081 | ||||||||
\(95\) | −3.21145e6 | −0.384299 | ||||||||
\(96\) | 4.99864e6 | 0.576637 | ||||||||
\(97\) | −4.51283e6 | −0.502051 | −0.251025 | − | 0.967980i | \(-0.580768\pi\) | ||||
−0.251025 | + | 0.967980i | \(0.580768\pi\) | |||||||
\(98\) | −3.89673e6 | −0.418224 | ||||||||
\(99\) | 2.46126e6 | 0.254938 | ||||||||
\(100\) | 7.41403e6 | 0.741403 | ||||||||
\(101\) | −1.70633e7 | −1.64793 | −0.823963 | − | 0.566644i | \(-0.808242\pi\) | ||||
−0.823963 | + | 0.566644i | \(0.808242\pi\) | |||||||
\(102\) | −3.57179e6 | −0.333262 | ||||||||
\(103\) | −4.18892e6 | −0.377721 | −0.188861 | − | 0.982004i | \(-0.560479\pi\) | ||||
−0.188861 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(104\) | −1.44189e7 | −1.25694 | ||||||||
\(105\) | 454116. | 0.0382829 | ||||||||
\(106\) | −1.34341e6 | −0.109556 | ||||||||
\(107\) | −1.20271e7 | −0.949116 | −0.474558 | − | 0.880224i | \(-0.657392\pi\) | ||||
−0.474558 | + | 0.880224i | \(0.657392\pi\) | |||||||
\(108\) | −2.02377e6 | −0.154589 | ||||||||
\(109\) | −1.96024e7 | −1.44983 | −0.724913 | − | 0.688840i | \(-0.758120\pi\) | ||||
−0.724913 | + | 0.688840i | \(0.758120\pi\) | |||||||
\(110\) | −1.31419e6 | −0.0941424 | ||||||||
\(111\) | −1.11011e7 | −0.770437 | ||||||||
\(112\) | −1.59333e6 | −0.107162 | ||||||||
\(113\) | −7.54916e6 | −0.492180 | −0.246090 | − | 0.969247i | \(-0.579146\pi\) | ||||
−0.246090 | + | 0.969247i | \(0.579146\pi\) | |||||||
\(114\) | 5.60947e6 | 0.354613 | ||||||||
\(115\) | 3.26708e6 | 0.200317 | ||||||||
\(116\) | 1.55993e7 | 0.927903 | ||||||||
\(117\) | 9.07501e6 | 0.523837 | ||||||||
\(118\) | −1.03062e6 | −0.0577447 | ||||||||
\(119\) | 5.71605e6 | 0.310944 | ||||||||
\(120\) | 2.42585e6 | 0.128153 | ||||||||
\(121\) | −8.08835e6 | −0.415060 | ||||||||
\(122\) | −2.50317e6 | −0.124805 | ||||||||
\(123\) | −1.44923e7 | −0.702214 | ||||||||
\(124\) | 2.46182e7 | 1.15952 | ||||||||
\(125\) | 1.16534e7 | 0.533663 | ||||||||
\(126\) | −793208. | −0.0353257 | ||||||||
\(127\) | −1.36062e7 | −0.589417 | −0.294709 | − | 0.955587i | \(-0.595223\pi\) | ||||
−0.294709 | + | 0.955587i | \(0.595223\pi\) | |||||||
\(128\) | −2.37552e7 | −1.00121 | ||||||||
\(129\) | 1.57472e7 | 0.645860 | ||||||||
\(130\) | −4.84562e6 | −0.193441 | ||||||||
\(131\) | −1.29419e7 | −0.502978 | −0.251489 | − | 0.967860i | \(-0.580920\pi\) | ||||
−0.251489 | + | 0.967860i | \(0.580920\pi\) | |||||||
\(132\) | −9.37268e6 | −0.354695 | ||||||||
\(133\) | −8.97700e6 | −0.330865 | ||||||||
\(134\) | 1.44093e7 | 0.517340 | ||||||||
\(135\) | −1.52679e6 | −0.0534084 | ||||||||
\(136\) | 3.05346e7 | 1.04089 | ||||||||
\(137\) | −7.65865e6 | −0.254466 | −0.127233 | − | 0.991873i | \(-0.540610\pi\) | ||||
−0.127233 | + | 0.991873i | \(0.540610\pi\) | |||||||
\(138\) | −5.70663e6 | −0.184843 | ||||||||
\(139\) | 4.87660e6 | 0.154016 | 0.0770080 | − | 0.997030i | \(-0.475463\pi\) | ||||
0.0770080 | + | 0.997030i | \(0.475463\pi\) | |||||||
\(140\) | −1.72931e6 | −0.0532630 | ||||||||
\(141\) | −1.58616e7 | −0.476518 | ||||||||
\(142\) | 5.42844e6 | 0.159098 | ||||||||
\(143\) | 4.20290e7 | 1.20191 | ||||||||
\(144\) | 5.35693e6 | 0.149502 | ||||||||
\(145\) | 1.17685e7 | 0.320578 | ||||||||
\(146\) | −23818.6 | −0.000633405 0 | ||||||||
\(147\) | −2.09663e7 | −0.544390 | ||||||||
\(148\) | 4.22740e7 | 1.07191 | ||||||||
\(149\) | 1.05059e6 | 0.0260186 | 0.0130093 | − | 0.999915i | \(-0.495859\pi\) | ||||
0.0130093 | + | 0.999915i | \(0.495859\pi\) | |||||||
\(150\) | −9.76991e6 | −0.236359 | ||||||||
\(151\) | 5.81661e7 | 1.37484 | 0.687418 | − | 0.726262i | \(-0.258744\pi\) | ||||
0.687418 | + | 0.726262i | \(0.258744\pi\) | |||||||
\(152\) | −4.79543e7 | −1.10758 | ||||||||
\(153\) | −1.92179e7 | −0.433797 | ||||||||
\(154\) | −3.67358e6 | −0.0810526 | ||||||||
\(155\) | 1.85726e7 | 0.400600 | ||||||||
\(156\) | −3.45584e7 | −0.728815 | ||||||||
\(157\) | 4.08109e7 | 0.841642 | 0.420821 | − | 0.907144i | \(-0.361742\pi\) | ||||
0.420821 | + | 0.907144i | \(0.361742\pi\) | |||||||
\(158\) | −7.09838e6 | −0.143173 | ||||||||
\(159\) | −7.22818e6 | −0.142606 | ||||||||
\(160\) | −1.43607e7 | −0.277175 | ||||||||
\(161\) | 9.13250e6 | 0.172464 | ||||||||
\(162\) | 2.66685e6 | 0.0492828 | ||||||||
\(163\) | −7.46918e7 | −1.35088 | −0.675439 | − | 0.737416i | \(-0.736046\pi\) | ||||
−0.675439 | + | 0.737416i | \(0.736046\pi\) | |||||||
\(164\) | 5.51879e7 | 0.976990 | ||||||||
\(165\) | −7.07099e6 | −0.122542 | ||||||||
\(166\) | 1.86797e7 | 0.316950 | ||||||||
\(167\) | −5.71426e7 | −0.949407 | −0.474704 | − | 0.880146i | \(-0.657445\pi\) | ||||
−0.474704 | + | 0.880146i | \(0.657445\pi\) | |||||||
\(168\) | 6.78100e6 | 0.110334 | ||||||||
\(169\) | 9.22184e7 | 1.46965 | ||||||||
\(170\) | 1.02615e7 | 0.160191 | ||||||||
\(171\) | 3.01816e7 | 0.461589 | ||||||||
\(172\) | −5.99665e7 | −0.898585 | ||||||||
\(173\) | 6.74021e7 | 0.989720 | 0.494860 | − | 0.868973i | \(-0.335219\pi\) | ||||
0.494860 | + | 0.868973i | \(0.335219\pi\) | |||||||
\(174\) | −2.05562e7 | −0.295815 | ||||||||
\(175\) | 1.56351e7 | 0.220530 | ||||||||
\(176\) | 2.48095e7 | 0.343024 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 5.25629e7 | 0.698569 | ||||||||
\(179\) | 5.40298e7 | 0.704122 | 0.352061 | − | 0.935977i | \(-0.385481\pi\) | ||||
0.352061 | + | 0.935977i | \(0.385481\pi\) | |||||||
\(180\) | 5.81413e6 | 0.0743072 | ||||||||
\(181\) | −2.98190e7 | −0.373782 | −0.186891 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186891 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(182\) | −1.35450e7 | −0.166544 | ||||||||
\(183\) | −1.34683e7 | −0.162455 | ||||||||
\(184\) | 4.87850e7 | 0.577330 | ||||||||
\(185\) | 3.18926e7 | 0.370330 | ||||||||
\(186\) | −3.24408e7 | −0.369655 | ||||||||
\(187\) | −8.90040e7 | −0.995322 | ||||||||
\(188\) | 6.04022e7 | 0.662979 | ||||||||
\(189\) | −4.26784e6 | −0.0459824 | ||||||||
\(190\) | −1.61155e7 | −0.170454 | ||||||||
\(191\) | −1.03129e8 | −1.07093 | −0.535466 | − | 0.844557i | \(-0.679864\pi\) | ||||
−0.535466 | + | 0.844557i | \(0.679864\pi\) | |||||||
\(192\) | −311953. | −0.00318079 | ||||||||
\(193\) | 1.72283e8 | 1.72501 | 0.862506 | − | 0.506047i | \(-0.168894\pi\) | ||||
0.862506 | + | 0.506047i | \(0.168894\pi\) | |||||||
\(194\) | −2.26460e7 | −0.222682 | ||||||||
\(195\) | −2.60717e7 | −0.251796 | ||||||||
\(196\) | 7.98413e7 | 0.757410 | ||||||||
\(197\) | −1.27602e8 | −1.18912 | −0.594562 | − | 0.804050i | \(-0.702674\pi\) | ||||
−0.594562 | + | 0.804050i | \(0.702674\pi\) | |||||||
\(198\) | 1.23510e7 | 0.113076 | ||||||||
\(199\) | −6.47395e7 | −0.582349 | −0.291175 | − | 0.956670i | \(-0.594046\pi\) | ||||
−0.291175 | + | 0.956670i | \(0.594046\pi\) | |||||||
\(200\) | 8.35213e7 | 0.738231 | ||||||||
\(201\) | 7.75289e7 | 0.673406 | ||||||||
\(202\) | −8.56260e7 | −0.730930 | ||||||||
\(203\) | 3.28967e7 | 0.276004 | ||||||||
\(204\) | 7.31835e7 | 0.603542 | ||||||||
\(205\) | 4.16351e7 | 0.337537 | ||||||||
\(206\) | −2.10206e7 | −0.167536 | ||||||||
\(207\) | −3.07044e7 | −0.240605 | ||||||||
\(208\) | 9.14762e7 | 0.704833 | ||||||||
\(209\) | 1.39780e8 | 1.05909 | ||||||||
\(210\) | 2.27882e6 | 0.0169802 | ||||||||
\(211\) | 1.42567e8 | 1.04479 | 0.522395 | − | 0.852704i | \(-0.325039\pi\) | ||||
0.522395 | + | 0.852704i | \(0.325039\pi\) | |||||||
\(212\) | 2.75255e7 | 0.198408 | ||||||||
\(213\) | 2.92076e7 | 0.207094 | ||||||||
\(214\) | −6.03539e7 | −0.420976 | ||||||||
\(215\) | −4.52403e7 | −0.310449 | ||||||||
\(216\) | −2.27984e7 | −0.153928 | ||||||||
\(217\) | 5.19161e7 | 0.344900 | ||||||||
\(218\) | −9.83675e7 | −0.643064 | ||||||||
\(219\) | −128155. | −0.000824485 0 | ||||||||
\(220\) | 2.69269e7 | 0.170493 | ||||||||
\(221\) | −3.28170e8 | −2.04515 | ||||||||
\(222\) | −5.57071e7 | −0.341724 | ||||||||
\(223\) | 2.35480e8 | 1.42196 | 0.710979 | − | 0.703213i | \(-0.248252\pi\) | ||||
0.710979 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(224\) | −4.01425e7 | −0.238636 | ||||||||
\(225\) | −5.25668e7 | −0.307661 | ||||||||
\(226\) | −3.78828e7 | −0.218304 | ||||||||
\(227\) | 3.35151e8 | 1.90174 | 0.950868 | − | 0.309598i | \(-0.100194\pi\) | ||||
0.950868 | + | 0.309598i | \(0.100194\pi\) | |||||||
\(228\) | −1.14934e8 | −0.642209 | ||||||||
\(229\) | −1.68231e8 | −0.925727 | −0.462864 | − | 0.886430i | \(-0.653178\pi\) | ||||
−0.462864 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(230\) | 1.63947e7 | 0.0888496 | ||||||||
\(231\) | −1.97656e7 | −0.105504 | ||||||||
\(232\) | 1.75731e8 | 0.923933 | ||||||||
\(233\) | −2.76156e8 | −1.43024 | −0.715120 | − | 0.699002i | \(-0.753628\pi\) | ||||
−0.715120 | + | 0.699002i | \(0.753628\pi\) | |||||||
\(234\) | 4.55397e7 | 0.232346 | ||||||||
\(235\) | 4.55689e7 | 0.229051 | ||||||||
\(236\) | 2.11167e7 | 0.104577 | ||||||||
\(237\) | −3.81927e7 | −0.186364 | ||||||||
\(238\) | 2.86840e7 | 0.137918 | ||||||||
\(239\) | 1.64969e8 | 0.781647 | 0.390824 | − | 0.920466i | \(-0.372190\pi\) | ||||
0.390824 | + | 0.920466i | \(0.372190\pi\) | |||||||
\(240\) | −1.53900e7 | −0.0718621 | ||||||||
\(241\) | 2.19804e8 | 1.01152 | 0.505761 | − | 0.862674i | \(-0.331212\pi\) | ||||
0.505761 | + | 0.862674i | \(0.331212\pi\) | |||||||
\(242\) | −4.05885e7 | −0.184098 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 5.12882e7 | 0.226023 | ||||||||
\(245\) | 6.02343e7 | 0.261675 | ||||||||
\(246\) | −7.27244e7 | −0.311464 | ||||||||
\(247\) | 5.15388e8 | 2.17618 | ||||||||
\(248\) | 2.77331e8 | 1.15456 | ||||||||
\(249\) | 1.00506e8 | 0.412565 | ||||||||
\(250\) | 5.84784e7 | 0.236704 | ||||||||
\(251\) | −2.64722e8 | −1.05665 | −0.528327 | − | 0.849041i | \(-0.677180\pi\) | ||||
−0.528327 | + | 0.849041i | \(0.677180\pi\) | |||||||
\(252\) | 1.62523e7 | 0.0639753 | ||||||||
\(253\) | −1.42201e8 | −0.552054 | ||||||||
\(254\) | −6.82777e7 | −0.261433 | ||||||||
\(255\) | 5.52116e7 | 0.208516 | ||||||||
\(256\) | −1.17728e8 | −0.438572 | ||||||||
\(257\) | −2.39775e8 | −0.881125 | −0.440563 | − | 0.897722i | \(-0.645221\pi\) | ||||
−0.440563 | + | 0.897722i | \(0.645221\pi\) | |||||||
\(258\) | 7.90215e7 | 0.286468 | ||||||||
\(259\) | 8.91498e7 | 0.318839 | ||||||||
\(260\) | 9.92834e7 | 0.350324 | ||||||||
\(261\) | −1.10602e8 | −0.385054 | ||||||||
\(262\) | −6.49444e7 | −0.223094 | ||||||||
\(263\) | 1.27661e8 | 0.432727 | 0.216364 | − | 0.976313i | \(-0.430580\pi\) | ||||
0.216364 | + | 0.976313i | \(0.430580\pi\) | |||||||
\(264\) | −1.05586e8 | −0.353178 | ||||||||
\(265\) | 2.07659e7 | 0.0685474 | ||||||||
\(266\) | −4.50479e7 | −0.146754 | ||||||||
\(267\) | 2.82814e8 | 0.909308 | ||||||||
\(268\) | −2.95236e8 | −0.936910 | ||||||||
\(269\) | 1.98210e8 | 0.620858 | 0.310429 | − | 0.950597i | \(-0.399527\pi\) | ||||
0.310429 | + | 0.950597i | \(0.399527\pi\) | |||||||
\(270\) | −7.66163e6 | −0.0236891 | ||||||||
\(271\) | 1.17159e8 | 0.357587 | 0.178794 | − | 0.983887i | \(-0.442781\pi\) | ||||
0.178794 | + | 0.983887i | \(0.442781\pi\) | |||||||
\(272\) | −1.93717e8 | −0.583683 | ||||||||
\(273\) | −7.28786e7 | −0.216786 | ||||||||
\(274\) | −3.84322e7 | −0.112867 | ||||||||
\(275\) | −2.43452e8 | −0.705910 | ||||||||
\(276\) | 1.16925e8 | 0.334754 | ||||||||
\(277\) | 2.80002e8 | 0.791555 | 0.395778 | − | 0.918346i | \(-0.370475\pi\) | ||||
0.395778 | + | 0.918346i | \(0.370475\pi\) | |||||||
\(278\) | 2.44715e7 | 0.0683131 | ||||||||
\(279\) | −1.74547e8 | −0.481169 | ||||||||
\(280\) | −1.94812e7 | −0.0530351 | ||||||||
\(281\) | −6.16699e7 | −0.165806 | −0.0829032 | − | 0.996558i | \(-0.526419\pi\) | ||||
−0.0829032 | + | 0.996558i | \(0.526419\pi\) | |||||||
\(282\) | −7.95956e7 | −0.211357 | ||||||||
\(283\) | −6.20410e8 | −1.62715 | −0.813573 | − | 0.581463i | \(-0.802481\pi\) | ||||
−0.813573 | + | 0.581463i | \(0.802481\pi\) | |||||||
\(284\) | −1.11225e8 | −0.288130 | ||||||||
\(285\) | −8.67092e7 | −0.221875 | ||||||||
\(286\) | 2.10908e8 | 0.533103 | ||||||||
\(287\) | 1.16383e8 | 0.290605 | ||||||||
\(288\) | 1.34963e8 | 0.332921 | ||||||||
\(289\) | 2.84620e8 | 0.693622 | ||||||||
\(290\) | 5.90561e7 | 0.142191 | ||||||||
\(291\) | −1.21846e8 | −0.289859 | ||||||||
\(292\) | 488027. | 0.00114711 | ||||||||
\(293\) | −7.47133e8 | −1.73525 | −0.867623 | − | 0.497222i | \(-0.834353\pi\) | ||||
−0.867623 | + | 0.497222i | \(0.834353\pi\) | |||||||
\(294\) | −1.05212e8 | −0.241462 | ||||||||
\(295\) | 1.59310e7 | 0.0361298 | ||||||||
\(296\) | 4.76230e8 | 1.06732 | ||||||||
\(297\) | 6.64540e7 | 0.147188 | ||||||||
\(298\) | 5.27203e6 | 0.0115404 | ||||||||
\(299\) | −5.24316e8 | −1.13434 | ||||||||
\(300\) | 2.00179e8 | 0.428049 | ||||||||
\(301\) | −1.26461e8 | −0.267284 | ||||||||
\(302\) | 2.91886e8 | 0.609802 | ||||||||
\(303\) | −4.60708e8 | −0.951430 | ||||||||
\(304\) | 3.04231e8 | 0.621077 | ||||||||
\(305\) | 3.86932e7 | 0.0780881 | ||||||||
\(306\) | −9.64384e7 | −0.192409 | ||||||||
\(307\) | 6.94608e8 | 1.37011 | 0.685056 | − | 0.728491i | \(-0.259778\pi\) | ||||
0.685056 | + | 0.728491i | \(0.259778\pi\) | |||||||
\(308\) | 7.52691e7 | 0.146788 | ||||||||
\(309\) | −1.13101e8 | −0.218077 | ||||||||
\(310\) | 9.31998e7 | 0.177684 | ||||||||
\(311\) | 1.27745e8 | 0.240815 | 0.120407 | − | 0.992725i | \(-0.461580\pi\) | ||||
0.120407 | + | 0.992725i | \(0.461580\pi\) | |||||||
\(312\) | −3.89311e8 | −0.725697 | ||||||||
\(313\) | −9.74255e8 | −1.79584 | −0.897920 | − | 0.440159i | \(-0.854922\pi\) | ||||
−0.897920 | + | 0.440159i | \(0.854922\pi\) | |||||||
\(314\) | 2.04795e8 | 0.373306 | ||||||||
\(315\) | 1.22611e7 | 0.0221026 | ||||||||
\(316\) | 1.45441e8 | 0.259288 | ||||||||
\(317\) | −8.99019e8 | −1.58512 | −0.792559 | − | 0.609795i | \(-0.791252\pi\) | ||||
−0.792559 | + | 0.609795i | \(0.791252\pi\) | |||||||
\(318\) | −3.62720e7 | −0.0632524 | ||||||||
\(319\) | −5.12230e8 | −0.883482 | ||||||||
\(320\) | 896215. | 0.00152893 | ||||||||
\(321\) | −3.24733e8 | −0.547972 | ||||||||
\(322\) | 4.58282e7 | 0.0764957 | ||||||||
\(323\) | −1.09143e9 | −1.80213 | ||||||||
\(324\) | −5.46418e7 | −0.0892519 | ||||||||
\(325\) | −8.97643e8 | −1.45048 | ||||||||
\(326\) | −3.74814e8 | −0.599176 | ||||||||
\(327\) | −5.29264e8 | −0.837058 | ||||||||
\(328\) | 6.21708e8 | 0.972810 | ||||||||
\(329\) | 1.27379e8 | 0.197203 | ||||||||
\(330\) | −3.54833e7 | −0.0543531 | ||||||||
\(331\) | −1.16605e9 | −1.76733 | −0.883666 | − | 0.468119i | \(-0.844932\pi\) | ||||
−0.883666 | + | 0.468119i | \(0.844932\pi\) | |||||||
\(332\) | −3.82733e8 | −0.574002 | ||||||||
\(333\) | −2.99731e8 | −0.444812 | ||||||||
\(334\) | −2.86750e8 | −0.421105 | ||||||||
\(335\) | −2.22734e8 | −0.323690 | ||||||||
\(336\) | −4.30198e7 | −0.0618702 | ||||||||
\(337\) | 1.23311e9 | 1.75509 | 0.877544 | − | 0.479496i | \(-0.159181\pi\) | ||||
0.877544 | + | 0.479496i | \(0.159181\pi\) | |||||||
\(338\) | 4.62765e8 | 0.651857 | ||||||||
\(339\) | −2.03827e8 | −0.284160 | ||||||||
\(340\) | −2.10250e8 | −0.290108 | ||||||||
\(341\) | −8.08379e8 | −1.10401 | ||||||||
\(342\) | 1.51456e8 | 0.204736 | ||||||||
\(343\) | 3.46941e8 | 0.464223 | ||||||||
\(344\) | −6.75541e8 | −0.894741 | ||||||||
\(345\) | 8.82112e7 | 0.115653 | ||||||||
\(346\) | 3.38233e8 | 0.438986 | ||||||||
\(347\) | −5.89436e8 | −0.757327 | −0.378664 | − | 0.925534i | \(-0.623616\pi\) | ||||
−0.378664 | + | 0.925534i | \(0.623616\pi\) | |||||||
\(348\) | 4.21182e8 | 0.535725 | ||||||||
\(349\) | 1.15878e9 | 1.45919 | 0.729596 | − | 0.683878i | \(-0.239708\pi\) | ||||
0.729596 | + | 0.683878i | \(0.239708\pi\) | |||||||
\(350\) | 7.84592e7 | 0.0978150 | ||||||||
\(351\) | 2.45025e8 | 0.302438 | ||||||||
\(352\) | 6.25054e8 | 0.763868 | ||||||||
\(353\) | −5.26080e8 | −0.636561 | −0.318281 | − | 0.947997i | \(-0.603105\pi\) | ||||
−0.318281 | + | 0.947997i | \(0.603105\pi\) | |||||||
\(354\) | −2.78268e7 | −0.0333389 | ||||||||
\(355\) | −8.39110e7 | −0.0995450 | ||||||||
\(356\) | −1.07698e9 | −1.26512 | ||||||||
\(357\) | 1.54333e8 | 0.179523 | ||||||||
\(358\) | 2.71129e8 | 0.312310 | ||||||||
\(359\) | 1.09995e9 | 1.25470 | 0.627351 | − | 0.778737i | \(-0.284139\pi\) | ||||
0.627351 | + | 0.778737i | \(0.284139\pi\) | |||||||
\(360\) | 6.54979e7 | 0.0739893 | ||||||||
\(361\) | 8.20202e8 | 0.917583 | ||||||||
\(362\) | −1.49636e8 | −0.165789 | ||||||||
\(363\) | −2.18385e8 | −0.239635 | ||||||||
\(364\) | 2.77528e8 | 0.301614 | ||||||||
\(365\) | 368180. | 0.000396310 0 | ||||||||
\(366\) | −6.75856e7 | −0.0720561 | ||||||||
\(367\) | 1.21755e9 | 1.28575 | 0.642874 | − | 0.765972i | \(-0.277742\pi\) | ||||
0.642874 | + | 0.765972i | \(0.277742\pi\) | |||||||
\(368\) | −3.09501e8 | −0.323738 | ||||||||
\(369\) | −3.91292e8 | −0.405423 | ||||||||
\(370\) | 1.60042e8 | 0.164258 | ||||||||
\(371\) | 5.80473e7 | 0.0590164 | ||||||||
\(372\) | 6.64690e8 | 0.669451 | ||||||||
\(373\) | 5.53595e8 | 0.552346 | 0.276173 | − | 0.961108i | \(-0.410934\pi\) | ||||
0.276173 | + | 0.961108i | \(0.410934\pi\) | |||||||
\(374\) | −4.46635e8 | −0.441471 | ||||||||
\(375\) | 3.14642e8 | 0.308111 | ||||||||
\(376\) | 6.80449e8 | 0.660143 | ||||||||
\(377\) | −1.88866e9 | −1.81535 | ||||||||
\(378\) | −2.14166e7 | −0.0203953 | ||||||||
\(379\) | −2.47132e8 | −0.233180 | −0.116590 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116590 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(380\) | 3.30196e8 | 0.308695 | ||||||||
\(381\) | −3.67367e8 | −0.340300 | ||||||||
\(382\) | −5.17514e8 | −0.475007 | ||||||||
\(383\) | −599846. | −0.000545562 0 | −0.000272781 | − | 1.00000i | \(-0.500087\pi\) | ||||
−0.000272781 | 1.00000i | \(0.500087\pi\) | ||||||||
\(384\) | −6.41391e8 | −0.578047 | ||||||||
\(385\) | 5.67850e7 | 0.0507132 | ||||||||
\(386\) | 8.64541e8 | 0.765121 | ||||||||
\(387\) | 4.25174e8 | 0.372888 | ||||||||
\(388\) | 4.64001e8 | 0.403281 | ||||||||
\(389\) | −8.92101e8 | −0.768406 | −0.384203 | − | 0.923249i | \(-0.625524\pi\) | ||||
−0.384203 | + | 0.923249i | \(0.625524\pi\) | |||||||
\(390\) | −1.30832e8 | −0.111683 | ||||||||
\(391\) | 1.11033e9 | 0.939364 | ||||||||
\(392\) | 8.99436e8 | 0.754170 | ||||||||
\(393\) | −3.49432e8 | −0.290395 | ||||||||
\(394\) | −6.40327e8 | −0.527430 | ||||||||
\(395\) | 1.09724e8 | 0.0895805 | ||||||||
\(396\) | −2.53062e8 | −0.204783 | ||||||||
\(397\) | −9.58791e8 | −0.769055 | −0.384527 | − | 0.923114i | \(-0.625636\pi\) | ||||
−0.384527 | + | 0.923114i | \(0.625636\pi\) | |||||||
\(398\) | −3.24872e8 | −0.258298 | ||||||||
\(399\) | −2.42379e8 | −0.191025 | ||||||||
\(400\) | −5.29874e8 | −0.413964 | ||||||||
\(401\) | 1.82830e9 | 1.41593 | 0.707966 | − | 0.706247i | \(-0.249613\pi\) | ||||
0.707966 | + | 0.706247i | \(0.249613\pi\) | |||||||
\(402\) | 3.89051e8 | 0.298686 | ||||||||
\(403\) | −2.98061e9 | −2.26849 | ||||||||
\(404\) | 1.75442e9 | 1.32373 | ||||||||
\(405\) | −4.12232e7 | −0.0308354 | ||||||||
\(406\) | 1.65080e8 | 0.122420 | ||||||||
\(407\) | −1.38814e9 | −1.02059 | ||||||||
\(408\) | 8.24435e8 | 0.600960 | ||||||||
\(409\) | −7.15047e8 | −0.516776 | −0.258388 | − | 0.966041i | \(-0.583191\pi\) | ||||
−0.258388 | + | 0.966041i | \(0.583191\pi\) | |||||||
\(410\) | 2.08931e8 | 0.149713 | ||||||||
\(411\) | −2.06784e8 | −0.146916 | ||||||||
\(412\) | 4.30697e8 | 0.303411 | ||||||||
\(413\) | 4.45320e7 | 0.0311062 | ||||||||
\(414\) | −1.54079e8 | −0.106719 | ||||||||
\(415\) | −2.88744e8 | −0.198310 | ||||||||
\(416\) | 2.30466e9 | 1.56957 | ||||||||
\(417\) | 1.31668e8 | 0.0889212 | ||||||||
\(418\) | 7.01435e8 | 0.469754 | ||||||||
\(419\) | 2.22875e9 | 1.48017 | 0.740086 | − | 0.672513i | \(-0.234785\pi\) | ||||
0.740086 | + | 0.672513i | \(0.234785\pi\) | |||||||
\(420\) | −4.66914e7 | −0.0307514 | ||||||||
\(421\) | 1.49109e9 | 0.973906 | 0.486953 | − | 0.873428i | \(-0.338108\pi\) | ||||
0.486953 | + | 0.873428i | \(0.338108\pi\) | |||||||
\(422\) | 7.15419e8 | 0.463412 | ||||||||
\(423\) | −4.28262e8 | −0.275118 | ||||||||
\(424\) | 3.10083e8 | 0.197559 | ||||||||
\(425\) | 1.90092e9 | 1.20116 | ||||||||
\(426\) | 1.46568e8 | 0.0918555 | ||||||||
\(427\) | 1.08159e8 | 0.0672306 | ||||||||
\(428\) | 1.23661e9 | 0.762394 | ||||||||
\(429\) | 1.13478e9 | 0.693925 | ||||||||
\(430\) | −2.27022e8 | −0.137698 | ||||||||
\(431\) | 2.66273e9 | 1.60198 | 0.800988 | − | 0.598680i | \(-0.204308\pi\) | ||||
0.800988 | + | 0.598680i | \(0.204308\pi\) | |||||||
\(432\) | 1.44637e8 | 0.0863151 | ||||||||
\(433\) | 7.09435e7 | 0.0419957 | 0.0209979 | − | 0.999780i | \(-0.493316\pi\) | ||||
0.0209979 | + | 0.999780i | \(0.493316\pi\) | |||||||
\(434\) | 2.60522e8 | 0.152979 | ||||||||
\(435\) | 3.17750e8 | 0.185086 | ||||||||
\(436\) | 2.01548e9 | 1.16460 | ||||||||
\(437\) | −1.74376e9 | −0.999546 | ||||||||
\(438\) | −643103. | −0.000365697 0 | ||||||||
\(439\) | 6.26733e7 | 0.0353555 | 0.0176777 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176777 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(440\) | 3.03340e8 | 0.169764 | ||||||||
\(441\) | −5.66089e8 | −0.314304 | ||||||||
\(442\) | −1.64680e9 | −0.907119 | ||||||||
\(443\) | −6.41984e8 | −0.350842 | −0.175421 | − | 0.984494i | \(-0.556129\pi\) | ||||
−0.175421 | + | 0.984494i | \(0.556129\pi\) | |||||||
\(444\) | 1.14140e9 | 0.618867 | ||||||||
\(445\) | −8.12500e8 | −0.437082 | ||||||||
\(446\) | 1.18167e9 | 0.630703 | ||||||||
\(447\) | 2.83661e7 | 0.0150218 | ||||||||
\(448\) | 2.50520e6 | 0.00131634 | ||||||||
\(449\) | −2.77507e9 | −1.44681 | −0.723406 | − | 0.690423i | \(-0.757425\pi\) | ||||
−0.723406 | + | 0.690423i | \(0.757425\pi\) | |||||||
\(450\) | −2.63788e8 | −0.136462 | ||||||||
\(451\) | −1.81219e9 | −0.930219 | ||||||||
\(452\) | 7.76191e8 | 0.395352 | ||||||||
\(453\) | 1.57048e9 | 0.793762 | ||||||||
\(454\) | 1.68184e9 | 0.843506 | ||||||||
\(455\) | 2.09374e8 | 0.104204 | ||||||||
\(456\) | −1.29477e9 | −0.639462 | ||||||||
\(457\) | 3.79393e9 | 1.85944 | 0.929721 | − | 0.368266i | \(-0.120048\pi\) | ||||
0.929721 | + | 0.368266i | \(0.120048\pi\) | |||||||
\(458\) | −8.44209e8 | −0.410602 | ||||||||
\(459\) | −5.18885e8 | −0.250453 | ||||||||
\(460\) | −3.35916e8 | −0.160908 | ||||||||
\(461\) | −3.74187e9 | −1.77884 | −0.889418 | − | 0.457095i | \(-0.848890\pi\) | ||||
−0.889418 | + | 0.457095i | \(0.848890\pi\) | |||||||
\(462\) | −9.91867e7 | −0.0467958 | ||||||||
\(463\) | 1.68652e9 | 0.789691 | 0.394846 | − | 0.918748i | \(-0.370798\pi\) | ||||
0.394846 | + | 0.918748i | \(0.370798\pi\) | |||||||
\(464\) | −1.11487e9 | −0.518097 | ||||||||
\(465\) | 5.01459e8 | 0.231287 | ||||||||
\(466\) | −1.38579e9 | −0.634376 | ||||||||
\(467\) | −1.90310e8 | −0.0864675 | −0.0432338 | − | 0.999065i | \(-0.513766\pi\) | ||||
−0.0432338 | + | 0.999065i | \(0.513766\pi\) | |||||||
\(468\) | −9.33077e8 | −0.420782 | ||||||||
\(469\) | −6.22610e8 | −0.278684 | ||||||||
\(470\) | 2.28671e8 | 0.101594 | ||||||||
\(471\) | 1.10189e9 | 0.485922 | ||||||||
\(472\) | 2.37886e8 | 0.104129 | ||||||||
\(473\) | 1.96910e9 | 0.855568 | ||||||||
\(474\) | −1.91656e8 | −0.0826607 | ||||||||
\(475\) | −2.98537e9 | −1.27812 | ||||||||
\(476\) | −5.87714e8 | −0.249771 | ||||||||
\(477\) | −1.95161e8 | −0.0823338 | ||||||||
\(478\) | 8.27840e8 | 0.346696 | ||||||||
\(479\) | 1.04486e9 | 0.434395 | 0.217197 | − | 0.976128i | \(-0.430308\pi\) | ||||
0.217197 | + | 0.976128i | \(0.430308\pi\) | |||||||
\(480\) | −3.87738e8 | −0.160027 | ||||||||
\(481\) | −5.11827e9 | −2.09708 | ||||||||
\(482\) | 1.10301e9 | 0.448656 | ||||||||
\(483\) | 2.46578e8 | 0.0995723 | ||||||||
\(484\) | 8.31630e8 | 0.333404 | ||||||||
\(485\) | 3.50054e8 | 0.139328 | ||||||||
\(486\) | 7.20049e7 | 0.0284534 | ||||||||
\(487\) | −4.52457e9 | −1.77511 | −0.887557 | − | 0.460697i | \(-0.847599\pi\) | ||||
−0.887557 | + | 0.460697i | \(0.847599\pi\) | |||||||
\(488\) | 5.77778e8 | 0.225056 | ||||||||
\(489\) | −2.01668e9 | −0.779930 | ||||||||
\(490\) | 3.02264e8 | 0.116065 | ||||||||
\(491\) | 1.28164e9 | 0.488630 | 0.244315 | − | 0.969696i | \(-0.421437\pi\) | ||||
0.244315 | + | 0.969696i | \(0.421437\pi\) | |||||||
\(492\) | 1.49007e9 | 0.564065 | ||||||||
\(493\) | 3.99958e9 | 1.50332 | ||||||||
\(494\) | 2.58629e9 | 0.965235 | ||||||||
\(495\) | −1.90917e8 | −0.0707499 | ||||||||
\(496\) | −1.75944e9 | −0.647423 | ||||||||
\(497\) | −2.34557e8 | −0.0857041 | ||||||||
\(498\) | 5.04351e8 | 0.182991 | ||||||||
\(499\) | −3.26234e9 | −1.17538 | −0.587689 | − | 0.809087i | \(-0.699962\pi\) | ||||
−0.587689 | + | 0.809087i | \(0.699962\pi\) | |||||||
\(500\) | −1.19818e9 | −0.428674 | ||||||||
\(501\) | −1.54285e9 | −0.548140 | ||||||||
\(502\) | −1.32841e9 | −0.468674 | ||||||||
\(503\) | 5.11806e8 | 0.179315 | 0.0896577 | − | 0.995973i | \(-0.471423\pi\) | ||||
0.0896577 | + | 0.995973i | \(0.471423\pi\) | |||||||
\(504\) | 1.83087e8 | 0.0637016 | ||||||||
\(505\) | 1.32358e9 | 0.457330 | ||||||||
\(506\) | −7.13586e8 | −0.244861 | ||||||||
\(507\) | 2.48990e9 | 0.848504 | ||||||||
\(508\) | 1.39896e9 | 0.473460 | ||||||||
\(509\) | 5.38317e9 | 1.80936 | 0.904682 | − | 0.426088i | \(-0.140108\pi\) | ||||
0.904682 | + | 0.426088i | \(0.140108\pi\) | |||||||
\(510\) | 2.77059e8 | 0.0924863 | ||||||||
\(511\) | 1.02918e6 | 0.000341206 0 | ||||||||
\(512\) | 2.44989e9 | 0.806681 | ||||||||
\(513\) | 8.14903e8 | 0.266499 | ||||||||
\(514\) | −1.20322e9 | −0.390819 | ||||||||
\(515\) | 3.24929e8 | 0.104825 | ||||||||
\(516\) | −1.61910e9 | −0.518799 | ||||||||
\(517\) | −1.98341e9 | −0.631241 | ||||||||
\(518\) | 4.47366e8 | 0.141419 | ||||||||
\(519\) | 1.81986e9 | 0.571415 | ||||||||
\(520\) | 1.11846e9 | 0.348825 | ||||||||
\(521\) | 1.92620e9 | 0.596720 | 0.298360 | − | 0.954453i | \(-0.403560\pi\) | ||||
0.298360 | + | 0.954453i | \(0.403560\pi\) | |||||||
\(522\) | −5.55016e8 | −0.170789 | ||||||||
\(523\) | 3.47164e9 | 1.06115 | 0.530577 | − | 0.847637i | \(-0.321975\pi\) | ||||
0.530577 | + | 0.847637i | \(0.321975\pi\) | |||||||
\(524\) | 1.33067e9 | 0.404026 | ||||||||
\(525\) | 4.22148e8 | 0.127323 | ||||||||
\(526\) | 6.40623e8 | 0.191934 | ||||||||
\(527\) | 6.31197e9 | 1.87857 | ||||||||
\(528\) | 6.69857e8 | 0.198045 | ||||||||
\(529\) | −1.63086e9 | −0.478984 | ||||||||
\(530\) | 1.04206e8 | 0.0304039 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | 9.23000e8 | 0.265773 | ||||||||
\(533\) | −6.68179e9 | −1.91138 | ||||||||
\(534\) | 1.41920e9 | 0.403319 | ||||||||
\(535\) | 9.32930e8 | 0.263397 | ||||||||
\(536\) | −3.32593e9 | −0.932902 | ||||||||
\(537\) | 1.45880e9 | 0.406525 | ||||||||
\(538\) | 9.94645e8 | 0.275379 | ||||||||
\(539\) | −2.62173e9 | −0.721152 | ||||||||
\(540\) | 1.56981e8 | 0.0429013 | ||||||||
\(541\) | −1.13960e9 | −0.309430 | −0.154715 | − | 0.987959i | \(-0.549446\pi\) | ||||
−0.154715 | + | 0.987959i | \(0.549446\pi\) | |||||||
\(542\) | 5.87919e8 | 0.158606 | ||||||||
\(543\) | −8.05114e8 | −0.215803 | ||||||||
\(544\) | −4.88053e9 | −1.29978 | ||||||||
\(545\) | 1.52053e9 | 0.402353 | ||||||||
\(546\) | −3.65715e8 | −0.0961543 | ||||||||
\(547\) | −3.40030e9 | −0.888303 | −0.444152 | − | 0.895952i | \(-0.646495\pi\) | ||||
−0.444152 | + | 0.895952i | \(0.646495\pi\) | |||||||
\(548\) | 7.87449e8 | 0.204405 | ||||||||
\(549\) | −3.63643e8 | −0.0937933 | ||||||||
\(550\) | −1.22168e9 | −0.313103 | ||||||||
\(551\) | −6.28131e9 | −1.59963 | ||||||||
\(552\) | 1.31719e9 | 0.333321 | ||||||||
\(553\) | 3.06714e8 | 0.0771250 | ||||||||
\(554\) | 1.40509e9 | 0.351091 | ||||||||
\(555\) | 8.61101e8 | 0.213810 | ||||||||
\(556\) | −5.01404e8 | −0.123716 | ||||||||
\(557\) | 1.94268e9 | 0.476331 | 0.238165 | − | 0.971225i | \(-0.423454\pi\) | ||||
0.238165 | + | 0.971225i | \(0.423454\pi\) | |||||||
\(558\) | −8.75903e8 | −0.213420 | ||||||||
\(559\) | 7.26036e9 | 1.75799 | ||||||||
\(560\) | 1.23592e8 | 0.0297395 | ||||||||
\(561\) | −2.40311e9 | −0.574650 | ||||||||
\(562\) | −3.09468e8 | −0.0735427 | ||||||||
\(563\) | 6.16858e9 | 1.45682 | 0.728410 | − | 0.685142i | \(-0.240260\pi\) | ||||
0.728410 | + | 0.685142i | \(0.240260\pi\) | |||||||
\(564\) | 1.63086e9 | 0.382771 | ||||||||
\(565\) | 5.85579e8 | 0.136589 | ||||||||
\(566\) | −3.11331e9 | −0.721713 | ||||||||
\(567\) | −1.15232e8 | −0.0265480 | ||||||||
\(568\) | −1.25298e9 | −0.286897 | ||||||||
\(569\) | −5.43476e9 | −1.23677 | −0.618383 | − | 0.785877i | \(-0.712212\pi\) | ||||
−0.618383 | + | 0.785877i | \(0.712212\pi\) | |||||||
\(570\) | −4.35119e8 | −0.0984116 | ||||||||
\(571\) | −5.20959e9 | −1.17105 | −0.585527 | − | 0.810653i | \(-0.699112\pi\) | ||||
−0.585527 | + | 0.810653i | \(0.699112\pi\) | |||||||
\(572\) | −4.32135e9 | −0.965458 | ||||||||
\(573\) | −2.78447e9 | −0.618303 | ||||||||
\(574\) | 5.84027e8 | 0.128897 | ||||||||
\(575\) | 3.03709e9 | 0.666223 | ||||||||
\(576\) | −8.42274e6 | −0.00183643 | ||||||||
\(577\) | 2.67350e9 | 0.579381 | 0.289691 | − | 0.957120i | \(-0.406448\pi\) | ||||
0.289691 | + | 0.957120i | \(0.406448\pi\) | |||||||
\(578\) | 1.42826e9 | 0.307653 | ||||||||
\(579\) | 4.65164e9 | 0.995936 | ||||||||
\(580\) | −1.21002e9 | −0.257510 | ||||||||
\(581\) | −8.07129e8 | −0.170737 | ||||||||
\(582\) | −6.11443e8 | −0.128566 | ||||||||
\(583\) | −9.03847e8 | −0.188910 | ||||||||
\(584\) | 5.49777e6 | 0.00114220 | ||||||||
\(585\) | −7.03937e8 | −0.145375 | ||||||||
\(586\) | −3.74922e9 | −0.769660 | ||||||||
\(587\) | 4.23836e9 | 0.864898 | 0.432449 | − | 0.901658i | \(-0.357650\pi\) | ||||
0.432449 | + | 0.901658i | \(0.357650\pi\) | |||||||
\(588\) | 2.15571e9 | 0.437291 | ||||||||
\(589\) | −9.91288e9 | −1.99892 | ||||||||
\(590\) | 7.99440e7 | 0.0160252 | ||||||||
\(591\) | −3.44526e9 | −0.686541 | ||||||||
\(592\) | −3.02129e9 | −0.598503 | ||||||||
\(593\) | −5.59276e9 | −1.10137 | −0.550687 | − | 0.834712i | \(-0.685634\pi\) | ||||
−0.550687 | + | 0.834712i | \(0.685634\pi\) | |||||||
\(594\) | 3.33476e8 | 0.0652847 | ||||||||
\(595\) | −4.43387e8 | −0.0862926 | ||||||||
\(596\) | −1.08020e8 | −0.0208999 | ||||||||
\(597\) | −1.74797e9 | −0.336220 | ||||||||
\(598\) | −2.63109e9 | −0.503132 | ||||||||
\(599\) | −2.76072e9 | −0.524842 | −0.262421 | − | 0.964953i | \(-0.584521\pi\) | ||||
−0.262421 | + | 0.964953i | \(0.584521\pi\) | |||||||
\(600\) | 2.25507e9 | 0.426218 | ||||||||
\(601\) | −3.38464e9 | −0.635992 | −0.317996 | − | 0.948092i | \(-0.603010\pi\) | ||||
−0.317996 | + | 0.948092i | \(0.603010\pi\) | |||||||
\(602\) | −6.34598e8 | −0.118552 | ||||||||
\(603\) | 2.09328e9 | 0.388791 | ||||||||
\(604\) | −5.98054e9 | −1.10436 | ||||||||
\(605\) | 6.27403e8 | 0.115187 | ||||||||
\(606\) | −2.31190e9 | −0.422003 | ||||||||
\(607\) | 3.57949e9 | 0.649622 | 0.324811 | − | 0.945779i | \(-0.394699\pi\) | ||||
0.324811 | + | 0.945779i | \(0.394699\pi\) | |||||||
\(608\) | 7.66483e9 | 1.38306 | ||||||||
\(609\) | 8.88210e8 | 0.159351 | ||||||||
\(610\) | 1.94168e8 | 0.0346356 | ||||||||
\(611\) | −7.31310e9 | −1.29705 | ||||||||
\(612\) | 1.97596e9 | 0.348455 | ||||||||
\(613\) | 9.92114e9 | 1.73960 | 0.869801 | − | 0.493403i | \(-0.164247\pi\) | ||||
0.869801 | + | 0.493403i | \(0.164247\pi\) | |||||||
\(614\) | 3.48564e9 | 0.607706 | ||||||||
\(615\) | 1.12415e9 | 0.194877 | ||||||||
\(616\) | 8.47929e8 | 0.146160 | ||||||||
\(617\) | −2.67237e9 | −0.458034 | −0.229017 | − | 0.973422i | \(-0.573551\pi\) | ||||
−0.229017 | + | 0.973422i | \(0.573551\pi\) | |||||||
\(618\) | −5.67556e8 | −0.0967272 | ||||||||
\(619\) | 5.77104e9 | 0.977996 | 0.488998 | − | 0.872285i | \(-0.337363\pi\) | ||||
0.488998 | + | 0.872285i | \(0.337363\pi\) | |||||||
\(620\) | −1.90960e9 | −0.321789 | ||||||||
\(621\) | −8.29019e8 | −0.138913 | ||||||||
\(622\) | 6.41044e8 | 0.106812 | ||||||||
\(623\) | −2.27119e9 | −0.376309 | ||||||||
\(624\) | 2.46986e9 | 0.406936 | ||||||||
\(625\) | 4.72951e9 | 0.774882 | ||||||||
\(626\) | −4.88895e9 | −0.796536 | ||||||||
\(627\) | 3.77406e9 | 0.611466 | ||||||||
\(628\) | −4.19610e9 | −0.676064 | ||||||||
\(629\) | 1.08388e10 | 1.73662 | ||||||||
\(630\) | 6.15282e7 | 0.00980352 | ||||||||
\(631\) | −1.33017e9 | −0.210768 | −0.105384 | − | 0.994432i | \(-0.533607\pi\) | ||||
−0.105384 | + | 0.994432i | \(0.533607\pi\) | |||||||
\(632\) | 1.63844e9 | 0.258178 | ||||||||
\(633\) | 3.84930e9 | 0.603210 | ||||||||
\(634\) | −4.51141e9 | −0.703072 | ||||||||
\(635\) | 1.05541e9 | 0.163574 | ||||||||
\(636\) | 7.43188e8 | 0.114551 | ||||||||
\(637\) | −9.66667e9 | −1.48180 | ||||||||
\(638\) | −2.57044e9 | −0.391864 | ||||||||
\(639\) | 7.88605e8 | 0.119566 | ||||||||
\(640\) | 1.84266e9 | 0.277853 | ||||||||
\(641\) | 8.97295e8 | 0.134565 | 0.0672825 | − | 0.997734i | \(-0.478567\pi\) | ||||
0.0672825 | + | 0.997734i | \(0.478567\pi\) | |||||||
\(642\) | −1.62956e9 | −0.243051 | ||||||||
\(643\) | 7.92605e9 | 1.17576 | 0.587879 | − | 0.808949i | \(-0.299963\pi\) | ||||
0.587879 | + | 0.808949i | \(0.299963\pi\) | |||||||
\(644\) | −9.38988e8 | −0.138535 | ||||||||
\(645\) | −1.22149e9 | −0.179238 | ||||||||
\(646\) | −5.47693e9 | −0.799325 | ||||||||
\(647\) | −9.72853e9 | −1.41215 | −0.706077 | − | 0.708135i | \(-0.749537\pi\) | ||||
−0.706077 | + | 0.708135i | \(0.749537\pi\) | |||||||
\(648\) | −6.15557e8 | −0.0888701 | ||||||||
\(649\) | −6.93403e8 | −0.0995702 | ||||||||
\(650\) | −4.50450e9 | −0.643354 | ||||||||
\(651\) | 1.40173e9 | 0.199128 | ||||||||
\(652\) | 7.67968e9 | 1.08512 | ||||||||
\(653\) | −4.58349e9 | −0.644170 | −0.322085 | − | 0.946711i | \(-0.604384\pi\) | ||||
−0.322085 | + | 0.946711i | \(0.604384\pi\) | |||||||
\(654\) | −2.65592e9 | −0.371273 | ||||||||
\(655\) | 1.00389e9 | 0.139586 | ||||||||
\(656\) | −3.94423e9 | −0.545505 | ||||||||
\(657\) | −3.46020e6 | −0.000476017 0 | ||||||||
\(658\) | 6.39208e8 | 0.0874684 | ||||||||
\(659\) | −1.15331e9 | −0.156982 | −0.0784908 | − | 0.996915i | \(-0.525010\pi\) | ||||
−0.0784908 | + | 0.996915i | \(0.525010\pi\) | |||||||
\(660\) | 7.27027e8 | 0.0984344 | ||||||||
\(661\) | −1.03408e8 | −0.0139267 | −0.00696334 | − | 0.999976i | \(-0.502217\pi\) | ||||
−0.00696334 | + | 0.999976i | \(0.502217\pi\) | |||||||
\(662\) | −5.85139e9 | −0.783892 | ||||||||
\(663\) | −8.86059e9 | −1.18077 | ||||||||
\(664\) | −4.31161e9 | −0.571546 | ||||||||
\(665\) | 6.96335e8 | 0.0918211 | ||||||||
\(666\) | −1.50409e9 | −0.197294 | ||||||||
\(667\) | 6.39011e9 | 0.833812 | ||||||||
\(668\) | 5.87530e9 | 0.762628 | ||||||||
\(669\) | 6.35796e9 | 0.820968 | ||||||||
\(670\) | −1.11771e9 | −0.143571 | ||||||||
\(671\) | −1.68414e9 | −0.215203 | ||||||||
\(672\) | −1.08385e9 | −0.137777 | ||||||||
\(673\) | −8.65901e9 | −1.09500 | −0.547502 | − | 0.836804i | \(-0.684421\pi\) | ||||
−0.547502 | + | 0.836804i | \(0.684421\pi\) | |||||||
\(674\) | 6.18795e9 | 0.778461 | ||||||||
\(675\) | −1.41930e9 | −0.177628 | ||||||||
\(676\) | −9.48174e9 | −1.18052 | ||||||||
\(677\) | 1.41759e10 | 1.75586 | 0.877930 | − | 0.478789i | \(-0.158924\pi\) | ||||
0.877930 | + | 0.478789i | \(0.158924\pi\) | |||||||
\(678\) | −1.02283e9 | −0.126038 | ||||||||
\(679\) | 9.78511e8 | 0.119956 | ||||||||
\(680\) | −2.36853e9 | −0.288867 | ||||||||
\(681\) | 9.04908e9 | 1.09797 | ||||||||
\(682\) | −4.05656e9 | −0.489681 | ||||||||
\(683\) | 2.10450e9 | 0.252742 | 0.126371 | − | 0.991983i | \(-0.459667\pi\) | ||||
0.126371 | + | 0.991983i | \(0.459667\pi\) | |||||||
\(684\) | −3.10322e9 | −0.370780 | ||||||||
\(685\) | 5.94072e8 | 0.0706191 | ||||||||
\(686\) | 1.74100e9 | 0.205904 | ||||||||
\(687\) | −4.54225e9 | −0.534469 | ||||||||
\(688\) | 4.28575e9 | 0.501727 | ||||||||
\(689\) | −3.33261e9 | −0.388166 | ||||||||
\(690\) | 4.42656e8 | 0.0512973 | ||||||||
\(691\) | 8.19673e9 | 0.945078 | 0.472539 | − | 0.881310i | \(-0.343338\pi\) | ||||
0.472539 | + | 0.881310i | \(0.343338\pi\) | |||||||
\(692\) | −6.93017e9 | −0.795010 | ||||||||
\(693\) | −5.33672e8 | −0.0609127 | ||||||||
\(694\) | −2.95787e9 | −0.335909 | ||||||||
\(695\) | −3.78272e8 | −0.0427423 | ||||||||
\(696\) | 4.74474e9 | 0.533433 | ||||||||
\(697\) | 1.41499e10 | 1.58284 | ||||||||
\(698\) | 5.81493e9 | 0.647218 | ||||||||
\(699\) | −7.45621e9 | −0.825749 | ||||||||
\(700\) | −1.60757e9 | −0.177145 | ||||||||
\(701\) | −1.58794e9 | −0.174109 | −0.0870547 | − | 0.996204i | \(-0.527745\pi\) | ||||
−0.0870547 | + | 0.996204i | \(0.527745\pi\) | |||||||
\(702\) | 1.22957e9 | 0.134145 | ||||||||
\(703\) | −1.70223e10 | −1.84788 | ||||||||
\(704\) | −3.90082e7 | −0.00421358 | ||||||||
\(705\) | 1.23036e9 | 0.132242 | ||||||||
\(706\) | −2.63994e9 | −0.282344 | ||||||||
\(707\) | 3.69981e9 | 0.393741 | ||||||||
\(708\) | 5.70151e8 | 0.0603773 | ||||||||
\(709\) | −1.39994e10 | −1.47519 | −0.737596 | − | 0.675242i | \(-0.764039\pi\) | ||||
−0.737596 | + | 0.675242i | \(0.764039\pi\) | |||||||
\(710\) | −4.21077e8 | −0.0441527 | ||||||||
\(711\) | −1.03120e9 | −0.107597 | ||||||||
\(712\) | −1.21325e10 | −1.25971 | ||||||||
\(713\) | 1.00846e10 | 1.04195 | ||||||||
\(714\) | 7.74467e8 | 0.0796268 | ||||||||
\(715\) | −3.26014e9 | −0.333553 | ||||||||
\(716\) | −5.55525e9 | −0.565598 | ||||||||
\(717\) | 4.45417e9 | 0.451284 | ||||||||
\(718\) | 5.51968e9 | 0.556517 | ||||||||
\(719\) | −3.63177e8 | −0.0364391 | −0.0182195 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182195 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(720\) | −4.15530e8 | −0.0414896 | ||||||||
\(721\) | 9.08277e8 | 0.0902495 | ||||||||
\(722\) | 4.11589e9 | 0.406990 | ||||||||
\(723\) | 5.93470e9 | 0.584002 | ||||||||
\(724\) | 3.06594e9 | 0.300247 | ||||||||
\(725\) | 1.09401e10 | 1.06619 | ||||||||
\(726\) | −1.09589e9 | −0.106289 | ||||||||
\(727\) | −7.18128e9 | −0.693157 | −0.346578 | − | 0.938021i | \(-0.612657\pi\) | ||||
−0.346578 | + | 0.938021i | \(0.612657\pi\) | |||||||
\(728\) | 3.12643e9 | 0.300324 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.84758e6 | 0.000175782 0 | ||||||||
\(731\) | −1.53751e10 | −1.45582 | ||||||||
\(732\) | 1.38478e9 | 0.130495 | ||||||||
\(733\) | 1.12100e10 | 1.05133 | 0.525667 | − | 0.850691i | \(-0.323816\pi\) | ||||
0.525667 | + | 0.850691i | \(0.323816\pi\) | |||||||
\(734\) | 6.10985e9 | 0.570288 | ||||||||
\(735\) | 1.62633e9 | 0.151078 | ||||||||
\(736\) | −7.79760e9 | −0.720922 | ||||||||
\(737\) | 9.69459e9 | 0.892059 | ||||||||
\(738\) | −1.96356e9 | −0.179824 | ||||||||
\(739\) | −2.61736e9 | −0.238566 | −0.119283 | − | 0.992860i | \(-0.538060\pi\) | ||||
−0.119283 | + | 0.992860i | \(0.538060\pi\) | |||||||
\(740\) | −3.27914e9 | −0.297474 | ||||||||
\(741\) | 1.39155e10 | 1.25642 | ||||||||
\(742\) | 2.91289e8 | 0.0261765 | ||||||||
\(743\) | −2.16513e10 | −1.93653 | −0.968264 | − | 0.249930i | \(-0.919593\pi\) | ||||
−0.968264 | + | 0.249930i | \(0.919593\pi\) | |||||||
\(744\) | 7.48794e9 | 0.666587 | ||||||||
\(745\) | −8.14933e7 | −0.00722063 | ||||||||
\(746\) | 2.77802e9 | 0.244991 | ||||||||
\(747\) | 2.71365e9 | 0.238194 | ||||||||
\(748\) | 9.15123e9 | 0.799510 | ||||||||
\(749\) | 2.60783e9 | 0.226774 | ||||||||
\(750\) | 1.57892e9 | 0.136661 | ||||||||
\(751\) | −1.23735e10 | −1.06599 | −0.532995 | − | 0.846118i | \(-0.678934\pi\) | ||||
−0.532995 | + | 0.846118i | \(0.678934\pi\) | |||||||
\(752\) | −4.31689e9 | −0.370176 | ||||||||
\(753\) | −7.14750e9 | −0.610059 | ||||||||
\(754\) | −9.47759e9 | −0.805190 | ||||||||
\(755\) | −4.51187e9 | −0.381542 | ||||||||
\(756\) | 4.38812e8 | 0.0369362 | ||||||||
\(757\) | −1.68097e9 | −0.140840 | −0.0704198 | − | 0.997517i | \(-0.522434\pi\) | ||||
−0.0704198 | + | 0.997517i | \(0.522434\pi\) | |||||||
\(758\) | −1.24014e9 | −0.103426 | ||||||||
\(759\) | −3.83943e9 | −0.318728 | ||||||||
\(760\) | 3.71976e9 | 0.307374 | ||||||||
\(761\) | 1.31161e10 | 1.07884 | 0.539421 | − | 0.842036i | \(-0.318643\pi\) | ||||
0.539421 | + | 0.842036i | \(0.318643\pi\) | |||||||
\(762\) | −1.84350e9 | −0.150939 | ||||||||
\(763\) | 4.25036e9 | 0.346409 | ||||||||
\(764\) | 1.06035e10 | 0.860246 | ||||||||
\(765\) | 1.49071e9 | 0.120387 | ||||||||
\(766\) | −3.01011e6 | −0.000241981 0 | ||||||||
\(767\) | −2.55668e9 | −0.204593 | ||||||||
\(768\) | −3.17866e9 | −0.253209 | ||||||||
\(769\) | 1.42811e10 | 1.13245 | 0.566224 | − | 0.824251i | \(-0.308404\pi\) | ||||
0.566224 | + | 0.824251i | \(0.308404\pi\) | |||||||
\(770\) | 2.84955e8 | 0.0224936 | ||||||||
\(771\) | −6.47392e9 | −0.508718 | ||||||||
\(772\) | −1.77138e10 | −1.38565 | ||||||||
\(773\) | −8.34783e9 | −0.650048 | −0.325024 | − | 0.945706i | \(-0.605372\pi\) | ||||
−0.325024 | + | 0.945706i | \(0.605372\pi\) | |||||||
\(774\) | 2.13358e9 | 0.165393 | ||||||||
\(775\) | 1.72651e10 | 1.33233 | ||||||||
\(776\) | 5.22711e9 | 0.401556 | ||||||||
\(777\) | 2.40704e9 | 0.184082 | ||||||||
\(778\) | −4.47669e9 | −0.340823 | ||||||||
\(779\) | −2.22223e10 | −1.68425 | ||||||||
\(780\) | 2.68065e9 | 0.202260 | ||||||||
\(781\) | 3.65226e9 | 0.274336 | ||||||||
\(782\) | 5.57180e9 | 0.416651 | ||||||||
\(783\) | −2.98625e9 | −0.222311 | ||||||||
\(784\) | −5.70618e9 | −0.422902 | ||||||||
\(785\) | −3.16565e9 | −0.233571 | ||||||||
\(786\) | −1.75350e9 | −0.128803 | ||||||||
\(787\) | 1.47026e10 | 1.07518 | 0.537591 | − | 0.843206i | \(-0.319334\pi\) | ||||
0.537591 | + | 0.843206i | \(0.319334\pi\) | |||||||
\(788\) | 1.31199e10 | 0.955184 | ||||||||
\(789\) | 3.44685e9 | 0.249835 | ||||||||
\(790\) | 5.50613e8 | 0.0397330 | ||||||||
\(791\) | 1.63687e9 | 0.117597 | ||||||||
\(792\) | −2.85083e9 | −0.203907 | ||||||||
\(793\) | −6.20965e9 | −0.442192 | ||||||||
\(794\) | −4.81135e9 | −0.341111 | ||||||||
\(795\) | 5.60681e8 | 0.0395759 | ||||||||
\(796\) | 6.65640e9 | 0.467782 | ||||||||
\(797\) | 3.94070e9 | 0.275721 | 0.137860 | − | 0.990452i | \(-0.455977\pi\) | ||||
0.137860 | + | 0.990452i | \(0.455977\pi\) | |||||||
\(798\) | −1.21629e9 | −0.0847282 | ||||||||
\(799\) | 1.54868e10 | 1.07411 | ||||||||
\(800\) | −1.33497e10 | −0.921843 | ||||||||
\(801\) | 7.63597e9 | 0.524989 | ||||||||
\(802\) | 9.17467e9 | 0.628030 | ||||||||
\(803\) | −1.60252e7 | −0.00109219 | ||||||||
\(804\) | −7.97138e9 | −0.540925 | ||||||||
\(805\) | −7.08397e8 | −0.0478620 | ||||||||
\(806\) | −1.49571e10 | −1.00618 | ||||||||
\(807\) | 5.35167e9 | 0.358452 | ||||||||
\(808\) | 1.97640e10 | 1.31806 | ||||||||
\(809\) | 2.12121e10 | 1.40852 | 0.704260 | − | 0.709942i | \(-0.251279\pi\) | ||||
0.704260 | + | 0.709942i | \(0.251279\pi\) | |||||||
\(810\) | −2.06864e8 | −0.0136769 | ||||||||
\(811\) | 4.13209e9 | 0.272018 | 0.136009 | − | 0.990708i | \(-0.456572\pi\) | ||||
0.136009 | + | 0.990708i | \(0.456572\pi\) | |||||||
\(812\) | −3.38238e9 | −0.221705 | ||||||||
\(813\) | 3.16329e9 | 0.206453 | ||||||||
\(814\) | −6.96589e9 | −0.452680 | ||||||||
\(815\) | 5.79375e9 | 0.374893 | ||||||||
\(816\) | −5.23036e9 | −0.336989 | ||||||||
\(817\) | 2.41465e10 | 1.54909 | ||||||||
\(818\) | −3.58821e9 | −0.229214 | ||||||||
\(819\) | −1.96772e9 | −0.125161 | ||||||||
\(820\) | −4.28085e9 | −0.271133 | ||||||||
\(821\) | 4.99283e9 | 0.314880 | 0.157440 | − | 0.987529i | \(-0.449676\pi\) | ||||
0.157440 | + | 0.987529i | \(0.449676\pi\) | |||||||
\(822\) | −1.03767e9 | −0.0651640 | ||||||||
\(823\) | 8.56606e9 | 0.535650 | 0.267825 | − | 0.963468i | \(-0.413695\pi\) | ||||
0.267825 | + | 0.963468i | \(0.413695\pi\) | |||||||
\(824\) | 4.85193e9 | 0.302113 | ||||||||
\(825\) | −6.57321e9 | −0.407557 | ||||||||
\(826\) | 2.23468e8 | 0.0137970 | ||||||||
\(827\) | 2.19884e10 | 1.35184 | 0.675920 | − | 0.736975i | \(-0.263747\pi\) | ||||
0.675920 | + | 0.736975i | \(0.263747\pi\) | |||||||
\(828\) | 3.15697e9 | 0.193270 | ||||||||
\(829\) | −1.74819e9 | −0.106573 | −0.0532867 | − | 0.998579i | \(-0.516970\pi\) | ||||
−0.0532867 | + | 0.998579i | \(0.516970\pi\) | |||||||
\(830\) | −1.44896e9 | −0.0879595 | ||||||||
\(831\) | 7.56004e9 | 0.457005 | ||||||||
\(832\) | −1.43829e8 | −0.00865792 | ||||||||
\(833\) | 2.04709e10 | 1.22710 | ||||||||
\(834\) | 6.60730e8 | 0.0394406 | ||||||||
\(835\) | 4.43248e9 | 0.263478 | ||||||||
\(836\) | −1.43719e10 | −0.850732 | ||||||||
\(837\) | −4.71277e9 | −0.277803 | ||||||||
\(838\) | 1.11842e10 | 0.656523 | ||||||||
\(839\) | 7.57544e8 | 0.0442834 | 0.0221417 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221417 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(840\) | −5.25993e8 | −0.0306198 | ||||||||
\(841\) | 5.76829e9 | 0.334396 | ||||||||
\(842\) | 7.48251e9 | 0.431972 | ||||||||
\(843\) | −1.66509e9 | −0.0957284 | ||||||||
\(844\) | −1.46584e10 | −0.839246 | ||||||||
\(845\) | −7.15327e9 | −0.407855 | ||||||||
\(846\) | −2.14908e9 | −0.122027 | ||||||||
\(847\) | 1.75379e9 | 0.0991710 | ||||||||
\(848\) | −1.96722e9 | −0.110782 | ||||||||
\(849\) | −1.67511e10 | −0.939433 | ||||||||
\(850\) | 9.53908e9 | 0.532771 | ||||||||
\(851\) | 1.73172e10 | 0.963215 | ||||||||
\(852\) | −3.00307e9 | −0.166352 | ||||||||
\(853\) | −1.72683e9 | −0.0952636 | −0.0476318 | − | 0.998865i | \(-0.515167\pi\) | ||||
−0.0476318 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(854\) | 5.42759e8 | 0.0298198 | ||||||||
\(855\) | −2.34115e9 | −0.128100 | ||||||||
\(856\) | 1.39308e10 | 0.759132 | ||||||||
\(857\) | −3.43055e10 | −1.86179 | −0.930895 | − | 0.365286i | \(-0.880971\pi\) | ||||
−0.930895 | + | 0.365286i | \(0.880971\pi\) | |||||||
\(858\) | 5.69451e9 | 0.307787 | ||||||||
\(859\) | −1.16013e10 | −0.624499 | −0.312249 | − | 0.950000i | \(-0.601082\pi\) | ||||
−0.312249 | + | 0.950000i | \(0.601082\pi\) | |||||||
\(860\) | 4.65153e9 | 0.249374 | ||||||||
\(861\) | 3.14234e9 | 0.167781 | ||||||||
\(862\) | 1.33619e10 | 0.710549 | ||||||||
\(863\) | 1.06656e10 | 0.564870 | 0.282435 | − | 0.959286i | \(-0.408858\pi\) | ||||
0.282435 | + | 0.959286i | \(0.408858\pi\) | |||||||
\(864\) | 3.64401e9 | 0.192212 | ||||||||
\(865\) | −5.22830e9 | −0.274665 | ||||||||
\(866\) | 3.56005e8 | 0.0186270 | ||||||||
\(867\) | 7.68474e9 | 0.400463 | ||||||||
\(868\) | −5.33792e9 | −0.277047 | ||||||||
\(869\) | −4.77580e9 | −0.246875 | ||||||||
\(870\) | 1.59452e9 | 0.0820940 | ||||||||
\(871\) | 3.57453e10 | 1.83297 | ||||||||
\(872\) | 2.27050e10 | 1.15962 | ||||||||
\(873\) | −3.28985e9 | −0.167350 | ||||||||
\(874\) | −8.75046e9 | −0.443344 | ||||||||
\(875\) | −2.52679e9 | −0.127509 | ||||||||
\(876\) | 1.31767e7 | 0.000662282 0 | ||||||||
\(877\) | −5.25940e9 | −0.263292 | −0.131646 | − | 0.991297i | \(-0.542026\pi\) | ||||
−0.131646 | + | 0.991297i | \(0.542026\pi\) | |||||||
\(878\) | 3.14503e8 | 0.0156817 | ||||||||
\(879\) | −2.01726e10 | −1.00184 | ||||||||
\(880\) | −1.92444e9 | −0.0951954 | ||||||||
\(881\) | −2.79482e10 | −1.37701 | −0.688507 | − | 0.725230i | \(-0.741734\pi\) | ||||
−0.688507 | + | 0.725230i | \(0.741734\pi\) | |||||||
\(882\) | −2.84072e9 | −0.139408 | ||||||||
\(883\) | 3.72423e9 | 0.182043 | 0.0910214 | − | 0.995849i | \(-0.470987\pi\) | ||||
0.0910214 | + | 0.995849i | \(0.470987\pi\) | |||||||
\(884\) | 3.37419e10 | 1.64281 | ||||||||
\(885\) | 4.30137e8 | 0.0208596 | ||||||||
\(886\) | −3.22157e9 | −0.155614 | ||||||||
\(887\) | 6.26596e9 | 0.301477 | 0.150739 | − | 0.988574i | \(-0.451835\pi\) | ||||
0.150739 | + | 0.988574i | \(0.451835\pi\) | |||||||
\(888\) | 1.28582e10 | 0.616219 | ||||||||
\(889\) | 2.95021e9 | 0.140830 | ||||||||
\(890\) | −4.07724e9 | −0.193866 | ||||||||
\(891\) | 1.79426e9 | 0.0849793 | ||||||||
\(892\) | −2.42116e10 | −1.14221 | ||||||||
\(893\) | −2.43219e10 | −1.14292 | ||||||||
\(894\) | 1.42345e8 | 0.00666286 | ||||||||
\(895\) | −4.19102e9 | −0.195407 | ||||||||
\(896\) | 5.15081e9 | 0.239220 | ||||||||
\(897\) | −1.41565e10 | −0.654912 | ||||||||
\(898\) | −1.39257e10 | −0.641727 | ||||||||
\(899\) | 3.63263e10 | 1.66748 | ||||||||
\(900\) | 5.40483e9 | 0.247134 | ||||||||
\(901\) | 7.05740e9 | 0.321446 | ||||||||
\(902\) | −9.09382e9 | −0.412594 | ||||||||
\(903\) | −3.41444e9 | −0.154316 | ||||||||
\(904\) | 8.74403e9 | 0.393661 | ||||||||
\(905\) | 2.31302e9 | 0.103731 | ||||||||
\(906\) | 7.88092e9 | 0.352069 | ||||||||
\(907\) | 8.21053e9 | 0.365381 | 0.182690 | − | 0.983170i | \(-0.441519\pi\) | ||||
0.182690 | + | 0.983170i | \(0.441519\pi\) | |||||||
\(908\) | −3.44596e10 | −1.52760 | ||||||||
\(909\) | −1.24391e10 | −0.549309 | ||||||||
\(910\) | 1.05067e9 | 0.0462191 | ||||||||
\(911\) | −1.57505e10 | −0.690207 | −0.345103 | − | 0.938565i | \(-0.612156\pi\) | ||||
−0.345103 | + | 0.938565i | \(0.612156\pi\) | |||||||
\(912\) | 8.21423e9 | 0.358579 | ||||||||
\(913\) | 1.25677e10 | 0.546523 | ||||||||
\(914\) | 1.90385e10 | 0.824746 | ||||||||
\(915\) | 1.04472e9 | 0.0450842 | ||||||||
\(916\) | 1.72973e10 | 0.743607 | ||||||||
\(917\) | 2.80618e9 | 0.120177 | ||||||||
\(918\) | −2.60384e9 | −0.111087 | ||||||||
\(919\) | −6.94140e9 | −0.295014 | −0.147507 | − | 0.989061i | \(-0.547125\pi\) | ||||
−0.147507 | + | 0.989061i | \(0.547125\pi\) | |||||||
\(920\) | −3.78419e9 | −0.160220 | ||||||||
\(921\) | 1.87544e10 | 0.791034 | ||||||||
\(922\) | −1.87773e10 | −0.788994 | ||||||||
\(923\) | 1.34664e10 | 0.563697 | ||||||||
\(924\) | 2.03227e9 | 0.0847478 | ||||||||
\(925\) | 2.96475e10 | 1.23166 | ||||||||
\(926\) | 8.46318e9 | 0.350264 | ||||||||
\(927\) | −3.05372e9 | −0.125907 | ||||||||
\(928\) | −2.80881e10 | −1.15373 | ||||||||
\(929\) | −1.64084e9 | −0.0671448 | −0.0335724 | − | 0.999436i | \(-0.510688\pi\) | ||||
−0.0335724 | + | 0.999436i | \(0.510688\pi\) | |||||||
\(930\) | 2.51639e9 | 0.102586 | ||||||||
\(931\) | −3.21493e10 | −1.30571 | ||||||||
\(932\) | 2.83939e10 | 1.14887 | ||||||||
\(933\) | 3.44912e9 | 0.139035 | ||||||||
\(934\) | −9.55004e8 | −0.0383523 | ||||||||
\(935\) | 6.90393e9 | 0.276220 | ||||||||
\(936\) | −1.05114e10 | −0.418981 | ||||||||
\(937\) | 3.84565e10 | 1.52715 | 0.763575 | − | 0.645719i | \(-0.223442\pi\) | ||||
0.763575 | + | 0.645719i | \(0.223442\pi\) | |||||||
\(938\) | −3.12435e9 | −0.123609 | ||||||||
\(939\) | −2.63049e10 | −1.03683 | ||||||||
\(940\) | −4.68532e9 | −0.183989 | ||||||||
\(941\) | 3.13483e10 | 1.22645 | 0.613226 | − | 0.789907i | \(-0.289871\pi\) | ||||
0.613226 | + | 0.789907i | \(0.289871\pi\) | |||||||
\(942\) | 5.52946e9 | 0.215529 | ||||||||
\(943\) | 2.26072e10 | 0.877921 | ||||||||
\(944\) | −1.50919e9 | −0.0583905 | ||||||||
\(945\) | 3.31051e8 | 0.0127610 | ||||||||
\(946\) | 9.88124e9 | 0.379483 | ||||||||
\(947\) | −4.56816e10 | −1.74790 | −0.873950 | − | 0.486016i | \(-0.838450\pi\) | ||||
−0.873950 | + | 0.486016i | \(0.838450\pi\) | |||||||
\(948\) | 3.92691e9 | 0.149700 | ||||||||
\(949\) | −5.90871e7 | −0.00224420 | ||||||||
\(950\) | −1.49810e10 | −0.566903 | ||||||||
\(951\) | −2.42735e10 | −0.915168 | ||||||||
\(952\) | −6.62078e9 | −0.248702 | ||||||||
\(953\) | −2.57557e10 | −0.963937 | −0.481968 | − | 0.876189i | \(-0.660078\pi\) | ||||
−0.481968 | + | 0.876189i | \(0.660078\pi\) | |||||||
\(954\) | −9.79345e8 | −0.0365188 | ||||||||
\(955\) | 7.99955e9 | 0.297204 | ||||||||
\(956\) | −1.69619e10 | −0.627872 | ||||||||
\(957\) | −1.38302e10 | −0.510079 | ||||||||
\(958\) | 5.24327e9 | 0.192674 | ||||||||
\(959\) | 1.66061e9 | 0.0608000 | ||||||||
\(960\) | 2.41978e7 | 0.000882728 0 | ||||||||
\(961\) | 2.98159e10 | 1.08372 | ||||||||
\(962\) | −2.56842e10 | −0.930151 | ||||||||
\(963\) | −8.76779e9 | −0.316372 | ||||||||
\(964\) | −2.25998e10 | −0.812522 | ||||||||
\(965\) | −1.33638e10 | −0.478723 | ||||||||
\(966\) | 1.23736e9 | 0.0441648 | ||||||||
\(967\) | 2.61784e10 | 0.931002 | 0.465501 | − | 0.885047i | \(-0.345874\pi\) | ||||
0.465501 | + | 0.885047i | \(0.345874\pi\) | |||||||
\(968\) | 9.36857e9 | 0.331978 | ||||||||
\(969\) | −2.94685e10 | −1.04046 | ||||||||
\(970\) | 1.75662e9 | 0.0617984 | ||||||||
\(971\) | −7.63541e9 | −0.267648 | −0.133824 | − | 0.991005i | \(-0.542726\pi\) | ||||
−0.133824 | + | 0.991005i | \(0.542726\pi\) | |||||||
\(972\) | −1.47533e9 | −0.0515296 | ||||||||
\(973\) | −1.05739e9 | −0.0367993 | ||||||||
\(974\) | −2.27050e10 | −0.787344 | ||||||||
\(975\) | −2.42364e10 | −0.837435 | ||||||||
\(976\) | −3.66552e9 | −0.126201 | ||||||||
\(977\) | −1.18991e10 | −0.408211 | −0.204105 | − | 0.978949i | \(-0.565429\pi\) | ||||
−0.204105 | + | 0.978949i | \(0.565429\pi\) | |||||||
\(978\) | −1.01200e10 | −0.345934 | ||||||||
\(979\) | 3.53644e10 | 1.20456 | ||||||||
\(980\) | −6.19319e9 | −0.210195 | ||||||||
\(981\) | −1.42901e10 | −0.483275 | ||||||||
\(982\) | 6.43144e9 | 0.216729 | ||||||||
\(983\) | −3.88296e10 | −1.30384 | −0.651921 | − | 0.758287i | \(-0.726037\pi\) | ||||
−0.651921 | + | 0.758287i | \(0.726037\pi\) | |||||||
\(984\) | 1.67861e10 | 0.561652 | ||||||||
\(985\) | 9.89796e9 | 0.330004 | ||||||||
\(986\) | 2.00705e10 | 0.666789 | ||||||||
\(987\) | 3.43924e9 | 0.113855 | ||||||||
\(988\) | −5.29913e10 | −1.74806 | ||||||||
\(989\) | −2.45647e10 | −0.807467 | ||||||||
\(990\) | −9.58048e8 | −0.0313808 | ||||||||
\(991\) | −4.18861e10 | −1.36714 | −0.683569 | − | 0.729886i | \(-0.739573\pi\) | ||||
−0.683569 | + | 0.729886i | \(0.739573\pi\) | |||||||
\(992\) | −4.43275e10 | −1.44172 | ||||||||
\(993\) | −3.14833e10 | −1.02037 | ||||||||
\(994\) | −1.17704e9 | −0.0380136 | ||||||||
\(995\) | 5.02176e9 | 0.161613 | ||||||||
\(996\) | −1.03338e10 | −0.331400 | ||||||||
\(997\) | −2.75354e10 | −0.879950 | −0.439975 | − | 0.898010i | \(-0.645013\pi\) | ||||
−0.439975 | + | 0.898010i | \(0.645013\pi\) | |||||||
\(998\) | −1.63709e10 | −0.521333 | ||||||||
\(999\) | −8.09273e9 | −0.256812 |
(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 | 177.8.a.b.1.12 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.d.1.6 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.12 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.d.1.6 | 17 | 3.2 | odd | 2 |