Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −118.157 | −1.30546 | −0.652731 | − | 0.757590i | \(-0.726377\pi\) | ||||
−0.652731 | + | 0.757590i | \(0.726377\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 5769.07 | 0.704232 | ||||||||
\(5\) | 218.169 | 0.00624437 | 0.00312218 | − | 0.999995i | \(-0.499006\pi\) | ||||
0.00312218 | + | 0.999995i | \(0.499006\pi\) | |||||||
\(6\) | −86136.4 | −0.753709 | ||||||||
\(7\) | 217680. | 0.699330 | 0.349665 | − | 0.936875i | \(-0.386295\pi\) | ||||
0.349665 | + | 0.936875i | \(0.386295\pi\) | |||||||
\(8\) | 286287. | 0.386114 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −25778.2 | −0.00815178 | ||||||||
\(11\) | 1.28409e6 | 0.218545 | 0.109273 | − | 0.994012i | \(-0.465148\pi\) | ||||
0.109273 | + | 0.994012i | \(0.465148\pi\) | |||||||
\(12\) | 4.20565e6 | 0.406588 | ||||||||
\(13\) | −2.15032e7 | −1.23558 | −0.617791 | − | 0.786342i | \(-0.711972\pi\) | ||||
−0.617791 | + | 0.786342i | \(0.711972\pi\) | |||||||
\(14\) | −2.57205e7 | −0.912949 | ||||||||
\(15\) | 159045. | 0.00360519 | ||||||||
\(16\) | −8.10869e7 | −1.20829 | ||||||||
\(17\) | −7.11178e7 | −0.714596 | −0.357298 | − | 0.933991i | \(-0.616302\pi\) | ||||
−0.357298 | + | 0.933991i | \(0.616302\pi\) | |||||||
\(18\) | −6.27934e7 | −0.435154 | ||||||||
\(19\) | 2.24678e8 | 1.09562 | 0.547812 | − | 0.836601i | \(-0.315461\pi\) | ||||
0.547812 | + | 0.836601i | \(0.315461\pi\) | |||||||
\(20\) | 1.25863e6 | 0.00439748 | ||||||||
\(21\) | 1.58689e8 | 0.403758 | ||||||||
\(22\) | −1.51724e8 | −0.285303 | ||||||||
\(23\) | −4.97569e8 | −0.700846 | −0.350423 | − | 0.936592i | \(-0.613962\pi\) | ||||
−0.350423 | + | 0.936592i | \(0.613962\pi\) | |||||||
\(24\) | 2.08703e8 | 0.222923 | ||||||||
\(25\) | −1.22066e9 | −0.999961 | ||||||||
\(26\) | 2.54076e9 | 1.61301 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 1.25581e9 | 0.492490 | ||||||||
\(29\) | −9.40726e8 | −0.293681 | −0.146841 | − | 0.989160i | \(-0.546910\pi\) | ||||
−0.146841 | + | 0.989160i | \(0.546910\pi\) | |||||||
\(30\) | −1.87923e7 | −0.00470643 | ||||||||
\(31\) | 1.59649e9 | 0.323084 | 0.161542 | − | 0.986866i | \(-0.448353\pi\) | ||||
0.161542 | + | 0.986866i | \(0.448353\pi\) | |||||||
\(32\) | 7.23572e9 | 1.19126 | ||||||||
\(33\) | 9.36098e8 | 0.126177 | ||||||||
\(34\) | 8.40306e9 | 0.932878 | ||||||||
\(35\) | 4.74912e7 | 0.00436687 | ||||||||
\(36\) | 3.06592e9 | 0.234744 | ||||||||
\(37\) | 2.40599e10 | 1.54164 | 0.770821 | − | 0.637052i | \(-0.219846\pi\) | ||||
0.770821 | + | 0.637052i | \(0.219846\pi\) | |||||||
\(38\) | −2.65473e10 | −1.43030 | ||||||||
\(39\) | −1.56759e10 | −0.713364 | ||||||||
\(40\) | 6.24589e7 | 0.00241104 | ||||||||
\(41\) | 7.98989e9 | 0.262691 | 0.131346 | − | 0.991337i | \(-0.458070\pi\) | ||||
0.131346 | + | 0.991337i | \(0.458070\pi\) | |||||||
\(42\) | −1.87502e10 | −0.527091 | ||||||||
\(43\) | −5.33738e10 | −1.28761 | −0.643803 | − | 0.765191i | \(-0.722645\pi\) | ||||
−0.643803 | + | 0.765191i | \(0.722645\pi\) | |||||||
\(44\) | 7.40797e9 | 0.153906 | ||||||||
\(45\) | 1.15944e8 | 0.00208146 | ||||||||
\(46\) | 5.87912e10 | 0.914927 | ||||||||
\(47\) | −2.52267e10 | −0.341369 | −0.170685 | − | 0.985326i | \(-0.554598\pi\) | ||||
−0.170685 | + | 0.985326i | \(0.554598\pi\) | |||||||
\(48\) | −5.91124e10 | −0.697606 | ||||||||
\(49\) | −4.95042e10 | −0.510937 | ||||||||
\(50\) | 1.44229e11 | 1.30541 | ||||||||
\(51\) | −5.18449e10 | −0.412572 | ||||||||
\(52\) | −1.24054e11 | −0.870137 | ||||||||
\(53\) | 1.07921e11 | 0.668825 | 0.334413 | − | 0.942427i | \(-0.391462\pi\) | ||||
0.334413 | + | 0.942427i | \(0.391462\pi\) | |||||||
\(54\) | −4.57764e10 | −0.251236 | ||||||||
\(55\) | 2.80148e8 | 0.00136468 | ||||||||
\(56\) | 6.23190e10 | 0.270021 | ||||||||
\(57\) | 1.63790e11 | 0.632559 | ||||||||
\(58\) | 1.11153e11 | 0.383390 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | 9.17543e8 | 0.00253889 | ||||||||
\(61\) | 4.38247e11 | 1.08912 | 0.544560 | − | 0.838722i | \(-0.316697\pi\) | ||||
0.544560 | + | 0.838722i | \(0.316697\pi\) | |||||||
\(62\) | −1.88637e11 | −0.421774 | ||||||||
\(63\) | 1.15684e11 | 0.233110 | ||||||||
\(64\) | −1.90687e11 | −0.346858 | ||||||||
\(65\) | −4.69134e9 | −0.00771543 | ||||||||
\(66\) | −1.10607e11 | −0.164720 | ||||||||
\(67\) | 1.41653e12 | 1.91311 | 0.956554 | − | 0.291556i | \(-0.0941731\pi\) | ||||
0.956554 | + | 0.291556i | \(0.0941731\pi\) | |||||||
\(68\) | −4.10283e11 | −0.503241 | ||||||||
\(69\) | −3.62728e11 | −0.404633 | ||||||||
\(70\) | −5.61141e9 | −0.00570079 | ||||||||
\(71\) | 1.03171e12 | 0.955824 | 0.477912 | − | 0.878408i | \(-0.341394\pi\) | ||||
0.477912 | + | 0.878408i | \(0.341394\pi\) | |||||||
\(72\) | 1.52144e11 | 0.128705 | ||||||||
\(73\) | −1.02339e12 | −0.791482 | −0.395741 | − | 0.918362i | \(-0.629512\pi\) | ||||
−0.395741 | + | 0.918362i | \(0.629512\pi\) | |||||||
\(74\) | −2.84285e12 | −2.01255 | ||||||||
\(75\) | −8.89858e11 | −0.577328 | ||||||||
\(76\) | 1.29618e12 | 0.771574 | ||||||||
\(77\) | 2.79520e11 | 0.152835 | ||||||||
\(78\) | 1.85221e12 | 0.931270 | ||||||||
\(79\) | 2.77802e12 | 1.28576 | 0.642880 | − | 0.765967i | \(-0.277739\pi\) | ||||
0.642880 | + | 0.765967i | \(0.277739\pi\) | |||||||
\(80\) | −1.76907e10 | −0.00754500 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −9.44061e11 | −0.342934 | ||||||||
\(83\) | 3.08697e12 | 1.03639 | 0.518196 | − | 0.855262i | \(-0.326604\pi\) | ||||
0.518196 | + | 0.855262i | \(0.326604\pi\) | |||||||
\(84\) | 9.15488e11 | 0.284339 | ||||||||
\(85\) | −1.55157e10 | −0.00446220 | ||||||||
\(86\) | 6.30649e12 | 1.68092 | ||||||||
\(87\) | −6.85790e11 | −0.169557 | ||||||||
\(88\) | 3.67616e11 | 0.0843835 | ||||||||
\(89\) | −3.67055e12 | −0.782881 | −0.391441 | − | 0.920203i | \(-0.628023\pi\) | ||||
−0.391441 | + | 0.920203i | \(0.628023\pi\) | |||||||
\(90\) | −1.36996e10 | −0.00271726 | ||||||||
\(91\) | −4.68083e12 | −0.864080 | ||||||||
\(92\) | −2.87051e12 | −0.493558 | ||||||||
\(93\) | 1.16384e12 | 0.186533 | ||||||||
\(94\) | 2.98071e12 | 0.445644 | ||||||||
\(95\) | 4.90178e10 | 0.00684148 | ||||||||
\(96\) | 5.27484e12 | 0.687775 | ||||||||
\(97\) | −1.37717e13 | −1.67869 | −0.839344 | − | 0.543600i | \(-0.817061\pi\) | ||||
−0.839344 | + | 0.543600i | \(0.817061\pi\) | |||||||
\(98\) | 5.84927e12 | 0.667009 | ||||||||
\(99\) | 6.82416e11 | 0.0728484 | ||||||||
\(100\) | −7.04204e12 | −0.704204 | ||||||||
\(101\) | −1.38391e13 | −1.29724 | −0.648618 | − | 0.761115i | \(-0.724653\pi\) | ||||
−0.648618 | + | 0.761115i | \(0.724653\pi\) | |||||||
\(102\) | 6.12583e12 | 0.538597 | ||||||||
\(103\) | −2.38900e12 | −0.197140 | −0.0985699 | − | 0.995130i | \(-0.531427\pi\) | ||||
−0.0985699 | + | 0.995130i | \(0.531427\pi\) | |||||||
\(104\) | −6.15609e12 | −0.477076 | ||||||||
\(105\) | 3.46211e10 | 0.00252122 | ||||||||
\(106\) | −1.27516e13 | −0.873126 | ||||||||
\(107\) | 1.77681e12 | 0.114458 | 0.0572289 | − | 0.998361i | \(-0.481774\pi\) | ||||
0.0572289 | + | 0.998361i | \(0.481774\pi\) | |||||||
\(108\) | 2.23505e12 | 0.135529 | ||||||||
\(109\) | −6.89102e12 | −0.393560 | −0.196780 | − | 0.980448i | \(-0.563049\pi\) | ||||
−0.196780 | + | 0.980448i | \(0.563049\pi\) | |||||||
\(110\) | −3.31014e10 | −0.00178153 | ||||||||
\(111\) | 1.75397e13 | 0.890067 | ||||||||
\(112\) | −1.76510e13 | −0.844993 | ||||||||
\(113\) | 1.27590e13 | 0.576511 | 0.288255 | − | 0.957554i | \(-0.406925\pi\) | ||||
0.288255 | + | 0.957554i | \(0.406925\pi\) | |||||||
\(114\) | −1.93529e13 | −0.825782 | ||||||||
\(115\) | −1.08554e11 | −0.00437634 | ||||||||
\(116\) | −5.42711e12 | −0.206820 | ||||||||
\(117\) | −1.14277e13 | −0.411861 | ||||||||
\(118\) | 4.98392e12 | 0.169957 | ||||||||
\(119\) | −1.54810e13 | −0.499738 | ||||||||
\(120\) | 4.55325e10 | 0.00139201 | ||||||||
\(121\) | −3.28738e13 | −0.952238 | ||||||||
\(122\) | −5.17820e13 | −1.42180 | ||||||||
\(123\) | 5.82463e12 | 0.151665 | ||||||||
\(124\) | 9.21027e12 | 0.227526 | ||||||||
\(125\) | −5.32629e11 | −0.0124885 | ||||||||
\(126\) | −1.36689e13 | −0.304316 | ||||||||
\(127\) | −9.02971e13 | −1.90963 | −0.954816 | − | 0.297198i | \(-0.903948\pi\) | ||||
−0.954816 | + | 0.297198i | \(0.903948\pi\) | |||||||
\(128\) | −3.67441e13 | −0.738452 | ||||||||
\(129\) | −3.89095e13 | −0.743400 | ||||||||
\(130\) | 5.54315e11 | 0.0100722 | ||||||||
\(131\) | 5.37302e13 | 0.928870 | 0.464435 | − | 0.885607i | \(-0.346257\pi\) | ||||
0.464435 | + | 0.885607i | \(0.346257\pi\) | |||||||
\(132\) | 5.40041e12 | 0.0888580 | ||||||||
\(133\) | 4.89080e13 | 0.766203 | ||||||||
\(134\) | −1.67373e14 | −2.49749 | ||||||||
\(135\) | 8.45232e10 | 0.00120173 | ||||||||
\(136\) | −2.03601e13 | −0.275916 | ||||||||
\(137\) | 1.09881e14 | 1.41984 | 0.709920 | − | 0.704283i | \(-0.248731\pi\) | ||||
0.709920 | + | 0.704283i | \(0.248731\pi\) | |||||||
\(138\) | 4.28588e13 | 0.528234 | ||||||||
\(139\) | 4.52947e13 | 0.532661 | 0.266331 | − | 0.963882i | \(-0.414189\pi\) | ||||
0.266331 | + | 0.963882i | \(0.414189\pi\) | |||||||
\(140\) | 2.73980e11 | 0.00307529 | ||||||||
\(141\) | −1.83903e13 | −0.197090 | ||||||||
\(142\) | −1.21904e14 | −1.24779 | ||||||||
\(143\) | −2.76120e13 | −0.270031 | ||||||||
\(144\) | −4.30929e13 | −0.402763 | ||||||||
\(145\) | −2.05237e11 | −0.00183385 | ||||||||
\(146\) | 1.20920e14 | 1.03325 | ||||||||
\(147\) | −3.60886e13 | −0.294990 | ||||||||
\(148\) | 1.38803e14 | 1.08567 | ||||||||
\(149\) | 1.54519e14 | 1.15683 | 0.578416 | − | 0.815742i | \(-0.303671\pi\) | ||||
0.578416 | + | 0.815742i | \(0.303671\pi\) | |||||||
\(150\) | 1.05143e14 | 0.753680 | ||||||||
\(151\) | −1.70906e14 | −1.17329 | −0.586646 | − | 0.809843i | \(-0.699552\pi\) | ||||
−0.586646 | + | 0.809843i | \(0.699552\pi\) | |||||||
\(152\) | 6.43223e13 | 0.423037 | ||||||||
\(153\) | −3.77949e13 | −0.238199 | ||||||||
\(154\) | −3.30273e13 | −0.199521 | ||||||||
\(155\) | 3.48305e11 | 0.00201746 | ||||||||
\(156\) | −9.04350e13 | −0.502374 | ||||||||
\(157\) | 2.23059e14 | 1.18870 | 0.594350 | − | 0.804207i | \(-0.297410\pi\) | ||||
0.594350 | + | 0.804207i | \(0.297410\pi\) | |||||||
\(158\) | −3.28243e14 | −1.67851 | ||||||||
\(159\) | 7.86744e13 | 0.386146 | ||||||||
\(160\) | 1.57861e12 | 0.00743867 | ||||||||
\(161\) | −1.08311e14 | −0.490122 | ||||||||
\(162\) | −3.33710e13 | −0.145051 | ||||||||
\(163\) | −5.23388e13 | −0.218577 | −0.109289 | − | 0.994010i | \(-0.534857\pi\) | ||||
−0.109289 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(164\) | 4.60942e13 | 0.184995 | ||||||||
\(165\) | 2.04228e11 | 0.000787896 0 | ||||||||
\(166\) | −3.64747e14 | −1.35297 | ||||||||
\(167\) | −7.33978e13 | −0.261834 | −0.130917 | − | 0.991393i | \(-0.541792\pi\) | ||||
−0.130917 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(168\) | 4.54306e13 | 0.155897 | ||||||||
\(169\) | 1.59514e14 | 0.526665 | ||||||||
\(170\) | 1.83329e12 | 0.00582523 | ||||||||
\(171\) | 1.19403e14 | 0.365208 | ||||||||
\(172\) | −3.07917e14 | −0.906773 | ||||||||
\(173\) | 6.36431e14 | 1.80490 | 0.902448 | − | 0.430800i | \(-0.141768\pi\) | ||||
0.902448 | + | 0.430800i | \(0.141768\pi\) | |||||||
\(174\) | 8.10308e13 | 0.221350 | ||||||||
\(175\) | −2.65713e14 | −0.699303 | ||||||||
\(176\) | −1.04123e14 | −0.264066 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | 4.33701e14 | 1.02202 | ||||||||
\(179\) | −5.87474e14 | −1.33488 | −0.667442 | − | 0.744662i | \(-0.732611\pi\) | ||||
−0.667442 | + | 0.744662i | \(0.732611\pi\) | |||||||
\(180\) | 6.68889e11 | 0.00146583 | ||||||||
\(181\) | −5.87159e14 | −1.24121 | −0.620605 | − | 0.784123i | \(-0.713113\pi\) | ||||
−0.620605 | + | 0.784123i | \(0.713113\pi\) | |||||||
\(182\) | 5.53073e14 | 1.12802 | ||||||||
\(183\) | 3.19482e14 | 0.628803 | ||||||||
\(184\) | −1.42447e14 | −0.270607 | ||||||||
\(185\) | 5.24914e12 | 0.00962657 | ||||||||
\(186\) | −1.37516e14 | −0.243512 | ||||||||
\(187\) | −9.13213e13 | −0.156171 | ||||||||
\(188\) | −1.45534e14 | −0.240403 | ||||||||
\(189\) | 8.43339e13 | 0.134586 | ||||||||
\(190\) | −5.79179e12 | −0.00893130 | ||||||||
\(191\) | 8.43064e14 | 1.25645 | 0.628223 | − | 0.778034i | \(-0.283783\pi\) | ||||
0.628223 | + | 0.778034i | \(0.283783\pi\) | |||||||
\(192\) | −1.39011e14 | −0.200258 | ||||||||
\(193\) | 1.20396e15 | 1.67683 | 0.838415 | − | 0.545033i | \(-0.183483\pi\) | ||||
0.838415 | + | 0.545033i | \(0.183483\pi\) | |||||||
\(194\) | 1.62722e15 | 2.19146 | ||||||||
\(195\) | −3.41999e12 | −0.00445451 | ||||||||
\(196\) | −2.85593e14 | −0.359818 | ||||||||
\(197\) | −1.10425e15 | −1.34598 | −0.672990 | − | 0.739652i | \(-0.734990\pi\) | ||||
−0.672990 | + | 0.739652i | \(0.734990\pi\) | |||||||
\(198\) | −8.06321e13 | −0.0951009 | ||||||||
\(199\) | −6.27234e14 | −0.715953 | −0.357976 | − | 0.933731i | \(-0.616533\pi\) | ||||
−0.357976 | + | 0.933731i | \(0.616533\pi\) | |||||||
\(200\) | −3.49457e14 | −0.386099 | ||||||||
\(201\) | 1.03265e15 | 1.10453 | ||||||||
\(202\) | 1.63518e15 | 1.69349 | ||||||||
\(203\) | −2.04778e14 | −0.205380 | ||||||||
\(204\) | −2.99096e14 | −0.290546 | ||||||||
\(205\) | 1.74315e12 | 0.00164034 | ||||||||
\(206\) | 2.82277e14 | 0.257358 | ||||||||
\(207\) | −2.64429e14 | −0.233615 | ||||||||
\(208\) | 1.74363e15 | 1.49294 | ||||||||
\(209\) | 2.88506e14 | 0.239444 | ||||||||
\(210\) | −4.09072e12 | −0.00329135 | ||||||||
\(211\) | 1.51733e15 | 1.18371 | 0.591853 | − | 0.806046i | \(-0.298397\pi\) | ||||
0.591853 | + | 0.806046i | \(0.298397\pi\) | |||||||
\(212\) | 6.22603e14 | 0.471008 | ||||||||
\(213\) | 7.52116e14 | 0.551845 | ||||||||
\(214\) | −2.09942e14 | −0.149420 | ||||||||
\(215\) | −1.16445e13 | −0.00804029 | ||||||||
\(216\) | 1.10913e14 | 0.0743078 | ||||||||
\(217\) | 3.47525e14 | 0.225943 | ||||||||
\(218\) | 8.14222e14 | 0.513778 | ||||||||
\(219\) | −7.46048e14 | −0.456962 | ||||||||
\(220\) | 1.61619e12 | 0.000961048 0 | ||||||||
\(221\) | 1.52926e15 | 0.882942 | ||||||||
\(222\) | −2.07244e15 | −1.16195 | ||||||||
\(223\) | 6.83896e14 | 0.372399 | 0.186199 | − | 0.982512i | \(-0.440383\pi\) | ||||
0.186199 | + | 0.982512i | \(0.440383\pi\) | |||||||
\(224\) | 1.57508e15 | 0.833085 | ||||||||
\(225\) | −6.48706e14 | −0.333320 | ||||||||
\(226\) | −1.50757e15 | −0.752613 | ||||||||
\(227\) | 2.00349e15 | 0.971893 | 0.485947 | − | 0.873988i | \(-0.338475\pi\) | ||||
0.485947 | + | 0.873988i | \(0.338475\pi\) | |||||||
\(228\) | 9.44916e14 | 0.445468 | ||||||||
\(229\) | −5.07557e14 | −0.232570 | −0.116285 | − | 0.993216i | \(-0.537099\pi\) | ||||
−0.116285 | + | 0.993216i | \(0.537099\pi\) | |||||||
\(230\) | 1.28264e13 | 0.00571314 | ||||||||
\(231\) | 2.03770e14 | 0.0882395 | ||||||||
\(232\) | −2.69317e14 | −0.113395 | ||||||||
\(233\) | 3.99269e15 | 1.63475 | 0.817376 | − | 0.576105i | \(-0.195428\pi\) | ||||
0.817376 | + | 0.576105i | \(0.195428\pi\) | |||||||
\(234\) | 1.35026e15 | 0.537669 | ||||||||
\(235\) | −5.50369e12 | −0.00213163 | ||||||||
\(236\) | −2.43342e14 | −0.0916831 | ||||||||
\(237\) | 2.02518e15 | 0.742334 | ||||||||
\(238\) | 1.82918e15 | 0.652389 | ||||||||
\(239\) | 4.90602e14 | 0.170272 | 0.0851359 | − | 0.996369i | \(-0.472868\pi\) | ||||
0.0851359 | + | 0.996369i | \(0.472868\pi\) | |||||||
\(240\) | −1.28965e13 | −0.00435611 | ||||||||
\(241\) | 3.13435e15 | 1.03047 | 0.515236 | − | 0.857048i | \(-0.327704\pi\) | ||||
0.515236 | + | 0.857048i | \(0.327704\pi\) | |||||||
\(242\) | 3.88427e15 | 1.24311 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 2.52828e15 | 0.766992 | ||||||||
\(245\) | −1.08003e13 | −0.00319048 | ||||||||
\(246\) | −6.88220e14 | −0.197993 | ||||||||
\(247\) | −4.83130e15 | −1.35374 | ||||||||
\(248\) | 4.57054e14 | 0.124748 | ||||||||
\(249\) | 2.25040e15 | 0.598362 | ||||||||
\(250\) | 6.29338e13 | 0.0163032 | ||||||||
\(251\) | 4.36614e15 | 1.10209 | 0.551047 | − | 0.834474i | \(-0.314229\pi\) | ||||
0.551047 | + | 0.834474i | \(0.314229\pi\) | |||||||
\(252\) | 6.67390e14 | 0.164163 | ||||||||
\(253\) | −6.38921e14 | −0.153167 | ||||||||
\(254\) | 1.06692e16 | 2.49295 | ||||||||
\(255\) | −1.13110e13 | −0.00257625 | ||||||||
\(256\) | 5.90367e15 | 1.31088 | ||||||||
\(257\) | 2.74218e15 | 0.593650 | 0.296825 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296825 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(258\) | 4.59743e15 | 0.970481 | ||||||||
\(259\) | 5.23738e15 | 1.07812 | ||||||||
\(260\) | −2.70647e13 | −0.00543345 | ||||||||
\(261\) | −4.99941e14 | −0.0978938 | ||||||||
\(262\) | −6.34860e15 | −1.21261 | ||||||||
\(263\) | −6.48120e15 | −1.20766 | −0.603828 | − | 0.797115i | \(-0.706359\pi\) | ||||
−0.603828 | + | 0.797115i | \(0.706359\pi\) | |||||||
\(264\) | 2.67992e14 | 0.0487188 | ||||||||
\(265\) | 2.35450e13 | 0.00417639 | ||||||||
\(266\) | −5.77882e15 | −1.00025 | ||||||||
\(267\) | −2.67583e15 | −0.451997 | ||||||||
\(268\) | 8.17205e15 | 1.34727 | ||||||||
\(269\) | −7.20753e15 | −1.15984 | −0.579918 | − | 0.814675i | \(-0.696915\pi\) | ||||
−0.579918 | + | 0.814675i | \(0.696915\pi\) | |||||||
\(270\) | −9.98700e12 | −0.00156881 | ||||||||
\(271\) | 1.69831e15 | 0.260445 | 0.130223 | − | 0.991485i | \(-0.458431\pi\) | ||||
0.130223 | + | 0.991485i | \(0.458431\pi\) | |||||||
\(272\) | 5.76672e15 | 0.863438 | ||||||||
\(273\) | −3.41233e15 | −0.498877 | ||||||||
\(274\) | −1.29832e16 | −1.85355 | ||||||||
\(275\) | −1.56743e15 | −0.218537 | ||||||||
\(276\) | −2.09260e15 | −0.284956 | ||||||||
\(277\) | 1.07690e16 | 1.43238 | 0.716191 | − | 0.697905i | \(-0.245884\pi\) | ||||
0.716191 | + | 0.697905i | \(0.245884\pi\) | |||||||
\(278\) | −5.35188e15 | −0.695369 | ||||||||
\(279\) | 8.48441e14 | 0.107695 | ||||||||
\(280\) | 1.35961e13 | 0.00168611 | ||||||||
\(281\) | −3.43346e15 | −0.416045 | −0.208023 | − | 0.978124i | \(-0.566703\pi\) | ||||
−0.208023 | + | 0.978124i | \(0.566703\pi\) | |||||||
\(282\) | 2.17294e15 | 0.257293 | ||||||||
\(283\) | 3.84777e15 | 0.445244 | 0.222622 | − | 0.974905i | \(-0.428538\pi\) | ||||
0.222622 | + | 0.974905i | \(0.428538\pi\) | |||||||
\(284\) | 5.95200e15 | 0.673121 | ||||||||
\(285\) | 3.57340e13 | 0.00394993 | ||||||||
\(286\) | 3.26255e15 | 0.352515 | ||||||||
\(287\) | 1.73924e15 | 0.183708 | ||||||||
\(288\) | 3.84536e15 | 0.397087 | ||||||||
\(289\) | −4.84684e15 | −0.489353 | ||||||||
\(290\) | 2.42502e13 | 0.00239403 | ||||||||
\(291\) | −1.00395e16 | −0.969191 | ||||||||
\(292\) | −5.90398e15 | −0.557386 | ||||||||
\(293\) | 1.96127e16 | 1.81092 | 0.905458 | − | 0.424436i | \(-0.139528\pi\) | ||||
0.905458 | + | 0.424436i | \(0.139528\pi\) | |||||||
\(294\) | 4.26412e15 | 0.385098 | ||||||||
\(295\) | −9.20249e12 | −0.000812947 0 | ||||||||
\(296\) | 6.88804e15 | 0.595250 | ||||||||
\(297\) | 4.97481e14 | 0.0420591 | ||||||||
\(298\) | −1.82575e16 | −1.51020 | ||||||||
\(299\) | 1.06993e16 | 0.865953 | ||||||||
\(300\) | −5.13365e15 | −0.406572 | ||||||||
\(301\) | −1.16184e16 | −0.900462 | ||||||||
\(302\) | 2.01937e16 | 1.53169 | ||||||||
\(303\) | −1.00887e16 | −0.748959 | ||||||||
\(304\) | −1.82184e16 | −1.32383 | ||||||||
\(305\) | 9.56120e13 | 0.00680086 | ||||||||
\(306\) | 4.46573e15 | 0.310959 | ||||||||
\(307\) | 2.18174e16 | 1.48731 | 0.743657 | − | 0.668561i | \(-0.233089\pi\) | ||||
0.743657 | + | 0.668561i | \(0.233089\pi\) | |||||||
\(308\) | 1.61257e15 | 0.107631 | ||||||||
\(309\) | −1.74158e15 | −0.113819 | ||||||||
\(310\) | −4.11547e13 | −0.00263371 | ||||||||
\(311\) | 1.35314e16 | 0.848007 | 0.424003 | − | 0.905661i | \(-0.360624\pi\) | ||||
0.424003 | + | 0.905661i | \(0.360624\pi\) | |||||||
\(312\) | −4.48779e15 | −0.275440 | ||||||||
\(313\) | −1.11477e16 | −0.670111 | −0.335055 | − | 0.942198i | \(-0.608755\pi\) | ||||
−0.335055 | + | 0.942198i | \(0.608755\pi\) | |||||||
\(314\) | −2.63560e16 | −1.55180 | ||||||||
\(315\) | 2.52388e13 | 0.00145562 | ||||||||
\(316\) | 1.60266e16 | 0.905472 | ||||||||
\(317\) | 1.09554e16 | 0.606376 | 0.303188 | − | 0.952931i | \(-0.401949\pi\) | ||||
0.303188 | + | 0.952931i | \(0.401949\pi\) | |||||||
\(318\) | −9.29592e15 | −0.504099 | ||||||||
\(319\) | −1.20797e15 | −0.0641827 | ||||||||
\(320\) | −4.16020e13 | −0.00216591 | ||||||||
\(321\) | 1.29529e15 | 0.0660822 | ||||||||
\(322\) | 1.27977e16 | 0.639836 | ||||||||
\(323\) | −1.59786e16 | −0.782929 | ||||||||
\(324\) | 1.62935e15 | 0.0782480 | ||||||||
\(325\) | 2.62480e16 | 1.23553 | ||||||||
\(326\) | 6.18420e15 | 0.285344 | ||||||||
\(327\) | −5.02355e15 | −0.227222 | ||||||||
\(328\) | 2.28740e15 | 0.101429 | ||||||||
\(329\) | −5.49136e15 | −0.238730 | ||||||||
\(330\) | −2.41309e13 | −0.00102857 | ||||||||
\(331\) | −1.39087e16 | −0.581306 | −0.290653 | − | 0.956828i | \(-0.593873\pi\) | ||||
−0.290653 | + | 0.956828i | \(0.593873\pi\) | |||||||
\(332\) | 1.78089e16 | 0.729861 | ||||||||
\(333\) | 1.27864e16 | 0.513881 | ||||||||
\(334\) | 8.67246e15 | 0.341814 | ||||||||
\(335\) | 3.09043e14 | 0.0119461 | ||||||||
\(336\) | −1.28676e16 | −0.487857 | ||||||||
\(337\) | 1.61764e16 | 0.601570 | 0.300785 | − | 0.953692i | \(-0.402751\pi\) | ||||
0.300785 | + | 0.953692i | \(0.402751\pi\) | |||||||
\(338\) | −1.88477e16 | −0.687541 | ||||||||
\(339\) | 9.30133e15 | 0.332849 | ||||||||
\(340\) | −8.95111e13 | −0.00314242 | ||||||||
\(341\) | 2.05003e15 | 0.0706085 | ||||||||
\(342\) | −1.41083e16 | −0.476766 | ||||||||
\(343\) | −3.18669e16 | −1.05664 | ||||||||
\(344\) | −1.52802e16 | −0.497164 | ||||||||
\(345\) | −7.91360e13 | −0.00252668 | ||||||||
\(346\) | −7.51988e16 | −2.35622 | ||||||||
\(347\) | −3.83778e16 | −1.18015 | −0.590077 | − | 0.807347i | \(-0.700902\pi\) | ||||
−0.590077 | + | 0.807347i | \(0.700902\pi\) | |||||||
\(348\) | −3.95636e15 | −0.119407 | ||||||||
\(349\) | −4.03032e16 | −1.19392 | −0.596959 | − | 0.802272i | \(-0.703625\pi\) | ||||
−0.596959 | + | 0.802272i | \(0.703625\pi\) | |||||||
\(350\) | 3.13958e16 | 0.912913 | ||||||||
\(351\) | −8.33079e15 | −0.237788 | ||||||||
\(352\) | 9.29129e15 | 0.260345 | ||||||||
\(353\) | 3.80218e16 | 1.04592 | 0.522958 | − | 0.852359i | \(-0.324829\pi\) | ||||
0.522958 | + | 0.852359i | \(0.324829\pi\) | |||||||
\(354\) | 3.63328e15 | 0.0981245 | ||||||||
\(355\) | 2.25087e14 | 0.00596851 | ||||||||
\(356\) | −2.11756e16 | −0.551330 | ||||||||
\(357\) | −1.12856e16 | −0.288524 | ||||||||
\(358\) | 6.94141e16 | 1.74264 | ||||||||
\(359\) | −3.01081e16 | −0.742282 | −0.371141 | − | 0.928576i | \(-0.621033\pi\) | ||||
−0.371141 | + | 0.928576i | \(0.621033\pi\) | |||||||
\(360\) | 3.31932e13 | 0.000803680 0 | ||||||||
\(361\) | 8.42716e15 | 0.200394 | ||||||||
\(362\) | 6.93770e16 | 1.62035 | ||||||||
\(363\) | −2.39650e16 | −0.549775 | ||||||||
\(364\) | −2.70040e16 | −0.608513 | ||||||||
\(365\) | −2.23271e14 | −0.00494230 | ||||||||
\(366\) | −3.77491e16 | −0.820879 | ||||||||
\(367\) | −3.20870e16 | −0.685487 | −0.342744 | − | 0.939429i | \(-0.611356\pi\) | ||||
−0.342744 | + | 0.939429i | \(0.611356\pi\) | |||||||
\(368\) | 4.03463e16 | 0.846824 | ||||||||
\(369\) | 4.24615e15 | 0.0875638 | ||||||||
\(370\) | −6.20222e14 | −0.0125671 | ||||||||
\(371\) | 2.34923e16 | 0.467729 | ||||||||
\(372\) | 6.71429e15 | 0.131362 | ||||||||
\(373\) | 4.35441e16 | 0.837186 | 0.418593 | − | 0.908174i | \(-0.362523\pi\) | ||||
0.418593 | + | 0.908174i | \(0.362523\pi\) | |||||||
\(374\) | 1.07902e16 | 0.203876 | ||||||||
\(375\) | −3.88287e14 | −0.00721023 | ||||||||
\(376\) | −7.22206e15 | −0.131808 | ||||||||
\(377\) | 2.02287e16 | 0.362868 | ||||||||
\(378\) | −9.96463e15 | −0.175697 | ||||||||
\(379\) | −1.07507e16 | −0.186330 | −0.0931648 | − | 0.995651i | \(-0.529698\pi\) | ||||
−0.0931648 | + | 0.995651i | \(0.529698\pi\) | |||||||
\(380\) | 2.82787e14 | 0.00481799 | ||||||||
\(381\) | −6.58266e16 | −1.10253 | ||||||||
\(382\) | −9.96138e16 | −1.64024 | ||||||||
\(383\) | 5.47465e16 | 0.886266 | 0.443133 | − | 0.896456i | \(-0.353867\pi\) | ||||
0.443133 | + | 0.896456i | \(0.353867\pi\) | |||||||
\(384\) | −2.67864e16 | −0.426346 | ||||||||
\(385\) | 6.09827e13 | 0.000954359 0 | ||||||||
\(386\) | −1.42256e17 | −2.18904 | ||||||||
\(387\) | −2.83650e16 | −0.429202 | ||||||||
\(388\) | −7.94496e16 | −1.18219 | ||||||||
\(389\) | 1.32070e17 | 1.93255 | 0.966277 | − | 0.257505i | \(-0.0829005\pi\) | ||||
0.966277 | + | 0.257505i | \(0.0829005\pi\) | |||||||
\(390\) | 4.04095e14 | 0.00581519 | ||||||||
\(391\) | 3.53860e16 | 0.500821 | ||||||||
\(392\) | −1.41724e16 | −0.197280 | ||||||||
\(393\) | 3.91693e16 | 0.536284 | ||||||||
\(394\) | 1.30475e17 | 1.75713 | ||||||||
\(395\) | 6.06079e14 | 0.00802875 | ||||||||
\(396\) | 3.93690e15 | 0.0513022 | ||||||||
\(397\) | 5.26848e16 | 0.675378 | 0.337689 | − | 0.941258i | \(-0.390355\pi\) | ||||
0.337689 | + | 0.941258i | \(0.390355\pi\) | |||||||
\(398\) | 7.41120e16 | 0.934650 | ||||||||
\(399\) | 3.56539e16 | 0.442368 | ||||||||
\(400\) | 9.89792e16 | 1.20824 | ||||||||
\(401\) | 1.39510e17 | 1.67559 | 0.837796 | − | 0.545984i | \(-0.183844\pi\) | ||||
0.837796 | + | 0.545984i | \(0.183844\pi\) | |||||||
\(402\) | −1.22015e17 | −1.44193 | ||||||||
\(403\) | −3.43297e16 | −0.399197 | ||||||||
\(404\) | −7.98386e16 | −0.913554 | ||||||||
\(405\) | 6.16174e13 | 0.000693818 0 | ||||||||
\(406\) | 2.41959e16 | 0.268116 | ||||||||
\(407\) | 3.08950e16 | 0.336919 | ||||||||
\(408\) | −1.48425e16 | −0.159300 | ||||||||
\(409\) | −1.00105e17 | −1.05743 | −0.528717 | − | 0.848798i | \(-0.677327\pi\) | ||||
−0.528717 | + | 0.848798i | \(0.677327\pi\) | |||||||
\(410\) | −2.05965e14 | −0.00214140 | ||||||||
\(411\) | 8.01033e16 | 0.819744 | ||||||||
\(412\) | −1.37823e16 | −0.138832 | ||||||||
\(413\) | −9.18188e15 | −0.0910450 | ||||||||
\(414\) | 3.12441e16 | 0.304976 | ||||||||
\(415\) | 6.73481e14 | 0.00647162 | ||||||||
\(416\) | −1.55591e17 | −1.47190 | ||||||||
\(417\) | 3.30198e16 | 0.307532 | ||||||||
\(418\) | −3.40889e16 | −0.312585 | ||||||||
\(419\) | 2.00711e17 | 1.81209 | 0.906044 | − | 0.423184i | \(-0.139088\pi\) | ||||
0.906044 | + | 0.423184i | \(0.139088\pi\) | |||||||
\(420\) | 1.99731e14 | 0.00177552 | ||||||||
\(421\) | 3.40145e15 | 0.0297735 | 0.0148867 | − | 0.999889i | \(-0.495261\pi\) | ||||
0.0148867 | + | 0.999889i | \(0.495261\pi\) | |||||||
\(422\) | −1.79283e17 | −1.54528 | ||||||||
\(423\) | −1.34065e16 | −0.113790 | ||||||||
\(424\) | 3.08963e16 | 0.258243 | ||||||||
\(425\) | 8.68103e16 | 0.714568 | ||||||||
\(426\) | −8.88677e16 | −0.720413 | ||||||||
\(427\) | 9.53979e16 | 0.761654 | ||||||||
\(428\) | 1.02505e16 | 0.0806048 | ||||||||
\(429\) | −2.01291e16 | −0.155902 | ||||||||
\(430\) | 1.37588e15 | 0.0104963 | ||||||||
\(431\) | 7.01521e16 | 0.527155 | 0.263577 | − | 0.964638i | \(-0.415098\pi\) | ||||
0.263577 | + | 0.964638i | \(0.415098\pi\) | |||||||
\(432\) | −3.14147e16 | −0.232535 | ||||||||
\(433\) | −1.17197e16 | −0.0854565 | −0.0427282 | − | 0.999087i | \(-0.513605\pi\) | ||||
−0.0427282 | + | 0.999087i | \(0.513605\pi\) | |||||||
\(434\) | −4.10625e16 | −0.294959 | ||||||||
\(435\) | −1.49618e14 | −0.00105878 | ||||||||
\(436\) | −3.97547e16 | −0.277158 | ||||||||
\(437\) | −1.11793e17 | −0.767864 | ||||||||
\(438\) | 8.81508e16 | 0.596547 | ||||||||
\(439\) | 2.16132e15 | 0.0144112 | 0.00720558 | − | 0.999974i | \(-0.497706\pi\) | ||||
0.00720558 | + | 0.999974i | \(0.497706\pi\) | |||||||
\(440\) | 8.02026e13 | 0.000526921 0 | ||||||||
\(441\) | −2.63086e16 | −0.170312 | ||||||||
\(442\) | −1.80693e17 | −1.15265 | ||||||||
\(443\) | 2.84823e17 | 1.79040 | 0.895201 | − | 0.445664i | \(-0.147032\pi\) | ||||
0.895201 | + | 0.445664i | \(0.147032\pi\) | |||||||
\(444\) | 1.01188e17 | 0.626813 | ||||||||
\(445\) | −8.00800e14 | −0.00488860 | ||||||||
\(446\) | −8.08071e16 | −0.486153 | ||||||||
\(447\) | 1.12644e17 | 0.667897 | ||||||||
\(448\) | −4.15089e16 | −0.242568 | ||||||||
\(449\) | 1.16611e17 | 0.671641 | 0.335820 | − | 0.941926i | \(-0.390986\pi\) | ||||
0.335820 | + | 0.941926i | \(0.390986\pi\) | |||||||
\(450\) | 7.66492e16 | 0.435137 | ||||||||
\(451\) | 1.02597e16 | 0.0574099 | ||||||||
\(452\) | 7.36076e16 | 0.405997 | ||||||||
\(453\) | −1.24590e17 | −0.677400 | ||||||||
\(454\) | −2.36726e17 | −1.26877 | ||||||||
\(455\) | −1.02121e15 | −0.00539563 | ||||||||
\(456\) | 4.68909e16 | 0.244240 | ||||||||
\(457\) | −5.01048e16 | −0.257291 | −0.128645 | − | 0.991691i | \(-0.541063\pi\) | ||||
−0.128645 | + | 0.991691i | \(0.541063\pi\) | |||||||
\(458\) | 5.99714e16 | 0.303612 | ||||||||
\(459\) | −2.75525e16 | −0.137524 | ||||||||
\(460\) | −6.26256e14 | −0.00308195 | ||||||||
\(461\) | −1.03469e17 | −0.502058 | −0.251029 | − | 0.967980i | \(-0.580769\pi\) | ||||
−0.251029 | + | 0.967980i | \(0.580769\pi\) | |||||||
\(462\) | −2.40769e16 | −0.115193 | ||||||||
\(463\) | −3.19974e17 | −1.50952 | −0.754759 | − | 0.656002i | \(-0.772246\pi\) | ||||
−0.754759 | + | 0.656002i | \(0.772246\pi\) | |||||||
\(464\) | 7.62806e16 | 0.354852 | ||||||||
\(465\) | 2.53915e14 | 0.00116478 | ||||||||
\(466\) | −4.71764e17 | −2.13411 | ||||||||
\(467\) | 2.29998e17 | 1.02604 | 0.513020 | − | 0.858377i | \(-0.328527\pi\) | ||||
0.513020 | + | 0.858377i | \(0.328527\pi\) | |||||||
\(468\) | −6.59271e16 | −0.290046 | ||||||||
\(469\) | 3.08351e17 | 1.33789 | ||||||||
\(470\) | 6.50299e14 | 0.00278277 | ||||||||
\(471\) | 1.62610e17 | 0.686296 | ||||||||
\(472\) | −1.20757e16 | −0.0502678 | ||||||||
\(473\) | −6.85365e16 | −0.281400 | ||||||||
\(474\) | −2.39289e17 | −0.969088 | ||||||||
\(475\) | −2.74254e17 | −1.09558 | ||||||||
\(476\) | −8.93107e16 | −0.351931 | ||||||||
\(477\) | 5.73536e16 | 0.222942 | ||||||||
\(478\) | −5.79680e16 | −0.222283 | ||||||||
\(479\) | 4.04507e15 | 0.0153019 | 0.00765095 | − | 0.999971i | \(-0.497565\pi\) | ||||
0.00765095 | + | 0.999971i | \(0.497565\pi\) | |||||||
\(480\) | 1.15081e15 | 0.00429472 | ||||||||
\(481\) | −5.17367e17 | −1.90483 | ||||||||
\(482\) | −3.70345e17 | −1.34524 | ||||||||
\(483\) | −7.89588e16 | −0.282972 | ||||||||
\(484\) | −1.89651e17 | −0.670596 | ||||||||
\(485\) | −3.00455e15 | −0.0104823 | ||||||||
\(486\) | −2.43275e16 | −0.0837454 | ||||||||
\(487\) | −3.43808e17 | −1.16782 | −0.583912 | − | 0.811817i | \(-0.698479\pi\) | ||||
−0.583912 | + | 0.811817i | \(0.698479\pi\) | |||||||
\(488\) | 1.25464e17 | 0.420525 | ||||||||
\(489\) | −3.81550e16 | −0.126196 | ||||||||
\(490\) | 1.27613e15 | 0.00416505 | ||||||||
\(491\) | 5.40973e17 | 1.74239 | 0.871196 | − | 0.490935i | \(-0.163345\pi\) | ||||
0.871196 | + | 0.490935i | \(0.163345\pi\) | |||||||
\(492\) | 3.36027e16 | 0.106807 | ||||||||
\(493\) | 6.69024e16 | 0.209863 | ||||||||
\(494\) | 5.70852e17 | 1.76725 | ||||||||
\(495\) | 1.48882e14 | 0.000454892 0 | ||||||||
\(496\) | −1.29455e17 | −0.390379 | ||||||||
\(497\) | 2.24583e17 | 0.668436 | ||||||||
\(498\) | −2.65900e17 | −0.781139 | ||||||||
\(499\) | 2.04271e17 | 0.592316 | 0.296158 | − | 0.955139i | \(-0.404295\pi\) | ||||
0.296158 | + | 0.955139i | \(0.404295\pi\) | |||||||
\(500\) | −3.07277e15 | −0.00879479 | ||||||||
\(501\) | −5.35070e16 | −0.151170 | ||||||||
\(502\) | −5.15890e17 | −1.43874 | ||||||||
\(503\) | −2.22410e17 | −0.612298 | −0.306149 | − | 0.951984i | \(-0.599041\pi\) | ||||
−0.306149 | + | 0.951984i | \(0.599041\pi\) | |||||||
\(504\) | 3.31189e16 | 0.0900072 | ||||||||
\(505\) | −3.01926e15 | −0.00810041 | ||||||||
\(506\) | 7.54930e16 | 0.199953 | ||||||||
\(507\) | 1.16286e17 | 0.304070 | ||||||||
\(508\) | −5.20930e17 | −1.34482 | ||||||||
\(509\) | −3.82791e17 | −0.975655 | −0.487827 | − | 0.872940i | \(-0.662210\pi\) | ||||
−0.487827 | + | 0.872940i | \(0.662210\pi\) | |||||||
\(510\) | 1.33647e15 | 0.00336320 | ||||||||
\(511\) | −2.22771e17 | −0.553507 | ||||||||
\(512\) | −3.96553e17 | −0.972851 | ||||||||
\(513\) | 8.70448e16 | 0.210853 | ||||||||
\(514\) | −3.24008e17 | −0.774988 | ||||||||
\(515\) | −5.21206e14 | −0.00123101 | ||||||||
\(516\) | −2.24471e17 | −0.523526 | ||||||||
\(517\) | −3.23932e16 | −0.0746046 | ||||||||
\(518\) | −6.18833e17 | −1.40744 | ||||||||
\(519\) | 4.63959e17 | 1.04206 | ||||||||
\(520\) | −1.34307e15 | −0.00297904 | ||||||||
\(521\) | 2.64905e17 | 0.580290 | 0.290145 | − | 0.956983i | \(-0.406296\pi\) | ||||
0.290145 | + | 0.956983i | \(0.406296\pi\) | |||||||
\(522\) | 5.90715e16 | 0.127797 | ||||||||
\(523\) | −3.20781e17 | −0.685406 | −0.342703 | − | 0.939444i | \(-0.611342\pi\) | ||||
−0.342703 | + | 0.939444i | \(0.611342\pi\) | |||||||
\(524\) | 3.09973e17 | 0.654140 | ||||||||
\(525\) | −1.93705e17 | −0.403743 | ||||||||
\(526\) | 7.65799e17 | 1.57655 | ||||||||
\(527\) | −1.13539e17 | −0.230875 | ||||||||
\(528\) | −7.59053e16 | −0.152459 | ||||||||
\(529\) | −2.56461e17 | −0.508815 | ||||||||
\(530\) | −2.78201e15 | −0.00545212 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 2.82153e17 | 0.539585 | ||||||||
\(533\) | −1.71808e17 | −0.324577 | ||||||||
\(534\) | 3.16168e17 | 0.590065 | ||||||||
\(535\) | 3.87644e14 | 0.000714716 0 | ||||||||
\(536\) | 4.05533e17 | 0.738678 | ||||||||
\(537\) | −4.28268e17 | −0.770696 | ||||||||
\(538\) | 8.51620e17 | 1.51412 | ||||||||
\(539\) | −6.35676e16 | −0.111663 | ||||||||
\(540\) | 4.87620e14 | 0.000846295 0 | ||||||||
\(541\) | 9.89247e17 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(542\) | −2.00667e17 | −0.340001 | ||||||||
\(543\) | −4.28039e17 | −0.716613 | ||||||||
\(544\) | −5.14589e17 | −0.851270 | ||||||||
\(545\) | −1.50341e15 | −0.00245753 | ||||||||
\(546\) | 4.03190e17 | 0.651265 | ||||||||
\(547\) | −8.63153e17 | −1.37775 | −0.688874 | − | 0.724881i | \(-0.741895\pi\) | ||||
−0.688874 | + | 0.724881i | \(0.741895\pi\) | |||||||
\(548\) | 6.33911e17 | 0.999895 | ||||||||
\(549\) | 2.32903e17 | 0.363040 | ||||||||
\(550\) | 1.85202e17 | 0.285291 | ||||||||
\(551\) | −2.11360e17 | −0.321765 | ||||||||
\(552\) | −1.03844e17 | −0.156235 | ||||||||
\(553\) | 6.04721e17 | 0.899170 | ||||||||
\(554\) | −1.27244e18 | −1.86992 | ||||||||
\(555\) | 3.82662e15 | 0.00555790 | ||||||||
\(556\) | 2.61308e17 | 0.375117 | ||||||||
\(557\) | 2.76225e17 | 0.391927 | 0.195963 | − | 0.980611i | \(-0.437217\pi\) | ||||
0.195963 | + | 0.980611i | \(0.437217\pi\) | |||||||
\(558\) | −1.00249e17 | −0.140591 | ||||||||
\(559\) | 1.14771e18 | 1.59094 | ||||||||
\(560\) | −3.85091e15 | −0.00527645 | ||||||||
\(561\) | −6.65732e16 | −0.0901657 | ||||||||
\(562\) | 4.05687e17 | 0.543132 | ||||||||
\(563\) | −6.74594e17 | −0.892766 | −0.446383 | − | 0.894842i | \(-0.647288\pi\) | ||||
−0.446383 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(564\) | −1.06095e17 | −0.138797 | ||||||||
\(565\) | 2.78363e15 | 0.00359995 | ||||||||
\(566\) | −4.54641e17 | −0.581249 | ||||||||
\(567\) | 6.14794e16 | 0.0777033 | ||||||||
\(568\) | 2.95364e17 | 0.369057 | ||||||||
\(569\) | 1.41670e17 | 0.175004 | 0.0875022 | − | 0.996164i | \(-0.472112\pi\) | ||||
0.0875022 | + | 0.996164i | \(0.472112\pi\) | |||||||
\(570\) | −4.22222e15 | −0.00515649 | ||||||||
\(571\) | −8.70534e17 | −1.05112 | −0.525559 | − | 0.850757i | \(-0.676144\pi\) | ||||
−0.525559 | + | 0.850757i | \(0.676144\pi\) | |||||||
\(572\) | −1.59295e17 | −0.190164 | ||||||||
\(573\) | 6.14593e17 | 0.725409 | ||||||||
\(574\) | −2.05504e17 | −0.239824 | ||||||||
\(575\) | 6.07360e17 | 0.700818 | ||||||||
\(576\) | −1.01339e17 | −0.115619 | ||||||||
\(577\) | −6.55997e17 | −0.740047 | −0.370023 | − | 0.929022i | \(-0.620650\pi\) | ||||
−0.370023 | + | 0.929022i | \(0.620650\pi\) | |||||||
\(578\) | 5.72687e17 | 0.638832 | ||||||||
\(579\) | 8.77685e17 | 0.968118 | ||||||||
\(580\) | −1.18403e15 | −0.00129146 | ||||||||
\(581\) | 6.71973e17 | 0.724781 | ||||||||
\(582\) | 1.18624e18 | 1.26524 | ||||||||
\(583\) | 1.38580e17 | 0.146169 | ||||||||
\(584\) | −2.92982e17 | −0.305603 | ||||||||
\(585\) | −2.49317e15 | −0.00257181 | ||||||||
\(586\) | −2.31738e18 | −2.36408 | ||||||||
\(587\) | 2.13669e17 | 0.215573 | 0.107786 | − | 0.994174i | \(-0.465624\pi\) | ||||
0.107786 | + | 0.994174i | \(0.465624\pi\) | |||||||
\(588\) | −2.08197e17 | −0.207741 | ||||||||
\(589\) | 3.58696e17 | 0.353979 | ||||||||
\(590\) | 1.08734e15 | 0.00106127 | ||||||||
\(591\) | −8.05001e17 | −0.777102 | ||||||||
\(592\) | −1.95095e18 | −1.86275 | ||||||||
\(593\) | −7.84408e17 | −0.740775 | −0.370387 | − | 0.928877i | \(-0.620775\pi\) | ||||
−0.370387 | + | 0.928877i | \(0.620775\pi\) | |||||||
\(594\) | −5.87808e16 | −0.0549065 | ||||||||
\(595\) | −3.37747e15 | −0.00312055 | ||||||||
\(596\) | 8.91428e17 | 0.814677 | ||||||||
\(597\) | −4.57253e17 | −0.413356 | ||||||||
\(598\) | −1.26420e18 | −1.13047 | ||||||||
\(599\) | −3.59041e17 | −0.317592 | −0.158796 | − | 0.987311i | \(-0.550761\pi\) | ||||
−0.158796 | + | 0.987311i | \(0.550761\pi\) | |||||||
\(600\) | −2.54754e17 | −0.222915 | ||||||||
\(601\) | 1.41352e18 | 1.22354 | 0.611768 | − | 0.791037i | \(-0.290459\pi\) | ||||
0.611768 | + | 0.791037i | \(0.290459\pi\) | |||||||
\(602\) | 1.37280e18 | 1.17552 | ||||||||
\(603\) | 7.52802e17 | 0.637702 | ||||||||
\(604\) | −9.85966e17 | −0.826269 | ||||||||
\(605\) | −7.17206e15 | −0.00594612 | ||||||||
\(606\) | 1.19205e18 | 0.977738 | ||||||||
\(607\) | 2.27581e17 | 0.184676 | 0.0923379 | − | 0.995728i | \(-0.470566\pi\) | ||||
0.0923379 | + | 0.995728i | \(0.470566\pi\) | |||||||
\(608\) | 1.62571e18 | 1.30518 | ||||||||
\(609\) | −1.49283e17 | −0.118576 | ||||||||
\(610\) | −1.12972e16 | −0.00887826 | ||||||||
\(611\) | 5.42455e17 | 0.421790 | ||||||||
\(612\) | −2.18041e17 | −0.167747 | ||||||||
\(613\) | 1.52616e18 | 1.16174 | 0.580869 | − | 0.813997i | \(-0.302713\pi\) | ||||
0.580869 | + | 0.813997i | \(0.302713\pi\) | |||||||
\(614\) | −2.57787e18 | −1.94163 | ||||||||
\(615\) | 1.27075e15 | 0.000947051 0 | ||||||||
\(616\) | 8.00229e16 | 0.0590119 | ||||||||
\(617\) | −1.51369e18 | −1.10455 | −0.552274 | − | 0.833663i | \(-0.686240\pi\) | ||||
−0.552274 | + | 0.833663i | \(0.686240\pi\) | |||||||
\(618\) | 2.05780e17 | 0.148586 | ||||||||
\(619\) | 2.31320e18 | 1.65281 | 0.826406 | − | 0.563075i | \(-0.190382\pi\) | ||||
0.826406 | + | 0.563075i | \(0.190382\pi\) | |||||||
\(620\) | 2.00940e15 | 0.00142076 | ||||||||
\(621\) | −1.92768e17 | −0.134878 | ||||||||
\(622\) | −1.59883e18 | −1.10704 | ||||||||
\(623\) | −7.99007e17 | −0.547492 | ||||||||
\(624\) | 1.27111e18 | 0.861950 | ||||||||
\(625\) | 1.48994e18 | 0.999883 | ||||||||
\(626\) | 1.31718e18 | 0.874804 | ||||||||
\(627\) | 2.10321e17 | 0.138243 | ||||||||
\(628\) | 1.28684e18 | 0.837119 | ||||||||
\(629\) | −1.71109e18 | −1.10165 | ||||||||
\(630\) | −2.98213e15 | −0.00190026 | ||||||||
\(631\) | −2.25313e18 | −1.42100 | −0.710501 | − | 0.703696i | \(-0.751532\pi\) | ||||
−0.710501 | + | 0.703696i | \(0.751532\pi\) | |||||||
\(632\) | 7.95311e17 | 0.496450 | ||||||||
\(633\) | 1.10613e18 | 0.683413 | ||||||||
\(634\) | −1.29445e18 | −0.791602 | ||||||||
\(635\) | −1.97000e16 | −0.0119244 | ||||||||
\(636\) | 4.53877e17 | 0.271936 | ||||||||
\(637\) | 1.06450e18 | 0.631305 | ||||||||
\(638\) | 1.42730e17 | 0.0837880 | ||||||||
\(639\) | 5.48292e17 | 0.318608 | ||||||||
\(640\) | −8.01642e15 | −0.00461116 | ||||||||
\(641\) | 4.56005e17 | 0.259652 | 0.129826 | − | 0.991537i | \(-0.458558\pi\) | ||||
0.129826 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(642\) | −1.53048e17 | −0.0862679 | ||||||||
\(643\) | 1.38951e17 | 0.0775337 | 0.0387669 | − | 0.999248i | \(-0.487657\pi\) | ||||
0.0387669 | + | 0.999248i | \(0.487657\pi\) | |||||||
\(644\) | −6.24854e17 | −0.345160 | ||||||||
\(645\) | −8.48885e15 | −0.00464206 | ||||||||
\(646\) | 1.88798e18 | 1.02208 | ||||||||
\(647\) | 1.65177e18 | 0.885264 | 0.442632 | − | 0.896703i | \(-0.354045\pi\) | ||||
0.442632 | + | 0.896703i | \(0.354045\pi\) | |||||||
\(648\) | 8.08558e16 | 0.0429016 | ||||||||
\(649\) | −5.41634e16 | −0.0284522 | ||||||||
\(650\) | −3.10139e18 | −1.61294 | ||||||||
\(651\) | 2.53346e17 | 0.130448 | ||||||||
\(652\) | −3.01946e17 | −0.153929 | ||||||||
\(653\) | 7.70105e17 | 0.388700 | 0.194350 | − | 0.980932i | \(-0.437740\pi\) | ||||
0.194350 | + | 0.980932i | \(0.437740\pi\) | |||||||
\(654\) | 5.93568e17 | 0.296630 | ||||||||
\(655\) | 1.17223e16 | 0.00580021 | ||||||||
\(656\) | −6.47876e17 | −0.317407 | ||||||||
\(657\) | −5.43869e17 | −0.263827 | ||||||||
\(658\) | 6.48842e17 | 0.311653 | ||||||||
\(659\) | 1.29640e18 | 0.616574 | 0.308287 | − | 0.951293i | \(-0.400244\pi\) | ||||
0.308287 | + | 0.951293i | \(0.400244\pi\) | |||||||
\(660\) | 1.17820e15 | 0.000554861 0 | ||||||||
\(661\) | 1.59296e18 | 0.742840 | 0.371420 | − | 0.928465i | \(-0.378871\pi\) | ||||
0.371420 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(662\) | 1.64341e18 | 0.758874 | ||||||||
\(663\) | 1.11483e18 | 0.509767 | ||||||||
\(664\) | 8.83757e17 | 0.400166 | ||||||||
\(665\) | 1.06702e16 | 0.00478445 | ||||||||
\(666\) | −1.51081e18 | −0.670852 | ||||||||
\(667\) | 4.68076e17 | 0.205825 | ||||||||
\(668\) | −4.23437e17 | −0.184392 | ||||||||
\(669\) | 4.98560e17 | 0.215005 | ||||||||
\(670\) | −3.65156e16 | −0.0155952 | ||||||||
\(671\) | 5.62747e17 | 0.238022 | ||||||||
\(672\) | 1.14823e18 | 0.480982 | ||||||||
\(673\) | 7.64288e17 | 0.317073 | 0.158537 | − | 0.987353i | \(-0.449322\pi\) | ||||
0.158537 | + | 0.987353i | \(0.449322\pi\) | |||||||
\(674\) | −1.91135e18 | −0.785327 | ||||||||
\(675\) | −4.72907e17 | −0.192443 | ||||||||
\(676\) | 9.20245e17 | 0.370894 | ||||||||
\(677\) | 1.17853e18 | 0.470452 | 0.235226 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235226 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(678\) | −1.09902e18 | −0.434522 | ||||||||
\(679\) | −2.99782e18 | −1.17396 | ||||||||
\(680\) | −4.44194e15 | −0.00172292 | ||||||||
\(681\) | 1.46054e18 | 0.561123 | ||||||||
\(682\) | −2.42226e17 | −0.0921768 | ||||||||
\(683\) | −2.54053e18 | −0.957613 | −0.478807 | − | 0.877920i | \(-0.658931\pi\) | ||||
−0.478807 | + | 0.877920i | \(0.658931\pi\) | |||||||
\(684\) | 6.88844e17 | 0.257191 | ||||||||
\(685\) | 2.39727e16 | 0.00886599 | ||||||||
\(686\) | 3.76530e18 | 1.37941 | ||||||||
\(687\) | −3.70009e17 | −0.134275 | ||||||||
\(688\) | 4.32792e18 | 1.55580 | ||||||||
\(689\) | −2.32065e18 | −0.826389 | ||||||||
\(690\) | 9.35047e15 | 0.00329848 | ||||||||
\(691\) | 1.34331e18 | 0.469429 | 0.234715 | − | 0.972064i | \(-0.424584\pi\) | ||||
0.234715 | + | 0.972064i | \(0.424584\pi\) | |||||||
\(692\) | 3.67161e18 | 1.27106 | ||||||||
\(693\) | 1.48549e17 | 0.0509451 | ||||||||
\(694\) | 4.53460e18 | 1.54065 | ||||||||
\(695\) | 9.88190e15 | 0.00332613 | ||||||||
\(696\) | −1.96332e17 | −0.0654684 | ||||||||
\(697\) | −5.68223e17 | −0.187718 | ||||||||
\(698\) | 4.76211e18 | 1.55862 | ||||||||
\(699\) | 2.91067e18 | 0.943825 | ||||||||
\(700\) | −1.53291e18 | −0.492471 | ||||||||
\(701\) | 4.56459e18 | 1.45290 | 0.726448 | − | 0.687221i | \(-0.241170\pi\) | ||||
0.726448 | + | 0.687221i | \(0.241170\pi\) | |||||||
\(702\) | 9.84341e17 | 0.310423 | ||||||||
\(703\) | 5.40574e18 | 1.68906 | ||||||||
\(704\) | −2.44858e17 | −0.0758041 | ||||||||
\(705\) | −4.01219e15 | −0.00123070 | ||||||||
\(706\) | −4.49254e18 | −1.36540 | ||||||||
\(707\) | −3.01250e18 | −0.907196 | ||||||||
\(708\) | −1.77396e17 | −0.0529333 | ||||||||
\(709\) | 6.17963e18 | 1.82710 | 0.913549 | − | 0.406729i | \(-0.133331\pi\) | ||||
0.913549 | + | 0.406729i | \(0.133331\pi\) | |||||||
\(710\) | −2.65956e16 | −0.00779167 | ||||||||
\(711\) | 1.47636e18 | 0.428586 | ||||||||
\(712\) | −1.05083e18 | −0.302282 | ||||||||
\(713\) | −7.94365e17 | −0.226432 | ||||||||
\(714\) | 1.33347e18 | 0.376657 | ||||||||
\(715\) | −6.02408e15 | −0.00168617 | ||||||||
\(716\) | −3.38917e18 | −0.940068 | ||||||||
\(717\) | 3.57649e17 | 0.0983064 | ||||||||
\(718\) | 3.55748e18 | 0.969022 | ||||||||
\(719\) | 4.19765e18 | 1.13310 | 0.566550 | − | 0.824028i | \(-0.308278\pi\) | ||||
0.566550 | + | 0.824028i | \(0.308278\pi\) | |||||||
\(720\) | −9.40155e15 | −0.00251500 | ||||||||
\(721\) | −5.20039e17 | −0.137866 | ||||||||
\(722\) | −9.95727e17 | −0.261606 | ||||||||
\(723\) | 2.28494e18 | 0.594943 | ||||||||
\(724\) | −3.38736e18 | −0.874099 | ||||||||
\(725\) | 1.14830e18 | 0.293670 | ||||||||
\(726\) | 2.83163e18 | 0.717710 | ||||||||
\(727\) | −6.06778e18 | −1.52425 | −0.762124 | − | 0.647431i | \(-0.775844\pi\) | ||||
−0.762124 | + | 0.647431i | \(0.775844\pi\) | |||||||
\(728\) | −1.34006e18 | −0.333634 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 2.63810e16 | 0.00645199 | ||||||||
\(731\) | 3.79583e18 | 0.920118 | ||||||||
\(732\) | 1.84311e18 | 0.442823 | ||||||||
\(733\) | −3.74219e18 | −0.891147 | −0.445574 | − | 0.895245i | \(-0.647000\pi\) | ||||
−0.445574 | + | 0.895245i | \(0.647000\pi\) | |||||||
\(734\) | 3.79130e18 | 0.894878 | ||||||||
\(735\) | −7.87341e15 | −0.00184202 | ||||||||
\(736\) | −3.60027e18 | −0.834891 | ||||||||
\(737\) | 1.81894e18 | 0.418101 | ||||||||
\(738\) | −5.01713e17 | −0.114311 | ||||||||
\(739\) | −7.18460e18 | −1.62261 | −0.811304 | − | 0.584624i | \(-0.801242\pi\) | ||||
−0.811304 | + | 0.584624i | \(0.801242\pi\) | |||||||
\(740\) | 3.02826e16 | 0.00677934 | ||||||||
\(741\) | −3.52202e18 | −0.781579 | ||||||||
\(742\) | −2.77578e18 | −0.610603 | ||||||||
\(743\) | −7.38192e18 | −1.60969 | −0.804844 | − | 0.593486i | \(-0.797751\pi\) | ||||
−0.804844 | + | 0.593486i | \(0.797751\pi\) | |||||||
\(744\) | 3.33193e17 | 0.0720230 | ||||||||
\(745\) | 3.37112e16 | 0.00722368 | ||||||||
\(746\) | −5.14504e18 | −1.09291 | ||||||||
\(747\) | 1.64054e18 | 0.345464 | ||||||||
\(748\) | −5.26839e17 | −0.109981 | ||||||||
\(749\) | 3.86776e17 | 0.0800438 | ||||||||
\(750\) | 4.58788e16 | 0.00941268 | ||||||||
\(751\) | 4.82403e18 | 0.981185 | 0.490592 | − | 0.871389i | \(-0.336780\pi\) | ||||
0.490592 | + | 0.871389i | \(0.336780\pi\) | |||||||
\(752\) | 2.04556e18 | 0.412473 | ||||||||
\(753\) | 3.18292e18 | 0.636294 | ||||||||
\(754\) | −2.39016e18 | −0.473710 | ||||||||
\(755\) | −3.72863e16 | −0.00732646 | ||||||||
\(756\) | 4.86528e17 | 0.0947798 | ||||||||
\(757\) | 2.59728e18 | 0.501644 | 0.250822 | − | 0.968033i | \(-0.419299\pi\) | ||||
0.250822 | + | 0.968033i | \(0.419299\pi\) | |||||||
\(758\) | 1.27027e18 | 0.243246 | ||||||||
\(759\) | −4.65773e17 | −0.0884307 | ||||||||
\(760\) | 1.40331e16 | 0.00264160 | ||||||||
\(761\) | −8.02151e18 | −1.49712 | −0.748559 | − | 0.663068i | \(-0.769254\pi\) | ||||
−0.748559 | + | 0.663068i | \(0.769254\pi\) | |||||||
\(762\) | 7.77787e18 | 1.43931 | ||||||||
\(763\) | −1.50004e18 | −0.275229 | ||||||||
\(764\) | 4.86369e18 | 0.884828 | ||||||||
\(765\) | −8.24568e15 | −0.00148740 | ||||||||
\(766\) | −6.46867e18 | −1.15699 | ||||||||
\(767\) | 9.07018e17 | 0.160859 | ||||||||
\(768\) | 4.30378e18 | 0.756836 | ||||||||
\(769\) | 6.41075e18 | 1.11786 | 0.558931 | − | 0.829214i | \(-0.311212\pi\) | ||||
0.558931 | + | 0.829214i | \(0.311212\pi\) | |||||||
\(770\) | −7.20553e15 | −0.00124588 | ||||||||
\(771\) | 1.99905e18 | 0.342744 | ||||||||
\(772\) | 6.94571e18 | 1.18088 | ||||||||
\(773\) | 1.06884e19 | 1.80196 | 0.900980 | − | 0.433861i | \(-0.142849\pi\) | ||||
0.900980 | + | 0.433861i | \(0.142849\pi\) | |||||||
\(774\) | 3.35153e18 | 0.560307 | ||||||||
\(775\) | −1.94877e18 | −0.323072 | ||||||||
\(776\) | −3.94264e18 | −0.648166 | ||||||||
\(777\) | 3.81805e18 | 0.622451 | ||||||||
\(778\) | −1.56050e19 | −2.52288 | ||||||||
\(779\) | 1.79515e18 | 0.287811 | ||||||||
\(780\) | −1.97301e16 | −0.00313700 | ||||||||
\(781\) | 1.32480e18 | 0.208891 | ||||||||
\(782\) | −4.18110e18 | −0.653803 | ||||||||
\(783\) | −3.64457e17 | −0.0565190 | ||||||||
\(784\) | 4.01414e18 | 0.617360 | ||||||||
\(785\) | 4.86646e16 | 0.00742267 | ||||||||
\(786\) | −4.62813e18 | −0.700098 | ||||||||
\(787\) | −1.40570e17 | −0.0210891 | −0.0105445 | − | 0.999944i | \(-0.503356\pi\) | ||||
−0.0105445 | + | 0.999944i | \(0.503356\pi\) | |||||||
\(788\) | −6.37051e18 | −0.947881 | ||||||||
\(789\) | −4.72480e18 | −0.697241 | ||||||||
\(790\) | −7.16124e16 | −0.0104812 | ||||||||
\(791\) | 2.77739e18 | 0.403172 | ||||||||
\(792\) | 1.95366e17 | 0.0281278 | ||||||||
\(793\) | −9.42373e18 | −1.34570 | ||||||||
\(794\) | −6.22507e18 | −0.881680 | ||||||||
\(795\) | 1.71643e16 | 0.00241124 | ||||||||
\(796\) | −3.61855e18 | −0.504197 | ||||||||
\(797\) | −9.38764e17 | −0.129741 | −0.0648705 | − | 0.997894i | \(-0.520663\pi\) | ||||
−0.0648705 | + | 0.997894i | \(0.520663\pi\) | |||||||
\(798\) | −4.21276e18 | −0.577494 | ||||||||
\(799\) | 1.79407e18 | 0.243941 | ||||||||
\(800\) | −8.83233e18 | −1.19122 | ||||||||
\(801\) | −1.95068e18 | −0.260960 | ||||||||
\(802\) | −1.64841e19 | −2.18742 | ||||||||
\(803\) | −1.31411e18 | −0.172975 | ||||||||
\(804\) | 5.95742e18 | 0.777847 | ||||||||
\(805\) | −2.36301e16 | −0.00306050 | ||||||||
\(806\) | 4.05630e18 | 0.521137 | ||||||||
\(807\) | −5.25429e18 | −0.669632 | ||||||||
\(808\) | −3.96195e18 | −0.500881 | ||||||||
\(809\) | −5.09036e18 | −0.638386 | −0.319193 | − | 0.947690i | \(-0.603412\pi\) | ||||
−0.319193 | + | 0.947690i | \(0.603412\pi\) | |||||||
\(810\) | −7.28053e15 | −0.000905754 0 | ||||||||
\(811\) | −1.71416e18 | −0.211552 | −0.105776 | − | 0.994390i | \(-0.533733\pi\) | ||||
−0.105776 | + | 0.994390i | \(0.533733\pi\) | |||||||
\(812\) | −1.18138e18 | −0.144635 | ||||||||
\(813\) | 1.23807e18 | 0.150368 | ||||||||
\(814\) | −3.65046e18 | −0.439834 | ||||||||
\(815\) | −1.14187e16 | −0.00136488 | ||||||||
\(816\) | 4.20394e18 | 0.498506 | ||||||||
\(817\) | −1.19919e19 | −1.41073 | ||||||||
\(818\) | 1.18281e19 | 1.38044 | ||||||||
\(819\) | −2.48759e18 | −0.288027 | ||||||||
\(820\) | 1.00563e16 | 0.00115518 | ||||||||
\(821\) | −7.13051e18 | −0.812625 | −0.406313 | − | 0.913734i | \(-0.633186\pi\) | ||||
−0.406313 | + | 0.913734i | \(0.633186\pi\) | |||||||
\(822\) | −9.46476e18 | −1.07015 | ||||||||
\(823\) | −2.67308e18 | −0.299856 | −0.149928 | − | 0.988697i | \(-0.547904\pi\) | ||||
−0.149928 | + | 0.988697i | \(0.547904\pi\) | |||||||
\(824\) | −6.83939e17 | −0.0761185 | ||||||||
\(825\) | −1.14265e18 | −0.126172 | ||||||||
\(826\) | 1.08490e18 | 0.118856 | ||||||||
\(827\) | 8.64840e18 | 0.940048 | 0.470024 | − | 0.882654i | \(-0.344245\pi\) | ||||
0.470024 | + | 0.882654i | \(0.344245\pi\) | |||||||
\(828\) | −1.52551e18 | −0.164519 | ||||||||
\(829\) | −7.23666e18 | −0.774343 | −0.387172 | − | 0.922008i | \(-0.626548\pi\) | ||||
−0.387172 | + | 0.922008i | \(0.626548\pi\) | |||||||
\(830\) | −7.95765e16 | −0.00844845 | ||||||||
\(831\) | 7.85063e18 | 0.826986 | ||||||||
\(832\) | 4.10039e18 | 0.428571 | ||||||||
\(833\) | 3.52063e18 | 0.365114 | ||||||||
\(834\) | −3.90152e18 | −0.401472 | ||||||||
\(835\) | −1.60131e16 | −0.00163499 | ||||||||
\(836\) | 1.66441e18 | 0.168624 | ||||||||
\(837\) | 6.18514e17 | 0.0621776 | ||||||||
\(838\) | −2.37154e19 | −2.36561 | ||||||||
\(839\) | −2.13793e18 | −0.211612 | −0.105806 | − | 0.994387i | \(-0.533742\pi\) | ||||
−0.105806 | + | 0.994387i | \(0.533742\pi\) | |||||||
\(840\) | 9.91155e15 | 0.000973478 0 | ||||||||
\(841\) | −9.37566e18 | −0.913751 | ||||||||
\(842\) | −4.01904e17 | −0.0388682 | ||||||||
\(843\) | −2.50299e18 | −0.240204 | ||||||||
\(844\) | 8.75357e18 | 0.833603 | ||||||||
\(845\) | 3.48010e16 | 0.00328869 | ||||||||
\(846\) | 1.58407e18 | 0.148548 | ||||||||
\(847\) | −7.15599e18 | −0.665929 | ||||||||
\(848\) | −8.75098e18 | −0.808134 | ||||||||
\(849\) | 2.80503e18 | 0.257062 | ||||||||
\(850\) | −1.02572e19 | −0.932841 | ||||||||
\(851\) | −1.19715e19 | −1.08045 | ||||||||
\(852\) | 4.33900e18 | 0.388627 | ||||||||
\(853\) | 9.16116e18 | 0.814295 | 0.407147 | − | 0.913362i | \(-0.366524\pi\) | ||||
0.407147 | + | 0.913362i | \(0.366524\pi\) | |||||||
\(854\) | −1.12719e19 | −0.994310 | ||||||||
\(855\) | 2.60501e16 | 0.00228049 | ||||||||
\(856\) | 5.08676e17 | 0.0441938 | ||||||||
\(857\) | 1.52454e19 | 1.31451 | 0.657254 | − | 0.753669i | \(-0.271718\pi\) | ||||
0.657254 | + | 0.753669i | \(0.271718\pi\) | |||||||
\(858\) | 2.37840e18 | 0.203525 | ||||||||
\(859\) | 2.09334e19 | 1.77781 | 0.888904 | − | 0.458094i | \(-0.151468\pi\) | ||||
0.888904 | + | 0.458094i | \(0.151468\pi\) | |||||||
\(860\) | −6.71780e16 | −0.00566222 | ||||||||
\(861\) | 1.26791e18 | 0.106064 | ||||||||
\(862\) | −8.28895e18 | −0.688181 | ||||||||
\(863\) | −1.62203e19 | −1.33656 | −0.668279 | − | 0.743911i | \(-0.732969\pi\) | ||||
−0.668279 | + | 0.743911i | \(0.732969\pi\) | |||||||
\(864\) | 2.80327e18 | 0.229258 | ||||||||
\(865\) | 1.38850e17 | 0.0112704 | ||||||||
\(866\) | 1.38476e18 | 0.111560 | ||||||||
\(867\) | −3.53334e18 | −0.282528 | ||||||||
\(868\) | 2.00490e18 | 0.159116 | ||||||||
\(869\) | 3.56722e18 | 0.280997 | ||||||||
\(870\) | 1.76784e16 | 0.00138219 | ||||||||
\(871\) | −3.04600e19 | −2.36380 | ||||||||
\(872\) | −1.97281e18 | −0.151959 | ||||||||
\(873\) | −7.31883e18 | −0.559563 | ||||||||
\(874\) | 1.32091e19 | 1.00242 | ||||||||
\(875\) | −1.15943e17 | −0.00873357 | ||||||||
\(876\) | −4.30400e18 | −0.321807 | ||||||||
\(877\) | 1.29181e19 | 0.958739 | 0.479369 | − | 0.877613i | \(-0.340865\pi\) | ||||
0.479369 | + | 0.877613i | \(0.340865\pi\) | |||||||
\(878\) | −2.55374e17 | −0.0188132 | ||||||||
\(879\) | 1.42977e19 | 1.04553 | ||||||||
\(880\) | −2.27163e16 | −0.00164892 | ||||||||
\(881\) | 8.42062e18 | 0.606737 | 0.303369 | − | 0.952873i | \(-0.401889\pi\) | ||||
0.303369 | + | 0.952873i | \(0.401889\pi\) | |||||||
\(882\) | 3.10854e18 | 0.222336 | ||||||||
\(883\) | 6.23507e17 | 0.0442687 | 0.0221343 | − | 0.999755i | \(-0.492954\pi\) | ||||
0.0221343 | + | 0.999755i | \(0.492954\pi\) | |||||||
\(884\) | 8.82241e18 | 0.621796 | ||||||||
\(885\) | −6.70862e15 | −0.000469355 0 | ||||||||
\(886\) | −3.36538e19 | −2.33730 | ||||||||
\(887\) | −1.24814e19 | −0.860518 | −0.430259 | − | 0.902705i | \(-0.641578\pi\) | ||||
−0.430259 | + | 0.902705i | \(0.641578\pi\) | |||||||
\(888\) | 5.02138e18 | 0.343668 | ||||||||
\(889\) | −1.96559e19 | −1.33546 | ||||||||
\(890\) | 9.46201e16 | 0.00638188 | ||||||||
\(891\) | 3.62664e17 | 0.0242828 | ||||||||
\(892\) | 3.94544e18 | 0.262255 | ||||||||
\(893\) | −5.66788e18 | −0.374012 | ||||||||
\(894\) | −1.33097e19 | −0.871914 | ||||||||
\(895\) | −1.28169e17 | −0.00833551 | ||||||||
\(896\) | −7.99846e18 | −0.516422 | ||||||||
\(897\) | 7.79982e18 | 0.499958 | ||||||||
\(898\) | −1.37784e19 | −0.876802 | ||||||||
\(899\) | −1.50186e18 | −0.0948838 | ||||||||
\(900\) | −3.74243e18 | −0.234735 | ||||||||
\(901\) | −7.67510e18 | −0.477939 | ||||||||
\(902\) | −1.21225e18 | −0.0749465 | ||||||||
\(903\) | −8.46984e18 | −0.519882 | ||||||||
\(904\) | 3.65274e18 | 0.222599 | ||||||||
\(905\) | −1.28100e17 | −0.00775057 | ||||||||
\(906\) | 1.47212e19 | 0.884321 | ||||||||
\(907\) | −3.91182e18 | −0.233309 | −0.116654 | − | 0.993173i | \(-0.537217\pi\) | ||||
−0.116654 | + | 0.993173i | \(0.537217\pi\) | |||||||
\(908\) | 1.15583e19 | 0.684438 | ||||||||
\(909\) | −7.35466e18 | −0.432412 | ||||||||
\(910\) | 1.20663e17 | 0.00704380 | ||||||||
\(911\) | −7.75067e18 | −0.449231 | −0.224615 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224615 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(912\) | −1.32812e19 | −0.764315 | ||||||||
\(913\) | 3.96393e18 | 0.226499 | ||||||||
\(914\) | 5.92023e18 | 0.335883 | ||||||||
\(915\) | 6.97012e16 | 0.00392648 | ||||||||
\(916\) | −2.92813e18 | −0.163783 | ||||||||
\(917\) | 1.16960e19 | 0.649587 | ||||||||
\(918\) | 3.25552e18 | 0.179532 | ||||||||
\(919\) | 1.47948e19 | 0.810137 | 0.405068 | − | 0.914286i | \(-0.367248\pi\) | ||||
0.405068 | + | 0.914286i | \(0.367248\pi\) | |||||||
\(920\) | −3.10776e16 | −0.00168977 | ||||||||
\(921\) | 1.59049e19 | 0.858702 | ||||||||
\(922\) | 1.22256e19 | 0.655417 | ||||||||
\(923\) | −2.21851e19 | −1.18100 | ||||||||
\(924\) | 1.17556e18 | 0.0621410 | ||||||||
\(925\) | −2.93689e19 | −1.54158 | ||||||||
\(926\) | 3.78072e19 | 1.97062 | ||||||||
\(927\) | −1.26961e18 | −0.0657132 | ||||||||
\(928\) | −6.80684e18 | −0.349851 | ||||||||
\(929\) | 1.88038e19 | 0.959720 | 0.479860 | − | 0.877345i | \(-0.340688\pi\) | ||||
0.479860 | + | 0.877345i | \(0.340688\pi\) | |||||||
\(930\) | −3.00018e16 | −0.00152057 | ||||||||
\(931\) | −1.11225e19 | −0.559796 | ||||||||
\(932\) | 2.30341e19 | 1.15124 | ||||||||
\(933\) | 9.86437e18 | 0.489597 | ||||||||
\(934\) | −2.71758e19 | −1.33946 | ||||||||
\(935\) | −1.99235e16 | −0.000975192 0 | ||||||||
\(936\) | −3.27160e18 | −0.159025 | ||||||||
\(937\) | 1.56979e19 | 0.757766 | 0.378883 | − | 0.925445i | \(-0.376308\pi\) | ||||
0.378883 | + | 0.925445i | \(0.376308\pi\) | |||||||
\(938\) | −3.64338e19 | −1.74657 | ||||||||
\(939\) | −8.12666e18 | −0.386889 | ||||||||
\(940\) | −3.17511e16 | −0.00150116 | ||||||||
\(941\) | 1.50749e19 | 0.707820 | 0.353910 | − | 0.935279i | \(-0.384852\pi\) | ||||
0.353910 | + | 0.935279i | \(0.384852\pi\) | |||||||
\(942\) | −1.92135e19 | −0.895933 | ||||||||
\(943\) | −3.97552e18 | −0.184106 | ||||||||
\(944\) | 3.42029e18 | 0.157306 | ||||||||
\(945\) | 1.83990e16 | 0.000840405 0 | ||||||||
\(946\) | 8.09807e18 | 0.367358 | ||||||||
\(947\) | 4.53176e18 | 0.204170 | 0.102085 | − | 0.994776i | \(-0.467449\pi\) | ||||
0.102085 | + | 0.994776i | \(0.467449\pi\) | |||||||
\(948\) | 1.16834e19 | 0.522775 | ||||||||
\(949\) | 2.20061e19 | 0.977941 | ||||||||
\(950\) | 3.24050e19 | 1.43024 | ||||||||
\(951\) | 7.98647e18 | 0.350092 | ||||||||
\(952\) | −4.43199e18 | −0.192956 | ||||||||
\(953\) | −3.51372e19 | −1.51937 | −0.759685 | − | 0.650292i | \(-0.774647\pi\) | ||||
−0.759685 | + | 0.650292i | \(0.774647\pi\) | |||||||
\(954\) | −6.77673e18 | −0.291042 | ||||||||
\(955\) | 1.83930e17 | 0.00784570 | ||||||||
\(956\) | 2.83031e18 | 0.119911 | ||||||||
\(957\) | −8.80612e17 | −0.0370559 | ||||||||
\(958\) | −4.77953e17 | −0.0199760 | ||||||||
\(959\) | 2.39190e19 | 0.992936 | ||||||||
\(960\) | −3.03279e16 | −0.00125049 | ||||||||
\(961\) | −2.18688e19 | −0.895617 | ||||||||
\(962\) | 6.11305e19 | 2.48668 | ||||||||
\(963\) | 9.44267e17 | 0.0381526 | ||||||||
\(964\) | 1.80823e19 | 0.725691 | ||||||||
\(965\) | 2.62666e17 | 0.0104707 | ||||||||
\(966\) | 9.32953e18 | 0.369410 | ||||||||
\(967\) | 3.06736e19 | 1.20641 | 0.603203 | − | 0.797588i | \(-0.293891\pi\) | ||||
0.603203 | + | 0.797588i | \(0.293891\pi\) | |||||||
\(968\) | −9.41134e18 | −0.367673 | ||||||||
\(969\) | −1.16484e19 | −0.452024 | ||||||||
\(970\) | 3.55009e17 | 0.0136843 | ||||||||
\(971\) | 4.82739e19 | 1.84836 | 0.924182 | − | 0.381953i | \(-0.124748\pi\) | ||||
0.924182 | + | 0.381953i | \(0.124748\pi\) | |||||||
\(972\) | 1.18780e18 | 0.0451765 | ||||||||
\(973\) | 9.85977e18 | 0.372506 | ||||||||
\(974\) | 4.06233e19 | 1.52455 | ||||||||
\(975\) | 1.91348e19 | 0.713336 | ||||||||
\(976\) | −3.55361e19 | −1.31597 | ||||||||
\(977\) | 4.71263e19 | 1.73360 | 0.866799 | − | 0.498658i | \(-0.166174\pi\) | ||||
0.866799 | + | 0.498658i | \(0.166174\pi\) | |||||||
\(978\) | 4.50828e18 | 0.164744 | ||||||||
\(979\) | −4.71330e18 | −0.171095 | ||||||||
\(980\) | −6.23076e16 | −0.00224684 | ||||||||
\(981\) | −3.66217e18 | −0.131187 | ||||||||
\(982\) | −6.39197e19 | −2.27463 | ||||||||
\(983\) | 5.36003e19 | 1.89483 | 0.947414 | − | 0.320011i | \(-0.103687\pi\) | ||||
0.947414 | + | 0.320011i | \(0.103687\pi\) | |||||||
\(984\) | 1.66751e18 | 0.0585600 | ||||||||
\(985\) | −2.40914e17 | −0.00840479 | ||||||||
\(986\) | −7.90498e18 | −0.273969 | ||||||||
\(987\) | −4.00320e18 | −0.137831 | ||||||||
\(988\) | −2.78721e19 | −0.953343 | ||||||||
\(989\) | 2.65572e19 | 0.902414 | ||||||||
\(990\) | −1.75914e16 | −0.000593845 0 | ||||||||
\(991\) | 7.95774e18 | 0.266877 | 0.133438 | − | 0.991057i | \(-0.457398\pi\) | ||||
0.133438 | + | 0.991057i | \(0.457398\pi\) | |||||||
\(992\) | 1.15518e19 | 0.384878 | ||||||||
\(993\) | −1.01395e19 | −0.335617 | ||||||||
\(994\) | −2.65360e19 | −0.872619 | ||||||||
\(995\) | −1.36843e17 | −0.00447067 | ||||||||
\(996\) | 1.29827e19 | 0.421385 | ||||||||
\(997\) | 4.41803e19 | 1.42466 | 0.712328 | − | 0.701847i | \(-0.247641\pi\) | ||||
0.712328 | + | 0.701847i | \(0.247641\pi\) | |||||||
\(998\) | −2.41361e19 | −0.773246 | ||||||||
\(999\) | 9.32132e18 | 0.296689 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.14.a.c.1.6 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.6 | ✓ | 31 | 1.1 | even | 1 | trivial |