Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,46,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 46, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 46);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 46 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(12.8255726074\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 148878150x + 389915850150 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{6}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-13344.8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.41537e6 | −1.08155 | −0.540775 | − | 0.841167i | \(-0.681869\pi\) | ||||
−0.540775 | + | 0.841167i | \(0.681869\pi\) | |||||||
\(3\) | −1.72036e10 | −0.316512 | −0.158256 | − | 0.987398i | \(-0.550587\pi\) | ||||
−0.158256 | + | 0.987398i | \(0.550587\pi\) | |||||||
\(4\) | 5.97255e12 | 0.169750 | ||||||||
\(5\) | 2.46761e15 | 0.462862 | 0.231431 | − | 0.972851i | \(-0.425659\pi\) | ||||
0.231431 | + | 0.972851i | \(0.425659\pi\) | |||||||
\(6\) | 1.10367e17 | 0.342324 | ||||||||
\(7\) | 1.29065e19 | 1.24767 | 0.623837 | − | 0.781554i | \(-0.285573\pi\) | ||||
0.623837 | + | 0.781554i | \(0.285573\pi\) | |||||||
\(8\) | 1.87405e20 | 0.897957 | ||||||||
\(9\) | −2.65835e21 | −0.899820 | ||||||||
\(10\) | −1.58306e22 | −0.500608 | ||||||||
\(11\) | 7.78755e22 | 0.288447 | 0.144223 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144223 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(12\) | −1.02749e23 | −0.0537280 | ||||||||
\(13\) | −1.84585e25 | −1.59393 | −0.796967 | − | 0.604022i | \(-0.793564\pi\) | ||||
−0.796967 | + | 0.604022i | \(0.793564\pi\) | |||||||
\(14\) | −8.27997e25 | −1.34942 | ||||||||
\(15\) | −4.24517e25 | −0.146502 | ||||||||
\(16\) | −1.41241e27 | −1.14094 | ||||||||
\(17\) | −2.82858e27 | −0.584073 | −0.292037 | − | 0.956407i | \(-0.594333\pi\) | ||||
−0.292037 | + | 0.956407i | \(0.594333\pi\) | |||||||
\(18\) | 1.70543e28 | 0.973200 | ||||||||
\(19\) | 8.52388e28 | 1.44106 | 0.720529 | − | 0.693425i | \(-0.243899\pi\) | ||||
0.720529 | + | 0.693425i | \(0.243899\pi\) | |||||||
\(20\) | 1.47379e28 | 0.0785709 | ||||||||
\(21\) | −2.22037e29 | −0.394904 | ||||||||
\(22\) | −4.99600e29 | −0.311970 | ||||||||
\(23\) | −2.09625e30 | −0.481468 | −0.240734 | − | 0.970591i | \(-0.577388\pi\) | ||||
−0.240734 | + | 0.970591i | \(0.577388\pi\) | |||||||
\(24\) | −3.22403e30 | −0.284214 | ||||||||
\(25\) | −2.23326e31 | −0.785759 | ||||||||
\(26\) | 1.18418e32 | 1.72392 | ||||||||
\(27\) | 9.65579e31 | 0.601316 | ||||||||
\(28\) | 7.70845e31 | 0.211793 | ||||||||
\(29\) | −1.33372e33 | −1.66383 | −0.831915 | − | 0.554903i | \(-0.812755\pi\) | ||||
−0.831915 | + | 0.554903i | \(0.812755\pi\) | |||||||
\(30\) | 2.72343e32 | 0.158449 | ||||||||
\(31\) | −9.42299e32 | −0.262150 | −0.131075 | − | 0.991372i | \(-0.541843\pi\) | ||||
−0.131075 | + | 0.991372i | \(0.541843\pi\) | |||||||
\(32\) | 2.46741e33 | 0.336022 | ||||||||
\(33\) | −1.33974e33 | −0.0912969 | ||||||||
\(34\) | 1.81464e34 | 0.631704 | ||||||||
\(35\) | 3.18481e34 | 0.577501 | ||||||||
\(36\) | −1.58771e34 | −0.152745 | ||||||||
\(37\) | −8.78606e34 | −0.456305 | −0.228153 | − | 0.973625i | \(-0.573269\pi\) | ||||
−0.228153 | + | 0.973625i | \(0.573269\pi\) | |||||||
\(38\) | −5.46838e35 | −1.55858 | ||||||||
\(39\) | 3.17552e35 | 0.504500 | ||||||||
\(40\) | 4.62441e35 | 0.415630 | ||||||||
\(41\) | 2.03901e36 | 1.05144 | 0.525718 | − | 0.850659i | \(-0.323797\pi\) | ||||
0.525718 | + | 0.850659i | \(0.323797\pi\) | |||||||
\(42\) | 1.42445e36 | 0.427109 | ||||||||
\(43\) | −6.02099e36 | −1.06323 | −0.531615 | − | 0.846986i | \(-0.678415\pi\) | ||||
−0.531615 | + | 0.846986i | \(0.678415\pi\) | |||||||
\(44\) | 4.65116e35 | 0.0489639 | ||||||||
\(45\) | −6.55977e36 | −0.416492 | ||||||||
\(46\) | 1.34482e37 | 0.520732 | ||||||||
\(47\) | −4.75078e37 | −1.13387 | −0.566935 | − | 0.823763i | \(-0.691871\pi\) | ||||
−0.566935 | + | 0.823763i | \(0.691871\pi\) | |||||||
\(48\) | 2.42985e37 | 0.361120 | ||||||||
\(49\) | 5.95698e37 | 0.556691 | ||||||||
\(50\) | 1.43272e38 | 0.849837 | ||||||||
\(51\) | 4.86617e37 | 0.184866 | ||||||||
\(52\) | −1.10244e38 | −0.270571 | ||||||||
\(53\) | −7.36820e38 | −1.17802 | −0.589012 | − | 0.808124i | \(-0.700483\pi\) | ||||
−0.589012 | + | 0.808124i | \(0.700483\pi\) | |||||||
\(54\) | −6.19454e38 | −0.650354 | ||||||||
\(55\) | 1.92166e38 | 0.133511 | ||||||||
\(56\) | 2.41873e39 | 1.12036 | ||||||||
\(57\) | −1.46641e39 | −0.456112 | ||||||||
\(58\) | 8.55629e39 | 1.79951 | ||||||||
\(59\) | −9.51309e39 | −1.36192 | −0.680960 | − | 0.732321i | \(-0.738437\pi\) | ||||
−0.680960 | + | 0.732321i | \(0.738437\pi\) | |||||||
\(60\) | −2.53545e38 | −0.0248687 | ||||||||
\(61\) | −1.95631e39 | −0.132287 | −0.0661433 | − | 0.997810i | \(-0.521069\pi\) | ||||
−0.0661433 | + | 0.997810i | \(0.521069\pi\) | |||||||
\(62\) | 6.04519e39 | 0.283529 | ||||||||
\(63\) | −3.43099e40 | −1.12268 | ||||||||
\(64\) | 3.38654e40 | 0.777511 | ||||||||
\(65\) | −4.55483e40 | −0.737772 | ||||||||
\(66\) | 8.59491e39 | 0.0987422 | ||||||||
\(67\) | 2.10749e41 | 1.72617 | 0.863083 | − | 0.505062i | \(-0.168530\pi\) | ||||
0.863083 | + | 0.505062i | \(0.168530\pi\) | |||||||
\(68\) | −1.68938e40 | −0.0991466 | ||||||||
\(69\) | 3.60631e40 | 0.152391 | ||||||||
\(70\) | −2.04317e41 | −0.624596 | ||||||||
\(71\) | −5.43331e41 | −1.20712 | −0.603561 | − | 0.797317i | \(-0.706252\pi\) | ||||
−0.603561 | + | 0.797317i | \(0.706252\pi\) | |||||||
\(72\) | −4.98187e41 | −0.807999 | ||||||||
\(73\) | 8.99506e41 | 1.06965 | 0.534823 | − | 0.844964i | \(-0.320378\pi\) | ||||
0.534823 | + | 0.844964i | \(0.320378\pi\) | |||||||
\(74\) | 5.63658e41 | 0.493517 | ||||||||
\(75\) | 3.84201e41 | 0.248702 | ||||||||
\(76\) | 5.09093e41 | 0.244620 | ||||||||
\(77\) | 1.00510e42 | 0.359888 | ||||||||
\(78\) | −2.03721e42 | −0.545642 | ||||||||
\(79\) | −7.61415e41 | −0.153113 | −0.0765565 | − | 0.997065i | \(-0.524393\pi\) | ||||
−0.0765565 | + | 0.997065i | \(0.524393\pi\) | |||||||
\(80\) | −3.48528e42 | −0.528095 | ||||||||
\(81\) | 6.19245e42 | 0.709496 | ||||||||
\(82\) | −1.30810e43 | −1.13718 | ||||||||
\(83\) | 6.62221e42 | 0.438274 | 0.219137 | − | 0.975694i | \(-0.429676\pi\) | ||||
0.219137 | + | 0.975694i | \(0.429676\pi\) | |||||||
\(84\) | −1.32613e42 | −0.0670351 | ||||||||
\(85\) | −6.97983e42 | −0.270345 | ||||||||
\(86\) | 3.86268e43 | 1.14994 | ||||||||
\(87\) | 2.29447e43 | 0.526623 | ||||||||
\(88\) | 1.45942e43 | 0.259013 | ||||||||
\(89\) | −6.63932e43 | −0.913794 | −0.456897 | − | 0.889520i | \(-0.651039\pi\) | ||||
−0.456897 | + | 0.889520i | \(0.651039\pi\) | |||||||
\(90\) | 4.20833e43 | 0.450457 | ||||||||
\(91\) | −2.38234e44 | −1.98871 | ||||||||
\(92\) | −1.25200e43 | −0.0817293 | ||||||||
\(93\) | 1.62109e43 | 0.0829738 | ||||||||
\(94\) | 3.04780e44 | 1.22634 | ||||||||
\(95\) | 2.10336e44 | 0.667011 | ||||||||
\(96\) | −4.24483e43 | −0.106355 | ||||||||
\(97\) | 1.95163e44 | 0.387288 | 0.193644 | − | 0.981072i | \(-0.437969\pi\) | ||||
0.193644 | + | 0.981072i | \(0.437969\pi\) | |||||||
\(98\) | −3.82162e44 | −0.602090 | ||||||||
\(99\) | −2.07020e44 | −0.259550 | ||||||||
\(100\) | −1.33383e44 | −0.133383 | ||||||||
\(101\) | −3.07178e44 | −0.245561 | −0.122780 | − | 0.992434i | \(-0.539181\pi\) | ||||
−0.122780 | + | 0.992434i | \(0.539181\pi\) | |||||||
\(102\) | −3.12182e44 | −0.199942 | ||||||||
\(103\) | 1.90315e45 | 0.978666 | 0.489333 | − | 0.872097i | \(-0.337240\pi\) | ||||
0.489333 | + | 0.872097i | \(0.337240\pi\) | |||||||
\(104\) | −3.45920e45 | −1.43128 | ||||||||
\(105\) | −5.47902e44 | −0.182786 | ||||||||
\(106\) | 4.72697e45 | 1.27409 | ||||||||
\(107\) | 1.11782e45 | 0.243915 | 0.121958 | − | 0.992535i | \(-0.461083\pi\) | ||||
0.121958 | + | 0.992535i | \(0.461083\pi\) | |||||||
\(108\) | 5.76697e44 | 0.102074 | ||||||||
\(109\) | 3.21871e45 | 0.463005 | 0.231502 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(110\) | −1.23282e45 | −0.144399 | ||||||||
\(111\) | 1.51152e45 | 0.144426 | ||||||||
\(112\) | −1.82292e46 | −1.42352 | ||||||||
\(113\) | −1.15806e46 | −0.740397 | −0.370198 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370198 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(114\) | 9.40757e45 | 0.493308 | ||||||||
\(115\) | −5.17274e45 | −0.222853 | ||||||||
\(116\) | −7.96570e45 | −0.282435 | ||||||||
\(117\) | 4.90691e46 | 1.43425 | ||||||||
\(118\) | 6.10300e46 | 1.47298 | ||||||||
\(119\) | −3.65069e46 | −0.728733 | ||||||||
\(120\) | −7.95565e45 | −0.131552 | ||||||||
\(121\) | −6.68259e46 | −0.916798 | ||||||||
\(122\) | 1.25504e46 | 0.143075 | ||||||||
\(123\) | −3.50783e46 | −0.332792 | ||||||||
\(124\) | −5.62793e45 | −0.0445001 | ||||||||
\(125\) | −1.25242e47 | −0.826560 | ||||||||
\(126\) | 2.20110e47 | 1.21424 | ||||||||
\(127\) | 6.85398e46 | 0.316489 | 0.158245 | − | 0.987400i | \(-0.449417\pi\) | ||||
0.158245 | + | 0.987400i | \(0.449417\pi\) | |||||||
\(128\) | −3.04073e47 | −1.17694 | ||||||||
\(129\) | 1.03583e47 | 0.336525 | ||||||||
\(130\) | 2.92209e47 | 0.797937 | ||||||||
\(131\) | −3.50099e46 | −0.0804613 | −0.0402306 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402306 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(132\) | −8.00166e45 | −0.0154977 | ||||||||
\(133\) | 1.10013e48 | 1.79797 | ||||||||
\(134\) | −1.35203e48 | −1.86693 | ||||||||
\(135\) | 2.38267e47 | 0.278326 | ||||||||
\(136\) | −5.30088e47 | −0.524472 | ||||||||
\(137\) | −1.53504e48 | −1.28798 | −0.643989 | − | 0.765035i | \(-0.722722\pi\) | ||||
−0.643989 | + | 0.765035i | \(0.722722\pi\) | |||||||
\(138\) | −2.31358e47 | −0.164818 | ||||||||
\(139\) | 1.45287e48 | 0.879818 | 0.439909 | − | 0.898042i | \(-0.355011\pi\) | ||||
0.439909 | + | 0.898042i | \(0.355011\pi\) | |||||||
\(140\) | 1.90215e47 | 0.0980309 | ||||||||
\(141\) | 8.17304e47 | 0.358884 | ||||||||
\(142\) | 3.48566e48 | 1.30556 | ||||||||
\(143\) | −1.43746e48 | −0.459765 | ||||||||
\(144\) | 3.75468e48 | 1.02664 | ||||||||
\(145\) | −3.29110e48 | −0.770123 | ||||||||
\(146\) | −5.77066e48 | −1.15688 | ||||||||
\(147\) | −1.02481e48 | −0.176200 | ||||||||
\(148\) | −5.24752e47 | −0.0774579 | ||||||||
\(149\) | 6.21806e47 | 0.0788794 | 0.0394397 | − | 0.999222i | \(-0.487443\pi\) | ||||
0.0394397 | + | 0.999222i | \(0.487443\pi\) | |||||||
\(150\) | −2.46479e48 | −0.268984 | ||||||||
\(151\) | −5.84550e48 | −0.549339 | −0.274670 | − | 0.961539i | \(-0.588568\pi\) | ||||
−0.274670 | + | 0.961539i | \(0.588568\pi\) | |||||||
\(152\) | 1.59741e49 | 1.29401 | ||||||||
\(153\) | 7.51935e48 | 0.525561 | ||||||||
\(154\) | −6.44807e48 | −0.389236 | ||||||||
\(155\) | −2.32523e48 | −0.121339 | ||||||||
\(156\) | 1.89660e48 | 0.0856389 | ||||||||
\(157\) | 2.07022e48 | 0.0809607 | 0.0404804 | − | 0.999180i | \(-0.487111\pi\) | ||||
0.0404804 | + | 0.999180i | \(0.487111\pi\) | |||||||
\(158\) | 4.88476e48 | 0.165599 | ||||||||
\(159\) | 1.26759e49 | 0.372859 | ||||||||
\(160\) | 6.08861e48 | 0.155532 | ||||||||
\(161\) | −2.70552e49 | −0.600715 | ||||||||
\(162\) | −3.97269e49 | −0.767355 | ||||||||
\(163\) | −4.16253e49 | −0.700062 | −0.350031 | − | 0.936738i | \(-0.613829\pi\) | ||||
−0.350031 | + | 0.936738i | \(0.613829\pi\) | |||||||
\(164\) | 1.21781e49 | 0.178481 | ||||||||
\(165\) | −3.30595e48 | −0.0422579 | ||||||||
\(166\) | −4.24839e49 | −0.474015 | ||||||||
\(167\) | 1.93069e50 | 1.88188 | 0.940941 | − | 0.338570i | \(-0.109943\pi\) | ||||
0.940941 | + | 0.338570i | \(0.109943\pi\) | |||||||
\(168\) | −4.16108e49 | −0.354607 | ||||||||
\(169\) | 2.06609e50 | 1.54063 | ||||||||
\(170\) | 4.47782e49 | 0.292392 | ||||||||
\(171\) | −2.26595e50 | −1.29669 | ||||||||
\(172\) | −3.59607e49 | −0.180484 | ||||||||
\(173\) | −8.78028e48 | −0.0386786 | −0.0193393 | − | 0.999813i | \(-0.506156\pi\) | ||||
−0.0193393 | + | 0.999813i | \(0.506156\pi\) | |||||||
\(174\) | −1.47199e50 | −0.569569 | ||||||||
\(175\) | −2.88235e50 | −0.980371 | ||||||||
\(176\) | −1.09992e50 | −0.329099 | ||||||||
\(177\) | 1.63659e50 | 0.431064 | ||||||||
\(178\) | 4.25937e50 | 0.988314 | ||||||||
\(179\) | 3.03604e50 | 0.621032 | 0.310516 | − | 0.950568i | \(-0.399498\pi\) | ||||
0.310516 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(180\) | −3.91786e49 | −0.0706997 | ||||||||
\(181\) | −1.05625e51 | −1.68268 | −0.841338 | − | 0.540509i | \(-0.818232\pi\) | ||||
−0.841338 | + | 0.540509i | \(0.818232\pi\) | |||||||
\(182\) | 1.52836e51 | 2.15089 | ||||||||
\(183\) | 3.36555e49 | 0.0418703 | ||||||||
\(184\) | −3.92847e50 | −0.432337 | ||||||||
\(185\) | −2.16806e50 | −0.211206 | ||||||||
\(186\) | −1.03999e50 | −0.0897403 | ||||||||
\(187\) | −2.20277e50 | −0.168474 | ||||||||
\(188\) | −2.83743e50 | −0.192475 | ||||||||
\(189\) | 1.24622e51 | 0.750247 | ||||||||
\(190\) | −1.34938e51 | −0.721405 | ||||||||
\(191\) | −1.95146e51 | −0.927060 | −0.463530 | − | 0.886081i | \(-0.653417\pi\) | ||||
−0.463530 | + | 0.886081i | \(0.653417\pi\) | |||||||
\(192\) | −5.82606e50 | −0.246092 | ||||||||
\(193\) | 2.53211e51 | 0.951574 | 0.475787 | − | 0.879561i | \(-0.342163\pi\) | ||||
0.475787 | + | 0.879561i | \(0.342163\pi\) | |||||||
\(194\) | −1.25205e51 | −0.418872 | ||||||||
\(195\) | 7.83594e50 | 0.233514 | ||||||||
\(196\) | 3.55784e50 | 0.0944985 | ||||||||
\(197\) | 5.70705e51 | 1.35183 | 0.675914 | − | 0.736981i | \(-0.263749\pi\) | ||||
0.675914 | + | 0.736981i | \(0.263749\pi\) | |||||||
\(198\) | 1.32811e51 | 0.280716 | ||||||||
\(199\) | 2.85140e51 | 0.538102 | 0.269051 | − | 0.963126i | \(-0.413290\pi\) | ||||
0.269051 | + | 0.963126i | \(0.413290\pi\) | |||||||
\(200\) | −4.18523e51 | −0.705577 | ||||||||
\(201\) | −3.62564e51 | −0.546353 | ||||||||
\(202\) | 1.97066e51 | 0.265586 | ||||||||
\(203\) | −1.72136e52 | −2.07592 | ||||||||
\(204\) | 2.90634e50 | 0.0313811 | ||||||||
\(205\) | 5.03149e51 | 0.486670 | ||||||||
\(206\) | −1.22094e52 | −1.05848 | ||||||||
\(207\) | 5.57257e51 | 0.433235 | ||||||||
\(208\) | 2.60709e52 | 1.81858 | ||||||||
\(209\) | 6.63802e51 | 0.415668 | ||||||||
\(210\) | 3.51499e51 | 0.197692 | ||||||||
\(211\) | −1.00404e52 | −0.507455 | −0.253728 | − | 0.967276i | \(-0.581657\pi\) | ||||
−0.253728 | + | 0.967276i | \(0.581657\pi\) | |||||||
\(212\) | −4.40070e51 | −0.199970 | ||||||||
\(213\) | 9.34723e51 | 0.382069 | ||||||||
\(214\) | −7.17125e51 | −0.263806 | ||||||||
\(215\) | −1.48574e52 | −0.492129 | ||||||||
\(216\) | 1.80954e52 | 0.539956 | ||||||||
\(217\) | −1.21617e52 | −0.327078 | ||||||||
\(218\) | −2.06492e52 | −0.500763 | ||||||||
\(219\) | −1.54747e52 | −0.338556 | ||||||||
\(220\) | 1.14772e51 | 0.0226635 | ||||||||
\(221\) | 5.22112e52 | 0.930975 | ||||||||
\(222\) | −9.69694e51 | −0.156204 | ||||||||
\(223\) | −1.08955e53 | −1.58630 | −0.793151 | − | 0.609025i | \(-0.791561\pi\) | ||||
−0.793151 | + | 0.609025i | \(0.791561\pi\) | |||||||
\(224\) | 3.18456e52 | 0.419246 | ||||||||
\(225\) | 5.93679e52 | 0.707041 | ||||||||
\(226\) | 7.42935e52 | 0.800776 | ||||||||
\(227\) | 8.59683e51 | 0.0838990 | 0.0419495 | − | 0.999120i | \(-0.486643\pi\) | ||||
0.0419495 | + | 0.999120i | \(0.486643\pi\) | |||||||
\(228\) | −8.75823e51 | −0.0774252 | ||||||||
\(229\) | 8.54768e52 | 0.684779 | 0.342389 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342389 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(230\) | 3.31850e52 | 0.241027 | ||||||||
\(231\) | −1.72913e52 | −0.113909 | ||||||||
\(232\) | −2.49945e53 | −1.49405 | ||||||||
\(233\) | 1.94501e53 | 1.05539 | 0.527695 | − | 0.849434i | \(-0.323057\pi\) | ||||
0.527695 | + | 0.849434i | \(0.323057\pi\) | |||||||
\(234\) | −3.14796e53 | −1.55122 | ||||||||
\(235\) | −1.17231e53 | −0.524825 | ||||||||
\(236\) | −5.68175e52 | −0.231186 | ||||||||
\(237\) | 1.30991e52 | 0.0484621 | ||||||||
\(238\) | 2.34205e53 | 0.788161 | ||||||||
\(239\) | −4.67858e52 | −0.143272 | −0.0716360 | − | 0.997431i | \(-0.522822\pi\) | ||||
−0.0716360 | + | 0.997431i | \(0.522822\pi\) | |||||||
\(240\) | 5.99592e52 | 0.167149 | ||||||||
\(241\) | 5.41561e53 | 1.37488 | 0.687438 | − | 0.726243i | \(-0.258735\pi\) | ||||
0.687438 | + | 0.726243i | \(0.258735\pi\) | |||||||
\(242\) | 4.28713e53 | 0.991563 | ||||||||
\(243\) | −3.91795e53 | −0.825881 | ||||||||
\(244\) | −1.16842e52 | −0.0224557 | ||||||||
\(245\) | 1.46995e53 | 0.257671 | ||||||||
\(246\) | 2.25040e53 | 0.359932 | ||||||||
\(247\) | −1.57338e54 | −2.29695 | ||||||||
\(248\) | −1.76591e53 | −0.235400 | ||||||||
\(249\) | −1.13926e53 | −0.138719 | ||||||||
\(250\) | 8.03473e53 | 0.893966 | ||||||||
\(251\) | 2.39905e53 | 0.243995 | 0.121997 | − | 0.992530i | \(-0.461070\pi\) | ||||
0.121997 | + | 0.992530i | \(0.461070\pi\) | |||||||
\(252\) | −2.04918e53 | −0.190576 | ||||||||
\(253\) | −1.63247e53 | −0.138878 | ||||||||
\(254\) | −4.39708e53 | −0.342299 | ||||||||
\(255\) | 1.20078e53 | 0.0855676 | ||||||||
\(256\) | 7.59209e53 | 0.495407 | ||||||||
\(257\) | 1.10513e54 | 0.660569 | 0.330285 | − | 0.943881i | \(-0.392855\pi\) | ||||
0.330285 | + | 0.943881i | \(0.392855\pi\) | |||||||
\(258\) | −6.64520e53 | −0.363969 | ||||||||
\(259\) | −1.13397e54 | −0.569321 | ||||||||
\(260\) | −2.72040e53 | −0.125237 | ||||||||
\(261\) | 3.54549e54 | 1.49715 | ||||||||
\(262\) | 2.24601e53 | 0.0870229 | ||||||||
\(263\) | 9.95471e53 | 0.354017 | 0.177009 | − | 0.984209i | \(-0.443358\pi\) | ||||
0.177009 | + | 0.984209i | \(0.443358\pi\) | |||||||
\(264\) | −2.51073e53 | −0.0819807 | ||||||||
\(265\) | −1.81818e54 | −0.545263 | ||||||||
\(266\) | −7.05775e54 | −1.94460 | ||||||||
\(267\) | 1.14220e54 | 0.289227 | ||||||||
\(268\) | 1.25871e54 | 0.293017 | ||||||||
\(269\) | −1.90365e54 | −0.407532 | −0.203766 | − | 0.979020i | \(-0.565318\pi\) | ||||
−0.203766 | + | 0.979020i | \(0.565318\pi\) | |||||||
\(270\) | −1.52857e54 | −0.301024 | ||||||||
\(271\) | −2.11803e54 | −0.383815 | −0.191908 | − | 0.981413i | \(-0.561467\pi\) | ||||
−0.191908 | + | 0.981413i | \(0.561467\pi\) | |||||||
\(272\) | 3.99511e54 | 0.666390 | ||||||||
\(273\) | 4.09847e54 | 0.629452 | ||||||||
\(274\) | 9.84787e54 | 1.39301 | ||||||||
\(275\) | −1.73916e54 | −0.226650 | ||||||||
\(276\) | 2.15389e53 | 0.0258683 | ||||||||
\(277\) | 7.86883e54 | 0.871195 | 0.435598 | − | 0.900141i | \(-0.356537\pi\) | ||||
0.435598 | + | 0.900141i | \(0.356537\pi\) | |||||||
\(278\) | −9.32067e54 | −0.951567 | ||||||||
\(279\) | 2.50496e54 | 0.235888 | ||||||||
\(280\) | 5.96848e54 | 0.518571 | ||||||||
\(281\) | −2.25442e55 | −1.80777 | −0.903883 | − | 0.427781i | \(-0.859296\pi\) | ||||
−0.903883 | + | 0.427781i | \(0.859296\pi\) | |||||||
\(282\) | −5.24330e54 | −0.388150 | ||||||||
\(283\) | −5.22384e54 | −0.357104 | −0.178552 | − | 0.983930i | \(-0.557141\pi\) | ||||
−0.178552 | + | 0.983930i | \(0.557141\pi\) | |||||||
\(284\) | −3.24507e54 | −0.204909 | ||||||||
\(285\) | −3.61854e54 | −0.211117 | ||||||||
\(286\) | 9.22186e54 | 0.497259 | ||||||||
\(287\) | 2.63164e55 | 1.31185 | ||||||||
\(288\) | −6.55924e54 | −0.302359 | ||||||||
\(289\) | −1.54523e55 | −0.658858 | ||||||||
\(290\) | 2.11136e55 | 0.832927 | ||||||||
\(291\) | −3.35751e54 | −0.122582 | ||||||||
\(292\) | 5.37235e54 | 0.181573 | ||||||||
\(293\) | 1.63631e55 | 0.512088 | 0.256044 | − | 0.966665i | \(-0.417581\pi\) | ||||
0.256044 | + | 0.966665i | \(0.417581\pi\) | |||||||
\(294\) | 6.57456e54 | 0.190569 | ||||||||
\(295\) | −2.34746e55 | −0.630381 | ||||||||
\(296\) | −1.64655e55 | −0.409742 | ||||||||
\(297\) | 7.51950e54 | 0.173448 | ||||||||
\(298\) | −3.98911e54 | −0.0853121 | ||||||||
\(299\) | 3.86936e55 | 0.767428 | ||||||||
\(300\) | 2.29466e54 | 0.0422173 | ||||||||
\(301\) | −7.77096e55 | −1.32657 | ||||||||
\(302\) | 3.75010e55 | 0.594138 | ||||||||
\(303\) | 5.28456e54 | 0.0777230 | ||||||||
\(304\) | −1.20392e56 | −1.64415 | ||||||||
\(305\) | −4.82741e54 | −0.0612305 | ||||||||
\(306\) | −4.82394e55 | −0.568420 | ||||||||
\(307\) | 1.67269e56 | 1.83148 | 0.915741 | − | 0.401768i | \(-0.131604\pi\) | ||||
0.915741 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(308\) | 6.00300e54 | 0.0610910 | ||||||||
\(309\) | −3.27409e55 | −0.309760 | ||||||||
\(310\) | 1.49172e55 | 0.131235 | ||||||||
\(311\) | 2.38430e56 | 1.95097 | 0.975487 | − | 0.220058i | \(-0.0706246\pi\) | ||||
0.975487 | + | 0.220058i | \(0.0706246\pi\) | |||||||
\(312\) | 5.95107e55 | 0.453019 | ||||||||
\(313\) | −7.01155e55 | −0.496668 | −0.248334 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248334 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(314\) | −1.32812e55 | −0.0875631 | ||||||||
\(315\) | −8.46634e55 | −0.519647 | ||||||||
\(316\) | −4.54759e54 | −0.0259910 | ||||||||
\(317\) | −2.68335e56 | −1.42838 | −0.714191 | − | 0.699951i | \(-0.753205\pi\) | ||||
−0.714191 | + | 0.699951i | \(0.753205\pi\) | |||||||
\(318\) | −8.13208e55 | −0.403266 | ||||||||
\(319\) | −1.03864e56 | −0.479926 | ||||||||
\(320\) | 8.35666e55 | 0.359880 | ||||||||
\(321\) | −1.92306e55 | −0.0772021 | ||||||||
\(322\) | 1.73569e56 | 0.649704 | ||||||||
\(323\) | −2.41105e56 | −0.841683 | ||||||||
\(324\) | 3.69848e55 | 0.120437 | ||||||||
\(325\) | 4.12226e56 | 1.25245 | ||||||||
\(326\) | 2.67042e56 | 0.757152 | ||||||||
\(327\) | −5.53733e55 | −0.146547 | ||||||||
\(328\) | 3.82120e56 | 0.944144 | ||||||||
\(329\) | −6.13157e56 | −1.41470 | ||||||||
\(330\) | 2.12089e55 | 0.0457040 | ||||||||
\(331\) | 1.90982e56 | 0.384470 | 0.192235 | − | 0.981349i | \(-0.438426\pi\) | ||||
0.192235 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(332\) | 3.95515e55 | 0.0743971 | ||||||||
\(333\) | 2.33564e56 | 0.410593 | ||||||||
\(334\) | −1.23861e57 | −2.03535 | ||||||||
\(335\) | 5.20047e56 | 0.798977 | ||||||||
\(336\) | 3.13608e56 | 0.450560 | ||||||||
\(337\) | 2.57253e56 | 0.345691 | 0.172845 | − | 0.984949i | \(-0.444704\pi\) | ||||
0.172845 | + | 0.984949i | \(0.444704\pi\) | |||||||
\(338\) | −1.32547e57 | −1.66627 | ||||||||
\(339\) | 1.99227e56 | 0.234345 | ||||||||
\(340\) | −4.16874e55 | −0.0458912 | ||||||||
\(341\) | −7.33820e55 | −0.0756164 | ||||||||
\(342\) | 1.45369e57 | 1.40244 | ||||||||
\(343\) | −6.12245e56 | −0.553105 | ||||||||
\(344\) | −1.12836e57 | −0.954735 | ||||||||
\(345\) | 8.89896e55 | 0.0705358 | ||||||||
\(346\) | 5.63287e55 | 0.0418329 | ||||||||
\(347\) | 1.10908e57 | 0.771878 | 0.385939 | − | 0.922524i | \(-0.373877\pi\) | ||||
0.385939 | + | 0.922524i | \(0.373877\pi\) | |||||||
\(348\) | 1.37039e56 | 0.0893943 | ||||||||
\(349\) | 1.91424e57 | 1.17064 | 0.585321 | − | 0.810802i | \(-0.300968\pi\) | ||||
0.585321 | + | 0.810802i | \(0.300968\pi\) | |||||||
\(350\) | 1.84913e57 | 1.06032 | ||||||||
\(351\) | −1.78231e57 | −0.958459 | ||||||||
\(352\) | 1.92151e56 | 0.0969243 | ||||||||
\(353\) | −1.00890e57 | −0.477437 | −0.238719 | − | 0.971089i | \(-0.576727\pi\) | ||||
−0.238719 | + | 0.971089i | \(0.576727\pi\) | |||||||
\(354\) | −1.04993e57 | −0.466217 | ||||||||
\(355\) | −1.34073e57 | −0.558731 | ||||||||
\(356\) | −3.96537e56 | −0.155117 | ||||||||
\(357\) | 6.28050e56 | 0.230653 | ||||||||
\(358\) | −1.94773e57 | −0.671677 | ||||||||
\(359\) | −5.19166e57 | −1.68144 | −0.840720 | − | 0.541470i | \(-0.817868\pi\) | ||||
−0.840720 | + | 0.541470i | \(0.817868\pi\) | |||||||
\(360\) | −1.22933e57 | −0.373992 | ||||||||
\(361\) | 3.76691e57 | 1.07665 | ||||||||
\(362\) | 6.77626e57 | 1.81990 | ||||||||
\(363\) | 1.14964e57 | 0.290178 | ||||||||
\(364\) | −1.42286e57 | −0.337584 | ||||||||
\(365\) | 2.21963e57 | 0.495098 | ||||||||
\(366\) | −2.15912e56 | −0.0452849 | ||||||||
\(367\) | 5.07031e57 | 1.00011 | 0.500056 | − | 0.865993i | \(-0.333313\pi\) | ||||
0.500056 | + | 0.865993i | \(0.333313\pi\) | |||||||
\(368\) | 2.96077e57 | 0.549324 | ||||||||
\(369\) | −5.42041e57 | −0.946103 | ||||||||
\(370\) | 1.39089e57 | 0.228430 | ||||||||
\(371\) | −9.50974e57 | −1.46979 | ||||||||
\(372\) | 9.68205e55 | 0.0140848 | ||||||||
\(373\) | −5.35043e57 | −0.732723 | −0.366362 | − | 0.930473i | \(-0.619397\pi\) | ||||
−0.366362 | + | 0.930473i | \(0.619397\pi\) | |||||||
\(374\) | 1.41316e57 | 0.182213 | ||||||||
\(375\) | 2.15461e57 | 0.261616 | ||||||||
\(376\) | −8.90317e57 | −1.01817 | ||||||||
\(377\) | 2.46184e58 | 2.65204 | ||||||||
\(378\) | −7.99496e57 | −0.811430 | ||||||||
\(379\) | −1.65597e58 | −1.58369 | −0.791846 | − | 0.610720i | \(-0.790880\pi\) | ||||
−0.791846 | + | 0.610720i | \(0.790880\pi\) | |||||||
\(380\) | 1.25624e57 | 0.113225 | ||||||||
\(381\) | −1.17913e57 | −0.100173 | ||||||||
\(382\) | 1.25193e58 | 1.00266 | ||||||||
\(383\) | 4.08813e56 | 0.0308711 | 0.0154356 | − | 0.999881i | \(-0.495087\pi\) | ||||
0.0154356 | + | 0.999881i | \(0.495087\pi\) | |||||||
\(384\) | 5.23115e57 | 0.372515 | ||||||||
\(385\) | 2.48019e57 | 0.166578 | ||||||||
\(386\) | −1.62444e58 | −1.02917 | ||||||||
\(387\) | 1.60059e58 | 0.956716 | ||||||||
\(388\) | 1.16562e57 | 0.0657423 | ||||||||
\(389\) | 8.62061e57 | 0.458851 | 0.229426 | − | 0.973326i | \(-0.426315\pi\) | ||||
0.229426 | + | 0.973326i | \(0.426315\pi\) | |||||||
\(390\) | −5.02705e57 | −0.252557 | ||||||||
\(391\) | 5.92941e57 | 0.281213 | ||||||||
\(392\) | 1.11637e58 | 0.499885 | ||||||||
\(393\) | 6.02296e56 | 0.0254670 | ||||||||
\(394\) | −3.66128e58 | −1.46207 | ||||||||
\(395\) | −1.87888e57 | −0.0708702 | ||||||||
\(396\) | −1.23644e57 | −0.0440587 | ||||||||
\(397\) | −9.58101e57 | −0.322571 | −0.161285 | − | 0.986908i | \(-0.551564\pi\) | ||||
−0.161285 | + | 0.986908i | \(0.551564\pi\) | |||||||
\(398\) | −1.82928e58 | −0.581984 | ||||||||
\(399\) | −1.89262e58 | −0.569080 | ||||||||
\(400\) | 3.15428e58 | 0.896500 | ||||||||
\(401\) | −3.87566e58 | −1.04135 | −0.520676 | − | 0.853755i | \(-0.674320\pi\) | ||||
−0.520676 | + | 0.853755i | \(0.674320\pi\) | |||||||
\(402\) | 2.32598e58 | 0.590908 | ||||||||
\(403\) | 1.73934e58 | 0.417850 | ||||||||
\(404\) | −1.83464e57 | −0.0416840 | ||||||||
\(405\) | 1.52806e58 | 0.328399 | ||||||||
\(406\) | 1.10431e59 | 2.24521 | ||||||||
\(407\) | −6.84219e57 | −0.131620 | ||||||||
\(408\) | 9.11941e57 | 0.166002 | ||||||||
\(409\) | −2.12182e58 | −0.365539 | −0.182769 | − | 0.983156i | \(-0.558506\pi\) | ||||
−0.182769 | + | 0.983156i | \(0.558506\pi\) | |||||||
\(410\) | −3.22788e58 | −0.526358 | ||||||||
\(411\) | 2.64083e58 | 0.407661 | ||||||||
\(412\) | 1.13666e58 | 0.166129 | ||||||||
\(413\) | −1.22780e59 | −1.69923 | ||||||||
\(414\) | −3.57501e58 | −0.468565 | ||||||||
\(415\) | 1.63410e58 | 0.202860 | ||||||||
\(416\) | −4.55447e58 | −0.535596 | ||||||||
\(417\) | −2.49945e58 | −0.278473 | ||||||||
\(418\) | −4.25853e58 | −0.449566 | ||||||||
\(419\) | 7.28603e58 | 0.728913 | 0.364456 | − | 0.931220i | \(-0.381255\pi\) | ||||
0.364456 | + | 0.931220i | \(0.381255\pi\) | |||||||
\(420\) | −3.27237e57 | −0.0310280 | ||||||||
\(421\) | 6.69387e58 | 0.601631 | 0.300815 | − | 0.953682i | \(-0.402741\pi\) | ||||
0.300815 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(422\) | 6.44132e58 | 0.548838 | ||||||||
\(423\) | 1.26292e59 | 1.02028 | ||||||||
\(424\) | −1.38083e59 | −1.05781 | ||||||||
\(425\) | 6.31695e58 | 0.458941 | ||||||||
\(426\) | −5.99659e58 | −0.413227 | ||||||||
\(427\) | −2.52490e58 | −0.165051 | ||||||||
\(428\) | 6.67627e57 | 0.0414046 | ||||||||
\(429\) | 2.47295e58 | 0.145521 | ||||||||
\(430\) | 9.53160e58 | 0.532262 | ||||||||
\(431\) | 1.33907e59 | 0.709684 | 0.354842 | − | 0.934926i | \(-0.384535\pi\) | ||||
0.354842 | + | 0.934926i | \(0.384535\pi\) | |||||||
\(432\) | −1.36379e59 | −0.686063 | ||||||||
\(433\) | −1.66678e59 | −0.795976 | −0.397988 | − | 0.917391i | \(-0.630292\pi\) | ||||
−0.397988 | + | 0.917391i | \(0.630292\pi\) | |||||||
\(434\) | 7.80220e58 | 0.353751 | ||||||||
\(435\) | 5.66186e58 | 0.243754 | ||||||||
\(436\) | 1.92239e58 | 0.0785952 | ||||||||
\(437\) | −1.78682e59 | −0.693823 | ||||||||
\(438\) | 9.92761e58 | 0.366165 | ||||||||
\(439\) | −1.80307e59 | −0.631774 | −0.315887 | − | 0.948797i | \(-0.602302\pi\) | ||||
−0.315887 | + | 0.948797i | \(0.602302\pi\) | |||||||
\(440\) | 3.60129e58 | 0.119887 | ||||||||
\(441\) | −1.58357e59 | −0.500922 | ||||||||
\(442\) | −3.34954e59 | −1.00690 | ||||||||
\(443\) | 1.21940e59 | 0.348388 | 0.174194 | − | 0.984711i | \(-0.444268\pi\) | ||||
0.174194 | + | 0.984711i | \(0.444268\pi\) | |||||||
\(444\) | 9.02762e57 | 0.0245164 | ||||||||
\(445\) | −1.63833e59 | −0.422961 | ||||||||
\(446\) | 6.98983e59 | 1.71566 | ||||||||
\(447\) | −1.06973e58 | −0.0249663 | ||||||||
\(448\) | 4.37082e59 | 0.970081 | ||||||||
\(449\) | 4.77895e59 | 1.00877 | 0.504383 | − | 0.863480i | \(-0.331720\pi\) | ||||
0.504383 | + | 0.863480i | \(0.331720\pi\) | |||||||
\(450\) | −3.80867e59 | −0.764701 | ||||||||
\(451\) | 1.58789e59 | 0.303283 | ||||||||
\(452\) | −6.91655e58 | −0.125682 | ||||||||
\(453\) | 1.00564e59 | 0.173873 | ||||||||
\(454\) | −5.51518e58 | −0.0907410 | ||||||||
\(455\) | −5.87868e59 | −0.920499 | ||||||||
\(456\) | −2.74812e59 | −0.409569 | ||||||||
\(457\) | 2.48102e59 | 0.351978 | 0.175989 | − | 0.984392i | \(-0.443688\pi\) | ||||
0.175989 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(458\) | −5.48365e59 | −0.740622 | ||||||||
\(459\) | −2.73121e59 | −0.351213 | ||||||||
\(460\) | −3.08944e58 | −0.0378294 | ||||||||
\(461\) | −1.59001e60 | −1.85408 | −0.927040 | − | 0.374962i | \(-0.877656\pi\) | ||||
−0.927040 | + | 0.374962i | \(0.877656\pi\) | |||||||
\(462\) | 1.10930e59 | 0.123198 | ||||||||
\(463\) | 9.67043e59 | 1.02300 | 0.511498 | − | 0.859285i | \(-0.329091\pi\) | ||||
0.511498 | + | 0.859285i | \(0.329091\pi\) | |||||||
\(464\) | 1.88375e60 | 1.89832 | ||||||||
\(465\) | 4.00022e58 | 0.0384054 | ||||||||
\(466\) | −1.24779e60 | −1.14146 | ||||||||
\(467\) | −1.81440e59 | −0.158162 | −0.0790812 | − | 0.996868i | \(-0.525199\pi\) | ||||
−0.0790812 | + | 0.996868i | \(0.525199\pi\) | |||||||
\(468\) | 2.93068e59 | 0.243465 | ||||||||
\(469\) | 2.72002e60 | 2.15369 | ||||||||
\(470\) | 7.52078e59 | 0.567624 | ||||||||
\(471\) | −3.56152e58 | −0.0256251 | ||||||||
\(472\) | −1.78280e60 | −1.22294 | ||||||||
\(473\) | −4.68887e59 | −0.306685 | ||||||||
\(474\) | −8.40353e58 | −0.0524142 | ||||||||
\(475\) | −1.90360e60 | −1.13232 | ||||||||
\(476\) | −2.18040e59 | −0.123703 | ||||||||
\(477\) | 1.95872e60 | 1.06001 | ||||||||
\(478\) | 3.00148e59 | 0.154956 | ||||||||
\(479\) | −1.15748e60 | −0.570117 | −0.285059 | − | 0.958510i | \(-0.592013\pi\) | ||||
−0.285059 | + | 0.958510i | \(0.592013\pi\) | |||||||
\(480\) | −1.04746e59 | −0.0492277 | ||||||||
\(481\) | 1.62177e60 | 0.727321 | ||||||||
\(482\) | −3.47431e60 | −1.48700 | ||||||||
\(483\) | 4.65446e59 | 0.190134 | ||||||||
\(484\) | −3.99121e59 | −0.155627 | ||||||||
\(485\) | 4.81587e59 | 0.179261 | ||||||||
\(486\) | 2.51351e60 | 0.893231 | ||||||||
\(487\) | −1.82685e60 | −0.619871 | −0.309935 | − | 0.950758i | \(-0.600307\pi\) | ||||
−0.309935 | + | 0.950758i | \(0.600307\pi\) | |||||||
\(488\) | −3.66621e59 | −0.118788 | ||||||||
\(489\) | 7.16104e59 | 0.221578 | ||||||||
\(490\) | −9.43028e59 | −0.278684 | ||||||||
\(491\) | −2.65564e60 | −0.749609 | −0.374805 | − | 0.927104i | \(-0.622290\pi\) | ||||
−0.374805 | + | 0.927104i | \(0.622290\pi\) | |||||||
\(492\) | −2.09507e59 | −0.0564916 | ||||||||
\(493\) | 3.77252e60 | 0.971799 | ||||||||
\(494\) | 1.00938e61 | 2.48427 | ||||||||
\(495\) | −5.10846e59 | −0.120136 | ||||||||
\(496\) | 1.33091e60 | 0.299096 | ||||||||
\(497\) | −7.01248e60 | −1.50610 | ||||||||
\(498\) | 7.30875e59 | 0.150032 | ||||||||
\(499\) | 2.18380e60 | 0.428500 | 0.214250 | − | 0.976779i | \(-0.431269\pi\) | ||||
0.214250 | + | 0.976779i | \(0.431269\pi\) | |||||||
\(500\) | −7.48014e59 | −0.140309 | ||||||||
\(501\) | −3.32148e60 | −0.595639 | ||||||||
\(502\) | −1.53908e60 | −0.263893 | ||||||||
\(503\) | −4.41130e60 | −0.723247 | −0.361624 | − | 0.932324i | \(-0.617777\pi\) | ||||
−0.361624 | + | 0.932324i | \(0.617777\pi\) | |||||||
\(504\) | −6.42983e60 | −1.00812 | ||||||||
\(505\) | −7.57995e59 | −0.113661 | ||||||||
\(506\) | 1.04729e60 | 0.150203 | ||||||||
\(507\) | −3.55441e60 | −0.487628 | ||||||||
\(508\) | 4.09357e59 | 0.0537241 | ||||||||
\(509\) | 3.40004e60 | 0.426908 | 0.213454 | − | 0.976953i | \(-0.431529\pi\) | ||||
0.213454 | + | 0.976953i | \(0.431529\pi\) | |||||||
\(510\) | −7.70344e59 | −0.0925457 | ||||||||
\(511\) | 1.16094e61 | 1.33457 | ||||||||
\(512\) | 5.82802e60 | 0.641131 | ||||||||
\(513\) | 8.23048e60 | 0.866532 | ||||||||
\(514\) | −7.08982e60 | −0.714439 | ||||||||
\(515\) | 4.69622e60 | 0.452987 | ||||||||
\(516\) | 6.18652e59 | 0.0571253 | ||||||||
\(517\) | −3.69969e60 | −0.327061 | ||||||||
\(518\) | 7.27483e60 | 0.615749 | ||||||||
\(519\) | 1.51052e59 | 0.0122423 | ||||||||
\(520\) | −8.53596e60 | −0.662487 | ||||||||
\(521\) | 7.11610e60 | 0.528924 | 0.264462 | − | 0.964396i | \(-0.414806\pi\) | ||||
0.264462 | + | 0.964396i | \(0.414806\pi\) | |||||||
\(522\) | −2.27456e61 | −1.61924 | ||||||||
\(523\) | −6.62508e60 | −0.451755 | −0.225878 | − | 0.974156i | \(-0.572525\pi\) | ||||
−0.225878 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(524\) | −2.09099e59 | −0.0136583 | ||||||||
\(525\) | 4.95867e60 | 0.310300 | ||||||||
\(526\) | −6.38631e60 | −0.382887 | ||||||||
\(527\) | 2.66536e60 | 0.153115 | ||||||||
\(528\) | 1.89226e60 | 0.104164 | ||||||||
\(529\) | −1.45620e61 | −0.768189 | ||||||||
\(530\) | 1.16643e61 | 0.589729 | ||||||||
\(531\) | 2.52891e61 | 1.22548 | ||||||||
\(532\) | 6.57059e60 | 0.305206 | ||||||||
\(533\) | −3.76371e61 | −1.67592 | ||||||||
\(534\) | −7.32763e60 | −0.312814 | ||||||||
\(535\) | 2.75836e60 | 0.112899 | ||||||||
\(536\) | 3.94953e61 | 1.55002 | ||||||||
\(537\) | −5.22307e60 | −0.196564 | ||||||||
\(538\) | 1.22126e61 | 0.440766 | ||||||||
\(539\) | 4.63903e60 | 0.160576 | ||||||||
\(540\) | 1.42306e60 | 0.0472460 | ||||||||
\(541\) | −3.34138e61 | −1.06411 | −0.532056 | − | 0.846709i | \(-0.678581\pi\) | ||||
−0.532056 | + | 0.846709i | \(0.678581\pi\) | |||||||
\(542\) | 1.35879e61 | 0.415116 | ||||||||
\(543\) | 1.81713e61 | 0.532588 | ||||||||
\(544\) | −6.97927e60 | −0.196261 | ||||||||
\(545\) | 7.94252e60 | 0.214307 | ||||||||
\(546\) | −2.62932e61 | −0.680783 | ||||||||
\(547\) | 3.86064e61 | 0.959277 | 0.479638 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479638 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(548\) | −9.16813e60 | −0.218634 | ||||||||
\(549\) | 5.20055e60 | 0.119034 | ||||||||
\(550\) | 1.11574e61 | 0.245133 | ||||||||
\(551\) | −1.13684e62 | −2.39767 | ||||||||
\(552\) | 6.75838e60 | 0.136840 | ||||||||
\(553\) | −9.82717e60 | −0.191035 | ||||||||
\(554\) | −5.04815e61 | −0.942241 | ||||||||
\(555\) | 3.72984e60 | 0.0668494 | ||||||||
\(556\) | 8.67733e60 | 0.149349 | ||||||||
\(557\) | 5.55735e61 | 0.918598 | 0.459299 | − | 0.888282i | \(-0.348101\pi\) | ||||
0.459299 | + | 0.888282i | \(0.348101\pi\) | |||||||
\(558\) | −1.60702e61 | −0.255125 | ||||||||
\(559\) | 1.11138e62 | 1.69472 | ||||||||
\(560\) | −4.49826e61 | −0.658891 | ||||||||
\(561\) | 3.78955e60 | 0.0533241 | ||||||||
\(562\) | 1.44629e62 | 1.95519 | ||||||||
\(563\) | −1.22198e61 | −0.158718 | −0.0793589 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793589 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(564\) | 4.88139e60 | 0.0609206 | ||||||||
\(565\) | −2.85763e61 | −0.342701 | ||||||||
\(566\) | 3.35128e61 | 0.386226 | ||||||||
\(567\) | 7.99227e61 | 0.885220 | ||||||||
\(568\) | −1.01823e62 | −1.08394 | ||||||||
\(569\) | −1.79144e62 | −1.83306 | −0.916529 | − | 0.399967i | \(-0.869022\pi\) | ||||
−0.916529 | + | 0.399967i | \(0.869022\pi\) | |||||||
\(570\) | 2.32142e61 | 0.228334 | ||||||||
\(571\) | −4.92064e61 | −0.465274 | −0.232637 | − | 0.972564i | \(-0.574735\pi\) | ||||
−0.232637 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(572\) | −8.58533e60 | −0.0780452 | ||||||||
\(573\) | 3.35720e61 | 0.293426 | ||||||||
\(574\) | −1.68829e62 | −1.41883 | ||||||||
\(575\) | 4.68148e61 | 0.378318 | ||||||||
\(576\) | −9.00260e61 | −0.699620 | ||||||||
\(577\) | 1.61247e62 | 1.20513 | 0.602566 | − | 0.798069i | \(-0.294145\pi\) | ||||
0.602566 | + | 0.798069i | \(0.294145\pi\) | |||||||
\(578\) | 9.91323e61 | 0.712588 | ||||||||
\(579\) | −4.35613e61 | −0.301185 | ||||||||
\(580\) | −1.96562e61 | −0.130729 | ||||||||
\(581\) | 8.54693e61 | 0.546823 | ||||||||
\(582\) | 2.15397e61 | 0.132578 | ||||||||
\(583\) | −5.73802e61 | −0.339797 | ||||||||
\(584\) | 1.68572e62 | 0.960495 | ||||||||
\(585\) | 1.21083e62 | 0.663862 | ||||||||
\(586\) | −1.04975e62 | −0.553849 | ||||||||
\(587\) | −1.02006e62 | −0.517925 | −0.258962 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258962 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(588\) | −6.12076e60 | −0.0299099 | ||||||||
\(589\) | −8.03204e61 | −0.377774 | ||||||||
\(590\) | 1.50598e62 | 0.681788 | ||||||||
\(591\) | −9.81816e61 | −0.427870 | ||||||||
\(592\) | 1.24095e62 | 0.520615 | ||||||||
\(593\) | 9.42772e61 | 0.380782 | 0.190391 | − | 0.981708i | \(-0.439024\pi\) | ||||
0.190391 | + | 0.981708i | \(0.439024\pi\) | |||||||
\(594\) | −4.82403e61 | −0.187592 | ||||||||
\(595\) | −9.00849e61 | −0.337303 | ||||||||
\(596\) | 3.71377e60 | 0.0133898 | ||||||||
\(597\) | −4.90543e61 | −0.170316 | ||||||||
\(598\) | −2.48234e62 | −0.830012 | ||||||||
\(599\) | −2.30170e62 | −0.741217 | −0.370609 | − | 0.928789i | \(-0.620851\pi\) | ||||
−0.370609 | + | 0.928789i | \(0.620851\pi\) | |||||||
\(600\) | 7.20010e61 | 0.223324 | ||||||||
\(601\) | 1.32397e62 | 0.395552 | 0.197776 | − | 0.980247i | \(-0.436628\pi\) | ||||
0.197776 | + | 0.980247i | \(0.436628\pi\) | |||||||
\(602\) | 4.98536e62 | 1.43475 | ||||||||
\(603\) | −5.60245e62 | −1.55324 | ||||||||
\(604\) | −3.49126e61 | −0.0932504 | ||||||||
\(605\) | −1.64900e62 | −0.424351 | ||||||||
\(606\) | −3.39024e61 | −0.0840613 | ||||||||
\(607\) | −1.86733e62 | −0.446145 | −0.223073 | − | 0.974802i | \(-0.571609\pi\) | ||||
−0.223073 | + | 0.974802i | \(0.571609\pi\) | |||||||
\(608\) | 2.10319e62 | 0.484227 | ||||||||
\(609\) | 2.96135e62 | 0.657053 | ||||||||
\(610\) | 3.09696e61 | 0.0662238 | ||||||||
\(611\) | 8.76921e62 | 1.80731 | ||||||||
\(612\) | 4.49097e61 | 0.0892141 | ||||||||
\(613\) | 7.96288e62 | 1.52479 | 0.762394 | − | 0.647113i | \(-0.224024\pi\) | ||||
0.762394 | + | 0.647113i | \(0.224024\pi\) | |||||||
\(614\) | −1.07309e63 | −1.98084 | ||||||||
\(615\) | −8.65596e61 | −0.154037 | ||||||||
\(616\) | 1.88360e62 | 0.323163 | ||||||||
\(617\) | −1.66014e62 | −0.274617 | −0.137309 | − | 0.990528i | \(-0.543845\pi\) | ||||
−0.137309 | + | 0.990528i | \(0.543845\pi\) | |||||||
\(618\) | 2.10045e62 | 0.335021 | ||||||||
\(619\) | 4.17933e62 | 0.642786 | 0.321393 | − | 0.946946i | \(-0.395849\pi\) | ||||
0.321393 | + | 0.946946i | \(0.395849\pi\) | |||||||
\(620\) | −1.38875e61 | −0.0205974 | ||||||||
\(621\) | −2.02410e62 | −0.289515 | ||||||||
\(622\) | −1.52961e63 | −2.11008 | ||||||||
\(623\) | −8.56901e62 | −1.14012 | ||||||||
\(624\) | −4.48513e62 | −0.575602 | ||||||||
\(625\) | 3.25683e62 | 0.403176 | ||||||||
\(626\) | 4.49817e62 | 0.537171 | ||||||||
\(627\) | −1.14198e62 | −0.131564 | ||||||||
\(628\) | 1.23645e61 | 0.0137431 | ||||||||
\(629\) | 2.48521e62 | 0.266516 | ||||||||
\(630\) | 5.43147e62 | 0.562024 | ||||||||
\(631\) | 4.78834e62 | 0.478106 | 0.239053 | − | 0.971007i | \(-0.423163\pi\) | ||||
0.239053 | + | 0.971007i | \(0.423163\pi\) | |||||||
\(632\) | −1.42693e62 | −0.137489 | ||||||||
\(633\) | 1.72732e62 | 0.160616 | ||||||||
\(634\) | 1.72147e63 | 1.54487 | ||||||||
\(635\) | 1.69129e62 | 0.146491 | ||||||||
\(636\) | 7.57077e61 | 0.0632929 | ||||||||
\(637\) | −1.09957e63 | −0.887330 | ||||||||
\(638\) | 6.66325e62 | 0.519064 | ||||||||
\(639\) | 1.44436e63 | 1.08619 | ||||||||
\(640\) | −7.50334e62 | −0.544760 | ||||||||
\(641\) | −2.18288e63 | −1.53011 | −0.765056 | − | 0.643964i | \(-0.777289\pi\) | ||||
−0.765056 | + | 0.643964i | \(0.777289\pi\) | |||||||
\(642\) | 1.23371e62 | 0.0834979 | ||||||||
\(643\) | −1.90128e63 | −1.24251 | −0.621255 | − | 0.783609i | \(-0.713377\pi\) | ||||
−0.621255 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(644\) | −1.61589e62 | −0.101972 | ||||||||
\(645\) | 2.55601e62 | 0.155765 | ||||||||
\(646\) | 1.54677e63 | 0.910323 | ||||||||
\(647\) | 5.73318e62 | 0.325874 | 0.162937 | − | 0.986637i | \(-0.447903\pi\) | ||||
0.162937 | + | 0.986637i | \(0.447903\pi\) | |||||||
\(648\) | 1.16049e63 | 0.637097 | ||||||||
\(649\) | −7.40837e62 | −0.392841 | ||||||||
\(650\) | −2.64458e63 | −1.35459 | ||||||||
\(651\) | 2.09225e62 | 0.103524 | ||||||||
\(652\) | −2.48609e62 | −0.118836 | ||||||||
\(653\) | 1.09427e63 | 0.505335 | 0.252667 | − | 0.967553i | \(-0.418692\pi\) | ||||
0.252667 | + | 0.967553i | \(0.418692\pi\) | |||||||
\(654\) | 3.55240e62 | 0.158498 | ||||||||
\(655\) | −8.63908e61 | −0.0372425 | ||||||||
\(656\) | −2.87992e63 | −1.19962 | ||||||||
\(657\) | −2.39120e63 | −0.962488 | ||||||||
\(658\) | 3.93363e63 | 1.53007 | ||||||||
\(659\) | 3.42421e63 | 1.28718 | 0.643589 | − | 0.765372i | \(-0.277445\pi\) | ||||
0.643589 | + | 0.765372i | \(0.277445\pi\) | |||||||
\(660\) | −1.97450e61 | −0.00717328 | ||||||||
\(661\) | 2.99634e61 | 0.0105210 | 0.00526051 | − | 0.999986i | \(-0.498326\pi\) | ||||
0.00526051 | + | 0.999986i | \(0.498326\pi\) | |||||||
\(662\) | −1.22522e63 | −0.415823 | ||||||||
\(663\) | −8.98220e62 | −0.294665 | ||||||||
\(664\) | 1.24103e63 | 0.393551 | ||||||||
\(665\) | 2.71470e63 | 0.832212 | ||||||||
\(666\) | −1.49840e63 | −0.444077 | ||||||||
\(667\) | 2.79581e63 | 0.801081 | ||||||||
\(668\) | 1.15312e63 | 0.319450 | ||||||||
\(669\) | 1.87441e63 | 0.502084 | ||||||||
\(670\) | −3.33629e63 | −0.864133 | ||||||||
\(671\) | −1.52349e62 | −0.0381576 | ||||||||
\(672\) | −5.47858e62 | −0.132696 | ||||||||
\(673\) | −5.41615e63 | −1.26868 | −0.634340 | − | 0.773054i | \(-0.718728\pi\) | ||||
−0.634340 | + | 0.773054i | \(0.718728\pi\) | |||||||
\(674\) | −1.65037e63 | −0.373882 | ||||||||
\(675\) | −2.15639e63 | −0.472490 | ||||||||
\(676\) | 1.23398e63 | 0.261522 | ||||||||
\(677\) | −4.55896e63 | −0.934588 | −0.467294 | − | 0.884102i | \(-0.654771\pi\) | ||||
−0.467294 | + | 0.884102i | \(0.654771\pi\) | |||||||
\(678\) | −1.27811e63 | −0.253455 | ||||||||
\(679\) | 2.51887e63 | 0.483210 | ||||||||
\(680\) | −1.30805e63 | −0.242758 | ||||||||
\(681\) | −1.47896e62 | −0.0265551 | ||||||||
\(682\) | 4.70772e62 | 0.0817829 | ||||||||
\(683\) | 1.04266e64 | 1.75257 | 0.876287 | − | 0.481790i | \(-0.160013\pi\) | ||||
0.876287 | + | 0.481790i | \(0.160013\pi\) | |||||||
\(684\) | −1.35335e63 | −0.220114 | ||||||||
\(685\) | −3.78789e63 | −0.596156 | ||||||||
\(686\) | 3.92777e63 | 0.598210 | ||||||||
\(687\) | −1.47051e63 | −0.216741 | ||||||||
\(688\) | 8.50410e63 | 1.21308 | ||||||||
\(689\) | 1.36006e64 | 1.87769 | ||||||||
\(690\) | −5.70901e62 | −0.0762880 | ||||||||
\(691\) | −9.60653e63 | −1.24254 | −0.621270 | − | 0.783597i | \(-0.713383\pi\) | ||||
−0.621270 | + | 0.783597i | \(0.713383\pi\) | |||||||
\(692\) | −5.24407e61 | −0.00656570 | ||||||||
\(693\) | −2.67190e63 | −0.323834 | ||||||||
\(694\) | −7.11514e63 | −0.834825 | ||||||||
\(695\) | 3.58511e63 | 0.407234 | ||||||||
\(696\) | 4.29994e63 | 0.472884 | ||||||||
\(697\) | −5.76750e63 | −0.614116 | ||||||||
\(698\) | −1.22805e64 | −1.26611 | ||||||||
\(699\) | −3.34611e63 | −0.334044 | ||||||||
\(700\) | −1.72150e63 | −0.166418 | ||||||||
\(701\) | −4.79975e63 | −0.449327 | −0.224664 | − | 0.974436i | \(-0.572128\pi\) | ||||
−0.224664 | + | 0.974436i | \(0.572128\pi\) | |||||||
\(702\) | 1.14342e64 | 1.03662 | ||||||||
\(703\) | −7.48914e63 | −0.657562 | ||||||||
\(704\) | 2.63728e63 | 0.224270 | ||||||||
\(705\) | 2.01679e63 | 0.166114 | ||||||||
\(706\) | 6.47245e63 | 0.516372 | ||||||||
\(707\) | −3.96458e63 | −0.306380 | ||||||||
\(708\) | 9.77464e62 | 0.0731732 | ||||||||
\(709\) | 9.62702e63 | 0.698155 | 0.349077 | − | 0.937094i | \(-0.386495\pi\) | ||||
0.349077 | + | 0.937094i | \(0.386495\pi\) | |||||||
\(710\) | 8.60126e63 | 0.604296 | ||||||||
\(711\) | 2.02411e63 | 0.137774 | ||||||||
\(712\) | −1.24424e64 | −0.820547 | ||||||||
\(713\) | 1.97530e63 | 0.126217 | ||||||||
\(714\) | −4.02917e63 | −0.249463 | ||||||||
\(715\) | −3.54710e63 | −0.212808 | ||||||||
\(716\) | 1.81329e63 | 0.105420 | ||||||||
\(717\) | 8.04883e62 | 0.0453474 | ||||||||
\(718\) | 3.33064e64 | 1.81856 | ||||||||
\(719\) | −2.96105e64 | −1.56692 | −0.783459 | − | 0.621443i | \(-0.786547\pi\) | ||||
−0.783459 | + | 0.621443i | \(0.786547\pi\) | |||||||
\(720\) | 9.26508e63 | 0.475191 | ||||||||
\(721\) | 2.45629e64 | 1.22106 | ||||||||
\(722\) | −2.41661e64 | −1.16445 | ||||||||
\(723\) | −9.31678e63 | −0.435165 | ||||||||
\(724\) | −6.30853e63 | −0.285635 | ||||||||
\(725\) | 2.97854e64 | 1.30737 | ||||||||
\(726\) | −7.37539e63 | −0.313842 | ||||||||
\(727\) | 2.01758e64 | 0.832350 | 0.416175 | − | 0.909284i | \(-0.363370\pi\) | ||||
0.416175 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(728\) | −4.46461e64 | −1.78578 | ||||||||
\(729\) | −1.15542e64 | −0.448095 | ||||||||
\(730\) | −1.42397e64 | −0.535473 | ||||||||
\(731\) | 1.70308e64 | 0.621005 | ||||||||
\(732\) | 2.01009e62 | 0.00710750 | ||||||||
\(733\) | −2.30546e64 | −0.790530 | −0.395265 | − | 0.918567i | \(-0.629347\pi\) | ||||
−0.395265 | + | 0.918567i | \(0.629347\pi\) | |||||||
\(734\) | −3.25279e64 | −1.08167 | ||||||||
\(735\) | −2.52884e63 | −0.0815561 | ||||||||
\(736\) | −5.17232e63 | −0.161784 | ||||||||
\(737\) | 1.64122e64 | 0.497907 | ||||||||
\(738\) | 3.47739e64 | 1.02326 | ||||||||
\(739\) | 4.27723e64 | 1.22085 | 0.610425 | − | 0.792074i | \(-0.290999\pi\) | ||||
0.610425 | + | 0.792074i | \(0.290999\pi\) | |||||||
\(740\) | −1.29488e63 | −0.0358523 | ||||||||
\(741\) | 2.70677e64 | 0.727013 | ||||||||
\(742\) | 6.10084e64 | 1.58965 | ||||||||
\(743\) | −6.07984e64 | −1.53689 | −0.768447 | − | 0.639913i | \(-0.778970\pi\) | ||||
−0.768447 | + | 0.639913i | \(0.778970\pi\) | |||||||
\(744\) | 3.03800e63 | 0.0745069 | ||||||||
\(745\) | 1.53437e63 | 0.0365103 | ||||||||
\(746\) | 3.43250e64 | 0.792477 | ||||||||
\(747\) | −1.76041e64 | −0.394368 | ||||||||
\(748\) | −1.31562e63 | −0.0285985 | ||||||||
\(749\) | 1.44272e64 | 0.304327 | ||||||||
\(750\) | −1.38226e64 | −0.282951 | ||||||||
\(751\) | −8.42750e64 | −1.67417 | −0.837086 | − | 0.547071i | \(-0.815743\pi\) | ||||
−0.837086 | + | 0.547071i | \(0.815743\pi\) | |||||||
\(752\) | 6.71004e64 | 1.29367 | ||||||||
\(753\) | −4.12723e63 | −0.0772274 | ||||||||
\(754\) | −1.57936e65 | −2.86831 | ||||||||
\(755\) | −1.44244e64 | −0.254268 | ||||||||
\(756\) | 7.44312e63 | 0.127355 | ||||||||
\(757\) | −1.62790e64 | −0.270377 | −0.135189 | − | 0.990820i | \(-0.543164\pi\) | ||||
−0.135189 | + | 0.990820i | \(0.543164\pi\) | |||||||
\(758\) | 1.06237e65 | 1.71284 | ||||||||
\(759\) | 2.80843e63 | 0.0439565 | ||||||||
\(760\) | 3.94180e64 | 0.598947 | ||||||||
\(761\) | −1.06343e65 | −1.56875 | −0.784373 | − | 0.620289i | \(-0.787015\pi\) | ||||
−0.784373 | + | 0.620289i | \(0.787015\pi\) | |||||||
\(762\) | 7.56455e63 | 0.108342 | ||||||||
\(763\) | 4.15421e64 | 0.577679 | ||||||||
\(764\) | −1.16552e64 | −0.157369 | ||||||||
\(765\) | 1.85548e64 | 0.243262 | ||||||||
\(766\) | −2.62269e63 | −0.0333886 | ||||||||
\(767\) | 1.75597e65 | 2.17081 | ||||||||
\(768\) | −1.30611e64 | −0.156802 | ||||||||
\(769\) | 3.91583e64 | 0.456542 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(770\) | −1.59113e64 | −0.180163 | ||||||||
\(771\) | −1.90122e64 | −0.209078 | ||||||||
\(772\) | 1.51231e64 | 0.161530 | ||||||||
\(773\) | −1.00996e65 | −1.04777 | −0.523885 | − | 0.851789i | \(-0.675518\pi\) | ||||
−0.523885 | + | 0.851789i | \(0.675518\pi\) | |||||||
\(774\) | −1.02684e65 | −1.03474 | ||||||||
\(775\) | 2.10440e64 | 0.205987 | ||||||||
\(776\) | 3.65745e64 | 0.347768 | ||||||||
\(777\) | 1.95083e64 | 0.180197 | ||||||||
\(778\) | −5.53044e64 | −0.496270 | ||||||||
\(779\) | 1.73803e65 | 1.51518 | ||||||||
\(780\) | 4.68006e63 | 0.0396390 | ||||||||
\(781\) | −4.23122e64 | −0.348190 | ||||||||
\(782\) | −3.80394e64 | −0.304145 | ||||||||
\(783\) | −1.28781e65 | −1.00049 | ||||||||
\(784\) | −8.41370e64 | −0.635149 | ||||||||
\(785\) | 5.10850e63 | 0.0374736 | ||||||||
\(786\) | −3.86395e63 | −0.0275438 | ||||||||
\(787\) | 1.02621e65 | 0.710896 | 0.355448 | − | 0.934696i | \(-0.384328\pi\) | ||||
0.355448 | + | 0.934696i | \(0.384328\pi\) | |||||||
\(788\) | 3.40856e64 | 0.229473 | ||||||||
\(789\) | −1.71257e64 | −0.112051 | ||||||||
\(790\) | 1.20537e64 | 0.0766496 | ||||||||
\(791\) | −1.49464e65 | −0.923774 | ||||||||
\(792\) | −3.87966e64 | −0.233065 | ||||||||
\(793\) | 3.61105e64 | 0.210856 | ||||||||
\(794\) | 6.14657e64 | 0.348876 | ||||||||
\(795\) | 3.12793e64 | 0.172582 | ||||||||
\(796\) | 1.70302e64 | 0.0913428 | ||||||||
\(797\) | −7.78531e64 | −0.405942 | −0.202971 | − | 0.979185i | \(-0.565060\pi\) | ||||
−0.202971 | + | 0.979185i | \(0.565060\pi\) | |||||||
\(798\) | 1.21418e65 | 0.615488 | ||||||||
\(799\) | 1.34379e65 | 0.662263 | ||||||||
\(800\) | −5.51038e64 | −0.264032 | ||||||||
\(801\) | 1.76496e65 | 0.822250 | ||||||||
\(802\) | 2.48638e65 | 1.12627 | ||||||||
\(803\) | 7.00495e64 | 0.308536 | ||||||||
\(804\) | −2.16543e64 | −0.0927435 | ||||||||
\(805\) | −6.67617e64 | −0.278048 | ||||||||
\(806\) | −1.11585e65 | −0.451926 | ||||||||
\(807\) | 3.27496e64 | 0.128989 | ||||||||
\(808\) | −5.75665e64 | −0.220503 | ||||||||
\(809\) | −3.71145e65 | −1.38262 | −0.691308 | − | 0.722560i | \(-0.742965\pi\) | ||||
−0.691308 | + | 0.722560i | \(0.742965\pi\) | |||||||
\(810\) | −9.80304e64 | −0.355180 | ||||||||
\(811\) | −1.97077e65 | −0.694490 | −0.347245 | − | 0.937774i | \(-0.612883\pi\) | ||||
−0.347245 | + | 0.937774i | \(0.612883\pi\) | |||||||
\(812\) | −1.02809e65 | −0.352387 | ||||||||
\(813\) | 3.64376e64 | 0.121482 | ||||||||
\(814\) | 4.38952e64 | 0.142353 | ||||||||
\(815\) | −1.02715e65 | −0.324032 | ||||||||
\(816\) | −6.87302e64 | −0.210921 | ||||||||
\(817\) | −5.13222e65 | −1.53218 | ||||||||
\(818\) | 1.36122e65 | 0.395349 | ||||||||
\(819\) | 6.33308e65 | 1.78948 | ||||||||
\(820\) | 3.00508e64 | 0.0826123 | ||||||||
\(821\) | 4.18847e65 | 1.12030 | 0.560150 | − | 0.828391i | \(-0.310743\pi\) | ||||
0.560150 | + | 0.828391i | \(0.310743\pi\) | |||||||
\(822\) | −1.69419e65 | −0.440905 | ||||||||
\(823\) | −5.89925e64 | −0.149383 | −0.0746914 | − | 0.997207i | \(-0.523797\pi\) | ||||
−0.0746914 | + | 0.997207i | \(0.523797\pi\) | |||||||
\(824\) | 3.56658e65 | 0.878799 | ||||||||
\(825\) | 2.99198e64 | 0.0717374 | ||||||||
\(826\) | 7.87681e65 | 1.83780 | ||||||||
\(827\) | −4.27471e65 | −0.970583 | −0.485292 | − | 0.874352i | \(-0.661287\pi\) | ||||
−0.485292 | + | 0.874352i | \(0.661287\pi\) | |||||||
\(828\) | 3.32825e64 | 0.0735416 | ||||||||
\(829\) | 6.40554e64 | 0.137746 | 0.0688730 | − | 0.997625i | \(-0.478060\pi\) | ||||
0.0688730 | + | 0.997625i | \(0.478060\pi\) | |||||||
\(830\) | −1.04834e65 | −0.219404 | ||||||||
\(831\) | −1.35372e65 | −0.275744 | ||||||||
\(832\) | −6.25103e65 | −1.23930 | ||||||||
\(833\) | −1.68498e65 | −0.325149 | ||||||||
\(834\) | 1.60349e65 | 0.301183 | ||||||||
\(835\) | 4.76420e65 | 0.871052 | ||||||||
\(836\) | 3.96459e64 | 0.0705598 | ||||||||
\(837\) | −9.09863e64 | −0.157635 | ||||||||
\(838\) | −4.67426e65 | −0.788356 | ||||||||
\(839\) | −9.87581e65 | −1.62154 | −0.810772 | − | 0.585363i | \(-0.800952\pi\) | ||||
−0.810772 | + | 0.585363i | \(0.800952\pi\) | |||||||
\(840\) | −1.02679e65 | −0.164134 | ||||||||
\(841\) | 1.13625e66 | 1.76833 | ||||||||
\(842\) | −4.29436e65 | −0.650694 | ||||||||
\(843\) | 3.87840e65 | 0.572180 | ||||||||
\(844\) | −5.99671e64 | −0.0861406 | ||||||||
\(845\) | 5.09830e65 | 0.713098 | ||||||||
\(846\) | −8.10211e65 | −1.10348 | ||||||||
\(847\) | −8.62486e65 | −1.14387 | ||||||||
\(848\) | 1.04069e66 | 1.34405 | ||||||||
\(849\) | 8.98687e64 | 0.113028 | ||||||||
\(850\) | −4.05256e65 | −0.496367 | ||||||||
\(851\) | 1.84178e65 | 0.219696 | ||||||||
\(852\) | 5.58268e64 | 0.0648563 | ||||||||
\(853\) | 5.47101e65 | 0.619034 | 0.309517 | − | 0.950894i | \(-0.399833\pi\) | ||||
0.309517 | + | 0.950894i | \(0.399833\pi\) | |||||||
\(854\) | 1.61982e65 | 0.178511 | ||||||||
\(855\) | −5.59147e65 | −0.600190 | ||||||||
\(856\) | 2.09485e65 | 0.219025 | ||||||||
\(857\) | 3.91129e65 | 0.398338 | 0.199169 | − | 0.979965i | \(-0.436176\pi\) | ||||
0.199169 | + | 0.979965i | \(0.436176\pi\) | |||||||
\(858\) | −1.58649e65 | −0.157389 | ||||||||
\(859\) | 1.59577e66 | 1.54214 | 0.771072 | − | 0.636748i | \(-0.219721\pi\) | ||||
0.771072 | + | 0.636748i | \(0.219721\pi\) | |||||||
\(860\) | −8.87369e64 | −0.0835390 | ||||||||
\(861\) | −4.52737e65 | −0.415217 | ||||||||
\(862\) | −8.59063e65 | −0.767559 | ||||||||
\(863\) | −1.43745e65 | −0.125127 | −0.0625633 | − | 0.998041i | \(-0.519928\pi\) | ||||
−0.0625633 | + | 0.998041i | \(0.519928\pi\) | |||||||
\(864\) | 2.38248e65 | 0.202055 | ||||||||
\(865\) | −2.16663e64 | −0.0179029 | ||||||||
\(866\) | 1.06930e66 | 0.860888 | ||||||||
\(867\) | 2.65835e65 | 0.208537 | ||||||||
\(868\) | −7.26366e64 | −0.0555216 | ||||||||
\(869\) | −5.92956e64 | −0.0441649 | ||||||||
\(870\) | −3.63229e65 | −0.263632 | ||||||||
\(871\) | −3.89011e66 | −2.75140 | ||||||||
\(872\) | 6.03201e65 | 0.415758 | ||||||||
\(873\) | −5.18813e65 | −0.348490 | ||||||||
\(874\) | 1.14631e66 | 0.750404 | ||||||||
\(875\) | −1.61643e66 | −1.03128 | ||||||||
\(876\) | −9.24237e64 | −0.0574699 | ||||||||
\(877\) | −9.07110e65 | −0.549755 | −0.274878 | − | 0.961479i | \(-0.588637\pi\) | ||||
−0.274878 | + | 0.961479i | \(0.588637\pi\) | |||||||
\(878\) | 1.15674e66 | 0.683295 | ||||||||
\(879\) | −2.81504e65 | −0.162082 | ||||||||
\(880\) | −2.71418e65 | −0.152327 | ||||||||
\(881\) | 2.58911e66 | 1.41642 | 0.708212 | − | 0.706000i | \(-0.249502\pi\) | ||||
0.708212 | + | 0.706000i | \(0.249502\pi\) | |||||||
\(882\) | 1.01592e66 | 0.541772 | ||||||||
\(883\) | 1.38977e66 | 0.722480 | 0.361240 | − | 0.932473i | \(-0.382353\pi\) | ||||
0.361240 | + | 0.932473i | \(0.382353\pi\) | |||||||
\(884\) | 3.11834e65 | 0.158033 | ||||||||
\(885\) | 4.03847e65 | 0.199523 | ||||||||
\(886\) | −7.82292e65 | −0.376799 | ||||||||
\(887\) | 1.62550e66 | 0.763319 | 0.381660 | − | 0.924303i | \(-0.375353\pi\) | ||||
0.381660 | + | 0.924303i | \(0.375353\pi\) | |||||||
\(888\) | 2.83265e65 | 0.129689 | ||||||||
\(889\) | 8.84606e65 | 0.394875 | ||||||||
\(890\) | 1.05105e66 | 0.457453 | ||||||||
\(891\) | 4.82241e65 | 0.204652 | ||||||||
\(892\) | −6.50737e65 | −0.269275 | ||||||||
\(893\) | −4.04951e66 | −1.63397 | ||||||||
\(894\) | 6.86270e64 | 0.0270023 | ||||||||
\(895\) | 7.49176e65 | 0.287452 | ||||||||
\(896\) | −3.92451e66 | −1.46844 | ||||||||
\(897\) | −6.65669e65 | −0.242901 | ||||||||
\(898\) | −3.06587e66 | −1.09103 | ||||||||
\(899\) | 1.25676e66 | 0.436173 | ||||||||
\(900\) | 3.54578e65 | 0.120020 | ||||||||
\(901\) | 2.08415e66 | 0.688052 | ||||||||
\(902\) | −1.01869e66 | −0.328016 | ||||||||
\(903\) | 1.33688e66 | 0.419874 | ||||||||
\(904\) | −2.17025e66 | −0.664844 | ||||||||
\(905\) | −2.60642e66 | −0.778847 | ||||||||
\(906\) | −6.45152e65 | −0.188052 | ||||||||
\(907\) | 6.17539e66 | 1.75590 | 0.877951 | − | 0.478751i | \(-0.158910\pi\) | ||||
0.877951 | + | 0.478751i | \(0.158910\pi\) | |||||||
\(908\) | 5.13451e64 | 0.0142419 | ||||||||
\(909\) | 8.16586e65 | 0.220960 | ||||||||
\(910\) | 3.77139e66 | 0.995566 | ||||||||
\(911\) | −2.64162e66 | −0.680311 | −0.340155 | − | 0.940369i | \(-0.610480\pi\) | ||||
−0.340155 | + | 0.940369i | \(0.610480\pi\) | |||||||
\(912\) | 2.07117e66 | 0.520395 | ||||||||
\(913\) | 5.15708e65 | 0.126419 | ||||||||
\(914\) | −1.59166e66 | −0.380682 | ||||||||
\(915\) | 8.30487e64 | 0.0193802 | ||||||||
\(916\) | 5.10515e65 | 0.116241 | ||||||||
\(917\) | −4.51854e65 | −0.100389 | ||||||||
\(918\) | 1.75217e66 | 0.379854 | ||||||||
\(919\) | −8.03936e66 | −1.70068 | −0.850340 | − | 0.526234i | \(-0.823604\pi\) | ||||
−0.850340 | + | 0.526234i | \(0.823604\pi\) | |||||||
\(920\) | −9.69394e65 | −0.200113 | ||||||||
\(921\) | −2.87763e66 | −0.579687 | ||||||||
\(922\) | 1.02005e67 | 2.00528 | ||||||||
\(923\) | 1.00291e67 | 1.92407 | ||||||||
\(924\) | −1.03273e65 | −0.0193360 | ||||||||
\(925\) | 1.96216e66 | 0.358546 | ||||||||
\(926\) | −6.20394e66 | −1.10642 | ||||||||
\(927\) | −5.05923e66 | −0.880623 | ||||||||
\(928\) | −3.29083e66 | −0.559083 | ||||||||
\(929\) | −6.85607e66 | −1.13690 | −0.568449 | − | 0.822718i | \(-0.692457\pi\) | ||||
−0.568449 | + | 0.822718i | \(0.692457\pi\) | |||||||
\(930\) | −2.56629e65 | −0.0415374 | ||||||||
\(931\) | 5.07766e66 | 0.802225 | ||||||||
\(932\) | 1.16167e66 | 0.179153 | ||||||||
\(933\) | −4.10184e66 | −0.617507 | ||||||||
\(934\) | 1.16400e66 | 0.171060 | ||||||||
\(935\) | −5.43558e65 | −0.0779802 | ||||||||
\(936\) | 9.19577e66 | 1.28790 | ||||||||
\(937\) | −5.58369e66 | −0.763450 | −0.381725 | − | 0.924276i | \(-0.624670\pi\) | ||||
−0.381725 | + | 0.924276i | \(0.624670\pi\) | |||||||
\(938\) | −1.74500e67 | −2.32933 | ||||||||
\(939\) | 1.20624e66 | 0.157202 | ||||||||
\(940\) | −7.00167e65 | −0.0890891 | ||||||||
\(941\) | 8.59076e66 | 1.06725 | 0.533624 | − | 0.845722i | \(-0.320830\pi\) | ||||
0.533624 | + | 0.845722i | \(0.320830\pi\) | |||||||
\(942\) | 2.28485e65 | 0.0277148 | ||||||||
\(943\) | −4.27428e66 | −0.506233 | ||||||||
\(944\) | 1.34364e67 | 1.55386 | ||||||||
\(945\) | 3.07519e66 | 0.347261 | ||||||||
\(946\) | 3.00808e66 | 0.331695 | ||||||||
\(947\) | 1.38497e67 | 1.49131 | 0.745654 | − | 0.666334i | \(-0.232137\pi\) | ||||
0.745654 | + | 0.666334i | \(0.232137\pi\) | |||||||
\(948\) | 7.82349e64 | 0.00822646 | ||||||||
\(949\) | −1.66035e67 | −1.70495 | ||||||||
\(950\) | 1.22123e67 | 1.22466 | ||||||||
\(951\) | 4.61633e66 | 0.452101 | ||||||||
\(952\) | −6.84156e66 | −0.654371 | ||||||||
\(953\) | 1.29710e67 | 1.21166 | 0.605831 | − | 0.795593i | \(-0.292841\pi\) | ||||
0.605831 | + | 0.795593i | \(0.292841\pi\) | |||||||
\(954\) | −1.25659e67 | −1.14645 | ||||||||
\(955\) | −4.81543e66 | −0.429101 | ||||||||
\(956\) | −2.79431e65 | −0.0243205 | ||||||||
\(957\) | 1.78683e66 | 0.151903 | ||||||||
\(958\) | 7.42566e66 | 0.616610 | ||||||||
\(959\) | −1.98120e67 | −1.60698 | ||||||||
\(960\) | −1.43764e66 | −0.113907 | ||||||||
\(961\) | −1.20325e67 | −0.931277 | ||||||||
\(962\) | −1.04043e67 | −0.786634 | ||||||||
\(963\) | −2.97157e66 | −0.219480 | ||||||||
\(964\) | 3.23450e66 | 0.233385 | ||||||||
\(965\) | 6.24825e66 | 0.440447 | ||||||||
\(966\) | −2.98601e66 | −0.205639 | ||||||||
\(967\) | 2.84025e66 | 0.191100 | 0.0955502 | − | 0.995425i | \(-0.469539\pi\) | ||||
0.0955502 | + | 0.995425i | \(0.469539\pi\) | |||||||
\(968\) | −1.25235e67 | −0.823245 | ||||||||
\(969\) | 4.14786e66 | 0.266403 | ||||||||
\(970\) | −3.08956e66 | −0.193880 | ||||||||
\(971\) | 2.77039e67 | 1.69866 | 0.849332 | − | 0.527858i | \(-0.177005\pi\) | ||||
0.849332 | + | 0.527858i | \(0.177005\pi\) | |||||||
\(972\) | −2.34001e66 | −0.140193 | ||||||||
\(973\) | 1.87514e67 | 1.09773 | ||||||||
\(974\) | 1.17199e67 | 0.670421 | ||||||||
\(975\) | −7.09176e66 | −0.396415 | ||||||||
\(976\) | 2.76311e66 | 0.150930 | ||||||||
\(977\) | 1.30344e67 | 0.695766 | 0.347883 | − | 0.937538i | \(-0.386901\pi\) | ||||
0.347883 | + | 0.937538i | \(0.386901\pi\) | |||||||
\(978\) | −4.59407e66 | −0.239648 | ||||||||
\(979\) | −5.17040e66 | −0.263581 | ||||||||
\(980\) | 8.77936e65 | 0.0437398 | ||||||||
\(981\) | −8.55645e66 | −0.416621 | ||||||||
\(982\) | 1.70369e67 | 0.810740 | ||||||||
\(983\) | −2.69857e67 | −1.25510 | −0.627551 | − | 0.778576i | \(-0.715943\pi\) | ||||
−0.627551 | + | 0.778576i | \(0.715943\pi\) | |||||||
\(984\) | −6.57383e66 | −0.298833 | ||||||||
\(985\) | 1.40828e67 | 0.625710 | ||||||||
\(986\) | −2.42021e67 | −1.05105 | ||||||||
\(987\) | 1.05485e67 | 0.447770 | ||||||||
\(988\) | −9.39709e66 | −0.389908 | ||||||||
\(989\) | 1.26215e67 | 0.511911 | ||||||||
\(990\) | 3.27726e66 | 0.129933 | ||||||||
\(991\) | −3.22029e67 | −1.24807 | −0.624034 | − | 0.781397i | \(-0.714507\pi\) | ||||
−0.624034 | + | 0.781397i | \(0.714507\pi\) | |||||||
\(992\) | −2.32504e66 | −0.0880882 | ||||||||
\(993\) | −3.28557e66 | −0.121689 | ||||||||
\(994\) | 4.49876e67 | 1.62892 | ||||||||
\(995\) | 7.03615e66 | 0.249067 | ||||||||
\(996\) | −6.80427e65 | −0.0235476 | ||||||||
\(997\) | −1.99799e67 | −0.676009 | −0.338005 | − | 0.941144i | \(-0.609752\pi\) | ||||
−0.338005 | + | 0.941144i | \(0.609752\pi\) | |||||||
\(998\) | −1.40099e67 | −0.463444 | ||||||||
\(999\) | −8.48364e66 | −0.274384 |
(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 | 1.46.a.a.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 9.46.a.b.1.3 | 3 | |||
4.3 | odd | 2 | 16.46.a.c.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.46.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.46.a.b.1.3 | 3 | 3.2 | odd | 2 | |||
16.46.a.c.1.2 | 3 | 4.3 | odd | 2 |