Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 148387471 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-12181.4\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | −701909. | −0.762545 | −0.381272 | − | 0.924463i | \(-0.624514\pi\) | ||||
−0.381272 | + | 0.924463i | \(0.624514\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | −2.44141e8 | −0.447214 | ||||||||
\(6\) | 2.87502e9 | 0.539200 | ||||||||
\(7\) | −7.10199e8 | −0.0193934 | −0.00969672 | − | 0.999953i | \(-0.503087\pi\) | ||||
−0.00969672 | + | 0.999953i | \(0.503087\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | −3.54612e11 | −0.418526 | ||||||||
\(10\) | 1.00000e12 | 0.316228 | ||||||||
\(11\) | 6.69047e12 | 0.642758 | 0.321379 | − | 0.946951i | \(-0.395854\pi\) | ||||
0.321379 | + | 0.946951i | \(0.395854\pi\) | |||||||
\(12\) | −1.17761e13 | −0.381272 | ||||||||
\(13\) | −4.06505e12 | −0.0483920 | −0.0241960 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241960 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(14\) | 2.90898e12 | 0.0137132 | ||||||||
\(15\) | 1.71365e14 | 0.341020 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 2.05623e15 | 0.855974 | 0.427987 | − | 0.903785i | \(-0.359223\pi\) | ||||
0.427987 | + | 0.903785i | \(0.359223\pi\) | |||||||
\(18\) | 1.45249e15 | 0.295942 | ||||||||
\(19\) | 1.32410e16 | 1.37246 | 0.686230 | − | 0.727384i | \(-0.259264\pi\) | ||||
0.686230 | + | 0.727384i | \(0.259264\pi\) | |||||||
\(20\) | −4.09600e15 | −0.223607 | ||||||||
\(21\) | 4.98495e14 | 0.0147884 | ||||||||
\(22\) | −2.74041e16 | −0.454499 | ||||||||
\(23\) | −2.83334e16 | −0.269588 | −0.134794 | − | 0.990874i | \(-0.543037\pi\) | ||||
−0.134794 | + | 0.990874i | \(0.543037\pi\) | |||||||
\(24\) | 4.82348e16 | 0.269600 | ||||||||
\(25\) | 5.96046e16 | 0.200000 | ||||||||
\(26\) | 1.66504e16 | 0.0342183 | ||||||||
\(27\) | 8.43625e17 | 1.08169 | ||||||||
\(28\) | −1.19152e16 | −0.00969672 | ||||||||
\(29\) | 8.79820e17 | 0.461763 | 0.230881 | − | 0.972982i | \(-0.425839\pi\) | ||||
0.230881 | + | 0.972982i | \(0.425839\pi\) | |||||||
\(30\) | −7.01909e17 | −0.241138 | ||||||||
\(31\) | −3.20276e17 | −0.0730302 | −0.0365151 | − | 0.999333i | \(-0.511626\pi\) | ||||
−0.0365151 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | −4.69610e18 | −0.490132 | ||||||||
\(34\) | −8.42232e18 | −0.605265 | ||||||||
\(35\) | 1.73388e17 | 0.00867301 | ||||||||
\(36\) | −5.94940e18 | −0.209263 | ||||||||
\(37\) | −4.64680e19 | −1.16047 | −0.580233 | − | 0.814450i | \(-0.697039\pi\) | ||||
−0.580233 | + | 0.814450i | \(0.697039\pi\) | |||||||
\(38\) | −5.42350e19 | −0.970476 | ||||||||
\(39\) | 2.85329e18 | 0.0369011 | ||||||||
\(40\) | 1.67772e19 | 0.158114 | ||||||||
\(41\) | −1.18387e20 | −0.819418 | −0.409709 | − | 0.912216i | \(-0.634370\pi\) | ||||
−0.409709 | + | 0.912216i | \(0.634370\pi\) | |||||||
\(42\) | −2.04184e18 | −0.0104569 | ||||||||
\(43\) | −1.34535e20 | −0.513426 | −0.256713 | − | 0.966488i | \(-0.582640\pi\) | ||||
−0.256713 | + | 0.966488i | \(0.582640\pi\) | |||||||
\(44\) | 1.12247e20 | 0.321379 | ||||||||
\(45\) | 8.65752e19 | 0.187170 | ||||||||
\(46\) | 1.16053e20 | 0.190627 | ||||||||
\(47\) | −7.78716e20 | −0.977587 | −0.488794 | − | 0.872399i | \(-0.662563\pi\) | ||||
−0.488794 | + | 0.872399i | \(0.662563\pi\) | |||||||
\(48\) | −1.97570e20 | −0.190636 | ||||||||
\(49\) | −1.34056e21 | −0.999624 | ||||||||
\(50\) | −2.44141e20 | −0.141421 | ||||||||
\(51\) | −1.44329e21 | −0.652718 | ||||||||
\(52\) | −6.82002e19 | −0.0241960 | ||||||||
\(53\) | −3.18129e21 | −0.889517 | −0.444759 | − | 0.895651i | \(-0.646711\pi\) | ||||
−0.444759 | + | 0.895651i | \(0.646711\pi\) | |||||||
\(54\) | −3.45549e21 | −0.764870 | ||||||||
\(55\) | −1.63341e21 | −0.287450 | ||||||||
\(56\) | 4.88045e19 | 0.00685661 | ||||||||
\(57\) | −9.29396e21 | −1.04656 | ||||||||
\(58\) | −3.60374e21 | −0.326516 | ||||||||
\(59\) | −2.03629e21 | −0.149001 | −0.0745005 | − | 0.997221i | \(-0.523736\pi\) | ||||
−0.0745005 | + | 0.997221i | \(0.523736\pi\) | |||||||
\(60\) | 2.87502e21 | 0.170510 | ||||||||
\(61\) | 3.16043e22 | 1.52448 | 0.762242 | − | 0.647292i | \(-0.224099\pi\) | ||||
0.762242 | + | 0.647292i | \(0.224099\pi\) | |||||||
\(62\) | 1.31185e21 | 0.0516402 | ||||||||
\(63\) | 2.51845e20 | 0.00811665 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 9.92443e20 | 0.0216416 | ||||||||
\(66\) | 1.92352e22 | 0.346576 | ||||||||
\(67\) | 4.98952e22 | 0.744945 | 0.372472 | − | 0.928043i | \(-0.378510\pi\) | ||||
0.372472 | + | 0.928043i | \(0.378510\pi\) | |||||||
\(68\) | 3.44978e22 | 0.427987 | ||||||||
\(69\) | 1.98875e22 | 0.205573 | ||||||||
\(70\) | −7.10199e20 | −0.00613274 | ||||||||
\(71\) | 1.16862e23 | 0.845169 | 0.422585 | − | 0.906324i | \(-0.361123\pi\) | ||||
0.422585 | + | 0.906324i | \(0.361123\pi\) | |||||||
\(72\) | 2.43688e22 | 0.147971 | ||||||||
\(73\) | −1.07622e23 | −0.550001 | −0.275001 | − | 0.961444i | \(-0.588678\pi\) | ||||
−0.275001 | + | 0.961444i | \(0.588678\pi\) | |||||||
\(74\) | 1.90333e23 | 0.820574 | ||||||||
\(75\) | −4.18370e22 | −0.152509 | ||||||||
\(76\) | 2.22147e23 | 0.686230 | ||||||||
\(77\) | −4.75156e21 | −0.0124653 | ||||||||
\(78\) | −1.16871e22 | −0.0260930 | ||||||||
\(79\) | 2.51396e23 | 0.478651 | 0.239326 | − | 0.970939i | \(-0.423074\pi\) | ||||
0.239326 | + | 0.970939i | \(0.423074\pi\) | |||||||
\(80\) | −6.87195e22 | −0.111803 | ||||||||
\(81\) | −2.91689e23 | −0.406310 | ||||||||
\(82\) | 4.84913e23 | 0.579416 | ||||||||
\(83\) | −1.47962e24 | −1.51941 | −0.759703 | − | 0.650270i | \(-0.774656\pi\) | ||||
−0.759703 | + | 0.650270i | \(0.774656\pi\) | |||||||
\(84\) | 8.36336e21 | 0.00739418 | ||||||||
\(85\) | −5.02010e23 | −0.382803 | ||||||||
\(86\) | 5.51054e23 | 0.363047 | ||||||||
\(87\) | −6.17554e23 | −0.352115 | ||||||||
\(88\) | −4.59765e23 | −0.227249 | ||||||||
\(89\) | −1.69758e24 | −0.728544 | −0.364272 | − | 0.931293i | \(-0.618682\pi\) | ||||
−0.364272 | + | 0.931293i | \(0.618682\pi\) | |||||||
\(90\) | −3.54612e23 | −0.132349 | ||||||||
\(91\) | 2.88699e21 | 0.000938487 0 | ||||||||
\(92\) | −4.75355e23 | −0.134794 | ||||||||
\(93\) | 2.24804e23 | 0.0556888 | ||||||||
\(94\) | 3.18962e24 | 0.691259 | ||||||||
\(95\) | −3.23266e24 | −0.613783 | ||||||||
\(96\) | 8.09246e23 | 0.134800 | ||||||||
\(97\) | −4.56953e24 | −0.668689 | −0.334345 | − | 0.942451i | \(-0.608515\pi\) | ||||
−0.334345 | + | 0.942451i | \(0.608515\pi\) | |||||||
\(98\) | 5.49095e24 | 0.706841 | ||||||||
\(99\) | −2.37252e24 | −0.269011 | ||||||||
\(100\) | 1.00000e24 | 0.100000 | ||||||||
\(101\) | −1.34474e25 | −1.18747 | −0.593735 | − | 0.804661i | \(-0.702347\pi\) | ||||
−0.593735 | + | 0.804661i | \(0.702347\pi\) | |||||||
\(102\) | 5.91170e24 | 0.461541 | ||||||||
\(103\) | −1.45443e25 | −1.00514 | −0.502571 | − | 0.864536i | \(-0.667612\pi\) | ||||
−0.502571 | + | 0.864536i | \(0.667612\pi\) | |||||||
\(104\) | 2.79348e23 | 0.0171092 | ||||||||
\(105\) | −1.21703e23 | −0.00661355 | ||||||||
\(106\) | 1.30305e25 | 0.628984 | ||||||||
\(107\) | −3.33812e25 | −1.43286 | −0.716432 | − | 0.697657i | \(-0.754226\pi\) | ||||
−0.716432 | + | 0.697657i | \(0.754226\pi\) | |||||||
\(108\) | 1.41537e25 | 0.540845 | ||||||||
\(109\) | 4.20504e25 | 1.43199 | 0.715993 | − | 0.698107i | \(-0.245974\pi\) | ||||
0.715993 | + | 0.698107i | \(0.245974\pi\) | |||||||
\(110\) | 6.69047e24 | 0.203258 | ||||||||
\(111\) | 3.26163e25 | 0.884908 | ||||||||
\(112\) | −1.99903e23 | −0.00484836 | ||||||||
\(113\) | 7.61141e25 | 1.65190 | 0.825952 | − | 0.563741i | \(-0.190638\pi\) | ||||
0.825952 | + | 0.563741i | \(0.190638\pi\) | |||||||
\(114\) | 3.80681e25 | 0.740031 | ||||||||
\(115\) | 6.91733e24 | 0.120563 | ||||||||
\(116\) | 1.47609e25 | 0.230881 | ||||||||
\(117\) | 1.44152e24 | 0.0202533 | ||||||||
\(118\) | 8.34063e24 | 0.105360 | ||||||||
\(119\) | −1.46033e24 | −0.0166003 | ||||||||
\(120\) | −1.17761e25 | −0.120569 | ||||||||
\(121\) | −6.35847e25 | −0.586862 | ||||||||
\(122\) | −1.29451e26 | −1.07797 | ||||||||
\(123\) | 8.30968e25 | 0.624843 | ||||||||
\(124\) | −5.37333e24 | −0.0365151 | ||||||||
\(125\) | −1.45519e25 | −0.0894427 | ||||||||
\(126\) | −1.03156e24 | −0.00573934 | ||||||||
\(127\) | −2.50269e26 | −1.26142 | −0.630710 | − | 0.776018i | \(-0.717236\pi\) | ||||
−0.630710 | + | 0.776018i | \(0.717236\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 9.44310e25 | 0.391510 | ||||||||
\(130\) | −4.06505e24 | −0.0153029 | ||||||||
\(131\) | −3.42885e26 | −1.17289 | −0.586445 | − | 0.809989i | \(-0.699473\pi\) | ||||
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(132\) | −7.87875e25 | −0.245066 | ||||||||
\(133\) | −9.40373e24 | −0.0266167 | ||||||||
\(134\) | −2.04371e26 | −0.526755 | ||||||||
\(135\) | −2.05963e26 | −0.483746 | ||||||||
\(136\) | −1.41303e26 | −0.302632 | ||||||||
\(137\) | 1.44437e26 | 0.282274 | 0.141137 | − | 0.989990i | \(-0.454924\pi\) | ||||
0.141137 | + | 0.989990i | \(0.454924\pi\) | |||||||
\(138\) | −8.14590e25 | −0.145362 | ||||||||
\(139\) | 4.93300e26 | 0.804314 | 0.402157 | − | 0.915571i | \(-0.368261\pi\) | ||||
0.402157 | + | 0.915571i | \(0.368261\pi\) | |||||||
\(140\) | 2.90898e24 | 0.00433650 | ||||||||
\(141\) | 5.46588e26 | 0.745454 | ||||||||
\(142\) | −4.78666e26 | −0.597625 | ||||||||
\(143\) | −2.71971e25 | −0.0311044 | ||||||||
\(144\) | −9.98144e25 | −0.104631 | ||||||||
\(145\) | −2.14800e26 | −0.206507 | ||||||||
\(146\) | 4.40818e26 | 0.388910 | ||||||||
\(147\) | 9.40954e26 | 0.762258 | ||||||||
\(148\) | −7.79604e26 | −0.580233 | ||||||||
\(149\) | 1.50844e27 | 1.03205 | 0.516023 | − | 0.856575i | \(-0.327412\pi\) | ||||
0.516023 | + | 0.856575i | \(0.327412\pi\) | |||||||
\(150\) | 1.71365e26 | 0.107840 | ||||||||
\(151\) | 1.70083e26 | 0.0985027 | 0.0492513 | − | 0.998786i | \(-0.484316\pi\) | ||||
0.0492513 | + | 0.998786i | \(0.484316\pi\) | |||||||
\(152\) | −9.09913e26 | −0.485238 | ||||||||
\(153\) | −7.29164e26 | −0.358247 | ||||||||
\(154\) | 1.94624e25 | 0.00881429 | ||||||||
\(155\) | 7.81923e25 | 0.0326601 | ||||||||
\(156\) | 4.78703e25 | 0.0184505 | ||||||||
\(157\) | 3.29198e27 | 1.17142 | 0.585708 | − | 0.810522i | \(-0.300816\pi\) | ||||
0.585708 | + | 0.810522i | \(0.300816\pi\) | |||||||
\(158\) | −1.02972e27 | −0.338458 | ||||||||
\(159\) | 2.23297e27 | 0.678296 | ||||||||
\(160\) | 2.81475e26 | 0.0790569 | ||||||||
\(161\) | 2.01223e25 | 0.00522823 | ||||||||
\(162\) | 1.19476e27 | 0.287305 | ||||||||
\(163\) | 5.07392e26 | 0.112979 | 0.0564896 | − | 0.998403i | \(-0.482009\pi\) | ||||
0.0564896 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(164\) | −1.98620e27 | −0.409709 | ||||||||
\(165\) | 1.14651e27 | 0.219194 | ||||||||
\(166\) | 6.06052e27 | 1.07438 | ||||||||
\(167\) | −8.44897e26 | −0.138947 | −0.0694733 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694733 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(168\) | −3.42563e25 | −0.00522847 | ||||||||
\(169\) | −7.03989e27 | −0.997658 | ||||||||
\(170\) | 2.05623e27 | 0.270683 | ||||||||
\(171\) | −4.69541e27 | −0.574410 | ||||||||
\(172\) | −2.25712e27 | −0.256713 | ||||||||
\(173\) | −7.54461e27 | −0.798106 | −0.399053 | − | 0.916928i | \(-0.630661\pi\) | ||||
−0.399053 | + | 0.916928i | \(0.630661\pi\) | |||||||
\(174\) | 2.52950e27 | 0.248983 | ||||||||
\(175\) | −4.23312e25 | −0.00387869 | ||||||||
\(176\) | 1.88320e27 | 0.160690 | ||||||||
\(177\) | 1.42929e27 | 0.113620 | ||||||||
\(178\) | 6.95330e27 | 0.515159 | ||||||||
\(179\) | −5.46396e27 | −0.377437 | −0.188718 | − | 0.982031i | \(-0.560433\pi\) | ||||
−0.188718 | + | 0.982031i | \(0.560433\pi\) | |||||||
\(180\) | 1.45249e27 | 0.0935852 | ||||||||
\(181\) | −2.74350e28 | −1.64939 | −0.824693 | − | 0.565581i | \(-0.808652\pi\) | ||||
−0.824693 | + | 0.565581i | \(0.808652\pi\) | |||||||
\(182\) | −1.18251e25 | −0.000663611 0 | ||||||||
\(183\) | −2.21833e28 | −1.16249 | ||||||||
\(184\) | 1.94705e27 | 0.0953137 | ||||||||
\(185\) | 1.13447e28 | 0.518976 | ||||||||
\(186\) | −9.20799e26 | −0.0393779 | ||||||||
\(187\) | 1.37571e28 | 0.550184 | ||||||||
\(188\) | −1.30647e28 | −0.488794 | ||||||||
\(189\) | −5.99142e26 | −0.0209777 | ||||||||
\(190\) | 1.32410e28 | 0.434010 | ||||||||
\(191\) | −2.53537e28 | −0.778258 | −0.389129 | − | 0.921183i | \(-0.627224\pi\) | ||||
−0.389129 | + | 0.921183i | \(0.627224\pi\) | |||||||
\(192\) | −3.31467e27 | −0.0953181 | ||||||||
\(193\) | 4.66476e27 | 0.125708 | 0.0628540 | − | 0.998023i | \(-0.479980\pi\) | ||||
0.0628540 | + | 0.998023i | \(0.479980\pi\) | |||||||
\(194\) | 1.87168e28 | 0.472835 | ||||||||
\(195\) | −6.96605e26 | −0.0165027 | ||||||||
\(196\) | −2.24909e28 | −0.499812 | ||||||||
\(197\) | −1.14775e28 | −0.239343 | −0.119672 | − | 0.992814i | \(-0.538184\pi\) | ||||
−0.119672 | + | 0.992814i | \(0.538184\pi\) | |||||||
\(198\) | 9.71784e27 | 0.190219 | ||||||||
\(199\) | 1.02205e29 | 1.87849 | 0.939243 | − | 0.343254i | \(-0.111529\pi\) | ||||
0.939243 | + | 0.343254i | \(0.111529\pi\) | |||||||
\(200\) | −4.09600e27 | −0.0707107 | ||||||||
\(201\) | −3.50219e28 | −0.568053 | ||||||||
\(202\) | 5.50807e28 | 0.839668 | ||||||||
\(203\) | −6.24848e26 | −0.00895517 | ||||||||
\(204\) | −2.42143e28 | −0.326359 | ||||||||
\(205\) | 2.89030e28 | 0.366455 | ||||||||
\(206\) | 5.95734e28 | 0.710742 | ||||||||
\(207\) | 1.00474e28 | 0.112829 | ||||||||
\(208\) | −1.14421e27 | −0.0120980 | ||||||||
\(209\) | 8.85883e28 | 0.882161 | ||||||||
\(210\) | 4.98495e26 | 0.00467649 | ||||||||
\(211\) | 1.45021e29 | 1.28204 | 0.641020 | − | 0.767524i | \(-0.278512\pi\) | ||||
0.641020 | + | 0.767524i | \(0.278512\pi\) | |||||||
\(212\) | −5.33731e28 | −0.444759 | ||||||||
\(213\) | −8.20264e28 | −0.644479 | ||||||||
\(214\) | 1.36729e29 | 1.01319 | ||||||||
\(215\) | 3.28453e28 | 0.229611 | ||||||||
\(216\) | −5.79735e28 | −0.382435 | ||||||||
\(217\) | 2.27460e26 | 0.00141631 | ||||||||
\(218\) | −1.72238e29 | −1.01257 | ||||||||
\(219\) | 7.55406e28 | 0.419400 | ||||||||
\(220\) | −2.74041e28 | −0.143725 | ||||||||
\(221\) | −8.35868e27 | −0.0414223 | ||||||||
\(222\) | −1.33597e29 | −0.625724 | ||||||||
\(223\) | −3.26058e29 | −1.44372 | −0.721861 | − | 0.692038i | \(-0.756713\pi\) | ||||
−0.721861 | + | 0.692038i | \(0.756713\pi\) | |||||||
\(224\) | 8.18804e26 | 0.00342831 | ||||||||
\(225\) | −2.11365e28 | −0.0837052 | ||||||||
\(226\) | −3.11763e29 | −1.16807 | ||||||||
\(227\) | −4.25210e29 | −1.50758 | −0.753791 | − | 0.657115i | \(-0.771777\pi\) | ||||
−0.753791 | + | 0.657115i | \(0.771777\pi\) | |||||||
\(228\) | −1.55927e29 | −0.523281 | ||||||||
\(229\) | 5.46098e29 | 1.73511 | 0.867555 | − | 0.497342i | \(-0.165690\pi\) | ||||
0.867555 | + | 0.497342i | \(0.165690\pi\) | |||||||
\(230\) | −2.83334e28 | −0.0852512 | ||||||||
\(231\) | 3.33517e27 | 0.00950534 | ||||||||
\(232\) | −6.04608e28 | −0.163258 | ||||||||
\(233\) | −2.50604e29 | −0.641268 | −0.320634 | − | 0.947203i | \(-0.603896\pi\) | ||||
−0.320634 | + | 0.947203i | \(0.603896\pi\) | |||||||
\(234\) | −5.90445e27 | −0.0143213 | ||||||||
\(235\) | 1.90116e29 | 0.437190 | ||||||||
\(236\) | −3.41632e28 | −0.0745005 | ||||||||
\(237\) | −1.76457e29 | −0.364993 | ||||||||
\(238\) | 5.98153e27 | 0.0117382 | ||||||||
\(239\) | 6.64864e29 | 1.23811 | 0.619055 | − | 0.785348i | \(-0.287516\pi\) | ||||
0.619055 | + | 0.785348i | \(0.287516\pi\) | |||||||
\(240\) | 4.82348e28 | 0.0852551 | ||||||||
\(241\) | 2.77555e29 | 0.465731 | 0.232866 | − | 0.972509i | \(-0.425190\pi\) | ||||
0.232866 | + | 0.972509i | \(0.425190\pi\) | |||||||
\(242\) | 2.60443e29 | 0.414974 | ||||||||
\(243\) | −5.10055e29 | −0.771859 | ||||||||
\(244\) | 5.30232e29 | 0.762242 | ||||||||
\(245\) | 3.27286e29 | 0.447045 | ||||||||
\(246\) | −3.40365e29 | −0.441830 | ||||||||
\(247\) | −5.38252e28 | −0.0664161 | ||||||||
\(248\) | 2.20092e28 | 0.0258201 | ||||||||
\(249\) | 1.03856e30 | 1.15862 | ||||||||
\(250\) | 5.96046e28 | 0.0632456 | ||||||||
\(251\) | −1.49015e30 | −1.50421 | −0.752105 | − | 0.659043i | \(-0.770962\pi\) | ||||
−0.752105 | + | 0.659043i | \(0.770962\pi\) | |||||||
\(252\) | 4.22526e27 | 0.00405833 | ||||||||
\(253\) | −1.89563e29 | −0.173280 | ||||||||
\(254\) | 1.02510e30 | 0.891959 | ||||||||
\(255\) | 3.52365e29 | 0.291904 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −7.29296e29 | −0.547948 | −0.273974 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273974 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(258\) | −3.86790e29 | −0.276840 | ||||||||
\(259\) | 3.30016e28 | 0.0225054 | ||||||||
\(260\) | 1.66504e28 | 0.0108208 | ||||||||
\(261\) | −3.11995e29 | −0.193260 | ||||||||
\(262\) | 1.40446e30 | 0.829358 | ||||||||
\(263\) | −5.88360e29 | −0.331281 | −0.165640 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165640 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(264\) | 3.22713e29 | 0.173288 | ||||||||
\(265\) | 7.76681e29 | 0.397804 | ||||||||
\(266\) | 3.85177e28 | 0.0188209 | ||||||||
\(267\) | 1.19155e30 | 0.555548 | ||||||||
\(268\) | 8.37103e29 | 0.372472 | ||||||||
\(269\) | 1.22413e30 | 0.519904 | 0.259952 | − | 0.965622i | \(-0.416293\pi\) | ||||
0.259952 | + | 0.965622i | \(0.416293\pi\) | |||||||
\(270\) | 8.43625e29 | 0.342060 | ||||||||
\(271\) | −1.53605e30 | −0.594688 | −0.297344 | − | 0.954770i | \(-0.596101\pi\) | ||||
−0.297344 | + | 0.954770i | \(0.596101\pi\) | |||||||
\(272\) | 5.78778e29 | 0.213993 | ||||||||
\(273\) | −2.02641e27 | −0.000715638 0 | ||||||||
\(274\) | −5.91613e29 | −0.199598 | ||||||||
\(275\) | 3.98783e29 | 0.128552 | ||||||||
\(276\) | 3.33656e29 | 0.102786 | ||||||||
\(277\) | −4.32632e29 | −0.127386 | −0.0636929 | − | 0.997970i | \(-0.520288\pi\) | ||||
−0.0636929 | + | 0.997970i | \(0.520288\pi\) | |||||||
\(278\) | −2.02056e30 | −0.568736 | ||||||||
\(279\) | 1.13574e29 | 0.0305650 | ||||||||
\(280\) | −1.19152e28 | −0.00306637 | ||||||||
\(281\) | −3.63667e30 | −0.895107 | −0.447554 | − | 0.894257i | \(-0.647705\pi\) | ||||
−0.447554 | + | 0.894257i | \(0.647705\pi\) | |||||||
\(282\) | −2.23882e30 | −0.527116 | ||||||||
\(283\) | −8.38888e30 | −1.88962 | −0.944808 | − | 0.327624i | \(-0.893752\pi\) | ||||
−0.944808 | + | 0.327624i | \(0.893752\pi\) | |||||||
\(284\) | 1.96062e30 | 0.422585 | ||||||||
\(285\) | 2.26903e30 | 0.468037 | ||||||||
\(286\) | 1.11399e29 | 0.0219941 | ||||||||
\(287\) | 8.40783e28 | 0.0158913 | ||||||||
\(288\) | 4.08840e29 | 0.0739856 | ||||||||
\(289\) | −1.54254e30 | −0.267309 | ||||||||
\(290\) | 8.79820e29 | 0.146022 | ||||||||
\(291\) | 3.20739e30 | 0.509906 | ||||||||
\(292\) | −1.80559e30 | −0.275001 | ||||||||
\(293\) | −8.70672e30 | −1.27060 | −0.635301 | − | 0.772265i | \(-0.719124\pi\) | ||||
−0.635301 | + | 0.772265i | \(0.719124\pi\) | |||||||
\(294\) | −3.85415e30 | −0.538998 | ||||||||
\(295\) | 4.97141e29 | 0.0666352 | ||||||||
\(296\) | 3.19326e30 | 0.410287 | ||||||||
\(297\) | 5.64425e30 | 0.695265 | ||||||||
\(298\) | −6.17856e30 | −0.729767 | ||||||||
\(299\) | 1.15177e29 | 0.0130459 | ||||||||
\(300\) | −7.01909e29 | −0.0762545 | ||||||||
\(301\) | 9.55463e28 | 0.00995710 | ||||||||
\(302\) | −6.96658e29 | −0.0696519 | ||||||||
\(303\) | 9.43888e30 | 0.905498 | ||||||||
\(304\) | 3.72700e30 | 0.343115 | ||||||||
\(305\) | −7.71589e30 | −0.681770 | ||||||||
\(306\) | 2.98666e30 | 0.253319 | ||||||||
\(307\) | 3.24336e30 | 0.264098 | 0.132049 | − | 0.991243i | \(-0.457844\pi\) | ||||
0.132049 | + | 0.991243i | \(0.457844\pi\) | |||||||
\(308\) | −7.97180e28 | −0.00623265 | ||||||||
\(309\) | 1.02088e31 | 0.766465 | ||||||||
\(310\) | −3.20276e29 | −0.0230942 | ||||||||
\(311\) | −1.24495e30 | −0.0862281 | −0.0431140 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431140 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(312\) | −1.96077e29 | −0.0130465 | ||||||||
\(313\) | 2.33420e31 | 1.49222 | 0.746112 | − | 0.665820i | \(-0.231918\pi\) | ||||
0.746112 | + | 0.665820i | \(0.231918\pi\) | |||||||
\(314\) | −1.34839e31 | −0.828316 | ||||||||
\(315\) | −6.14857e28 | −0.00362988 | ||||||||
\(316\) | 4.21772e30 | 0.239326 | ||||||||
\(317\) | 2.11447e31 | 1.15335 | 0.576674 | − | 0.816974i | \(-0.304350\pi\) | ||||
0.576674 | + | 0.816974i | \(0.304350\pi\) | |||||||
\(318\) | −9.14626e30 | −0.479628 | ||||||||
\(319\) | 5.88641e30 | 0.296802 | ||||||||
\(320\) | −1.15292e30 | −0.0559017 | ||||||||
\(321\) | 2.34306e31 | 1.09262 | ||||||||
\(322\) | −8.24211e28 | −0.00369692 | ||||||||
\(323\) | 2.72265e31 | 1.17479 | ||||||||
\(324\) | −4.89374e30 | −0.203155 | ||||||||
\(325\) | −2.42296e29 | −0.00967840 | ||||||||
\(326\) | −2.07828e30 | −0.0798883 | ||||||||
\(327\) | −2.95156e31 | −1.09195 | ||||||||
\(328\) | 8.13549e30 | 0.289708 | ||||||||
\(329\) | 5.53043e29 | 0.0189588 | ||||||||
\(330\) | −4.69610e30 | −0.154993 | ||||||||
\(331\) | −4.35367e31 | −1.38359 | −0.691793 | − | 0.722096i | \(-0.743179\pi\) | ||||
−0.691793 | + | 0.722096i | \(0.743179\pi\) | |||||||
\(332\) | −2.48239e31 | −0.759703 | ||||||||
\(333\) | 1.64781e31 | 0.485685 | ||||||||
\(334\) | 3.46070e30 | 0.0982501 | ||||||||
\(335\) | −1.21815e31 | −0.333149 | ||||||||
\(336\) | 1.40314e29 | 0.00369709 | ||||||||
\(337\) | −5.97252e30 | −0.151630 | −0.0758148 | − | 0.997122i | \(-0.524156\pi\) | ||||
−0.0758148 | + | 0.997122i | \(0.524156\pi\) | |||||||
\(338\) | 2.88354e31 | 0.705451 | ||||||||
\(339\) | −5.34252e31 | −1.25965 | ||||||||
\(340\) | −8.42232e30 | −0.191402 | ||||||||
\(341\) | −2.14279e30 | −0.0469408 | ||||||||
\(342\) | 1.92324e31 | 0.406169 | ||||||||
\(343\) | 1.90449e30 | 0.0387796 | ||||||||
\(344\) | 9.24514e30 | 0.181524 | ||||||||
\(345\) | −4.85534e30 | −0.0919349 | ||||||||
\(346\) | 3.09027e31 | 0.564346 | ||||||||
\(347\) | −9.71425e31 | −1.71116 | −0.855580 | − | 0.517670i | \(-0.826799\pi\) | ||||
−0.855580 | + | 0.517670i | \(0.826799\pi\) | |||||||
\(348\) | −1.03608e31 | −0.176057 | ||||||||
\(349\) | −7.20784e31 | −1.18165 | −0.590823 | − | 0.806801i | \(-0.701197\pi\) | ||||
−0.590823 | + | 0.806801i | \(0.701197\pi\) | |||||||
\(350\) | 1.73388e29 | 0.00274265 | ||||||||
\(351\) | −3.42938e30 | −0.0523451 | ||||||||
\(352\) | −7.71358e30 | −0.113625 | ||||||||
\(353\) | 6.98207e31 | 0.992660 | 0.496330 | − | 0.868134i | \(-0.334681\pi\) | ||||
0.496330 | + | 0.868134i | \(0.334681\pi\) | |||||||
\(354\) | −5.85437e30 | −0.0803414 | ||||||||
\(355\) | −2.85307e31 | −0.377971 | ||||||||
\(356\) | −2.84807e31 | −0.364272 | ||||||||
\(357\) | 1.02502e30 | 0.0126584 | ||||||||
\(358\) | 2.23804e31 | 0.266888 | ||||||||
\(359\) | −1.33870e32 | −1.54171 | −0.770857 | − | 0.637009i | \(-0.780171\pi\) | ||||
−0.770857 | + | 0.637009i | \(0.780171\pi\) | |||||||
\(360\) | −5.94940e30 | −0.0661747 | ||||||||
\(361\) | 8.22469e31 | 0.883649 | ||||||||
\(362\) | 1.12374e32 | 1.16629 | ||||||||
\(363\) | 4.46307e31 | 0.447508 | ||||||||
\(364\) | 4.84357e28 | 0.000469244 0 | ||||||||
\(365\) | 2.62748e31 | 0.245968 | ||||||||
\(366\) | 9.08629e31 | 0.822003 | ||||||||
\(367\) | 6.63971e31 | 0.580528 | 0.290264 | − | 0.956947i | \(-0.406257\pi\) | ||||
0.290264 | + | 0.956947i | \(0.406257\pi\) | |||||||
\(368\) | −7.97514e30 | −0.0673970 | ||||||||
\(369\) | 4.19814e31 | 0.342947 | ||||||||
\(370\) | −4.64680e31 | −0.366972 | ||||||||
\(371\) | 2.25935e30 | 0.0172508 | ||||||||
\(372\) | 3.77159e30 | 0.0278444 | ||||||||
\(373\) | 2.18553e32 | 1.56026 | 0.780129 | − | 0.625619i | \(-0.215154\pi\) | ||||
0.780129 | + | 0.625619i | \(0.215154\pi\) | |||||||
\(374\) | −5.63493e31 | −0.389039 | ||||||||
\(375\) | 1.02141e31 | 0.0682041 | ||||||||
\(376\) | 5.35129e31 | 0.345629 | ||||||||
\(377\) | −3.57651e30 | −0.0223456 | ||||||||
\(378\) | 2.45409e30 | 0.0148334 | ||||||||
\(379\) | −1.48811e32 | −0.870253 | −0.435126 | − | 0.900369i | \(-0.643296\pi\) | ||||
−0.435126 | + | 0.900369i | \(0.643296\pi\) | |||||||
\(380\) | −5.42350e31 | −0.306892 | ||||||||
\(381\) | 1.75666e32 | 0.961889 | ||||||||
\(382\) | 1.03849e32 | 0.550311 | ||||||||
\(383\) | −2.09320e32 | −1.07356 | −0.536779 | − | 0.843723i | \(-0.680359\pi\) | ||||
−0.536779 | + | 0.843723i | \(0.680359\pi\) | |||||||
\(384\) | 1.35769e31 | 0.0674001 | ||||||||
\(385\) | 1.16005e30 | 0.00557465 | ||||||||
\(386\) | −1.91068e31 | −0.0888889 | ||||||||
\(387\) | 4.77076e31 | 0.214882 | ||||||||
\(388\) | −7.66639e31 | −0.334345 | ||||||||
\(389\) | −2.78926e32 | −1.17793 | −0.588965 | − | 0.808158i | \(-0.700465\pi\) | ||||
−0.588965 | + | 0.808158i | \(0.700465\pi\) | |||||||
\(390\) | 2.85329e30 | 0.0116691 | ||||||||
\(391\) | −5.82600e31 | −0.230760 | ||||||||
\(392\) | 9.21229e31 | 0.353420 | ||||||||
\(393\) | 2.40674e32 | 0.894381 | ||||||||
\(394\) | 4.70120e31 | 0.169241 | ||||||||
\(395\) | −6.13759e31 | −0.214059 | ||||||||
\(396\) | −3.98043e31 | −0.134505 | ||||||||
\(397\) | 4.22963e32 | 1.38491 | 0.692455 | − | 0.721461i | \(-0.256529\pi\) | ||||
0.692455 | + | 0.721461i | \(0.256529\pi\) | |||||||
\(398\) | −4.18631e32 | −1.32829 | ||||||||
\(399\) | 6.60056e30 | 0.0202964 | ||||||||
\(400\) | 1.67772e31 | 0.0500000 | ||||||||
\(401\) | −2.59389e32 | −0.749284 | −0.374642 | − | 0.927169i | \(-0.622234\pi\) | ||||
−0.374642 | + | 0.927169i | \(0.622234\pi\) | |||||||
\(402\) | 1.43450e32 | 0.401674 | ||||||||
\(403\) | 1.30194e30 | 0.00353408 | ||||||||
\(404\) | −2.25611e32 | −0.593735 | ||||||||
\(405\) | 7.12132e31 | 0.181708 | ||||||||
\(406\) | 2.55938e30 | 0.00633226 | ||||||||
\(407\) | −3.10893e32 | −0.745900 | ||||||||
\(408\) | 9.91820e31 | 0.230771 | ||||||||
\(409\) | 7.31347e32 | 1.65037 | 0.825186 | − | 0.564861i | \(-0.191070\pi\) | ||||
0.825186 | + | 0.564861i | \(0.191070\pi\) | |||||||
\(410\) | −1.18387e32 | −0.259123 | ||||||||
\(411\) | −1.01381e32 | −0.215246 | ||||||||
\(412\) | −2.44013e32 | −0.502571 | ||||||||
\(413\) | 1.44617e30 | 0.00288964 | ||||||||
\(414\) | −4.11540e31 | −0.0797825 | ||||||||
\(415\) | 3.61235e32 | 0.679499 | ||||||||
\(416\) | 4.68668e30 | 0.00855458 | ||||||||
\(417\) | −3.46252e32 | −0.613325 | ||||||||
\(418\) | −3.62858e32 | −0.623782 | ||||||||
\(419\) | −6.24972e32 | −1.04276 | −0.521381 | − | 0.853324i | \(-0.674583\pi\) | ||||
−0.521381 | + | 0.853324i | \(0.674583\pi\) | |||||||
\(420\) | −2.04184e30 | −0.00330678 | ||||||||
\(421\) | −2.51168e32 | −0.394855 | −0.197427 | − | 0.980318i | \(-0.563259\pi\) | ||||
−0.197427 | + | 0.980318i | \(0.563259\pi\) | |||||||
\(422\) | −5.94008e32 | −0.906539 | ||||||||
\(423\) | 2.76142e32 | 0.409146 | ||||||||
\(424\) | 2.18616e32 | 0.314492 | ||||||||
\(425\) | 1.22561e32 | 0.171195 | ||||||||
\(426\) | 3.35980e32 | 0.455716 | ||||||||
\(427\) | −2.24453e31 | −0.0295650 | ||||||||
\(428\) | −5.60044e32 | −0.716432 | ||||||||
\(429\) | 1.90899e31 | 0.0237185 | ||||||||
\(430\) | −1.34535e32 | −0.162360 | ||||||||
\(431\) | −1.55381e33 | −1.82151 | −0.910754 | − | 0.412948i | \(-0.864499\pi\) | ||||
−0.910754 | + | 0.412948i | \(0.864499\pi\) | |||||||
\(432\) | 2.37459e32 | 0.270422 | ||||||||
\(433\) | 1.08349e33 | 1.19874 | 0.599370 | − | 0.800472i | \(-0.295418\pi\) | ||||
0.599370 | + | 0.800472i | \(0.295418\pi\) | |||||||
\(434\) | −9.31674e29 | −0.00100148 | ||||||||
\(435\) | 1.50770e32 | 0.157471 | ||||||||
\(436\) | 7.05489e32 | 0.715993 | ||||||||
\(437\) | −3.75161e32 | −0.369999 | ||||||||
\(438\) | −3.09414e32 | −0.296561 | ||||||||
\(439\) | 1.66407e33 | 1.55012 | 0.775058 | − | 0.631890i | \(-0.217721\pi\) | ||||
0.775058 | + | 0.631890i | \(0.217721\pi\) | |||||||
\(440\) | 1.12247e32 | 0.101629 | ||||||||
\(441\) | 4.75380e32 | 0.418368 | ||||||||
\(442\) | 3.42371e31 | 0.0292900 | ||||||||
\(443\) | 3.77416e32 | 0.313887 | 0.156944 | − | 0.987608i | \(-0.449836\pi\) | ||||
0.156944 | + | 0.987608i | \(0.449836\pi\) | |||||||
\(444\) | 5.47211e32 | 0.442454 | ||||||||
\(445\) | 4.14449e32 | 0.325815 | ||||||||
\(446\) | 1.33553e33 | 1.02087 | ||||||||
\(447\) | −1.05879e33 | −0.786981 | ||||||||
\(448\) | −3.35382e30 | −0.00242418 | ||||||||
\(449\) | 2.15921e33 | 1.51781 | 0.758903 | − | 0.651204i | \(-0.225736\pi\) | ||||
0.758903 | + | 0.651204i | \(0.225736\pi\) | |||||||
\(450\) | 8.65752e31 | 0.0591885 | ||||||||
\(451\) | −7.92063e32 | −0.526688 | ||||||||
\(452\) | 1.27698e33 | 0.825952 | ||||||||
\(453\) | −1.19383e32 | −0.0751127 | ||||||||
\(454\) | 1.74166e33 | 1.06602 | ||||||||
\(455\) | −7.04832e29 | −0.000419704 0 | ||||||||
\(456\) | 6.38676e32 | 0.370016 | ||||||||
\(457\) | 8.65127e30 | 0.00487671 | 0.00243836 | − | 0.999997i | \(-0.499224\pi\) | ||||
0.00243836 | + | 0.999997i | \(0.499224\pi\) | |||||||
\(458\) | −2.23682e33 | −1.22691 | ||||||||
\(459\) | 1.73469e33 | 0.925897 | ||||||||
\(460\) | 1.16053e32 | 0.0602817 | ||||||||
\(461\) | −3.15151e33 | −1.59315 | −0.796575 | − | 0.604539i | \(-0.793357\pi\) | ||||
−0.796575 | + | 0.604539i | \(0.793357\pi\) | |||||||
\(462\) | −1.36608e31 | −0.00672129 | ||||||||
\(463\) | −2.93719e33 | −1.40660 | −0.703298 | − | 0.710895i | \(-0.748290\pi\) | ||||
−0.703298 | + | 0.710895i | \(0.748290\pi\) | |||||||
\(464\) | 2.47647e32 | 0.115441 | ||||||||
\(465\) | −5.48839e31 | −0.0249048 | ||||||||
\(466\) | 1.02648e33 | 0.453445 | ||||||||
\(467\) | −2.28078e33 | −0.980895 | −0.490448 | − | 0.871471i | \(-0.663167\pi\) | ||||
−0.490448 | + | 0.871471i | \(0.663167\pi\) | |||||||
\(468\) | 2.41846e31 | 0.0101267 | ||||||||
\(469\) | −3.54356e31 | −0.0144470 | ||||||||
\(470\) | −7.78716e32 | −0.309140 | ||||||||
\(471\) | −2.31067e33 | −0.893257 | ||||||||
\(472\) | 1.39933e32 | 0.0526798 | ||||||||
\(473\) | −9.00099e32 | −0.330009 | ||||||||
\(474\) | 7.22768e32 | 0.258089 | ||||||||
\(475\) | 7.89224e32 | 0.274492 | ||||||||
\(476\) | −2.45003e31 | −0.00830013 | ||||||||
\(477\) | 1.12812e33 | 0.372286 | ||||||||
\(478\) | −2.72328e33 | −0.875476 | ||||||||
\(479\) | −7.97173e32 | −0.249666 | −0.124833 | − | 0.992178i | \(-0.539839\pi\) | ||||
−0.124833 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(480\) | −1.97570e32 | −0.0602844 | ||||||||
\(481\) | 1.88895e32 | 0.0561573 | ||||||||
\(482\) | −1.13686e33 | −0.329322 | ||||||||
\(483\) | −1.41241e31 | −0.00398676 | ||||||||
\(484\) | −1.06677e33 | −0.293431 | ||||||||
\(485\) | 1.11561e33 | 0.299047 | ||||||||
\(486\) | 2.08918e33 | 0.545787 | ||||||||
\(487\) | −7.32515e32 | −0.186511 | −0.0932555 | − | 0.995642i | \(-0.529727\pi\) | ||||
−0.0932555 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(488\) | −2.17183e33 | −0.538987 | ||||||||
\(489\) | −3.56143e32 | −0.0861516 | ||||||||
\(490\) | −1.34056e33 | −0.316109 | ||||||||
\(491\) | −2.35651e33 | −0.541690 | −0.270845 | − | 0.962623i | \(-0.587303\pi\) | ||||
−0.270845 | + | 0.962623i | \(0.587303\pi\) | |||||||
\(492\) | 1.39413e33 | 0.312421 | ||||||||
\(493\) | 1.80911e33 | 0.395257 | ||||||||
\(494\) | 2.20468e32 | 0.0469633 | ||||||||
\(495\) | 5.79229e32 | 0.120305 | ||||||||
\(496\) | −9.01496e31 | −0.0182576 | ||||||||
\(497\) | −8.29952e31 | −0.0163907 | ||||||||
\(498\) | −4.25394e33 | −0.819265 | ||||||||
\(499\) | 1.11697e33 | 0.209789 | 0.104895 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104895 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(500\) | −2.44141e32 | −0.0447214 | ||||||||
\(501\) | 5.93041e32 | 0.105953 | ||||||||
\(502\) | 6.10366e33 | 1.06364 | ||||||||
\(503\) | 3.79303e33 | 0.644743 | 0.322372 | − | 0.946613i | \(-0.395520\pi\) | ||||
0.322372 | + | 0.946613i | \(0.395520\pi\) | |||||||
\(504\) | −1.73067e31 | −0.00286967 | ||||||||
\(505\) | 3.28307e33 | 0.531052 | ||||||||
\(506\) | 7.76452e32 | 0.122527 | ||||||||
\(507\) | 4.94136e33 | 0.760759 | ||||||||
\(508\) | −4.19881e33 | −0.630710 | ||||||||
\(509\) | −7.62370e33 | −1.11736 | −0.558681 | − | 0.829383i | \(-0.688692\pi\) | ||||
−0.558681 | + | 0.829383i | \(0.688692\pi\) | |||||||
\(510\) | −1.44329e33 | −0.206408 | ||||||||
\(511\) | 7.64328e31 | 0.0106664 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 1.11704e34 | 1.48458 | ||||||||
\(514\) | 2.98720e33 | 0.387458 | ||||||||
\(515\) | 3.55085e33 | 0.449513 | ||||||||
\(516\) | 1.58429e33 | 0.195755 | ||||||||
\(517\) | −5.20997e33 | −0.628353 | ||||||||
\(518\) | −1.35174e32 | −0.0159137 | ||||||||
\(519\) | 5.29563e33 | 0.608592 | ||||||||
\(520\) | −6.82002e31 | −0.00765145 | ||||||||
\(521\) | 5.33662e33 | 0.584514 | 0.292257 | − | 0.956340i | \(-0.405594\pi\) | ||||
0.292257 | + | 0.956340i | \(0.405594\pi\) | |||||||
\(522\) | 1.27793e33 | 0.136655 | ||||||||
\(523\) | 1.14894e34 | 1.19957 | 0.599786 | − | 0.800160i | \(-0.295252\pi\) | ||||
0.599786 | + | 0.800160i | \(0.295252\pi\) | |||||||
\(524\) | −5.75265e33 | −0.586445 | ||||||||
\(525\) | 2.97126e31 | 0.00295767 | ||||||||
\(526\) | 2.40992e33 | 0.234251 | ||||||||
\(527\) | −6.58561e32 | −0.0625120 | ||||||||
\(528\) | −1.32183e33 | −0.122533 | ||||||||
\(529\) | −1.02430e34 | −0.927322 | ||||||||
\(530\) | −3.18129e33 | −0.281290 | ||||||||
\(531\) | 7.22092e32 | 0.0623607 | ||||||||
\(532\) | −1.57768e32 | −0.0133084 | ||||||||
\(533\) | 4.81248e32 | 0.0396533 | ||||||||
\(534\) | −4.88059e33 | −0.392831 | ||||||||
\(535\) | 8.14971e33 | 0.640796 | ||||||||
\(536\) | −3.42877e33 | −0.263378 | ||||||||
\(537\) | 3.83520e33 | 0.287812 | ||||||||
\(538\) | −5.01403e33 | −0.367628 | ||||||||
\(539\) | −8.96900e33 | −0.642517 | ||||||||
\(540\) | −3.45549e33 | −0.241873 | ||||||||
\(541\) | −2.08461e34 | −1.42580 | −0.712901 | − | 0.701265i | \(-0.752619\pi\) | ||||
−0.712901 | + | 0.701265i | \(0.752619\pi\) | |||||||
\(542\) | 6.29167e33 | 0.420508 | ||||||||
\(543\) | 1.92569e34 | 1.25773 | ||||||||
\(544\) | −2.37067e33 | −0.151316 | ||||||||
\(545\) | −1.02662e34 | −0.640404 | ||||||||
\(546\) | 8.30016e30 | 0.000506033 0 | ||||||||
\(547\) | −5.82664e33 | −0.347197 | −0.173599 | − | 0.984816i | \(-0.555540\pi\) | ||||
−0.173599 | + | 0.984816i | \(0.555540\pi\) | |||||||
\(548\) | 2.42324e33 | 0.141137 | ||||||||
\(549\) | −1.12073e34 | −0.638036 | ||||||||
\(550\) | −1.63341e33 | −0.0908998 | ||||||||
\(551\) | 1.16497e34 | 0.633751 | ||||||||
\(552\) | −1.36666e33 | −0.0726809 | ||||||||
\(553\) | −1.78541e32 | −0.00928270 | ||||||||
\(554\) | 1.77206e33 | 0.0900754 | ||||||||
\(555\) | −7.96297e33 | −0.395743 | ||||||||
\(556\) | 8.27619e33 | 0.402157 | ||||||||
\(557\) | −2.41168e34 | −1.14586 | −0.572928 | − | 0.819606i | \(-0.694193\pi\) | ||||
−0.572928 | + | 0.819606i | \(0.694193\pi\) | |||||||
\(558\) | −4.65198e32 | −0.0216127 | ||||||||
\(559\) | 5.46889e32 | 0.0248457 | ||||||||
\(560\) | 4.88045e31 | 0.00216825 | ||||||||
\(561\) | −9.65626e33 | −0.419540 | ||||||||
\(562\) | 1.48958e34 | 0.632937 | ||||||||
\(563\) | 1.42755e34 | 0.593248 | 0.296624 | − | 0.954994i | \(-0.404139\pi\) | ||||
0.296624 | + | 0.954994i | \(0.404139\pi\) | |||||||
\(564\) | 9.17022e33 | 0.372727 | ||||||||
\(565\) | −1.85826e34 | −0.738754 | ||||||||
\(566\) | 3.43609e34 | 1.33616 | ||||||||
\(567\) | 2.07158e32 | 0.00787975 | ||||||||
\(568\) | −8.03069e33 | −0.298812 | ||||||||
\(569\) | −4.47698e34 | −1.62960 | −0.814802 | − | 0.579739i | \(-0.803154\pi\) | ||||
−0.814802 | + | 0.579739i | \(0.803154\pi\) | |||||||
\(570\) | −9.29396e33 | −0.330952 | ||||||||
\(571\) | −1.37949e33 | −0.0480581 | −0.0240291 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240291 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(572\) | −4.56291e32 | −0.0155522 | ||||||||
\(573\) | 1.77960e34 | 0.593456 | ||||||||
\(574\) | −3.44385e32 | −0.0112369 | ||||||||
\(575\) | −1.68880e33 | −0.0539176 | ||||||||
\(576\) | −1.67461e33 | −0.0523157 | ||||||||
\(577\) | −2.32241e33 | −0.0709973 | −0.0354986 | − | 0.999370i | \(-0.511302\pi\) | ||||
−0.0354986 | + | 0.999370i | \(0.511302\pi\) | |||||||
\(578\) | 6.31825e33 | 0.189016 | ||||||||
\(579\) | −3.27424e33 | −0.0958579 | ||||||||
\(580\) | −3.60374e33 | −0.103253 | ||||||||
\(581\) | 1.05082e33 | 0.0294665 | ||||||||
\(582\) | −1.31375e34 | −0.360558 | ||||||||
\(583\) | −2.12843e34 | −0.571745 | ||||||||
\(584\) | 7.39570e33 | 0.194455 | ||||||||
\(585\) | −3.51932e32 | −0.00905755 | ||||||||
\(586\) | 3.56627e34 | 0.898451 | ||||||||
\(587\) | 4.35047e34 | 1.07290 | 0.536451 | − | 0.843931i | \(-0.319765\pi\) | ||||
0.536451 | + | 0.843931i | \(0.319765\pi\) | |||||||
\(588\) | 1.57866e34 | 0.381129 | ||||||||
\(589\) | −4.24076e33 | −0.100231 | ||||||||
\(590\) | −2.03629e33 | −0.0471182 | ||||||||
\(591\) | 8.05619e33 | 0.182510 | ||||||||
\(592\) | −1.30796e34 | −0.290117 | ||||||||
\(593\) | 5.31713e34 | 1.15476 | 0.577382 | − | 0.816474i | \(-0.304074\pi\) | ||||
0.577382 | + | 0.816474i | \(0.304074\pi\) | |||||||
\(594\) | −2.31188e34 | −0.491626 | ||||||||
\(595\) | 3.56527e32 | 0.00742387 | ||||||||
\(596\) | 2.53074e34 | 0.516023 | ||||||||
\(597\) | −7.17385e34 | −1.43243 | ||||||||
\(598\) | −4.71763e32 | −0.00922484 | ||||||||
\(599\) | 7.13123e34 | 1.36562 | 0.682809 | − | 0.730597i | \(-0.260758\pi\) | ||||
0.682809 | + | 0.730597i | \(0.260758\pi\) | |||||||
\(600\) | 2.87502e33 | 0.0539200 | ||||||||
\(601\) | 3.07608e34 | 0.565023 | 0.282512 | − | 0.959264i | \(-0.408832\pi\) | ||||
0.282512 | + | 0.959264i | \(0.408832\pi\) | |||||||
\(602\) | −3.91358e32 | −0.00704073 | ||||||||
\(603\) | −1.76935e34 | −0.311779 | ||||||||
\(604\) | 2.85351e33 | 0.0492513 | ||||||||
\(605\) | 1.55236e34 | 0.262452 | ||||||||
\(606\) | −3.86617e34 | −0.640284 | ||||||||
\(607\) | 2.76184e34 | 0.448064 | 0.224032 | − | 0.974582i | \(-0.428078\pi\) | ||||
0.224032 | + | 0.974582i | \(0.428078\pi\) | |||||||
\(608\) | −1.52658e34 | −0.242619 | ||||||||
\(609\) | 4.38586e32 | 0.00682871 | ||||||||
\(610\) | 3.16043e34 | 0.482084 | ||||||||
\(611\) | 3.16552e33 | 0.0473074 | ||||||||
\(612\) | −1.22333e34 | −0.179124 | ||||||||
\(613\) | 4.94974e34 | 0.710112 | 0.355056 | − | 0.934845i | \(-0.384462\pi\) | ||||
0.355056 | + | 0.934845i | \(0.384462\pi\) | |||||||
\(614\) | −1.32848e34 | −0.186746 | ||||||||
\(615\) | −2.02873e34 | −0.279438 | ||||||||
\(616\) | 3.26525e32 | 0.00440715 | ||||||||
\(617\) | 1.12825e35 | 1.49225 | 0.746126 | − | 0.665805i | \(-0.231912\pi\) | ||||
0.746126 | + | 0.665805i | \(0.231912\pi\) | |||||||
\(618\) | −4.18151e34 | −0.541973 | ||||||||
\(619\) | 5.35184e34 | 0.679782 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(620\) | 1.31185e33 | 0.0163301 | ||||||||
\(621\) | −2.39027e34 | −0.291610 | ||||||||
\(622\) | 5.09934e33 | 0.0609725 | ||||||||
\(623\) | 1.20562e33 | 0.0141290 | ||||||||
\(624\) | 8.03131e32 | 0.00922527 | ||||||||
\(625\) | 3.55271e33 | 0.0400000 | ||||||||
\(626\) | −9.56089e34 | −1.05516 | ||||||||
\(627\) | −6.21809e34 | −0.672687 | ||||||||
\(628\) | 5.52302e34 | 0.585708 | ||||||||
\(629\) | −9.55490e34 | −0.993329 | ||||||||
\(630\) | 2.51845e32 | 0.00256671 | ||||||||
\(631\) | −9.73214e34 | −0.972392 | −0.486196 | − | 0.873850i | \(-0.661616\pi\) | ||||
−0.486196 | + | 0.873850i | \(0.661616\pi\) | |||||||
\(632\) | −1.72758e34 | −0.169229 | ||||||||
\(633\) | −1.01792e35 | −0.977612 | ||||||||
\(634\) | −8.66087e34 | −0.815541 | ||||||||
\(635\) | 6.11007e34 | 0.564124 | ||||||||
\(636\) | 3.74631e34 | 0.339148 | ||||||||
\(637\) | 5.44946e33 | 0.0483738 | ||||||||
\(638\) | −2.41107e34 | −0.209871 | ||||||||
\(639\) | −4.14406e34 | −0.353725 | ||||||||
\(640\) | 4.72237e33 | 0.0395285 | ||||||||
\(641\) | −2.79912e34 | −0.229772 | −0.114886 | − | 0.993379i | \(-0.536650\pi\) | ||||
−0.114886 | + | 0.993379i | \(0.536650\pi\) | |||||||
\(642\) | −9.59717e34 | −0.772601 | ||||||||
\(643\) | −1.80728e35 | −1.42688 | −0.713442 | − | 0.700714i | \(-0.752865\pi\) | ||||
−0.713442 | + | 0.700714i | \(0.752865\pi\) | |||||||
\(644\) | 3.37597e32 | 0.00261412 | ||||||||
\(645\) | −2.30545e34 | −0.175089 | ||||||||
\(646\) | −1.11520e35 | −0.830702 | ||||||||
\(647\) | 7.31933e34 | 0.534771 | 0.267385 | − | 0.963590i | \(-0.413840\pi\) | ||||
0.267385 | + | 0.963590i | \(0.413840\pi\) | |||||||
\(648\) | 2.00447e34 | 0.143652 | ||||||||
\(649\) | −1.36237e34 | −0.0957716 | ||||||||
\(650\) | 9.92443e32 | 0.00684367 | ||||||||
\(651\) | −1.59656e32 | −0.00108000 | ||||||||
\(652\) | 8.51262e33 | 0.0564896 | ||||||||
\(653\) | −7.32271e32 | −0.00476713 | −0.00238357 | − | 0.999997i | \(-0.500759\pi\) | ||||
−0.00238357 | + | 0.999997i | \(0.500759\pi\) | |||||||
\(654\) | 1.20896e35 | 0.772128 | ||||||||
\(655\) | 8.37121e34 | 0.524532 | ||||||||
\(656\) | −3.33229e34 | −0.204854 | ||||||||
\(657\) | 3.81639e34 | 0.230190 | ||||||||
\(658\) | −2.26526e33 | −0.0134059 | ||||||||
\(659\) | 3.37009e35 | 1.95692 | 0.978460 | − | 0.206434i | \(-0.0661860\pi\) | ||||
0.978460 | + | 0.206434i | \(0.0661860\pi\) | |||||||
\(660\) | 1.92352e34 | 0.109597 | ||||||||
\(661\) | 1.22749e34 | 0.0686275 | 0.0343138 | − | 0.999411i | \(-0.489075\pi\) | ||||
0.0343138 | + | 0.999411i | \(0.489075\pi\) | |||||||
\(662\) | 1.78326e35 | 0.978343 | ||||||||
\(663\) | 5.86703e33 | 0.0315863 | ||||||||
\(664\) | 1.01679e35 | 0.537191 | ||||||||
\(665\) | 2.29583e33 | 0.0119034 | ||||||||
\(666\) | −6.74944e34 | −0.343431 | ||||||||
\(667\) | −2.49283e34 | −0.124486 | ||||||||
\(668\) | −1.41750e34 | −0.0694733 | ||||||||
\(669\) | 2.28863e35 | 1.10090 | ||||||||
\(670\) | 4.98952e34 | 0.235572 | ||||||||
\(671\) | 2.11447e35 | 0.979875 | ||||||||
\(672\) | −5.74726e32 | −0.00261424 | ||||||||
\(673\) | −4.17789e35 | −1.86538 | −0.932692 | − | 0.360673i | \(-0.882547\pi\) | ||||
−0.932692 | + | 0.360673i | \(0.882547\pi\) | |||||||
\(674\) | 2.44634e34 | 0.107218 | ||||||||
\(675\) | 5.02840e34 | 0.216338 | ||||||||
\(676\) | −1.18110e35 | −0.498829 | ||||||||
\(677\) | 2.87478e35 | 1.19192 | 0.595959 | − | 0.803014i | \(-0.296772\pi\) | ||||
0.595959 | + | 0.803014i | \(0.296772\pi\) | |||||||
\(678\) | 2.18830e35 | 0.890707 | ||||||||
\(679\) | 3.24527e33 | 0.0129682 | ||||||||
\(680\) | 3.44978e34 | 0.135341 | ||||||||
\(681\) | 2.98459e35 | 1.14960 | ||||||||
\(682\) | 8.77688e33 | 0.0331922 | ||||||||
\(683\) | −3.52227e35 | −1.30787 | −0.653935 | − | 0.756551i | \(-0.726883\pi\) | ||||
−0.653935 | + | 0.756551i | \(0.726883\pi\) | |||||||
\(684\) | −7.87759e34 | −0.287205 | ||||||||
\(685\) | −3.52629e34 | −0.126237 | ||||||||
\(686\) | −7.80081e33 | −0.0274213 | ||||||||
\(687\) | −3.83311e35 | −1.32310 | ||||||||
\(688\) | −3.78681e34 | −0.128357 | ||||||||
\(689\) | 1.29321e34 | 0.0430455 | ||||||||
\(690\) | 1.98875e34 | 0.0650078 | ||||||||
\(691\) | −1.41869e35 | −0.455421 | −0.227711 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227711 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(692\) | −1.26578e35 | −0.399053 | ||||||||
\(693\) | 1.68496e33 | 0.00521705 | ||||||||
\(694\) | 3.97896e35 | 1.20997 | ||||||||
\(695\) | −1.20434e35 | −0.359700 | ||||||||
\(696\) | 4.24380e34 | 0.124491 | ||||||||
\(697\) | −2.43431e35 | −0.701400 | ||||||||
\(698\) | 2.95233e35 | 0.835550 | ||||||||
\(699\) | 1.75901e35 | 0.488995 | ||||||||
\(700\) | −7.10199e32 | −0.00193934 | ||||||||
\(701\) | 4.11949e35 | 1.10502 | 0.552508 | − | 0.833508i | \(-0.313671\pi\) | ||||
0.552508 | + | 0.833508i | \(0.313671\pi\) | |||||||
\(702\) | 1.40467e34 | 0.0370136 | ||||||||
\(703\) | −6.15282e35 | −1.59270 | ||||||||
\(704\) | 3.15948e34 | 0.0803448 | ||||||||
\(705\) | −1.33444e35 | −0.333377 | ||||||||
\(706\) | −2.85986e35 | −0.701917 | ||||||||
\(707\) | 9.55036e33 | 0.0230291 | ||||||||
\(708\) | 2.39795e34 | 0.0568099 | ||||||||
\(709\) | −3.69515e35 | −0.860110 | −0.430055 | − | 0.902803i | \(-0.641506\pi\) | ||||
−0.430055 | + | 0.902803i | \(0.641506\pi\) | |||||||
\(710\) | 1.16862e35 | 0.267266 | ||||||||
\(711\) | −8.91480e34 | −0.200328 | ||||||||
\(712\) | 1.16657e35 | 0.257579 | ||||||||
\(713\) | 9.07449e33 | 0.0196881 | ||||||||
\(714\) | −4.19849e33 | −0.00895087 | ||||||||
\(715\) | 6.63991e33 | 0.0139103 | ||||||||
\(716\) | −9.16700e34 | −0.188718 | ||||||||
\(717\) | −4.66674e35 | −0.944114 | ||||||||
\(718\) | 5.48333e35 | 1.09016 | ||||||||
\(719\) | 2.40654e35 | 0.470200 | 0.235100 | − | 0.971971i | \(-0.424458\pi\) | ||||
0.235100 | + | 0.971971i | \(0.424458\pi\) | |||||||
\(720\) | 2.43688e34 | 0.0467926 | ||||||||
\(721\) | 1.03293e34 | 0.0194931 | ||||||||
\(722\) | −3.36883e35 | −0.624834 | ||||||||
\(723\) | −1.94818e35 | −0.355141 | ||||||||
\(724\) | −4.60282e35 | −0.824693 | ||||||||
\(725\) | 5.24414e34 | 0.0923526 | ||||||||
\(726\) | −1.82807e35 | −0.316436 | ||||||||
\(727\) | −2.82511e34 | −0.0480680 | −0.0240340 | − | 0.999711i | \(-0.507651\pi\) | ||||
−0.0240340 | + | 0.999711i | \(0.507651\pi\) | |||||||
\(728\) | −1.98393e32 | −0.000331805 0 | ||||||||
\(729\) | 6.05157e35 | 0.994888 | ||||||||
\(730\) | −1.07622e35 | −0.173926 | ||||||||
\(731\) | −2.76634e35 | −0.439479 | ||||||||
\(732\) | −3.72175e35 | −0.581244 | ||||||||
\(733\) | 1.13647e36 | 1.74486 | 0.872428 | − | 0.488743i | \(-0.162544\pi\) | ||||
0.872428 | + | 0.488743i | \(0.162544\pi\) | |||||||
\(734\) | −2.71963e35 | −0.410495 | ||||||||
\(735\) | −2.29725e35 | −0.340892 | ||||||||
\(736\) | 3.26662e34 | 0.0476568 | ||||||||
\(737\) | 3.33822e35 | 0.478819 | ||||||||
\(738\) | −1.71956e35 | −0.242500 | ||||||||
\(739\) | −7.59548e35 | −1.05317 | −0.526587 | − | 0.850121i | \(-0.676528\pi\) | ||||
−0.526587 | + | 0.850121i | \(0.676528\pi\) | |||||||
\(740\) | 1.90333e35 | 0.259488 | ||||||||
\(741\) | 3.77804e34 | 0.0506453 | ||||||||
\(742\) | −9.25428e33 | −0.0121982 | ||||||||
\(743\) | −2.06273e35 | −0.267352 | −0.133676 | − | 0.991025i | \(-0.542678\pi\) | ||||
−0.133676 | + | 0.991025i | \(0.542678\pi\) | |||||||
\(744\) | −1.54484e34 | −0.0196890 | ||||||||
\(745\) | −3.68271e35 | −0.461545 | ||||||||
\(746\) | −8.95193e35 | −1.10327 | ||||||||
\(747\) | 5.24691e35 | 0.635911 | ||||||||
\(748\) | 2.30807e35 | 0.275092 | ||||||||
\(749\) | 2.37073e34 | 0.0277881 | ||||||||
\(750\) | −4.18370e34 | −0.0482276 | ||||||||
\(751\) | −7.61805e34 | −0.0863664 | −0.0431832 | − | 0.999067i | \(-0.513750\pi\) | ||||
−0.0431832 | + | 0.999067i | \(0.513750\pi\) | |||||||
\(752\) | −2.19189e35 | −0.244397 | ||||||||
\(753\) | 1.04595e36 | 1.14703 | ||||||||
\(754\) | 1.46494e34 | 0.0158008 | ||||||||
\(755\) | −4.15241e34 | −0.0440517 | ||||||||
\(756\) | −1.00519e34 | −0.0104888 | ||||||||
\(757\) | 1.93605e36 | 1.98709 | 0.993546 | − | 0.113428i | \(-0.0361831\pi\) | ||||
0.993546 | + | 0.113428i | \(0.0361831\pi\) | |||||||
\(758\) | 6.09530e35 | 0.615362 | ||||||||
\(759\) | 1.33056e35 | 0.132134 | ||||||||
\(760\) | 2.22147e35 | 0.217005 | ||||||||
\(761\) | 1.19339e36 | 1.14677 | 0.573383 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573383 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(762\) | −7.19527e35 | −0.680158 | ||||||||
\(763\) | −2.98642e34 | −0.0277711 | ||||||||
\(764\) | −4.25364e35 | −0.389129 | ||||||||
\(765\) | 1.78019e35 | 0.160213 | ||||||||
\(766\) | 8.57374e35 | 0.759121 | ||||||||
\(767\) | 8.27761e33 | 0.00721046 | ||||||||
\(768\) | −5.56110e34 | −0.0476590 | ||||||||
\(769\) | −9.68810e35 | −0.816882 | −0.408441 | − | 0.912785i | \(-0.633927\pi\) | ||||
−0.408441 | + | 0.912785i | \(0.633927\pi\) | |||||||
\(770\) | −4.75156e33 | −0.00394187 | ||||||||
\(771\) | 5.11899e35 | 0.417835 | ||||||||
\(772\) | 7.82616e34 | 0.0628540 | ||||||||
\(773\) | −8.25175e35 | −0.652082 | −0.326041 | − | 0.945356i | \(-0.605715\pi\) | ||||
−0.326041 | + | 0.945356i | \(0.605715\pi\) | |||||||
\(774\) | −1.95410e35 | −0.151945 | ||||||||
\(775\) | −1.90899e34 | −0.0146060 | ||||||||
\(776\) | 3.14015e35 | 0.236417 | ||||||||
\(777\) | −2.31641e34 | −0.0171614 | ||||||||
\(778\) | 1.14248e36 | 0.832923 | ||||||||
\(779\) | −1.56756e36 | −1.12462 | ||||||||
\(780\) | −1.16871e34 | −0.00825133 | ||||||||
\(781\) | 7.81861e35 | 0.543240 | ||||||||
\(782\) | 2.38633e35 | 0.163172 | ||||||||
\(783\) | 7.42239e35 | 0.499484 | ||||||||
\(784\) | −3.77335e35 | −0.249906 | ||||||||
\(785\) | −8.03706e35 | −0.523873 | ||||||||
\(786\) | −9.85801e35 | −0.632423 | ||||||||
\(787\) | 8.02076e35 | 0.506444 | 0.253222 | − | 0.967408i | \(-0.418510\pi\) | ||||
0.253222 | + | 0.967408i | \(0.418510\pi\) | |||||||
\(788\) | −1.92561e35 | −0.119672 | ||||||||
\(789\) | 4.12975e35 | 0.252616 | ||||||||
\(790\) | 2.51396e35 | 0.151363 | ||||||||
\(791\) | −5.40562e34 | −0.0320361 | ||||||||
\(792\) | 1.63038e35 | 0.0951097 | ||||||||
\(793\) | −1.28473e35 | −0.0737729 | ||||||||
\(794\) | −1.73246e36 | −0.979279 | ||||||||
\(795\) | −5.45160e35 | −0.303343 | ||||||||
\(796\) | 1.71471e36 | 0.939243 | ||||||||
\(797\) | 8.65699e35 | 0.466807 | 0.233404 | − | 0.972380i | \(-0.425014\pi\) | ||||
0.233404 | + | 0.972380i | \(0.425014\pi\) | |||||||
\(798\) | −2.70359e34 | −0.0143518 | ||||||||
\(799\) | −1.60122e36 | −0.836789 | ||||||||
\(800\) | −6.87195e34 | −0.0353553 | ||||||||
\(801\) | 6.01984e35 | 0.304915 | ||||||||
\(802\) | 1.06246e36 | 0.529824 | ||||||||
\(803\) | −7.20038e35 | −0.353518 | ||||||||
\(804\) | −5.87570e35 | −0.284027 | ||||||||
\(805\) | −4.91268e33 | −0.00233814 | ||||||||
\(806\) | −5.33273e33 | −0.00249897 | ||||||||
\(807\) | −8.59226e35 | −0.396450 | ||||||||
\(808\) | 9.24101e35 | 0.419834 | ||||||||
\(809\) | −3.72457e36 | −1.66617 | −0.833086 | − | 0.553144i | \(-0.813428\pi\) | ||||
−0.833086 | + | 0.553144i | \(0.813428\pi\) | |||||||
\(810\) | −2.91689e35 | −0.128487 | ||||||||
\(811\) | 6.42225e35 | 0.278565 | 0.139282 | − | 0.990253i | \(-0.455520\pi\) | ||||
0.139282 | + | 0.990253i | \(0.455520\pi\) | |||||||
\(812\) | −1.04832e34 | −0.00447758 | ||||||||
\(813\) | 1.07817e36 | 0.453476 | ||||||||
\(814\) | 1.27342e36 | 0.527431 | ||||||||
\(815\) | −1.23875e35 | −0.0505258 | ||||||||
\(816\) | −4.06249e35 | −0.163180 | ||||||||
\(817\) | −1.78137e36 | −0.704657 | ||||||||
\(818\) | −2.99560e36 | −1.16699 | ||||||||
\(819\) | −1.02376e33 | −0.000392781 0 | ||||||||
\(820\) | 4.84913e35 | 0.183227 | ||||||||
\(821\) | −2.68244e36 | −0.998254 | −0.499127 | − | 0.866529i | \(-0.666346\pi\) | ||||
−0.499127 | + | 0.866529i | \(0.666346\pi\) | |||||||
\(822\) | 4.15258e35 | 0.152202 | ||||||||
\(823\) | −8.11664e35 | −0.293007 | −0.146504 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146504 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(824\) | 9.99476e35 | 0.355371 | ||||||||
\(825\) | −2.79909e35 | −0.0980264 | ||||||||
\(826\) | −5.92351e33 | −0.00204328 | ||||||||
\(827\) | −1.42939e36 | −0.485661 | −0.242830 | − | 0.970069i | \(-0.578076\pi\) | ||||
−0.242830 | + | 0.970069i | \(0.578076\pi\) | |||||||
\(828\) | 1.68567e35 | 0.0564147 | ||||||||
\(829\) | −1.47702e36 | −0.486915 | −0.243458 | − | 0.969912i | \(-0.578282\pi\) | ||||
−0.243458 | + | 0.969912i | \(0.578282\pi\) | |||||||
\(830\) | −1.47962e36 | −0.480478 | ||||||||
\(831\) | 3.03668e35 | 0.0971374 | ||||||||
\(832\) | −1.91966e34 | −0.00604900 | ||||||||
\(833\) | −2.75651e36 | −0.855652 | ||||||||
\(834\) | 1.41825e36 | 0.433687 | ||||||||
\(835\) | 2.06274e35 | 0.0621388 | ||||||||
\(836\) | 1.48626e36 | 0.441080 | ||||||||
\(837\) | −2.70193e35 | −0.0789960 | ||||||||
\(838\) | 2.55989e36 | 0.737344 | ||||||||
\(839\) | 3.59874e36 | 1.02124 | 0.510618 | − | 0.859808i | \(-0.329417\pi\) | ||||
0.510618 | + | 0.859808i | \(0.329417\pi\) | |||||||
\(840\) | 8.36336e33 | 0.00233824 | ||||||||
\(841\) | −2.85628e36 | −0.786775 | ||||||||
\(842\) | 1.02878e36 | 0.279204 | ||||||||
\(843\) | 2.55261e36 | 0.682559 | ||||||||
\(844\) | 2.43306e36 | 0.641020 | ||||||||
\(845\) | 1.71872e36 | 0.446166 | ||||||||
\(846\) | −1.13108e36 | −0.289310 | ||||||||
\(847\) | 4.51578e34 | 0.0113813 | ||||||||
\(848\) | −8.95452e35 | −0.222379 | ||||||||
\(849\) | 5.88823e36 | 1.44092 | ||||||||
\(850\) | −5.02010e35 | −0.121053 | ||||||||
\(851\) | 1.31660e36 | 0.312848 | ||||||||
\(852\) | −1.37618e36 | −0.322240 | ||||||||
\(853\) | 2.51059e36 | 0.579312 | 0.289656 | − | 0.957131i | \(-0.406459\pi\) | ||||
0.289656 | + | 0.957131i | \(0.406459\pi\) | |||||||
\(854\) | 9.19361e34 | 0.0209056 | ||||||||
\(855\) | 1.14634e36 | 0.256884 | ||||||||
\(856\) | 2.29394e36 | 0.506594 | ||||||||
\(857\) | −1.62785e36 | −0.354286 | −0.177143 | − | 0.984185i | \(-0.556686\pi\) | ||||
−0.177143 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(858\) | −7.81921e34 | −0.0167715 | ||||||||
\(859\) | 1.44920e36 | 0.306348 | 0.153174 | − | 0.988199i | \(-0.451051\pi\) | ||||
0.153174 | + | 0.988199i | \(0.451051\pi\) | |||||||
\(860\) | 5.51054e35 | 0.114806 | ||||||||
\(861\) | −5.90153e34 | −0.0121178 | ||||||||
\(862\) | 6.36440e36 | 1.28800 | ||||||||
\(863\) | 5.15478e36 | 1.02819 | 0.514097 | − | 0.857732i | \(-0.328127\pi\) | ||||
0.514097 | + | 0.857732i | \(0.328127\pi\) | |||||||
\(864\) | −9.72634e35 | −0.191217 | ||||||||
\(865\) | 1.84195e36 | 0.356924 | ||||||||
\(866\) | −4.43796e36 | −0.847637 | ||||||||
\(867\) | 1.08272e36 | 0.203835 | ||||||||
\(868\) | 3.81614e33 | 0.000708154 0 | ||||||||
\(869\) | 1.68196e36 | 0.307657 | ||||||||
\(870\) | −6.17554e35 | −0.111348 | ||||||||
\(871\) | −2.02826e35 | −0.0360494 | ||||||||
\(872\) | −2.88968e36 | −0.506284 | ||||||||
\(873\) | 1.62041e36 | 0.279864 | ||||||||
\(874\) | 1.53666e36 | 0.261629 | ||||||||
\(875\) | 1.03348e34 | 0.00173460 | ||||||||
\(876\) | 1.26736e36 | 0.209700 | ||||||||
\(877\) | −1.01431e37 | −1.65453 | −0.827266 | − | 0.561810i | \(-0.810105\pi\) | ||||
−0.827266 | + | 0.561810i | \(0.810105\pi\) | |||||||
\(878\) | −6.81602e36 | −1.09610 | ||||||||
\(879\) | 6.11132e36 | 0.968890 | ||||||||
\(880\) | −4.59765e35 | −0.0718626 | ||||||||
\(881\) | −3.63479e36 | −0.560120 | −0.280060 | − | 0.959983i | \(-0.590354\pi\) | ||||
−0.280060 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(882\) | −1.94716e36 | −0.295831 | ||||||||
\(883\) | 4.65240e36 | 0.696896 | 0.348448 | − | 0.937328i | \(-0.386709\pi\) | ||||
0.348448 | + | 0.937328i | \(0.386709\pi\) | |||||||
\(884\) | −1.40235e35 | −0.0207111 | ||||||||
\(885\) | −3.48947e35 | −0.0508123 | ||||||||
\(886\) | −1.54589e36 | −0.221952 | ||||||||
\(887\) | 9.05035e35 | 0.128121 | 0.0640604 | − | 0.997946i | \(-0.479595\pi\) | ||||
0.0640604 | + | 0.997946i | \(0.479595\pi\) | |||||||
\(888\) | −2.24138e36 | −0.312862 | ||||||||
\(889\) | 1.77741e35 | 0.0244633 | ||||||||
\(890\) | −1.69758e36 | −0.230386 | ||||||||
\(891\) | −1.95154e36 | −0.261159 | ||||||||
\(892\) | −5.47034e36 | −0.721861 | ||||||||
\(893\) | −1.03110e37 | −1.34170 | ||||||||
\(894\) | 4.33679e36 | 0.556480 | ||||||||
\(895\) | 1.33397e36 | 0.168795 | ||||||||
\(896\) | 1.37373e34 | 0.00171415 | ||||||||
\(897\) | −8.08434e34 | −0.00994808 | ||||||||
\(898\) | −8.84413e36 | −1.07325 | ||||||||
\(899\) | −2.81785e35 | −0.0337227 | ||||||||
\(900\) | −3.54612e35 | −0.0418526 | ||||||||
\(901\) | −6.54146e36 | −0.761403 | ||||||||
\(902\) | 3.24429e36 | 0.372424 | ||||||||
\(903\) | −6.70648e34 | −0.00759273 | ||||||||
\(904\) | −5.23052e36 | −0.584036 | ||||||||
\(905\) | 6.69799e36 | 0.737628 | ||||||||
\(906\) | 4.88991e35 | 0.0531127 | ||||||||
\(907\) | −3.58423e36 | −0.383977 | −0.191988 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191988 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(908\) | −7.13385e36 | −0.753791 | ||||||||
\(909\) | 4.76862e36 | 0.496986 | ||||||||
\(910\) | 2.88699e33 | 0.000296776 0 | ||||||||
\(911\) | 5.15388e36 | 0.522582 | 0.261291 | − | 0.965260i | \(-0.415852\pi\) | ||||
0.261291 | + | 0.965260i | \(0.415852\pi\) | |||||||
\(912\) | −2.61602e36 | −0.261641 | ||||||||
\(913\) | −9.89934e36 | −0.976611 | ||||||||
\(914\) | −3.54356e34 | −0.00344836 | ||||||||
\(915\) | 5.41585e36 | 0.519880 | ||||||||
\(916\) | 9.16200e36 | 0.867555 | ||||||||
\(917\) | 2.43517e35 | 0.0227464 | ||||||||
\(918\) | −7.10528e36 | −0.654708 | ||||||||
\(919\) | 1.45442e36 | 0.132205 | 0.0661023 | − | 0.997813i | \(-0.478944\pi\) | ||||
0.0661023 | + | 0.997813i | \(0.478944\pi\) | |||||||
\(920\) | −4.75355e35 | −0.0426256 | ||||||||
\(921\) | −2.27655e36 | −0.201387 | ||||||||
\(922\) | 1.29086e37 | 1.12653 | ||||||||
\(923\) | −4.75049e35 | −0.0408994 | ||||||||
\(924\) | 5.59548e34 | 0.00475267 | ||||||||
\(925\) | −2.76971e36 | −0.232093 | ||||||||
\(926\) | 1.20307e37 | 0.994614 | ||||||||
\(927\) | 5.15758e36 | 0.420678 | ||||||||
\(928\) | −1.01436e36 | −0.0816289 | ||||||||
\(929\) | 1.48492e37 | 1.17898 | 0.589491 | − | 0.807775i | \(-0.299328\pi\) | ||||
0.589491 | + | 0.807775i | \(0.299328\pi\) | |||||||
\(930\) | 2.24804e35 | 0.0176103 | ||||||||
\(931\) | −1.77504e37 | −1.37194 | ||||||||
\(932\) | −4.20444e36 | −0.320634 | ||||||||
\(933\) | 8.73845e35 | 0.0657528 | ||||||||
\(934\) | 9.34208e36 | 0.693598 | ||||||||
\(935\) | −3.35868e36 | −0.246050 | ||||||||
\(936\) | −9.90602e34 | −0.00716063 | ||||||||
\(937\) | 4.13990e36 | 0.295288 | 0.147644 | − | 0.989041i | \(-0.452831\pi\) | ||||
0.147644 | + | 0.989041i | \(0.452831\pi\) | |||||||
\(938\) | 1.45144e35 | 0.0102156 | ||||||||
\(939\) | −1.63840e37 | −1.13789 | ||||||||
\(940\) | 3.18962e36 | 0.218595 | ||||||||
\(941\) | 3.04574e36 | 0.205979 | 0.102989 | − | 0.994682i | \(-0.467159\pi\) | ||||
0.102989 | + | 0.994682i | \(0.467159\pi\) | |||||||
\(942\) | 9.46450e36 | 0.631628 | ||||||||
\(943\) | 3.35430e36 | 0.220905 | ||||||||
\(944\) | −5.73164e35 | −0.0372502 | ||||||||
\(945\) | 1.46275e35 | 0.00938150 | ||||||||
\(946\) | 3.68680e36 | 0.233352 | ||||||||
\(947\) | 1.93836e37 | 1.21076 | 0.605382 | − | 0.795935i | \(-0.293020\pi\) | ||||
0.605382 | + | 0.795935i | \(0.293020\pi\) | |||||||
\(948\) | −2.96046e36 | −0.182497 | ||||||||
\(949\) | 4.37487e35 | 0.0266157 | ||||||||
\(950\) | −3.23266e36 | −0.194095 | ||||||||
\(951\) | −1.48417e37 | −0.879480 | ||||||||
\(952\) | 1.00353e35 | 0.00586908 | ||||||||
\(953\) | −7.72509e35 | −0.0445905 | −0.0222952 | − | 0.999751i | \(-0.507097\pi\) | ||||
−0.0222952 | + | 0.999751i | \(0.507097\pi\) | |||||||
\(954\) | −4.62079e36 | −0.263246 | ||||||||
\(955\) | 6.18986e36 | 0.348048 | ||||||||
\(956\) | 1.11546e37 | 0.619055 | ||||||||
\(957\) | −4.13172e36 | −0.226325 | ||||||||
\(958\) | 3.26522e36 | 0.176540 | ||||||||
\(959\) | −1.02579e35 | −0.00547425 | ||||||||
\(960\) | 8.09246e35 | 0.0426275 | ||||||||
\(961\) | −1.91302e37 | −0.994667 | ||||||||
\(962\) | −7.73713e35 | −0.0397092 | ||||||||
\(963\) | 1.18374e37 | 0.599690 | ||||||||
\(964\) | 4.65659e36 | 0.232866 | ||||||||
\(965\) | −1.13886e36 | −0.0562183 | ||||||||
\(966\) | 5.78521e34 | 0.00281907 | ||||||||
\(967\) | −6.95372e36 | −0.334492 | −0.167246 | − | 0.985915i | \(-0.553487\pi\) | ||||
−0.167246 | + | 0.985915i | \(0.553487\pi\) | |||||||
\(968\) | 4.36951e36 | 0.207487 | ||||||||
\(969\) | −1.91105e37 | −0.895830 | ||||||||
\(970\) | −4.56953e36 | −0.211458 | ||||||||
\(971\) | 2.67539e37 | 1.22221 | 0.611106 | − | 0.791549i | \(-0.290725\pi\) | ||||
0.611106 | + | 0.791549i | \(0.290725\pi\) | |||||||
\(972\) | −8.55729e36 | −0.385930 | ||||||||
\(973\) | −3.50341e35 | −0.0155984 | ||||||||
\(974\) | 3.00038e36 | 0.131883 | ||||||||
\(975\) | 1.70070e35 | 0.00738021 | ||||||||
\(976\) | 8.89581e36 | 0.381121 | ||||||||
\(977\) | 2.82491e37 | 1.19488 | 0.597438 | − | 0.801915i | \(-0.296185\pi\) | ||||
0.597438 | + | 0.801915i | \(0.296185\pi\) | |||||||
\(978\) | 1.45876e36 | 0.0609184 | ||||||||
\(979\) | −1.13576e37 | −0.468278 | ||||||||
\(980\) | 5.49095e36 | 0.223523 | ||||||||
\(981\) | −1.49116e37 | −0.599323 | ||||||||
\(982\) | 9.65226e36 | 0.383032 | ||||||||
\(983\) | 3.52532e37 | 1.38127 | 0.690636 | − | 0.723203i | \(-0.257331\pi\) | ||||
0.690636 | + | 0.723203i | \(0.257331\pi\) | |||||||
\(984\) | −5.71037e36 | −0.220915 | ||||||||
\(985\) | 2.80213e36 | 0.107037 | ||||||||
\(986\) | −7.41013e36 | −0.279489 | ||||||||
\(987\) | −3.88186e35 | −0.0144569 | ||||||||
\(988\) | −9.03037e35 | −0.0332081 | ||||||||
\(989\) | 3.81182e36 | 0.138413 | ||||||||
\(990\) | −2.37252e36 | −0.0850687 | ||||||||
\(991\) | −1.01549e36 | −0.0359547 | −0.0179774 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179774 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(992\) | 3.69253e35 | 0.0129100 | ||||||||
\(993\) | 3.05588e37 | 1.05505 | ||||||||
\(994\) | 3.39948e35 | 0.0115900 | ||||||||
\(995\) | −2.49523e37 | −0.840084 | ||||||||
\(996\) | 1.74241e37 | 0.579308 | ||||||||
\(997\) | −5.04007e37 | −1.65481 | −0.827403 | − | 0.561608i | \(-0.810183\pi\) | ||||
−0.827403 | + | 0.561608i | \(0.810183\pi\) | |||||||
\(998\) | −4.57509e36 | −0.148343 | ||||||||
\(999\) | −3.92016e37 | −1.25526 |
(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 | 10.26.a.c.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.26.b.c.49.2 | 4 | |||
5.3 | odd | 4 | 50.26.b.c.49.3 | 4 | |||
5.4 | even | 2 | 50.26.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.26.a.e.1.2 | 2 | 5.4 | even | 2 | |||
50.26.b.c.49.2 | 4 | 5.2 | odd | 4 | |||
50.26.b.c.49.3 | 4 | 5.3 | odd | 4 |