Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(172.457072203\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26286285043 x^{14} + \cdots + 16\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | multiple of \( 2^{85}\cdot 3^{26}\cdot 5^{66}\cdot 7^{4}\cdot 11^{8} \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(78034.2\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 156068. | 1.68392 | 0.841958 | − | 0.539544i | \(-0.181403\pi\) | ||||
0.841958 | + | 0.539544i | \(0.181403\pi\) | |||||||
\(3\) | −6.96239e7 | −0.933808 | −0.466904 | − | 0.884308i | \(-0.654631\pi\) | ||||
−0.466904 | + | 0.884308i | \(0.654631\pi\) | |||||||
\(4\) | 1.57674e10 | 1.83557 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.08661e13 | −1.57245 | ||||||||
\(7\) | −1.55193e14 | −1.76504 | −0.882520 | − | 0.470275i | \(-0.844155\pi\) | ||||
−0.882520 | + | 0.470275i | \(0.844155\pi\) | |||||||
\(8\) | 1.12018e15 | 1.40703 | ||||||||
\(9\) | −7.11573e14 | −0.128002 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.13199e16 | 0.271132 | 0.135566 | − | 0.990768i | \(-0.456715\pi\) | ||||
0.135566 | + | 0.990768i | \(0.456715\pi\) | |||||||
\(12\) | −1.09779e18 | −1.71407 | ||||||||
\(13\) | −2.38246e18 | −0.993025 | −0.496513 | − | 0.868029i | \(-0.665386\pi\) | ||||
−0.496513 | + | 0.868029i | \(0.665386\pi\) | |||||||
\(14\) | −2.42207e19 | −2.97218 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.93836e19 | 0.533747 | ||||||||
\(17\) | −2.91772e20 | −1.45424 | −0.727120 | − | 0.686511i | \(-0.759142\pi\) | ||||
−0.727120 | + | 0.686511i | \(0.759142\pi\) | |||||||
\(18\) | −1.11054e20 | −0.215545 | ||||||||
\(19\) | −3.61361e20 | −0.287414 | −0.143707 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143707 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.08051e22 | 1.64821 | ||||||||
\(22\) | 6.44874e21 | 0.456563 | ||||||||
\(23\) | 3.81748e22 | 1.29798 | 0.648989 | − | 0.760798i | \(-0.275192\pi\) | ||||
0.648989 | + | 0.760798i | \(0.275192\pi\) | |||||||
\(24\) | −7.79913e22 | −1.31390 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.71827e23 | −1.67217 | ||||||||
\(27\) | 4.36586e23 | 1.05334 | ||||||||
\(28\) | −2.44699e24 | −3.23985 | ||||||||
\(29\) | 1.65188e24 | 1.22577 | 0.612887 | − | 0.790170i | \(-0.290008\pi\) | ||||
0.612887 | + | 0.790170i | \(0.290008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76253e24 | −0.682086 | −0.341043 | − | 0.940048i | \(-0.610780\pi\) | ||||
−0.341043 | + | 0.940048i | \(0.610780\pi\) | |||||||
\(32\) | −3.47573e24 | −0.508244 | ||||||||
\(33\) | −2.87685e24 | −0.253185 | ||||||||
\(34\) | −4.55364e25 | −2.44882 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.12197e25 | −0.234957 | ||||||||
\(37\) | −8.70723e24 | −0.116025 | −0.0580125 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580125 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(38\) | −5.63971e25 | −0.483980 | ||||||||
\(39\) | 1.65876e26 | 0.927295 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.69048e26 | 0.659015 | 0.329508 | − | 0.944153i | \(-0.393117\pi\) | ||||
0.329508 | + | 0.944153i | \(0.393117\pi\) | |||||||
\(42\) | 1.68634e27 | 2.77544 | ||||||||
\(43\) | −1.33984e26 | −0.149563 | −0.0747815 | − | 0.997200i | \(-0.523826\pi\) | ||||
−0.0747815 | + | 0.997200i | \(0.523826\pi\) | |||||||
\(44\) | 6.51509e26 | 0.497681 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.95788e27 | 2.18568 | ||||||||
\(47\) | −2.88434e27 | −0.742047 | −0.371024 | − | 0.928623i | \(-0.620993\pi\) | ||||
−0.371024 | + | 0.928623i | \(0.620993\pi\) | |||||||
\(48\) | −2.74204e27 | −0.498418 | ||||||||
\(49\) | 1.63539e28 | 2.11537 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.03143e28 | 1.35798 | ||||||||
\(52\) | −3.75653e28 | −1.82277 | ||||||||
\(53\) | −2.92563e28 | −1.03673 | −0.518367 | − | 0.855158i | \(-0.673460\pi\) | ||||
−0.518367 | + | 0.855158i | \(0.673460\pi\) | |||||||
\(54\) | 6.81373e28 | 1.77373 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73844e29 | −2.48346 | ||||||||
\(57\) | 2.51594e28 | 0.268389 | ||||||||
\(58\) | 2.57806e29 | 2.06410 | ||||||||
\(59\) | 1.51134e29 | 0.912650 | 0.456325 | − | 0.889813i | \(-0.349166\pi\) | ||||
0.456325 | + | 0.889813i | \(0.349166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.88604e29 | 1.00545 | 0.502725 | − | 0.864446i | \(-0.332331\pi\) | ||||
0.502725 | + | 0.864446i | \(0.332331\pi\) | |||||||
\(62\) | −4.31144e29 | −1.14857 | ||||||||
\(63\) | 1.10431e29 | 0.225929 | ||||||||
\(64\) | −8.80755e29 | −1.38959 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.48986e29 | −0.426342 | ||||||||
\(67\) | −8.72314e29 | −0.646307 | −0.323153 | − | 0.946347i | \(-0.604743\pi\) | ||||
−0.323153 | + | 0.946347i | \(0.604743\pi\) | |||||||
\(68\) | −4.60049e30 | −2.66936 | ||||||||
\(69\) | −2.65788e30 | −1.21206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.08526e30 | 0.878069 | 0.439034 | − | 0.898470i | \(-0.355321\pi\) | ||||
0.439034 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(72\) | −7.97090e29 | −0.180103 | ||||||||
\(73\) | 2.41300e30 | 0.434240 | 0.217120 | − | 0.976145i | \(-0.430334\pi\) | ||||
0.217120 | + | 0.976145i | \(0.430334\pi\) | |||||||
\(74\) | −1.35892e30 | −0.195376 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.69774e30 | −0.527568 | ||||||||
\(77\) | −6.41256e30 | −0.478558 | ||||||||
\(78\) | 2.58880e31 | 1.56149 | ||||||||
\(79\) | −3.21352e31 | −1.57085 | −0.785423 | − | 0.618960i | \(-0.787554\pi\) | ||||
−0.785423 | + | 0.618960i | \(0.787554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.64411e31 | −0.855613 | ||||||||
\(82\) | 4.19898e31 | 1.10973 | ||||||||
\(83\) | 7.79056e31 | 1.68570 | 0.842850 | − | 0.538148i | \(-0.180876\pi\) | ||||
0.842850 | + | 0.538148i | \(0.180876\pi\) | |||||||
\(84\) | 1.70369e32 | 3.02540 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.09107e31 | −0.251851 | ||||||||
\(87\) | −1.15010e32 | −1.14464 | ||||||||
\(88\) | 4.62857e31 | 0.381490 | ||||||||
\(89\) | 1.41115e32 | 0.965245 | 0.482623 | − | 0.875828i | \(-0.339684\pi\) | ||||
0.482623 | + | 0.875828i | \(0.339684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.69741e32 | 1.75273 | ||||||||
\(92\) | 6.01918e32 | 2.38253 | ||||||||
\(93\) | 1.92338e32 | 0.636937 | ||||||||
\(94\) | −4.50154e32 | −1.24954 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.41994e32 | 0.474602 | ||||||||
\(97\) | 7.13656e32 | 1.17966 | 0.589828 | − | 0.807529i | \(-0.299196\pi\) | ||||
0.589828 | + | 0.807529i | \(0.299196\pi\) | |||||||
\(98\) | 2.55232e33 | 3.56210 | ||||||||
\(99\) | −2.94021e31 | −0.0347055 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.02530e32 | −0.765877 | −0.382939 | − | 0.923774i | \(-0.625088\pi\) | ||||
−0.382939 | + | 0.923774i | \(0.625088\pi\) | |||||||
\(102\) | 3.17042e33 | 2.28672 | ||||||||
\(103\) | 6.15871e32 | 0.378160 | 0.189080 | − | 0.981962i | \(-0.439449\pi\) | ||||
0.189080 | + | 0.981962i | \(0.439449\pi\) | |||||||
\(104\) | −2.66878e33 | −1.39722 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.56598e33 | −1.74577 | ||||||||
\(107\) | −4.51029e33 | −1.47697 | −0.738485 | − | 0.674270i | \(-0.764459\pi\) | ||||
−0.738485 | + | 0.674270i | \(0.764459\pi\) | |||||||
\(108\) | 6.88384e33 | 1.93348 | ||||||||
\(109\) | −1.07835e33 | −0.260149 | −0.130074 | − | 0.991504i | \(-0.541522\pi\) | ||||
−0.130074 | + | 0.991504i | \(0.541522\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.06231e32 | 0.108345 | ||||||||
\(112\) | −6.11206e33 | −0.942085 | ||||||||
\(113\) | 2.37121e31 | 0.00315629 | 0.00157814 | − | 0.999999i | \(-0.499498\pi\) | ||||
0.00157814 | + | 0.999999i | \(0.499498\pi\) | |||||||
\(114\) | 3.92659e33 | 0.451944 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.60458e34 | 2.24999 | ||||||||
\(117\) | 1.69529e33 | 0.127110 | ||||||||
\(118\) | 2.35873e34 | 1.53682 | ||||||||
\(119\) | 4.52809e34 | 2.56679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.15178e34 | −0.926488 | ||||||||
\(122\) | 4.50420e34 | 1.69309 | ||||||||
\(123\) | −1.87321e34 | −0.615394 | ||||||||
\(124\) | −4.35580e34 | −1.25202 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.72348e34 | 0.380446 | ||||||||
\(127\) | −6.78580e34 | −1.31474 | −0.657370 | − | 0.753568i | \(-0.728331\pi\) | ||||
−0.657370 | + | 0.753568i | \(0.728331\pi\) | |||||||
\(128\) | −1.07602e35 | −1.83170 | ||||||||
\(129\) | 9.32850e33 | 0.139663 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.18678e34 | 0.834753 | 0.417377 | − | 0.908734i | \(-0.362950\pi\) | ||||
0.417377 | + | 0.908734i | \(0.362950\pi\) | |||||||
\(132\) | −4.53606e34 | −0.464739 | ||||||||
\(133\) | 5.60808e34 | 0.507296 | ||||||||
\(134\) | −1.36141e35 | −1.08833 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.26837e35 | −2.04616 | ||||||||
\(137\) | −1.24185e34 | −0.0688940 | −0.0344470 | − | 0.999407i | \(-0.510967\pi\) | ||||
−0.0344470 | + | 0.999407i | \(0.510967\pi\) | |||||||
\(138\) | −4.14811e35 | −2.04101 | ||||||||
\(139\) | 3.36802e34 | 0.147106 | 0.0735531 | − | 0.997291i | \(-0.476566\pi\) | ||||
0.0735531 | + | 0.997291i | \(0.476566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00819e35 | 0.692930 | ||||||||
\(142\) | 4.81511e35 | 1.47859 | ||||||||
\(143\) | −9.84431e34 | −0.269241 | ||||||||
\(144\) | −2.80243e34 | −0.0683210 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.76593e35 | 0.731223 | ||||||||
\(147\) | −1.13862e36 | −1.97535 | ||||||||
\(148\) | −1.37291e35 | −0.212972 | ||||||||
\(149\) | 7.60967e35 | 1.05631 | 0.528156 | − | 0.849147i | \(-0.322884\pi\) | ||||
0.528156 | + | 0.849147i | \(0.322884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.06240e35 | 0.341147 | 0.170574 | − | 0.985345i | \(-0.445438\pi\) | ||||
0.170574 | + | 0.985345i | \(0.445438\pi\) | |||||||
\(152\) | −4.04790e35 | −0.404399 | ||||||||
\(153\) | 2.07617e35 | 0.186146 | ||||||||
\(154\) | −1.00080e36 | −0.805851 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.61544e36 | 1.70212 | ||||||||
\(157\) | 2.10956e36 | 1.23551 | 0.617755 | − | 0.786370i | \(-0.288042\pi\) | ||||
0.617755 | + | 0.786370i | \(0.288042\pi\) | |||||||
\(158\) | −5.01528e36 | −2.64517 | ||||||||
\(159\) | 2.03694e36 | 0.968110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.92446e36 | −2.29098 | ||||||||
\(162\) | −4.12663e36 | −1.44078 | ||||||||
\(163\) | 2.09987e36 | 0.662365 | 0.331182 | − | 0.943567i | \(-0.392552\pi\) | ||||
0.331182 | + | 0.943567i | \(0.392552\pi\) | |||||||
\(164\) | 4.24219e36 | 1.20967 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.21586e37 | 2.83858 | ||||||||
\(167\) | 4.97146e36 | 1.05114 | 0.525572 | − | 0.850749i | \(-0.323851\pi\) | ||||
0.525572 | + | 0.850749i | \(0.323851\pi\) | |||||||
\(168\) | 1.21037e37 | 2.31908 | ||||||||
\(169\) | −8.00138e34 | −0.0139006 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.57135e35 | 0.0367896 | ||||||||
\(172\) | −2.11259e36 | −0.274533 | ||||||||
\(173\) | 1.51427e37 | 1.78831 | 0.894157 | − | 0.447753i | \(-0.147776\pi\) | ||||
0.894157 | + | 0.447753i | \(0.147776\pi\) | |||||||
\(174\) | −1.79494e37 | −1.92747 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.62733e36 | 0.144716 | ||||||||
\(177\) | −1.05225e37 | −0.852240 | ||||||||
\(178\) | 2.20236e37 | 1.62539 | ||||||||
\(179\) | 9.15862e36 | 0.616247 | 0.308124 | − | 0.951346i | \(-0.400299\pi\) | ||||
0.308124 | + | 0.951346i | \(0.400299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.09431e37 | 0.612975 | 0.306488 | − | 0.951875i | \(-0.400846\pi\) | ||||
0.306488 | + | 0.951875i | \(0.400846\pi\) | |||||||
\(182\) | 5.77049e37 | 2.95145 | ||||||||
\(183\) | −2.00938e37 | −0.938898 | ||||||||
\(184\) | 4.27626e37 | 1.82629 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.00179e37 | 1.07255 | ||||||||
\(187\) | −1.20560e37 | −0.394290 | ||||||||
\(188\) | −4.54786e37 | −1.36208 | ||||||||
\(189\) | −6.77551e37 | −1.85918 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.18522e37 | −0.504016 | −0.252008 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252008 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(192\) | 6.13216e37 | 1.29761 | ||||||||
\(193\) | 7.41572e37 | 1.44032 | 0.720158 | − | 0.693810i | \(-0.244069\pi\) | ||||
0.720158 | + | 0.693810i | \(0.244069\pi\) | |||||||
\(194\) | 1.11379e38 | 1.98644 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.57859e38 | 3.88290 | ||||||||
\(197\) | −9.94695e37 | −1.37720 | −0.688601 | − | 0.725141i | \(-0.741775\pi\) | ||||
−0.688601 | + | 0.725141i | \(0.741775\pi\) | |||||||
\(198\) | −4.58875e36 | −0.0584411 | ||||||||
\(199\) | 1.85341e37 | 0.217217 | 0.108609 | − | 0.994085i | \(-0.465360\pi\) | ||||
0.108609 | + | 0.994085i | \(0.465360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.07339e37 | 0.603526 | ||||||||
\(202\) | −1.40857e38 | −1.28967 | ||||||||
\(203\) | −2.56360e38 | −2.16354 | ||||||||
\(204\) | 3.20304e38 | 2.49267 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.61180e37 | 0.636789 | ||||||||
\(207\) | −2.71642e37 | −0.166144 | ||||||||
\(208\) | −9.38299e37 | −0.530025 | ||||||||
\(209\) | −1.49314e37 | −0.0779269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.61345e38 | −1.16561 | −0.582805 | − | 0.812612i | \(-0.698045\pi\) | ||||
−0.582805 | + | 0.812612i | \(0.698045\pi\) | |||||||
\(212\) | −4.61296e38 | −1.90300 | ||||||||
\(213\) | −2.14808e38 | −0.819948 | ||||||||
\(214\) | −7.03914e38 | −2.48709 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.89055e38 | 1.48208 | ||||||||
\(217\) | 4.28725e38 | 1.20391 | ||||||||
\(218\) | −1.68296e38 | −0.438068 | ||||||||
\(219\) | −1.68002e38 | −0.405496 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.95134e38 | 1.44410 | ||||||||
\(222\) | 9.46135e37 | 0.182444 | ||||||||
\(223\) | −2.67594e38 | −0.479122 | −0.239561 | − | 0.970881i | \(-0.577003\pi\) | ||||
−0.239561 | + | 0.970881i | \(0.577003\pi\) | |||||||
\(224\) | 5.39410e38 | 0.897070 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.70072e36 | 0.00531492 | ||||||||
\(227\) | −3.53241e38 | −0.471677 | −0.235838 | − | 0.971792i | \(-0.575784\pi\) | ||||
−0.235838 | + | 0.971792i | \(0.575784\pi\) | |||||||
\(228\) | 3.96699e38 | 0.492647 | ||||||||
\(229\) | 1.17673e39 | 1.35954 | 0.679769 | − | 0.733427i | \(-0.262080\pi\) | ||||
0.679769 | + | 0.733427i | \(0.262080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.46468e38 | 0.446881 | ||||||||
\(232\) | 1.85040e39 | 1.72470 | ||||||||
\(233\) | 1.12975e38 | 0.0980870 | 0.0490435 | − | 0.998797i | \(-0.484383\pi\) | ||||
0.0490435 | + | 0.998797i | \(0.484383\pi\) | |||||||
\(234\) | 2.64582e38 | 0.214042 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.38299e39 | 1.67523 | ||||||||
\(237\) | 2.23738e39 | 1.46687 | ||||||||
\(238\) | 7.06692e39 | 4.32226 | ||||||||
\(239\) | 9.43852e38 | 0.538690 | 0.269345 | − | 0.963044i | \(-0.413193\pi\) | ||||
0.269345 | + | 0.963044i | \(0.413193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.67029e38 | 0.381532 | 0.190766 | − | 0.981636i | \(-0.438903\pi\) | ||||
0.190766 | + | 0.981636i | \(0.438903\pi\) | |||||||
\(242\) | −3.35825e39 | −1.56013 | ||||||||
\(243\) | −5.86073e38 | −0.254359 | ||||||||
\(244\) | 4.55055e39 | 1.84558 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.92350e39 | −1.03627 | ||||||||
\(247\) | 8.60929e38 | 0.285409 | ||||||||
\(248\) | −3.09453e39 | −0.959714 | ||||||||
\(249\) | −5.42409e39 | −1.57412 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.55001e39 | −0.648524 | −0.324262 | − | 0.945967i | \(-0.605116\pi\) | ||||
−0.324262 | + | 0.945967i | \(0.605116\pi\) | |||||||
\(252\) | 1.74122e39 | 0.414709 | ||||||||
\(253\) | 1.57738e39 | 0.351923 | ||||||||
\(254\) | −1.05905e40 | −2.21391 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.22761e39 | −1.69484 | ||||||||
\(257\) | −7.67124e39 | −1.32120 | −0.660601 | − | 0.750737i | \(-0.729698\pi\) | ||||
−0.660601 | + | 0.750737i | \(0.729698\pi\) | |||||||
\(258\) | 1.45588e39 | 0.235181 | ||||||||
\(259\) | 1.35130e39 | 0.204789 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.17543e39 | −0.156902 | ||||||||
\(262\) | 1.12163e40 | 1.40565 | ||||||||
\(263\) | −1.76090e39 | −0.207236 | −0.103618 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103618 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(264\) | −3.22259e39 | −0.356238 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.75244e39 | 0.854244 | ||||||||
\(267\) | −9.82497e39 | −0.901354 | ||||||||
\(268\) | −1.37541e40 | −1.18634 | ||||||||
\(269\) | 1.37145e38 | 0.0111241 | 0.00556206 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556206 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.20503e40 | 0.864978 | 0.432489 | − | 0.901639i | \(-0.357635\pi\) | ||||
0.432489 | + | 0.901639i | \(0.357635\pi\) | |||||||
\(272\) | −1.14910e40 | −0.776197 | ||||||||
\(273\) | −2.57428e40 | −1.63671 | ||||||||
\(274\) | −1.93814e39 | −0.116012 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.19079e40 | −2.22483 | ||||||||
\(277\) | −1.15971e40 | −0.580005 | −0.290002 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290002 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(278\) | 5.25642e39 | 0.247714 | ||||||||
\(279\) | 1.96574e39 | 0.0873086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.63872e40 | −1.43646 | −0.718232 | − | 0.695804i | \(-0.755048\pi\) | ||||
−0.718232 | + | 0.695804i | \(0.755048\pi\) | |||||||
\(282\) | 3.13415e40 | 1.16684 | ||||||||
\(283\) | −1.87432e40 | −0.658213 | −0.329107 | − | 0.944293i | \(-0.606748\pi\) | ||||
−0.329107 | + | 0.944293i | \(0.606748\pi\) | |||||||
\(284\) | 4.86466e40 | 1.61176 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.53639e40 | −0.453378 | ||||||||
\(287\) | −4.17543e40 | −1.16319 | ||||||||
\(288\) | 2.47324e39 | 0.0650564 | ||||||||
\(289\) | 4.48762e40 | 1.11481 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.96875e40 | −1.10157 | ||||||||
\(292\) | 3.80467e40 | 0.797077 | ||||||||
\(293\) | −2.34908e40 | −0.465139 | −0.232569 | − | 0.972580i | \(-0.574713\pi\) | ||||
−0.232569 | + | 0.972580i | \(0.574713\pi\) | |||||||
\(294\) | −1.77703e41 | −3.32631 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.75366e39 | −0.163250 | ||||||||
\(297\) | 1.80397e40 | 0.285593 | ||||||||
\(298\) | 1.18763e41 | 1.77874 | ||||||||
\(299\) | −9.09499e40 | −1.28893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.07934e40 | 0.263985 | ||||||||
\(302\) | 4.77944e40 | 0.574463 | ||||||||
\(303\) | 6.28377e40 | 0.715182 | ||||||||
\(304\) | −1.42317e40 | −0.153406 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.24024e40 | 0.313454 | ||||||||
\(307\) | −2.12921e40 | −0.195180 | −0.0975901 | − | 0.995227i | \(-0.531113\pi\) | ||||
−0.0975901 | + | 0.995227i | \(0.531113\pi\) | |||||||
\(308\) | −1.01110e41 | −0.878427 | ||||||||
\(309\) | −4.28793e40 | −0.353129 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.65601e40 | 0.714910 | 0.357455 | − | 0.933930i | \(-0.383645\pi\) | ||||
0.357455 | + | 0.933930i | \(0.383645\pi\) | |||||||
\(312\) | 1.85811e41 | 1.30473 | ||||||||
\(313\) | −2.25901e40 | −0.150465 | −0.0752327 | − | 0.997166i | \(-0.523970\pi\) | ||||
−0.0752327 | + | 0.997166i | \(0.523970\pi\) | |||||||
\(314\) | 3.29235e41 | 2.08050 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.06689e41 | −2.88340 | ||||||||
\(317\) | −1.90392e40 | −0.102842 | −0.0514209 | − | 0.998677i | \(-0.516375\pi\) | ||||
−0.0514209 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(318\) | 3.17901e41 | 1.63021 | ||||||||
\(319\) | 6.82554e40 | 0.332346 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.14024e41 | 1.37921 | ||||||||
\(322\) | −9.24621e41 | −3.85782 | ||||||||
\(323\) | 1.05435e41 | 0.417968 | ||||||||
\(324\) | −4.16909e41 | −1.57054 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.27724e41 | 1.11537 | ||||||||
\(327\) | 7.50788e40 | 0.242929 | ||||||||
\(328\) | 3.01382e41 | 0.927253 | ||||||||
\(329\) | 4.47629e41 | 1.30974 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.34163e39 | 0.0220846 | 0.0110423 | − | 0.999939i | \(-0.496485\pi\) | ||||
0.0110423 | + | 0.999939i | \(0.496485\pi\) | |||||||
\(332\) | 1.22837e42 | 3.09422 | ||||||||
\(333\) | 6.19583e39 | 0.0148515 | ||||||||
\(334\) | 7.75889e41 | 1.77004 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.25546e41 | 0.879727 | ||||||||
\(337\) | 1.27475e41 | 0.250918 | 0.125459 | − | 0.992099i | \(-0.459960\pi\) | ||||
0.125459 | + | 0.992099i | \(0.459960\pi\) | |||||||
\(338\) | −1.24876e40 | −0.0234075 | ||||||||
\(339\) | −1.65093e39 | −0.00294737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14147e41 | −0.184935 | ||||||||
\(342\) | 4.01307e40 | 0.0619506 | ||||||||
\(343\) | −1.33821e42 | −1.96866 | ||||||||
\(344\) | −1.50086e41 | −0.210439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.36330e42 | 3.01137 | ||||||||
\(347\) | −2.90496e41 | −0.352943 | −0.176471 | − | 0.984306i | \(-0.556468\pi\) | ||||
−0.176471 | + | 0.984306i | \(0.556468\pi\) | |||||||
\(348\) | −1.81341e42 | −2.10106 | ||||||||
\(349\) | −1.05476e42 | −1.16556 | −0.582779 | − | 0.812631i | \(-0.698035\pi\) | ||||
−0.582779 | + | 0.812631i | \(0.698035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.04015e42 | −1.04599 | ||||||||
\(352\) | −1.43617e41 | −0.137801 | ||||||||
\(353\) | −1.42033e42 | −1.30049 | −0.650246 | − | 0.759724i | \(-0.725334\pi\) | ||||
−0.650246 | + | 0.759724i | \(0.725334\pi\) | |||||||
\(354\) | −1.64224e42 | −1.43510 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.22502e42 | 1.77177 | ||||||||
\(357\) | −3.15263e42 | −2.39689 | ||||||||
\(358\) | 1.42937e42 | 1.03771 | ||||||||
\(359\) | −3.15371e41 | −0.218657 | −0.109329 | − | 0.994006i | \(-0.534870\pi\) | ||||
−0.109329 | + | 0.994006i | \(0.534870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.45019e42 | −0.917393 | ||||||||
\(362\) | 1.70787e42 | 1.03220 | ||||||||
\(363\) | 1.49815e42 | 0.865162 | ||||||||
\(364\) | 5.82987e42 | 3.21726 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.13600e42 | −1.58102 | ||||||||
\(367\) | −3.83973e41 | −0.185059 | −0.0925297 | − | 0.995710i | \(-0.529495\pi\) | ||||
−0.0925297 | + | 0.995710i | \(0.529495\pi\) | |||||||
\(368\) | 1.50346e42 | 0.692792 | ||||||||
\(369\) | −1.91447e41 | −0.0843555 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.54037e42 | 1.82988 | ||||||||
\(372\) | 3.03268e42 | 1.16914 | ||||||||
\(373\) | 2.58713e42 | 0.954164 | 0.477082 | − | 0.878859i | \(-0.341695\pi\) | ||||
0.477082 | + | 0.878859i | \(0.341695\pi\) | |||||||
\(374\) | −1.88156e42 | −0.663951 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.23098e42 | −1.04408 | ||||||||
\(377\) | −3.93553e42 | −1.21723 | ||||||||
\(378\) | −1.05744e43 | −3.13071 | ||||||||
\(379\) | 1.90182e42 | 0.539042 | 0.269521 | − | 0.962994i | \(-0.413135\pi\) | ||||
0.269521 | + | 0.962994i | \(0.413135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.72454e42 | 1.22771 | ||||||||
\(382\) | −3.41044e42 | −0.848720 | ||||||||
\(383\) | 6.82259e42 | 1.62618 | 0.813092 | − | 0.582135i | \(-0.197783\pi\) | ||||
0.813092 | + | 0.582135i | \(0.197783\pi\) | |||||||
\(384\) | 7.49165e42 | 1.71046 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.15736e43 | 2.42537 | ||||||||
\(387\) | 9.53396e40 | 0.0191444 | ||||||||
\(388\) | 1.12525e43 | 2.16534 | ||||||||
\(389\) | −2.03241e42 | −0.374837 | −0.187419 | − | 0.982280i | \(-0.560012\pi\) | ||||
−0.187419 | + | 0.982280i | \(0.560012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11383e43 | −1.88757 | ||||||||
\(392\) | 1.83193e43 | 2.97638 | ||||||||
\(393\) | −5.00372e42 | −0.779499 | ||||||||
\(394\) | −1.55241e43 | −2.31909 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.63596e41 | −0.0637044 | ||||||||
\(397\) | −7.63461e42 | −1.00634 | −0.503168 | − | 0.864188i | \(-0.667832\pi\) | ||||
−0.503168 | + | 0.864188i | \(0.667832\pi\) | |||||||
\(398\) | 2.89258e42 | 0.365776 | ||||||||
\(399\) | −3.90456e42 | −0.473717 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.09608e43 | −1.22450 | −0.612250 | − | 0.790664i | \(-0.709736\pi\) | ||||
−0.612250 | + | 0.790664i | \(0.709736\pi\) | |||||||
\(402\) | 9.47864e42 | 1.01629 | ||||||||
\(403\) | 6.58162e42 | 0.677328 | ||||||||
\(404\) | −1.42306e43 | −1.40582 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00097e43 | −3.64322 | ||||||||
\(407\) | −3.59782e41 | −0.0314580 | ||||||||
\(408\) | 2.27557e43 | 1.91072 | ||||||||
\(409\) | 1.27736e43 | 1.03010 | 0.515050 | − | 0.857160i | \(-0.327773\pi\) | ||||
0.515050 | + | 0.857160i | \(0.327773\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.64628e41 | 0.0643338 | ||||||||
\(412\) | 9.71070e42 | 0.694139 | ||||||||
\(413\) | −2.34549e43 | −1.61086 | ||||||||
\(414\) | −4.23947e42 | −0.279773 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.28080e42 | 0.504699 | ||||||||
\(417\) | −2.34495e42 | −0.137369 | ||||||||
\(418\) | −2.33032e42 | −0.131222 | ||||||||
\(419\) | 1.81304e43 | 0.981467 | 0.490734 | − | 0.871310i | \(-0.336729\pi\) | ||||
0.490734 | + | 0.871310i | \(0.336729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.35628e43 | 0.678724 | 0.339362 | − | 0.940656i | \(-0.389789\pi\) | ||||
0.339362 | + | 0.940656i | \(0.389789\pi\) | |||||||
\(422\) | −4.07877e43 | −1.96279 | ||||||||
\(423\) | 2.05242e42 | 0.0949839 | ||||||||
\(424\) | −3.27723e43 | −1.45871 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.35247e43 | −1.38072 | ||||||||
\(427\) | −4.47894e43 | −1.77466 | ||||||||
\(428\) | −7.11156e43 | −2.71108 | ||||||||
\(429\) | 6.85399e42 | 0.251419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.12465e43 | 1.40124 | 0.700620 | − | 0.713535i | \(-0.252907\pi\) | ||||
0.700620 | + | 0.713535i | \(0.252907\pi\) | |||||||
\(432\) | 1.71943e43 | 0.562216 | ||||||||
\(433\) | −5.05620e43 | −1.59138 | −0.795690 | − | 0.605704i | \(-0.792892\pi\) | ||||
−0.795690 | + | 0.605704i | \(0.792892\pi\) | |||||||
\(434\) | 6.69105e43 | 2.02728 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.70028e43 | −0.477521 | ||||||||
\(437\) | −1.37949e43 | −0.373056 | ||||||||
\(438\) | −2.62198e43 | −0.682822 | ||||||||
\(439\) | −2.66416e43 | −0.668182 | −0.334091 | − | 0.942541i | \(-0.608429\pi\) | ||||
−0.334091 | + | 0.942541i | \(0.608429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.16370e43 | −0.270772 | ||||||||
\(442\) | 1.08489e44 | 2.43174 | ||||||||
\(443\) | −1.04497e43 | −0.225653 | −0.112826 | − | 0.993615i | \(-0.535990\pi\) | ||||
−0.112826 | + | 0.993615i | \(0.535990\pi\) | |||||||
\(444\) | 9.55870e42 | 0.198875 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.17630e43 | −0.806800 | ||||||||
\(447\) | −5.29815e43 | −0.986393 | ||||||||
\(448\) | 1.36687e44 | 2.45268 | ||||||||
\(449\) | −5.66906e43 | −0.980497 | −0.490248 | − | 0.871583i | \(-0.663094\pi\) | ||||
−0.490248 | + | 0.871583i | \(0.663094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.11170e43 | 0.178680 | ||||||||
\(452\) | 3.73879e41 | 0.00579358 | ||||||||
\(453\) | −2.13216e43 | −0.318566 | ||||||||
\(454\) | −5.51298e43 | −0.794264 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.81830e43 | 0.377631 | ||||||||
\(457\) | −1.11812e44 | −1.44501 | −0.722505 | − | 0.691366i | \(-0.757009\pi\) | ||||
−0.722505 | + | 0.691366i | \(0.757009\pi\) | |||||||
\(458\) | 1.83650e44 | 2.28935 | ||||||||
\(459\) | −1.27383e44 | −1.53181 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.91705e43 | −0.326496 | −0.163248 | − | 0.986585i | \(-0.552197\pi\) | ||||
−0.163248 | + | 0.986585i | \(0.552197\pi\) | |||||||
\(462\) | 6.96795e43 | 0.752510 | ||||||||
\(463\) | −1.20018e44 | −1.25072 | −0.625362 | − | 0.780335i | \(-0.715048\pi\) | ||||
−0.625362 | + | 0.780335i | \(0.715048\pi\) | |||||||
\(464\) | 6.50569e43 | 0.654254 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.76319e43 | 0.165170 | ||||||||
\(467\) | 2.20756e43 | 0.199611 | 0.0998054 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998054 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(468\) | 2.67304e43 | 0.233319 | ||||||||
\(469\) | 1.35377e44 | 1.14076 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.46875e44 | −1.15373 | ||||||||
\(472\) | 1.69297e44 | 1.28412 | ||||||||
\(473\) | −5.53622e42 | −0.0405512 | ||||||||
\(474\) | 3.49184e44 | 2.47008 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.13964e44 | 4.71152 | ||||||||
\(477\) | 2.08180e43 | 0.132704 | ||||||||
\(478\) | 1.47306e44 | 0.907108 | ||||||||
\(479\) | 7.80915e43 | 0.464588 | 0.232294 | − | 0.972646i | \(-0.425377\pi\) | ||||
0.232294 | + | 0.972646i | \(0.425377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.07446e43 | 0.115216 | ||||||||
\(482\) | 1.19709e44 | 0.642467 | ||||||||
\(483\) | 4.12484e44 | 2.13934 | ||||||||
\(484\) | −3.39281e44 | −1.70063 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.14674e43 | −0.428320 | ||||||||
\(487\) | 4.19385e44 | 1.89839 | 0.949194 | − | 0.314693i | \(-0.101901\pi\) | ||||
0.949194 | + | 0.314693i | \(0.101901\pi\) | |||||||
\(488\) | 3.23289e44 | 1.41470 | ||||||||
\(489\) | −1.46201e44 | −0.618522 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.24412e44 | 1.67859 | 0.839293 | − | 0.543680i | \(-0.182969\pi\) | ||||
0.839293 | + | 0.543680i | \(0.182969\pi\) | |||||||
\(492\) | −2.95358e44 | −1.12960 | ||||||||
\(493\) | −4.81971e44 | −1.78257 | ||||||||
\(494\) | 1.34364e44 | 0.480604 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.08798e44 | −0.364061 | ||||||||
\(497\) | −4.78810e44 | −1.54983 | ||||||||
\(498\) | −8.46530e44 | −2.65069 | ||||||||
\(499\) | 6.09953e44 | 1.84772 | 0.923862 | − | 0.382726i | \(-0.125015\pi\) | ||||
0.923862 | + | 0.382726i | \(0.125015\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.46133e44 | −0.981567 | ||||||||
\(502\) | −3.97976e44 | −1.09206 | ||||||||
\(503\) | 3.00762e44 | 0.798639 | 0.399320 | − | 0.916812i | \(-0.369246\pi\) | ||||
0.399320 | + | 0.916812i | \(0.369246\pi\) | |||||||
\(504\) | 1.23703e44 | 0.317889 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.46179e44 | 0.592608 | ||||||||
\(507\) | 5.57087e42 | 0.0129805 | ||||||||
\(508\) | −1.06995e45 | −2.41330 | ||||||||
\(509\) | 1.45444e44 | 0.317578 | 0.158789 | − | 0.987313i | \(-0.449241\pi\) | ||||
0.158789 | + | 0.987313i | \(0.449241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.74480e44 | −0.766450 | ||||||||
\(512\) | −5.15847e44 | −1.02227 | ||||||||
\(513\) | −1.57765e44 | −0.302744 | ||||||||
\(514\) | −1.19724e45 | −2.22479 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.47086e44 | 0.256361 | ||||||||
\(517\) | −1.19181e44 | −0.201192 | ||||||||
\(518\) | 2.10895e44 | 0.344847 | ||||||||
\(519\) | −1.05430e45 | −1.66994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.35096e44 | 0.498135 | 0.249067 | − | 0.968486i | \(-0.419876\pi\) | ||||
0.249067 | + | 0.968486i | \(0.419876\pi\) | |||||||
\(522\) | −1.83448e44 | −0.264210 | ||||||||
\(523\) | 7.95243e44 | 1.10974 | 0.554871 | − | 0.831937i | \(-0.312768\pi\) | ||||
0.554871 | + | 0.831937i | \(0.312768\pi\) | |||||||
\(524\) | 1.13317e45 | 1.53225 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.74821e44 | −0.348967 | ||||||||
\(527\) | 8.06028e44 | 0.991916 | ||||||||
\(528\) | −1.13301e44 | −0.135137 | ||||||||
\(529\) | 5.92309e44 | 0.684747 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.07543e44 | −0.116821 | ||||||||
\(532\) | 8.84249e44 | 0.931178 | ||||||||
\(533\) | −6.40995e44 | −0.654419 | ||||||||
\(534\) | −1.53337e45 | −1.51780 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.77149e44 | −0.909372 | ||||||||
\(537\) | −6.37659e44 | −0.575457 | ||||||||
\(538\) | 2.14039e43 | 0.0187321 | ||||||||
\(539\) | 6.75741e44 | 0.573542 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21161e45 | 0.967402 | 0.483701 | − | 0.875233i | \(-0.339292\pi\) | ||||
0.483701 | + | 0.875233i | \(0.339292\pi\) | |||||||
\(542\) | 1.88067e45 | 1.45655 | ||||||||
\(543\) | −7.61900e44 | −0.572401 | ||||||||
\(544\) | 1.01412e45 | 0.739108 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.01764e45 | −2.75609 | ||||||||
\(547\) | 1.99236e45 | 1.32610 | 0.663052 | − | 0.748573i | \(-0.269261\pi\) | ||||
0.663052 | + | 0.748573i | \(0.269261\pi\) | |||||||
\(548\) | −1.95808e44 | −0.126460 | ||||||||
\(549\) | −2.05363e44 | −0.128700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.96924e44 | −0.352304 | ||||||||
\(552\) | −2.97730e45 | −1.70541 | ||||||||
\(553\) | 4.98715e45 | 2.77260 | ||||||||
\(554\) | −1.80993e45 | −0.976679 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.31051e44 | 0.270024 | ||||||||
\(557\) | 1.74444e45 | 0.861082 | 0.430541 | − | 0.902571i | \(-0.358323\pi\) | ||||
0.430541 | + | 0.902571i | \(0.358323\pi\) | |||||||
\(558\) | 3.06790e44 | 0.147020 | ||||||||
\(559\) | 3.19212e44 | 0.148520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.39384e44 | 0.368191 | ||||||||
\(562\) | −5.67890e45 | −2.41888 | ||||||||
\(563\) | −1.30371e45 | −0.539251 | −0.269626 | − | 0.962965i | \(-0.586900\pi\) | ||||
−0.269626 | + | 0.962965i | \(0.586900\pi\) | |||||||
\(564\) | 3.16640e45 | 1.27192 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.92522e45 | −1.10838 | ||||||||
\(567\) | 4.10348e45 | 1.51019 | ||||||||
\(568\) | 3.45604e45 | 1.23547 | ||||||||
\(569\) | 8.99757e43 | 0.0312445 | 0.0156222 | − | 0.999878i | \(-0.495027\pi\) | ||||
0.0156222 | + | 0.999878i | \(0.495027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.85011e45 | 0.934039 | 0.467020 | − | 0.884247i | \(-0.345328\pi\) | ||||
0.467020 | + | 0.884247i | \(0.345328\pi\) | |||||||
\(572\) | −1.55219e45 | −0.494210 | ||||||||
\(573\) | 1.52143e45 | 0.470654 | ||||||||
\(574\) | −6.51653e45 | −1.95871 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.26722e44 | 0.177870 | ||||||||
\(577\) | 6.49472e45 | 1.79126 | 0.895632 | − | 0.444797i | \(-0.146724\pi\) | ||||
0.895632 | + | 0.444797i | \(0.146724\pi\) | |||||||
\(578\) | 7.00376e45 | 1.87725 | ||||||||
\(579\) | −5.16312e45 | −1.34498 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.20904e46 | −2.97533 | ||||||||
\(582\) | −7.75465e45 | −1.85495 | ||||||||
\(583\) | −1.20887e45 | −0.281091 | ||||||||
\(584\) | 2.70299e45 | 0.610988 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.66618e45 | −0.783254 | ||||||||
\(587\) | −5.04614e44 | −0.104817 | −0.0524084 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524084 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(588\) | −1.79531e46 | −3.62588 | ||||||||
\(589\) | 9.98271e44 | 0.196041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.92546e45 | 1.28604 | ||||||||
\(592\) | −3.42922e44 | −0.0619280 | ||||||||
\(593\) | 1.38106e45 | 0.242555 | 0.121277 | − | 0.992619i | \(-0.461301\pi\) | ||||
0.121277 | + | 0.992619i | \(0.461301\pi\) | |||||||
\(594\) | 2.81543e45 | 0.480915 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.19985e46 | 1.93894 | ||||||||
\(597\) | −1.29041e45 | −0.202839 | ||||||||
\(598\) | −1.41944e46 | −2.17044 | ||||||||
\(599\) | −7.75620e45 | −1.15374 | −0.576868 | − | 0.816837i | \(-0.695725\pi\) | ||||
−0.576868 | + | 0.816837i | \(0.695725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97032e45 | −0.277400 | −0.138700 | − | 0.990334i | \(-0.544292\pi\) | ||||
−0.138700 | + | 0.990334i | \(0.544292\pi\) | |||||||
\(602\) | 3.24520e45 | 0.444528 | ||||||||
\(603\) | 6.20715e44 | 0.0827288 | ||||||||
\(604\) | 4.82861e45 | 0.626200 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.80698e45 | 1.20431 | ||||||||
\(607\) | −3.36784e45 | −0.402474 | −0.201237 | − | 0.979543i | \(-0.564496\pi\) | ||||
−0.201237 | + | 0.979543i | \(0.564496\pi\) | |||||||
\(608\) | 1.25600e45 | 0.146076 | ||||||||
\(609\) | 1.78488e46 | 2.02033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.87182e45 | 0.736872 | ||||||||
\(612\) | 3.27358e45 | 0.341684 | ||||||||
\(613\) | 9.87239e45 | 1.00305 | 0.501527 | − | 0.865142i | \(-0.332772\pi\) | ||||
0.501527 | + | 0.865142i | \(0.332772\pi\) | |||||||
\(614\) | −3.32303e45 | −0.328667 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.18322e45 | −0.673345 | ||||||||
\(617\) | 3.29814e45 | 0.300998 | 0.150499 | − | 0.988610i | \(-0.451912\pi\) | ||||
0.150499 | + | 0.988610i | \(0.451912\pi\) | |||||||
\(618\) | −6.69211e45 | −0.594639 | ||||||||
\(619\) | 1.65886e46 | 1.43521 | 0.717604 | − | 0.696451i | \(-0.245239\pi\) | ||||
0.717604 | + | 0.696451i | \(0.245239\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.66666e46 | 1.36721 | ||||||||
\(622\) | 1.50700e46 | 1.20385 | ||||||||
\(623\) | −2.19000e46 | −1.70370 | ||||||||
\(624\) | 6.53280e45 | 0.494941 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.52560e45 | −0.253371 | ||||||||
\(627\) | 1.03958e45 | 0.0727688 | ||||||||
\(628\) | 3.32623e46 | 2.26787 | ||||||||
\(629\) | 2.54052e45 | 0.168728 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.39111e45 | 0.339777 | 0.169888 | − | 0.985463i | \(-0.445659\pi\) | ||||
0.169888 | + | 0.985463i | \(0.445659\pi\) | |||||||
\(632\) | −3.59972e46 | −2.21023 | ||||||||
\(633\) | 1.81958e46 | 1.08846 | ||||||||
\(634\) | −2.97141e45 | −0.173177 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.21172e46 | 1.77703 | ||||||||
\(637\) | −3.89625e46 | −2.10061 | ||||||||
\(638\) | 1.06525e46 | 0.559643 | ||||||||
\(639\) | −2.19539e45 | −0.112395 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.59612e46 | −1.74854 | −0.874271 | − | 0.485438i | \(-0.838660\pi\) | ||||
−0.874271 | + | 0.485438i | \(0.838660\pi\) | |||||||
\(642\) | 4.90092e46 | 2.32247 | ||||||||
\(643\) | −3.23556e46 | −1.49441 | −0.747203 | − | 0.664596i | \(-0.768604\pi\) | ||||
−0.747203 | + | 0.664596i | \(0.768604\pi\) | |||||||
\(644\) | −9.34135e46 | −4.20526 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.64551e46 | 0.703823 | ||||||||
\(647\) | −5.30852e45 | −0.221336 | −0.110668 | − | 0.993857i | \(-0.535299\pi\) | ||||
−0.110668 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(648\) | −2.96188e46 | −1.20387 | ||||||||
\(649\) | 6.24485e45 | 0.247448 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.98495e46 | −1.12422 | ||||||||
\(652\) | 3.31096e46 | 1.21582 | ||||||||
\(653\) | 2.38611e46 | 0.854326 | 0.427163 | − | 0.904175i | \(-0.359513\pi\) | ||||
0.427163 | + | 0.904175i | \(0.359513\pi\) | |||||||
\(654\) | 1.17174e46 | 0.409072 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.05961e46 | 0.351748 | ||||||||
\(657\) | −1.71702e45 | −0.0555837 | ||||||||
\(658\) | 6.98608e46 | 2.20550 | ||||||||
\(659\) | 2.81962e46 | 0.868122 | 0.434061 | − | 0.900883i | \(-0.357080\pi\) | ||||
0.434061 | + | 0.900883i | \(0.357080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.38643e46 | 0.991786 | 0.495893 | − | 0.868384i | \(-0.334841\pi\) | ||||
0.495893 | + | 0.868384i | \(0.334841\pi\) | |||||||
\(662\) | 1.30187e45 | 0.0371886 | ||||||||
\(663\) | −4.83980e46 | −1.34851 | ||||||||
\(664\) | 8.72683e46 | 2.37183 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.66973e44 | 0.0250086 | ||||||||
\(667\) | 6.30600e46 | 1.59103 | ||||||||
\(668\) | 7.83872e46 | 1.92945 | ||||||||
\(669\) | 1.86309e46 | 0.447408 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.19251e46 | 0.272609 | ||||||||
\(672\) | −3.75558e46 | −0.837692 | ||||||||
\(673\) | 3.57808e46 | 0.778756 | 0.389378 | − | 0.921078i | \(-0.372690\pi\) | ||||
0.389378 | + | 0.921078i | \(0.372690\pi\) | |||||||
\(674\) | 1.98949e46 | 0.422525 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.26161e45 | −0.0255156 | ||||||||
\(677\) | −6.06906e46 | −1.19787 | −0.598933 | − | 0.800799i | \(-0.704409\pi\) | ||||
−0.598933 | + | 0.800799i | \(0.704409\pi\) | |||||||
\(678\) | −2.57658e44 | −0.00496311 | ||||||||
\(679\) | −1.10754e47 | −2.08214 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.45940e46 | 0.440456 | ||||||||
\(682\) | −1.78148e46 | −0.311415 | ||||||||
\(683\) | −6.22121e46 | −1.06153 | −0.530766 | − | 0.847518i | \(-0.678096\pi\) | ||||
−0.530766 | + | 0.847518i | \(0.678096\pi\) | |||||||
\(684\) | 4.05436e45 | 0.0675299 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.08853e47 | −3.31506 | ||||||||
\(687\) | −8.19285e46 | −1.26955 | ||||||||
\(688\) | −5.27678e45 | −0.0798289 | ||||||||
\(689\) | 6.97019e46 | 1.02950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.23978e47 | 1.74565 | 0.872825 | − | 0.488033i | \(-0.162285\pi\) | ||||
0.872825 | + | 0.488033i | \(0.162285\pi\) | |||||||
\(692\) | 2.38762e47 | 3.28258 | ||||||||
\(693\) | 4.56301e45 | 0.0612566 | ||||||||
\(694\) | −4.53373e46 | −0.594326 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.28832e47 | −1.61054 | ||||||||
\(697\) | −7.85005e46 | −0.958366 | ||||||||
\(698\) | −1.64615e47 | −1.96270 | ||||||||
\(699\) | −7.86579e45 | −0.0915944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.57725e46 | −0.841713 | −0.420857 | − | 0.907127i | \(-0.638270\pi\) | ||||
−0.420857 | + | 0.907127i | \(0.638270\pi\) | |||||||
\(702\) | −1.62334e47 | −1.76136 | ||||||||
\(703\) | 3.14645e45 | 0.0333471 | ||||||||
\(704\) | −3.63927e46 | −0.376761 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.21669e47 | −2.18992 | ||||||||
\(707\) | 1.40066e47 | 1.35180 | ||||||||
\(708\) | −1.65913e47 | −1.56435 | ||||||||
\(709\) | −9.15900e46 | −0.843694 | −0.421847 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421847 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.28665e46 | 0.201072 | ||||||||
\(712\) | 1.58074e47 | 1.35813 | ||||||||
\(713\) | −1.05459e47 | −0.885332 | ||||||||
\(714\) | −4.92027e47 | −4.03616 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.44408e47 | 1.13117 | ||||||||
\(717\) | −6.57147e46 | −0.503033 | ||||||||
\(718\) | −4.92195e46 | −0.368200 | ||||||||
\(719\) | 1.43667e47 | 1.05034 | 0.525169 | − | 0.850998i | \(-0.324002\pi\) | ||||
0.525169 | + | 0.850998i | \(0.324002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.55788e46 | −0.667467 | ||||||||
\(722\) | −2.26329e47 | −1.54481 | ||||||||
\(723\) | −5.34036e46 | −0.356277 | ||||||||
\(724\) | 1.72544e47 | 1.12516 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.33815e47 | 1.45686 | ||||||||
\(727\) | −9.62263e46 | −0.586106 | −0.293053 | − | 0.956096i | \(-0.594671\pi\) | ||||
−0.293053 | + | 0.956096i | \(0.594671\pi\) | |||||||
\(728\) | 4.14177e47 | 2.46614 | ||||||||
\(729\) | 1.87793e47 | 1.09314 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.90928e46 | 0.217500 | ||||||||
\(732\) | −3.16827e47 | −1.72341 | ||||||||
\(733\) | 1.83322e47 | 0.974988 | 0.487494 | − | 0.873126i | \(-0.337911\pi\) | ||||
0.487494 | + | 0.873126i | \(0.337911\pi\) | |||||||
\(734\) | −5.99261e46 | −0.311624 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.32685e47 | −0.659689 | ||||||||
\(737\) | −3.60439e46 | −0.175234 | ||||||||
\(738\) | −2.98788e46 | −0.142048 | ||||||||
\(739\) | 2.28000e47 | 1.05999 | 0.529996 | − | 0.848000i | \(-0.322194\pi\) | ||||
0.529996 | + | 0.848000i | \(0.322194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.99412e46 | −0.266517 | ||||||||
\(742\) | 7.08608e47 | 3.08135 | ||||||||
\(743\) | 4.61345e46 | 0.196205 | 0.0981026 | − | 0.995176i | \(-0.468723\pi\) | ||||
0.0981026 | + | 0.995176i | \(0.468723\pi\) | |||||||
\(744\) | 2.15453e47 | 0.896189 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.03770e47 | 1.60673 | ||||||||
\(747\) | −5.54356e46 | −0.215774 | ||||||||
\(748\) | −1.90092e47 | −0.723747 | ||||||||
\(749\) | 6.99965e47 | 2.60691 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.50719e46 | −0.124997 | −0.0624986 | − | 0.998045i | \(-0.519907\pi\) | ||||
−0.0624986 | + | 0.998045i | \(0.519907\pi\) | |||||||
\(752\) | −1.13596e47 | −0.396066 | ||||||||
\(753\) | 1.77542e47 | 0.605597 | ||||||||
\(754\) | −6.14212e47 | −2.04970 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.06832e48 | −3.41266 | ||||||||
\(757\) | −1.87145e47 | −0.584921 | −0.292460 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292460 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(758\) | 2.96814e47 | 0.907701 | ||||||||
\(759\) | −1.09823e47 | −0.328628 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.20228e47 | 0.630994 | 0.315497 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315497 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(762\) | 7.37352e47 | 2.06737 | ||||||||
\(763\) | 1.67352e47 | 0.459173 | ||||||||
\(764\) | −3.44553e47 | −0.925157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.06479e48 | 2.73836 | ||||||||
\(767\) | −3.60071e47 | −0.906284 | ||||||||
\(768\) | 6.42462e47 | 1.58266 | ||||||||
\(769\) | −2.66239e47 | −0.641928 | −0.320964 | − | 0.947091i | \(-0.604007\pi\) | ||||
−0.320964 | + | 0.947091i | \(0.604007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.34102e47 | 1.23375 | ||||||||
\(772\) | 1.16927e48 | 2.64380 | ||||||||
\(773\) | 5.04292e45 | 0.0111614 | 0.00558072 | − | 0.999984i | \(-0.498224\pi\) | ||||
0.00558072 | + | 0.999984i | \(0.498224\pi\) | |||||||
\(774\) | 1.48795e46 | 0.0322376 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.99423e47 | 1.65981 | ||||||||
\(777\) | −9.40828e46 | −0.191233 | ||||||||
\(778\) | −3.17195e47 | −0.631194 | ||||||||
\(779\) | −9.72234e46 | −0.189410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.27483e47 | 0.238072 | ||||||||
\(782\) | −1.73834e48 | −3.17851 | ||||||||
\(783\) | 7.21186e47 | 1.29115 | ||||||||
\(784\) | 6.44075e47 | 1.12907 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.80922e47 | −1.31261 | ||||||||
\(787\) | 1.14740e48 | 1.88857 | 0.944283 | − | 0.329133i | \(-0.106757\pi\) | ||||
0.944283 | + | 0.329133i | \(0.106757\pi\) | |||||||
\(788\) | −1.56838e48 | −2.52795 | ||||||||
\(789\) | 1.22601e47 | 0.193518 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.67996e45 | −0.00557097 | ||||||||
\(792\) | −3.29357e46 | −0.0488316 | ||||||||
\(793\) | −6.87589e47 | −0.998438 | ||||||||
\(794\) | −1.19152e48 | −1.69459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.92234e47 | 0.398718 | ||||||||
\(797\) | 1.04385e48 | 1.39501 | 0.697503 | − | 0.716582i | \(-0.254294\pi\) | ||||
0.697503 | + | 0.716582i | \(0.254294\pi\) | |||||||
\(798\) | −6.09379e47 | −0.797700 | ||||||||
\(799\) | 8.41568e47 | 1.07911 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.00414e47 | −0.123554 | ||||||||
\(802\) | −1.71063e48 | −2.06196 | ||||||||
\(803\) | 9.97048e46 | 0.117736 | ||||||||
\(804\) | 9.57617e47 | 1.10781 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.02718e48 | 1.14056 | ||||||||
\(807\) | −9.54854e45 | −0.0103878 | ||||||||
\(808\) | −1.01100e48 | −1.07761 | ||||||||
\(809\) | 1.19411e48 | 1.24707 | 0.623537 | − | 0.781794i | \(-0.285695\pi\) | ||||
0.623537 | + | 0.781794i | \(0.285695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.04748e48 | −1.05027 | −0.525134 | − | 0.851019i | \(-0.675985\pi\) | ||||
−0.525134 | + | 0.851019i | \(0.675985\pi\) | |||||||
\(812\) | −4.04213e48 | −3.97133 | ||||||||
\(813\) | −8.38990e47 | −0.807723 | ||||||||
\(814\) | −5.61506e46 | −0.0529727 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.00050e47 | 0.724819 | ||||||||
\(817\) | 4.84167e46 | 0.0429864 | ||||||||
\(818\) | 1.99356e48 | 1.73460 | ||||||||
\(819\) | −2.63098e47 | −0.224354 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.56741e47 | 0.701758 | 0.350879 | − | 0.936421i | \(-0.385883\pi\) | ||||
0.350879 | + | 0.936421i | \(0.385883\pi\) | |||||||
\(822\) | 1.34941e47 | 0.108333 | ||||||||
\(823\) | 4.60629e47 | 0.362455 | 0.181228 | − | 0.983441i | \(-0.441993\pi\) | ||||
0.181228 | + | 0.983441i | \(0.441993\pi\) | |||||||
\(824\) | 6.89886e47 | 0.532082 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.66058e48 | −2.71256 | ||||||||
\(827\) | 2.09756e48 | 1.52361 | 0.761803 | − | 0.647808i | \(-0.224314\pi\) | ||||
0.761803 | + | 0.647808i | \(0.224314\pi\) | |||||||
\(828\) | −4.28309e47 | −0.304970 | ||||||||
\(829\) | −2.34867e48 | −1.63935 | −0.819675 | − | 0.572828i | \(-0.805846\pi\) | ||||
−0.819675 | + | 0.572828i | \(0.805846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.07432e47 | 0.541613 | ||||||||
\(832\) | 2.09836e48 | 1.37989 | ||||||||
\(833\) | −4.77160e48 | −3.07625 | ||||||||
\(834\) | −3.65973e47 | −0.231318 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.35430e47 | −0.143040 | ||||||||
\(837\) | −1.20608e48 | −0.718467 | ||||||||
\(838\) | 2.82958e48 | 1.65271 | ||||||||
\(839\) | 3.05667e48 | 1.75056 | 0.875279 | − | 0.483618i | \(-0.160678\pi\) | ||||
0.875279 | + | 0.483618i | \(0.160678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.12620e47 | 0.502523 | ||||||||
\(842\) | 2.11672e48 | 1.14291 | ||||||||
\(843\) | 2.53342e48 | 1.34138 | ||||||||
\(844\) | −4.12074e48 | −2.13956 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.20318e47 | 0.159945 | ||||||||
\(847\) | 3.33942e48 | 1.63529 | ||||||||
\(848\) | −1.15222e48 | −0.553354 | ||||||||
\(849\) | 1.30497e48 | 0.614645 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.32397e47 | −0.150598 | ||||||||
\(852\) | −3.38696e48 | −1.50507 | ||||||||
\(853\) | 3.72611e48 | 1.62404 | 0.812021 | − | 0.583629i | \(-0.198368\pi\) | ||||
0.812021 | + | 0.583629i | \(0.198368\pi\) | |||||||
\(854\) | −6.99021e48 | −2.98838 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.05233e48 | −2.07814 | ||||||||
\(857\) | −6.05125e47 | −0.244153 | −0.122076 | − | 0.992521i | \(-0.538955\pi\) | ||||
−0.122076 | + | 0.992521i | \(0.538955\pi\) | |||||||
\(858\) | 1.06969e48 | 0.423368 | ||||||||
\(859\) | 2.95430e48 | 1.14701 | 0.573505 | − | 0.819202i | \(-0.305583\pi\) | ||||
0.573505 | + | 0.819202i | \(0.305583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.90710e48 | 1.08619 | ||||||||
\(862\) | 6.43728e48 | 2.35957 | ||||||||
\(863\) | 5.76096e47 | 0.207165 | 0.103583 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103583 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(864\) | −1.51746e48 | −0.535352 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.89113e48 | −2.67975 | ||||||||
\(867\) | −3.12446e48 | −1.04102 | ||||||||
\(868\) | 6.75989e48 | 2.20986 | ||||||||
\(869\) | −1.32782e48 | −0.425906 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.07825e48 | 0.641799 | ||||||||
\(872\) | −1.20794e48 | −0.366037 | ||||||||
\(873\) | −5.07818e47 | −0.150999 | ||||||||
\(874\) | −2.15295e48 | −0.628195 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.64896e48 | −0.744317 | ||||||||
\(877\) | 1.47230e48 | 0.405980 | 0.202990 | − | 0.979181i | \(-0.434934\pi\) | ||||
0.202990 | + | 0.979181i | \(0.434934\pi\) | |||||||
\(878\) | −4.15791e48 | −1.12516 | ||||||||
\(879\) | 1.63552e48 | 0.434350 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.01645e48 | −1.53900 | −0.769499 | − | 0.638648i | \(-0.779494\pi\) | ||||
−0.769499 | + | 0.638648i | \(0.779494\pi\) | |||||||
\(882\) | −1.81617e48 | −0.455957 | ||||||||
\(883\) | 1.72340e48 | 0.424654 | 0.212327 | − | 0.977199i | \(-0.431896\pi\) | ||||
0.212327 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(884\) | 1.09605e49 | 2.65074 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.63086e48 | −0.379980 | ||||||||
\(887\) | −4.24957e48 | −0.971863 | −0.485931 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485931 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(888\) | 6.79088e47 | 0.152445 | ||||||||
\(889\) | 1.05311e49 | 2.32057 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.09255e48 | −0.231984 | ||||||||
\(892\) | −4.21927e48 | −0.879462 | ||||||||
\(893\) | 1.04229e48 | 0.213274 | ||||||||
\(894\) | −8.26874e48 | −1.66100 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.66990e49 | 3.23303 | ||||||||
\(897\) | 6.33229e48 | 1.20361 | ||||||||
\(898\) | −8.84761e48 | −1.65107 | ||||||||
\(899\) | −4.56336e48 | −0.836083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.53615e48 | 1.50766 | ||||||||
\(902\) | 1.73502e48 | 0.300882 | ||||||||
\(903\) | −1.44772e48 | −0.246511 | ||||||||
\(904\) | 2.65619e46 | 0.00444099 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.32763e48 | −0.536438 | ||||||||
\(907\) | −1.37448e48 | −0.217579 | −0.108789 | − | 0.994065i | \(-0.534697\pi\) | ||||
−0.108789 | + | 0.994065i | \(0.534697\pi\) | |||||||
\(908\) | −5.56970e48 | −0.865796 | ||||||||
\(909\) | 6.42216e47 | 0.0980341 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.36073e48 | −0.936383 | −0.468192 | − | 0.883627i | \(-0.655094\pi\) | ||||
−0.468192 | + | 0.883627i | \(0.655094\pi\) | |||||||
\(912\) | 9.90867e47 | 0.143252 | ||||||||
\(913\) | 3.21905e48 | 0.457047 | ||||||||
\(914\) | −1.74503e49 | −2.43327 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.85540e49 | 2.49553 | ||||||||
\(917\) | −1.11534e49 | −1.47337 | ||||||||
\(918\) | −1.98805e49 | −2.57943 | ||||||||
\(919\) | 1.02620e49 | 1.30775 | 0.653876 | − | 0.756601i | \(-0.273142\pi\) | ||||
0.653876 | + | 0.756601i | \(0.273142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.48244e48 | 0.182261 | ||||||||
\(922\) | −4.55259e48 | −0.549792 | ||||||||
\(923\) | −7.35050e48 | −0.871945 | ||||||||
\(924\) | 7.03965e48 | 0.820282 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.87311e49 | −2.10611 | ||||||||
\(927\) | −4.38237e47 | −0.0484054 | ||||||||
\(928\) | −5.74148e48 | −0.622992 | ||||||||
\(929\) | −8.18502e48 | −0.872490 | −0.436245 | − | 0.899828i | \(-0.643692\pi\) | ||||
−0.436245 | + | 0.899828i | \(0.643692\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.90966e48 | −0.607985 | ||||||||
\(932\) | 1.78133e48 | 0.180046 | ||||||||
\(933\) | −6.72289e48 | −0.667589 | ||||||||
\(934\) | 3.44530e48 | 0.336128 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.89904e48 | 0.178847 | ||||||||
\(937\) | 2.10406e49 | 1.94695 | 0.973474 | − | 0.228800i | \(-0.0734800\pi\) | ||||
0.973474 | + | 0.228800i | \(0.0734800\pi\) | |||||||
\(938\) | 2.11281e49 | 1.92094 | ||||||||
\(939\) | 1.57281e48 | 0.140506 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.12511e49 | 0.970434 | 0.485217 | − | 0.874394i | \(-0.338741\pi\) | ||||
0.485217 | + | 0.874394i | \(0.338741\pi\) | |||||||
\(942\) | −2.29226e49 | −1.94278 | ||||||||
\(943\) | 1.02708e49 | 0.855387 | ||||||||
\(944\) | 5.95220e48 | 0.487124 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.64029e47 | −0.0682849 | ||||||||
\(947\) | −1.47061e49 | −1.14215 | −0.571075 | − | 0.820898i | \(-0.693474\pi\) | ||||
−0.571075 | + | 0.820898i | \(0.693474\pi\) | |||||||
\(948\) | 3.52777e49 | 2.69254 | ||||||||
\(949\) | −5.74887e48 | −0.431211 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.32558e48 | 0.0960346 | ||||||||
\(952\) | 5.07228e49 | 3.61155 | ||||||||
\(953\) | 6.20681e47 | 0.0434346 | 0.0217173 | − | 0.999764i | \(-0.493087\pi\) | ||||
0.0217173 | + | 0.999764i | \(0.493087\pi\) | |||||||
\(954\) | 3.24903e48 | 0.223463 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.48821e49 | 0.988803 | ||||||||
\(957\) | −4.75221e48 | −0.310348 | ||||||||
\(958\) | 1.21876e49 | 0.782327 | ||||||||
\(959\) | 1.92727e48 | 0.121601 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.77191e48 | −0.534759 | ||||||||
\(962\) | 3.23758e48 | 0.194013 | ||||||||
\(963\) | 3.20940e48 | 0.189056 | ||||||||
\(964\) | 1.20941e49 | 0.700328 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.43757e49 | 3.60246 | ||||||||
\(967\) | 1.22644e49 | 0.674699 | 0.337350 | − | 0.941379i | \(-0.390470\pi\) | ||||
0.337350 | + | 0.941379i | \(0.390470\pi\) | |||||||
\(968\) | −2.41038e49 | −1.30360 | ||||||||
\(969\) | −7.34080e48 | −0.390302 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.12879e49 | 0.580090 | 0.290045 | − | 0.957013i | \(-0.406330\pi\) | ||||
0.290045 | + | 0.957013i | \(0.406330\pi\) | |||||||
\(972\) | −9.24086e48 | −0.466895 | ||||||||
\(973\) | −5.22694e48 | −0.259648 | ||||||||
\(974\) | 6.54527e49 | 3.19672 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.13663e49 | 0.536657 | ||||||||
\(977\) | −4.11771e49 | −1.91159 | −0.955796 | − | 0.294029i | \(-0.905004\pi\) | ||||
−0.955796 | + | 0.294029i | \(0.905004\pi\) | |||||||
\(978\) | −2.28174e49 | −1.04154 | ||||||||
\(979\) | 5.83085e48 | 0.261708 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.67323e47 | 0.0332996 | ||||||||
\(982\) | 6.62374e49 | 2.82660 | ||||||||
\(983\) | 1.02350e49 | 0.429494 | 0.214747 | − | 0.976670i | \(-0.431107\pi\) | ||||
0.214747 | + | 0.976670i | \(0.431107\pi\) | |||||||
\(984\) | −2.09834e49 | −0.865877 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.52204e49 | −3.00170 | ||||||||
\(987\) | −3.11657e49 | −1.22305 | ||||||||
\(988\) | 1.35746e49 | 0.523888 | ||||||||
\(989\) | −5.11482e48 | −0.194129 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.68749e49 | 0.619478 | 0.309739 | − | 0.950822i | \(-0.399758\pi\) | ||||
0.309739 | + | 0.950822i | \(0.399758\pi\) | |||||||
\(992\) | 9.60182e48 | 0.346666 | ||||||||
\(993\) | −5.80777e47 | −0.0206228 | ||||||||
\(994\) | −7.47272e49 | −2.60978 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.55240e49 | −2.88941 | ||||||||
\(997\) | −1.90551e49 | −0.633200 | −0.316600 | − | 0.948559i | \(-0.602541\pi\) | ||||
−0.316600 | + | 0.948559i | \(0.602541\pi\) | |||||||
\(998\) | 9.51944e49 | 3.11141 | ||||||||
\(999\) | −3.80145e48 | −0.122213 |
(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 | 25.34.a.f.1.14 | 16 | ||
5.2 | odd | 4 | 5.34.b.a.4.14 | yes | 16 | ||
5.3 | odd | 4 | 5.34.b.a.4.3 | ✓ | 16 | ||
5.4 | even | 2 | inner | 25.34.a.f.1.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.b.a.4.3 | ✓ | 16 | 5.3 | odd | 4 | ||
5.34.b.a.4.14 | yes | 16 | 5.2 | odd | 4 | ||
25.34.a.f.1.3 | 16 | 5.4 | even | 2 | inner | ||
25.34.a.f.1.14 | 16 | 1.1 | even | 1 | trivial |