Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(19.2085795140\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{151}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 151 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(12.2882\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 83.7292 | 1.85017 | 0.925086 | − | 0.379757i | \(-0.123993\pi\) | ||||
0.925086 | + | 0.379757i | \(0.123993\pi\) | |||||||
\(3\) | 503.223 | 1.19562 | 0.597810 | − | 0.801638i | \(-0.296038\pi\) | ||||
0.597810 | + | 0.801638i | \(0.296038\pi\) | |||||||
\(4\) | 4962.58 | 2.42314 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 42134.4 | 2.21210 | ||||||||
\(7\) | −15973.7 | −0.359224 | −0.179612 | − | 0.983738i | \(-0.557484\pi\) | ||||
−0.179612 | + | 0.983738i | \(0.557484\pi\) | |||||||
\(8\) | 244036. | 2.63305 | ||||||||
\(9\) | 76086.0 | 0.429508 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 339729. | 0.636024 | 0.318012 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318012 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(12\) | 2.49728e6 | 2.89715 | ||||||||
\(13\) | −2.02328e6 | −1.51136 | −0.755680 | − | 0.654941i | \(-0.772693\pi\) | ||||
−0.755680 | + | 0.654941i | \(0.772693\pi\) | |||||||
\(14\) | −1.33746e6 | −0.664626 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.02696e7 | 2.44846 | ||||||||
\(17\) | 2.45063e6 | 0.418610 | 0.209305 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209305 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(18\) | 6.37062e6 | 0.794663 | ||||||||
\(19\) | −4.08504e6 | −0.378487 | −0.189244 | − | 0.981930i | \(-0.560604\pi\) | ||||
−0.189244 | + | 0.981930i | \(0.560604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.03830e6 | −0.429495 | ||||||||
\(22\) | 2.84453e7 | 1.17675 | ||||||||
\(23\) | −2.86497e7 | −0.928149 | −0.464074 | − | 0.885796i | \(-0.653613\pi\) | ||||
−0.464074 | + | 0.885796i | \(0.653613\pi\) | |||||||
\(24\) | 1.22804e8 | 3.14813 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.69408e8 | −2.79628 | ||||||||
\(27\) | −5.08562e7 | −0.682092 | ||||||||
\(28\) | −7.92706e7 | −0.870448 | ||||||||
\(29\) | −9.41230e6 | −0.0852132 | −0.0426066 | − | 0.999092i | \(-0.513566\pi\) | ||||
−0.0426066 | + | 0.999092i | \(0.513566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.99399e8 | 1.87828 | 0.939141 | − | 0.343532i | \(-0.111623\pi\) | ||||
0.939141 | + | 0.343532i | \(0.111623\pi\) | |||||||
\(32\) | 3.60078e8 | 1.89702 | ||||||||
\(33\) | 1.70959e8 | 0.760443 | ||||||||
\(34\) | 2.05190e8 | 0.774500 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.77583e8 | 1.04076 | ||||||||
\(37\) | 4.57279e8 | 1.08411 | 0.542053 | − | 0.840344i | \(-0.317647\pi\) | ||||
0.542053 | + | 0.840344i | \(0.317647\pi\) | |||||||
\(38\) | −3.42037e8 | −0.700267 | ||||||||
\(39\) | −1.01816e9 | −1.80701 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.83814e8 | 0.247780 | 0.123890 | − | 0.992296i | \(-0.460463\pi\) | ||||
0.123890 | + | 0.992296i | \(0.460463\pi\) | |||||||
\(42\) | −6.73041e8 | −0.794640 | ||||||||
\(43\) | −6.56811e8 | −0.681340 | −0.340670 | − | 0.940183i | \(-0.610654\pi\) | ||||
−0.340670 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(44\) | 1.68594e9 | 1.54117 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.39882e9 | −1.71724 | ||||||||
\(47\) | 1.97090e8 | 0.125350 | 0.0626752 | − | 0.998034i | \(-0.480037\pi\) | ||||
0.0626752 | + | 0.998034i | \(0.480037\pi\) | |||||||
\(48\) | 5.16788e9 | 2.92742 | ||||||||
\(49\) | −1.72217e9 | −0.870958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.23321e9 | 0.500498 | ||||||||
\(52\) | −1.00407e10 | −3.66223 | ||||||||
\(53\) | −5.15890e9 | −1.69449 | −0.847247 | − | 0.531199i | \(-0.821742\pi\) | ||||
−0.847247 | + | 0.531199i | \(0.821742\pi\) | |||||||
\(54\) | −4.25815e9 | −1.26199 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.89815e9 | −0.945854 | ||||||||
\(57\) | −2.05568e9 | −0.452527 | ||||||||
\(58\) | −7.88085e8 | −0.157659 | ||||||||
\(59\) | −6.62200e8 | −0.120588 | −0.0602939 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602939 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.58296e8 | 0.0846351 | 0.0423176 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423176 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(62\) | 2.50684e10 | 3.47515 | ||||||||
\(63\) | −1.21537e9 | −0.154289 | ||||||||
\(64\) | 9.11694e9 | 1.06135 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.43143e10 | 1.40695 | ||||||||
\(67\) | −1.01206e10 | −0.915787 | −0.457894 | − | 0.889007i | \(-0.651396\pi\) | ||||
−0.457894 | + | 0.889007i | \(0.651396\pi\) | |||||||
\(68\) | 1.21615e10 | 1.01435 | ||||||||
\(69\) | −1.44172e10 | −1.10971 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.78161e10 | 1.17190 | 0.585952 | − | 0.810346i | \(-0.300721\pi\) | ||||
0.585952 | + | 0.810346i | \(0.300721\pi\) | |||||||
\(72\) | 1.85677e10 | 1.13091 | ||||||||
\(73\) | 2.33380e10 | 1.31761 | 0.658807 | − | 0.752312i | \(-0.271061\pi\) | ||||
0.658807 | + | 0.752312i | \(0.271061\pi\) | |||||||
\(74\) | 3.82876e10 | 2.00578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.02724e10 | −0.917127 | ||||||||
\(77\) | −5.42672e9 | −0.228475 | ||||||||
\(78\) | −8.52498e10 | −3.34328 | ||||||||
\(79\) | 1.24957e10 | 0.456888 | 0.228444 | − | 0.973557i | \(-0.426636\pi\) | ||||
0.228444 | + | 0.973557i | \(0.426636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.90704e10 | −1.24503 | ||||||||
\(82\) | 1.53906e10 | 0.458436 | ||||||||
\(83\) | −3.37037e10 | −0.939179 | −0.469589 | − | 0.882885i | \(-0.655598\pi\) | ||||
−0.469589 | + | 0.882885i | \(0.655598\pi\) | |||||||
\(84\) | −3.98908e10 | −1.04073 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.49943e10 | −1.26060 | ||||||||
\(87\) | −4.73648e9 | −0.101883 | ||||||||
\(88\) | 8.29062e10 | 1.67468 | ||||||||
\(89\) | 2.94282e10 | 0.558623 | 0.279311 | − | 0.960201i | \(-0.409894\pi\) | ||||
0.279311 | + | 0.960201i | \(0.409894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23192e10 | 0.542916 | ||||||||
\(92\) | −1.42177e11 | −2.24903 | ||||||||
\(93\) | 1.50664e11 | 2.24571 | ||||||||
\(94\) | 1.65022e10 | 0.231920 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.81199e11 | 2.26811 | ||||||||
\(97\) | 1.13262e11 | 1.33918 | 0.669588 | − | 0.742732i | \(-0.266471\pi\) | ||||
0.669588 | + | 0.742732i | \(0.266471\pi\) | |||||||
\(98\) | −1.44196e11 | −1.61142 | ||||||||
\(99\) | 2.58486e10 | 0.273177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.19564e11 | 1.13196 | 0.565982 | − | 0.824417i | \(-0.308497\pi\) | ||||
0.565982 | + | 0.824417i | \(0.308497\pi\) | |||||||
\(102\) | 1.03256e11 | 0.926008 | ||||||||
\(103\) | 9.46874e10 | 0.804799 | 0.402399 | − | 0.915464i | \(-0.368176\pi\) | ||||
0.402399 | + | 0.915464i | \(0.368176\pi\) | |||||||
\(104\) | −4.93753e11 | −3.97948 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.31951e11 | −3.13511 | ||||||||
\(107\) | −1.52769e11 | −1.05299 | −0.526497 | − | 0.850177i | \(-0.676495\pi\) | ||||
−0.526497 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(108\) | −2.52378e11 | −1.65280 | ||||||||
\(109\) | 2.85078e11 | 1.77467 | 0.887337 | − | 0.461122i | \(-0.152553\pi\) | ||||
0.887337 | + | 0.461122i | \(0.152553\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.30113e11 | 1.29618 | ||||||||
\(112\) | −1.64043e11 | −0.879544 | ||||||||
\(113\) | 2.35563e11 | 1.20275 | 0.601374 | − | 0.798968i | \(-0.294620\pi\) | ||||
0.601374 | + | 0.798968i | \(0.294620\pi\) | |||||||
\(114\) | −1.72121e11 | −0.837253 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.67093e10 | −0.206483 | ||||||||
\(117\) | −1.53943e11 | −0.649140 | ||||||||
\(118\) | −5.54455e10 | −0.223108 | ||||||||
\(119\) | −3.91456e10 | −0.150375 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.69896e11 | −0.595474 | ||||||||
\(122\) | 4.67457e10 | 0.156590 | ||||||||
\(123\) | 9.24991e10 | 0.296251 | ||||||||
\(124\) | 1.48579e12 | 4.55133 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.01762e11 | −0.285462 | ||||||||
\(127\) | 1.25786e11 | 0.337840 | 0.168920 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168920 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(128\) | 2.59156e10 | 0.0666664 | ||||||||
\(129\) | −3.30522e11 | −0.814624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.97347e11 | −0.673397 | −0.336698 | − | 0.941613i | \(-0.609310\pi\) | ||||
−0.336698 | + | 0.941613i | \(0.609310\pi\) | |||||||
\(132\) | 8.48401e11 | 1.84266 | ||||||||
\(133\) | 6.52530e10 | 0.135962 | ||||||||
\(134\) | −8.47389e11 | −1.69436 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.98043e11 | 1.10222 | ||||||||
\(137\) | 6.29203e10 | 0.111385 | 0.0556926 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556926 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(138\) | −1.20714e12 | −2.05316 | ||||||||
\(139\) | −5.11416e11 | −0.835974 | −0.417987 | − | 0.908453i | \(-0.637264\pi\) | ||||
−0.417987 | + | 0.908453i | \(0.637264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.91800e10 | 0.149871 | ||||||||
\(142\) | 1.49173e12 | 2.16823 | ||||||||
\(143\) | −6.87368e11 | −0.961260 | ||||||||
\(144\) | 7.81370e11 | 1.05163 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.95407e12 | 2.43781 | ||||||||
\(147\) | −8.66634e11 | −1.04134 | ||||||||
\(148\) | 2.26929e12 | 2.62694 | ||||||||
\(149\) | 7.94154e11 | 0.885891 | 0.442945 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442945 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.24629e12 | 1.29195 | 0.645974 | − | 0.763360i | \(-0.276452\pi\) | ||||
0.645974 | + | 0.763360i | \(0.276452\pi\) | |||||||
\(152\) | −9.96896e11 | −0.996576 | ||||||||
\(153\) | 1.86459e11 | 0.179796 | ||||||||
\(154\) | −4.54375e11 | −0.422718 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.05271e12 | −4.37864 | ||||||||
\(157\) | −9.73519e11 | −0.814510 | −0.407255 | − | 0.913315i | \(-0.633514\pi\) | ||||
−0.407255 | + | 0.913315i | \(0.633514\pi\) | |||||||
\(158\) | 1.04625e12 | 0.845322 | ||||||||
\(159\) | −2.59608e12 | −2.02597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.57641e11 | 0.333413 | ||||||||
\(162\) | −3.27133e12 | −2.30352 | ||||||||
\(163\) | −1.26084e12 | −0.858281 | −0.429140 | − | 0.903238i | \(-0.641183\pi\) | ||||
−0.429140 | + | 0.903238i | \(0.641183\pi\) | |||||||
\(164\) | 9.12190e11 | 0.600405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.82199e12 | −1.73764 | ||||||||
\(167\) | 3.01398e12 | 1.79556 | 0.897780 | − | 0.440443i | \(-0.145179\pi\) | ||||
0.897780 | + | 0.440443i | \(0.145179\pi\) | |||||||
\(168\) | −1.96164e12 | −1.13088 | ||||||||
\(169\) | 2.30151e12 | 1.28421 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10814e11 | −0.162563 | ||||||||
\(172\) | −3.25948e12 | −1.65098 | ||||||||
\(173\) | 3.07482e11 | 0.150857 | 0.0754285 | − | 0.997151i | \(-0.475968\pi\) | ||||
0.0754285 | + | 0.997151i | \(0.475968\pi\) | |||||||
\(174\) | −3.96582e11 | −0.188500 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.48887e12 | 1.55728 | ||||||||
\(177\) | −3.33234e11 | −0.144177 | ||||||||
\(178\) | 2.46400e12 | 1.03355 | ||||||||
\(179\) | −1.91470e12 | −0.778769 | −0.389384 | − | 0.921075i | \(-0.627312\pi\) | ||||
−0.389384 | + | 0.921075i | \(0.627312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10300e11 | 0.0422032 | 0.0211016 | − | 0.999777i | \(-0.493283\pi\) | ||||
0.0211016 | + | 0.999777i | \(0.493283\pi\) | |||||||
\(182\) | 2.70606e12 | 1.00449 | ||||||||
\(183\) | 2.80947e11 | 0.101191 | ||||||||
\(184\) | −6.99157e12 | −2.44386 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.26150e13 | 4.15495 | ||||||||
\(187\) | 8.32552e11 | 0.266246 | ||||||||
\(188\) | 9.78074e11 | 0.303741 | ||||||||
\(189\) | 8.12359e11 | 0.245024 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.43991e12 | −1.26384 | −0.631918 | − | 0.775035i | \(-0.717732\pi\) | ||||
−0.631918 | + | 0.775035i | \(0.717732\pi\) | |||||||
\(192\) | 4.58785e12 | 1.26897 | ||||||||
\(193\) | −3.15713e12 | −0.848647 | −0.424324 | − | 0.905511i | \(-0.639488\pi\) | ||||
−0.424324 | + | 0.905511i | \(0.639488\pi\) | |||||||
\(194\) | 9.48330e12 | 2.47771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54641e12 | −2.11045 | ||||||||
\(197\) | 3.58626e12 | 0.861147 | 0.430574 | − | 0.902555i | \(-0.358311\pi\) | ||||
0.430574 | + | 0.902555i | \(0.358311\pi\) | |||||||
\(198\) | 2.16429e12 | 0.505424 | ||||||||
\(199\) | 4.14823e12 | 0.942260 | 0.471130 | − | 0.882064i | \(-0.343846\pi\) | ||||
0.471130 | + | 0.882064i | \(0.343846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.09291e12 | −1.09493 | ||||||||
\(202\) | 1.00110e13 | 2.09433 | ||||||||
\(203\) | 1.50349e11 | 0.0306106 | ||||||||
\(204\) | 6.11993e12 | 1.21278 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.92810e12 | 1.48902 | ||||||||
\(207\) | −2.17984e12 | −0.398647 | ||||||||
\(208\) | −2.07782e13 | −3.70050 | ||||||||
\(209\) | −1.38781e12 | −0.240727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.14275e12 | 0.188104 | 0.0940519 | − | 0.995567i | \(-0.470018\pi\) | ||||
0.0940519 | + | 0.995567i | \(0.470018\pi\) | |||||||
\(212\) | −2.56015e13 | −4.10599 | ||||||||
\(213\) | 8.96547e12 | 1.40115 | ||||||||
\(214\) | −1.27913e13 | −1.94822 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.24107e13 | −1.79598 | ||||||||
\(217\) | −4.78249e12 | −0.674724 | ||||||||
\(218\) | 2.38694e13 | 3.28345 | ||||||||
\(219\) | 1.17442e13 | 1.57537 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.95832e12 | −0.632670 | ||||||||
\(222\) | 1.92672e13 | 2.39816 | ||||||||
\(223\) | −3.54889e12 | −0.430939 | −0.215469 | − | 0.976511i | \(-0.569128\pi\) | ||||
−0.215469 | + | 0.976511i | \(0.569128\pi\) | |||||||
\(224\) | −5.75175e12 | −0.681454 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.97235e13 | 2.22529 | ||||||||
\(227\) | −3.90543e12 | −0.430058 | −0.215029 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215029 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(228\) | −1.02015e13 | −1.09654 | ||||||||
\(229\) | −4.85126e12 | −0.509048 | −0.254524 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254524 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73085e12 | −0.273169 | ||||||||
\(232\) | −2.29694e12 | −0.224370 | ||||||||
\(233\) | −1.03473e13 | −0.987115 | −0.493557 | − | 0.869713i | \(-0.664304\pi\) | ||||
−0.493557 | + | 0.869713i | \(0.664304\pi\) | |||||||
\(234\) | −1.28896e13 | −1.20102 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.28622e12 | −0.292201 | ||||||||
\(237\) | 6.28810e12 | 0.546265 | ||||||||
\(238\) | −3.27763e12 | −0.278219 | ||||||||
\(239\) | 1.85140e12 | 0.153572 | 0.0767859 | − | 0.997048i | \(-0.475534\pi\) | ||||
0.0767859 | + | 0.997048i | \(0.475534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.73018e12 | 0.216321 | 0.108160 | − | 0.994133i | \(-0.465504\pi\) | ||||
0.108160 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(242\) | −1.42252e13 | −1.10173 | ||||||||
\(243\) | −1.06521e13 | −0.806492 | ||||||||
\(244\) | 2.77059e12 | 0.205083 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.74488e12 | 0.548115 | ||||||||
\(247\) | 8.26518e12 | 0.572031 | ||||||||
\(248\) | 7.30641e13 | 4.94561 | ||||||||
\(249\) | −1.69605e13 | −1.12290 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.18976e13 | 0.753796 | 0.376898 | − | 0.926255i | \(-0.376991\pi\) | ||||
0.376898 | + | 0.926255i | \(0.376991\pi\) | |||||||
\(252\) | −6.03138e12 | −0.373864 | ||||||||
\(253\) | −9.73316e12 | −0.590324 | ||||||||
\(254\) | 1.05319e13 | 0.625062 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.65016e13 | −0.938007 | ||||||||
\(257\) | −3.53878e10 | −0.00196889 | −0.000984443 | − | 1.00000i | \(-0.500313\pi\) | ||||
−0.000984443 | 1.00000i | \(0.500313\pi\) | ||||||||
\(258\) | −2.76744e13 | −1.50719 | ||||||||
\(259\) | −7.30442e12 | −0.389437 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.16144e11 | −0.0365997 | ||||||||
\(262\) | −2.48966e13 | −1.24590 | ||||||||
\(263\) | 1.19904e13 | 0.587592 | 0.293796 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293796 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(264\) | 4.17202e13 | 2.00228 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.46358e12 | 0.251553 | ||||||||
\(267\) | 1.48089e13 | 0.667901 | ||||||||
\(268\) | −5.02243e13 | −2.21908 | ||||||||
\(269\) | −3.81149e13 | −1.64990 | −0.824948 | − | 0.565208i | \(-0.808796\pi\) | ||||
−0.824948 | + | 0.565208i | \(0.808796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13510e13 | −0.471740 | −0.235870 | − | 0.971785i | \(-0.575794\pi\) | ||||
−0.235870 | + | 0.971785i | \(0.575794\pi\) | |||||||
\(272\) | 2.51670e13 | 1.02495 | ||||||||
\(273\) | 1.62637e13 | 0.649122 | ||||||||
\(274\) | 5.26827e12 | 0.206082 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.15466e13 | −2.68899 | ||||||||
\(277\) | −3.02533e13 | −1.11464 | −0.557320 | − | 0.830298i | \(-0.688170\pi\) | ||||
−0.557320 | + | 0.830298i | \(0.688170\pi\) | |||||||
\(278\) | −4.28205e13 | −1.54670 | ||||||||
\(279\) | 2.27801e13 | 0.806736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.72047e13 | 1.60731 | 0.803657 | − | 0.595093i | \(-0.202885\pi\) | ||||
0.803657 | + | 0.595093i | \(0.202885\pi\) | |||||||
\(282\) | 8.30426e12 | 0.277288 | ||||||||
\(283\) | 8.68805e12 | 0.284510 | 0.142255 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142255 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(284\) | 8.84140e13 | 2.83969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.75528e13 | −1.77850 | ||||||||
\(287\) | −2.93617e12 | −0.0890085 | ||||||||
\(288\) | 2.73969e13 | 0.814783 | ||||||||
\(289\) | −2.82663e13 | −0.824766 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.69958e13 | 1.60115 | ||||||||
\(292\) | 1.15817e14 | 3.19276 | ||||||||
\(293\) | −2.17869e13 | −0.589417 | −0.294709 | − | 0.955587i | \(-0.595223\pi\) | ||||
−0.294709 | + | 0.955587i | \(0.595223\pi\) | |||||||
\(294\) | −7.25626e13 | −1.92665 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.11593e14 | 2.85450 | ||||||||
\(297\) | −1.72773e13 | −0.433827 | ||||||||
\(298\) | 6.64939e13 | 1.63905 | ||||||||
\(299\) | 5.79665e13 | 1.40277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.04917e13 | 0.244754 | ||||||||
\(302\) | 1.04351e14 | 2.39033 | ||||||||
\(303\) | 6.01673e13 | 1.35340 | ||||||||
\(304\) | −4.19516e13 | −0.926710 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56121e13 | 0.332654 | ||||||||
\(307\) | −2.05380e13 | −0.429829 | −0.214915 | − | 0.976633i | \(-0.568947\pi\) | ||||
−0.214915 | + | 0.976633i | \(0.568947\pi\) | |||||||
\(308\) | −2.69305e13 | −0.553626 | ||||||||
\(309\) | 4.76488e13 | 0.962234 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.37156e13 | −1.43674 | −0.718369 | − | 0.695663i | \(-0.755111\pi\) | ||||
−0.718369 | + | 0.695663i | \(0.755111\pi\) | |||||||
\(312\) | −2.48468e14 | −4.75795 | ||||||||
\(313\) | 2.82026e13 | 0.530634 | 0.265317 | − | 0.964161i | \(-0.414523\pi\) | ||||
0.265317 | + | 0.964161i | \(0.414523\pi\) | |||||||
\(314\) | −8.15120e13 | −1.50698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.20108e13 | 1.10710 | ||||||||
\(317\) | −2.56938e13 | −0.450819 | −0.225410 | − | 0.974264i | \(-0.572372\pi\) | ||||
−0.225410 | + | 0.974264i | \(0.572372\pi\) | |||||||
\(318\) | −2.17367e14 | −3.74840 | ||||||||
\(319\) | −3.19763e12 | −0.0541976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.68771e13 | −1.25898 | ||||||||
\(322\) | 3.83179e13 | 0.616872 | ||||||||
\(323\) | −1.00109e13 | −0.158439 | ||||||||
\(324\) | −1.93890e14 | −3.01688 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.05569e14 | −1.58797 | ||||||||
\(327\) | 1.43458e14 | 2.12184 | ||||||||
\(328\) | 4.48571e13 | 0.652417 | ||||||||
\(329\) | −3.14824e12 | −0.0450288 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.14309e13 | −0.849831 | −0.424916 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424916 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(332\) | −1.67258e14 | −2.27576 | ||||||||
\(333\) | 3.47925e13 | 0.465632 | ||||||||
\(334\) | 2.52358e14 | 3.32210 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.25499e13 | −1.05160 | ||||||||
\(337\) | −1.35566e14 | −1.69898 | −0.849488 | − | 0.527608i | \(-0.823089\pi\) | ||||
−0.849488 | + | 0.527608i | \(0.823089\pi\) | |||||||
\(338\) | 1.92703e14 | 2.37600 | ||||||||
\(339\) | 1.18540e14 | 1.43803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.01715e14 | 1.19463 | ||||||||
\(342\) | −2.60242e13 | −0.300770 | ||||||||
\(343\) | 5.90945e13 | 0.672093 | ||||||||
\(344\) | −1.60285e14 | −1.79400 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.57452e13 | 0.279111 | ||||||||
\(347\) | 2.88020e13 | 0.307334 | 0.153667 | − | 0.988123i | \(-0.450892\pi\) | ||||
0.153667 | + | 0.988123i | \(0.450892\pi\) | |||||||
\(348\) | −2.35052e13 | −0.246876 | ||||||||
\(349\) | 3.70742e13 | 0.383294 | 0.191647 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191647 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.02896e14 | 1.03089 | ||||||||
\(352\) | 1.22329e14 | 1.20655 | ||||||||
\(353\) | 5.64627e13 | 0.548278 | 0.274139 | − | 0.961690i | \(-0.411607\pi\) | ||||
0.274139 | + | 0.961690i | \(0.411607\pi\) | |||||||
\(354\) | −2.79014e13 | −0.266753 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.46040e14 | 1.35362 | ||||||||
\(357\) | −1.96989e13 | −0.179791 | ||||||||
\(358\) | −1.60316e14 | −1.44086 | ||||||||
\(359\) | −1.96868e14 | −1.74243 | −0.871217 | − | 0.490899i | \(-0.836668\pi\) | ||||
−0.871217 | + | 0.490899i | \(0.836668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.98027e13 | −0.856747 | ||||||||
\(362\) | 9.23537e12 | 0.0780831 | ||||||||
\(363\) | −8.54954e13 | −0.711961 | ||||||||
\(364\) | 1.60387e14 | 1.31556 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.35235e13 | 0.187222 | ||||||||
\(367\) | 1.00444e14 | 0.787514 | 0.393757 | − | 0.919214i | \(-0.371175\pi\) | ||||
0.393757 | + | 0.919214i | \(0.371175\pi\) | |||||||
\(368\) | −2.94221e14 | −2.27253 | ||||||||
\(369\) | 1.39856e13 | 0.106423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.24065e13 | 0.608703 | ||||||||
\(372\) | 7.47684e14 | 5.44167 | ||||||||
\(373\) | 7.09849e13 | 0.509058 | 0.254529 | − | 0.967065i | \(-0.418079\pi\) | ||||
0.254529 | + | 0.967065i | \(0.418079\pi\) | |||||||
\(374\) | 6.97090e13 | 0.492600 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.80970e13 | 0.330054 | ||||||||
\(377\) | 1.90437e13 | 0.128788 | ||||||||
\(378\) | 6.80182e13 | 0.453336 | ||||||||
\(379\) | 6.79976e13 | 0.446661 | 0.223330 | − | 0.974743i | \(-0.428307\pi\) | ||||
0.223330 | + | 0.974743i | \(0.428307\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.32982e13 | 0.403928 | ||||||||
\(382\) | −3.71750e14 | −2.33831 | ||||||||
\(383\) | −1.89007e14 | −1.17188 | −0.585942 | − | 0.810353i | \(-0.699275\pi\) | ||||
−0.585942 | + | 0.810353i | \(0.699275\pi\) | |||||||
\(384\) | 1.30413e13 | 0.0797076 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.64344e14 | −1.57014 | ||||||||
\(387\) | −4.99741e13 | −0.292641 | ||||||||
\(388\) | 5.62070e14 | 3.24501 | ||||||||
\(389\) | −2.90163e14 | −1.65165 | −0.825826 | − | 0.563924i | \(-0.809291\pi\) | ||||
−0.825826 | + | 0.563924i | \(0.809291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.02100e13 | −0.388532 | ||||||||
\(392\) | −4.20271e14 | −2.29328 | ||||||||
\(393\) | −1.49632e14 | −0.805127 | ||||||||
\(394\) | 3.00275e14 | 1.59327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.28276e14 | 0.661945 | ||||||||
\(397\) | 5.15115e13 | 0.262154 | 0.131077 | − | 0.991372i | \(-0.458157\pi\) | ||||
0.131077 | + | 0.991372i | \(0.458157\pi\) | |||||||
\(398\) | 3.47328e14 | 1.74334 | ||||||||
\(399\) | 3.28368e13 | 0.162559 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.11012e14 | −0.534657 | −0.267329 | − | 0.963605i | \(-0.586141\pi\) | ||||
−0.267329 | + | 0.963605i | \(0.586141\pi\) | |||||||
\(402\) | −4.26426e14 | −2.02582 | ||||||||
\(403\) | −6.05768e14 | −2.83876 | ||||||||
\(404\) | 5.93346e14 | 2.74291 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.25886e13 | 0.0566349 | ||||||||
\(407\) | 1.55351e14 | 0.689517 | ||||||||
\(408\) | 3.00949e14 | 1.31784 | ||||||||
\(409\) | −1.92951e14 | −0.833623 | −0.416811 | − | 0.908993i | \(-0.636852\pi\) | ||||
−0.416811 | + | 0.908993i | \(0.636852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.16629e13 | 0.133174 | ||||||||
\(412\) | 4.69894e14 | 1.95014 | ||||||||
\(413\) | 1.05778e13 | 0.0433180 | ||||||||
\(414\) | −1.82517e14 | −0.737565 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.28538e14 | −2.86707 | ||||||||
\(417\) | −2.57356e14 | −0.999508 | ||||||||
\(418\) | −1.16200e14 | −0.445386 | ||||||||
\(419\) | 2.28750e14 | 0.865336 | 0.432668 | − | 0.901553i | \(-0.357572\pi\) | ||||
0.432668 | + | 0.901553i | \(0.357572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00332e14 | −1.47526 | −0.737630 | − | 0.675205i | \(-0.764055\pi\) | ||||
−0.737630 | + | 0.675205i | \(0.764055\pi\) | |||||||
\(422\) | 9.56816e13 | 0.348024 | ||||||||
\(423\) | 1.49958e13 | 0.0538389 | ||||||||
\(424\) | −1.25896e15 | −4.46169 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.50672e14 | 2.59237 | ||||||||
\(427\) | −8.91803e12 | −0.0304030 | ||||||||
\(428\) | −7.58132e14 | −2.55155 | ||||||||
\(429\) | −3.45899e14 | −1.14930 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.29757e14 | 0.420250 | 0.210125 | − | 0.977675i | \(-0.432613\pi\) | ||||
0.210125 | + | 0.977675i | \(0.432613\pi\) | |||||||
\(432\) | −5.22271e14 | −1.67007 | ||||||||
\(433\) | 3.09354e14 | 0.976725 | 0.488363 | − | 0.872641i | \(-0.337594\pi\) | ||||
0.488363 | + | 0.872641i | \(0.337594\pi\) | |||||||
\(434\) | −4.00435e14 | −1.24835 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.41473e15 | 4.30028 | ||||||||
\(437\) | 1.17035e14 | 0.351293 | ||||||||
\(438\) | 9.83334e14 | 2.91470 | ||||||||
\(439\) | −6.15652e13 | −0.180211 | −0.0901054 | − | 0.995932i | \(-0.528720\pi\) | ||||
−0.0901054 | + | 0.995932i | \(0.528720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.31033e14 | −0.374083 | ||||||||
\(442\) | −4.15156e14 | −1.17055 | ||||||||
\(443\) | 2.42894e13 | 0.0676389 | 0.0338194 | − | 0.999428i | \(-0.489233\pi\) | ||||
0.0338194 | + | 0.999428i | \(0.489233\pi\) | |||||||
\(444\) | 1.14196e15 | 3.14082 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.97146e14 | −0.797311 | ||||||||
\(447\) | 3.99636e14 | 1.05919 | ||||||||
\(448\) | −1.45631e14 | −0.381263 | ||||||||
\(449\) | 6.65728e14 | 1.72164 | 0.860820 | − | 0.508910i | \(-0.169951\pi\) | ||||
0.860820 | + | 0.508910i | \(0.169951\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24468e13 | 0.157594 | ||||||||
\(452\) | 1.16900e15 | 2.91442 | ||||||||
\(453\) | 6.27160e14 | 1.54468 | ||||||||
\(454\) | −3.26999e14 | −0.795681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.01661e14 | −1.19153 | ||||||||
\(457\) | −6.99716e14 | −1.64204 | −0.821018 | − | 0.570902i | \(-0.806594\pi\) | ||||
−0.821018 | + | 0.570902i | \(0.806594\pi\) | |||||||
\(458\) | −4.06192e14 | −0.941827 | ||||||||
\(459\) | −1.24630e14 | −0.285531 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.43320e14 | 0.767971 | 0.383985 | − | 0.923339i | \(-0.374551\pi\) | ||||
0.383985 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(462\) | −2.28652e14 | −0.505410 | ||||||||
\(463\) | −3.77708e14 | −0.825012 | −0.412506 | − | 0.910955i | \(-0.635346\pi\) | ||||
−0.412506 | + | 0.910955i | \(0.635346\pi\) | |||||||
\(464\) | −9.66603e13 | −0.208641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.66368e14 | −1.82633 | ||||||||
\(467\) | 5.01733e14 | 1.04527 | 0.522637 | − | 0.852555i | \(-0.324948\pi\) | ||||
0.522637 | + | 0.852555i | \(0.324948\pi\) | |||||||
\(468\) | −7.63957e14 | −1.57296 | ||||||||
\(469\) | 1.61663e14 | 0.328972 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.89897e14 | −0.973844 | ||||||||
\(472\) | −1.61601e14 | −0.317513 | ||||||||
\(473\) | −2.23138e14 | −0.433348 | ||||||||
\(474\) | 5.26498e14 | 1.01068 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.94263e14 | −0.364378 | ||||||||
\(477\) | −3.92520e14 | −0.727798 | ||||||||
\(478\) | 1.55016e14 | 0.284134 | ||||||||
\(479\) | 9.56649e14 | 1.73343 | 0.866717 | − | 0.498800i | \(-0.166226\pi\) | ||||
0.866717 | + | 0.498800i | \(0.166226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.25204e14 | −1.63847 | ||||||||
\(482\) | 2.28596e14 | 0.400231 | ||||||||
\(483\) | 2.30295e14 | 0.398635 | ||||||||
\(484\) | −8.43122e14 | −1.44292 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.91890e14 | −1.49215 | ||||||||
\(487\) | −1.81856e14 | −0.300828 | −0.150414 | − | 0.988623i | \(-0.548061\pi\) | ||||
−0.150414 | + | 0.988623i | \(0.548061\pi\) | |||||||
\(488\) | 1.36244e14 | 0.222848 | ||||||||
\(489\) | −6.34485e14 | −1.02618 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.28536e14 | 1.46842 | 0.734210 | − | 0.678922i | \(-0.237553\pi\) | ||||
0.734210 | + | 0.678922i | \(0.237553\pi\) | |||||||
\(492\) | 4.59035e14 | 0.717856 | ||||||||
\(493\) | −2.30661e13 | −0.0356711 | ||||||||
\(494\) | 6.92037e14 | 1.05835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.07470e15 | 4.59889 | ||||||||
\(497\) | −2.84589e14 | −0.420976 | ||||||||
\(498\) | −1.42009e15 | −2.07756 | ||||||||
\(499\) | 1.10604e15 | 1.60036 | 0.800178 | − | 0.599763i | \(-0.204739\pi\) | ||||
0.800178 | + | 0.599763i | \(0.204739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.51670e15 | 2.14681 | ||||||||
\(502\) | 9.96177e14 | 1.39465 | ||||||||
\(503\) | 1.07467e15 | 1.48816 | 0.744081 | − | 0.668089i | \(-0.232888\pi\) | ||||
0.744081 | + | 0.668089i | \(0.232888\pi\) | |||||||
\(504\) | −2.96594e14 | −0.406251 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.14950e14 | −1.09220 | ||||||||
\(507\) | 1.15817e15 | 1.53542 | ||||||||
\(508\) | 6.24222e14 | 0.818632 | ||||||||
\(509\) | −1.50116e15 | −1.94750 | −0.973752 | − | 0.227610i | \(-0.926909\pi\) | ||||
−0.973752 | + | 0.227610i | \(0.926909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.72793e14 | −0.473318 | ||||||||
\(512\) | −1.43474e15 | −1.80214 | ||||||||
\(513\) | 2.07750e14 | 0.258163 | ||||||||
\(514\) | −2.96299e12 | −0.00364278 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.64024e15 | −1.97395 | ||||||||
\(517\) | 6.69571e13 | 0.0797258 | ||||||||
\(518\) | −6.11593e14 | −0.720525 | ||||||||
\(519\) | 1.54732e14 | 0.180368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.31060e13 | −0.0948473 | −0.0474237 | − | 0.998875i | \(-0.515101\pi\) | ||||
−0.0474237 | + | 0.998875i | \(0.515101\pi\) | |||||||
\(522\) | −5.99622e13 | −0.0677158 | ||||||||
\(523\) | 9.42223e14 | 1.05292 | 0.526459 | − | 0.850201i | \(-0.323519\pi\) | ||||
0.526459 | + | 0.850201i | \(0.323519\pi\) | |||||||
\(524\) | −1.47561e15 | −1.63173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.00394e15 | 1.08715 | ||||||||
\(527\) | 7.33717e14 | 0.786267 | ||||||||
\(528\) | 1.75568e15 | 1.86191 | ||||||||
\(529\) | −1.32002e14 | −0.138540 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.03841e13 | −0.0517933 | ||||||||
\(532\) | 3.23824e14 | 0.329454 | ||||||||
\(533\) | −3.71906e14 | −0.374485 | ||||||||
\(534\) | 1.23994e15 | 1.23573 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.46979e15 | −2.41131 | ||||||||
\(537\) | −9.63519e14 | −0.931112 | ||||||||
\(538\) | −3.19133e15 | −3.05259 | ||||||||
\(539\) | −5.85071e14 | −0.553950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.18229e15 | 1.09683 | 0.548416 | − | 0.836206i | \(-0.315231\pi\) | ||||
0.548416 | + | 0.836206i | \(0.315231\pi\) | |||||||
\(542\) | −9.50410e14 | −0.872800 | ||||||||
\(543\) | 5.55056e13 | 0.0504589 | ||||||||
\(544\) | 8.82418e14 | 0.794110 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.36175e15 | 1.20099 | ||||||||
\(547\) | −1.57701e15 | −1.37691 | −0.688453 | − | 0.725281i | \(-0.741710\pi\) | ||||
−0.688453 | + | 0.725281i | \(0.741710\pi\) | |||||||
\(548\) | 3.12247e14 | 0.269902 | ||||||||
\(549\) | 4.24785e13 | 0.0363514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.84496e13 | 0.0322521 | ||||||||
\(552\) | −3.51831e15 | −2.92193 | ||||||||
\(553\) | −1.99601e14 | −0.164125 | ||||||||
\(554\) | −2.53309e15 | −2.06228 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.53795e15 | −2.02568 | ||||||||
\(557\) | −4.53070e14 | −0.358065 | −0.179033 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179033 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(558\) | 1.90736e15 | 1.49260 | ||||||||
\(559\) | 1.32891e15 | 1.02975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.18959e14 | 0.318329 | ||||||||
\(562\) | 3.95241e15 | 2.97381 | ||||||||
\(563\) | −4.23450e13 | −0.0315505 | −0.0157752 | − | 0.999876i | \(-0.505022\pi\) | ||||
−0.0157752 | + | 0.999876i | \(0.505022\pi\) | |||||||
\(564\) | 4.92189e14 | 0.363159 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.27444e14 | 0.526392 | ||||||||
\(567\) | 6.24097e14 | 0.447245 | ||||||||
\(568\) | 4.34777e15 | 3.08568 | ||||||||
\(569\) | −9.72594e14 | −0.683619 | −0.341810 | − | 0.939769i | \(-0.611040\pi\) | ||||
−0.341810 | + | 0.939769i | \(0.611040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.07663e15 | −1.43173 | −0.715863 | − | 0.698241i | \(-0.753966\pi\) | ||||
−0.715863 | + | 0.698241i | \(0.753966\pi\) | |||||||
\(572\) | −3.41112e15 | −2.32927 | ||||||||
\(573\) | −2.23426e15 | −1.51107 | ||||||||
\(574\) | −2.45844e14 | −0.164681 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.93671e14 | 0.455858 | ||||||||
\(577\) | −2.62999e15 | −1.71194 | −0.855968 | − | 0.517028i | \(-0.827038\pi\) | ||||
−0.855968 | + | 0.517028i | \(0.827038\pi\) | |||||||
\(578\) | −2.36671e15 | −1.52596 | ||||||||
\(579\) | −1.58874e15 | −1.01466 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.38371e14 | 0.337375 | ||||||||
\(582\) | 4.77221e15 | 2.96240 | ||||||||
\(583\) | −1.75263e15 | −1.07774 | ||||||||
\(584\) | 5.69531e15 | 3.46934 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.82420e15 | −1.09052 | ||||||||
\(587\) | 2.89275e15 | 1.71317 | 0.856587 | − | 0.516003i | \(-0.172581\pi\) | ||||
0.856587 | + | 0.516003i | \(0.172581\pi\) | |||||||
\(588\) | −4.30075e15 | −2.52330 | ||||||||
\(589\) | −1.22306e15 | −0.710906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.80469e15 | 1.02960 | ||||||||
\(592\) | 4.69606e15 | 2.65439 | ||||||||
\(593\) | 1.15734e15 | 0.648125 | 0.324063 | − | 0.946036i | \(-0.394951\pi\) | ||||
0.324063 | + | 0.946036i | \(0.394951\pi\) | |||||||
\(594\) | −1.44662e15 | −0.802654 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.94106e15 | 2.14663 | ||||||||
\(597\) | 2.08748e15 | 1.12659 | ||||||||
\(598\) | 4.85349e15 | 2.59536 | ||||||||
\(599\) | 2.42056e14 | 0.128253 | 0.0641265 | − | 0.997942i | \(-0.479574\pi\) | ||||
0.0641265 | + | 0.997942i | \(0.479574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.08465e15 | −1.60471 | −0.802354 | − | 0.596848i | \(-0.796419\pi\) | ||||
−0.802354 | + | 0.596848i | \(0.796419\pi\) | |||||||
\(602\) | 8.78460e14 | 0.452836 | ||||||||
\(603\) | −7.70035e14 | −0.393337 | ||||||||
\(604\) | 6.18480e15 | 3.13057 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.03776e15 | 2.50402 | ||||||||
\(607\) | −2.71223e15 | −1.33595 | −0.667973 | − | 0.744186i | \(-0.732838\pi\) | ||||
−0.667973 | + | 0.744186i | \(0.732838\pi\) | |||||||
\(608\) | −1.47093e15 | −0.717997 | ||||||||
\(609\) | 7.56589e13 | 0.0365987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.98768e14 | −0.189449 | ||||||||
\(612\) | 9.25318e14 | 0.435671 | ||||||||
\(613\) | 1.80466e15 | 0.842097 | 0.421049 | − | 0.907038i | \(-0.361662\pi\) | ||||
0.421049 | + | 0.907038i | \(0.361662\pi\) | |||||||
\(614\) | −1.71963e15 | −0.795258 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.32431e15 | −0.601585 | ||||||||
\(617\) | −4.28183e14 | −0.192780 | −0.0963898 | − | 0.995344i | \(-0.530730\pi\) | ||||
−0.0963898 | + | 0.995344i | \(0.530730\pi\) | |||||||
\(618\) | 3.98960e15 | 1.78030 | ||||||||
\(619\) | 2.39110e15 | 1.05754 | 0.528772 | − | 0.848764i | \(-0.322653\pi\) | ||||
0.528772 | + | 0.848764i | \(0.322653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.45702e15 | 0.633083 | ||||||||
\(622\) | −6.17215e15 | −2.65821 | ||||||||
\(623\) | −4.70076e14 | −0.200671 | ||||||||
\(624\) | −1.04561e16 | −4.42439 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36138e15 | 0.981763 | ||||||||
\(627\) | −6.98376e14 | −0.287818 | ||||||||
\(628\) | −4.83117e15 | −1.97367 | ||||||||
\(629\) | 1.12062e15 | 0.453818 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.26028e15 | 1.29746 | 0.648730 | − | 0.761019i | \(-0.275301\pi\) | ||||
0.648730 | + | 0.761019i | \(0.275301\pi\) | |||||||
\(632\) | 3.04939e15 | 1.20301 | ||||||||
\(633\) | 5.75057e14 | 0.224901 | ||||||||
\(634\) | −2.15132e15 | −0.834093 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.28832e16 | −4.90921 | ||||||||
\(637\) | 3.48443e15 | 1.31633 | ||||||||
\(638\) | −2.67735e14 | −0.100275 | ||||||||
\(639\) | 1.35556e15 | 0.503342 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.32104e15 | −0.847157 | −0.423579 | − | 0.905859i | \(-0.639226\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639226\pi\) | |||||||
\(642\) | −6.43686e15 | −2.32933 | ||||||||
\(643\) | 2.55397e15 | 0.916336 | 0.458168 | − | 0.888866i | \(-0.348506\pi\) | ||||
0.458168 | + | 0.888866i | \(0.348506\pi\) | |||||||
\(644\) | 2.27108e15 | 0.807906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.38208e14 | −0.293139 | ||||||||
\(647\) | 1.70408e15 | 0.590902 | 0.295451 | − | 0.955358i | \(-0.404530\pi\) | ||||
0.295451 | + | 0.955358i | \(0.404530\pi\) | |||||||
\(648\) | −9.53458e15 | −3.27823 | ||||||||
\(649\) | −2.24969e14 | −0.0766966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40666e15 | −0.806713 | ||||||||
\(652\) | −6.25704e15 | −2.07973 | ||||||||
\(653\) | 2.20439e15 | 0.726552 | 0.363276 | − | 0.931682i | \(-0.381658\pi\) | ||||
0.363276 | + | 0.931682i | \(0.381658\pi\) | |||||||
\(654\) | 1.20116e16 | 3.92576 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.88769e15 | 0.606679 | ||||||||
\(657\) | 1.77570e15 | 0.565925 | ||||||||
\(658\) | −2.63600e14 | −0.0833111 | ||||||||
\(659\) | 1.97759e14 | 0.0619821 | 0.0309910 | − | 0.999520i | \(-0.490134\pi\) | ||||
0.0309910 | + | 0.999520i | \(0.490134\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.43414e15 | −1.05855 | −0.529274 | − | 0.848451i | \(-0.677536\pi\) | ||||
−0.529274 | + | 0.848451i | \(0.677536\pi\) | |||||||
\(662\) | −5.14356e15 | −1.57233 | ||||||||
\(663\) | −2.49514e15 | −0.756433 | ||||||||
\(664\) | −8.22492e15 | −2.47290 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.91315e15 | 0.861499 | ||||||||
\(667\) | 2.69660e14 | 0.0790905 | ||||||||
\(668\) | 1.49571e16 | 4.35089 | ||||||||
\(669\) | −1.78588e15 | −0.515239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.89670e14 | 0.0538299 | ||||||||
\(672\) | −2.89441e15 | −0.814760 | ||||||||
\(673\) | −2.01250e15 | −0.561892 | −0.280946 | − | 0.959724i | \(-0.590648\pi\) | ||||
−0.280946 | + | 0.959724i | \(0.590648\pi\) | |||||||
\(674\) | −1.13509e16 | −3.14340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.14214e16 | 3.11181 | ||||||||
\(677\) | 1.01903e15 | 0.275392 | 0.137696 | − | 0.990475i | \(-0.456030\pi\) | ||||
0.137696 | + | 0.990475i | \(0.456030\pi\) | |||||||
\(678\) | 9.92530e15 | 2.66060 | ||||||||
\(679\) | −1.80920e15 | −0.481064 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.96530e15 | −0.514186 | ||||||||
\(682\) | 8.51648e15 | 2.21027 | ||||||||
\(683\) | −2.86885e15 | −0.738575 | −0.369287 | − | 0.929315i | \(-0.620398\pi\) | ||||
−0.369287 | + | 0.929315i | \(0.620398\pi\) | |||||||
\(684\) | −1.54244e15 | −0.393913 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.94793e15 | 1.24349 | ||||||||
\(687\) | −2.44126e15 | −0.608629 | ||||||||
\(688\) | −6.74517e15 | −1.66823 | ||||||||
\(689\) | 1.04379e16 | 2.56099 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79931e15 | −0.434487 | −0.217243 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217243 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(692\) | 1.52590e15 | 0.365547 | ||||||||
\(693\) | −4.12897e14 | −0.0981316 | ||||||||
\(694\) | 2.41157e15 | 0.568621 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.15587e15 | −0.268262 | ||||||||
\(697\) | 4.50460e14 | 0.103723 | ||||||||
\(698\) | 3.10420e15 | 0.709160 | ||||||||
\(699\) | −5.20697e15 | −1.18021 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.99337e15 | 0.667899 | 0.333949 | − | 0.942591i | \(-0.391619\pi\) | ||||
0.333949 | + | 0.942591i | \(0.391619\pi\) | |||||||
\(702\) | 8.61543e15 | 1.90732 | ||||||||
\(703\) | −1.86800e15 | −0.410321 | ||||||||
\(704\) | 3.09729e15 | 0.675045 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.72758e15 | 1.01441 | ||||||||
\(707\) | −1.90987e15 | −0.406629 | ||||||||
\(708\) | −1.65370e15 | −0.349361 | ||||||||
\(709\) | 2.74187e15 | 0.574769 | 0.287384 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287384 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.50744e14 | 0.196237 | ||||||||
\(712\) | 7.18154e15 | 1.47088 | ||||||||
\(713\) | −8.57770e15 | −1.74333 | ||||||||
\(714\) | −1.64938e15 | −0.332644 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.50185e15 | −1.88706 | ||||||||
\(717\) | 9.31666e14 | 0.183614 | ||||||||
\(718\) | −1.64836e16 | −3.22380 | ||||||||
\(719\) | −4.38021e15 | −0.850131 | −0.425065 | − | 0.905163i | \(-0.639749\pi\) | ||||
−0.425065 | + | 0.905163i | \(0.639749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51250e15 | −0.289103 | ||||||||
\(722\) | −8.35640e15 | −1.58513 | ||||||||
\(723\) | 1.37389e15 | 0.258637 | ||||||||
\(724\) | 5.47375e14 | 0.102264 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.15846e15 | −1.31725 | ||||||||
\(727\) | −6.60205e15 | −1.20570 | −0.602851 | − | 0.797854i | \(-0.705969\pi\) | ||||
−0.602851 | + | 0.797854i | \(0.705969\pi\) | |||||||
\(728\) | 7.88704e15 | 1.42952 | ||||||||
\(729\) | 1.56084e15 | 0.280773 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.60960e15 | −0.285216 | ||||||||
\(732\) | 1.39422e15 | 0.245201 | ||||||||
\(733\) | 8.22795e15 | 1.43622 | 0.718108 | − | 0.695932i | \(-0.245008\pi\) | ||||
0.718108 | + | 0.695932i | \(0.245008\pi\) | |||||||
\(734\) | 8.41006e15 | 1.45704 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.03161e16 | −1.76071 | ||||||||
\(737\) | −3.43826e15 | −0.582462 | ||||||||
\(738\) | 1.17101e15 | 0.196902 | ||||||||
\(739\) | −1.10770e16 | −1.84875 | −0.924376 | − | 0.381483i | \(-0.875414\pi\) | ||||
−0.924376 | + | 0.381483i | \(0.875414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.15923e15 | 0.683931 | ||||||||
\(742\) | 6.89984e15 | 1.12620 | ||||||||
\(743\) | 3.86160e15 | 0.625646 | 0.312823 | − | 0.949811i | \(-0.398725\pi\) | ||||
0.312823 | + | 0.949811i | \(0.398725\pi\) | |||||||
\(744\) | 3.67675e16 | 5.91307 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.94352e15 | 0.941846 | ||||||||
\(747\) | −2.56438e15 | −0.403384 | ||||||||
\(748\) | 4.13161e15 | 0.645150 | ||||||||
\(749\) | 2.44029e15 | 0.378260 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.05947e15 | 0.161834 | 0.0809168 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809168 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(752\) | 2.02403e15 | 0.306915 | ||||||||
\(753\) | 5.98714e15 | 0.901254 | ||||||||
\(754\) | 1.59452e15 | 0.238280 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.03140e15 | 0.593726 | ||||||||
\(757\) | 7.04375e15 | 1.02986 | 0.514928 | − | 0.857233i | \(-0.327818\pi\) | ||||
0.514928 | + | 0.857233i | \(0.327818\pi\) | |||||||
\(758\) | 5.69339e15 | 0.826400 | ||||||||
\(759\) | −4.89794e15 | −0.705804 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.63598e15 | 0.516424 | 0.258212 | − | 0.966088i | \(-0.416867\pi\) | ||||
0.258212 | + | 0.966088i | \(0.416867\pi\) | |||||||
\(762\) | 5.29991e15 | 0.747337 | ||||||||
\(763\) | −4.55374e15 | −0.637505 | ||||||||
\(764\) | −2.20334e16 | −3.06245 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.58254e16 | −2.16819 | ||||||||
\(767\) | 1.33982e15 | 0.182251 | ||||||||
\(768\) | −8.30398e15 | −1.12150 | ||||||||
\(769\) | −5.34829e15 | −0.717167 | −0.358583 | − | 0.933498i | \(-0.616740\pi\) | ||||
−0.358583 | + | 0.933498i | \(0.616740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.78079e13 | −0.00235404 | ||||||||
\(772\) | −1.56675e16 | −2.05639 | ||||||||
\(773\) | −8.06669e15 | −1.05126 | −0.525628 | − | 0.850715i | \(-0.676169\pi\) | ||||
−0.525628 | + | 0.850715i | \(0.676169\pi\) | |||||||
\(774\) | −4.18429e15 | −0.541436 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.76399e16 | 3.52612 | ||||||||
\(777\) | −3.67575e15 | −0.465618 | ||||||||
\(778\) | −2.42951e16 | −3.05584 | ||||||||
\(779\) | −7.50886e14 | −0.0937816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.05266e15 | 0.745359 | ||||||||
\(782\) | −5.87863e15 | −0.718851 | ||||||||
\(783\) | 4.78674e14 | 0.0581233 | ||||||||
\(784\) | −1.76859e16 | −2.13250 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.25285e16 | −1.48962 | ||||||||
\(787\) | 8.56068e15 | 1.01076 | 0.505379 | − | 0.862897i | \(-0.331353\pi\) | ||||
0.505379 | + | 0.862897i | \(0.331353\pi\) | |||||||
\(788\) | 1.77971e16 | 2.08668 | ||||||||
\(789\) | 6.03383e15 | 0.702537 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.76279e15 | −0.432056 | ||||||||
\(792\) | 6.30799e15 | 0.719288 | ||||||||
\(793\) | −1.12959e15 | −0.127914 | ||||||||
\(794\) | 4.31302e15 | 0.485030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.05859e16 | 2.28323 | ||||||||
\(797\) | 1.47001e16 | 1.61919 | 0.809596 | − | 0.586987i | \(-0.199686\pi\) | ||||
0.809596 | + | 0.586987i | \(0.199686\pi\) | |||||||
\(798\) | 2.74940e15 | 0.300761 | ||||||||
\(799\) | 4.82995e14 | 0.0524729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.23907e15 | 0.239933 | ||||||||
\(802\) | −9.29494e15 | −0.989208 | ||||||||
\(803\) | 7.92861e15 | 0.838033 | ||||||||
\(804\) | −2.52740e16 | −2.65317 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.07205e16 | −5.25219 | ||||||||
\(807\) | −1.91803e16 | −1.97265 | ||||||||
\(808\) | 2.91779e16 | 2.98052 | ||||||||
\(809\) | 5.20792e15 | 0.528382 | 0.264191 | − | 0.964470i | \(-0.414895\pi\) | ||||
0.264191 | + | 0.964470i | \(0.414895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.95571e16 | 1.95745 | 0.978724 | − | 0.205183i | \(-0.0657789\pi\) | ||||
0.978724 | + | 0.205183i | \(0.0657789\pi\) | |||||||
\(812\) | 7.46119e14 | 0.0741737 | ||||||||
\(813\) | −5.71207e15 | −0.564022 | ||||||||
\(814\) | 1.30074e16 | 1.27573 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.26646e16 | 1.22545 | ||||||||
\(817\) | 2.68310e15 | 0.257879 | ||||||||
\(818\) | −1.61557e16 | −1.54235 | ||||||||
\(819\) | 2.45904e15 | 0.233187 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.02440e16 | 0.958476 | 0.479238 | − | 0.877685i | \(-0.340913\pi\) | ||||
0.479238 | + | 0.877685i | \(0.340913\pi\) | |||||||
\(822\) | 2.65111e15 | 0.246396 | ||||||||
\(823\) | 1.40372e16 | 1.29593 | 0.647964 | − | 0.761671i | \(-0.275621\pi\) | ||||
0.647964 | + | 0.761671i | \(0.275621\pi\) | |||||||
\(824\) | 2.31071e16 | 2.11907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.85667e14 | 0.0801457 | ||||||||
\(827\) | −8.80160e14 | −0.0791191 | −0.0395596 | − | 0.999217i | \(-0.512595\pi\) | ||||
−0.0395596 | + | 0.999217i | \(0.512595\pi\) | |||||||
\(828\) | −1.08177e16 | −0.965976 | ||||||||
\(829\) | 4.54642e14 | 0.0403292 | 0.0201646 | − | 0.999797i | \(-0.493581\pi\) | ||||
0.0201646 | + | 0.999797i | \(0.493581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.52242e16 | −1.33269 | ||||||||
\(832\) | −1.84461e16 | −1.60408 | ||||||||
\(833\) | −4.22041e15 | −0.364592 | ||||||||
\(834\) | −2.15482e16 | −1.84926 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.88711e15 | −0.583314 | ||||||||
\(837\) | −1.52263e16 | −1.28116 | ||||||||
\(838\) | 1.91531e16 | 1.60102 | ||||||||
\(839\) | 1.32346e16 | 1.09906 | 0.549529 | − | 0.835474i | \(-0.314807\pi\) | ||||
0.549529 | + | 0.835474i | \(0.314807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.21119e16 | −0.992739 | ||||||||
\(842\) | −3.35195e16 | −2.72949 | ||||||||
\(843\) | 2.37545e16 | 1.92174 | ||||||||
\(844\) | 5.67099e15 | 0.455801 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.25558e15 | 0.0996113 | ||||||||
\(847\) | 2.71386e15 | 0.213908 | ||||||||
\(848\) | −5.29797e16 | −4.14889 | ||||||||
\(849\) | 4.37202e15 | 0.340166 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.31009e16 | −1.00621 | ||||||||
\(852\) | 4.44919e16 | 3.39519 | ||||||||
\(853\) | 2.60074e15 | 0.197186 | 0.0985932 | − | 0.995128i | \(-0.468566\pi\) | ||||
0.0985932 | + | 0.995128i | \(0.468566\pi\) | |||||||
\(854\) | −7.46700e14 | −0.0562507 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.72812e16 | −2.77258 | ||||||||
\(857\) | 1.68895e16 | 1.24802 | 0.624011 | − | 0.781415i | \(-0.285502\pi\) | ||||
0.624011 | + | 0.781415i | \(0.285502\pi\) | |||||||
\(858\) | −2.89619e16 | −2.12641 | ||||||||
\(859\) | 8.98241e15 | 0.655285 | 0.327643 | − | 0.944802i | \(-0.393746\pi\) | ||||
0.327643 | + | 0.944802i | \(0.393746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.47755e15 | −0.106420 | ||||||||
\(862\) | 1.08645e16 | 0.777534 | ||||||||
\(863\) | 1.16178e16 | 0.826164 | 0.413082 | − | 0.910694i | \(-0.364452\pi\) | ||||
0.413082 | + | 0.910694i | \(0.364452\pi\) | |||||||
\(864\) | −1.83122e16 | −1.29394 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.59020e16 | 1.80711 | ||||||||
\(867\) | −1.42242e16 | −0.986107 | ||||||||
\(868\) | −2.37335e16 | −1.63495 | ||||||||
\(869\) | 4.24514e15 | 0.290592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04768e16 | 1.38408 | ||||||||
\(872\) | 6.95694e16 | 4.67280 | ||||||||
\(873\) | 8.61761e15 | 0.575186 | ||||||||
\(874\) | 9.79928e15 | 0.649952 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.82817e16 | 3.81733 | ||||||||
\(877\) | −4.73202e15 | −0.307999 | −0.153999 | − | 0.988071i | \(-0.549215\pi\) | ||||
−0.153999 | + | 0.988071i | \(0.549215\pi\) | |||||||
\(878\) | −5.15481e15 | −0.333421 | ||||||||
\(879\) | −1.09636e16 | −0.704719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.81982e15 | 0.179000 | 0.0895002 | − | 0.995987i | \(-0.471473\pi\) | ||||
0.0895002 | + | 0.995987i | \(0.471473\pi\) | |||||||
\(882\) | −1.09713e16 | −0.692118 | ||||||||
\(883\) | −1.91741e16 | −1.20208 | −0.601038 | − | 0.799221i | \(-0.705246\pi\) | ||||
−0.601038 | + | 0.799221i | \(0.705246\pi\) | |||||||
\(884\) | −2.46061e16 | −1.53305 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.03373e15 | 0.125144 | ||||||||
\(887\) | −2.08389e15 | −0.127437 | −0.0637183 | − | 0.997968i | \(-0.520296\pi\) | ||||
−0.0637183 | + | 0.997968i | \(0.520296\pi\) | |||||||
\(888\) | 5.61559e16 | 3.41290 | ||||||||
\(889\) | −2.00926e15 | −0.121360 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.32734e16 | −0.791869 | ||||||||
\(892\) | −1.76117e16 | −1.04422 | ||||||||
\(893\) | −8.05119e14 | −0.0474435 | ||||||||
\(894\) | 3.34612e16 | 1.95968 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.13967e14 | −0.0239481 | ||||||||
\(897\) | 2.91700e16 | 1.67718 | ||||||||
\(898\) | 5.57409e16 | 3.18533 | ||||||||
\(899\) | −2.81803e15 | −0.160054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26426e16 | −0.709332 | ||||||||
\(902\) | 5.22863e15 | 0.291576 | ||||||||
\(903\) | 5.27965e15 | 0.292632 | ||||||||
\(904\) | 5.74857e16 | 3.16689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.25116e16 | 2.85792 | ||||||||
\(907\) | −3.20443e16 | −1.73345 | −0.866723 | − | 0.498791i | \(-0.833778\pi\) | ||||
−0.866723 | + | 0.498791i | \(0.833778\pi\) | |||||||
\(908\) | −1.93810e16 | −1.04209 | ||||||||
\(909\) | 9.09714e15 | 0.486187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.44282e15 | −0.445797 | −0.222898 | − | 0.974842i | \(-0.571552\pi\) | ||||
−0.222898 | + | 0.974842i | \(0.571552\pi\) | |||||||
\(912\) | −2.11110e16 | −1.10799 | ||||||||
\(913\) | −1.14501e16 | −0.597340 | ||||||||
\(914\) | −5.85867e16 | −3.03805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.40748e16 | −1.23349 | ||||||||
\(917\) | 4.74971e15 | 0.241900 | ||||||||
\(918\) | −1.04352e16 | −0.528281 | ||||||||
\(919\) | −1.08277e16 | −0.544880 | −0.272440 | − | 0.962173i | \(-0.587831\pi\) | ||||
−0.272440 | + | 0.962173i | \(0.587831\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.03352e16 | −0.513913 | ||||||||
\(922\) | 2.87460e16 | 1.42088 | ||||||||
\(923\) | −3.60470e16 | −1.77117 | ||||||||
\(924\) | −1.35521e16 | −0.661926 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.16252e16 | −1.52641 | ||||||||
\(927\) | 7.20438e15 | 0.345667 | ||||||||
\(928\) | −3.38916e15 | −0.161651 | ||||||||
\(929\) | −1.30338e16 | −0.617994 | −0.308997 | − | 0.951063i | \(-0.599993\pi\) | ||||
−0.308997 | + | 0.951063i | \(0.599993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.03513e15 | 0.329647 | ||||||||
\(932\) | −5.13491e16 | −2.39191 | ||||||||
\(933\) | −3.70954e16 | −1.71779 | ||||||||
\(934\) | 4.20098e16 | 1.93394 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.75677e16 | −1.70922 | ||||||||
\(937\) | 2.06679e16 | 0.934819 | 0.467410 | − | 0.884041i | \(-0.345187\pi\) | ||||
0.467410 | + | 0.884041i | \(0.345187\pi\) | |||||||
\(938\) | 1.35359e16 | 0.608656 | ||||||||
\(939\) | 1.41922e16 | 0.634436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48692e16 | −1.54063 | −0.770317 | − | 0.637661i | \(-0.779902\pi\) | ||||
−0.770317 | + | 0.637661i | \(0.779902\pi\) | |||||||
\(942\) | −4.10187e16 | −1.80178 | ||||||||
\(943\) | −5.26621e15 | −0.229977 | ||||||||
\(944\) | −6.80051e15 | −0.295254 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86832e16 | −0.801769 | ||||||||
\(947\) | 2.53080e15 | 0.107977 | 0.0539887 | − | 0.998542i | \(-0.482807\pi\) | ||||
0.0539887 | + | 0.998542i | \(0.482807\pi\) | |||||||
\(948\) | 3.12052e16 | 1.32368 | ||||||||
\(949\) | −4.72194e16 | −1.99139 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29297e16 | −0.539008 | ||||||||
\(952\) | −9.55293e15 | −0.395944 | ||||||||
\(953\) | 1.68411e16 | 0.693999 | 0.347000 | − | 0.937865i | \(-0.387201\pi\) | ||||
0.347000 | + | 0.937865i | \(0.387201\pi\) | |||||||
\(954\) | −3.28654e16 | −1.34655 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.18773e15 | 0.372126 | ||||||||
\(957\) | −1.60912e15 | −0.0647997 | ||||||||
\(958\) | 8.00995e16 | 3.20715 | ||||||||
\(959\) | −1.00507e15 | −0.0400122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.42312e16 | 2.52794 | ||||||||
\(962\) | −7.74666e16 | −3.03146 | ||||||||
\(963\) | −1.16236e16 | −0.452269 | ||||||||
\(964\) | 1.35488e16 | 0.524175 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.92825e16 | 0.737544 | ||||||||
\(967\) | 2.82761e16 | 1.07541 | 0.537705 | − | 0.843133i | \(-0.319292\pi\) | ||||
0.537705 | + | 0.843133i | \(0.319292\pi\) | |||||||
\(968\) | −4.14607e16 | −1.56791 | ||||||||
\(969\) | −5.03773e15 | −0.189432 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.55089e16 | 0.948386 | 0.474193 | − | 0.880421i | \(-0.342740\pi\) | ||||
0.474193 | + | 0.880421i | \(0.342740\pi\) | |||||||
\(972\) | −5.28618e16 | −1.95424 | ||||||||
\(973\) | 8.16918e15 | 0.300302 | ||||||||
\(974\) | −1.52266e16 | −0.556583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.73346e15 | 0.207225 | ||||||||
\(977\) | −5.16659e16 | −1.85688 | −0.928441 | − | 0.371480i | \(-0.878850\pi\) | ||||
−0.928441 | + | 0.371480i | \(0.878850\pi\) | |||||||
\(978\) | −5.31249e16 | −1.89861 | ||||||||
\(979\) | 9.99762e15 | 0.355297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16905e16 | 0.762236 | ||||||||
\(982\) | 7.77456e16 | 2.71683 | ||||||||
\(983\) | −1.06975e15 | −0.0371740 | −0.0185870 | − | 0.999827i | \(-0.505917\pi\) | ||||
−0.0185870 | + | 0.999827i | \(0.505917\pi\) | |||||||
\(984\) | 2.25731e16 | 0.780043 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.93131e15 | −0.0659976 | ||||||||
\(987\) | −1.58427e15 | −0.0538374 | ||||||||
\(988\) | 4.10167e16 | 1.38611 | ||||||||
\(989\) | 1.88175e16 | 0.632385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.05333e16 | 0.682423 | 0.341211 | − | 0.939987i | \(-0.389163\pi\) | ||||
0.341211 | + | 0.939987i | \(0.389163\pi\) | |||||||
\(992\) | 1.07807e17 | 3.56313 | ||||||||
\(993\) | −3.09134e16 | −1.01608 | ||||||||
\(994\) | −2.38284e16 | −0.778878 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.41678e16 | −2.72094 | ||||||||
\(997\) | 1.61931e16 | 0.520603 | 0.260301 | − | 0.965527i | \(-0.416178\pi\) | ||||
0.260301 | + | 0.965527i | \(0.416178\pi\) | |||||||
\(998\) | 9.26076e16 | 2.96093 | ||||||||
\(999\) | −2.32555e16 | −0.739461 |
(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 | 25.12.a.c.1.2 | 2 | ||
3.2 | odd | 2 | 225.12.a.h.1.1 | 2 | |||
5.2 | odd | 4 | 25.12.b.c.24.4 | 4 | |||
5.3 | odd | 4 | 25.12.b.c.24.1 | 4 | |||
5.4 | even | 2 | 5.12.a.b.1.1 | ✓ | 2 | ||
15.2 | even | 4 | 225.12.b.f.199.1 | 4 | |||
15.8 | even | 4 | 225.12.b.f.199.4 | 4 | |||
15.14 | odd | 2 | 45.12.a.d.1.2 | 2 | |||
20.19 | odd | 2 | 80.12.a.j.1.2 | 2 | |||
35.34 | odd | 2 | 245.12.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.12.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
25.12.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
25.12.b.c.24.1 | 4 | 5.3 | odd | 4 | |||
25.12.b.c.24.4 | 4 | 5.2 | odd | 4 | |||
45.12.a.d.1.2 | 2 | 15.14 | odd | 2 | |||
80.12.a.j.1.2 | 2 | 20.19 | odd | 2 | |||
225.12.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
225.12.b.f.199.1 | 4 | 15.2 | even | 4 | |||
225.12.b.f.199.4 | 4 | 15.8 | even | 4 | |||
245.12.a.b.1.1 | 2 | 35.34 | odd | 2 |