Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,12,Mod(24,25)]
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([1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(19.2085795140\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{151})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 75x^{2} + 1444 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Root | \(-6.14410 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.12.b.c.24.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 83.7292i | 1.85017i | 0.379757 | + | 0.925086i | \(0.376007\pi\) | ||||
−0.379757 | + | 0.925086i | \(0.623993\pi\) | |||||||
\(3\) | − 503.223i | − 1.19562i | −0.801638 | − | 0.597810i | \(-0.796038\pi\) | ||||
0.801638 | − | 0.597810i | \(-0.203962\pi\) | |||||||
\(4\) | −4962.58 | −2.42314 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 42134.4 | 2.21210 | ||||||||
\(7\) | − 15973.7i | − 0.359224i | −0.983738 | − | 0.179612i | \(-0.942516\pi\) | ||||
0.983738 | − | 0.179612i | \(-0.0574842\pi\) | |||||||
\(8\) | − 244036.i | − 2.63305i | ||||||||
\(9\) | −76086.0 | −0.429508 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 339729. | 0.636024 | 0.318012 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318012 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(12\) | 2.49728e6i | 2.89715i | ||||||||
\(13\) | 2.02328e6i | 1.51136i | 0.654941 | + | 0.755680i | \(0.272693\pi\) | ||||
−0.654941 | + | 0.755680i | \(0.727307\pi\) | |||||||
\(14\) | 1.33746e6 | 0.664626 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.02696e7 | 2.44846 | ||||||||
\(17\) | 2.45063e6i | 0.418610i | 0.977850 | + | 0.209305i | \(0.0671201\pi\) | ||||
−0.977850 | + | 0.209305i | \(0.932880\pi\) | |||||||
\(18\) | − 6.37062e6i | − 0.794663i | ||||||||
\(19\) | 4.08504e6 | 0.378487 | 0.189244 | − | 0.981930i | \(-0.439396\pi\) | ||||
0.189244 | + | 0.981930i | \(0.439396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.03830e6 | −0.429495 | ||||||||
\(22\) | 2.84453e7i | 1.17675i | ||||||||
\(23\) | 2.86497e7i | 0.928149i | 0.885796 | + | 0.464074i | \(0.153613\pi\) | ||||
−0.885796 | + | 0.464074i | \(0.846387\pi\) | |||||||
\(24\) | −1.22804e8 | −3.14813 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.69408e8 | −2.79628 | ||||||||
\(27\) | − 5.08562e7i | − 0.682092i | ||||||||
\(28\) | 7.92706e7i | 0.870448i | ||||||||
\(29\) | 9.41230e6 | 0.0852132 | 0.0426066 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426066 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.99399e8 | 1.87828 | 0.939141 | − | 0.343532i | \(-0.111623\pi\) | ||||
0.939141 | + | 0.343532i | \(0.111623\pi\) | |||||||
\(32\) | 3.60078e8i | 1.89702i | ||||||||
\(33\) | − 1.70959e8i | − 0.760443i | ||||||||
\(34\) | −2.05190e8 | −0.774500 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.77583e8 | 1.04076 | ||||||||
\(37\) | 4.57279e8i | 1.08411i | 0.840344 | + | 0.542053i | \(0.182353\pi\) | ||||
−0.840344 | + | 0.542053i | \(0.817647\pi\) | |||||||
\(38\) | 3.42037e8i | 0.700267i | ||||||||
\(39\) | 1.01816e9 | 1.80701 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.83814e8 | 0.247780 | 0.123890 | − | 0.992296i | \(-0.460463\pi\) | ||||
0.123890 | + | 0.992296i | \(0.460463\pi\) | |||||||
\(42\) | − 6.73041e8i | − 0.794640i | ||||||||
\(43\) | 6.56811e8i | 0.681340i | 0.940183 | + | 0.340670i | \(0.110654\pi\) | ||||
−0.940183 | + | 0.340670i | \(0.889346\pi\) | |||||||
\(44\) | −1.68594e9 | −1.54117 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.39882e9 | −1.71724 | ||||||||
\(47\) | 1.97090e8i | 0.125350i | 0.998034 | + | 0.0626752i | \(0.0199632\pi\) | ||||
−0.998034 | + | 0.0626752i | \(0.980037\pi\) | |||||||
\(48\) | − 5.16788e9i | − 2.92742i | ||||||||
\(49\) | 1.72217e9 | 0.870958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.23321e9 | 0.500498 | ||||||||
\(52\) | − 1.00407e10i | − 3.66223i | ||||||||
\(53\) | 5.15890e9i | 1.69449i | 0.531199 | + | 0.847247i | \(0.321742\pi\) | ||||
−0.531199 | + | 0.847247i | \(0.678258\pi\) | |||||||
\(54\) | 4.25815e9 | 1.26199 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.89815e9 | −0.945854 | ||||||||
\(57\) | − 2.05568e9i | − 0.452527i | ||||||||
\(58\) | 7.88085e8i | 0.157659i | ||||||||
\(59\) | 6.62200e8 | 0.120588 | 0.0602939 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602939 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.58296e8 | 0.0846351 | 0.0423176 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423176 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(62\) | 2.50684e10i | 3.47515i | ||||||||
\(63\) | 1.21537e9i | 0.154289i | ||||||||
\(64\) | −9.11694e9 | −1.06135 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.43143e10 | 1.40695 | ||||||||
\(67\) | − 1.01206e10i | − 0.915787i | −0.889007 | − | 0.457894i | \(-0.848604\pi\) | ||||
0.889007 | − | 0.457894i | \(-0.151396\pi\) | |||||||
\(68\) | − 1.21615e10i | − 1.01435i | ||||||||
\(69\) | 1.44172e10 | 1.10971 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.78161e10 | 1.17190 | 0.585952 | − | 0.810346i | \(-0.300721\pi\) | ||||
0.585952 | + | 0.810346i | \(0.300721\pi\) | |||||||
\(72\) | 1.85677e10i | 1.13091i | ||||||||
\(73\) | − 2.33380e10i | − 1.31761i | −0.752312 | − | 0.658807i | \(-0.771061\pi\) | ||||
0.752312 | − | 0.658807i | \(-0.228939\pi\) | |||||||
\(74\) | −3.82876e10 | −2.00578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.02724e10 | −0.917127 | ||||||||
\(77\) | − 5.42672e9i | − 0.228475i | ||||||||
\(78\) | 8.52498e10i | 3.34328i | ||||||||
\(79\) | −1.24957e10 | −0.456888 | −0.228444 | − | 0.973557i | \(-0.573364\pi\) | ||||
−0.228444 | + | 0.973557i | \(0.573364\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.90704e10 | −1.24503 | ||||||||
\(82\) | 1.53906e10i | 0.458436i | ||||||||
\(83\) | 3.37037e10i | 0.939179i | 0.882885 | + | 0.469589i | \(0.155598\pi\) | ||||
−0.882885 | + | 0.469589i | \(0.844402\pi\) | |||||||
\(84\) | 3.98908e10 | 1.04073 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.49943e10 | −1.26060 | ||||||||
\(87\) | − 4.73648e9i | − 0.101883i | ||||||||
\(88\) | − 8.29062e10i | − 1.67468i | ||||||||
\(89\) | −2.94282e10 | −0.558623 | −0.279311 | − | 0.960201i | \(-0.590106\pi\) | ||||
−0.279311 | + | 0.960201i | \(0.590106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23192e10 | 0.542916 | ||||||||
\(92\) | − 1.42177e11i | − 2.24903i | ||||||||
\(93\) | − 1.50664e11i | − 2.24571i | ||||||||
\(94\) | −1.65022e10 | −0.231920 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.81199e11 | 2.26811 | ||||||||
\(97\) | 1.13262e11i | 1.33918i | 0.742732 | + | 0.669588i | \(0.233529\pi\) | ||||
−0.742732 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(98\) | 1.44196e11i | 1.61142i | ||||||||
\(99\) | −2.58486e10 | −0.273177 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.19564e11 | 1.13196 | 0.565982 | − | 0.824417i | \(-0.308497\pi\) | ||||
0.565982 | + | 0.824417i | \(0.308497\pi\) | |||||||
\(102\) | 1.03256e11i | 0.926008i | ||||||||
\(103\) | − 9.46874e10i | − 0.804799i | −0.915464 | − | 0.402399i | \(-0.868176\pi\) | ||||
0.915464 | − | 0.402399i | \(-0.131824\pi\) | |||||||
\(104\) | 4.93753e11 | 3.97948 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.31951e11 | −3.13511 | ||||||||
\(107\) | − 1.52769e11i | − 1.05299i | −0.850177 | − | 0.526497i | \(-0.823505\pi\) | ||||
0.850177 | − | 0.526497i | \(-0.176495\pi\) | |||||||
\(108\) | 2.52378e11i | 1.65280i | ||||||||
\(109\) | −2.85078e11 | −1.77467 | −0.887337 | − | 0.461122i | \(-0.847447\pi\) | ||||
−0.887337 | + | 0.461122i | \(0.847447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.30113e11 | 1.29618 | ||||||||
\(112\) | − 1.64043e11i | − 0.879544i | ||||||||
\(113\) | − 2.35563e11i | − 1.20275i | −0.798968 | − | 0.601374i | \(-0.794620\pi\) | ||||
0.798968 | − | 0.601374i | \(-0.205380\pi\) | |||||||
\(114\) | 1.72121e11 | 0.837253 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.67093e10 | −0.206483 | ||||||||
\(117\) | − 1.53943e11i | − 0.649140i | ||||||||
\(118\) | 5.54455e10i | 0.223108i | ||||||||
\(119\) | 3.91456e10 | 0.150375 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.69896e11 | −0.595474 | ||||||||
\(122\) | 4.67457e10i | 0.156590i | ||||||||
\(123\) | − 9.24991e10i | − 0.296251i | ||||||||
\(124\) | −1.48579e12 | −4.55133 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.01762e11 | −0.285462 | ||||||||
\(127\) | 1.25786e11i | 0.337840i | 0.985630 | + | 0.168920i | \(0.0540279\pi\) | ||||
−0.985630 | + | 0.168920i | \(0.945972\pi\) | |||||||
\(128\) | − 2.59156e10i | − 0.0666664i | ||||||||
\(129\) | 3.30522e11 | 0.814624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.97347e11 | −0.673397 | −0.336698 | − | 0.941613i | \(-0.609310\pi\) | ||||
−0.336698 | + | 0.941613i | \(0.609310\pi\) | |||||||
\(132\) | 8.48401e11i | 1.84266i | ||||||||
\(133\) | − 6.52530e10i | − 0.135962i | ||||||||
\(134\) | 8.47389e11 | 1.69436 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.98043e11 | 1.10222 | ||||||||
\(137\) | 6.29203e10i | 0.111385i | 0.998448 | + | 0.0556926i | \(0.0177367\pi\) | ||||
−0.998448 | + | 0.0556926i | \(0.982263\pi\) | |||||||
\(138\) | 1.20714e12i | 2.05316i | ||||||||
\(139\) | 5.11416e11 | 0.835974 | 0.417987 | − | 0.908453i | \(-0.362736\pi\) | ||||
0.417987 | + | 0.908453i | \(0.362736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.91800e10 | 0.149871 | ||||||||
\(142\) | 1.49173e12i | 2.16823i | ||||||||
\(143\) | 6.87368e11i | 0.961260i | ||||||||
\(144\) | −7.81370e11 | −1.05163 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.95407e12 | 2.43781 | ||||||||
\(147\) | − 8.66634e11i | − 1.04134i | ||||||||
\(148\) | − 2.26929e12i | − 2.62694i | ||||||||
\(149\) | −7.94154e11 | −0.885891 | −0.442945 | − | 0.896549i | \(-0.646066\pi\) | ||||
−0.442945 | + | 0.896549i | \(0.646066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.24629e12 | 1.29195 | 0.645974 | − | 0.763360i | \(-0.276452\pi\) | ||||
0.645974 | + | 0.763360i | \(0.276452\pi\) | |||||||
\(152\) | − 9.96896e11i | − 0.996576i | ||||||||
\(153\) | − 1.86459e11i | − 0.179796i | ||||||||
\(154\) | 4.54375e11 | 0.422718 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.05271e12 | −4.37864 | ||||||||
\(157\) | − 9.73519e11i | − 0.814510i | −0.913315 | − | 0.407255i | \(-0.866486\pi\) | ||||
0.913315 | − | 0.407255i | \(-0.133514\pi\) | |||||||
\(158\) | − 1.04625e12i | − 0.845322i | ||||||||
\(159\) | 2.59608e12 | 2.02597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.57641e11 | 0.333413 | ||||||||
\(162\) | − 3.27133e12i | − 2.30352i | ||||||||
\(163\) | 1.26084e12i | 0.858281i | 0.903238 | + | 0.429140i | \(0.141183\pi\) | ||||
−0.903238 | + | 0.429140i | \(0.858817\pi\) | |||||||
\(164\) | −9.12190e11 | −0.600405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.82199e12 | −1.73764 | ||||||||
\(167\) | 3.01398e12i | 1.79556i | 0.440443 | + | 0.897780i | \(0.354821\pi\) | ||||
−0.440443 | + | 0.897780i | \(0.645179\pi\) | |||||||
\(168\) | 1.96164e12i | 1.13088i | ||||||||
\(169\) | −2.30151e12 | −1.28421 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10814e11 | −0.162563 | ||||||||
\(172\) | − 3.25948e12i | − 1.65098i | ||||||||
\(173\) | − 3.07482e11i | − 0.150857i | −0.997151 | − | 0.0754285i | \(-0.975968\pi\) | ||||
0.997151 | − | 0.0754285i | \(-0.0240325\pi\) | |||||||
\(174\) | 3.96582e11 | 0.188500 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.48887e12 | 1.55728 | ||||||||
\(177\) | − 3.33234e11i | − 0.144177i | ||||||||
\(178\) | − 2.46400e12i | − 1.03355i | ||||||||
\(179\) | 1.91470e12 | 0.778769 | 0.389384 | − | 0.921075i | \(-0.372688\pi\) | ||||
0.389384 | + | 0.921075i | \(0.372688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.10300e11 | 0.0422032 | 0.0211016 | − | 0.999777i | \(-0.493283\pi\) | ||||
0.0211016 | + | 0.999777i | \(0.493283\pi\) | |||||||
\(182\) | 2.70606e12i | 1.00449i | ||||||||
\(183\) | − 2.80947e11i | − 0.101191i | ||||||||
\(184\) | 6.99157e12 | 2.44386 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.26150e13 | 4.15495 | ||||||||
\(187\) | 8.32552e11i | 0.266246i | ||||||||
\(188\) | − 9.78074e11i | − 0.303741i | ||||||||
\(189\) | −8.12359e11 | −0.245024 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.43991e12 | −1.26384 | −0.631918 | − | 0.775035i | \(-0.717732\pi\) | ||||
−0.631918 | + | 0.775035i | \(0.717732\pi\) | |||||||
\(192\) | 4.58785e12i | 1.26897i | ||||||||
\(193\) | 3.15713e12i | 0.848647i | 0.905511 | + | 0.424324i | \(0.139488\pi\) | ||||
−0.905511 | + | 0.424324i | \(0.860512\pi\) | |||||||
\(194\) | −9.48330e12 | −2.47771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54641e12 | −2.11045 | ||||||||
\(197\) | 3.58626e12i | 0.861147i | 0.902555 | + | 0.430574i | \(0.141689\pi\) | ||||
−0.902555 | + | 0.430574i | \(0.858311\pi\) | |||||||
\(198\) | − 2.16429e12i | − 0.505424i | ||||||||
\(199\) | −4.14823e12 | −0.942260 | −0.471130 | − | 0.882064i | \(-0.656154\pi\) | ||||
−0.471130 | + | 0.882064i | \(0.656154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.09291e12 | −1.09493 | ||||||||
\(202\) | 1.00110e13i | 2.09433i | ||||||||
\(203\) | − 1.50349e11i | − 0.0306106i | ||||||||
\(204\) | −6.11993e12 | −1.21278 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.92810e12 | 1.48902 | ||||||||
\(207\) | − 2.17984e12i | − 0.398647i | ||||||||
\(208\) | 2.07782e13i | 3.70050i | ||||||||
\(209\) | 1.38781e12 | 0.240727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.14275e12 | 0.188104 | 0.0940519 | − | 0.995567i | \(-0.470018\pi\) | ||||
0.0940519 | + | 0.995567i | \(0.470018\pi\) | |||||||
\(212\) | − 2.56015e13i | − 4.10599i | ||||||||
\(213\) | − 8.96547e12i | − 1.40115i | ||||||||
\(214\) | 1.27913e13 | 1.94822 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.24107e13 | −1.79598 | ||||||||
\(217\) | − 4.78249e12i | − 0.674724i | ||||||||
\(218\) | − 2.38694e13i | − 3.28345i | ||||||||
\(219\) | −1.17442e13 | −1.57537 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.95832e12 | −0.632670 | ||||||||
\(222\) | 1.92672e13i | 2.39816i | ||||||||
\(223\) | 3.54889e12i | 0.430939i | 0.976511 | + | 0.215469i | \(0.0691282\pi\) | ||||
−0.976511 | + | 0.215469i | \(0.930872\pi\) | |||||||
\(224\) | 5.75175e12 | 0.681454 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.97235e13 | 2.22529 | ||||||||
\(227\) | − 3.90543e12i | − 0.430058i | −0.976608 | − | 0.215029i | \(-0.931015\pi\) | ||||
0.976608 | − | 0.215029i | \(-0.0689846\pi\) | |||||||
\(228\) | 1.02015e13i | 1.09654i | ||||||||
\(229\) | 4.85126e12 | 0.509048 | 0.254524 | − | 0.967066i | \(-0.418081\pi\) | ||||
0.254524 | + | 0.967066i | \(0.418081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73085e12 | −0.273169 | ||||||||
\(232\) | − 2.29694e12i | − 0.224370i | ||||||||
\(233\) | 1.03473e13i | 0.987115i | 0.869713 | + | 0.493557i | \(0.164304\pi\) | ||||
−0.869713 | + | 0.493557i | \(0.835696\pi\) | |||||||
\(234\) | 1.28896e13 | 1.20102 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.28622e12 | −0.292201 | ||||||||
\(237\) | 6.28810e12i | 0.546265i | ||||||||
\(238\) | 3.27763e12i | 0.278219i | ||||||||
\(239\) | −1.85140e12 | −0.153572 | −0.0767859 | − | 0.997048i | \(-0.524466\pi\) | ||||
−0.0767859 | + | 0.997048i | \(0.524466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.73018e12 | 0.216321 | 0.108160 | − | 0.994133i | \(-0.465504\pi\) | ||||
0.108160 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(242\) | − 1.42252e13i | − 1.10173i | ||||||||
\(243\) | 1.06521e13i | 0.806492i | ||||||||
\(244\) | −2.77059e12 | −0.205083 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.74488e12 | 0.548115 | ||||||||
\(247\) | 8.26518e12i | 0.572031i | ||||||||
\(248\) | − 7.30641e13i | − 4.94561i | ||||||||
\(249\) | 1.69605e13 | 1.12290 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.18976e13 | 0.753796 | 0.376898 | − | 0.926255i | \(-0.376991\pi\) | ||||
0.376898 | + | 0.926255i | \(0.376991\pi\) | |||||||
\(252\) | − 6.03138e12i | − 0.373864i | ||||||||
\(253\) | 9.73316e12i | 0.590324i | ||||||||
\(254\) | −1.05319e13 | −0.625062 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.65016e13 | −0.938007 | ||||||||
\(257\) | − 3.53878e10i | − 0.00196889i | −1.00000 | 0.000984443i | \(-0.999687\pi\) | |||||
1.00000 | 0.000984443i | \(-0.000313358\pi\) | ||||||||
\(258\) | 2.76744e13i | 1.50719i | ||||||||
\(259\) | 7.30442e12 | 0.389437 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.16144e11 | −0.0365997 | ||||||||
\(262\) | − 2.48966e13i | − 1.24590i | ||||||||
\(263\) | − 1.19904e13i | − 0.587592i | −0.955868 | − | 0.293796i | \(-0.905081\pi\) | ||||
0.955868 | − | 0.293796i | \(-0.0949187\pi\) | |||||||
\(264\) | −4.17202e13 | −2.00228 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.46358e12 | 0.251553 | ||||||||
\(267\) | 1.48089e13i | 0.667901i | ||||||||
\(268\) | 5.02243e13i | 2.21908i | ||||||||
\(269\) | 3.81149e13 | 1.64990 | 0.824948 | − | 0.565208i | \(-0.191204\pi\) | ||||
0.824948 | + | 0.565208i | \(0.191204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.13510e13 | −0.471740 | −0.235870 | − | 0.971785i | \(-0.575794\pi\) | ||||
−0.235870 | + | 0.971785i | \(0.575794\pi\) | |||||||
\(272\) | 2.51670e13i | 1.02495i | ||||||||
\(273\) | − 1.62637e13i | − 0.649122i | ||||||||
\(274\) | −5.26827e12 | −0.206082 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.15466e13 | −2.68899 | ||||||||
\(277\) | − 3.02533e13i | − 1.11464i | −0.830298 | − | 0.557320i | \(-0.811830\pi\) | ||||
0.830298 | − | 0.557320i | \(-0.188170\pi\) | |||||||
\(278\) | 4.28205e13i | 1.54670i | ||||||||
\(279\) | −2.27801e13 | −0.806736 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.72047e13 | 1.60731 | 0.803657 | − | 0.595093i | \(-0.202885\pi\) | ||||
0.803657 | + | 0.595093i | \(0.202885\pi\) | |||||||
\(282\) | 8.30426e12i | 0.277288i | ||||||||
\(283\) | − 8.68805e12i | − 0.284510i | −0.989830 | − | 0.142255i | \(-0.954565\pi\) | ||||
0.989830 | − | 0.142255i | \(-0.0454353\pi\) | |||||||
\(284\) | −8.84140e13 | −2.83969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.75528e13 | −1.77850 | ||||||||
\(287\) | − 2.93617e12i | − 0.0890085i | ||||||||
\(288\) | − 2.73969e13i | − 0.814783i | ||||||||
\(289\) | 2.82663e13 | 0.824766 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.69958e13 | 1.60115 | ||||||||
\(292\) | 1.15817e14i | 3.19276i | ||||||||
\(293\) | 2.17869e13i | 0.589417i | 0.955587 | + | 0.294709i | \(0.0952226\pi\) | ||||
−0.955587 | + | 0.294709i | \(0.904777\pi\) | |||||||
\(294\) | 7.25626e13 | 1.92665 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.11593e14 | 2.85450 | ||||||||
\(297\) | − 1.72773e13i | − 0.433827i | ||||||||
\(298\) | − 6.64939e13i | − 1.63905i | ||||||||
\(299\) | −5.79665e13 | −1.40277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.04917e13 | 0.244754 | ||||||||
\(302\) | 1.04351e14i | 2.39033i | ||||||||
\(303\) | − 6.01673e13i | − 1.35340i | ||||||||
\(304\) | 4.19516e13 | 0.926710 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56121e13 | 0.332654 | ||||||||
\(307\) | − 2.05380e13i | − 0.429829i | −0.976633 | − | 0.214915i | \(-0.931053\pi\) | ||||
0.976633 | − | 0.214915i | \(-0.0689473\pi\) | |||||||
\(308\) | 2.69305e13i | 0.553626i | ||||||||
\(309\) | −4.76488e13 | −0.962234 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.37156e13 | −1.43674 | −0.718369 | − | 0.695663i | \(-0.755111\pi\) | ||||
−0.718369 | + | 0.695663i | \(0.755111\pi\) | |||||||
\(312\) | − 2.48468e14i | − 4.75795i | ||||||||
\(313\) | − 2.82026e13i | − 0.530634i | −0.964161 | − | 0.265317i | \(-0.914523\pi\) | ||||
0.964161 | − | 0.265317i | \(-0.0854765\pi\) | |||||||
\(314\) | 8.15120e13 | 1.50698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.20108e13 | 1.10710 | ||||||||
\(317\) | − 2.56938e13i | − 0.450819i | −0.974264 | − | 0.225410i | \(-0.927628\pi\) | ||||
0.974264 | − | 0.225410i | \(-0.0723720\pi\) | |||||||
\(318\) | 2.17367e14i | 3.74840i | ||||||||
\(319\) | 3.19763e12 | 0.0541976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.68771e13 | −1.25898 | ||||||||
\(322\) | 3.83179e13i | 0.616872i | ||||||||
\(323\) | 1.00109e13i | 0.158439i | ||||||||
\(324\) | 1.93890e14 | 3.01688 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.05569e14 | −1.58797 | ||||||||
\(327\) | 1.43458e14i | 2.12184i | ||||||||
\(328\) | − 4.48571e13i | − 0.652417i | ||||||||
\(329\) | 3.14824e12 | 0.0450288 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.14309e13 | −0.849831 | −0.424916 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424916 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(332\) | − 1.67258e14i | − 2.27576i | ||||||||
\(333\) | − 3.47925e13i | − 0.465632i | ||||||||
\(334\) | −2.52358e14 | −3.32210 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.25499e13 | −1.05160 | ||||||||
\(337\) | − 1.35566e14i | − 1.69898i | −0.527608 | − | 0.849488i | \(-0.676911\pi\) | ||||
0.527608 | − | 0.849488i | \(-0.323089\pi\) | |||||||
\(338\) | − 1.92703e14i | − 2.37600i | ||||||||
\(339\) | −1.18540e14 | −1.43803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.01715e14 | 1.19463 | ||||||||
\(342\) | − 2.60242e13i | − 0.300770i | ||||||||
\(343\) | − 5.90945e13i | − 0.672093i | ||||||||
\(344\) | 1.60285e14 | 1.79400 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.57452e13 | 0.279111 | ||||||||
\(347\) | 2.88020e13i | 0.307334i | 0.988123 | + | 0.153667i | \(0.0491083\pi\) | ||||
−0.988123 | + | 0.153667i | \(0.950892\pi\) | |||||||
\(348\) | 2.35052e13i | 0.246876i | ||||||||
\(349\) | −3.70742e13 | −0.383294 | −0.191647 | − | 0.981464i | \(-0.561383\pi\) | ||||
−0.191647 | + | 0.981464i | \(0.561383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.02896e14 | 1.03089 | ||||||||
\(352\) | 1.22329e14i | 1.20655i | ||||||||
\(353\) | − 5.64627e13i | − 0.548278i | −0.961690 | − | 0.274139i | \(-0.911607\pi\) | ||||
0.961690 | − | 0.274139i | \(-0.0883928\pi\) | |||||||
\(354\) | 2.79014e13 | 0.266753 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.46040e14 | 1.35362 | ||||||||
\(357\) | − 1.96989e13i | − 0.179791i | ||||||||
\(358\) | 1.60316e14i | 1.44086i | ||||||||
\(359\) | 1.96868e14 | 1.74243 | 0.871217 | − | 0.490899i | \(-0.163332\pi\) | ||||
0.871217 | + | 0.490899i | \(0.163332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.98027e13 | −0.856747 | ||||||||
\(362\) | 9.23537e12i | 0.0780831i | ||||||||
\(363\) | 8.54954e13i | 0.711961i | ||||||||
\(364\) | −1.60387e14 | −1.31556 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.35235e13 | 0.187222 | ||||||||
\(367\) | 1.00444e14i | 0.787514i | 0.919214 | + | 0.393757i | \(0.128825\pi\) | ||||
−0.919214 | + | 0.393757i | \(0.871175\pi\) | |||||||
\(368\) | 2.94221e14i | 2.27253i | ||||||||
\(369\) | −1.39856e13 | −0.106423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.24065e13 | 0.608703 | ||||||||
\(372\) | 7.47684e14i | 5.44167i | ||||||||
\(373\) | − 7.09849e13i | − 0.509058i | −0.967065 | − | 0.254529i | \(-0.918079\pi\) | ||||
0.967065 | − | 0.254529i | \(-0.0819205\pi\) | |||||||
\(374\) | −6.97090e13 | −0.492600 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.80970e13 | 0.330054 | ||||||||
\(377\) | 1.90437e13i | 0.128788i | ||||||||
\(378\) | − 6.80182e13i | − 0.453336i | ||||||||
\(379\) | −6.79976e13 | −0.446661 | −0.223330 | − | 0.974743i | \(-0.571693\pi\) | ||||
−0.223330 | + | 0.974743i | \(0.571693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.32982e13 | 0.403928 | ||||||||
\(382\) | − 3.71750e14i | − 2.33831i | ||||||||
\(383\) | 1.89007e14i | 1.17188i | 0.810353 | + | 0.585942i | \(0.199275\pi\) | ||||
−0.810353 | + | 0.585942i | \(0.800725\pi\) | |||||||
\(384\) | −1.30413e13 | −0.0797076 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.64344e14 | −1.57014 | ||||||||
\(387\) | − 4.99741e13i | − 0.292641i | ||||||||
\(388\) | − 5.62070e14i | − 3.24501i | ||||||||
\(389\) | 2.90163e14 | 1.65165 | 0.825826 | − | 0.563924i | \(-0.190709\pi\) | ||||
0.825826 | + | 0.563924i | \(0.190709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.02100e13 | −0.388532 | ||||||||
\(392\) | − 4.20271e14i | − 2.29328i | ||||||||
\(393\) | 1.49632e14i | 0.805127i | ||||||||
\(394\) | −3.00275e14 | −1.59327 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.28276e14 | 0.661945 | ||||||||
\(397\) | 5.15115e13i | 0.262154i | 0.991372 | + | 0.131077i | \(0.0418435\pi\) | ||||
−0.991372 | + | 0.131077i | \(0.958157\pi\) | |||||||
\(398\) | − 3.47328e14i | − 1.74334i | ||||||||
\(399\) | −3.28368e13 | −0.162559 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.11012e14 | −0.534657 | −0.267329 | − | 0.963605i | \(-0.586141\pi\) | ||||
−0.267329 | + | 0.963605i | \(0.586141\pi\) | |||||||
\(402\) | − 4.26426e14i | − 2.02582i | ||||||||
\(403\) | 6.05768e14i | 2.83876i | ||||||||
\(404\) | −5.93346e14 | −2.74291 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.25886e13 | 0.0566349 | ||||||||
\(407\) | 1.55351e14i | 0.689517i | ||||||||
\(408\) | − 3.00949e14i | − 1.31784i | ||||||||
\(409\) | 1.92951e14 | 0.833623 | 0.416811 | − | 0.908993i | \(-0.363148\pi\) | ||||
0.416811 | + | 0.908993i | \(0.363148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.16629e13 | 0.133174 | ||||||||
\(412\) | 4.69894e14i | 1.95014i | ||||||||
\(413\) | − 1.05778e13i | − 0.0433180i | ||||||||
\(414\) | 1.82517e14 | 0.737565 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.28538e14 | −2.86707 | ||||||||
\(417\) | − 2.57356e14i | − 0.999508i | ||||||||
\(418\) | 1.16200e14i | 0.445386i | ||||||||
\(419\) | −2.28750e14 | −0.865336 | −0.432668 | − | 0.901553i | \(-0.642428\pi\) | ||||
−0.432668 | + | 0.901553i | \(0.642428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00332e14 | −1.47526 | −0.737630 | − | 0.675205i | \(-0.764055\pi\) | ||||
−0.737630 | + | 0.675205i | \(0.764055\pi\) | |||||||
\(422\) | 9.56816e13i | 0.348024i | ||||||||
\(423\) | − 1.49958e13i | − 0.0538389i | ||||||||
\(424\) | 1.25896e15 | 4.46169 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.50672e14 | 2.59237 | ||||||||
\(427\) | − 8.91803e12i | − 0.0304030i | ||||||||
\(428\) | 7.58132e14i | 2.55155i | ||||||||
\(429\) | 3.45899e14 | 1.14930 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.29757e14 | 0.420250 | 0.210125 | − | 0.977675i | \(-0.432613\pi\) | ||||
0.210125 | + | 0.977675i | \(0.432613\pi\) | |||||||
\(432\) | − 5.22271e14i | − 1.67007i | ||||||||
\(433\) | − 3.09354e14i | − 0.976725i | −0.872641 | − | 0.488363i | \(-0.837594\pi\) | ||||
0.872641 | − | 0.488363i | \(-0.162406\pi\) | |||||||
\(434\) | 4.00435e14 | 1.24835 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.41473e15 | 4.30028 | ||||||||
\(437\) | 1.17035e14i | 0.351293i | ||||||||
\(438\) | − 9.83334e14i | − 2.91470i | ||||||||
\(439\) | 6.15652e13 | 0.180211 | 0.0901054 | − | 0.995932i | \(-0.471280\pi\) | ||||
0.0901054 | + | 0.995932i | \(0.471280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.31033e14 | −0.374083 | ||||||||
\(442\) | − 4.15156e14i | − 1.17055i | ||||||||
\(443\) | − 2.42894e13i | − 0.0676389i | −0.999428 | − | 0.0338194i | \(-0.989233\pi\) | ||||
0.999428 | − | 0.0338194i | \(-0.0107671\pi\) | |||||||
\(444\) | −1.14196e15 | −3.14082 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.97146e14 | −0.797311 | ||||||||
\(447\) | 3.99636e14i | 1.05919i | ||||||||
\(448\) | 1.45631e14i | 0.381263i | ||||||||
\(449\) | −6.65728e14 | −1.72164 | −0.860820 | − | 0.508910i | \(-0.830049\pi\) | ||||
−0.860820 | + | 0.508910i | \(0.830049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24468e13 | 0.157594 | ||||||||
\(452\) | 1.16900e15i | 2.91442i | ||||||||
\(453\) | − 6.27160e14i | − 1.54468i | ||||||||
\(454\) | 3.26999e14 | 0.795681 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.01661e14 | −1.19153 | ||||||||
\(457\) | − 6.99716e14i | − 1.64204i | −0.570902 | − | 0.821018i | \(-0.693406\pi\) | ||||
0.570902 | − | 0.821018i | \(-0.306594\pi\) | |||||||
\(458\) | 4.06192e14i | 0.941827i | ||||||||
\(459\) | 1.24630e14 | 0.285531 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.43320e14 | 0.767971 | 0.383985 | − | 0.923339i | \(-0.374551\pi\) | ||||
0.383985 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(462\) | − 2.28652e14i | − 0.505410i | ||||||||
\(463\) | 3.77708e14i | 0.825012i | 0.910955 | + | 0.412506i | \(0.135346\pi\) | ||||
−0.910955 | + | 0.412506i | \(0.864654\pi\) | |||||||
\(464\) | 9.66603e13 | 0.208641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.66368e14 | −1.82633 | ||||||||
\(467\) | 5.01733e14i | 1.04527i | 0.852555 | + | 0.522637i | \(0.175052\pi\) | ||||
−0.852555 | + | 0.522637i | \(0.824948\pi\) | |||||||
\(468\) | 7.63957e14i | 1.57296i | ||||||||
\(469\) | −1.61663e14 | −0.328972 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.89897e14 | −0.973844 | ||||||||
\(472\) | − 1.61601e14i | − 0.317513i | ||||||||
\(473\) | 2.23138e14i | 0.433348i | ||||||||
\(474\) | −5.26498e14 | −1.01068 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.94263e14 | −0.364378 | ||||||||
\(477\) | − 3.92520e14i | − 0.727798i | ||||||||
\(478\) | − 1.55016e14i | − 0.284134i | ||||||||
\(479\) | −9.56649e14 | −1.73343 | −0.866717 | − | 0.498800i | \(-0.833774\pi\) | ||||
−0.866717 | + | 0.498800i | \(0.833774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.25204e14 | −1.63847 | ||||||||
\(482\) | 2.28596e14i | 0.400231i | ||||||||
\(483\) | − 2.30295e14i | − 0.398635i | ||||||||
\(484\) | 8.43122e14 | 1.44292 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.91890e14 | −1.49215 | ||||||||
\(487\) | − 1.81856e14i | − 0.300828i | −0.988623 | − | 0.150414i | \(-0.951939\pi\) | ||||
0.988623 | − | 0.150414i | \(-0.0480606\pi\) | |||||||
\(488\) | − 1.36244e14i | − 0.222848i | ||||||||
\(489\) | 6.34485e14 | 1.02618 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.28536e14 | 1.46842 | 0.734210 | − | 0.678922i | \(-0.237553\pi\) | ||||
0.734210 | + | 0.678922i | \(0.237553\pi\) | |||||||
\(492\) | 4.59035e14i | 0.717856i | ||||||||
\(493\) | 2.30661e13i | 0.0356711i | ||||||||
\(494\) | −6.92037e14 | −1.05835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.07470e15 | 4.59889 | ||||||||
\(497\) | − 2.84589e14i | − 0.420976i | ||||||||
\(498\) | 1.42009e15i | 2.07756i | ||||||||
\(499\) | −1.10604e15 | −1.60036 | −0.800178 | − | 0.599763i | \(-0.795261\pi\) | ||||
−0.800178 | + | 0.599763i | \(0.795261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.51670e15 | 2.14681 | ||||||||
\(502\) | 9.96177e14i | 1.39465i | ||||||||
\(503\) | − 1.07467e15i | − 1.48816i | −0.668089 | − | 0.744081i | \(-0.732888\pi\) | ||||
0.668089 | − | 0.744081i | \(-0.267112\pi\) | |||||||
\(504\) | 2.96594e14 | 0.406251 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.14950e14 | −1.09220 | ||||||||
\(507\) | 1.15817e15i | 1.53542i | ||||||||
\(508\) | − 6.24222e14i | − 0.818632i | ||||||||
\(509\) | 1.50116e15 | 1.94750 | 0.973752 | − | 0.227610i | \(-0.0730910\pi\) | ||||
0.973752 | + | 0.227610i | \(0.0730910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.72793e14 | −0.473318 | ||||||||
\(512\) | − 1.43474e15i | − 1.80214i | ||||||||
\(513\) | − 2.07750e14i | − 0.258163i | ||||||||
\(514\) | 2.96299e12 | 0.00364278 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.64024e15 | −1.97395 | ||||||||
\(517\) | 6.69571e13i | 0.0797258i | ||||||||
\(518\) | 6.11593e14i | 0.720525i | ||||||||
\(519\) | −1.54732e14 | −0.180368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.31060e13 | −0.0948473 | −0.0474237 | − | 0.998875i | \(-0.515101\pi\) | ||||
−0.0474237 | + | 0.998875i | \(0.515101\pi\) | |||||||
\(522\) | − 5.99622e13i | − 0.0677158i | ||||||||
\(523\) | − 9.42223e14i | − 1.05292i | −0.850201 | − | 0.526459i | \(-0.823519\pi\) | ||||
0.850201 | − | 0.526459i | \(-0.176481\pi\) | |||||||
\(524\) | 1.47561e15 | 1.63173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.00394e15 | 1.08715 | ||||||||
\(527\) | 7.33717e14i | 0.786267i | ||||||||
\(528\) | − 1.75568e15i | − 1.86191i | ||||||||
\(529\) | 1.32002e14 | 0.138540 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.03841e13 | −0.0517933 | ||||||||
\(532\) | 3.23824e14i | 0.329454i | ||||||||
\(533\) | 3.71906e14i | 0.374485i | ||||||||
\(534\) | −1.23994e15 | −1.23573 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.46979e15 | −2.41131 | ||||||||
\(537\) | − 9.63519e14i | − 0.931112i | ||||||||
\(538\) | 3.19133e15i | 3.05259i | ||||||||
\(539\) | 5.85071e14 | 0.553950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.18229e15 | 1.09683 | 0.548416 | − | 0.836206i | \(-0.315231\pi\) | ||||
0.548416 | + | 0.836206i | \(0.315231\pi\) | |||||||
\(542\) | − 9.50410e14i | − 0.872800i | ||||||||
\(543\) | − 5.55056e13i | − 0.0504589i | ||||||||
\(544\) | −8.82418e14 | −0.794110 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.36175e15 | 1.20099 | ||||||||
\(547\) | − 1.57701e15i | − 1.37691i | −0.725281 | − | 0.688453i | \(-0.758290\pi\) | ||||
0.725281 | − | 0.688453i | \(-0.241710\pi\) | |||||||
\(548\) | − 3.12247e14i | − 0.269902i | ||||||||
\(549\) | −4.24785e13 | −0.0363514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.84496e13 | 0.0322521 | ||||||||
\(552\) | − 3.51831e15i | − 2.92193i | ||||||||
\(553\) | 1.99601e14i | 0.164125i | ||||||||
\(554\) | 2.53309e15 | 2.06228 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.53795e15 | −2.02568 | ||||||||
\(557\) | − 4.53070e14i | − 0.358065i | −0.983843 | − | 0.179033i | \(-0.942703\pi\) | ||||
0.983843 | − | 0.179033i | \(-0.0572968\pi\) | |||||||
\(558\) | − 1.90736e15i | − 1.49260i | ||||||||
\(559\) | −1.32891e15 | −1.02975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.18959e14 | 0.318329 | ||||||||
\(562\) | 3.95241e15i | 2.97381i | ||||||||
\(563\) | 4.23450e13i | 0.0315505i | 0.999876 | + | 0.0157752i | \(0.00502163\pi\) | ||||
−0.999876 | + | 0.0157752i | \(0.994978\pi\) | |||||||
\(564\) | −4.92189e14 | −0.363159 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.27444e14 | 0.526392 | ||||||||
\(567\) | 6.24097e14i | 0.447245i | ||||||||
\(568\) | − 4.34777e15i | − 3.08568i | ||||||||
\(569\) | 9.72594e14 | 0.683619 | 0.341810 | − | 0.939769i | \(-0.388960\pi\) | ||||
0.341810 | + | 0.939769i | \(0.388960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.07663e15 | −1.43173 | −0.715863 | − | 0.698241i | \(-0.753966\pi\) | ||||
−0.715863 | + | 0.698241i | \(0.753966\pi\) | |||||||
\(572\) | − 3.41112e15i | − 2.32927i | ||||||||
\(573\) | 2.23426e15i | 1.51107i | ||||||||
\(574\) | 2.45844e14 | 0.164681 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.93671e14 | 0.455858 | ||||||||
\(577\) | − 2.62999e15i | − 1.71194i | −0.517028 | − | 0.855968i | \(-0.672962\pi\) | ||||
0.517028 | − | 0.855968i | \(-0.327038\pi\) | |||||||
\(578\) | 2.36671e15i | 1.52596i | ||||||||
\(579\) | 1.58874e15 | 1.01466 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.38371e14 | 0.337375 | ||||||||
\(582\) | 4.77221e15i | 2.96240i | ||||||||
\(583\) | 1.75263e15i | 1.07774i | ||||||||
\(584\) | −5.69531e15 | −3.46934 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.82420e15 | −1.09052 | ||||||||
\(587\) | 2.89275e15i | 1.71317i | 0.516003 | + | 0.856587i | \(0.327419\pi\) | ||||
−0.516003 | + | 0.856587i | \(0.672581\pi\) | |||||||
\(588\) | 4.30075e15i | 2.52330i | ||||||||
\(589\) | 1.22306e15 | 0.710906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.80469e15 | 1.02960 | ||||||||
\(592\) | 4.69606e15i | 2.65439i | ||||||||
\(593\) | − 1.15734e15i | − 0.648125i | −0.946036 | − | 0.324063i | \(-0.894951\pi\) | ||||
0.946036 | − | 0.324063i | \(-0.105049\pi\) | |||||||
\(594\) | 1.44662e15 | 0.802654 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.94106e15 | 2.14663 | ||||||||
\(597\) | 2.08748e15i | 1.12659i | ||||||||
\(598\) | − 4.85349e15i | − 2.59536i | ||||||||
\(599\) | −2.42056e14 | −0.128253 | −0.0641265 | − | 0.997942i | \(-0.520426\pi\) | ||||
−0.0641265 | + | 0.997942i | \(0.520426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.08465e15 | −1.60471 | −0.802354 | − | 0.596848i | \(-0.796419\pi\) | ||||
−0.802354 | + | 0.596848i | \(0.796419\pi\) | |||||||
\(602\) | 8.78460e14i | 0.452836i | ||||||||
\(603\) | 7.70035e14i | 0.393337i | ||||||||
\(604\) | −6.18480e15 | −3.13057 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.03776e15 | 2.50402 | ||||||||
\(607\) | − 2.71223e15i | − 1.33595i | −0.744186 | − | 0.667973i | \(-0.767162\pi\) | ||||
0.744186 | − | 0.667973i | \(-0.232838\pi\) | |||||||
\(608\) | 1.47093e15i | 0.717997i | ||||||||
\(609\) | −7.56589e13 | −0.0365987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.98768e14 | −0.189449 | ||||||||
\(612\) | 9.25318e14i | 0.435671i | ||||||||
\(613\) | − 1.80466e15i | − 0.842097i | −0.907038 | − | 0.421049i | \(-0.861662\pi\) | ||||
0.907038 | − | 0.421049i | \(-0.138338\pi\) | |||||||
\(614\) | 1.71963e15 | 0.795258 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.32431e15 | −0.601585 | ||||||||
\(617\) | − 4.28183e14i | − 0.192780i | −0.995344 | − | 0.0963898i | \(-0.969270\pi\) | ||||
0.995344 | − | 0.0963898i | \(-0.0307295\pi\) | |||||||
\(618\) | − 3.98960e15i | − 1.78030i | ||||||||
\(619\) | −2.39110e15 | −1.05754 | −0.528772 | − | 0.848764i | \(-0.677347\pi\) | ||||
−0.528772 | + | 0.848764i | \(0.677347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.45702e15 | 0.633083 | ||||||||
\(622\) | − 6.17215e15i | − 2.65821i | ||||||||
\(623\) | 4.70076e14i | 0.200671i | ||||||||
\(624\) | 1.04561e16 | 4.42439 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36138e15 | 0.981763 | ||||||||
\(627\) | − 6.98376e14i | − 0.287818i | ||||||||
\(628\) | 4.83117e15i | 1.97367i | ||||||||
\(629\) | −1.12062e15 | −0.453818 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.26028e15 | 1.29746 | 0.648730 | − | 0.761019i | \(-0.275301\pi\) | ||||
0.648730 | + | 0.761019i | \(0.275301\pi\) | |||||||
\(632\) | 3.04939e15i | 1.20301i | ||||||||
\(633\) | − 5.75057e14i | − 0.224901i | ||||||||
\(634\) | 2.15132e15 | 0.834093 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.28832e16 | −4.90921 | ||||||||
\(637\) | 3.48443e15i | 1.31633i | ||||||||
\(638\) | 2.67735e14i | 0.100275i | ||||||||
\(639\) | −1.35556e15 | −0.503342 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.32104e15 | −0.847157 | −0.423579 | − | 0.905859i | \(-0.639226\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639226\pi\) | |||||||
\(642\) | − 6.43686e15i | − 2.32933i | ||||||||
\(643\) | − 2.55397e15i | − 0.916336i | −0.888866 | − | 0.458168i | \(-0.848506\pi\) | ||||
0.888866 | − | 0.458168i | \(-0.151494\pi\) | |||||||
\(644\) | −2.27108e15 | −0.807906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.38208e14 | −0.293139 | ||||||||
\(647\) | 1.70408e15i | 0.590902i | 0.955358 | + | 0.295451i | \(0.0954699\pi\) | ||||
−0.955358 | + | 0.295451i | \(0.904530\pi\) | |||||||
\(648\) | 9.53458e15i | 3.27823i | ||||||||
\(649\) | 2.24969e14 | 0.0766966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40666e15 | −0.806713 | ||||||||
\(652\) | − 6.25704e15i | − 2.07973i | ||||||||
\(653\) | − 2.20439e15i | − 0.726552i | −0.931682 | − | 0.363276i | \(-0.881658\pi\) | ||||
0.931682 | − | 0.363276i | \(-0.118342\pi\) | |||||||
\(654\) | −1.20116e16 | −3.92576 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.88769e15 | 0.606679 | ||||||||
\(657\) | 1.77570e15i | 0.565925i | ||||||||
\(658\) | 2.63600e14i | 0.0833111i | ||||||||
\(659\) | −1.97759e14 | −0.0619821 | −0.0309910 | − | 0.999520i | \(-0.509866\pi\) | ||||
−0.0309910 | + | 0.999520i | \(0.509866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.43414e15 | −1.05855 | −0.529274 | − | 0.848451i | \(-0.677536\pi\) | ||||
−0.529274 | + | 0.848451i | \(0.677536\pi\) | |||||||
\(662\) | − 5.14356e15i | − 1.57233i | ||||||||
\(663\) | 2.49514e15i | 0.756433i | ||||||||
\(664\) | 8.22492e15 | 2.47290 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.91315e15 | 0.861499 | ||||||||
\(667\) | 2.69660e14i | 0.0790905i | ||||||||
\(668\) | − 1.49571e16i | − 4.35089i | ||||||||
\(669\) | 1.78588e15 | 0.515239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.89670e14 | 0.0538299 | ||||||||
\(672\) | − 2.89441e15i | − 0.814760i | ||||||||
\(673\) | 2.01250e15i | 0.561892i | 0.959724 | + | 0.280946i | \(0.0906481\pi\) | ||||
−0.959724 | + | 0.280946i | \(0.909352\pi\) | |||||||
\(674\) | 1.13509e16 | 3.14340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.14214e16 | 3.11181 | ||||||||
\(677\) | 1.01903e15i | 0.275392i | 0.990475 | + | 0.137696i | \(0.0439696\pi\) | ||||
−0.990475 | + | 0.137696i | \(0.956030\pi\) | |||||||
\(678\) | − 9.92530e15i | − 2.66060i | ||||||||
\(679\) | 1.80920e15 | 0.481064 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.96530e15 | −0.514186 | ||||||||
\(682\) | 8.51648e15i | 2.21027i | ||||||||
\(683\) | 2.86885e15i | 0.738575i | 0.929315 | + | 0.369287i | \(0.120398\pi\) | ||||
−0.929315 | + | 0.369287i | \(0.879602\pi\) | |||||||
\(684\) | 1.54244e15 | 0.393913 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.94793e15 | 1.24349 | ||||||||
\(687\) | − 2.44126e15i | − 0.608629i | ||||||||
\(688\) | 6.74517e15i | 1.66823i | ||||||||
\(689\) | −1.04379e16 | −2.56099 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79931e15 | −0.434487 | −0.217243 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217243 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(692\) | 1.52590e15i | 0.365547i | ||||||||
\(693\) | 4.12897e14i | 0.0981316i | ||||||||
\(694\) | −2.41157e15 | −0.568621 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.15587e15 | −0.268262 | ||||||||
\(697\) | 4.50460e14i | 0.103723i | ||||||||
\(698\) | − 3.10420e15i | − 0.709160i | ||||||||
\(699\) | 5.20697e15 | 1.18021 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.99337e15 | 0.667899 | 0.333949 | − | 0.942591i | \(-0.391619\pi\) | ||||
0.333949 | + | 0.942591i | \(0.391619\pi\) | |||||||
\(702\) | 8.61543e15i | 1.90732i | ||||||||
\(703\) | 1.86800e15i | 0.410321i | ||||||||
\(704\) | −3.09729e15 | −0.675045 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.72758e15 | 1.01441 | ||||||||
\(707\) | − 1.90987e15i | − 0.406629i | ||||||||
\(708\) | 1.65370e15i | 0.349361i | ||||||||
\(709\) | −2.74187e15 | −0.574769 | −0.287384 | − | 0.957815i | \(-0.592786\pi\) | ||||
−0.287384 | + | 0.957815i | \(0.592786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.50744e14 | 0.196237 | ||||||||
\(712\) | 7.18154e15i | 1.47088i | ||||||||
\(713\) | 8.57770e15i | 1.74333i | ||||||||
\(714\) | 1.64938e15 | 0.332644 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.50185e15 | −1.88706 | ||||||||
\(717\) | 9.31666e14i | 0.183614i | ||||||||
\(718\) | 1.64836e16i | 3.22380i | ||||||||
\(719\) | 4.38021e15 | 0.850131 | 0.425065 | − | 0.905163i | \(-0.360251\pi\) | ||||
0.425065 | + | 0.905163i | \(0.360251\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51250e15 | −0.289103 | ||||||||
\(722\) | − 8.35640e15i | − 1.58513i | ||||||||
\(723\) | − 1.37389e15i | − 0.258637i | ||||||||
\(724\) | −5.47375e14 | −0.102264 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.15846e15 | −1.31725 | ||||||||
\(727\) | − 6.60205e15i | − 1.20570i | −0.797854 | − | 0.602851i | \(-0.794031\pi\) | ||||
0.797854 | − | 0.602851i | \(-0.205969\pi\) | |||||||
\(728\) | − 7.88704e15i | − 1.42952i | ||||||||
\(729\) | −1.56084e15 | −0.280773 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.60960e15 | −0.285216 | ||||||||
\(732\) | 1.39422e15i | 0.245201i | ||||||||
\(733\) | − 8.22795e15i | − 1.43622i | −0.695932 | − | 0.718108i | \(-0.745008\pi\) | ||||
0.695932 | − | 0.718108i | \(-0.254992\pi\) | |||||||
\(734\) | −8.41006e15 | −1.45704 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.03161e16 | −1.76071 | ||||||||
\(737\) | − 3.43826e15i | − 0.582462i | ||||||||
\(738\) | − 1.17101e15i | − 0.196902i | ||||||||
\(739\) | 1.10770e16 | 1.84875 | 0.924376 | − | 0.381483i | \(-0.124586\pi\) | ||||
0.924376 | + | 0.381483i | \(0.124586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.15923e15 | 0.683931 | ||||||||
\(742\) | 6.89984e15i | 1.12620i | ||||||||
\(743\) | − 3.86160e15i | − 0.625646i | −0.949811 | − | 0.312823i | \(-0.898725\pi\) | ||||
0.949811 | − | 0.312823i | \(-0.101275\pi\) | |||||||
\(744\) | −3.67675e16 | −5.91307 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.94352e15 | 0.941846 | ||||||||
\(747\) | − 2.56438e15i | − 0.403384i | ||||||||
\(748\) | − 4.13161e15i | − 0.645150i | ||||||||
\(749\) | −2.44029e15 | −0.378260 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.05947e15 | 0.161834 | 0.0809168 | − | 0.996721i | \(-0.474215\pi\) | ||||
0.0809168 | + | 0.996721i | \(0.474215\pi\) | |||||||
\(752\) | 2.02403e15i | 0.306915i | ||||||||
\(753\) | − 5.98714e15i | − 0.901254i | ||||||||
\(754\) | −1.59452e15 | −0.238280 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.03140e15 | 0.593726 | ||||||||
\(757\) | 7.04375e15i | 1.02986i | 0.857233 | + | 0.514928i | \(0.172182\pi\) | ||||
−0.857233 | + | 0.514928i | \(0.827818\pi\) | |||||||
\(758\) | − 5.69339e15i | − 0.826400i | ||||||||
\(759\) | 4.89794e15 | 0.705804 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.63598e15 | 0.516424 | 0.258212 | − | 0.966088i | \(-0.416867\pi\) | ||||
0.258212 | + | 0.966088i | \(0.416867\pi\) | |||||||
\(762\) | 5.29991e15i | 0.747337i | ||||||||
\(763\) | 4.55374e15i | 0.637505i | ||||||||
\(764\) | 2.20334e16 | 3.06245 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.58254e16 | −2.16819 | ||||||||
\(767\) | 1.33982e15i | 0.182251i | ||||||||
\(768\) | 8.30398e15i | 1.12150i | ||||||||
\(769\) | 5.34829e15 | 0.717167 | 0.358583 | − | 0.933498i | \(-0.383260\pi\) | ||||
0.358583 | + | 0.933498i | \(0.383260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.78079e13 | −0.00235404 | ||||||||
\(772\) | − 1.56675e16i | − 2.05639i | ||||||||
\(773\) | 8.06669e15i | 1.05126i | 0.850715 | + | 0.525628i | \(0.176169\pi\) | ||||
−0.850715 | + | 0.525628i | \(0.823831\pi\) | |||||||
\(774\) | 4.18429e15 | 0.541436 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.76399e16 | 3.52612 | ||||||||
\(777\) | − 3.67575e15i | − 0.465618i | ||||||||
\(778\) | 2.42951e16i | 3.05584i | ||||||||
\(779\) | 7.50886e14 | 0.0937816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.05266e15 | 0.745359 | ||||||||
\(782\) | − 5.87863e15i | − 0.718851i | ||||||||
\(783\) | − 4.78674e14i | − 0.0581233i | ||||||||
\(784\) | 1.76859e16 | 2.13250 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.25285e16 | −1.48962 | ||||||||
\(787\) | 8.56068e15i | 1.01076i | 0.862897 | + | 0.505379i | \(0.168647\pi\) | ||||
−0.862897 | + | 0.505379i | \(0.831353\pi\) | |||||||
\(788\) | − 1.77971e16i | − 2.08668i | ||||||||
\(789\) | −6.03383e15 | −0.702537 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.76279e15 | −0.432056 | ||||||||
\(792\) | 6.30799e15i | 0.719288i | ||||||||
\(793\) | 1.12959e15i | 0.127914i | ||||||||
\(794\) | −4.31302e15 | −0.485030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.05859e16 | 2.28323 | ||||||||
\(797\) | 1.47001e16i | 1.61919i | 0.586987 | + | 0.809596i | \(0.300314\pi\) | ||||
−0.586987 | + | 0.809596i | \(0.699686\pi\) | |||||||
\(798\) | − 2.74940e15i | − 0.300761i | ||||||||
\(799\) | −4.82995e14 | −0.0524729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.23907e15 | 0.239933 | ||||||||
\(802\) | − 9.29494e15i | − 0.989208i | ||||||||
\(803\) | − 7.92861e15i | − 0.838033i | ||||||||
\(804\) | 2.52740e16 | 2.65317 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.07205e16 | −5.25219 | ||||||||
\(807\) | − 1.91803e16i | − 1.97265i | ||||||||
\(808\) | − 2.91779e16i | − 2.98052i | ||||||||
\(809\) | −5.20792e15 | −0.528382 | −0.264191 | − | 0.964470i | \(-0.585105\pi\) | ||||
−0.264191 | + | 0.964470i | \(0.585105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.95571e16 | 1.95745 | 0.978724 | − | 0.205183i | \(-0.0657789\pi\) | ||||
0.978724 | + | 0.205183i | \(0.0657789\pi\) | |||||||
\(812\) | 7.46119e14i | 0.0741737i | ||||||||
\(813\) | 5.71207e15i | 0.564022i | ||||||||
\(814\) | −1.30074e16 | −1.27573 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.26646e16 | 1.22545 | ||||||||
\(817\) | 2.68310e15i | 0.257879i | ||||||||
\(818\) | 1.61557e16i | 1.54235i | ||||||||
\(819\) | −2.45904e15 | −0.233187 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.02440e16 | 0.958476 | 0.479238 | − | 0.877685i | \(-0.340913\pi\) | ||||
0.479238 | + | 0.877685i | \(0.340913\pi\) | |||||||
\(822\) | 2.65111e15i | 0.246396i | ||||||||
\(823\) | − 1.40372e16i | − 1.29593i | −0.761671 | − | 0.647964i | \(-0.775621\pi\) | ||||
0.761671 | − | 0.647964i | \(-0.224379\pi\) | |||||||
\(824\) | −2.31071e16 | −2.11907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.85667e14 | 0.0801457 | ||||||||
\(827\) | − 8.80160e14i | − 0.0791191i | −0.999217 | − | 0.0395596i | \(-0.987405\pi\) | ||||
0.999217 | − | 0.0395596i | \(-0.0125955\pi\) | |||||||
\(828\) | 1.08177e16i | 0.965976i | ||||||||
\(829\) | −4.54642e14 | −0.0403292 | −0.0201646 | − | 0.999797i | \(-0.506419\pi\) | ||||
−0.0201646 | + | 0.999797i | \(0.506419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.52242e16 | −1.33269 | ||||||||
\(832\) | − 1.84461e16i | − 1.60408i | ||||||||
\(833\) | 4.22041e15i | 0.364592i | ||||||||
\(834\) | 2.15482e16 | 1.84926 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.88711e15 | −0.583314 | ||||||||
\(837\) | − 1.52263e16i | − 1.28116i | ||||||||
\(838\) | − 1.91531e16i | − 1.60102i | ||||||||
\(839\) | −1.32346e16 | −1.09906 | −0.549529 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549529 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.21119e16 | −0.992739 | ||||||||
\(842\) | − 3.35195e16i | − 2.72949i | ||||||||
\(843\) | − 2.37545e16i | − 1.92174i | ||||||||
\(844\) | −5.67099e15 | −0.455801 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.25558e15 | 0.0996113 | ||||||||
\(847\) | 2.71386e15i | 0.213908i | ||||||||
\(848\) | 5.29797e16i | 4.14889i | ||||||||
\(849\) | −4.37202e15 | −0.340166 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.31009e16 | −1.00621 | ||||||||
\(852\) | 4.44919e16i | 3.39519i | ||||||||
\(853\) | − 2.60074e15i | − 0.197186i | −0.995128 | − | 0.0985932i | \(-0.968566\pi\) | ||||
0.995128 | − | 0.0985932i | \(-0.0314343\pi\) | |||||||
\(854\) | 7.46700e14 | 0.0562507 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.72812e16 | −2.77258 | ||||||||
\(857\) | 1.68895e16i | 1.24802i | 0.781415 | + | 0.624011i | \(0.214498\pi\) | ||||
−0.781415 | + | 0.624011i | \(0.785502\pi\) | |||||||
\(858\) | 2.89619e16i | 2.12641i | ||||||||
\(859\) | −8.98241e15 | −0.655285 | −0.327643 | − | 0.944802i | \(-0.606254\pi\) | ||||
−0.327643 | + | 0.944802i | \(0.606254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.47755e15 | −0.106420 | ||||||||
\(862\) | 1.08645e16i | 0.777534i | ||||||||
\(863\) | − 1.16178e16i | − 0.826164i | −0.910694 | − | 0.413082i | \(-0.864452\pi\) | ||||
0.910694 | − | 0.413082i | \(-0.135548\pi\) | |||||||
\(864\) | 1.83122e16 | 1.29394 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.59020e16 | 1.80711 | ||||||||
\(867\) | − 1.42242e16i | − 0.986107i | ||||||||
\(868\) | 2.37335e16i | 1.63495i | ||||||||
\(869\) | −4.24514e15 | −0.290592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04768e16 | 1.38408 | ||||||||
\(872\) | 6.95694e16i | 4.67280i | ||||||||
\(873\) | − 8.61761e15i | − 0.575186i | ||||||||
\(874\) | −9.79928e15 | −0.649952 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.82817e16 | 3.81733 | ||||||||
\(877\) | − 4.73202e15i | − 0.307999i | −0.988071 | − | 0.153999i | \(-0.950785\pi\) | ||||
0.988071 | − | 0.153999i | \(-0.0492154\pi\) | |||||||
\(878\) | 5.15481e15i | 0.333421i | ||||||||
\(879\) | 1.09636e16 | 0.704719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.81982e15 | 0.179000 | 0.0895002 | − | 0.995987i | \(-0.471473\pi\) | ||||
0.0895002 | + | 0.995987i | \(0.471473\pi\) | |||||||
\(882\) | − 1.09713e16i | − 0.692118i | ||||||||
\(883\) | 1.91741e16i | 1.20208i | 0.799221 | + | 0.601038i | \(0.205246\pi\) | ||||
−0.799221 | + | 0.601038i | \(0.794754\pi\) | |||||||
\(884\) | 2.46061e16 | 1.53305 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.03373e15 | 0.125144 | ||||||||
\(887\) | − 2.08389e15i | − 0.127437i | −0.997968 | − | 0.0637183i | \(-0.979704\pi\) | ||||
0.997968 | − | 0.0637183i | \(-0.0202959\pi\) | |||||||
\(888\) | − 5.61559e16i | − 3.41290i | ||||||||
\(889\) | 2.00926e15 | 0.121360 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.32734e16 | −0.791869 | ||||||||
\(892\) | − 1.76117e16i | − 1.04422i | ||||||||
\(893\) | 8.05119e14i | 0.0474435i | ||||||||
\(894\) | −3.34612e16 | −1.95968 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.13967e14 | −0.0239481 | ||||||||
\(897\) | 2.91700e16i | 1.67718i | ||||||||
\(898\) | − 5.57409e16i | − 3.18533i | ||||||||
\(899\) | 2.81803e15 | 0.160054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26426e16 | −0.709332 | ||||||||
\(902\) | 5.22863e15i | 0.291576i | ||||||||
\(903\) | − 5.27965e15i | − 0.292632i | ||||||||
\(904\) | −5.74857e16 | −3.16689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.25116e16 | 2.85792 | ||||||||
\(907\) | − 3.20443e16i | − 1.73345i | −0.498791 | − | 0.866723i | \(-0.666222\pi\) | ||||
0.498791 | − | 0.866723i | \(-0.333778\pi\) | |||||||
\(908\) | 1.93810e16i | 1.04209i | ||||||||
\(909\) | −9.09714e15 | −0.486187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.44282e15 | −0.445797 | −0.222898 | − | 0.974842i | \(-0.571552\pi\) | ||||
−0.222898 | + | 0.974842i | \(0.571552\pi\) | |||||||
\(912\) | − 2.11110e16i | − 1.10799i | ||||||||
\(913\) | 1.14501e16i | 0.597340i | ||||||||
\(914\) | 5.85867e16 | 3.03805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.40748e16 | −1.23349 | ||||||||
\(917\) | 4.74971e15i | 0.241900i | ||||||||
\(918\) | 1.04352e16i | 0.528281i | ||||||||
\(919\) | 1.08277e16 | 0.544880 | 0.272440 | − | 0.962173i | \(-0.412169\pi\) | ||||
0.272440 | + | 0.962173i | \(0.412169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.03352e16 | −0.513913 | ||||||||
\(922\) | 2.87460e16i | 1.42088i | ||||||||
\(923\) | 3.60470e16i | 1.77117i | ||||||||
\(924\) | 1.35521e16 | 0.661926 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.16252e16 | −1.52641 | ||||||||
\(927\) | 7.20438e15i | 0.345667i | ||||||||
\(928\) | 3.38916e15i | 0.161651i | ||||||||
\(929\) | 1.30338e16 | 0.617994 | 0.308997 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308997 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.03513e15 | 0.329647 | ||||||||
\(932\) | − 5.13491e16i | − 2.39191i | ||||||||
\(933\) | 3.70954e16i | 1.71779i | ||||||||
\(934\) | −4.20098e16 | −1.93394 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.75677e16 | −1.70922 | ||||||||
\(937\) | 2.06679e16i | 0.934819i | 0.884041 | + | 0.467410i | \(0.154813\pi\) | ||||
−0.884041 | + | 0.467410i | \(0.845187\pi\) | |||||||
\(938\) | − 1.35359e16i | − 0.608656i | ||||||||
\(939\) | −1.41922e16 | −0.634436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48692e16 | −1.54063 | −0.770317 | − | 0.637661i | \(-0.779902\pi\) | ||||
−0.770317 | + | 0.637661i | \(0.779902\pi\) | |||||||
\(942\) | − 4.10187e16i | − 1.80178i | ||||||||
\(943\) | 5.26621e15i | 0.229977i | ||||||||
\(944\) | 6.80051e15 | 0.295254 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86832e16 | −0.801769 | ||||||||
\(947\) | 2.53080e15i | 0.107977i | 0.998542 | + | 0.0539887i | \(0.0171935\pi\) | ||||
−0.998542 | + | 0.0539887i | \(0.982807\pi\) | |||||||
\(948\) | − 3.12052e16i | − 1.32368i | ||||||||
\(949\) | 4.72194e16 | 1.99139 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29297e16 | −0.539008 | ||||||||
\(952\) | − 9.55293e15i | − 0.395944i | ||||||||
\(953\) | − 1.68411e16i | − 0.693999i | −0.937865 | − | 0.347000i | \(-0.887201\pi\) | ||||
0.937865 | − | 0.347000i | \(-0.112799\pi\) | |||||||
\(954\) | 3.28654e16 | 1.34655 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.18773e15 | 0.372126 | ||||||||
\(957\) | − 1.60912e15i | − 0.0647997i | ||||||||
\(958\) | − 8.00995e16i | − 3.20715i | ||||||||
\(959\) | 1.00507e15 | 0.0400122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.42312e16 | 2.52794 | ||||||||
\(962\) | − 7.74666e16i | − 3.03146i | ||||||||
\(963\) | 1.16236e16i | 0.452269i | ||||||||
\(964\) | −1.35488e16 | −0.524175 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.92825e16 | 0.737544 | ||||||||
\(967\) | 2.82761e16i | 1.07541i | 0.843133 | + | 0.537705i | \(0.180708\pi\) | ||||
−0.843133 | + | 0.537705i | \(0.819292\pi\) | |||||||
\(968\) | 4.14607e16i | 1.56791i | ||||||||
\(969\) | 5.03773e15 | 0.189432 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.55089e16 | 0.948386 | 0.474193 | − | 0.880421i | \(-0.342740\pi\) | ||||
0.474193 | + | 0.880421i | \(0.342740\pi\) | |||||||
\(972\) | − 5.28618e16i | − 1.95424i | ||||||||
\(973\) | − 8.16918e15i | − 0.300302i | ||||||||
\(974\) | 1.52266e16 | 0.556583 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.73346e15 | 0.207225 | ||||||||
\(977\) | − 5.16659e16i | − 1.85688i | −0.371480 | − | 0.928441i | \(-0.621150\pi\) | ||||
0.371480 | − | 0.928441i | \(-0.378850\pi\) | |||||||
\(978\) | 5.31249e16i | 1.89861i | ||||||||
\(979\) | −9.99762e15 | −0.355297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16905e16 | 0.762236 | ||||||||
\(982\) | 7.77456e16i | 2.71683i | ||||||||
\(983\) | 1.06975e15i | 0.0371740i | 0.999827 | + | 0.0185870i | \(0.00591677\pi\) | ||||
−0.999827 | + | 0.0185870i | \(0.994083\pi\) | |||||||
\(984\) | −2.25731e16 | −0.780043 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.93131e15 | −0.0659976 | ||||||||
\(987\) | − 1.58427e15i | − 0.0538374i | ||||||||
\(988\) | − 4.10167e16i | − 1.38611i | ||||||||
\(989\) | −1.88175e16 | −0.632385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.05333e16 | 0.682423 | 0.341211 | − | 0.939987i | \(-0.389163\pi\) | ||||
0.341211 | + | 0.939987i | \(0.389163\pi\) | |||||||
\(992\) | 1.07807e17i | 3.56313i | ||||||||
\(993\) | 3.09134e16i | 1.01608i | ||||||||
\(994\) | 2.38284e16 | 0.778878 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.41678e16 | −2.72094 | ||||||||
\(997\) | 1.61931e16i | 0.520603i | 0.965527 | + | 0.260301i | \(0.0838219\pi\) | ||||
−0.965527 | + | 0.260301i | \(0.916178\pi\) | |||||||
\(998\) | − 9.26076e16i | − 2.96093i | ||||||||
\(999\) | 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.b.c.24.4 | 4 | ||
3.2 | odd | 2 | 225.12.b.f.199.1 | 4 | |||
5.2 | odd | 4 | 5.12.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 25.12.a.c.1.2 | 2 | |||
5.4 | even | 2 | inner | 25.12.b.c.24.1 | 4 | ||
15.2 | even | 4 | 45.12.a.d.1.2 | 2 | |||
15.8 | even | 4 | 225.12.a.h.1.1 | 2 | |||
15.14 | odd | 2 | 225.12.b.f.199.4 | 4 | |||
20.7 | even | 4 | 80.12.a.j.1.2 | 2 | |||
35.27 | even | 4 | 245.12.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.12.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
25.12.a.c.1.2 | 2 | 5.3 | odd | 4 | |||
25.12.b.c.24.1 | 4 | 5.4 | even | 2 | inner | ||
25.12.b.c.24.4 | 4 | 1.1 | even | 1 | trivial | ||
45.12.a.d.1.2 | 2 | 15.2 | even | 4 | |||
80.12.a.j.1.2 | 2 | 20.7 | even | 4 | |||
225.12.a.h.1.1 | 2 | 15.8 | even | 4 | |||
225.12.b.f.199.1 | 4 | 3.2 | odd | 2 | |||
225.12.b.f.199.4 | 4 | 15.14 | odd | 2 | |||
245.12.a.b.1.1 | 2 | 35.27 | even | 4 |