Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,11,Mod(157,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.157");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.k (of order \(4\), degree \(2\), 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: | \(190.607175802\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 63831600 x^{13} + 120528248672 x^{12} - 17600989215600 x^{11} + \cdots + 38\!\cdots\!56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{12}\cdot 5^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 157.8 | ||
Root | \(-380.484 - 380.484i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.157 |
Dual form | 300.11.k.c.193.8 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 99.2043 | − | 99.2043i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17583.1 | + | 17583.1i | 1.04618 | + | 1.04618i | 0.998881 | + | 0.0472951i | \(0.0150601\pi\) |
0.0472951 | + | 0.998881i | \(0.484940\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 19683.0i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −245351. | −1.52344 | −0.761719 | − | 0.647908i | \(-0.775644\pi\) | ||||
−0.761719 | + | 0.647908i | \(0.775644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25882.8 | − | 25882.8i | 0.0697100 | − | 0.0697100i | −0.671392 | − | 0.741102i | \(-0.734303\pi\) |
0.741102 | + | 0.671392i | \(0.234303\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.01646e6 | − | 1.01646e6i | −0.715886 | − | 0.715886i | 0.251874 | − | 0.967760i | \(-0.418953\pi\) |
−0.967760 | + | 0.251874i | \(0.918953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.08723e6i | − | 0.842952i | −0.906840 | − | 0.421476i | \(-0.861512\pi\) | ||
0.906840 | − | 0.421476i | \(-0.138488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.48864e6 | 0.854199 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.16272e6 | + | 4.16272e6i | −0.646752 | + | 0.646752i | −0.952207 | − | 0.305454i | \(-0.901192\pi\) |
0.305454 | + | 0.952207i | \(0.401192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.95264e6 | − | 1.95264e6i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.48858e7i | − | 1.21328i | −0.794975 | − | 0.606642i | \(-0.792516\pi\) | ||
0.794975 | − | 0.606642i | \(-0.207484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.39967e7 | 1.53678 | 0.768391 | − | 0.639981i | \(-0.221058\pi\) | ||||
0.768391 | + | 0.639981i | \(0.221058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.43399e7 | + | 2.43399e7i | −0.621941 | + | 0.621941i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.21011e7 | + | 8.21011e7i | 1.18397 | + | 1.18397i | 0.978707 | + | 0.205263i | \(0.0658049\pi\) |
0.205263 | + | 0.978707i | \(0.434195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.13538e6i | − | 0.0569180i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41660e7 | 0.294900 | 0.147450 | − | 0.989070i | \(-0.452893\pi\) | ||||
0.147450 | + | 0.989070i | \(0.452893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.69545e7 | + | 5.69545e7i | −0.387424 | + | 0.387424i | −0.873767 | − | 0.486344i | \(-0.838330\pi\) |
0.486344 | + | 0.873767i | \(0.338330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.56181e8 | + | 1.56181e8i | 0.680989 | + | 0.680989i | 0.960223 | − | 0.279234i | \(-0.0900805\pi\) |
−0.279234 | + | 0.960223i | \(0.590080\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.35854e8i | 1.18897i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.01674e8 | −0.584518 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.10269e7 | + | 9.10269e7i | −0.217666 | + | 0.217666i | −0.807514 | − | 0.589848i | \(-0.799188\pi\) |
0.589848 | + | 0.807514i | \(0.299188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.07062e8 | − | 2.07062e8i | −0.344134 | − | 0.344134i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.50313e8i | − | 0.210251i | −0.994459 | − | 0.105125i | \(-0.966476\pi\) | ||
0.994459 | − | 0.105125i | \(-0.0335244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.58473e9 | 1.87632 | 0.938160 | − | 0.346202i | \(-0.112529\pi\) | ||||
0.938160 | + | 0.346202i | \(0.112529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.46088e8 | − | 3.46088e8i | 0.348725 | − | 0.348725i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.08379e7 | − | 9.08379e7i | −0.0672811 | − | 0.0672811i | 0.672666 | − | 0.739947i | \(-0.265149\pi\) |
−0.739947 | + | 0.672666i | \(0.765149\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.25920e8i | 0.528071i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.33819e9 | −1.85020 | −0.925100 | − | 0.379723i | \(-0.876019\pi\) | ||||
−0.925100 | + | 0.379723i | \(0.876019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.15460e8 | + | 6.15460e8i | −0.296883 | + | 0.296883i | −0.839792 | − | 0.542909i | \(-0.817323\pi\) |
0.542909 | + | 0.839792i | \(0.317323\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.31403e9 | − | 4.31403e9i | −1.59378 | − | 1.59378i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.25540e9i | − | 0.407988i | −0.978972 | − | 0.203994i | \(-0.934608\pi\) | ||
0.978972 | − | 0.203994i | \(-0.0653923\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.87420e8 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.20145e9 | + | 2.20145e9i | −0.558881 | + | 0.558881i | −0.928989 | − | 0.370108i | \(-0.879321\pi\) |
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.46878e9 | − | 2.46878e9i | −0.495321 | − | 0.495321i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.39933e9i | 0.966918i | 0.875367 | + | 0.483459i | \(0.160620\pi\) | ||||
−0.875367 | + | 0.483459i | \(0.839380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.10200e8 | 0.145858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.36467e9 | − | 4.36467e9i | 0.627388 | − | 0.627388i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.66166e9 | + | 6.66166e9i | 0.775754 | + | 0.775754i | 0.979106 | − | 0.203352i | \(-0.0651835\pi\) |
−0.203352 | + | 0.979106i | \(0.565183\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82925e9i | 0.507813i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.10333e9 | −0.580711 | −0.290355 | − | 0.956919i | \(-0.593774\pi\) | ||||
−0.290355 | + | 0.956919i | \(0.593774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.03828e9 | + | 6.03828e9i | −0.520868 | + | 0.520868i | −0.917833 | − | 0.396966i | \(-0.870063\pi\) |
0.396966 | + | 0.917833i | \(0.370063\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.44897e10 | + | 1.44897e10i | 1.03309 | + | 1.03309i | 0.999433 | + | 0.0336592i | \(0.0107161\pi\) |
0.0336592 | + | 0.999433i | \(0.489284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.56984e10i | 1.67022i | 0.550081 | + | 0.835111i | \(0.314597\pi\) | ||||
−0.550081 | + | 0.835111i | \(0.685403\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.62896e10 | 0.966707 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.51562e10 | + | 2.51562e10i | −1.36538 | + | 1.36538i | −0.498474 | + | 0.866904i | \(0.666106\pi\) |
−0.866904 | + | 0.498474i | \(0.833894\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09452e8 | − | 5.09452e8i | −0.0232367 | − | 0.0232367i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.57448e10i | − | 1.49788i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.42598e10 | 1.32086 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.38942e9 | − | 3.38942e9i | 0.120392 | − | 0.120392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.56680e10 | − | 2.56680e10i | −0.776914 | − | 0.776914i | 0.202391 | − | 0.979305i | \(-0.435129\pi\) |
−0.979305 | + | 0.202391i | \(0.935129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.13003e10i | 0.316330i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.75211e10 | −0.972565 | −0.486283 | − | 0.873802i | \(-0.661647\pi\) | ||||
−0.486283 | + | 0.873802i | \(0.661647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.67000e10 | − | 3.67000e10i | 0.881876 | − | 0.881876i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.09695e9 | + | 5.09695e9i | 0.105611 | + | 0.105611i | 0.757938 | − | 0.652327i | \(-0.226207\pi\) |
−0.652327 | + | 0.757938i | \(0.726207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.00719e9i | − | 0.0386825i | −0.999813 | − | 0.0193412i | \(-0.993843\pi\) | ||
0.999813 | − | 0.0193412i | \(-0.00615689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.09878e10 | 0.556025 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.35038e9 | + | 6.35038e9i | −0.106199 | + | 0.106199i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.33182e10 | + | 3.33182e10i | 0.485394 | + | 0.485394i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.97699e10i | 0.541531i | 0.962645 | + | 0.270765i | \(0.0872768\pi\) | ||||
−0.962645 | + | 0.270765i | \(0.912723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.92476e10 | −1.26426 | −0.632128 | − | 0.774864i | \(-0.717819\pi\) | ||||
−0.632128 | + | 0.774864i | \(0.717819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00069e10 | + | 2.00069e10i | −0.238629 | + | 0.238629i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.76032e10 | − | 2.76032e10i | −0.289375 | − | 0.289375i | 0.547458 | − | 0.836833i | \(-0.315596\pi\) |
−0.836833 | + | 0.547458i | \(0.815596\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.80605e10i | 0.177723i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.46387e11 | −1.35323 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.34584e11 | − | 1.34584e11i | 1.16965 | − | 1.16965i | 0.187355 | − | 0.982292i | \(-0.440009\pi\) |
0.982292 | − | 0.187355i | \(-0.0599915\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.12320e11 | + | 1.12320e11i | 0.864717 | + | 0.864717i | 0.991882 | − | 0.127164i | \(-0.0405875\pi\) |
−0.127164 | + | 0.991882i | \(0.540588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.36519e11i | 0.990281i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.10830e10 | −0.280984 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.60619e10 | + | 2.60619e10i | −0.168180 | + | 0.168180i | −0.786179 | − | 0.617999i | \(-0.787944\pi\) |
0.617999 | + | 0.786179i | \(0.287944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.49117e10 | − | 1.49117e10i | −0.0858345 | − | 0.0858345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.37045e9i | − | 0.0237827i | −0.999929 | − | 0.0118913i | \(-0.996215\pi\) | ||
0.999929 | − | 0.0118913i | \(-0.00378522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.96965e11 | −1.01390 | −0.506952 | − | 0.861974i | \(-0.669228\pi\) | ||||
−0.506952 | + | 0.861974i | \(0.669228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.57212e11 | − | 1.57212e11i | 0.766005 | − | 0.766005i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.49388e11 | + | 2.49388e11i | 1.09061 | + | 1.09061i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 6.86668e10i | − | 0.284733i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.91592e11 | 1.14712 | 0.573559 | − | 0.819164i | \(-0.305562\pi\) | ||||
0.573559 | + | 0.819164i | \(0.305562\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.04238e11 | + | 2.04238e11i | −0.762693 | + | 0.762693i | −0.976808 | − | 0.214116i | \(-0.931313\pi\) |
0.214116 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68621e10 | − | 2.68621e10i | −0.0905335 | − | 0.0905335i | 0.660390 | − | 0.750923i | \(-0.270391\pi\) |
−0.750923 | + | 0.660390i | \(0.770391\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.32496e11i | − | 0.424557i | −0.977209 | − | 0.212278i | \(-0.931912\pi\) | ||
0.977209 | − | 0.212278i | \(-0.0680884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.80230e10 | −0.0549348 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.37570e11 | − | 4.37570e11i | 1.26931 | − | 1.26931i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.19348e10 | + | 8.19348e10i | 0.215584 | + | 0.215584i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.12105e11i | 1.28418i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.62184e11 | 0.865998 | 0.432999 | − | 0.901394i | \(-0.357455\pi\) | ||||
0.432999 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.31162e11 | + | 3.31162e11i | −0.755341 | + | 0.755341i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.73598e11 | + | 7.73598e11i | 1.60774 | + | 1.60774i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.22113e11i | 0.242404i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.26175e10 | −0.0998088 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.84416e11 | + | 4.84416e11i | −0.878404 | + | 0.878404i | −0.993369 | − | 0.114966i | \(-0.963324\pi\) |
0.114966 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.13763e11 | + | 4.13763e11i | 0.686471 | + | 0.686471i | 0.961450 | − | 0.274979i | \(-0.0886709\pi\) |
−0.274979 | + | 0.961450i | \(0.588671\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.11849e11i | 0.336395i | 0.985753 | + | 0.168197i | \(0.0537946\pi\) | ||||
−0.985753 | + | 0.168197i | \(0.946205\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.55941e11 | −1.30132 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.33034e11 | − | 5.33034e11i | 0.776203 | − | 0.776203i | −0.202980 | − | 0.979183i | \(-0.565063\pi\) |
0.979183 | + | 0.202980i | \(0.0650625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.24541e11 | − | 1.24541e11i | −0.166560 | − | 0.166560i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.42513e12i | 1.82753i | 0.406244 | + | 0.913765i | \(0.366838\pi\) | ||||
−0.406244 | + | 0.913765i | \(0.633162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05869e12 | −1.30221 | −0.651107 | − | 0.758986i | \(-0.725695\pi\) | ||||
−0.651107 | + | 0.758986i | \(0.725695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.84338e10 | + | 3.84338e10i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.40235e10 | − | 5.40235e10i | −0.0587622 | − | 0.0587622i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.36788e11i | 0.456324i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.21882e12 | −1.22341 | −0.611704 | − | 0.791087i | \(-0.709516\pi\) | ||||
−0.611704 | + | 0.791087i | \(0.709516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.02133e12 | − | 1.02133e12i | 0.985287 | − | 0.985287i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.16474e11 | + | 2.16474e11i | 0.193081 | + | 0.193081i | 0.797026 | − | 0.603945i | \(-0.206405\pi\) |
−0.603945 | + | 0.797026i | \(0.706405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.88718e12i | 2.47728i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.89828e11 | −0.404428 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.22079e11 | + | 4.22079e11i | −0.335440 | + | 0.335440i | −0.854648 | − | 0.519208i | \(-0.826227\pi\) |
0.519208 | + | 0.854648i | \(0.326227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.35637e11 | + | 5.35637e11i | 0.394743 | + | 0.394743i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.97700e12i | 1.40361i | 0.712370 | + | 0.701804i | \(0.247622\pi\) | ||||
−0.712370 | + | 0.701804i | \(0.752378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.14114e12 | −0.780718 | −0.390359 | − | 0.920663i | \(-0.627649\pi\) | ||||
−0.390359 | + | 0.920663i | \(0.627649\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.02958e10 | − | 9.02958e10i | 0.0595462 | − | 0.0595462i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.80834e10 | − | 1.80834e10i | −0.0110887 | − | 0.0110887i | 0.701541 | − | 0.712629i | \(-0.252496\pi\) |
−0.712629 | + | 0.701541i | \(0.752496\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.65988e11i | − | 0.512260i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.83399e11 | 0.275914 | 0.137957 | − | 0.990438i | \(-0.455946\pi\) | ||||
0.137957 | + | 0.990438i | \(0.455946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.30550e12 | + | 1.30550e12i | −0.719192 | + | 0.719192i | −0.968440 | − | 0.249248i | \(-0.919817\pi\) |
0.249248 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00744e11 | + | 6.00744e11i | 0.308517 | + | 0.308517i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.03680e10i | 0.0249842i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.32173e12 | 0.633400 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.79363e11 | − | 1.79363e11i | 0.0830606 | − | 0.0830606i | −0.664356 | − | 0.747416i | \(-0.731294\pi\) |
0.747416 | + | 0.664356i | \(0.231294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.79082e11 | + | 4.79082e11i | 0.207314 | + | 0.207314i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.15486e11i | 0.0901702i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00287e12 | −0.810626 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.05477e11 | + | 6.05477e11i | −0.237074 | + | 0.237074i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.02370e12 | + | 2.02370e12i | 0.742085 | + | 0.742085i | 0.972979 | − | 0.230894i | \(-0.0741650\pi\) |
−0.230894 | + | 0.972979i | \(0.574165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.19805e12i | 0.425287i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.23387e11 | −0.145524 | −0.0727622 | − | 0.997349i | \(-0.523181\pi\) | ||||
−0.0727622 | + | 0.997349i | \(0.523181\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.30038e12 | − | 3.30038e12i | 1.09861 | − | 1.09861i | 0.104032 | − | 0.994574i | \(-0.466826\pi\) |
0.994574 | − | 0.104032i | \(-0.0331744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.57425e12 | + | 3.57425e12i | 1.11658 | + | 1.11658i | 0.992240 | + | 0.124336i | \(0.0396801\pi\) |
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.10577e12i | 1.84836i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.87487e12 | 0.843517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.12158e12 | + | 2.12158e12i | −0.603457 | + | 0.603457i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.54940e12 | + | 2.54940e12i | 0.681865 | + | 0.681865i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.49230e12i | 1.42487i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.13628e11 | −0.229948 | −0.114974 | − | 0.993369i | \(-0.536678\pi\) | ||||
−0.114974 | + | 0.993369i | \(0.536678\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.61600e12 | − | 1.61600e12i | 0.394657 | − | 0.394657i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.53730e12 | + | 3.53730e12i | 0.813808 | + | 0.813808i | 0.985202 | − | 0.171395i | \(-0.0548274\pi\) |
−0.171395 | + | 0.985202i | \(0.554827\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.99121e12i | 1.11483i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.07947e13 | −2.34119 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.38566e11 | + | 9.38566e11i | −0.197694 | + | 0.197694i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.02321e12 | + | 4.02321e12i | 0.799697 | + | 0.799697i | 0.983048 | − | 0.183351i | \(-0.0586944\pi\) |
−0.183351 | + | 0.983048i | \(0.558694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.01641e12i | − | 0.775730i | −0.921716 | − | 0.387865i | \(-0.873213\pi\) | ||
0.921716 | − | 0.387865i | \(-0.126787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.01080e11 | −0.0189727 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.80344e11 | + | 4.80344e11i | −0.0876353 | + | 0.0876353i | −0.749565 | − | 0.661930i | \(-0.769738\pi\) |
0.661930 | + | 0.749565i | \(0.269738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.54604e12 | − | 3.54604e12i | −0.611509 | − | 0.611509i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1.16724e13i | − | 1.95743i | −0.205217 | − | 0.978716i | \(-0.565790\pi\) | ||
0.205217 | − | 0.978716i | \(-0.434210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.77453e12 | 0.289432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.39872e12 | − | 3.39872e12i | 0.539240 | − | 0.539240i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.48825e11 | − | 3.48825e11i | −0.0523935 | − | 0.0523935i | 0.680425 | − | 0.732818i | \(-0.261795\pi\) |
−0.732818 | + | 0.680425i | \(0.761795\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.72490e11i | − | 0.0983000i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.20107e12 | −0.455434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.19857e12 | − | 3.19857e12i | 0.443008 | − | 0.443008i | −0.450013 | − | 0.893022i | \(-0.648581\pi\) |
0.893022 | + | 0.450013i | \(0.148581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.44116e11 | − | 6.44116e11i | −0.0845780 | − | 0.0845780i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.46898e12i | 1.08302i | 0.840695 | + | 0.541508i | \(0.182147\pi\) | ||||
−0.840695 | + | 0.541508i | \(0.817853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.09275e12 | −0.634348 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.15121e12 | − | 7.15121e12i | 0.867732 | − | 0.867732i | −0.124489 | − | 0.992221i | \(-0.539729\pi\) |
0.992221 | + | 0.124489i | \(0.0397293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.12104e12 | + | 1.12104e12i | 0.129141 | + | 0.129141i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.37482e12i | 0.715682i | 0.933783 | + | 0.357841i | \(0.116487\pi\) | ||||
−0.933783 | + | 0.357841i | \(0.883513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.46243e12 | 0.926001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.72225e12 | + | 3.72225e12i | −0.397048 | + | 0.397048i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.32306e12 | − | 2.32306e12i | −0.235563 | − | 0.235563i | 0.579447 | − | 0.815010i | \(-0.303269\pi\) |
−0.815010 | + | 0.579447i | \(0.803269\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 7.28159e12i | − | 0.720049i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.57234e13 | −1.51644 | −0.758219 | − | 0.652000i | \(-0.773930\pi\) | ||||
−0.758219 | + | 0.652000i | \(0.773930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.13876e12 | − | 1.13876e12i | 0.107129 | − | 0.107129i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.01436e13 | − | 2.01436e13i | −1.80370 | − | 1.80370i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.69349e12i | − | 0.410090i | −0.978753 | − | 0.205045i | \(-0.934266\pi\) | ||
0.978753 | − | 0.205045i | \(-0.0657340\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.01128e12 | 0.0862307 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.64297e12 | − | 2.64297e12i | 0.219959 | − | 0.219959i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.99122e11 | − | 1.99122e11i | −0.0157920 | − | 0.0157920i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.55630e12i | 0.430244i | 0.976587 | + | 0.215122i | \(0.0690150\pi\) | ||||
−0.976587 | + | 0.215122i | \(0.930985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.57057e12 | 0.421201 | 0.210600 | − | 0.977572i | \(-0.432458\pi\) | ||||
0.210600 | + | 0.977572i | \(0.432458\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.07412e12 | − | 3.07412e12i | 0.226996 | − | 0.226996i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.78645e13 | + | 2.78645e13i | 1.96296 | + | 1.96296i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.25997e12i | 0.0867110i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.81802e13 | 1.22240 | 0.611199 | − | 0.791477i | \(-0.290687\pi\) | ||||
0.611199 | + | 0.791477i | \(0.290687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.48843e12 | + | 7.48843e12i | −0.491984 | + | 0.491984i | −0.908931 | − | 0.416947i | \(-0.863100\pi\) |
0.416947 | + | 0.908931i | \(0.363100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.68856e12 | + | 8.68856e12i | 0.545181 | + | 0.545181i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.55826e13i | − | 0.955688i | −0.878445 | − | 0.477844i | \(-0.841418\pi\) | ||
0.878445 | − | 0.477844i | \(-0.158582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.61062e12 | 0.396323 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.09695e13 | + | 1.09695e13i | −0.642935 | + | 0.642935i | −0.951276 | − | 0.308341i | \(-0.900226\pi\) |
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.94535e12 | + | 3.94535e12i | 0.221079 | + | 0.221079i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.28951e12i | 0.454252i | 0.973865 | + | 0.227126i | \(0.0729330\pi\) | ||||
−0.973865 | + | 0.227126i | \(0.927067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.38267e12 | −0.449262 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.84579e12 | + | 9.84579e12i | −0.516131 | + | 0.516131i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.58586e13 | − | 2.58586e13i | −1.29725 | − | 1.29725i | −0.930202 | − | 0.367048i | \(-0.880368\pi\) |
−0.367048 | − | 0.930202i | \(-0.619632\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.96954e12i | 0.194839i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.93741e13 | 1.41078 | 0.705392 | − | 0.708817i | \(-0.250771\pi\) | ||||
0.705392 | + | 0.708817i | \(0.250771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.41383e13 | + | 1.41383e13i | −0.664494 | + | 0.664494i | −0.956436 | − | 0.291942i | \(-0.905699\pi\) |
0.291942 | + | 0.956436i | \(0.405699\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.42118e12 | + | 5.42118e12i | 0.244067 | + | 0.244067i | 0.818530 | − | 0.574463i | \(-0.194789\pi\) |
−0.574463 | + | 0.818530i | \(0.694789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.19442e12i | − | 0.140776i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.47672e12 | −0.236274 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.39739e13 | − | 1.39739e13i | 0.590216 | − | 0.590216i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.79168e12 | + | 1.79168e12i | 0.0725553 | + | 0.0725553i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.01084e13i | − | 0.797442i | −0.917072 | − | 0.398721i | \(-0.869454\pi\) | ||
0.917072 | − | 0.398721i | \(-0.130546\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.25002e12 | 0.165069 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.45222e13 | + | 1.45222e13i | −0.552455 | + | 0.552455i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.04347e13 | − | 3.04347e13i | −1.11103 | − | 1.11103i | −0.993012 | − | 0.118015i | \(-0.962347\pi\) |
−0.118015 | − | 0.993012i | \(-0.537653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.67026e13i | − | 0.955013i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.96582e13 | 1.03929 | 0.519645 | − | 0.854382i | \(-0.326064\pi\) | ||||
0.519645 | + | 0.854382i | \(0.326064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.52953e13 | + | 2.52953e13i | −0.868572 | + | 0.868572i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.86956e13 | − | 5.86956e13i | −1.93564 | − | 1.93564i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.43963e13i | − | 1.43497i | −0.696572 | − | 0.717487i | \(-0.745292\pi\) | ||
0.696572 | − | 0.717487i | \(-0.254708\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.22852e13 | 0.706039 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.95547e13 | − | 2.95547e13i | 0.917881 | − | 0.917881i | −0.0789944 | − | 0.996875i | \(-0.525171\pi\) |
0.996875 | + | 0.0789944i | \(0.0251709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.35432e13 | + | 1.35432e13i | 0.404281 | + | 0.404281i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.33159e13i | 0.389747i | 0.980828 | + | 0.194873i | \(0.0624296\pi\) | ||||
−0.980828 | + | 0.194873i | \(0.937570\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.16434e13 | −0.621184 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.07561e12 | + | 4.07561e12i | −0.114711 | + | 0.114711i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.83193e13 | − | 3.83193e13i | −1.03744 | − | 1.03744i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.17090e12i | 0.137319i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.57642e13 | −0.410661 | −0.205331 | − | 0.978693i | \(-0.565827\pi\) | ||||
−0.205331 | + | 0.978693i | \(0.565827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.20803e13 | − | 1.20803e13i | 0.308723 | − | 0.308723i | −0.535691 | − | 0.844414i | \(-0.679949\pi\) |
0.844414 | + | 0.535691i | \(0.179949\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.47207e13 | − | 4.47207e13i | −1.10016 | − | 1.10016i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.77005e12i | 0.163423i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.95862e12 | −0.0700836 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.84313e11 | − | 8.84313e11i | 0.0205575 | − | 0.0205575i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.33568e11 | − | 4.33568e11i | −0.00970924 | − | 0.00970924i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.24022e13i | − | 1.81132i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.08818e13 | 1.09793 | 0.548966 | − | 0.835844i | \(-0.315021\pi\) | ||||
0.548966 | + | 0.835844i | \(0.315021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.95398e13 | + | 1.95398e13i | −0.413924 | + | 0.413924i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49260e13 | + | 1.49260e13i | 0.304794 | + | 0.304794i | 0.842886 | − | 0.538092i | \(-0.180855\pi\) |
−0.538092 | + | 0.842886i | \(0.680855\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.11923e13i | − | 0.625440i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.19425e13 | −1.02274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.20738e13 | − | 2.20738e13i | 0.426827 | − | 0.426827i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.17195e12 | − | 1.17195e12i | −0.0218592 | − | 0.0218592i | 0.696093 | − | 0.717952i | \(-0.254920\pi\) |
−0.717952 | + | 0.696093i | \(0.754920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.94829e12i | 0.0540146i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.94808e13 | 0.890477 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.14141e13 | + | 5.14141e13i | −0.908951 | + | 0.908951i | −0.996188 | − | 0.0872368i | \(-0.972196\pi\) |
0.0872368 | + | 0.996188i | \(0.472196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.81205e12 | − | 6.81205e12i | −0.116242 | − | 0.116242i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.04638e13i | 0.510767i | 0.966840 | + | 0.255384i | \(0.0822018\pi\) | ||||
−0.966840 | + | 0.255384i | \(0.917798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.28538e13 | 1.20025 | 0.600125 | − | 0.799906i | \(-0.295117\pi\) | ||||
0.600125 | + | 0.799906i | \(0.295117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.89272e13 | − | 2.89272e13i | 0.468309 | − | 0.468309i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.24079e13 | + | 7.24079e13i | 1.13216 | + | 1.13216i | 0.989818 | + | 0.142339i | \(0.0454624\pi\) |
0.142339 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.05226e13i | 0.622736i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.74167e13 | −1.16938 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.23336e13 | − | 2.23336e13i | 0.331600 | − | 0.331600i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.23536e13 | − | 8.23536e13i | −1.18166 | − | 1.18166i | −0.979314 | − | 0.202345i | \(-0.935144\pi\) |
−0.202345 | − | 0.979314i | \(-0.564856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.18314e13i | − | 1.29543i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.32968e12 | −0.0739203 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.89458e13 | − | 5.89458e13i | 0.803858 | − | 0.803858i | −0.179839 | − | 0.983696i | \(-0.557558\pi\) |
0.983696 | + | 0.179839i | \(0.0575575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.31441e13 | − | 1.31441e13i | −0.173325 | − | 0.173325i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.95878e13i | − | 1.03208i | −0.856565 | − | 0.516039i | \(-0.827406\pi\) | ||
0.856565 | − | 0.516039i | \(-0.172594\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.52648e14 | 1.94679 | 0.973396 | − | 0.229130i | \(-0.0735882\pi\) | ||||
0.973396 | + | 0.229130i | \(0.0735882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.78796e12 | + | 1.78796e12i | −0.0224270 | + | 0.0224270i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.73177e13 | − | 1.73177e13i | −0.210158 | − | 0.210158i | 0.594176 | − | 0.804335i | \(-0.297478\pi\) |
−0.804335 | + | 0.594176i | \(0.797478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 8.68177e13i | − | 1.03639i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.08484e12 | 0.0949435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.17442e13 | + | 7.17442e13i | −0.828866 | + | 0.828866i | −0.987360 | − | 0.158494i | \(-0.949336\pi\) |
0.158494 | + | 0.987360i | \(0.449336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.30842e13 | + | 3.30842e13i | 0.369994 | + | 0.369994i | 0.867475 | − | 0.497481i | \(-0.165742\pi\) |
−0.497481 | + | 0.867475i | \(0.665742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.50831e14i | − | 1.65973i | −0.557965 | − | 0.829865i | \(-0.688418\pi\) | ||
0.557965 | − | 0.829865i | \(-0.311582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.62566e13 | 0.176024 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.49369e13 | + | 9.49369e13i | −1.01157 | + | 1.01157i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.08030e13 | + | 5.08030e13i | 0.524266 | + | 0.524266i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.66904e14i | − | 1.69517i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.51439e13 | 0.651219 | 0.325609 | − | 0.945504i | \(-0.394431\pi\) | ||||
0.325609 | + | 0.945504i | \(0.394431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.59302e13 | − | 3.59302e13i | 0.353542 | − | 0.353542i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.69286e12 | + | 8.69286e12i | 0.0828830 | + | 0.0828830i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.57055e13i | 0.616733i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.33777e13 | −0.770477 | −0.385238 | − | 0.922817i | \(-0.625881\pi\) | ||||
−0.385238 | + | 0.922817i | \(0.625881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.00080e13 | + | 9.00080e13i | −0.818891 | + | 0.818891i | −0.985947 | − | 0.167056i | \(-0.946574\pi\) |
0.167056 | + | 0.985947i | \(0.446574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.21631e14 | − | 1.21631e14i | −1.07281 | − | 1.07281i | −0.997132 | − | 0.0756761i | \(-0.975889\pi\) |
−0.0756761 | − | 0.997132i | \(-0.524111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.68796e13i | 0.320304i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.53489e14 | 1.31272 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.39661e14 | − | 1.39661e14i | 1.17628 | − | 1.17628i | 0.195595 | − | 0.980685i | \(-0.437336\pi\) |
0.980685 | − | 0.195595i | \(-0.0626639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.21141e13 | + | 1.21141e13i | 0.0989610 | + | 0.0989610i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.95289e14i | 1.57127i | 0.618693 | + | 0.785633i | \(0.287663\pi\) | ||||
−0.618693 | + | 0.785633i | \(0.712337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.92478e12 | 0.0707278 | 0.0353639 | − | 0.999375i | \(-0.488741\pi\) | ||||
0.0353639 | + | 0.999375i | \(0.488741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.21988e12 | + | 5.21988e12i | −0.0407468 | + | 0.0407468i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.03593e14 | + | 1.03593e14i | 0.784694 | + | 0.784694i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.61124e13i | 0.717214i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.88816e14 | −2.85846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.20625e13 | − | 3.20625e13i | 0.232232 | − | 0.232232i | −0.581392 | − | 0.813624i | \(-0.697492\pi\) |
0.813624 | + | 0.581392i | \(0.197492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.96987e13 | − | 4.96987e13i | −0.349463 | − | 0.349463i | 0.510446 | − | 0.859910i | \(-0.329480\pi\) |
−0.859910 | + | 0.510446i | \(0.829480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.34265e14i | 1.62315i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.20942e13 | 0.560502 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.01777e14 | − | 2.01777e14i | 1.35759 | − | 1.35759i | 0.480704 | − | 0.876883i | \(-0.340381\pi\) |
0.876883 | − | 0.480704i | \(-0.159619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.10163e13 | + | 2.10163e13i | 0.137333 | + | 0.137333i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.71207e12i | 0.0303470i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.96254e13 | −0.441955 | −0.220977 | − | 0.975279i | \(-0.570925\pi\) | ||||
−0.220977 | + | 0.975279i | \(0.570925\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.49131e13 | + | 8.49131e13i | −0.531261 | + | 0.531261i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.47282e13 | − | 3.47282e13i | −0.211115 | − | 0.211115i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.05759e14i | − | 0.633767i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.15316e14 | −0.681242 | −0.340621 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340621 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.71364e14 | − | 1.71364e14i | 0.998029 | − | 0.998029i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.07315e14 | − | 1.07315e14i | −0.607526 | − | 0.607526i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.88271e13i | 0.328357i | 0.986431 | + | 0.164178i | \(0.0524973\pi\) | ||||
−0.986431 | + | 0.164178i | \(0.947503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.47101e13 | −0.135996 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.83146e14 | + | 1.83146e14i | −0.993917 | + | 0.993917i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.41379e14 | + | 1.41379e14i | 0.746086 | + | 0.746086i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.84801e14i | 0.961745i | 0.876790 | + | 0.480873i | \(0.159680\pi\) | ||||
−0.876790 | + | 0.480873i | \(0.840320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.12343e14 | −1.08984 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.05026e14 | + | 1.05026e14i | −0.531627 | + | 0.531627i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.34341e13 | − | 3.34341e13i | −0.164633 | − | 0.164633i | 0.619983 | − | 0.784616i | \(-0.287140\pi\) |
−0.784616 | + | 0.619983i | \(0.787140\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.62560e12i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.15783e14 | 0.554702 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.34429e13 | − | 1.34429e13i | 0.0635291 | − | 0.0635291i | −0.674628 | − | 0.738157i | \(-0.735696\pi\) |
0.738157 | + | 0.674628i | \(0.235696\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.22872e13 | + | 2.22872e13i | 0.102499 | + | 0.102499i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.19414e12i | − | 0.0417147i | −0.999782 | − | 0.0208573i | \(-0.993360\pi\) | ||
0.999782 | − | 0.0208573i | \(-0.00663958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.07187e13 | −0.0479791 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.45280e13 | − | 3.45280e13i | 0.152485 | − | 0.152485i | −0.626742 | − | 0.779227i | \(-0.715612\pi\) |
0.779227 | + | 0.626742i | \(0.215612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.33312e13 | + | 4.33312e13i | 0.186294 | + | 0.186294i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.09546e14i | 2.16159i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.78104e14 | −1.16415 | −0.582073 | − | 0.813136i | \(-0.697758\pi\) | ||||
−0.582073 | + | 0.813136i | \(0.697758\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.20912e14 | + | 1.20912e14i | −0.499454 | + | 0.499454i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.20330e14 | + | 2.20330e14i | 0.886327 | + | 0.886327i | 0.994168 | − | 0.107841i | \(-0.0343939\pi\) |
−0.107841 | + | 0.994168i | \(0.534394\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.02640e14i | − | 0.804483i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.15151e14 | 1.62661 | 0.813303 | − | 0.581840i | \(-0.197667\pi\) | ||||
0.813303 | + | 0.581840i | \(0.197667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.51858e14 | + | 4.51858e14i | −1.74735 | + | 1.74735i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.89054e12 | − | 3.89054e12i | −0.0146566 | − | 0.0146566i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.28902e14i | 1.22302i | 0.791235 | + | 0.611512i | \(0.209438\pi\) | ||||
−0.791235 | + | 0.611512i | \(0.790562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.29503e13 | 0.157650 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.53823e14 | − | 3.53823e14i | 1.28200 | − | 1.28200i | 0.342475 | − | 0.939527i | \(-0.388735\pi\) |
0.939527 | − | 0.342475i | \(-0.111265\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.86421e14 | + | 2.86421e14i | 1.01135 | + | 1.01135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 7.13124e13i | − | 0.248587i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.19028e14 | 2.81867 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.85931e13 | + | 4.85931e13i | −0.165107 | + | 0.165107i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.42715e14 | + | 3.42715e14i | 1.13517 | + | 1.13517i | 0.989305 | + | 0.145862i | \(0.0465955\pi\) |
0.145862 | + | 0.989305i | \(0.453404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.37441e13i | 0.273885i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.84648e14 | −2.85685 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.10174e13 | − | 4.10174e13i | 0.130798 | − | 0.130798i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.34436e14 | − | 3.34436e14i | −1.03997 | − | 1.03997i | −0.999167 | − | 0.0408030i | \(-0.987008\pi\) |
−0.0408030 | − | 0.999167i | \(-0.512992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.17503e14i | − | 0.975021i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.06275e14 | 0.322306 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.51004e14 | − | 1.51004e14i | 0.452283 | − | 0.452283i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.96127e14 | + | 1.96127e14i | 0.573020 | + | 0.573020i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.58044e14i | 1.32180i | 0.750475 | + | 0.660898i | \(0.229825\pi\) | ||||
−0.750475 | + | 0.660898i | \(0.770175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.39895e14 | −0.683780 | −0.341890 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341890 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.13206e14 | + | 1.13206e14i | −0.318727 | + | 0.318727i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.18877e14 | + | 1.18877e14i | 0.326579 | + | 0.326579i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.79155e13i | − | 0.0486193i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.01069e14 | −1.07523 | −0.537617 | − | 0.843189i | \(-0.680675\pi\) | ||||
−0.537617 | + | 0.843189i | \(0.680675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.07810e14 | + | 1.07810e14i | −0.285534 | + | 0.285534i | −0.835311 | − | 0.549777i | \(-0.814713\pi\) |
0.549777 | + | 0.835311i | \(0.314713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.85157e14 | + | 2.85157e14i | 0.737150 | + | 0.737150i | 0.972025 | − | 0.234876i | \(-0.0754683\pi\) |
−0.234876 | + | 0.972025i | \(0.575468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.81396e14i | 1.22950i | 0.788720 | + | 0.614752i | \(0.210744\pi\) | ||||
−0.788720 | + | 0.614752i | \(0.789256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.58790e12 | −0.00905388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.41381e14 | − | 3.41381e14i | 0.851165 | − | 0.851165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.59097e13 | − | 8.59097e13i | −0.209129 | − | 0.209129i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.74082e14i | 1.62145i | 0.585430 | + | 0.810723i | \(0.300926\pi\) | ||||
−0.585430 | + | 0.810723i | \(0.699074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.98598e14 | −0.472058 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.79553e13 | − | 4.79553e13i | 0.112641 | − | 0.112641i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.02393e14 | + | 6.02393e14i | 1.38186 | + | 1.38186i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.59023e14i | 0.587218i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.83528e14 | −1.53147 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.47427e13 | − | 2.47427e13i | 0.0547900 | − | 0.0547900i | −0.679181 | − | 0.733971i | \(-0.737665\pi\) |
0.733971 | + | 0.679181i | \(0.237665\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.73644e14 | − | 4.73644e14i | −1.02458 | − | 1.02458i | −0.999690 | − | 0.0248941i | \(-0.992075\pi\) |
−0.0248941 | − | 0.999690i | \(-0.507925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.26066e13i | 0.198005i | 0.995087 | + | 0.0990025i | \(0.0315652\pi\) | ||||
−0.995087 | + | 0.0990025i | \(0.968435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.19193e14 | 0.251903 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.31608e14 | − | 5.31608e14i | 1.11055 | − | 1.11055i | 0.117473 | − | 0.993076i | \(-0.462521\pi\) |
0.993076 | − | 0.117473i | \(-0.0374795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.99672e12 | + | 4.99672e12i | 0.0101998 | + | 0.0101998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.08014e14i | 0.621544i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.70228e12 | −0.00938033 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.31122e14 | − | 1.31122e14i | 0.258585 | − | 0.258585i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.18639e14 | + | 7.18639e14i | 1.38520 | + | 1.38520i | 0.835094 | + | 0.550107i | \(0.185413\pi\) |
0.550107 | + | 0.835094i | \(0.314587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.55872e13i | − | 0.0678187i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.44985e14 | −0.461593 | −0.230797 | − | 0.973002i | \(-0.574133\pi\) | ||||
−0.230797 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.71238e14 | + | 2.71238e14i | −0.505297 | + | 0.505297i | −0.913079 | − | 0.407782i | \(-0.866302\pi\) |
0.407782 | + | 0.913079i | \(0.366302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.10781e14 | − | 2.10781e14i | −0.383895 | − | 0.383895i | 0.488608 | − | 0.872503i | \(-0.337505\pi\) |
−0.872503 | + | 0.488608i | \(0.837505\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 9.02644e14i | − | 1.62558i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.50541e13 | 0.169271 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.25987e14 | − | 3.25987e14i | 0.574041 | − | 0.574041i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.13771e13 | + | 2.13771e13i | 0.0368118 | + | 0.0368118i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.09490e15i | − | 1.86455i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.85050e14 | 0.311648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.98694e14 | + | 1.98694e14i | −0.330937 | + | 0.330937i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.15726e14 | − | 6.15726e14i | −1.00312 | − | 1.00312i | −0.999995 | − | 0.00312037i | \(-0.999007\pi\) |
−0.00312037 | − | 0.999995i | \(-0.500993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.20132e14i | 0.193570i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.02185e15 | −1.62853 | −0.814267 | − | 0.580490i | \(-0.802861\pi\) | ||||
−0.814267 | + | 0.580490i | \(0.802861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.40129e14 | − | 5.40129e14i | 0.851420 | − | 0.851420i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.59736e14 | − | 6.59736e14i | −1.01747 | − | 1.01747i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.05732e15i | 1.61298i | 0.591249 | + | 0.806489i | \(0.298635\pi\) | ||||
−0.591249 | + | 0.806489i | \(0.701365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.01519e14 | 0.605910 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.64017e13 | + | 8.64017e13i | −0.128977 | + | 0.128977i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.18852e14 | + | 1.18852e14i | 0.173623 | + | 0.173623i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.32216e14i | − | 0.335594i | −0.985822 | − | 0.167797i | \(-0.946335\pi\) | ||
0.985822 | − | 0.167797i | \(-0.0536653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.01006e14 | 1.00224 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.20019e13 | + | 4.20019e13i | −0.0594101 | + | 0.0594101i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.15284e14 | + | 4.15284e14i | 0.574973 | + | 0.574973i | 0.933514 | − | 0.358541i | \(-0.116726\pi\) |
−0.358541 | + | 0.933514i | \(0.616726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 6.54823e14i | − | 0.897008i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.25302e14 | −0.847504 | −0.423752 | − | 0.905778i | \(-0.639287\pi\) | ||||
−0.423752 | + | 0.905778i | \(0.639287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.42223e14 | + | 1.42223e14i | −0.190727 | + | 0.190727i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.21564e14 | + | 2.21564e14i | 0.290903 | + | 0.290903i | 0.837437 | − | 0.546534i | \(-0.184053\pi\) |
−0.546534 | + | 0.837437i | \(0.684053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.18597e13i | 0.0413914i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.09162e14 | 0.911681 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.17069e14 | + | 7.17069e14i | −0.912213 | + | 0.912213i | −0.996446 | − | 0.0842326i | \(-0.973156\pi\) |
0.0842326 | + | 0.996446i | \(0.473156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.05719e14 | + | 6.05719e14i | 0.754591 | + | 0.754591i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.79240e14i | 0.220975i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.11608e15 | 1.36170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.85200e14 | − | 2.85200e14i | 0.344364 | − | 0.344364i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.11433e14 | − | 2.11433e14i | −0.250058 | − | 0.250058i | 0.570936 | − | 0.820994i | \(-0.306580\pi\) |
−0.820994 | + | 0.570936i | \(0.806580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.20939e14i | 0.492721i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.45574e15 | −1.68651 | −0.843255 | − | 0.537514i | \(-0.819363\pi\) | ||||
−0.843255 | + | 0.537514i | \(0.819363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.52925e13 | − | 3.52925e13i | 0.0404687 | − | 0.0404687i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.31622e14 | − | 3.31622e14i | −0.372538 | − | 0.372538i | 0.495863 | − | 0.868401i | \(-0.334852\pi\) |
−0.868401 | + | 0.495863i | \(0.834852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.32473e15i | − | 1.47304i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.05822e14 | 0.556741 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.11608e14 | + | 9.11608e14i | −0.993209 | + | 0.993209i | −0.999977 | − | 0.00676795i | \(-0.997846\pi\) |
0.00676795 | + | 0.999977i | \(0.497846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.44860e14 | + | 5.44860e14i | 0.581700 | + | 0.581700i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 4.74171e14i | − | 0.501134i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.69307e14 | 0.804881 | 0.402440 | − | 0.915446i | \(-0.368162\pi\) | ||||
0.402440 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.06358e13 | + | 9.06358e13i | −0.0938758 | + | 0.0938758i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.07674e14 | + | 1.07674e14i | 0.109304 | + | 0.109304i | 0.759644 | − | 0.650340i | \(-0.225373\pi\) |
−0.650340 | + | 0.759644i | \(0.725373\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.20628e14i | − | 0.322236i |
(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 | 300.11.k.c.157.8 | yes | 16 | |
5.2 | odd | 4 | inner | 300.11.k.c.193.1 | yes | 16 | |
5.3 | odd | 4 | inner | 300.11.k.c.193.8 | yes | 16 | |
5.4 | even | 2 | inner | 300.11.k.c.157.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.11.k.c.157.1 | ✓ | 16 | 5.4 | even | 2 | inner | |
300.11.k.c.157.8 | yes | 16 | 1.1 | even | 1 | trivial | |
300.11.k.c.193.1 | yes | 16 | 5.2 | odd | 4 | inner | |
300.11.k.c.193.8 | yes | 16 | 5.3 | odd | 4 | inner |