Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,8,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), 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: | \(78.7210264220\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} + \cdots + 34\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{13}\cdot 7^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.8 | ||
Root | \(95.9276 - 166.152i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.8.k.e.109.8 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 173.134 | − | 299.876i | 0.619422 | − | 1.07287i | −0.370170 | − | 0.928964i | \(-0.620700\pi\) |
0.989591 | − | 0.143906i | \(-0.0459662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 334.186 | − | 843.720i | 0.368252 | − | 0.929726i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 437.706 | + | 758.129i | 0.0991535 | + | 0.171739i | 0.911335 | − | 0.411667i | \(-0.135053\pi\) |
−0.812181 | + | 0.583406i | \(0.801720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −507.478 | −0.0640643 | −0.0320321 | − | 0.999487i | \(-0.510198\pi\) | ||||
−0.0320321 | + | 0.999487i | \(0.510198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9804.06 | − | 16981.1i | −0.483988 | − | 0.838292i | 0.515843 | − | 0.856683i | \(-0.327479\pi\) |
−0.999831 | + | 0.0183914i | \(0.994146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17766.7 | − | 30772.7i | 0.594248 | − | 1.02927i | −0.399404 | − | 0.916775i | \(-0.630783\pi\) |
0.993652 | − | 0.112493i | \(-0.0358837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 48754.4 | − | 84445.0i | 0.835538 | − | 1.44719i | −0.0580543 | − | 0.998313i | \(-0.518490\pi\) |
0.893592 | − | 0.448880i | \(-0.148177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20888.0 | − | 36179.1i | −0.267367 | − | 0.463092i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 56682.8 | 0.431577 | 0.215789 | − | 0.976440i | \(-0.430768\pi\) | ||||
0.215789 | + | 0.976440i | \(0.430768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26332.7 | + | 45609.6i | 0.158756 | + | 0.274973i | 0.934420 | − | 0.356172i | \(-0.115918\pi\) |
−0.775664 | + | 0.631146i | \(0.782585\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −195153. | − | 246291.i | −0.769372 | − | 0.970979i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −171941. | + | 297810.i | −0.558049 | + | 0.966569i | 0.439610 | + | 0.898189i | \(0.355117\pi\) |
−0.997659 | + | 0.0683807i | \(0.978217\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 279731. | 0.633865 | 0.316933 | − | 0.948448i | \(-0.397347\pi\) | ||||
0.316933 | + | 0.948448i | \(0.397347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 73777.2 | 0.141509 | 0.0707543 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707543 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −514934. | + | 891892.i | −0.723451 | + | 1.25305i | 0.236157 | + | 0.971715i | \(0.424112\pi\) |
−0.959608 | + | 0.281339i | \(0.909221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −600182. | − | 563919.i | −0.728781 | − | 0.684747i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 186831. | + | 323600.i | 0.172378 | + | 0.298568i | 0.939251 | − | 0.343231i | \(-0.111522\pi\) |
−0.766873 | + | 0.641799i | \(0.778188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 303127. | 0.245671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 520363. | + | 901296.i | 0.329856 | + | 0.571328i | 0.982483 | − | 0.186352i | \(-0.0596664\pi\) |
−0.652627 | + | 0.757679i | \(0.726333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 161336. | − | 279442.i | 0.0910073 | − | 0.157629i | −0.816928 | − | 0.576740i | \(-0.804325\pi\) |
0.907935 | + | 0.419110i | \(0.137658\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −87861.6 | + | 152181.i | −0.0396828 | + | 0.0687326i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50274e6 | − | 2.60282e6i | −0.610410 | − | 1.05726i | −0.991171 | − | 0.132587i | \(-0.957672\pi\) |
0.380762 | − | 0.924673i | \(-0.375662\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.97728e6 | −0.987224 | −0.493612 | − | 0.869682i | \(-0.664324\pi\) | ||||
−0.493612 | + | 0.869682i | \(0.664324\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.26966e6 | − | 2.19911e6i | −0.381994 | − | 0.661633i | 0.609353 | − | 0.792899i | \(-0.291429\pi\) |
−0.991347 | + | 0.131266i | \(0.958096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 785924. | − | 115945.i | 0.196184 | − | 0.0289424i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 936558. | − | 1.62217e6i | 0.213717 | − | 0.370169i | −0.739158 | − | 0.673532i | \(-0.764776\pi\) |
0.952875 | + | 0.303363i | \(0.0981095\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.44787e6 | 0.661878 | 0.330939 | − | 0.943652i | \(-0.392635\pi\) | ||||
0.330939 | + | 0.943652i | \(0.392635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.78965e6 | −1.19917 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.03292e6 | − | 8.71726e6i | 0.756754 | − | 1.31074i | −0.187744 | − | 0.982218i | \(-0.560118\pi\) |
0.944498 | − | 0.328518i | \(-0.106549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −169592. | + | 428169.i | −0.0235918 | + | 0.0595622i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.15201e6 | − | 1.06556e7i | −0.736181 | − | 1.27510i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.52465e7 | −1.69617 | −0.848085 | − | 0.529860i | \(-0.822244\pi\) | ||||
−0.848085 | + | 0.529860i | \(0.822244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13213e6 | + | 1.96091e6i | 0.109338 | + | 0.189379i | 0.915502 | − | 0.402313i | \(-0.131794\pi\) |
−0.806164 | + | 0.591692i | \(0.798460\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 281141. | − | 486950.i | 0.0253509 | − | 0.0439091i | −0.853072 | − | 0.521794i | \(-0.825263\pi\) |
0.878423 | + | 0.477885i | \(0.158596\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.95243e6 | + | 1.37740e7i | −0.627562 | + | 1.08697i | 0.360477 | + | 0.932768i | \(0.382614\pi\) |
−0.988039 | + | 0.154201i | \(0.950720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.02223e6 | − | 1.04308e7i | −0.445415 | − | 0.771481i | 0.552666 | − | 0.833403i | \(-0.313610\pi\) |
−0.998081 | + | 0.0619216i | \(0.980277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.75416e7 | 1.14366 | 0.571828 | − | 0.820374i | \(-0.306235\pi\) | ||||
0.571828 | + | 0.820374i | \(0.306235\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.68820e7 | − | 2.92405e7i | −1.03510 | − | 1.79285i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.76037e7 | + | 2.59702e6i | −0.957611 | + | 0.141273i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.36041e6 | − | 1.62127e7i | 0.480337 | − | 0.831968i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.25865e7 | 0.576393 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.98177e7 | −0.858499 | −0.429250 | − | 0.903186i | \(-0.641222\pi\) | ||||
−0.429250 | + | 0.903186i | \(0.641222\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.15059e7 | + | 1.99289e7i | −0.447170 | + | 0.774521i | −0.998201 | − | 0.0599637i | \(-0.980901\pi\) |
0.551030 | + | 0.834485i | \(0.314235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00262e7 | − | 2.52739e7i | −0.738104 | − | 0.931519i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.94076e6 | + | 6.82560e6i | 0.130936 | + | 0.226787i | 0.924038 | − | 0.382302i | \(-0.124869\pi\) |
−0.793102 | + | 0.609089i | \(0.791535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.33107e7 | −1.05204 | −0.526020 | − | 0.850472i | \(-0.676316\pi\) | ||||
−0.526020 | + | 0.850472i | \(0.676316\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −222126. | − | 384734.i | −0.00635220 | − | 0.0110023i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.81371e6 | − | 1.69978e7i | 0.267328 | − | 0.463026i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.85252e7 | + | 4.94071e7i | −0.706443 | + | 1.22360i | 0.259725 | + | 0.965683i | \(0.416368\pi\) |
−0.966168 | + | 0.257913i | \(0.916965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.16251e7 | − | 5.47762e7i | −0.747502 | − | 1.29471i | −0.949017 | − | 0.315226i | \(-0.897920\pi\) |
0.201515 | − | 0.979485i | \(-0.435414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.82363e7 | 0.393347 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.92448e6 | − | 1.02615e7i | −0.122180 | − | 0.211623i | 0.798447 | − | 0.602065i | \(-0.205655\pi\) |
−0.920627 | + | 0.390443i | \(0.872322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.49549e7 | − | 6.93554e7i | −1.03780 | − | 1.30975i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.57630e7 | + | 4.46228e7i | −0.465950 | + | 0.807049i | −0.999244 | − | 0.0388808i | \(-0.987621\pi\) |
0.533294 | + | 0.845930i | \(0.320954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.95166e7 | 1.65344 | 0.826719 | − | 0.562615i | \(-0.190205\pi\) | ||||
0.826719 | + | 0.562615i | \(0.190205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24910e7 | −0.995896 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.24458e7 | − | 9.08388e7i | 0.770104 | − | 1.33386i | −0.167401 | − | 0.985889i | \(-0.553538\pi\) |
0.937505 | − | 0.347971i | \(-0.113129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.75055e7 | + | 5.53307e6i | −0.529007 | + | 0.0780428i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.92027e7 | − | 1.19863e8i | −0.901856 | − | 1.56206i | −0.825082 | − | 0.565012i | \(-0.808871\pi\) |
−0.0767740 | − | 0.997049i | \(-0.524462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.73519e7 | 0.468206 | 0.234103 | − | 0.972212i | \(-0.424785\pi\) | ||||
0.234103 | + | 0.972212i | \(0.424785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.95374e7 | + | 1.03122e8i | 0.691335 | + | 1.19743i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.58259e6 | − | 1.48655e7i | 0.0959782 | − | 0.166239i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.95067e7 | + | 6.84276e7i | −0.410255 | + | 0.710582i | −0.994917 | − | 0.100694i | \(-0.967894\pi\) |
0.584663 | + | 0.811277i | \(0.301227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.99903e7 | − | 5.19448e7i | −0.300283 | − | 0.520105i | 0.675917 | − | 0.736978i | \(-0.263748\pi\) |
−0.976200 | + | 0.216873i | \(0.930414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.03085e8 | −0.960650 | −0.480325 | − | 0.877091i | \(-0.659481\pi\) | ||||
−0.480325 | + | 0.877091i | \(0.659481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.91440e7 | − | 3.31584e7i | −0.172205 | − | 0.298268i | 0.766985 | − | 0.641665i | \(-0.221756\pi\) |
−0.939191 | + | 0.343396i | \(0.888423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.89426e7 | − | 4.78244e7i | 0.158929 | − | 0.401249i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.84308e7 | − | 8.38847e7i | 0.392630 | − | 0.680055i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.11063e7 | 0.235687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.27808e8 | 0.936635 | 0.468318 | − | 0.883560i | \(-0.344860\pi\) | ||||
0.468318 | + | 0.883560i | \(0.344860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.27733e7 | − | 2.21240e7i | 0.0876535 | − | 0.151820i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.72817e7 | − | 6.97533e6i | 0.314112 | − | 0.0463399i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.97535e6 | + | 8.61755e6i | 0.0310063 | + | 0.0537045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.36267e7 | −0.384213 | −0.192107 | − | 0.981374i | \(-0.561532\pi\) | ||||
−0.192107 | + | 0.981374i | \(0.561532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.87102e7 | + | 1.53651e8i | 0.503365 | + | 0.871854i | 0.999992 | + | 0.00388995i | \(0.00123821\pi\) |
−0.496627 | + | 0.867964i | \(0.665428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.96856e7 | + | 8.60580e7i | −0.273405 | + | 0.473551i | −0.969731 | − | 0.244174i | \(-0.921483\pi\) |
0.696326 | + | 0.717725i | \(0.254817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.33649e8 | + | 2.31486e8i | −0.692180 | + | 1.19889i | 0.278943 | + | 0.960308i | \(0.410016\pi\) |
−0.971122 | + | 0.238582i | \(0.923317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.78305e8 | + | 3.08833e8i | 0.896243 | + | 1.55234i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.52202e8 | 0.721152 | 0.360576 | − | 0.932730i | \(-0.382580\pi\) | ||||
0.360576 | + | 0.932730i | \(0.382580\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.05229e8 | + | 1.82262e8i | 0.484256 | + | 0.838757i | 0.999836 | − | 0.0180846i | \(-0.00575684\pi\) |
−0.515580 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.73018e8 | + | 8.23471e7i | −1.18607 | + | 0.357740i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.01619e6 | + | 1.56165e7i | −0.0380701 | + | 0.0659393i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.72017e8 | 0.686615 | 0.343307 | − | 0.939223i | \(-0.388453\pi\) | ||||
0.343307 | + | 0.939223i | \(0.388453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.53603e7 | 0.331386 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.04935e7 | + | 5.28163e7i | −0.112058 | + | 0.194089i | −0.916600 | − | 0.399806i | \(-0.869077\pi\) |
0.804542 | + | 0.593896i | \(0.202411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.93808e8 | + | 2.44594e8i | 0.693142 | + | 0.874774i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.37264e7 | − | 7.57363e7i | −0.148217 | − | 0.256720i | 0.782351 | − | 0.622837i | \(-0.214020\pi\) |
−0.930569 | + | 0.366118i | \(0.880687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.29387e8 | 0.427100 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.71329e8 | − | 4.69955e8i | −0.849890 | − | 1.47205i | −0.881306 | − | 0.472547i | \(-0.843335\pi\) |
0.0314155 | − | 0.999506i | \(-0.489999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.54907e7 | + | 4.41512e7i | −0.0778018 | + | 0.134757i | −0.902301 | − | 0.431106i | \(-0.858123\pi\) |
0.824499 | + | 0.565863i | \(0.191457\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.82856e7 | − | 3.16716e7i | 0.0530207 | − | 0.0918345i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11619e8 | + | 1.93330e8i | 0.315543 | + | 0.546536i | 0.979553 | − | 0.201187i | \(-0.0644800\pi\) |
−0.664010 | + | 0.747724i | \(0.731147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.34774e8 | 1.16894 | 0.584469 | − | 0.811416i | \(-0.301303\pi\) | ||||
0.584469 | + | 0.811416i | \(0.301303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.24748e8 | + | 5.62480e8i | 0.851714 | + | 1.47521i | 0.879660 | + | 0.475602i | \(0.157770\pi\) |
−0.0279467 | + | 0.999609i | \(0.508897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.34822e7 | − | 2.36014e8i | 0.233422 | − | 0.589321i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.29303e7 | − | 2.23959e7i | 0.0315112 | − | 0.0545790i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.61039e7 | 0.153529 | 0.0767645 | − | 0.997049i | \(-0.475541\pi\) | ||||
0.0767645 | + | 0.997049i | \(0.475541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.60370e8 | 0.817280 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.47418e7 | + | 4.28540e7i | −0.0535281 | + | 0.0927134i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.46553e7 | − | 6.22473e7i | 0.0521108 | − | 0.131564i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.58653e7 | − | 9.67615e7i | −0.112744 | − | 0.195278i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.80890e8 | 1.14580 | 0.572901 | − | 0.819625i | \(-0.305818\pi\) | ||||
0.572901 | + | 0.819625i | \(0.305818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.05179e7 | − | 3.55381e7i | −0.0386787 | − | 0.0669935i | 0.846038 | − | 0.533123i | \(-0.178982\pi\) |
−0.884717 | + | 0.466129i | \(0.845648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.58978e8 | − | 2.75359e8i | 0.293044 | − | 0.507567i | −0.681484 | − | 0.731833i | \(-0.738665\pi\) |
0.974528 | + | 0.224266i | \(0.0719985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.78346e8 | − | 6.55314e8i | 0.667085 | − | 1.15543i | −0.311630 | − | 0.950203i | \(-0.600875\pi\) |
0.978715 | − | 0.205222i | \(-0.0657916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.48104e7 | + | 4.29729e7i | 0.0427924 | + | 0.0741186i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.96741e8 | −1.15044 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.06002e7 | + | 1.83601e7i | 0.0171286 | + | 0.0296677i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.80423e8 | + | 7.32518e8i | 0.898584 | + | 1.13405i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.07896e8 | + | 3.60086e8i | −0.315100 | + | 0.545769i | −0.979459 | − | 0.201645i | \(-0.935371\pi\) |
0.664359 | + | 0.747414i | \(0.268705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.04070e9 | −1.51240 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.71149e8 | 1.09757 | 0.548787 | − | 0.835962i | \(-0.315090\pi\) | ||||
0.548787 | + | 0.835962i | \(0.315090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.30520e7 | + | 3.99272e7i | −0.0314824 | + | 0.0545291i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.76362e8 | + | 3.17932e8i | −0.905002 | + | 0.425407i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.96630e8 | + | 8.60189e8i | 0.638087 | + | 1.10520i | 0.985852 | + | 0.167618i | \(0.0536075\pi\) |
−0.347765 | + | 0.937582i | \(0.613059\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.57730e8 | 0.324546 | 0.162273 | − | 0.986746i | \(-0.448118\pi\) | ||||
0.162273 | + | 0.986746i | \(0.448118\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.84532e8 | + | 8.39235e8i | 0.586288 | + | 1.01548i | 0.994713 | + | 0.102689i | \(0.0327448\pi\) |
−0.408425 | + | 0.912792i | \(0.633922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.15468e8 | + | 8.92816e8i | −0.611508 | + | 1.05916i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.83984e7 | + | 3.18669e7i | −0.0209869 | + | 0.0363504i | −0.876328 | − | 0.481715i | \(-0.840014\pi\) |
0.855341 | + | 0.518065i | \(0.173348\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.84372e8 | − | 3.19342e8i | −0.206262 | − | 0.357257i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.79282e8 | −0.946462 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.21654e8 | + | 9.03531e8i | 0.550872 | + | 0.954139i | 0.998212 | + | 0.0597748i | \(0.0190382\pi\) |
−0.447339 | + | 0.894364i | \(0.647628\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.35464e8 | − | 4.94900e7i | 0.341065 | − | 0.0503163i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17534e8 | − | 5.49986e8i | 0.316818 | − | 0.548745i | −0.663004 | − | 0.748616i | \(-0.730719\pi\) |
0.979822 | + | 0.199871i | \(0.0640523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.87653e7 | −0.0276487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23849e9 | −1.16857 | −0.584284 | − | 0.811550i | \(-0.698624\pi\) | ||||
−0.584284 | + | 0.811550i | \(0.698624\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.63548e8 | + | 2.83273e8i | −0.148747 | + | 0.257638i | −0.930765 | − | 0.365619i | \(-0.880857\pi\) |
0.782017 | + | 0.623257i | \(0.214191\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.01301e8 | − | 2.55754e8i | 0.0904690 | − | 0.228407i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.96563e7 | + | 1.03328e8i | 0.0513846 | + | 0.0890008i | 0.890574 | − | 0.454839i | \(-0.150303\pi\) |
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.91196e9 | −1.61756 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.24299e8 | − | 5.61703e8i | −0.264762 | − | 0.458582i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.15614e9 | − | 2.00250e9i | 0.927353 | − | 1.60622i | 0.139620 | − | 0.990205i | \(-0.455412\pi\) |
0.787733 | − | 0.616017i | \(-0.211255\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.43632e8 | − | 1.63442e9i | 0.730798 | − | 1.26578i | −0.225745 | − | 0.974187i | \(-0.572481\pi\) |
0.956543 | − | 0.291593i | \(-0.0941852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.33633e7 | − | 2.31459e7i | −0.0101706 | − | 0.0176159i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.01038e8 | −0.221330 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.34476e8 | − | 1.61856e9i | −0.675362 | − | 1.16976i | −0.976363 | − | 0.216138i | \(-0.930654\pi\) |
0.301001 | − | 0.953624i | \(-0.402679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.34339e8 | − | 1.37840e8i | 0.652649 | − | 0.0962832i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.96943e8 | − | 1.03394e9i | 0.409982 | − | 0.710109i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.19342e9 | −0.792584 | −0.396292 | − | 0.918125i | \(-0.629703\pi\) | ||||
−0.396292 | + | 0.918125i | \(0.629703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.94195e7 | −0.0322783 | −0.0161392 | − | 0.999870i | \(-0.505137\pi\) | ||||
−0.0161392 | + | 0.999870i | \(0.505137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.09575e8 | + | 7.09404e8i | −0.258804 | + | 0.448262i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.81854e8 | − | 2.29508e8i | −0.113038 | − | 0.142659i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.26012e8 | + | 1.43069e9i | 0.496954 | + | 0.860749i | 0.999994 | − | 0.00351400i | \(-0.00111854\pi\) |
−0.503040 | + | 0.864263i | \(0.667785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.35353e9 | −1.39320 | −0.696598 | − | 0.717462i | \(-0.745304\pi\) | ||||
−0.696598 | + | 0.717462i | \(0.745304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.73240e9 | − | 3.00061e9i | −0.993034 | − | 1.71999i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.32030e8 | + | 1.09471e9i | −0.356543 | + | 0.617551i | −0.987381 | − | 0.158364i | \(-0.949378\pi\) |
0.630838 | + | 0.775915i | \(0.282711\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.58299e9 | − | 2.74182e9i | 0.865099 | − | 1.49840i | −0.00184942 | − | 0.999998i | \(-0.500589\pi\) |
0.866949 | − | 0.498398i | \(-0.166078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.74273e9 | − | 3.01850e9i | −0.937499 | − | 1.62380i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.54070e9 | 1.84598 | 0.922989 | − | 0.384827i | \(-0.125739\pi\) | ||||
0.922989 | + | 0.384827i | \(0.125739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.22440e8 | + | 2.12072e8i | 0.0628500 | + | 0.108859i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.90357e7 | + | 1.24987e8i | 0.0492892 | + | 0.0622051i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.67457e9 | − | 2.90044e9i | 0.820724 | − | 1.42154i | −0.0844204 | − | 0.996430i | \(-0.526904\pi\) |
0.905144 | − | 0.425105i | \(-0.139763\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58651e9 | −1.22959 | −0.614795 | − | 0.788687i | \(-0.710761\pi\) | ||||
−0.614795 | + | 0.788687i | \(0.710761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.17364e9 | −0.549544 | −0.274772 | − | 0.961509i | \(-0.588602\pi\) | ||||
−0.274772 | + | 0.961509i | \(0.588602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.66720e8 | + | 8.08383e8i | −0.212054 | + | 0.367289i | −0.952357 | − | 0.304984i | \(-0.901349\pi\) |
0.740303 | + | 0.672273i | \(0.234682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.69824e9 | + | 3.98063e8i | −1.20775 | + | 0.178175i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.22927e7 | + | 5.59327e7i | 0.0140311 | + | 0.0243025i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.48444e9 | −0.635529 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.06626e8 | + | 5.31091e8i | 0.127478 | + | 0.220798i | 0.922699 | − | 0.385522i | \(-0.125979\pi\) |
−0.795221 | + | 0.606320i | \(0.792645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.72561e7 | − | 1.51132e8i | 0.0357510 | − | 0.0619225i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.63968e9 | + | 4.57207e9i | −1.05064 | + | 1.81977i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.79545e8 | + | 3.10981e8i | 0.0704403 | + | 0.122006i | 0.899094 | − | 0.437755i | \(-0.144226\pi\) |
−0.828654 | + | 0.559761i | \(0.810893\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.24919e9 | −0.857514 | −0.428757 | − | 0.903420i | \(-0.641048\pi\) | ||||
−0.428757 | + | 0.903420i | \(0.641048\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.55722e8 | − | 9.62539e8i | −0.208878 | − | 0.361788i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.94967e8 | + | 2.51199e9i | −0.363547 | + | 0.917848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.31886e9 | + | 2.28433e9i | −0.475168 | + | 0.823015i | −0.999595 | − | 0.0284401i | \(-0.990946\pi\) |
0.524428 | + | 0.851455i | \(0.324279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.36665e9 | 1.52989 | 0.764946 | − | 0.644094i | \(-0.222766\pi\) | ||||
0.764946 | + | 0.644094i | \(0.222766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.84040e8 | 0.270906 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.37515e8 | − | 1.45062e9i | 0.281501 | − | 0.487575i | −0.690253 | − | 0.723568i | \(-0.742501\pi\) |
0.971755 | + | 0.235993i | \(0.0758343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.27974e9 | + | 3.36322e8i | −0.755808 | + | 0.111502i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.73498e7 | − | 1.68615e8i | −0.0314058 | − | 0.0543965i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.01559e8 | −0.286931 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.53370e9 | + | 2.65645e9i | 0.475125 | + | 0.822941i | 0.999594 | − | 0.0284883i | \(-0.00906933\pi\) |
−0.524469 | + | 0.851430i | \(0.675736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.71080e8 | − | 6.42729e8i | 0.113426 | − | 0.196459i | −0.803724 | − | 0.595003i | \(-0.797151\pi\) |
0.917149 | + | 0.398544i | \(0.130484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.16335e8 | − | 8.94318e8i | 0.153672 | − | 0.266167i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.05156e9 | − | 5.28546e9i | −0.896246 | − | 1.55234i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.41957e8 | −0.0406081 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.75367e9 | + | 4.76949e9i | 0.777451 | + | 1.34658i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.64820e8 | − | 7.01846e8i | 0.0453366 | − | 0.193055i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.27287e9 | − | 3.93672e9i | 0.617139 | − | 1.06892i | −0.372866 | − | 0.927885i | \(-0.621625\pi\) |
0.990005 | − | 0.141031i | \(-0.0450419\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.17060e9 | −1.10360 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.93020e9 | 0.504252 | 0.252126 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252126 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00706e9 | − | 1.74429e9i | 0.256464 | − | 0.444209i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.05567e9 | − | 1.33230e9i | −0.265454 | − | 0.335014i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.03481e9 | − | 3.52440e9i | −0.498920 | − | 0.864155i | 0.501079 | − | 0.865402i | \(-0.332937\pi\) |
−0.999999 | + | 0.00124625i | \(0.999603\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.74403e7 | −0.00906564 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.00511e9 | + | 3.47296e9i | 0.473543 | + | 0.820201i | 0.999541 | − | 0.0302848i | \(-0.00964142\pi\) |
−0.525998 | + | 0.850486i | \(0.676308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.03704e9 | − | 5.26032e9i | 0.708405 | − | 1.22699i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.19263e9 | + | 2.06570e9i | −0.271402 | + | 0.470083i | −0.969221 | − | 0.246192i | \(-0.920821\pi\) |
0.697819 | + | 0.716274i | \(0.254154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.06291e8 | + | 1.05013e9i | 0.136287 | + | 0.236056i | 0.926088 | − | 0.377307i | \(-0.123150\pi\) |
−0.789801 | + | 0.613363i | \(0.789816\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.07353e9 | −0.893579 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.05691e9 | + | 5.29472e9i | 0.662471 | + | 1.14743i | 0.979964 | + | 0.199173i | \(0.0638256\pi\) |
−0.317493 | + | 0.948261i | \(0.602841\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.15223e9 | − | 2.90904e9i | 0.243738 | − | 0.615365i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.63554e8 | + | 2.83284e8i | −0.0341838 | + | 0.0592081i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.73746e9 | 1.78300 | 0.891502 | − | 0.453018i | \(-0.149653\pi\) | ||||
0.891502 | + | 0.453018i | \(0.149653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.87138e9 | 0.377362 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.48503e9 | − | 2.57215e9i | 0.292445 | − | 0.506529i | −0.681943 | − | 0.731406i | \(-0.738865\pi\) |
0.974387 | + | 0.224877i | \(0.0721980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.26901e9 | + | 5.72856e9i | −0.441597 | + | 1.11490i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.58591e9 | − | 4.47892e9i | −0.491608 | − | 0.851491i | 0.508345 | − | 0.861154i | \(-0.330257\pi\) |
−0.999953 | + | 0.00966288i | \(0.996924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.35291e8 | −0.0442125 | −0.0221062 | − | 0.999756i | \(-0.507037\pi\) | ||||
−0.0221062 | + | 0.999756i | \(0.507037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.24120e9 | − | 5.61393e9i | −0.595063 | − | 1.03068i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.12330e9 | + | 5.40971e9i | −0.566830 | + | 0.981778i | 0.430047 | + | 0.902807i | \(0.358497\pi\) |
−0.996877 | + | 0.0789718i | \(0.974836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.61318e8 | − | 4.52616e8i | 0.0463474 | − | 0.0802760i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50079e9 | + | 6.06355e9i | 0.613840 | + | 1.06320i | 0.990587 | + | 0.136885i | \(0.0437092\pi\) |
−0.376747 | + | 0.926316i | \(0.622957\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.98807e9 | 1.02633 | 0.513167 | − | 0.858289i | \(-0.328472\pi\) | ||||
0.513167 | + | 0.858289i | \(0.328472\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.02918e9 | + | 8.71079e9i | 0.852275 | + | 1.47618i | 0.879150 | + | 0.476544i | \(0.158111\pi\) |
−0.0268758 | + | 0.999639i | \(0.508556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.67300e9 | − | 7.15956e9i | −0.939949 | − | 1.18626i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.81102e9 | − | 6.60087e9i | 0.624397 | − | 1.08149i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.74286e9 | 1.08036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.39565e9 | 1.48876 | 0.744379 | − | 0.667757i | \(-0.232746\pi\) | ||||
0.744379 | + | 0.667757i | \(0.232746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.43111e9 | + | 5.94285e9i | −0.531773 | + | 0.921058i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.04579e8 | + | 2.86177e8i | 0.0466888 | + | 0.0438678i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.20822e9 | + | 3.82475e9i | 0.331161 | + | 0.573588i | 0.982740 | − | 0.184993i | \(-0.0592263\pi\) |
−0.651579 | + | 0.758581i | \(0.725893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.74949e9 | −1.29791 | −0.648954 | − | 0.760827i | \(-0.724793\pi\) | ||||
−0.648954 | + | 0.760827i | \(0.724793\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.90059e9 | + | 8.48807e9i | 0.711350 | + | 1.23209i | 0.964351 | + | 0.264628i | \(0.0852492\pi\) |
−0.253001 | + | 0.967466i | \(0.581417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.55532e8 | + | 7.89005e8i | −0.0654128 | + | 0.113298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.61621e9 | + | 7.99551e9i | −0.648768 | + | 1.12370i | 0.334649 | + | 0.942343i | \(0.391382\pi\) |
−0.983417 | + | 0.181357i | \(0.941951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.98413e9 | + | 6.90072e9i | 0.553974 | + | 0.959511i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.45582e9 | −0.334270 | −0.167135 | − | 0.985934i | \(-0.553452\pi\) | ||||
−0.167135 | + | 0.985934i | \(0.553452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.69707e9 | + | 8.13557e9i | 0.632590 | + | 1.09568i | 0.987020 | + | 0.160595i | \(0.0513414\pi\) |
−0.354431 | + | 0.935082i | \(0.615325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.10463e10 | + | 1.62962e9i | −1.45660 | + | 0.214887i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.76354e9 | − | 4.78658e9i | 0.360599 | − | 0.624576i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.82471e8 | 0.0360948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.12505e10 | 1.42272 | 0.711362 | − | 0.702825i | \(-0.248079\pi\) | ||||
0.711362 | + | 0.702825i | \(0.248079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.57926e8 | − | 1.31277e9i | 0.0938785 | − | 0.162602i | −0.815261 | − | 0.579093i | \(-0.803407\pi\) |
0.909140 | + | 0.416491i | \(0.136740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.09517e9 | + | 1.28638e10i | −0.624618 | + | 1.57697i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.96753e9 | − | 3.40787e9i | −0.236293 | − | 0.409271i | 0.723355 | − | 0.690476i | \(-0.242599\pi\) |
−0.959648 | + | 0.281206i | \(0.909266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.72911e9 | 0.324418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.48125e7 | − | 1.64220e8i | −0.0110433 | − | 0.0191275i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.25151e8 | − | 9.09587e8i | 0.0605495 | − | 0.104875i | −0.834162 | − | 0.551520i | \(-0.814048\pi\) |
0.894711 | + | 0.446645i | \(0.147381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.76720e9 | + | 9.98909e9i | −0.651656 | + | 1.12870i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.74250e9 | − | 4.75015e9i | −0.306783 | − | 0.531364i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.15758e10 | 1.26922 | 0.634609 | − | 0.772834i | \(-0.281161\pi\) | ||||
0.634609 | + | 0.772834i | \(0.281161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.10962e9 | + | 1.05822e10i | 0.663240 | + | 1.14876i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.03280e9 | − | 2.99892e8i | 0.216335 | − | 0.0319152i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.50354e9 | − | 1.47286e10i | 0.896061 | − | 1.55202i | 0.0635758 | − | 0.997977i | \(-0.479750\pi\) |
0.832486 | − | 0.554047i | \(-0.186917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.13534e9 | 0.530586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.53830e8 | −0.0157388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.12756e8 | − | 3.68504e8i | 0.0213467 | − | 0.0369735i | −0.855155 | − | 0.518373i | \(-0.826538\pi\) |
0.876501 | + | 0.481399i | \(0.159871\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.16896e8 | − | 3.99936e8i | −0.0314879 | − | 0.0397390i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18399e9 | − | 2.05073e9i | −0.115389 | − | 0.199860i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.28106e9 | 0.316697 | 0.158348 | − | 0.987383i | \(-0.449383\pi\) | ||||
0.158348 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.23316e8 | − | 1.25282e9i | −0.0684884 | − | 0.118625i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.71639e9 | − | 6.43698e9i | 0.348544 | − | 0.603696i | −0.637447 | − | 0.770494i | \(-0.720010\pi\) |
0.985991 | + | 0.166798i | \(0.0533429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.31551e9 | − | 2.27854e9i | 0.121049 | − | 0.209662i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.35283e9 | − | 9.27138e9i | −0.487897 | − | 0.845062i | 0.512006 | − | 0.858982i | \(-0.328902\pi\) |
−0.999903 | + | 0.0139196i | \(0.995569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.15663e9 | −0.282333 | −0.141167 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141167 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.87735e9 | + | 1.71081e10i | 0.875172 | + | 1.51584i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.96381e9 | + | 1.13127e10i | 0.779482 | + | 0.983739i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38864e9 | + | 2.40519e9i | −0.119632 | + | 0.207209i | −0.919622 | − | 0.392805i | \(-0.871505\pi\) |
0.799990 | + | 0.600014i | \(0.204838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.19015e10 | −1.85208 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22142e9 | 0.102336 | 0.0511682 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511682 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.08867e10 | − | 1.88563e10i | 0.895466 | − | 1.55099i | 0.0622399 | − | 0.998061i | \(-0.480176\pi\) |
0.833226 | − | 0.552932i | \(-0.186491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.08132e10 | + | 1.59524e9i | −0.881291 | + | 0.130014i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.64073e8 | − | 4.57388e8i | −0.0211320 | − | 0.0366017i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.87936e10 | −1.49028 | −0.745138 | − | 0.666910i | \(-0.767617\pi\) | ||||
−0.745138 | + | 0.666910i | \(0.767617\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.59566e9 | − | 7.95992e9i | −0.357866 | − | 0.619841i | 0.629738 | − | 0.776807i | \(-0.283162\pi\) |
−0.987604 | + | 0.156966i | \(0.949829\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.10008e9 | − | 1.90539e9i | 0.0848920 | − | 0.147037i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.96988e9 | − | 8.60809e9i | 0.376674 | − | 0.652418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30317e9 | − | 2.25716e9i | −0.0978868 | − | 0.169545i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10291e9 | −0.302725 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.75830e9 | + | 1.51698e10i | 0.640484 | + | 1.10935i | 0.985325 | + | 0.170690i | \(0.0545995\pi\) |
−0.344841 | + | 0.938661i | \(0.612067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.86217e9 | − | 1.48002e10i | 0.421154 | − | 1.06329i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.18744e7 | + | 1.41811e8i | −0.00583032 | + | 0.0100984i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.13809e10 | 0.796290 | 0.398145 | − | 0.917323i | \(-0.369654\pi\) | ||||
0.398145 | + | 0.917323i | \(0.369654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.01938e10 | 1.40057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.11147e9 | − | 1.92513e9i | 0.0757521 | − | 0.131207i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.03126e10 | + | 4.47192e9i | −2.04803 | + | 0.302140i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.27014e9 | − | 1.43243e10i | −0.549153 | − | 0.951160i | −0.998333 | − | 0.0577191i | \(-0.981617\pi\) |
0.449180 | − | 0.893441i | \(-0.351716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.76982e10 | −1.16508 | −0.582540 | − | 0.812802i | \(-0.697941\pi\) | ||||
−0.582540 | + | 0.812802i | \(0.697941\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.92088e9 | + | 1.54514e10i | 0.577239 | + | 0.999808i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31077e9 | − | 2.27033e9i | 0.0840912 | − | 0.145650i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.88453e9 | + | 6.72821e9i | −0.244984 | + | 0.424325i | −0.962127 | − | 0.272601i | \(-0.912116\pi\) |
0.717143 | + | 0.696926i | \(0.245449\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.92292e9 | − | 1.19908e10i | −0.432902 | − | 0.749809i | 0.564220 | − | 0.825625i | \(-0.309177\pi\) |
−0.997122 | + | 0.0758162i | \(0.975844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.07058e10 | −0.658189 | −0.329095 | − | 0.944297i | \(-0.606743\pi\) | ||||
−0.329095 | + | 0.944297i | \(0.606743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.39466e8 | + | 1.62720e9i | 0.0572717 | + | 0.0991975i | 0.893240 | − | 0.449581i | \(-0.148427\pi\) |
−0.835968 | + | 0.548778i | \(0.815093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.69175e9 | + | 1.57205e10i | −0.221297 | + | 0.942340i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.72297e10 | − | 2.98427e10i | 1.02418 | − | 1.77392i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.56049e9 | 0.558873 | 0.279437 | − | 0.960164i | \(-0.409852\pi\) | ||||
0.279437 | + | 0.960164i | \(0.409852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40369e10 | −0.813741 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.08193e10 | + | 1.87396e10i | −0.616879 | + | 1.06847i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.05509e10 | − | 1.33156e10i | −0.596617 | − | 0.752956i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.67657e10 | + | 2.90391e10i | 0.932542 | + | 1.61521i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.45947e9 | −0.466683 | −0.233341 | − | 0.972395i | \(-0.574966\pi\) | ||||
−0.233341 | + | 0.972395i | \(0.574966\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.17128e10 | − | 2.02872e10i | −0.635664 | − | 1.10100i | −0.986374 | − | 0.164519i | \(-0.947393\pi\) |
0.350710 | − | 0.936484i | \(-0.385940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.32662e9 | − | 7.49393e9i | 0.232902 | − | 0.403398i | −0.725759 | − | 0.687949i | \(-0.758511\pi\) |
0.958661 | + | 0.284551i | \(0.0918446\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.46757e10 | − | 2.54191e10i | 0.777251 | − | 1.34624i | −0.156270 | − | 0.987714i | \(-0.549947\pi\) |
0.933521 | − | 0.358523i | \(-0.116720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.81603e10 | − | 3.14545e10i | −0.954039 | − | 1.65244i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.63975e9 | 0.0847633 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62607e8 | + | 1.32087e9i | 0.0391054 | + | 0.0677326i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.20622e9 | − | 1.06194e10i | 0.212258 | − | 0.535887i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.88074e9 | − | 1.36498e10i | 0.394519 | − | 0.683328i | −0.598520 | − | 0.801108i | \(-0.704244\pi\) |
0.993040 | + | 0.117780i | \(0.0375778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.80407e10 | −1.87427 | −0.937136 | − | 0.348966i | \(-0.886533\pi\) | ||||
−0.937136 | + | 0.348966i | \(0.886533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.42019e9 | 0.264943 | 0.132471 | − | 0.991187i | \(-0.457709\pi\) | ||||
0.132471 | + | 0.991187i | \(0.457709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.67590e10 | + | 2.90275e10i | −0.806337 | + | 1.39662i | 0.109047 | + | 0.994037i | \(0.465220\pi\) |
−0.915385 | + | 0.402580i | \(0.868113\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.62280e9 | + | 1.67206e10i | −0.316144 | + | 0.798169i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.82973e10 | + | 3.16919e10i | 0.859819 | + | 1.48925i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.79253e10 | −2.23452 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.49261e9 | + | 2.58528e9i | 0.0685154 | + | 0.118672i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.66340e9 | − | 6.34519e9i | 0.166858 | − | 0.289007i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.46686e9 | − | 1.12009e10i | 0.290017 | − | 0.502324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.63551e9 | − | 1.14930e10i | −0.295290 | − | 0.511457i | 0.679762 | − | 0.733433i | \(-0.262083\pi\) |
−0.975052 | + | 0.221975i | \(0.928750\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.05061e9 | −0.352788 | −0.176394 | − | 0.984320i | \(-0.556443\pi\) | ||||
−0.176394 | + | 0.984320i | \(0.556443\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50916e9 | + | 2.61393e9i | 0.0656276 | + | 0.113670i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.29693e10 | + | 1.63677e10i | 0.555421 | + | 0.700965i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.18095e10 | − | 3.77751e10i | 0.926917 | − | 1.60547i | 0.138467 | − | 0.990367i | \(-0.455782\pi\) |
0.788449 | − | 0.615100i | \(-0.210884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.51091e9 | 0.0632458 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.43660e10 | 0.596815 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.54582e9 | + | 1.48018e10i | −0.349702 | + | 0.605702i | −0.986196 | − | 0.165579i | \(-0.947051\pi\) |
0.636494 | + | 0.771282i | \(0.280384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.80166e10 | + | 8.45031e9i | −1.13787 | + | 0.343201i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.97187e9 | − | 5.14743e9i | −0.118902 | − | 0.205944i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.55752e10 | −1.80984 | −0.904919 | − | 0.425583i | \(-0.860069\pi\) | ||||
−0.904919 | + | 0.425583i | \(0.860069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.19139e9 | − | 5.52765e9i | −0.124858 | − | 0.216260i | 0.796819 | − | 0.604217i | \(-0.206514\pi\) |
−0.921677 | + | 0.387957i | \(0.873181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.36381e10 | − | 2.36219e10i | 0.529618 | − | 0.917326i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.37414e10 | − | 4.11214e10i | 0.908410 | − | 1.57341i | 0.0921376 | − | 0.995746i | \(-0.470630\pi\) |
0.816273 | − | 0.577667i | \(-0.196037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.44324e8 | + | 1.11600e9i | 0.0244722 | + | 0.0423870i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.56713e10 | 0.586517 | 0.293259 | − | 0.956033i | \(-0.405260\pi\) | ||||
0.293259 | + | 0.956033i | \(0.405260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.36799e10 | + | 2.36942e10i | 0.508242 | + | 0.880300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.07584e9 | − | 1.04388e9i | 0.259067 | − | 0.0382194i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.23695e10 | − | 2.14246e10i | 0.449593 | − | 0.778718i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.07693e10 | −0.744007 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.24362e10 | −1.86483 | −0.932413 | − | 0.361395i | \(-0.882300\pi\) | ||||
−0.932413 | + | 0.361395i | \(0.882300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.58851e9 | − | 9.67959e9i | 0.195898 | − | 0.339304i | −0.751297 | − | 0.659964i | \(-0.770571\pi\) |
0.947194 | + | 0.320660i | \(0.103905\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.11320e10 | + | 2.81049e10i | −0.387416 | + | 0.978108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.68816e10 | − | 2.92399e10i | −0.579140 | − | 1.00310i | −0.995578 | − | 0.0939364i | \(-0.970055\pi\) |
0.416438 | − | 0.909164i | \(-0.363278\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.81175e9 | 0.300139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.02803e9 | − | 1.04409e10i | −0.202413 | − | 0.350590i | 0.746892 | − | 0.664945i | \(-0.231545\pi\) |
−0.949305 | + | 0.314355i | \(0.898212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.78475e10 | + | 3.09128e10i | −0.595047 | + | 1.03065i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.59696e9 | − | 6.23012e9i | 0.118236 | − | 0.204790i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.67462e10 | − | 2.90053e10i | −0.546586 | − | 0.946715i | −0.998505 | − | 0.0546562i | \(-0.982594\pi\) |
0.451919 | − | 0.892059i | \(-0.350740\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.32579e10 | −0.426671 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.76848e10 | + | 4.79515e10i | 0.884725 | + | 1.53239i | 0.846028 | + | 0.533138i | \(0.178988\pi\) |
0.0386975 | + | 0.999251i | \(0.487679\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.8.k.e.37.8 | yes | 16 | |
3.2 | odd | 2 | inner | 252.8.k.e.37.1 | ✓ | 16 | |
7.4 | even | 3 | inner | 252.8.k.e.109.8 | yes | 16 | |
21.11 | odd | 6 | inner | 252.8.k.e.109.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.8.k.e.37.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
252.8.k.e.37.8 | yes | 16 | 1.1 | even | 1 | trivial | |
252.8.k.e.109.1 | yes | 16 | 21.11 | odd | 6 | inner | |
252.8.k.e.109.8 | yes | 16 | 7.4 | even | 3 | inner |