Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
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, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 233.10 | ||
Character | \(\chi\) | \(=\) | 252.233 |
Dual form | 252.9.bk.a.53.10 |
$q$-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 | ||||||||
\(5\) | −36.7886 | − | 21.2399i | −0.0588617 | − | 0.0339838i | 0.470280 | − | 0.882517i | \(-0.344153\pi\) |
−0.529142 | + | 0.848533i | \(0.677486\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −115.865 | + | 2398.20i | −0.0482569 | + | 0.998835i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18785.5 | + | 10845.8i | −1.28308 | + | 0.740784i | −0.977410 | − | 0.211354i | \(-0.932213\pi\) |
−0.305667 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −33631.9 | −1.17755 | −0.588773 | − | 0.808299i | \(-0.700389\pi\) | ||||
−0.588773 | + | 0.808299i | \(0.700389\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15399.5 | − | 8890.88i | 0.184378 | − | 0.106451i | −0.404970 | − | 0.914330i | \(-0.632718\pi\) |
0.589348 | + | 0.807879i | \(0.299385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −57432.8 | + | 99476.6i | −0.440703 | + | 0.763320i | −0.997742 | − | 0.0671667i | \(-0.978604\pi\) |
0.557039 | + | 0.830486i | \(0.311937\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72299.8 | − | 41742.3i | −0.258360 | − | 0.149164i | 0.365226 | − | 0.930919i | \(-0.380992\pi\) |
−0.623586 | + | 0.781754i | \(0.714325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −194410. | − | 336728.i | −0.497690 | − | 0.862025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.22285e6i | − | 1.72894i | −0.502682 | − | 0.864471i | \(-0.667653\pi\) | ||
0.502682 | − | 0.864471i | \(-0.332347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 559905. | + | 969784.i | 0.606272 | + | 1.05009i | 0.991849 | + | 0.127418i | \(0.0406691\pi\) |
−0.385577 | + | 0.922676i | \(0.625998\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 55200.1 | − | 85765.5i | 0.0367847 | − | 0.0571532i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 532365. | − | 922084.i | 0.284055 | − | 0.491998i | −0.688324 | − | 0.725403i | \(-0.741653\pi\) |
0.972380 | + | 0.233405i | \(0.0749868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.39326e6i | 1.90861i | 0.298841 | + | 0.954303i | \(0.403400\pi\) | ||||
−0.298841 | + | 0.954303i | \(0.596600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 504960. | 0.147701 | 0.0738504 | − | 0.997269i | \(-0.476471\pi\) | ||||
0.0738504 | + | 0.997269i | \(0.476471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 118413. | + | 68365.6i | 0.0242665 | + | 0.0140103i | 0.512084 | − | 0.858935i | \(-0.328874\pi\) |
−0.487818 | + | 0.872946i | \(0.662207\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.73795e6 | − | 555735.i | −0.995343 | − | 0.0964014i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.58967e6 | − | 2.64985e6i | 0.581672 | − | 0.335828i | −0.180126 | − | 0.983644i | \(-0.557651\pi\) |
0.761797 | + | 0.647815i | \(0.224317\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 921457. | 0.100699 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.36414e6 | − | 1.94229e6i | 0.277630 | − | 0.160290i | −0.354720 | − | 0.934973i | \(-0.615424\pi\) |
0.632350 | + | 0.774683i | \(0.282091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.93925e6 | − | 1.37512e7i | 0.573404 | − | 0.993164i | −0.422809 | − | 0.906219i | \(-0.638956\pi\) |
0.996213 | − | 0.0869455i | \(-0.0277106\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.23727e6 | + | 714337.i | 0.0693124 | + | 0.0400175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00195e7 | + | 1.73543e7i | 0.497218 | + | 0.861207i | 0.999995 | − | 0.00320907i | \(-0.00102148\pi\) |
−0.502777 | + | 0.864416i | \(0.667688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.52625e7i | − | 0.600608i | −0.953844 | − | 0.300304i | \(-0.902912\pi\) | ||
0.953844 | − | 0.300304i | \(-0.0970881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.41130e7 | − | 2.44444e7i | −0.496967 | − | 0.860773i | 0.503027 | − | 0.864271i | \(-0.332220\pi\) |
−0.999994 | + | 0.00349825i | \(0.998886\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.38339e7 | − | 4.63081e7i | −0.678004 | − | 1.31733i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.48788e7 | + | 4.30914e7i | −0.638737 | + | 1.10632i | 0.346974 | + | 0.937875i | \(0.387209\pi\) |
−0.985710 | + | 0.168449i | \(0.946124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.84892e7i | 0.600299i | 0.953892 | + | 0.300150i | \(0.0970366\pi\) | ||||
−0.953892 | + | 0.300150i | \(0.902963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −755366. | −0.0144704 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.02063e7 | + | 3.47601e7i | 0.959582 | + | 0.554015i | 0.896044 | − | 0.443964i | \(-0.146428\pi\) |
0.0635378 | + | 0.997979i | \(0.479762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.89675e6 | − | 8.06561e7i | 0.0568247 | − | 1.17617i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.22574e6 | − | 2.43973e6i | 0.0518811 | − | 0.0299535i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.48273e8 | −1.67485 | −0.837426 | − | 0.546551i | \(-0.815940\pi\) | ||||
−0.837426 | + | 0.546551i | \(0.815940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.13350e8 | − | 6.54429e7i | 1.08928 | − | 0.628893i | 0.155892 | − | 0.987774i | \(-0.450175\pi\) |
0.933383 | + | 0.358881i | \(0.116841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.04450e8 | − | 1.80912e8i | 0.928022 | − | 1.60738i | 0.141394 | − | 0.989953i | \(-0.454841\pi\) |
0.786628 | − | 0.617428i | \(-0.211825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.71997e8 | + | 9.93025e7i | 1.31216 | + | 0.757574i | 0.982453 | − | 0.186511i | \(-0.0597179\pi\) |
0.329703 | + | 0.944085i | \(0.393051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.46870e7 | + | 1.29362e8i | 0.529102 | + | 0.916431i | 0.999424 | + | 0.0339362i | \(0.0108043\pi\) |
−0.470322 | + | 0.882495i | \(0.655862\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.38996e8i | − | 1.46580i | −0.680334 | − | 0.732902i | \(-0.738165\pi\) | ||
0.680334 | − | 0.732902i | \(-0.261835\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.77321e6 | + | 3.07128e6i | 0.0101384 | + | 0.0175602i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.95379e7 | + | 3.79612e7i | 0.0974293 | + | 0.189301i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28084e8 | − | 2.21849e8i | 0.597523 | − | 1.03494i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.31107e7i | 0.135621i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.59877e8 | −0.614570 | −0.307285 | − | 0.951617i | \(-0.599421\pi\) | ||||
−0.307285 | + | 0.951617i | \(0.599421\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.80415e8 | − | 1.04163e8i | −0.612616 | − | 0.353694i | 0.161372 | − | 0.986894i | \(-0.448408\pi\) |
−0.773989 | + | 0.633199i | \(0.781741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.31911e8 | − | 1.49261e8i | −0.741163 | − | 0.477025i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.66138e8 | − | 3.26860e8i | 1.60709 | − | 0.927853i | 0.617071 | − | 0.786907i | \(-0.288319\pi\) |
0.990017 | − | 0.140946i | \(-0.0450144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.58488e8 | −0.960318 | −0.480159 | − | 0.877181i | \(-0.659421\pi\) | ||||
−0.480159 | + | 0.877181i | \(0.659421\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.31792e8 | − | 3.64765e8i | 1.51088 | − | 0.872307i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.59732e7 | + | 4.49868e7i | −0.0587561 | + | 0.101769i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.80699e8 | + | 1.04327e8i | 0.366615 | + | 0.211665i | 0.671979 | − | 0.740570i | \(-0.265445\pi\) |
−0.305363 | + | 0.952236i | \(0.598778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.05301e8 | − | 7.02001e8i | −0.779596 | − | 1.35030i | −0.932175 | − | 0.362008i | \(-0.882091\pi\) |
0.152579 | − | 0.988291i | \(-0.451242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.75693e7i | − | 0.0824138i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.51790e8 | − | 6.09318e8i | −0.579008 | − | 1.00287i | −0.995593 | − | 0.0937753i | \(-0.970106\pi\) |
0.416585 | − | 0.909097i | \(-0.363227\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.08484e8 | − | 1.68553e8i | 0.161458 | − | 0.250861i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.15949e7 | + | 1.41326e8i | −0.115588 | + | 0.200204i | −0.918015 | − | 0.396547i | \(-0.870209\pi\) |
0.802427 | + | 0.596751i | \(0.203542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.62258e8i | − | 1.10859i | −0.832320 | − | 0.554296i | \(-0.812988\pi\) | ||
0.832320 | − | 0.554296i | \(-0.187012\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.15372e8 | 0.386613 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.81642e8 | + | 5.66751e8i | 1.09589 | + | 0.632715i | 0.935139 | − | 0.354280i | \(-0.115274\pi\) |
0.160754 | + | 0.986994i | \(0.448607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.30068e8 | − | 4.27220e8i | 0.885037 | − | 0.455512i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.42406e9 | − | 8.22183e8i | 1.38713 | − | 0.800860i | 0.394139 | − | 0.919051i | \(-0.371043\pi\) |
0.992991 | + | 0.118191i | \(0.0377095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.31417e8 | 0.681476 | 0.340738 | − | 0.940158i | \(-0.389323\pi\) | ||||
0.340738 | + | 0.940158i | \(0.389323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.91699e7 | + | 2.26148e7i | −0.0334400 | + | 0.0193066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.92858e8 | + | 3.34040e8i | −0.157714 | + | 0.273169i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.70610e8 | + | 9.85016e7i | 0.128195 | + | 0.0740133i | 0.562726 | − | 0.826643i | \(-0.309753\pi\) |
−0.434531 | + | 0.900657i | \(0.643086\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.24715e9 | − | 2.16013e9i | −0.898856 | − | 1.55686i | −0.828958 | − | 0.559311i | \(-0.811066\pi\) |
−0.0698981 | − | 0.997554i | \(-0.522267\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.04300e8i | 0.534014i | 0.963695 | + | 0.267007i | \(0.0860348\pi\) | ||||
−0.963695 | + | 0.267007i | \(0.913965\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12218e8 | − | 1.06039e9i | −0.390386 | − | 0.676168i | 0.602115 | − | 0.798410i | \(-0.294325\pi\) |
−0.992500 | + | 0.122242i | \(0.960992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.93264e9 | + | 1.41685e8i | 1.72693 | + | 0.0834334i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.14552e8 | − | 1.98410e8i | 0.0648617 | − | 0.112344i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.49163e9i | − | 1.30586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.13755e9 | −1.07842 | −0.539209 | − | 0.842172i | \(-0.681277\pi\) | ||||
−0.539209 | + | 0.842172i | \(0.681277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.85768e7 | − | 1.07253e7i | −0.00869393 | − | 0.00501944i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.39061e9 | + | 1.23040e9i | −1.07813 | + | 0.554892i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.17913e8 | + | 2.99017e8i | −0.217114 | + | 0.125351i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.10739e9 | 0.447796 | 0.223898 | − | 0.974613i | \(-0.428122\pi\) | ||||
0.223898 | + | 0.974613i | \(0.428122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.99760e8 | − | 2.88536e8i | 0.188216 | − | 0.108667i | −0.402931 | − | 0.915230i | \(-0.632008\pi\) |
0.591147 | + | 0.806564i | \(0.298675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.10895e8 | − | 3.65281e8i | 0.0766875 | − | 0.132827i | −0.825131 | − | 0.564941i | \(-0.808899\pi\) |
0.901819 | + | 0.432114i | \(0.142232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.05174e9 | − | 1.18457e9i | −0.696143 | − | 0.401919i | 0.109766 | − | 0.993957i | \(-0.464990\pi\) |
−0.805909 | + | 0.592039i | \(0.798323\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.90416e6 | − | 5.03015e6i | −0.000952245 | − | 0.00164934i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.72360e9i | − | 0.834741i | −0.908736 | − | 0.417371i | \(-0.862952\pi\) | ||
0.908736 | − | 0.417371i | \(-0.137048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.47981e9 | + | 2.56311e9i | 0.438671 | + | 0.759801i | 0.997587 | − | 0.0694233i | \(-0.0221159\pi\) |
−0.558916 | + | 0.829224i | \(0.688783\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.99287e8 | + | 1.42318e8i | 0.0553115 | + | 0.0394999i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.93157e9 | − | 3.34558e9i | 0.518948 | − | 0.898844i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.86049e9i | 0.468740i | 0.972147 | + | 0.234370i | \(0.0753027\pi\) | ||||
−0.972147 | + | 0.234370i | \(0.924697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.81092e9 | 0.441995 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.11838e8 | + | 1.22305e8i | 0.0485593 | + | 0.0280357i | 0.524083 | − | 0.851667i | \(-0.324408\pi\) |
−0.475524 | + | 0.879703i | \(0.657741\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.14966e9 | + | 1.38356e9i | 0.477717 | + | 0.307467i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.55911e9 | + | 3.78691e9i | −1.37095 | + | 0.791519i | −0.991048 | − | 0.133507i | \(-0.957376\pi\) |
−0.379904 | + | 0.925026i | \(0.624043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.25130e8 | −0.0456509 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.16447e9 | − | 1.82701e9i | 0.604354 | − | 0.348924i | −0.166398 | − | 0.986059i | \(-0.553214\pi\) |
0.770753 | + | 0.637135i | \(0.219880\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.22002e9 | + | 2.11313e9i | −0.226198 | + | 0.391787i | −0.956678 | − | 0.291147i | \(-0.905963\pi\) |
0.730480 | + | 0.682934i | \(0.239296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.30420e9 | + | 4.21708e9i | 1.27715 | + | 0.737362i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.45825e8 | + | 1.63822e9i | 0.160654 | + | 0.278261i | 0.935103 | − | 0.354375i | \(-0.115306\pi\) |
−0.774449 | + | 0.632636i | \(0.781973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.87749e9i | 0.301129i | 0.988600 | + | 0.150565i | \(0.0481091\pi\) | ||||
−0.988600 | + | 0.150565i | \(0.951891\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.80108e9 | − | 4.85161e9i | −0.436696 | − | 0.756380i | 0.560736 | − | 0.827995i | \(-0.310518\pi\) |
−0.997432 | + | 0.0716145i | \(0.977185\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.29341e10 | − | 6.24890e8i | −1.90638 | − | 0.0921034i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.32978e9 | + | 5.76735e9i | −0.477336 | + | 0.826771i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.86272e9i | 1.06685i | 0.845848 | + | 0.533423i | \(0.179095\pi\) | ||||
−0.845848 | + | 0.533423i | \(0.820905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.65016e8 | −0.0217890 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.43158e9 | + | 1.40387e9i | 0.304231 | + | 0.175648i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.85071e7 | + | 1.21100e9i | −0.00712759 | + | 0.147529i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.84148e8 | + | 3.37258e8i | −0.0675030 | + | 0.0389729i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.09045e9 | 0.573063 | 0.286532 | − | 0.958071i | \(-0.407498\pi\) | ||||
0.286532 | + | 0.958071i | \(0.407498\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.22409e10 | + | 7.06727e9i | −1.30849 | + | 0.755458i | −0.981844 | − | 0.189688i | \(-0.939252\pi\) |
−0.326647 | + | 0.945146i | \(0.605919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.17243e9 | − | 5.49481e9i | 0.330533 | − | 0.572500i | −0.652083 | − | 0.758147i | \(-0.726105\pi\) |
0.982616 | + | 0.185647i | \(0.0594381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.47036e10 | − | 8.48911e9i | −1.45608 | − | 0.840669i | −0.457266 | − | 0.889330i | \(-0.651171\pi\) |
−0.998815 | + | 0.0486607i | \(0.984505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.32628e10 | + | 2.29718e10i | 1.28077 | + | 2.21836i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.04251e9i | 0.187653i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.53838e9 | + | 1.13248e10i | 0.586053 | + | 1.01507i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.77674e8 | + | 2.76056e8i | −0.0151650 | + | 0.0235621i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.71794e9 | + | 9.90376e9i | −0.476351 | + | 0.825065i | −0.999633 | − | 0.0270950i | \(-0.991374\pi\) |
0.523281 | + | 0.852160i | \(0.324708\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8.51253e8i | − | 0.0675895i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.74137e8 | 0.0135011 | 0.00675057 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675057 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.10362e10 | − | 1.21453e10i | −1.55579 | − | 0.898234i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.99759e9 | − | 1.36964e10i | 0.144321 | − | 0.989531i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.57377e9 | + | 3.21801e9i | −0.384442 | + | 0.221958i | −0.679749 | − | 0.733445i | \(-0.737911\pi\) |
0.295307 | + | 0.955402i | \(0.404578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.50707e10 | −1.01585 | −0.507927 | − | 0.861400i | \(-0.669588\pi\) | ||||
−0.507927 | + | 0.861400i | \(0.669588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.16201e9 | + | 4.71234e9i | −0.525652 | + | 0.303485i | −0.739244 | − | 0.673438i | \(-0.764817\pi\) |
0.213592 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.24173e8 | + | 5.61484e8i | −0.0204110 | + | 0.0353528i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.01053e10 | + | 5.83431e9i | 0.608377 | + | 0.351247i | 0.772330 | − | 0.635222i | \(-0.219091\pi\) |
−0.163953 | + | 0.986468i | \(0.552425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.89472e9 | + | 3.28175e9i | 0.111562 | + | 0.193231i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.19903e9i | 0.0675554i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.81752e9 | + | 1.00762e10i | 0.320682 | + | 0.555437i | 0.980629 | − | 0.195875i | \(-0.0627547\pi\) |
−0.659947 | + | 0.751312i | \(0.729421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.82309e9 | + | 1.13140e10i | 0.307367 | + | 0.597200i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.19418e9 | + | 2.06839e9i | −0.0616930 | + | 0.106855i | −0.895222 | − | 0.445620i | \(-0.852983\pi\) |
0.833529 | + | 0.552475i | \(0.186317\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.11267e10i | 2.03591i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.64970e10 | 1.28422 | 0.642111 | − | 0.766612i | \(-0.278059\pi\) | ||||
0.642111 | + | 0.766612i | \(0.278059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.54637e9 | + | 8.92799e8i | 0.0718653 | + | 0.0414915i | 0.535502 | − | 0.844534i | \(-0.320122\pi\) |
−0.463637 | + | 0.886025i | \(0.653456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.06764e8 | + | 2.20984e9i | −0.00485941 | + | 0.100581i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.68915e9 | + | 3.86198e9i | −0.292127 | + | 0.168660i | −0.638901 | − | 0.769289i | \(-0.720611\pi\) |
0.346773 | + | 0.937949i | \(0.387277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.48450e9 | −0.0635147 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.83051e9 | − | 1.05685e9i | 0.0751943 | − | 0.0434134i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.26609e9 | + | 1.08532e10i | −0.252252 | + | 0.436913i | −0.964145 | − | 0.265374i | \(-0.914504\pi\) |
0.711894 | + | 0.702287i | \(0.247838\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.36803e10 | − | 2.52188e10i | −1.68930 | − | 0.975321i | −0.955049 | − | 0.296448i | \(-0.904198\pi\) |
−0.734256 | − | 0.678873i | \(-0.762469\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.88307e10 | − | 3.26157e10i | −0.713913 | − | 1.23653i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.30958e10i | 0.841695i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.47481e10 | + | 2.55445e10i | 0.527041 | + | 0.912861i | 0.999503 | + | 0.0315105i | \(0.0100318\pi\) |
−0.472463 | + | 0.881351i | \(0.656635\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26821e9 | + | 8.29293e9i | 0.146705 | + | 0.285041i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.05107e8 | − | 1.04808e9i | 0.0204005 | − | 0.0353346i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.10551e10i | − | 1.33202i | −0.745943 | − | 0.666010i | \(-0.768001\pi\) | ||
0.745943 | − | 0.666010i | \(-0.231999\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.48209e9 | 0.110844 | 0.0554220 | − | 0.998463i | \(-0.482350\pi\) | ||||
0.0554220 | + | 0.998463i | \(0.482350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.98763e9 | − | 3.45696e9i | −0.183527 | − | 0.105959i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.20583e10 | + | 2.06332e10i | 0.964336 | + | 0.620663i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.06204e10 | − | 1.76787e10i | 0.887363 | − | 0.512319i | 0.0142842 | − | 0.999898i | \(-0.495453\pi\) |
0.873079 | + | 0.487578i | \(0.162120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.35769e10 | 0.670711 | 0.335356 | − | 0.942092i | \(-0.391144\pi\) | ||||
0.335356 | + | 0.942092i | \(0.391144\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.30477e9 | − | 4.79476e9i | 0.227720 | − | 0.131474i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.29664e9 | + | 9.17406e9i | −0.142608 | + | 0.247004i | −0.928478 | − | 0.371388i | \(-0.878882\pi\) |
0.785870 | + | 0.618391i | \(0.212215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.71355e10 | + | 2.14402e10i | 0.964217 | + | 0.556691i | 0.897468 | − | 0.441079i | \(-0.145404\pi\) |
0.0667485 | + | 0.997770i | \(0.478737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.47660e9 | − | 2.55755e9i | −0.0376551 | − | 0.0652206i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.15632e10i | − | 0.776598i | −0.921534 | − | 0.388299i | \(-0.873063\pi\) | ||
0.921534 | − | 0.388299i | \(-0.126937\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.84944e10 | − | 1.01315e11i | −1.41387 | − | 2.44889i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.85648e9 | + | 2.88445e9i | −0.0433157 | + | 0.0673005i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.83048e8 | − | 8.36663e8i | 0.0110745 | − | 0.0191816i | −0.860435 | − | 0.509560i | \(-0.829808\pi\) |
0.871510 | + | 0.490379i | \(0.163141\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.56175e10i | − | 1.01002i | −0.863115 | − | 0.505008i | \(-0.831490\pi\) | ||
0.863115 | − | 0.505008i | \(-0.168510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.50463e10 | −1.85068 | −0.925341 | − | 0.379137i | \(-0.876221\pi\) | ||||
−0.925341 | + | 0.379137i | \(0.876221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.11963e10 | + | 6.46421e9i | 0.235401 | + | 0.135909i | 0.613061 | − | 0.790035i | \(-0.289938\pi\) |
−0.377660 | + | 0.925944i | \(0.623271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.27800e10 | + | 2.20181e10i | −0.884198 | + | 0.455080i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.48593e9 | + | 5.47671e9i | −0.189511 | + | 0.109415i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.46621e10 | 0.877334 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.52914e10 | − | 2.03755e10i | 0.670389 | − | 0.387049i | −0.125835 | − | 0.992051i | \(-0.540161\pi\) |
0.796224 | + | 0.605002i | \(0.206828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.79044e10 | + | 3.10114e10i | −0.334488 | + | 0.579350i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.45477e9 | + | 3.14931e9i | 0.0985846 | + | 0.0569179i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.71661e8 | + | 4.70530e8i | 0.00482960 | + | 0.00836511i | 0.868430 | − | 0.495812i | \(-0.165129\pi\) |
−0.863601 | + | 0.504177i | \(0.831796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.77606e10i | 0.477643i | 0.971063 | + | 0.238822i | \(0.0767611\pi\) | ||||
−0.971063 | + | 0.238822i | \(0.923239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.08722e10 | − | 1.88312e10i | −0.184047 | − | 0.318780i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.66025e10 | + | 1.76838e9i | 0.599908 | + | 0.0289835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.04720e10 | − | 5.27790e10i | 0.491472 | − | 0.851254i | −0.508480 | − | 0.861074i | \(-0.669792\pi\) |
0.999952 | + | 0.00981965i | \(0.00312574\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.07172e10i | 0.167421i | 0.996490 | + | 0.0837103i | \(0.0266770\pi\) | ||||
−0.996490 | + | 0.0837103i | \(0.973323\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.56000e9 | −0.0854888 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.18625e10 | + | 3.57163e10i | 0.921629 | + | 0.532103i | 0.884154 | − | 0.467195i | \(-0.154735\pi\) |
0.0374744 | + | 0.999298i | \(0.488069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.02579e10 | − | 3.10136e10i | 0.883752 | − | 0.454850i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.68511e9 | + | 4.43700e9i | −0.109250 | + | 0.0630755i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.96593e9 | −0.0415143 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.55227e10 | − | 4.36031e10i | 1.02501 | − | 0.591788i | 0.109457 | − | 0.993992i | \(-0.465089\pi\) |
0.915550 | + | 0.402204i | \(0.131756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.58953e10 | − | 6.21724e10i | 0.479767 | − | 0.830981i | −0.519964 | − | 0.854188i | \(-0.674054\pi\) |
0.999731 | + | 0.0232074i | \(0.00738780\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.72445e10 | + | 9.95610e9i | 0.223567 | + | 0.129076i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.56706e10 | − | 6.17834e10i | −0.455500 | − | 0.788949i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.81386e11i | − | 2.24747i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.21835e9 | − | 7.30639e9i | −0.0514905 | − | 0.0891842i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.13818e11 | − | 5.17931e10i | 1.34851 | − | 0.613644i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.84279e10 | − | 3.19180e10i | 0.215123 | − | 0.372603i | −0.738188 | − | 0.674595i | \(-0.764318\pi\) |
0.953311 | + | 0.301992i | \(0.0976515\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 6.34538e9i | − | 0.0719236i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.06513e10 | 0.118974 | 0.0594870 | − | 0.998229i | \(-0.481054\pi\) | ||||
0.0594870 | + | 0.998229i | \(0.481054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.21645e11 | + | 7.02316e10i | 1.31974 | + | 0.761950i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.00459e11 | − | 6.46573e10i | −1.07421 | − | 0.691380i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.64764e10 | + | 4.41537e10i | −0.794523 | + | 0.458718i | −0.841553 | − | 0.540175i | \(-0.818358\pi\) |
0.0470291 | + | 0.998894i | \(0.485025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.69827e10 | −0.173924 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.39954e11 | − | 8.08027e10i | 1.39301 | − | 0.804253i | 0.399359 | − | 0.916794i | \(-0.369233\pi\) |
0.993647 | + | 0.112542i | \(0.0358992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.07624e9 | + | 8.79231e9i | −0.0498136 | + | 0.0862798i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.02934e11 | − | 5.94289e10i | −0.981995 | − | 0.566955i | −0.0791229 | − | 0.996865i | \(-0.525212\pi\) |
−0.902872 | + | 0.429910i | \(0.858545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.38083e9 | + | 2.39167e9i | 0.0129896 | + | 0.0224987i | 0.872447 | − | 0.488708i | \(-0.162532\pi\) |
−0.859458 | + | 0.511207i | \(0.829198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.24605e10i | 0.296951i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.45450e9 | + | 1.29116e10i | 0.0672536 | + | 0.116487i | 0.897691 | − | 0.440625i | \(-0.145243\pi\) |
−0.830438 | + | 0.557111i | \(0.811910\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.83228e10 | − | 3.30090e9i | −0.599600 | − | 0.0289686i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.74795e10 | + | 9.95575e10i | −0.497553 | + | 0.861786i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.54651e11i | 1.30256i | 0.758836 | + | 0.651282i | \(0.225769\pi\) | ||||
−0.758836 | + | 0.651282i | \(0.774231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.28628e11 | −1.06874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.76058e11 | − | 1.01647e11i | −1.42376 | − | 0.822007i | −0.427140 | − | 0.904185i | \(-0.640479\pi\) |
−0.996618 | + | 0.0821785i | \(0.973812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.75203e7 | − | 1.81152e9i | 0.000698299 | − | 0.0144536i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.94736e11 | − | 1.12431e11i | 1.51265 | − | 0.873329i | 0.512759 | − | 0.858532i | \(-0.328623\pi\) |
0.999891 | − | 0.0147963i | \(-0.00470998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.77363e11 | −1.35945 | −0.679726 | − | 0.733466i | \(-0.737901\pi\) | ||||
−0.679726 | + | 0.733466i | \(0.737901\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.42409e9 | + | 5.44100e9i | −0.0703425 | + | 0.0406123i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.03220e11 | − | 1.78782e11i | 0.760343 | − | 1.31695i | −0.182331 | − | 0.983237i | \(-0.558364\pi\) |
0.942674 | − | 0.333715i | \(-0.108302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.98244e9 | − | 2.29926e9i | −0.0285749 | − | 0.0164977i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.92529e10 | + | 1.54591e11i | 0.632092 | + | 1.09482i | 0.987123 | + | 0.159961i | \(0.0511369\pi\) |
−0.355031 | + | 0.934854i | \(0.615530\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.92670e9i | 0.0546956i | 0.999626 | + | 0.0273478i | \(0.00870615\pi\) | ||||
−0.999626 | + | 0.0273478i | \(0.991294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.30080e10 | − | 1.61095e11i | −0.633516 | − | 1.09728i | −0.986827 | − | 0.161776i | \(-0.948278\pi\) |
0.353311 | − | 0.935506i | \(-0.385056\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.03377e10 | + | 1.40360e11i | −0.599676 | + | 0.931729i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.52382e10 | + | 1.30316e11i | −0.493081 | + | 0.854042i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.89328e10i | − | 0.120952i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.65626e11 | 1.04474 | 0.522372 | − | 0.852717i | \(-0.325047\pi\) | ||||
0.522372 | + | 0.852717i | \(0.325047\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.88165e9 | + | 3.39577e9i | 0.0361747 | + | 0.0208855i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.92978e11 | + | 1.86904e10i | 1.17206 | + | 0.113517i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.35061e11 | − | 7.79773e10i | 0.800012 | − | 0.461887i | −0.0434633 | − | 0.999055i | \(-0.513839\pi\) |
0.843475 | + | 0.537168i | \(0.180506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.44491e11 | 1.43027 | 0.715136 | − | 0.698986i | \(-0.246365\pi\) | ||||
0.715136 | + | 0.698986i | \(0.246365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.45655e10 | − | 4.30504e10i | 0.425521 | − | 0.245675i | −0.271916 | − | 0.962321i | \(-0.587657\pi\) |
0.697437 | + | 0.716647i | \(0.254324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.21314e10 | + | 7.29738e10i | −0.237480 | + | 0.411328i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.96231e9 | − | 3.44234e9i | −0.0327915 | − | 0.0189322i | 0.483515 | − | 0.875336i | \(-0.339360\pi\) |
−0.516306 | + | 0.856404i | \(0.672693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.42482e9 | + | 7.66401e9i | 0.0240398 | + | 0.0416381i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.39086e10i | − | 0.338858i | −0.985542 | − | 0.169429i | \(-0.945808\pi\) | ||
0.985542 | − | 0.169429i | \(-0.0541923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.36970e9 | − | 1.10326e10i | −0.0333667 | − | 0.0577928i | 0.848860 | − | 0.528618i | \(-0.177290\pi\) |
−0.882227 | + | 0.470825i | \(0.843956\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.36136e9 | + | 1.04169e10i | 0.0274150 | + | 0.0532661i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.10445e10 | + | 8.84117e10i | −0.257897 | + | 0.446690i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.44431e11i | 1.69907i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.95055e10 | 0.192574 | 0.0962870 | − | 0.995354i | \(-0.469303\pi\) | ||||
0.0962870 | + | 0.995354i | \(0.469303\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.56598e11 | − | 1.48147e11i | −1.22152 | − | 0.705243i | −0.256275 | − | 0.966604i | \(-0.582495\pi\) |
−0.965241 | + | 0.261361i | \(0.915829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.71797e10 | − | 3.55590e11i | 0.0808232 | − | 1.67290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.29563e11 | + | 1.32538e11i | −1.05492 | + | 0.609058i | −0.924023 | − | 0.382338i | \(-0.875119\pi\) |
−0.130897 | + | 0.991396i | \(0.541786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.77699e10 | −0.126128 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.54359e11 | + | 8.91193e10i | −0.684945 | + | 0.395453i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44204e11 | + | 2.49769e11i | −0.632507 | + | 1.09553i | 0.354531 | + | 0.935044i | \(0.384641\pi\) |
−0.987038 | + | 0.160490i | \(0.948693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.31883e10 | + | 7.61424e9i | 0.0565260 | + | 0.0326353i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.79509e10 | + | 8.30534e10i | 0.203173 | + | 0.351906i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.31307e11i | 0.957894i | 0.877844 | + | 0.478947i | \(0.158981\pi\) | ||||
−0.877844 | + | 0.478947i | \(0.841019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.11505e10 | + | 1.05916e11i | 0.250368 | + | 0.433650i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.43812e11 | + | 2.79420e11i | 0.575596 | + | 1.11835i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00350e11 | + | 1.73811e11i | −0.397129 | + | 0.687848i | −0.993370 | − | 0.114957i | \(-0.963327\pi\) |
0.596241 | + | 0.802805i | \(0.296660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.34870e10i | − | 0.361737i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.09903e10 | −0.118577 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.75820e10 | − | 5.05655e10i | −0.327717 | − | 0.189208i | 0.327110 | − | 0.944986i | \(-0.393925\pi\) |
−0.654827 | + | 0.755779i | \(0.727259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.21762e11 | + | 2.71453e11i | 1.56072 | + | 1.00451i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.11768e11 | + | 2.37734e11i | −1.49039 | + | 0.860478i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.13682e11 | −0.406963 | −0.203481 | − | 0.979079i | \(-0.565226\pi\) | ||||
−0.203481 | + | 0.979079i | \(0.565226\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.77611e9 | − | 4.48954e9i | 0.0272328 | − | 0.0157229i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.85533e11 | + | 3.21352e11i | −0.642695 | + | 1.11318i | 0.342133 | + | 0.939651i | \(0.388851\pi\) |
−0.984829 | + | 0.173529i | \(0.944483\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.76443e11 | − | 2.17340e11i | −1.27594 | − | 0.736663i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.37581e10 | + | 2.38297e10i | 0.0461297 | + | 0.0798990i | 0.888168 | − | 0.459518i | \(-0.151978\pi\) |
−0.842039 | + | 0.539417i | \(0.818645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.06856e11i | − | 1.33501i | −0.744605 | − | 0.667506i | \(-0.767362\pi\) | ||
0.744605 | − | 0.667506i | \(-0.232638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.43177e9 | − | 7.67606e9i | −0.0143864 | − | 0.0249180i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.58076e11 | + | 4.00978e11i | −0.820012 | + | 1.27407i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.46757e11 | − | 2.54190e11i | 0.461359 | − | 0.799097i | −0.537670 | − | 0.843155i | \(-0.680695\pi\) |
0.999029 | + | 0.0440583i | \(0.0140287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.44342e10i | 0.105975i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.73267e9 | 0.0296380 | 0.0148190 | − | 0.999890i | \(-0.495283\pi\) | ||||
0.0148190 | + | 0.999890i | \(0.495283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.39468e11 | − | 1.38257e11i | −0.714018 | − | 0.412238i | 0.0985291 | − | 0.995134i | \(-0.468586\pi\) |
−0.812547 | + | 0.582896i | \(0.801920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.18889e11 | + | 1.64126e11i | −0.940896 | + | 0.484261i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.13142e11 | + | 6.53228e10i | −0.326922 | + | 0.188748i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.57246e11 | 1.02156 | 0.510778 | − | 0.859713i | \(-0.329358\pi\) | ||||
0.510778 | + | 0.859713i | \(0.329358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.39187e11 | − | 1.95830e11i | 0.949995 | − | 0.548480i | 0.0569158 | − | 0.998379i | \(-0.481873\pi\) |
0.893079 | + | 0.449899i | \(0.148540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17703e11 | − | 3.77072e11i | 0.603471 | − | 1.04524i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.36503e11 | − | 3.09750e11i | −1.45688 | − | 0.841128i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.65534e11 | + | 2.86713e11i | 0.444921 | + | 0.770626i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.98879e10i | 0.0787077i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.47643e11 | + | 2.55726e11i | 0.384871 | + | 0.666616i | 0.991751 | − | 0.128177i | \(-0.0409127\pi\) |
−0.606880 | + | 0.794793i | \(0.707579\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.73160e11 | + | 2.76912e10i | 1.46410 | + | 0.0707352i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67012e11 | + | 4.62478e11i | −0.675209 | + | 1.16950i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.63028e10i | 0.189107i | 0.995520 | + | 0.0945534i | \(0.0301423\pi\) | ||||
−0.995520 | + | 0.0945534i | \(0.969858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.43132e9 | 0.00596562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.30240e11 | + | 3.06134e11i | 1.27529 | + | 0.736291i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.57101e9 | + | 3.89665e9i | −0.0180289 | + | 0.00927915i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.14896e11 | + | 3.55010e11i | −1.43551 | + | 0.828795i | −0.997534 | − | 0.0701899i | \(-0.977639\pi\) |
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.28420e11 | 1.68383 | 0.841916 | − | 0.539609i | \(-0.181428\pi\) | ||||
0.841916 | + | 0.539609i | \(0.181428\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00352e9 | − | 3.46613e9i | 0.0136074 | − | 0.00785624i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.90013e10 | + | 5.02317e10i | −0.0650922 | + | 0.112743i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.30592e11 | − | 2.48602e11i | −0.947748 | − | 0.547183i | −0.0553673 | − | 0.998466i | \(-0.517633\pi\) |
−0.892381 | + | 0.451284i | \(0.850966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.29315e10 | − | 7.43596e10i | −0.0935787 | − | 0.162083i | 0.815436 | − | 0.578847i | \(-0.196497\pi\) |
−0.909015 | + | 0.416764i | \(0.863164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.26379e11i | 1.98046i | 0.139432 | + | 0.990232i | \(0.455472\pi\) | ||||
−0.139432 | + | 0.990232i | \(0.544528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.36477e11 | − | 7.56001e11i | −0.924152 | − | 1.60068i | −0.792919 | − | 0.609328i | \(-0.791439\pi\) |
−0.131234 | − | 0.991351i | \(-0.541894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.33024e10 | + | 4.24574e10i | −0.193782 | + | 0.0881808i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.83143e10 | + | 3.17213e10i | −0.0376742 | + | 0.0652536i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.86462e11i | 1.38538i | 0.721236 | + | 0.692689i | \(0.243574\pi\) | ||||
−0.721236 | + | 0.692689i | \(0.756426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.95111e11 | −1.98924 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.16021e10 | − | 6.69847e9i | −0.0227567 | − | 0.0131386i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.17198e11 | + | 3.32877e11i | 1.00490 | + | 0.646770i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.69798e10 | + | 4.44443e10i | −0.146777 | + | 0.0847419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.47904e11 | 1.60159 | 0.800793 | − | 0.598941i | \(-0.204411\pi\) | ||||
0.800793 | + | 0.598941i | \(0.204411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.03566e11 | − | 1.75264e11i | 0.562769 | − | 0.324915i | −0.191487 | − | 0.981495i | \(-0.561331\pi\) |
0.754256 | + | 0.656580i | \(0.227998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.15123e11 | + | 5.45809e11i | −0.578772 | + | 1.00246i | 0.416848 | + | 0.908976i | \(0.363135\pi\) |
−0.995621 | + | 0.0934868i | \(0.970199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.44008e10 | + | 3.71818e10i | 0.116104 | + | 0.0670328i | 0.556927 | − | 0.830561i | \(-0.311980\pi\) |
−0.440823 | + | 0.897594i | \(0.645313\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.40755e10 | − | 4.16999e10i | −0.0430041 | − | 0.0744854i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.07933e12i | − | 1.89266i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.36975e11 | − | 5.83657e11i | −0.585497 | − | 1.01411i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.94061e10 | − | 3.83636e9i | −0.135463 | − | 0.00654467i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.03583e11 | + | 5.25822e11i | −0.513192 | + | 0.888874i | 0.486691 | + | 0.873574i | \(0.338204\pi\) |
−0.999883 | + | 0.0152999i | \(0.995130\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.79724e11i | 0.298334i | 0.988812 | + | 0.149167i | \(0.0476593\pi\) | ||||
−0.988812 | + | 0.149167i | \(0.952341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.97608e11 | 0.654051 | 0.327026 | − | 0.945015i | \(-0.393954\pi\) | ||||
0.327026 | + | 0.945015i | \(0.393954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.64234e10 | + | 3.25761e10i | 0.0911518 | + | 0.0526265i | 0.544883 | − | 0.838512i | \(-0.316574\pi\) |
−0.453731 | + | 0.891139i | \(0.649907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.85241e10 | − | 3.83418e11i | 0.0296573 | − | 0.613854i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.36016e10 | + | 7.85286e9i | −0.0213886 | + | 0.0123487i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.98523e10 | −0.108865 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.18590e12 | − | 6.84679e11i | 1.81555 | − | 1.04821i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.71190e10 | − | 8.16124e10i | 0.0714984 | − | 0.123839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.69078e10 | − | 1.55352e10i | −0.0401129 | − | 0.0231592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.26093e11 | − | 3.91605e11i | −0.334086 | − | 0.578653i | 0.649223 | − | 0.760598i | \(-0.275094\pi\) |
−0.983309 | + | 0.181945i | \(0.941761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.36713e12i | − | 1.98489i | −0.122678 | − | 0.992447i | \(-0.539148\pi\) | ||
0.122678 | − | 0.992447i | \(-0.460852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.08989e11 | − | 5.35184e11i | −0.444692 | − | 0.770230i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.70708e11 | − | 4.20604e11i | 0.382845 | − | 0.594834i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.01410e10 | − | 6.95262e10i | 0.0562763 | − | 0.0974735i | −0.836515 | − | 0.547944i | \(-0.815411\pi\) |
0.892791 | + | 0.450471i | \(0.148744\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.13305e11i | 0.707243i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.13989e11 | −0.565486 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.66173e11 | + | 9.59400e10i | 0.223099 | + | 0.128806i | 0.607384 | − | 0.794408i | \(-0.292219\pi\) |
−0.384285 | + | 0.923214i | \(0.625552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.84829e11 | − | 5.38874e11i | 0.512235 | − | 0.717280i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.41899e10 | − | 8.19257e9i | 0.0185667 | − | 0.0107195i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.82042e10 | 0.0884816 | 0.0442408 | − | 0.999021i | \(-0.485913\pi\) | ||||
0.0442408 | + | 0.999021i | \(0.485913\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.33449e11 | − | 2.50252e11i | 0.552814 | − | 0.319168i | −0.197442 | − | 0.980315i | \(-0.563263\pi\) |
0.750256 | + | 0.661147i | \(0.229930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.25127e11 | − | 3.89932e11i | 0.284696 | − | 0.493108i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.85222e11 | − | 2.80143e11i | −0.603310 | − | 0.348321i | 0.167033 | − | 0.985951i | \(-0.446581\pi\) |
−0.770343 | + | 0.637630i | \(0.779915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.74647e11 | + | 8.22112e11i | 0.585202 | + | 1.01360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.76236e11i | − | 0.456131i | −0.973646 | − | 0.228065i | \(-0.926760\pi\) | ||
0.973646 | − | 0.228065i | \(-0.0732400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.18433e9 | − | 7.24747e9i | −0.00503051 | − | 0.00871310i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.18281e11 | + | 1.39558e12i | 0.849219 | + | 1.64999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00542e11 | + | 3.47349e11i | −0.235132 | + | 0.407260i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05958e11i | 0.122186i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.30742e11 | −1.06445 | −0.532223 | − | 0.846604i | \(-0.678643\pi\) | ||||
−0.532223 | + | 0.846604i | \(0.678643\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.48063e12 | − | 8.54843e11i | −1.66560 | − | 0.961633i | −0.969968 | − | 0.243232i | \(-0.921792\pi\) |
−0.695629 | − | 0.718401i | \(-0.744874\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.15361e10 | − | 8.59726e11i | 0.0463420 | − | 0.959199i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.06224e12 | − | 6.13285e11i | 1.16586 | − | 0.673107i | 0.213155 | − | 0.977018i | \(-0.431626\pi\) |
0.952700 | + | 0.303912i | \(0.0982927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50801e12 | −1.64162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.11814e12 | − | 6.45558e11i | 1.19752 | − | 0.691386i | 0.237516 | − | 0.971384i | \(-0.423667\pi\) |
0.960001 | + | 0.279997i | \(0.0903336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.70832e10 | − | 2.95890e10i | 0.0181479 | − | 0.0314330i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.65085e10 | − | 2.10782e10i | −0.0381601 | − | 0.0220317i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36853e11 | + | 2.37037e11i | 0.141893 | + | 0.245766i | 0.928209 | − | 0.372058i | \(-0.121348\pi\) |
−0.786317 | + | 0.617824i | \(0.788014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.20138e10i | 0.0530672i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.53655e11 | − | 1.30537e12i | −0.762767 | − | 1.32115i | −0.941419 | − | 0.337240i | \(-0.890507\pi\) |
0.178651 | − | 0.983912i | \(-0.442827\pi\) | |||||||
\(998\) | 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 | 252.9.bk.a.233.10 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.233.13 | yes | 44 | |
7.4 | even | 3 | inner | 252.9.bk.a.53.13 | yes | 44 | |
21.11 | odd | 6 | inner | 252.9.bk.a.53.10 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.10 | ✓ | 44 | 21.11 | odd | 6 | inner | |
252.9.bk.a.53.13 | yes | 44 | 7.4 | even | 3 | inner | |
252.9.bk.a.233.10 | yes | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.233.13 | yes | 44 | 3.2 | odd | 2 | inner |