Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,16,Mod(37,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.37");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.g (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: | \(179.793816426\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 11644556445 x^{8} + 11479653183988 x^{7} + \cdots + 46\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{7}\cdot 5^{2}\cdot 7^{7} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(33130.3 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.37 |
Dual form | 126.16.g.e.109.4 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 64.0000 | − | 110.851i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8192.00 | − | 14189.0i | −0.250000 | − | 0.433013i | ||||
\(5\) | 36165.1 | − | 62639.7i | 0.207021 | − | 0.358571i | −0.743754 | − | 0.668454i | \(-0.766957\pi\) |
0.950775 | + | 0.309883i | \(0.100290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 780333. | − | 2.03437e6i | 0.358133 | − | 0.933670i | ||||
\(8\) | −2.09715e6 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.62913e6 | − | 8.01788e6i | −0.146386 | − | 0.253548i | ||||
\(11\) | 4.41234e7 | + | 7.64240e7i | 0.682691 | + | 1.18246i | 0.974157 | + | 0.225874i | \(0.0725238\pi\) |
−0.291466 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.28410e8 | −0.567574 | −0.283787 | − | 0.958887i | \(-0.591591\pi\) | ||||
−0.283787 | + | 0.958887i | \(0.591591\pi\) | |||||||
\(14\) | −1.75571e8 | − | 2.16700e8i | −0.445135 | − | 0.549413i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.34218e8 | + | 2.32472e8i | −0.125000 | + | 0.216506i | ||||
\(17\) | −8.93874e7 | − | 1.54823e8i | −0.0528335 | − | 0.0915103i | 0.838399 | − | 0.545057i | \(-0.183492\pi\) |
−0.891233 | + | 0.453547i | \(0.850159\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51228e9 | − | 4.35140e9i | 0.644787 | − | 1.11680i | −0.339564 | − | 0.940583i | \(-0.610279\pi\) |
0.984351 | − | 0.176221i | \(-0.0563873\pi\) | |||||||
\(20\) | −1.18506e9 | −0.207021 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.12956e10 | 0.965471 | ||||||||
\(23\) | −3.50108e9 | + | 6.06404e9i | −0.214409 | + | 0.371367i | −0.953090 | − | 0.302688i | \(-0.902116\pi\) |
0.738681 | + | 0.674056i | \(0.235449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.26430e10 | + | 2.18983e10i | 0.414285 | + | 0.717562i | ||||
\(26\) | −8.21822e9 | + | 1.42344e10i | −0.200668 | + | 0.347567i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.52580e10 | + | 5.59341e9i | −0.493824 | + | 0.0783414i | ||||
\(29\) | −1.06127e11 | −1.14246 | −0.571229 | − | 0.820791i | \(-0.693533\pi\) | ||||
−0.571229 | + | 0.820791i | \(0.693533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.64697e10 | − | 1.32449e11i | −0.499202 | − | 0.864644i | 0.500797 | − | 0.865565i | \(-0.333040\pi\) |
−1.00000 | 0.000920959i | \(0.999707\pi\) | ||||||||
\(32\) | 1.71799e10 | + | 2.97564e10i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.28832e10 | −0.0747178 | ||||||||
\(35\) | −9.92113e10 | − | 1.22453e11i | −0.260646 | − | 0.321705i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00321e11 | + | 3.46966e11i | −0.346907 | + | 0.600861i | −0.985698 | − | 0.168519i | \(-0.946101\pi\) |
0.638791 | + | 0.769380i | \(0.279435\pi\) | |||||||
\(38\) | −3.21572e11 | − | 5.56979e11i | −0.455933 | − | 0.789700i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.58436e10 | + | 1.31365e11i | −0.0731929 | + | 0.126774i | ||||
\(41\) | −4.37251e10 | −0.0350633 | −0.0175316 | − | 0.999846i | \(-0.505581\pi\) | ||||
−0.0175316 | + | 0.999846i | \(0.505581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.44454e12 | −1.37146 | −0.685731 | − | 0.727855i | \(-0.740517\pi\) | ||||
−0.685731 | + | 0.727855i | \(0.740517\pi\) | |||||||
\(44\) | 7.22918e11 | − | 1.25213e12i | 0.341345 | − | 0.591228i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.48138e11 | + | 7.76198e11i | 0.151610 | + | 0.262596i | ||||
\(47\) | −1.20549e12 | + | 2.08797e12i | −0.347080 | + | 0.601160i | −0.985729 | − | 0.168338i | \(-0.946160\pi\) |
0.638650 | + | 0.769498i | \(0.279493\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.52972e12 | − | 3.17496e12i | −0.743481 | − | 0.668757i | ||||
\(50\) | 3.23660e12 | 0.585887 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.05193e12 | + | 1.82200e12i | 0.141894 | + | 0.245767i | ||||
\(53\) | 5.08120e12 | + | 8.80091e12i | 0.594152 | + | 1.02910i | 0.993666 | + | 0.112375i | \(0.0358456\pi\) |
−0.399514 | + | 0.916727i | \(0.630821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.38290e12 | 0.565325 | ||||||||
\(56\) | −1.63648e12 | + | 4.26637e12i | −0.126619 | + | 0.330102i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.79212e12 | + | 1.17643e13i | −0.403920 | + | 0.699610i | ||||
\(59\) | −1.13900e13 | − | 1.97280e13i | −0.595845 | − | 1.03203i | −0.993427 | − | 0.114467i | \(-0.963484\pi\) |
0.397582 | − | 0.917567i | \(-0.369849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.02342e13 | − | 3.50467e13i | 0.824351 | − | 1.42782i | −0.0780625 | − | 0.996948i | \(-0.524873\pi\) |
0.902414 | − | 0.430870i | \(-0.141793\pi\) | |||||||
\(62\) | −1.95762e13 | −0.705979 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.39805e12 | 0.125000 | ||||||||
\(65\) | −4.64394e12 | + | 8.04355e12i | −0.117500 | + | 0.203515i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.61618e13 | − | 4.53136e13i | −0.527360 | − | 0.913414i | −0.999492 | − | 0.0318859i | \(-0.989849\pi\) |
0.472132 | − | 0.881528i | \(-0.343485\pi\) | |||||||
\(68\) | −1.46452e12 | + | 2.53663e12i | −0.0264167 | + | 0.0457551i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.99236e13 | + | 3.16072e12i | −0.289156 | + | 0.0458723i | ||||
\(71\) | −4.87140e13 | −0.635647 | −0.317824 | − | 0.948150i | \(-0.602952\pi\) | ||||
−0.317824 | + | 0.948150i | \(0.602952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.90981e13 | − | 5.03994e13i | −0.308278 | − | 0.533954i | 0.669707 | − | 0.742625i | \(-0.266420\pi\) |
−0.977986 | + | 0.208671i | \(0.933086\pi\) | |||||||
\(74\) | 2.56411e13 | + | 4.44116e13i | 0.245300 | + | 0.424873i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.23224e13 | −0.644787 | ||||||||
\(77\) | 1.89905e14 | − | 3.01270e13i | 1.34852 | − | 0.213932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.16442e13 | + | 1.41412e14i | −0.478324 | + | 0.828482i | −0.999691 | − | 0.0248508i | \(-0.992089\pi\) |
0.521367 | + | 0.853333i | \(0.325422\pi\) | |||||||
\(80\) | 9.70798e12 | + | 1.68147e13i | 0.0517552 | + | 0.0896427i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.79841e12 | + | 4.84699e12i | −0.0123967 | + | 0.0214718i | ||||
\(83\) | 1.62502e14 | 0.657315 | 0.328658 | − | 0.944449i | \(-0.393404\pi\) | ||||
0.328658 | + | 0.944449i | \(0.393404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29308e13 | −0.0437505 | ||||||||
\(86\) | −1.56451e14 | + | 2.70980e14i | −0.484885 | + | 0.839846i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.25335e13 | − | 1.60273e14i | −0.241368 | − | 0.418061i | ||||
\(89\) | −4.92355e13 | + | 8.52783e13i | −0.117992 | + | 0.204368i | −0.918972 | − | 0.394323i | \(-0.870979\pi\) |
0.800980 | + | 0.598691i | \(0.204312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00202e14 | + | 2.61232e14i | −0.203267 | + | 0.529927i | ||||
\(92\) | 1.14723e14 | 0.214409 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.54303e14 | + | 2.67260e14i | 0.245422 | + | 0.425084i | ||||
\(95\) | −1.81714e14 | − | 3.14737e14i | −0.266969 | − | 0.462403i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.71892e14 | −0.844329 | −0.422164 | − | 0.906519i | \(-0.638730\pi\) | ||||
−0.422164 | + | 0.906519i | \(0.638730\pi\) | |||||||
\(98\) | −5.77851e14 | + | 1.88076e14i | −0.672389 | + | 0.218846i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.07142e14 | − | 3.58781e14i | 0.207142 | − | 0.358781i | ||||
\(101\) | −3.66484e14 | − | 6.34768e14i | −0.340130 | − | 0.589122i | 0.644327 | − | 0.764750i | \(-0.277138\pi\) |
−0.984457 | + | 0.175628i | \(0.943804\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.49597e14 | − | 9.51930e14i | 0.440317 | − | 0.762651i | −0.557396 | − | 0.830247i | \(-0.688200\pi\) |
0.997713 | + | 0.0675959i | \(0.0215329\pi\) | |||||||
\(104\) | 2.69295e14 | 0.200668 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.30079e15 | 0.840258 | ||||||||
\(107\) | −1.56756e15 | + | 2.71509e15i | −0.943726 | + | 1.63458i | −0.185444 | + | 0.982655i | \(0.559372\pi\) |
−0.758282 | + | 0.651926i | \(0.773961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.81694e14 | + | 1.18073e15i | 0.357183 | + | 0.618659i | 0.987489 | − | 0.157688i | \(-0.0504040\pi\) |
−0.630306 | + | 0.776347i | \(0.717071\pi\) | |||||||
\(110\) | 4.08506e14 | − | 7.07553e14i | 0.199873 | − | 0.346189i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.68198e14 | + | 4.54453e14i | 0.157379 | + | 0.194247i | ||||
\(113\) | −1.37056e15 | −0.548036 | −0.274018 | − | 0.961725i | \(-0.588353\pi\) | ||||
−0.274018 | + | 0.961725i | \(0.588353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53233e14 | + | 4.38613e14i | 0.0887742 | + | 0.153762i | ||||
\(116\) | 8.69391e14 | + | 1.50583e15i | 0.285615 | + | 0.494699i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.91584e15 | −0.842652 | ||||||||
\(119\) | −3.84719e14 | + | 6.10327e13i | −0.104362 | + | 0.0165562i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.80513e15 | + | 3.12658e15i | −0.432134 | + | 0.748477i | ||||
\(122\) | −2.58998e15 | − | 4.48597e15i | −0.582904 | − | 1.00962i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.25288e15 | + | 2.17005e15i | −0.249601 | + | 0.432322i | ||||
\(125\) | 4.03627e15 | 0.757104 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.19653e15 | −1.19838 | −0.599191 | − | 0.800606i | \(-0.704511\pi\) | ||||
−0.599191 | + | 0.800606i | \(0.704511\pi\) | |||||||
\(128\) | 2.81475e14 | − | 4.87529e14i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.94425e14 | + | 1.02957e15i | 0.0830848 | + | 0.143907i | ||||
\(131\) | −7.14085e15 | + | 1.23683e16i | −0.942357 | + | 1.63221i | −0.181399 | + | 0.983410i | \(0.558062\pi\) |
−0.760958 | + | 0.648801i | \(0.775271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.89192e15 | − | 8.50644e15i | −0.811807 | − | 1.00198i | ||||
\(134\) | −6.69743e15 | −0.745799 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.87459e14 | + | 3.24688e14i | 0.0186795 | + | 0.0323538i | ||||
\(137\) | −5.66307e15 | − | 9.80872e15i | −0.534130 | − | 0.925141i | −0.999205 | − | 0.0398695i | \(-0.987306\pi\) |
0.465074 | − | 0.885272i | \(-0.346028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.40279e16 | 1.18681 | 0.593407 | − | 0.804903i | \(-0.297783\pi\) | ||||
0.593407 | + | 0.804903i | \(0.297783\pi\) | |||||||
\(140\) | −9.24739e14 | + | 2.41084e15i | −0.0741410 | + | 0.193289i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.11770e15 | + | 5.40001e15i | −0.224735 | + | 0.389253i | ||||
\(143\) | −5.66588e15 | − | 9.81358e15i | −0.387478 | − | 0.671131i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.83808e15 | + | 6.64776e15i | −0.236513 | + | 0.409652i | ||||
\(146\) | −7.44911e15 | −0.435972 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.56411e15 | 0.346907 | ||||||||
\(149\) | 2.73587e15 | − | 4.73867e15i | 0.137467 | − | 0.238100i | −0.789070 | − | 0.614303i | \(-0.789437\pi\) |
0.926537 | + | 0.376203i | \(0.122771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.44081e16 | + | 2.49556e16i | 0.655059 | + | 1.13460i | 0.981879 | + | 0.189509i | \(0.0606897\pi\) |
−0.326820 | + | 0.945087i | \(0.605977\pi\) | |||||||
\(152\) | −5.26864e15 | + | 9.12555e15i | −0.227967 | + | 0.394850i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.81433e15 | − | 2.29794e16i | 0.345767 | − | 0.901431i | ||||
\(155\) | −1.10621e16 | −0.413381 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.68210e15 | − | 6.37759e15i | −0.124982 | − | 0.216476i | 0.796744 | − | 0.604317i | \(-0.206554\pi\) |
−0.921726 | + | 0.387842i | \(0.873221\pi\) | |||||||
\(158\) | 1.04505e16 | + | 1.81007e16i | 0.338226 | + | 0.585825i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.48524e15 | 0.0731929 | ||||||||
\(161\) | 9.60447e15 | + | 1.18544e16i | 0.269948 | + | 0.333186i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.57987e16 | + | 6.20052e16i | −0.917193 | + | 1.58862i | −0.113534 | + | 0.993534i | \(0.536217\pi\) |
−0.803659 | + | 0.595090i | \(0.797116\pi\) | |||||||
\(164\) | 3.58196e14 | + | 6.20414e14i | 0.00876581 | + | 0.0151828i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04001e16 | − | 1.80136e16i | 0.232396 | − | 0.402522i | ||||
\(167\) | 9.04861e16 | 1.93290 | 0.966448 | − | 0.256862i | \(-0.0826886\pi\) | ||||
0.966448 | + | 0.256862i | \(0.0826886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.46968e16 | −0.677860 | ||||||||
\(170\) | −8.27571e14 | + | 1.43339e15i | −0.0154681 | + | 0.0267916i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00257e16 | + | 3.46855e16i | 0.342866 | + | 0.593861i | ||||
\(173\) | −3.18743e14 | + | 5.52079e14i | −0.00522511 | + | 0.00905015i | −0.868626 | − | 0.495468i | \(-0.834997\pi\) |
0.863401 | + | 0.504518i | \(0.168330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.44148e16 | − | 8.63248e15i | 0.818336 | − | 0.129823i | ||||
\(176\) | −2.36886e16 | −0.341345 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.30214e15 | + | 1.09156e16i | 0.0834330 | + | 0.144510i | ||||
\(179\) | −2.71119e16 | − | 4.69593e16i | −0.344162 | − | 0.596106i | 0.641039 | − | 0.767508i | \(-0.278504\pi\) |
−0.985201 | + | 0.171402i | \(0.945170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.48558e17 | −1.73503 | −0.867514 | − | 0.497412i | \(-0.834284\pi\) | ||||
−0.867514 | + | 0.497412i | \(0.834284\pi\) | |||||||
\(182\) | 2.25450e16 | + | 2.78264e16i | 0.252647 | + | 0.311833i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.34229e15 | − | 1.27172e16i | 0.0758050 | − | 0.131298i | ||||
\(185\) | 1.44892e16 | + | 2.50961e16i | 0.143634 | + | 0.248781i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.88815e15 | − | 1.36627e16i | 0.0721379 | − | 0.124946i | ||||
\(188\) | 3.95014e16 | 0.347080 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.65187e16 | −0.377551 | ||||||||
\(191\) | −9.39211e16 | + | 1.62676e17i | −0.732846 | + | 1.26933i | 0.222815 | + | 0.974861i | \(0.428475\pi\) |
−0.955662 | + | 0.294467i | \(0.904858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.20643e16 | + | 1.24819e17i | 0.520044 | + | 0.900743i | 0.999728 | + | 0.0233020i | \(0.00741792\pi\) |
−0.479684 | + | 0.877441i | \(0.659249\pi\) | |||||||
\(194\) | −4.30011e16 | + | 7.44801e16i | −0.298515 | + | 0.517044i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61340e16 | + | 7.60924e16i | −0.103710 | + | 0.489126i | ||||
\(197\) | 8.85598e16 | 0.547949 | 0.273974 | − | 0.961737i | \(-0.411662\pi\) | ||||
0.273974 | + | 0.961737i | \(0.411662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.61131e16 | + | 7.98703e16i | 0.264501 | + | 0.458129i | 0.967433 | − | 0.253129i | \(-0.0814595\pi\) |
−0.702932 | + | 0.711257i | \(0.748126\pi\) | |||||||
\(200\) | −2.65142e16 | − | 4.59240e16i | −0.146472 | − | 0.253697i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.38198e16 | −0.481016 | ||||||||
\(203\) | −8.28143e16 | + | 2.15901e17i | −0.409152 | + | 1.06668i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58132e15 | + | 2.73893e15i | −0.00725882 | + | 0.0125727i | ||||
\(206\) | −7.03484e16 | − | 1.21847e17i | −0.311351 | − | 0.539275i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.72349e16 | − | 2.98516e16i | 0.0709468 | − | 0.122883i | ||||
\(209\) | 4.43402e17 | 1.76076 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.05813e17 | 1.87013 | 0.935065 | − | 0.354476i | \(-0.115341\pi\) | ||||
0.935065 | + | 0.354476i | \(0.115341\pi\) | |||||||
\(212\) | 8.32505e16 | − | 1.44194e17i | 0.297076 | − | 0.514551i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00648e17 | + | 3.47532e17i | 0.667315 | + | 1.15582i | ||||
\(215\) | −8.84070e16 | + | 1.53125e17i | −0.283921 | + | 0.491766i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.29122e17 | + | 5.22127e16i | −0.986073 | + | 0.156433i | ||||
\(218\) | 1.74514e17 | 0.505133 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.22888e16 | − | 9.05668e16i | −0.141331 | − | 0.244793i | ||||
\(221\) | 1.14782e16 | + | 1.98808e16i | 0.0299869 | + | 0.0519389i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.23682e17 | −0.790373 | −0.395187 | − | 0.918601i | \(-0.629320\pi\) | ||||
−0.395187 | + | 0.918601i | \(0.629320\pi\) | |||||||
\(224\) | 7.39414e16 | − | 1.17302e16i | 0.174593 | − | 0.0276979i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.77157e16 | + | 1.51928e17i | −0.193760 | + | 0.335602i | ||||
\(227\) | −3.65320e16 | − | 6.32753e16i | −0.0780692 | − | 0.135220i | 0.824348 | − | 0.566084i | \(-0.191542\pi\) |
−0.902417 | + | 0.430864i | \(0.858209\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.54581e17 | + | 6.14153e17i | −0.709495 | + | 1.22888i | 0.255549 | + | 0.966796i | \(0.417744\pi\) |
−0.965045 | + | 0.262086i | \(0.915590\pi\) | |||||||
\(230\) | 6.48277e16 | 0.125546 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.22564e17 | 0.403920 | ||||||||
\(233\) | 3.75817e17 | − | 6.50934e17i | 0.660400 | − | 1.14385i | −0.320111 | − | 0.947380i | \(-0.603720\pi\) |
0.980511 | − | 0.196466i | \(-0.0629466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.71931e16 | + | 1.51023e17i | 0.143705 | + | 0.248905i | ||||
\(236\) | −1.86614e17 | + | 3.23224e17i | −0.297922 | + | 0.516017i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.78565e16 | + | 4.65527e16i | −0.0267589 | + | 0.0697618i | ||||
\(239\) | −4.14880e17 | −0.602474 | −0.301237 | − | 0.953549i | \(-0.597400\pi\) | ||||
−0.301237 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.73589e17 | + | 6.47074e17i | 0.509643 | + | 0.882727i | 0.999938 | + | 0.0111705i | \(0.00355575\pi\) |
−0.490295 | + | 0.871557i | \(0.663111\pi\) | |||||||
\(242\) | 2.31057e17 | + | 4.00202e17i | 0.305565 | + | 0.529253i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.63034e17 | −0.824351 | ||||||||
\(245\) | −3.26531e17 | + | 1.06278e17i | −0.393713 | + | 0.128144i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.22601e17 | + | 5.58762e17i | −0.365964 | + | 0.633869i | ||||
\(248\) | 1.60369e17 | + | 2.77766e17i | 0.176495 | + | 0.305698i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.58322e17 | − | 4.47426e17i | 0.267677 | − | 0.463630i | ||||
\(251\) | −1.85024e18 | −1.86070 | −0.930350 | − | 0.366674i | \(-0.880497\pi\) | ||||
−0.930350 | + | 0.366674i | \(0.880497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.17918e17 | −0.585500 | ||||||||
\(254\) | −4.60578e17 | + | 7.97744e17i | −0.423692 | + | 0.733856i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.60288e16 | − | 6.24037e16i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.65713e17 | + | 8.06638e17i | −0.392301 | + | 0.679485i | −0.992753 | − | 0.120176i | \(-0.961654\pi\) |
0.600452 | + | 0.799661i | \(0.294988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.49538e17 | + | 6.78274e17i | 0.436767 | + | 0.539085i | ||||
\(260\) | 1.52173e17 | 0.117500 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.14029e17 | + | 1.58315e18i | 0.666347 | + | 1.15415i | ||||
\(263\) | −5.22388e17 | − | 9.04802e17i | −0.370105 | − | 0.641040i | 0.619477 | − | 0.785015i | \(-0.287345\pi\) |
−0.989581 | + | 0.143975i | \(0.954012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.35048e17 | 0.492008 | ||||||||
\(266\) | −1.38403e18 | + | 2.19566e17i | −0.900604 | + | 0.142874i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.28635e17 | + | 7.42418e17i | −0.263680 | + | 0.456707i | ||||
\(269\) | 1.33019e18 | + | 2.30396e18i | 0.795741 | + | 1.37826i | 0.922368 | + | 0.386313i | \(0.126252\pi\) |
−0.126627 | + | 0.991950i | \(0.540415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.29784e18 | + | 2.24793e18i | −0.734433 | + | 1.27208i | 0.220539 | + | 0.975378i | \(0.429218\pi\) |
−0.954972 | + | 0.296697i | \(0.904115\pi\) | |||||||
\(272\) | 4.79895e16 | 0.0264167 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.44974e18 | −0.755375 | ||||||||
\(275\) | −1.11570e18 | + | 1.93245e18i | −0.565657 | + | 0.979746i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.20822e17 | + | 1.42171e18i | 0.394140 | + | 0.682671i | 0.992991 | − | 0.118190i | \(-0.0377091\pi\) |
−0.598851 | + | 0.800861i | \(0.704376\pi\) | |||||||
\(278\) | 8.97787e17 | − | 1.55501e18i | 0.419602 | − | 0.726772i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.08061e17 | + | 2.56802e17i | 0.0921522 | + | 0.113740i | ||||
\(281\) | 1.24946e18 | 0.538797 | 0.269398 | − | 0.963029i | \(-0.413175\pi\) | ||||
0.269398 | + | 0.963029i | \(0.413175\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.65425e17 | − | 1.49896e18i | −0.353860 | − | 0.612903i | 0.633062 | − | 0.774101i | \(-0.281798\pi\) |
−0.986922 | + | 0.161198i | \(0.948464\pi\) | |||||||
\(284\) | 3.99065e17 | + | 6.91201e17i | 0.158912 | + | 0.275243i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.45046e18 | −0.547976 | ||||||||
\(287\) | −3.41202e16 | + | 8.89529e16i | −0.0125573 | + | 0.0327375i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41523e18 | − | 2.45125e18i | 0.494417 | − | 0.856356i | ||||
\(290\) | 4.91275e17 | + | 8.50913e17i | 0.167240 | + | 0.289668i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.76743e17 | + | 8.25744e17i | −0.154139 | + | 0.266977i | ||||
\(293\) | −2.19771e18 | −0.692568 | −0.346284 | − | 0.938130i | \(-0.612557\pi\) | ||||
−0.346284 | + | 0.938130i | \(0.612557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.64768e18 | −0.493409 | ||||||||
\(296\) | 4.20103e17 | − | 7.27640e17i | 0.122650 | − | 0.212436i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50191e17 | − | 6.06549e17i | −0.0972039 | − | 0.168362i | ||||
\(299\) | 4.49572e17 | − | 7.78682e17i | 0.121693 | − | 0.210778i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.90756e18 | + | 4.97309e18i | −0.491166 | + | 1.28049i | ||||
\(302\) | 3.68848e18 | 0.926394 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.74385e17 | + | 1.16807e18i | 0.161197 | + | 0.279201i | ||||
\(305\) | −1.46354e18 | − | 2.53493e18i | −0.341316 | − | 0.591176i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.50631e18 | 0.778596 | 0.389298 | − | 0.921112i | \(-0.372718\pi\) | ||||
0.389298 | + | 0.921112i | \(0.372718\pi\) | |||||||
\(308\) | −1.98318e18 | − | 2.44776e18i | −0.429765 | − | 0.530442i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.07976e17 | + | 1.22625e18i | −0.146152 | + | 0.253143i | ||||
\(311\) | 5.52066e17 | + | 9.56206e17i | 0.111247 | + | 0.192685i | 0.916273 | − | 0.400554i | \(-0.131182\pi\) |
−0.805026 | + | 0.593239i | \(0.797849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.42097e18 | + | 4.19325e18i | −0.464951 | + | 0.805319i | −0.999199 | − | 0.0400086i | \(-0.987261\pi\) |
0.534248 | + | 0.845328i | \(0.320595\pi\) | |||||||
\(314\) | −9.42618e17 | −0.176752 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.67532e18 | 0.478324 | ||||||||
\(317\) | −3.78325e18 | + | 6.55279e18i | −0.660573 | + | 1.14415i | 0.319892 | + | 0.947454i | \(0.396353\pi\) |
−0.980465 | + | 0.196693i | \(0.936980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.68268e18 | − | 8.11064e18i | −0.779946 | − | 1.35091i | ||||
\(320\) | 1.59056e17 | − | 2.75492e17i | 0.0258776 | − | 0.0448213i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.92877e18 | − | 3.05984e17i | 0.299475 | − | 0.0475094i | ||||
\(323\) | −8.98265e17 | −0.136265 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.62348e18 | − | 2.81195e18i | −0.235137 | − | 0.407270i | ||||
\(326\) | 4.58224e18 | + | 7.93667e18i | 0.648553 | + | 1.12333i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.16982e16 | 0.0123967 | ||||||||
\(329\) | 3.30701e18 | + | 4.08171e18i | 0.436984 | + | 0.539353i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.69106e17 | − | 1.15893e18i | 0.0844860 | − | 0.146334i | −0.820686 | − | 0.571379i | \(-0.806409\pi\) |
0.905172 | + | 0.425045i | \(0.139742\pi\) | |||||||
\(332\) | −1.33122e18 | − | 2.30574e18i | −0.164329 | − | 0.284626i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.79111e18 | − | 1.00305e19i | 0.683382 | − | 1.18365i | ||||
\(335\) | −3.78457e18 | −0.436698 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.59109e18 | 0.506631 | 0.253315 | − | 0.967384i | \(-0.418479\pi\) | ||||
0.253315 | + | 0.967384i | \(0.418479\pi\) | |||||||
\(338\) | −2.22060e18 | + | 3.84619e18i | −0.239660 | + | 0.415103i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.05929e17 | + | 1.83475e17i | 0.0109376 | + | 0.0189445i | ||||
\(341\) | 6.74821e18 | − | 1.16882e19i | 0.681602 | − | 1.18057i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.21340e18 | + | 4.70322e18i | −0.890664 | + | 0.454662i | ||||
\(344\) | 5.12657e18 | 0.484885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.07991e16 | + | 7.06662e16i | 0.00369471 | + | 0.00639942i | ||||
\(347\) | −1.36492e18 | − | 2.36411e18i | −0.120959 | − | 0.209506i | 0.799187 | − | 0.601082i | \(-0.205264\pi\) |
−0.920146 | + | 0.391576i | \(0.871930\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.58227e18 | 0.388947 | 0.194473 | − | 0.980908i | \(-0.437700\pi\) | ||||
0.194473 | + | 0.980908i | \(0.437700\pi\) | |||||||
\(350\) | 2.52563e18 | − | 6.58443e18i | 0.209826 | − | 0.547025i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.51607e18 | + | 2.62591e18i | −0.120684 | + | 0.209031i | ||||
\(353\) | −1.05464e19 | − | 1.82670e19i | −0.821856 | − | 1.42350i | −0.904299 | − | 0.426900i | \(-0.859606\pi\) |
0.0824430 | − | 0.996596i | \(-0.473728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.76175e18 | + | 3.05143e18i | −0.131592 | + | 0.227925i | ||||
\(356\) | 1.61335e18 | 0.117992 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.94066e18 | −0.486719 | ||||||||
\(359\) | 5.56822e18 | − | 9.64444e18i | 0.382391 | − | 0.662321i | −0.609012 | − | 0.793161i | \(-0.708434\pi\) |
0.991404 | + | 0.130840i | \(0.0417674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.03255e18 | − | 8.71664e18i | −0.331501 | − | 0.574176i | ||||
\(362\) | −9.50771e18 | + | 1.64678e19i | −0.613425 | + | 1.06248i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.52747e18 | − | 7.18248e17i | 0.280282 | − | 0.0444645i | ||||
\(365\) | −4.20934e18 | −0.255280 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.78163e18 | − | 6.54998e18i | −0.220132 | − | 0.381280i | 0.734716 | − | 0.678375i | \(-0.237316\pi\) |
−0.954848 | + | 0.297095i | \(0.903982\pi\) | |||||||
\(368\) | −9.39813e17 | − | 1.62780e18i | −0.0536022 | − | 0.0928418i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.70924e18 | 0.203129 | ||||||||
\(371\) | 2.18693e19 | − | 3.46939e18i | 1.17363 | − | 0.186187i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.71030e19 | − | 2.96233e19i | 0.881569 | − | 1.52692i | 0.0319720 | − | 0.999489i | \(-0.489821\pi\) |
0.849597 | − | 0.527433i | \(-0.176845\pi\) | |||||||
\(374\) | −1.00968e18 | − | 1.74882e18i | −0.0510092 | − | 0.0883505i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.52809e18 | − | 4.37878e18i | 0.122711 | − | 0.212542i | ||||
\(377\) | 1.36277e19 | 0.648430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.47705e19 | 1.13277 | 0.566383 | − | 0.824142i | \(-0.308342\pi\) | ||||
0.566383 | + | 0.824142i | \(0.308342\pi\) | |||||||
\(380\) | −2.97720e18 | + | 5.15665e18i | −0.133484 | + | 0.231202i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.20219e19 | + | 2.08225e19i | 0.518201 | + | 0.897550i | ||||
\(383\) | 1.79587e19 | − | 3.11053e19i | 0.759073 | − | 1.31475i | −0.184251 | − | 0.982879i | \(-0.558986\pi\) |
0.943324 | − | 0.331874i | \(-0.107681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.98079e18 | − | 1.29852e19i | 0.202462 | − | 0.527827i | ||||
\(386\) | 1.84485e19 | 0.735454 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.50414e18 | + | 9.53345e18i | 0.211082 | + | 0.365605i | ||||
\(389\) | −1.43129e19 | − | 2.47907e19i | −0.538402 | − | 0.932539i | −0.998990 | − | 0.0449254i | \(-0.985695\pi\) |
0.460589 | − | 0.887614i | \(-0.347638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25181e18 | 0.0453119 | ||||||||
\(392\) | 7.40236e18 | + | 6.65838e18i | 0.262860 | + | 0.236441i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.66783e18 | − | 9.81697e18i | 0.193729 | − | 0.335549i | ||||
\(395\) | 5.90534e18 | + | 1.02283e19i | 0.198046 | + | 0.343026i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.58957e19 | − | 2.75322e19i | 0.513277 | − | 0.889023i | −0.486604 | − | 0.873623i | \(-0.661765\pi\) |
0.999881 | − | 0.0154000i | \(-0.00490216\pi\) | |||||||
\(398\) | 1.18050e19 | 0.374060 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.78764e18 | −0.207142 | ||||||||
\(401\) | −7.62440e18 | + | 1.32058e19i | −0.228361 | + | 0.395534i | −0.957323 | − | 0.289021i | \(-0.906670\pi\) |
0.728961 | + | 0.684555i | \(0.240003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.81945e18 | + | 1.70078e19i | 0.283334 | + | 0.490749i | ||||
\(404\) | −6.00447e18 | + | 1.04000e19i | −0.170065 | + | 0.294561i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.86328e19 | + | 2.29977e19i | 0.508548 | + | 0.627682i | ||||
\(407\) | −3.53554e19 | −0.947321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.56830e19 | − | 2.71637e19i | −0.405046 | − | 0.701560i | 0.589281 | − | 0.807928i | \(-0.299411\pi\) |
−0.994327 | + | 0.106368i | \(0.966078\pi\) | |||||||
\(410\) | 2.02409e17 | + | 3.50583e17i | 0.00513276 | + | 0.00889021i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.80092e19 | −0.440317 | ||||||||
\(413\) | −4.90220e19 | + | 7.77696e18i | −1.17697 | + | 0.186717i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.87690e18 | − | 1.01791e19i | 0.136078 | − | 0.235694i | ||||
\(416\) | −2.20606e18 | − | 3.82101e18i | −0.0501669 | − | 0.0868917i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.83777e19 | − | 4.91517e19i | 0.622523 | − | 1.07824i | ||||
\(419\) | −2.28320e18 | −0.0491970 | −0.0245985 | − | 0.999697i | \(-0.507831\pi\) | ||||
−0.0245985 | + | 0.999697i | \(0.507831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.61315e19 | −0.959140 | −0.479570 | − | 0.877504i | \(-0.659207\pi\) | ||||
−0.479570 | + | 0.877504i | \(0.659207\pi\) | |||||||
\(422\) | 3.23720e19 | − | 5.60700e19i | 0.661191 | − | 1.14522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.06561e19 | − | 1.84568e19i | −0.210065 | − | 0.363842i | ||||
\(425\) | 2.26024e18 | − | 3.91486e18i | 0.0437762 | − | 0.0758226i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.55083e19 | − | 6.85118e19i | −1.03788 | − | 1.28102i | ||||
\(428\) | 5.13658e19 | 0.943726 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.13161e19 | + | 1.96000e19i | 0.200763 | + | 0.347731i | ||||
\(431\) | −2.85381e19 | − | 4.94295e19i | −0.497560 | − | 0.861800i | 0.502436 | − | 0.864615i | \(-0.332437\pi\) |
−0.999996 | + | 0.00281486i | \(0.999104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.74941e19 | −1.64180 | −0.820898 | − | 0.571075i | \(-0.806526\pi\) | ||||
−0.820898 | + | 0.571075i | \(0.806526\pi\) | |||||||
\(434\) | −1.52760e19 | + | 3.98252e19i | −0.252834 | + | 0.659151i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.11689e19 | − | 1.93451e19i | 0.178591 | − | 0.309329i | ||||
\(437\) | 1.75914e19 | + | 3.04692e19i | 0.276496 | + | 0.478905i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.76963e19 | − | 4.79714e19i | 0.420667 | − | 0.728616i | −0.575338 | − | 0.817916i | \(-0.695130\pi\) |
0.996005 | + | 0.0892995i | \(0.0284628\pi\) | |||||||
\(440\) | −1.33859e19 | −0.199873 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.93842e18 | 0.0424079 | ||||||||
\(443\) | 5.80429e19 | − | 1.00533e20i | 0.823610 | − | 1.42653i | −0.0793678 | − | 0.996845i | \(-0.525290\pi\) |
0.902977 | − | 0.429688i | \(-0.141377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.56121e18 | + | 6.16819e18i | 0.0488537 | + | 0.0846170i | ||||
\(446\) | −2.07157e19 | + | 3.58806e19i | −0.279439 | + | 0.484003i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.43194e18 | − | 8.94723e18i | 0.0447667 | − | 0.116709i | ||||
\(449\) | −1.86141e19 | −0.238778 | −0.119389 | − | 0.992848i | \(-0.538094\pi\) | ||||
−0.119389 | + | 0.992848i | \(0.538094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.92930e18 | − | 3.34165e18i | −0.0239374 | − | 0.0414607i | ||||
\(452\) | 1.12276e19 | + | 1.94468e19i | 0.137009 | + | 0.237307i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.35220e18 | −0.110407 | ||||||||
\(455\) | 1.27397e19 | + | 1.57241e19i | 0.147936 | + | 0.182592i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.24394e19 | + | 3.88662e19i | −0.252139 | + | 0.436717i | −0.964114 | − | 0.265487i | \(-0.914467\pi\) |
0.711976 | + | 0.702204i | \(0.247801\pi\) | |||||||
\(458\) | 4.53864e19 | + | 7.86115e19i | 0.501689 | + | 0.868951i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.14897e18 | − | 7.18623e18i | 0.0443871 | − | 0.0768808i | ||||
\(461\) | −7.40406e19 | −0.779315 | −0.389657 | − | 0.920960i | \(-0.627407\pi\) | ||||
−0.389657 | + | 0.920960i | \(0.627407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.23960e20 | 1.26306 | 0.631528 | − | 0.775353i | \(-0.282428\pi\) | ||||
0.631528 | + | 0.775353i | \(0.282428\pi\) | |||||||
\(464\) | 1.42441e19 | − | 2.46715e19i | 0.142807 | − | 0.247349i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.81046e19 | − | 8.33196e19i | −0.466973 | − | 0.808821i | ||||
\(467\) | −9.76171e19 | + | 1.69078e20i | −0.932501 | + | 1.61514i | −0.153471 | + | 0.988153i | \(0.549045\pi\) |
−0.779030 | + | 0.626987i | \(0.784288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.12599e20 | + | 1.78630e19i | −1.04169 | + | 0.165256i | ||||
\(470\) | 2.23214e19 | 0.203230 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.38865e19 | + | 4.13727e19i | 0.210663 | + | 0.364879i | ||||
\(473\) | −1.07862e20 | − | 1.86822e20i | −0.936285 | − | 1.62169i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.27051e20 | 1.06850 | ||||||||
\(476\) | 4.01761e18 | + | 4.95879e18i | 0.0332595 | + | 0.0410510i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.65523e19 | + | 4.59900e19i | −0.213007 | + | 0.368939i | ||||
\(479\) | −5.76848e19 | − | 9.99130e19i | −0.455559 | − | 0.789052i | 0.543161 | − | 0.839629i | \(-0.317227\pi\) |
−0.998720 | + | 0.0505766i | \(0.983894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.57231e19 | − | 4.45538e19i | 0.196895 | − | 0.341033i | ||||
\(482\) | 9.56387e19 | 0.720744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.91505e19 | 0.432134 | ||||||||
\(485\) | −2.42990e19 | + | 4.20871e19i | −0.174794 | + | 0.302752i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.32998e18 | − | 1.44279e19i | −0.0581001 | − | 0.100632i | 0.835512 | − | 0.549472i | \(-0.185171\pi\) |
−0.893613 | + | 0.448839i | \(0.851838\pi\) | |||||||
\(488\) | −4.24342e19 | + | 7.34982e19i | −0.291452 | + | 0.504810i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.11696e18 | + | 4.29982e19i | −0.0607267 | + | 0.286405i | ||||
\(491\) | 1.91764e19 | 0.125793 | 0.0628963 | − | 0.998020i | \(-0.479966\pi\) | ||||
0.0628963 | + | 0.998020i | \(0.479966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.48640e18 | + | 1.64309e19i | 0.0603600 | + | 0.104547i | ||||
\(494\) | 4.12930e19 | + | 7.15215e19i | 0.258776 | + | 0.448213i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.10543e19 | 0.249601 | ||||||||
\(497\) | −3.80132e19 | + | 9.91021e19i | −0.227646 | + | 0.593485i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.96084e18 | − | 1.37886e19i | 0.0462599 | − | 0.0801246i | −0.841968 | − | 0.539527i | \(-0.818603\pi\) |
0.888228 | + | 0.459402i | \(0.151936\pi\) | |||||||
\(500\) | −3.30652e19 | − | 5.72705e19i | −0.189276 | − | 0.327836i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.18416e20 | + | 2.05102e20i | −0.657857 | + | 1.13944i | ||||
\(503\) | −2.23533e20 | −1.22344 | −0.611718 | − | 0.791076i | \(-0.709521\pi\) | ||||
−0.611718 | + | 0.791076i | \(0.709521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30156e19 | −0.281656 | ||||||||
\(506\) | −3.95468e19 | + | 6.84970e19i | −0.207006 | + | 0.358544i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.89539e19 | + | 1.02111e20i | 0.299595 | + | 0.518914i | ||||
\(509\) | 1.34304e20 | − | 2.32621e20i | 0.672521 | − | 1.16484i | −0.304666 | − | 0.952459i | \(-0.598545\pi\) |
0.977187 | − | 0.212381i | \(-0.0681217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.25237e20 | + | 1.98679e19i | −0.608942 | + | 0.0966038i | ||||
\(512\) | −9.22337e18 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.96112e19 | + | 1.03250e20i | 0.277399 | + | 0.480469i | ||||
\(515\) | −3.97524e19 | − | 6.88532e19i | −0.182309 | − | 0.315769i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.12761e20 | −0.947792 | ||||||||
\(518\) | 1.10358e20 | − | 1.75074e19i | 0.484541 | − | 0.0768687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.73905e18 | − | 1.68685e19i | 0.0415424 | − | 0.0719536i | ||||
\(521\) | 9.34825e19 | + | 1.61916e20i | 0.393050 | + | 0.680782i | 0.992850 | − | 0.119368i | \(-0.0380867\pi\) |
−0.599801 | + | 0.800150i | \(0.704753\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.72709e18 | + | 1.51158e19i | −0.0356539 | + | 0.0617543i | −0.883302 | − | 0.468805i | \(-0.844685\pi\) |
0.847648 | + | 0.530559i | \(0.178018\pi\) | |||||||
\(524\) | 2.33992e20 | 0.942357 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.33731e20 | −0.523407 | ||||||||
\(527\) | −1.36708e19 | + | 2.36786e19i | −0.0527492 | + | 0.0913643i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.08803e20 | + | 1.88452e20i | 0.408058 | + | 0.706777i | ||||
\(530\) | 4.70431e19 | − | 8.14810e19i | 0.173951 | − | 0.301292i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.42389e19 | + | 1.67474e20i | −0.230920 | + | 0.602019i | ||||
\(533\) | 5.61473e18 | 0.0199010 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.13382e20 | + | 1.96383e20i | 0.390742 | + | 0.676785i | ||||
\(536\) | 5.48653e19 | + | 9.50295e19i | 0.186450 | + | 0.322941i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.40529e20 | 1.12535 | ||||||||
\(539\) | 8.69001e19 | − | 4.09846e20i | 0.283207 | − | 1.33569i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.34892e20 | − | 2.33640e20i | 0.427570 | − | 0.740573i | −0.569087 | − | 0.822278i | \(-0.692703\pi\) |
0.996657 | + | 0.0817047i | \(0.0260364\pi\) | |||||||
\(542\) | 1.66124e20 | + | 2.87735e20i | 0.519323 | + | 0.899493i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.07133e18 | − | 5.31969e18i | 0.00933973 | − | 0.0161769i | ||||
\(545\) | 9.86140e19 | 0.295777 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.48513e20 | −0.725177 | −0.362588 | − | 0.931949i | \(-0.618107\pi\) | ||||
−0.362588 | + | 0.931949i | \(0.618107\pi\) | |||||||
\(548\) | −9.27837e19 | + | 1.60706e20i | −0.267065 | + | 0.462571i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.42810e20 | + | 2.47354e20i | 0.399980 | + | 0.692785i | ||||
\(551\) | −2.66621e20 | + | 4.61800e20i | −0.736642 | + | 1.27590i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.23974e20 | + | 2.76443e20i | 0.602225 | + | 0.743304i | ||||
\(554\) | 2.10130e20 | 0.557398 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.14917e20 | − | 1.99042e20i | −0.296703 | − | 0.513905i | ||||
\(557\) | 2.06737e20 | + | 3.58079e20i | 0.526628 | + | 0.912146i | 0.999519 | + | 0.0310252i | \(0.00987722\pi\) |
−0.472891 | + | 0.881121i | \(0.656789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.13903e20 | 0.778407 | ||||||||
\(560\) | 4.17827e19 | − | 6.62850e18i | 0.102232 | − | 0.0162183i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.99654e19 | − | 1.38504e20i | 0.190493 | − | 0.329944i | ||||
\(563\) | −2.02086e20 | − | 3.50024e20i | −0.475033 | − | 0.822782i | 0.524558 | − | 0.851375i | \(-0.324231\pi\) |
−0.999591 | + | 0.0285928i | \(0.990897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.95663e19 | + | 8.58514e19i | −0.113455 | + | 0.196510i | ||||
\(566\) | −2.21549e20 | −0.500433 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.02161e20 | 0.224735 | ||||||||
\(569\) | 2.21048e19 | − | 3.82867e19i | 0.0479894 | − | 0.0831200i | −0.841033 | − | 0.540984i | \(-0.818052\pi\) |
0.889022 | + | 0.457864i | \(0.151385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.47868e20 | − | 2.56116e20i | −0.312683 | − | 0.541583i | 0.666259 | − | 0.745720i | \(-0.267894\pi\) |
−0.978942 | + | 0.204137i | \(0.934561\pi\) | |||||||
\(572\) | −9.28297e19 | + | 1.60786e20i | −0.193739 | + | 0.335566i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.67685e18 | + | 9.47525e18i | 0.0156079 | + | 0.0192642i | ||||
\(575\) | −1.77056e20 | −0.355305 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.74354e19 | + | 1.34122e20i | 0.151398 | + | 0.262230i | 0.931742 | − | 0.363122i | \(-0.118289\pi\) |
−0.780343 | + | 0.625351i | \(0.784956\pi\) | |||||||
\(578\) | −1.81150e20 | − | 3.13760e20i | −0.349606 | − | 0.605535i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.25766e20 | 0.236513 | ||||||||
\(581\) | 1.26806e20 | − | 3.30589e20i | 0.235406 | − | 0.613716i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.48400e20 | + | 7.76652e20i | −0.811245 | + | 1.40512i | ||||
\(584\) | 6.10231e19 | + | 1.05695e20i | 0.108993 | + | 0.188781i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40653e20 | + | 2.43619e20i | −0.244860 | + | 0.424110i | ||||
\(587\) | −2.59838e20 | −0.446599 | −0.223299 | − | 0.974750i | \(-0.571683\pi\) | ||||
−0.223299 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.68453e20 | −1.28752 | ||||||||
\(590\) | −1.05451e20 | + | 1.82647e20i | −0.174447 | + | 0.302150i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.37732e19 | − | 9.31379e19i | −0.0867267 | − | 0.150215i | ||||
\(593\) | −8.67311e19 | + | 1.50223e20i | −0.138123 | + | 0.239235i | −0.926786 | − | 0.375590i | \(-0.877440\pi\) |
0.788663 | + | 0.614825i | \(0.210773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00903e19 | + | 2.63060e19i | −0.0156685 | + | 0.0408486i | ||||
\(596\) | −8.96490e19 | −0.137467 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.75452e19 | − | 9.96713e19i | −0.0860499 | − | 0.149043i | ||||
\(599\) | 1.33101e20 | + | 2.30537e20i | 0.196553 | + | 0.340439i | 0.947408 | − | 0.320027i | \(-0.103692\pi\) |
−0.750856 | + | 0.660466i | \(0.770359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.46615e20 | 0.211165 | 0.105582 | − | 0.994411i | \(-0.466329\pi\) | ||||
0.105582 | + | 0.994411i | \(0.466329\pi\) | |||||||
\(602\) | 4.29190e20 | + | 5.29733e20i | 0.610486 | + | 0.753500i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.36063e20 | − | 4.08873e20i | 0.327530 | − | 0.567298i | ||||
\(605\) | 1.30565e20 | + | 2.26146e20i | 0.178921 | + | 0.309901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.88783e20 | + | 6.73392e20i | −0.519747 | + | 0.900229i | 0.479989 | + | 0.877274i | \(0.340641\pi\) |
−0.999737 | + | 0.0229544i | \(0.992693\pi\) | |||||||
\(608\) | 1.72643e20 | 0.227967 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.74667e20 | −0.482694 | ||||||||
\(611\) | 1.54796e20 | − | 2.68115e20i | 0.196993 | − | 0.341203i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.58828e20 | − | 2.75099e20i | −0.197231 | − | 0.341614i | 0.750399 | − | 0.660985i | \(-0.229861\pi\) |
−0.947629 | + | 0.319372i | \(0.896528\pi\) | |||||||
\(614\) | 2.24404e20 | − | 3.88679e20i | 0.275275 | − | 0.476791i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.98260e20 | + | 6.31809e19i | −0.476773 | + | 0.0756363i | ||||
\(617\) | 5.23730e20 | 0.619396 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.24614e20 | − | 2.15838e20i | −0.143842 | − | 0.249142i | 0.785098 | − | 0.619372i | \(-0.212613\pi\) |
−0.928940 | + | 0.370229i | \(0.879279\pi\) | |||||||
\(620\) | 9.06209e19 | + | 1.56960e20i | 0.103345 | + | 0.178999i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.41329e20 | 0.157327 | ||||||||
\(623\) | 1.35067e20 | + | 1.66708e20i | 0.148556 | + | 0.183357i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.39861e20 | + | 4.15451e20i | −0.257548 | + | 0.446087i | ||||
\(626\) | 3.09885e20 | + | 5.36736e20i | 0.328770 | + | 0.569447i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.03276e19 | + | 1.04490e20i | −0.0624912 | + | 0.108238i | ||||
\(629\) | 7.16246e19 | 0.0733132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.47167e21 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(632\) | 1.71220e20 | − | 2.96562e20i | 0.169113 | − | 0.292913i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.84257e20 | + | 8.38757e20i | 0.467096 | + | 0.809034i | ||||
\(635\) | −2.60263e20 | + | 4.50788e20i | −0.248090 | + | 0.429704i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.53251e20 | + | 4.07696e20i | 0.421981 | + | 0.379569i | ||||
\(638\) | −1.19877e21 | −1.10301 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.03591e19 | − | 3.52630e19i | −0.0182982 | − | 0.0316935i | ||||
\(641\) | −7.33100e20 | − | 1.26977e21i | −0.651221 | − | 1.12795i | −0.982827 | − | 0.184529i | \(-0.940924\pi\) |
0.331606 | − | 0.943418i | \(-0.392409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.96832e20 | 0.865047 | 0.432523 | − | 0.901623i | \(-0.357623\pi\) | ||||
0.432523 | + | 0.901623i | \(0.357623\pi\) | |||||||
\(644\) | 8.95224e19 | − | 2.33389e20i | 0.0767870 | − | 0.200187i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.74890e19 | + | 9.95738e19i | −0.0481771 | + | 0.0834452i | ||||
\(647\) | 1.86678e20 | + | 3.23336e20i | 0.154636 | + | 0.267838i | 0.932927 | − | 0.360067i | \(-0.117246\pi\) |
−0.778290 | + | 0.627905i | \(0.783913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.00513e21 | − | 1.74094e21i | 0.813556 | − | 1.40912i | ||||
\(650\) | −4.15611e20 | −0.332534 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.17305e21 | 0.917193 | ||||||||
\(653\) | −8.78143e20 | + | 1.52099e21i | −0.678760 | + | 1.17565i | 0.296594 | + | 0.955004i | \(0.404149\pi\) |
−0.975354 | + | 0.220644i | \(0.929184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.16499e20 | + | 8.94602e20i | 0.390175 | + | 0.675803i | ||||
\(656\) | 5.86869e18 | − | 1.01649e19i | 0.00438291 | − | 0.00759142i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.64111e20 | − | 1.05356e20i | 0.484782 | − | 0.0769069i | ||||
\(659\) | −1.29884e21 | −0.937379 | −0.468690 | − | 0.883363i | \(-0.655274\pi\) | ||||
−0.468690 | + | 0.883363i | \(0.655274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.44597e20 | − | 1.63609e21i | −0.666401 | − | 1.15424i | −0.978904 | − | 0.204323i | \(-0.934501\pi\) |
0.312503 | − | 0.949917i | \(-0.398833\pi\) | |||||||
\(662\) | −8.56455e19 | − | 1.48342e20i | −0.0597406 | − | 0.103474i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.40792e20 | −0.232396 | ||||||||
\(665\) | −7.82087e20 | + | 1.24072e20i | −0.527343 | + | 0.0836588i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.71558e20 | − | 6.43558e20i | 0.244953 | − | 0.424271i | ||||
\(668\) | −7.41262e20 | − | 1.28390e21i | −0.483224 | − | 0.836969i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.42213e20 | + | 4.19525e20i | −0.154396 | + | 0.267422i | ||||
\(671\) | 3.57121e21 | 2.25111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00920e21 | 1.23854 | 0.619270 | − | 0.785178i | \(-0.287429\pi\) | ||||
0.619270 | + | 0.785178i | \(0.287429\pi\) | |||||||
\(674\) | 2.93830e20 | − | 5.08928e20i | 0.179121 | − | 0.310247i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.84237e20 | + | 4.92312e20i | 0.169465 | + | 0.293522i | ||||
\(677\) | −1.16940e21 | + | 2.02545e21i | −0.689520 | + | 1.19428i | 0.282474 | + | 0.959275i | \(0.408845\pi\) |
−0.971993 | + | 0.235008i | \(0.924488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.24300e20 | + | 1.36687e21i | −0.302382 | + | 0.788325i | ||||
\(680\) | 2.71178e19 | 0.0154681 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.63771e20 | − | 1.49609e21i | −0.481965 | − | 0.834788i | ||||
\(683\) | −1.75583e21 | − | 3.04119e21i | −0.969010 | − | 1.67837i | −0.698433 | − | 0.715675i | \(-0.746119\pi\) |
−0.270577 | − | 0.962698i | \(-0.587214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.19220e20 | −0.442305 | ||||||||
\(686\) | −6.83000e19 | + | 1.32232e21i | −0.0364745 | + | 0.706165i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.28101e20 | − | 5.68287e20i | 0.171433 | − | 0.296930i | ||||
\(689\) | −6.52476e20 | − | 1.13012e21i | −0.337225 | − | 0.584092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.04240e21 | − | 1.80548e21i | 0.527167 | − | 0.913079i | −0.472332 | − | 0.881421i | \(-0.656588\pi\) |
0.999499 | − | 0.0316586i | \(-0.0100789\pi\) | |||||||
\(692\) | 1.04446e19 | 0.00522511 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.49420e20 | −0.171061 | ||||||||
\(695\) | 5.07321e20 | − | 8.78705e20i | 0.245695 | − | 0.425556i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.90847e18 | + | 6.76968e18i | 0.00185251 | + | 0.00320865i | ||||
\(698\) | 2.93265e20 | − | 5.07951e20i | 0.137513 | − | 0.238180i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.68252e20 | − | 7.01372e20i | −0.260799 | − | 0.321894i | ||||
\(701\) | 3.59508e21 | 1.63239 | 0.816194 | − | 0.577778i | \(-0.196080\pi\) | ||||
0.816194 | + | 0.577778i | \(0.196080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00652e21 | + | 1.74335e21i | 0.447362 | + | 0.774854i | ||||
\(704\) | 1.94057e20 | + | 3.36116e20i | 0.0853364 | + | 0.147807i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.69989e21 | −1.16228 | ||||||||
\(707\) | −1.57733e21 | + | 2.50231e20i | −0.671857 | + | 0.106585i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.12666e20 | − | 5.41553e20i | 0.130387 | − | 0.225836i | −0.793439 | − | 0.608650i | \(-0.791711\pi\) |
0.923826 | + | 0.382813i | \(0.125045\pi\) | |||||||
\(710\) | 2.25503e20 | + | 3.90583e20i | 0.0930498 | + | 0.161167i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.03254e20 | − | 1.78842e20i | 0.0417165 | − | 0.0722551i | ||||
\(713\) | 1.07090e21 | 0.428134 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.19627e20 | −0.320864 | ||||||||
\(716\) | −4.44202e20 | + | 7.69381e20i | −0.172081 | + | 0.298053i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.12732e20 | − | 1.23449e21i | −0.270391 | − | 0.468332i | ||||
\(719\) | 1.24093e20 | − | 2.14936e20i | 0.0465889 | − | 0.0806943i | −0.841791 | − | 0.539804i | \(-0.818498\pi\) |
0.888379 | + | 0.459110i | \(0.151832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.50770e21 | − | 1.86090e21i | −0.554372 | − | 0.684241i | ||||
\(722\) | −1.28833e21 | −0.468813 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.21699e21 | + | 2.10788e21i | 0.433757 | + | 0.751289i | ||||
\(725\) | −1.34176e21 | − | 2.32399e21i | −0.473303 | − | 0.819785i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.16365e20 | 0.212976 | 0.106488 | − | 0.994314i | \(-0.466039\pi\) | ||||
0.106488 | + | 0.994314i | \(0.466039\pi\) | |||||||
\(728\) | 2.10139e20 | − | 5.47844e20i | 0.0718658 | − | 0.187358i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.69398e20 | + | 4.66610e20i | −0.0902552 | + | 0.156327i | ||||
\(731\) | 2.18511e20 | + | 3.78472e20i | 0.0724591 | + | 0.125503i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.55870e20 | + | 2.69976e20i | −0.0506389 | + | 0.0877091i | −0.890234 | − | 0.455504i | \(-0.849459\pi\) |
0.839595 | + | 0.543213i | \(0.182792\pi\) | |||||||
\(734\) | −9.68098e20 | −0.311314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.40592e20 | −0.0758050 | ||||||||
\(737\) | 2.30870e21 | − | 3.99878e21i | 0.720047 | − | 1.24716i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.06784e21 | − | 3.58160e21i | −0.631950 | − | 1.09457i | −0.987153 | − | 0.159781i | \(-0.948921\pi\) |
0.355202 | − | 0.934789i | \(-0.384412\pi\) | |||||||
\(740\) | 2.37391e20 | − | 4.11174e20i | 0.0718170 | − | 0.124391i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.01505e21 | − | 2.64628e21i | 0.300924 | − | 0.784524i | ||||
\(743\) | −3.96804e21 | −1.16456 | −0.582278 | − | 0.812990i | \(-0.697838\pi\) | ||||
−0.582278 | + | 0.812990i | \(0.697838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.97886e20 | − | 3.42748e20i | −0.0569171 | − | 0.0985833i | ||||
\(746\) | −2.18918e21 | − | 3.79178e21i | −0.623363 | − | 1.07970i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.58479e20 | −0.0721379 | ||||||||
\(749\) | 4.30027e21 | + | 5.30767e21i | 1.18818 | + | 1.46653i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.09838e21 | − | 1.90245e21i | 0.297476 | − | 0.515244i | −0.678082 | − | 0.734987i | \(-0.737188\pi\) |
0.975558 | + | 0.219743i | \(0.0705217\pi\) | |||||||
\(752\) | −3.23596e20 | − | 5.60484e20i | −0.0867699 | − | 0.150290i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.72174e20 | − | 1.51065e21i | 0.229255 | − | 0.397080i | ||||
\(755\) | 2.08428e21 | 0.542444 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22748e21 | 0.313181 | 0.156590 | − | 0.987664i | \(-0.449950\pi\) | ||||
0.156590 | + | 0.987664i | \(0.449950\pi\) | |||||||
\(758\) | 1.58531e21 | − | 2.74584e21i | 0.400494 | − | 0.693675i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.81081e20 | + | 6.60052e20i | 0.0943877 | + | 0.163484i | ||||
\(761\) | −1.12372e21 | + | 1.94634e21i | −0.275597 | + | 0.477347i | −0.970285 | − | 0.241963i | \(-0.922209\pi\) |
0.694689 | + | 0.719310i | \(0.255542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.93398e21 | − | 4.65453e20i | 0.705543 | − | 0.111929i | ||||
\(764\) | 3.07761e21 | 0.732846 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.29871e21 | − | 3.98148e21i | −0.536746 | − | 0.929671i | ||||
\(767\) | 1.46258e21 | + | 2.53327e21i | 0.338186 | + | 0.585756i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.98944e21 | 1.81163 | 0.905813 | − | 0.423677i | \(-0.139261\pi\) | ||||
0.905813 | + | 0.423677i | \(0.139261\pi\) | |||||||
\(770\) | −1.12065e21 | − | 1.38318e21i | −0.251646 | − | 0.310597i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.18070e21 | − | 2.04504e21i | 0.260022 | − | 0.450372i | ||||
\(773\) | −6.92027e19 | − | 1.19863e20i | −0.0150930 | − | 0.0261419i | 0.858380 | − | 0.513014i | \(-0.171471\pi\) |
−0.873473 | + | 0.486872i | \(0.838138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.93361e21 | − | 3.34911e21i | 0.413624 | − | 0.716417i | ||||
\(776\) | 1.40906e21 | 0.298515 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.66411e21 | −0.761415 | ||||||||
\(779\) | −1.09850e20 | + | 1.90265e20i | −0.0226083 | + | 0.0391588i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.14943e21 | − | 3.72292e21i | −0.433951 | − | 0.751625i | ||||
\(782\) | 8.01157e19 | − | 1.38765e20i | 0.0160202 | − | 0.0277477i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.21184e21 | − | 3.94425e20i | 0.237725 | − | 0.0773738i | ||||
\(785\) | −5.32654e20 | −0.103496 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.81188e20 | − | 8.33442e20i | −0.0917285 | − | 0.158878i | 0.816510 | − | 0.577331i | \(-0.195906\pi\) |
−0.908239 | + | 0.418453i | \(0.862573\pi\) | |||||||
\(788\) | −7.25482e20 | − | 1.25657e21i | −0.136987 | − | 0.237269i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.51177e21 | 0.280080 | ||||||||
\(791\) | −1.06949e21 | + | 2.78822e21i | −0.196270 | + | 0.511685i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.59827e21 | + | 4.50033e21i | −0.467881 | + | 0.810393i | ||||
\(794\) | −2.03466e21 | − | 3.52413e21i | −0.362942 | − | 0.628634i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.55518e20 | − | 1.30860e21i | 0.132250 | − | 0.229064i | ||||
\(797\) | 1.00646e22 | 1.74525 | 0.872626 | − | 0.488388i | \(-0.162415\pi\) | ||||
0.872626 | + | 0.488388i | \(0.162415\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.31022e20 | 0.0733497 | ||||||||
\(800\) | −4.34409e20 | + | 7.52419e20i | −0.0732359 | + | 0.126848i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.75923e20 | + | 1.69035e21i | 0.161476 | + | 0.279684i | ||||
\(803\) | 2.56782e21 | − | 4.44759e21i | 0.420918 | − | 0.729051i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.08991e21 | − | 1.72905e20i | 0.175356 | − | 0.0278188i | ||||
\(806\) | 2.51378e21 | 0.400695 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.68572e20 | + | 1.33121e21i | 0.120254 | + | 0.208286i | ||||
\(809\) | 3.61656e21 | + | 6.26406e21i | 0.560636 | + | 0.971051i | 0.997441 | + | 0.0714944i | \(0.0227768\pi\) |
−0.436805 | + | 0.899556i | \(0.643890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.62138e21 | 0.551084 | 0.275542 | − | 0.961289i | \(-0.411143\pi\) | ||||
0.275542 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(812\) | 3.74182e21 | − | 5.93611e20i | 0.564174 | − | 0.0895018i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.26274e21 | + | 3.91919e21i | −0.334929 | + | 0.580113i | ||||
\(815\) | 2.58933e21 | + | 4.48484e21i | 0.379756 | + | 0.657757i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.14137e21 | + | 1.06372e22i | −0.884301 | + | 1.53165i | ||||
\(818\) | −4.01485e21 | −0.572821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.18168e19 | 0.00725882 | ||||||||
\(821\) | 1.00290e21 | − | 1.73708e21i | 0.139214 | − | 0.241126i | −0.787985 | − | 0.615694i | \(-0.788876\pi\) |
0.927199 | + | 0.374568i | \(0.122209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.22285e21 | + | 5.58214e21i | 0.439280 | + | 0.760856i | 0.997634 | − | 0.0687472i | \(-0.0219002\pi\) |
−0.558354 | + | 0.829603i | \(0.688567\pi\) | |||||||
\(824\) | −1.15259e21 | + | 1.99634e21i | −0.155675 | + | 0.269638i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.27532e21 | + | 5.93188e21i | −0.301782 | + | 0.786759i | ||||
\(827\) | 5.67524e21 | 0.745921 | 0.372961 | − | 0.927847i | \(-0.378343\pi\) | ||||
0.372961 | + | 0.927847i | \(0.378343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.62506e21 | − | 9.74289e21i | −0.726053 | − | 1.25756i | −0.958539 | − | 0.284961i | \(-0.908019\pi\) |
0.232486 | − | 0.972600i | \(-0.425314\pi\) | |||||||
\(830\) | −7.52244e20 | − | 1.30292e21i | −0.0962216 | − | 0.166661i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.64752e20 | −0.0709468 | ||||||||
\(833\) | −1.76046e20 | + | 8.30286e20i | −0.0219174 | + | 0.103369i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.27244e21 | − | 5.66803e21i | 0.400150 | − | 0.693080i | ||||
\(836\) | −3.63235e21 | − | 6.29141e21i | −0.440190 | − | 0.762432i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.46125e20 | + | 2.53095e20i | −0.0173938 | + | 0.0301269i | ||||
\(839\) | −3.23304e20 | −0.0381413 | −0.0190707 | − | 0.999818i | \(-0.506071\pi\) | ||||
−0.0190707 | + | 0.999818i | \(0.506071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.63372e21 | 0.305211 | ||||||||
\(842\) | −2.95242e21 | + | 5.11374e21i | −0.339107 | + | 0.587351i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.14362e21 | − | 7.17696e21i | −0.467532 | − | 0.809790i | ||||
\(845\) | −1.25481e21 | + | 2.17340e21i | −0.140331 | + | 0.243061i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.95200e21 | + | 6.11206e21i | 0.544070 | + | 0.671525i | ||||
\(848\) | −2.72795e21 | −0.297076 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.89311e20 | − | 5.01102e20i | −0.0309545 | − | 0.0536147i | ||||
\(851\) | −1.40268e21 | − | 2.42951e21i | −0.148760 | − | 0.257660i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.31226e21 | −0.240946 | −0.120473 | − | 0.992717i | \(-0.538441\pi\) | ||||
−0.120473 | + | 0.992717i | \(0.538441\pi\) | |||||||
\(854\) | −1.11472e22 | + | 1.76841e21i | −1.15141 | + | 0.182662i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.28741e21 | − | 5.69396e21i | 0.333657 | − | 0.577912i | ||||
\(857\) | −6.20465e21 | − | 1.07468e22i | −0.624253 | − | 1.08124i | −0.988685 | − | 0.150008i | \(-0.952070\pi\) |
0.364431 | − | 0.931230i | \(-0.381263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.50563e21 | + | 1.30001e22i | −0.742059 | + | 1.28528i | 0.209497 | + | 0.977809i | \(0.432817\pi\) |
−0.951556 | + | 0.307475i | \(0.900516\pi\) | |||||||
\(860\) | 2.89692e21 | 0.283921 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.30576e21 | −0.703656 | ||||||||
\(863\) | −4.02642e21 | + | 6.97396e21i | −0.384448 | + | 0.665884i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) |
0.607244 | + | 0.794515i | \(0.292275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.30547e19 | + | 3.99320e19i | 0.00216341 | + | 0.00374714i | ||||
\(866\) | −6.23962e21 | + | 1.08073e22i | −0.580462 | + | 1.00539i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.43701e21 | + | 4.24218e21i | 0.314256 | + | 0.387874i | ||||
\(869\) | −1.44097e22 | −1.30619 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.35943e21 | + | 5.81871e21i | 0.299316 | + | 0.518430i | ||||
\(872\) | −1.42962e21 | − | 2.47617e21i | −0.126283 | − | 0.218729i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.50339e21 | 0.391025 | ||||||||
\(875\) | 3.14964e21 | − | 8.21126e21i | 0.271144 | − | 0.706886i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.39079e21 | + | 1.45333e22i | −0.710078 | + | 1.22989i | 0.254750 | + | 0.967007i | \(0.418007\pi\) |
−0.964828 | + | 0.262884i | \(0.915326\pi\) | |||||||
\(878\) | −3.54513e21 | − | 6.14034e21i | −0.297456 | − | 0.515209i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.56699e20 | + | 1.48385e21i | −0.0706656 | + | 0.122396i | ||||
\(881\) | −1.27876e22 | −1.04585 | −0.522923 | − | 0.852380i | \(-0.675159\pi\) | ||||
−0.522923 | + | 0.852380i | \(0.675159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.05362e22 | 0.847190 | 0.423595 | − | 0.905852i | \(-0.360768\pi\) | ||||
0.423595 | + | 0.905852i | \(0.360768\pi\) | |||||||
\(884\) | 1.88059e20 | − | 3.25728e20i | 0.0149935 | − | 0.0259694i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.42949e21 | − | 1.28683e22i | −0.582380 | − | 1.00871i | ||||
\(887\) | 1.46329e21 | − | 2.53449e21i | 0.113737 | − | 0.196999i | −0.803537 | − | 0.595255i | \(-0.797051\pi\) |
0.917274 | + | 0.398256i | \(0.130384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.61569e21 | + | 1.46404e22i | −0.429180 | + | 1.11889i | ||||
\(890\) | 9.11669e20 | 0.0690895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.65160e21 | + | 4.59271e21i | 0.197593 | + | 0.342242i | ||||
\(893\) | 6.05705e21 | + | 1.04911e22i | 0.447585 | + | 0.775240i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.92202e21 | −0.284995 | ||||||||
\(896\) | −7.72168e20 | − | 9.53058e20i | −0.0556419 | − | 0.0686767i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.19130e21 | + | 2.06340e21i | −0.0844208 | + | 0.146221i | ||||
\(899\) | 8.11549e21 | + | 1.40564e22i | 0.570318 | + | 0.987819i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.08391e20 | − | 1.57338e21i | 0.0627823 | − | 0.108742i | ||||
\(902\) | −4.93901e20 | −0.0338525 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.87427e21 | 0.193760 | ||||||||
\(905\) | −5.37261e21 | + | 9.30563e21i | −0.359187 | + | 0.622130i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.61058e21 | − | 1.14499e22i | −0.434695 | − | 0.752914i | 0.562575 | − | 0.826746i | \(-0.309811\pi\) |
−0.997271 | + | 0.0738316i | \(0.976477\pi\) | |||||||
\(908\) | −5.98541e20 | + | 1.03670e21i | −0.0390346 | + | 0.0676099i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.55838e21 | − | 4.05867e20i | 0.164117 | − | 0.0260359i | ||||
\(911\) | −3.71366e21 | −0.236273 | −0.118137 | − | 0.992997i | \(-0.537692\pi\) | ||||
−0.118137 | + | 0.992997i | \(0.537692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.17016e21 | + | 1.24191e22i | 0.448743 | + | 0.777246i | ||||
\(914\) | 2.87224e21 | + | 4.97487e21i | 0.178289 | + | 0.308806i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.16189e22 | 0.709495 | ||||||||
\(917\) | 1.95894e22 | + | 2.41785e22i | 1.18646 | + | 1.46440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.40486e20 | + | 1.45576e21i | −0.0500800 | + | 0.0867410i | −0.889979 | − | 0.456002i | \(-0.849281\pi\) |
0.839899 | + | 0.542743i | \(0.182614\pi\) | |||||||
\(920\) | −5.31069e20 | − | 9.19838e20i | −0.0313864 | − | 0.0543629i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.73860e21 | + | 8.20749e21i | −0.275529 | + | 0.477231i | ||||
\(923\) | 6.25535e21 | 0.360777 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01306e22 | −0.574873 | ||||||||
\(926\) | 7.93342e21 | − | 1.37411e22i | 0.446558 | − | 0.773461i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.82325e21 | − | 3.15795e21i | −0.100980 | − | 0.174902i | ||||
\(929\) | 4.28845e21 | − | 7.42781e21i | 0.235604 | − | 0.408078i | −0.723844 | − | 0.689963i | \(-0.757627\pi\) |
0.959448 | + | 0.281886i | \(0.0909599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.26832e22 | + | 7.38283e21i | −1.22626 | + | 0.399117i | ||||
\(932\) | −1.23148e22 | −0.660400 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.24950e22 | + | 2.16420e22i | 0.659378 | + | 1.14208i | ||||
\(935\) | −5.70551e20 | − | 9.88223e20i | −0.0298681 | − | 0.0517330i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.98160e21 | 0.205121 | 0.102561 | − | 0.994727i | \(-0.467296\pi\) | ||||
0.102561 | + | 0.994727i | \(0.467296\pi\) | |||||||
\(938\) | −5.22622e21 | + | 1.36250e22i | −0.267096 | + | 0.696331i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.42857e21 | − | 2.47436e21i | 0.0718527 | − | 0.124453i | ||||
\(941\) | 5.87738e21 | + | 1.01799e22i | 0.293266 | + | 0.507952i | 0.974580 | − | 0.224039i | \(-0.0719245\pi\) |
−0.681314 | + | 0.731991i | \(0.738591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.53085e20 | − | 2.65151e20i | 0.00751787 | − | 0.0130213i | ||||
\(944\) | 6.11495e21 | 0.297922 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.76125e22 | −1.32411 | ||||||||
\(947\) | 6.89281e21 | − | 1.19387e22i | 0.327922 | − | 0.567978i | −0.654177 | − | 0.756342i | \(-0.726985\pi\) |
0.982099 | + | 0.188363i | \(0.0603182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.73648e21 | + | 6.47177e21i | 0.174971 | + | 0.303058i | ||||
\(950\) | 8.13125e21 | − | 1.40837e22i | 0.377772 | − | 0.654321i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.06815e20 | − | 1.27995e20i | 0.0368975 | − | 0.00585350i | ||||
\(953\) | −2.93636e22 | −1.33233 | −0.666165 | − | 0.745804i | \(-0.732065\pi\) | ||||
−0.666165 | + | 0.745804i | \(0.732065\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.79332e21 | + | 1.17664e22i | 0.303429 | + | 0.525554i | ||||
\(956\) | 3.39870e21 | + | 5.88672e21i | 0.150619 | + | 0.260879i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.47673e22 | −0.644258 | ||||||||
\(959\) | −2.43736e22 | + | 3.86668e21i | −1.05507 | + | 0.167378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.74106e19 | − | 6.47971e19i | 0.00159430 | − | 0.00276141i | ||||
\(962\) | −3.29256e21 | − | 5.70288e21i | −0.139226 | − | 0.241147i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.12088e21 | − | 1.06017e22i | 0.254821 | − | 0.441364i | ||||
\(965\) | 1.04248e22 | 0.430640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.59444e21 | −0.0648498 | −0.0324249 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324249 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(968\) | 3.78563e21 | − | 6.55691e21i | 0.152782 | − | 0.264627i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.11027e21 | + | 5.38715e21i | 0.123598 | + | 0.214078i | ||||
\(971\) | −1.12632e22 | + | 1.95084e22i | −0.444136 | + | 0.769266i | −0.997992 | − | 0.0633464i | \(-0.979823\pi\) |
0.553855 | + | 0.832613i | \(0.313156\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09464e22 | − | 2.85379e22i | 0.425037 | − | 1.10809i | ||||
\(974\) | −2.13247e21 | −0.0821659 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.43158e21 | + | 9.40777e21i | 0.206088 | + | 0.356955i | ||||
\(977\) | −1.60354e22 | − | 2.77741e22i | −0.603769 | − | 1.04576i | −0.992245 | − | 0.124299i | \(-0.960332\pi\) |
0.388476 | − | 0.921459i | \(-0.373002\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.68975e21 | −0.322209 | ||||||||
\(980\) | 4.18292e21 | + | 3.76251e21i | 0.153916 | + | 0.138447i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.22729e21 | − | 2.12572e21i | 0.0444744 | − | 0.0770319i | ||||
\(983\) | 2.20571e22 | + | 3.82040e22i | 0.793226 | + | 1.37391i | 0.923960 | + | 0.382490i | \(0.124933\pi\) |
−0.130734 | + | 0.991418i | \(0.541733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20277e21 | − | 5.54736e21i | 0.113437 | − | 0.196478i | ||||
\(986\) | 2.42852e21 | 0.0853620 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.05710e22 | 0.365964 | ||||||||
\(989\) | 8.55853e21 | − | 1.48238e22i | 0.294054 | − | 0.509316i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.13751e21 | − | 1.06305e22i | −0.207702 | − | 0.359750i | 0.743289 | − | 0.668971i | \(-0.233265\pi\) |
−0.950990 | + | 0.309221i | \(0.899932\pi\) | |||||||
\(992\) | 2.62748e21 | − | 4.55093e21i | 0.0882473 | − | 0.152849i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.55275e21 | + | 1.05563e22i | 0.282949 | + | 0.349233i | ||||
\(995\) | 6.67074e21 | 0.219029 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.56992e21 | + | 9.64739e21i | 0.180151 | + | 0.312030i | 0.941932 | − | 0.335805i | \(-0.109008\pi\) |
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(998\) | −1.01899e21 | − | 1.76494e21i | −0.0327107 | − | 0.0566566i | ||||
\(999\) | 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 | 126.16.g.e.37.4 | 10 | ||
3.2 | odd | 2 | 14.16.c.a.9.4 | ✓ | 10 | ||
7.4 | even | 3 | inner | 126.16.g.e.109.4 | 10 | ||
21.2 | odd | 6 | 98.16.a.j.1.2 | 5 | |||
21.5 | even | 6 | 98.16.a.k.1.4 | 5 | |||
21.11 | odd | 6 | 14.16.c.a.11.4 | yes | 10 | ||
21.17 | even | 6 | 98.16.c.m.67.2 | 10 | |||
21.20 | even | 2 | 98.16.c.m.79.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.16.c.a.9.4 | ✓ | 10 | 3.2 | odd | 2 | ||
14.16.c.a.11.4 | yes | 10 | 21.11 | odd | 6 | ||
98.16.a.j.1.2 | 5 | 21.2 | odd | 6 | |||
98.16.a.k.1.4 | 5 | 21.5 | even | 6 | |||
98.16.c.m.67.2 | 10 | 21.17 | even | 6 | |||
98.16.c.m.79.2 | 10 | 21.20 | even | 2 | |||
126.16.g.e.37.4 | 10 | 1.1 | even | 1 | trivial | ||
126.16.g.e.109.4 | 10 | 7.4 | even | 3 | inner |