Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,18,Mod(37,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.37");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.d (of order \(2\), degree \(1\), 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: | \(131.919902888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 109505575668 x^{14} - 766539029536 x^{13} + \cdots + 23\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{120}\cdot 3^{20}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.15 | ||
Root | \(0.500000 + 83132.4i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.37 |
Dual form | 72.18.d.b.37.16 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 362.025 | − | 3.13586i | 0.999962 | − | 0.00866168i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 131052. | − | 2270.52i | 0.999850 | − | 0.0173227i | ||||
\(5\) | − | 665059.i | − | 0.761404i | −0.924698 | − | 0.380702i | \(-0.875682\pi\) | ||
0.924698 | − | 0.380702i | \(-0.124318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.57536e6 | −0.496672 | −0.248336 | − | 0.968674i | \(-0.579884\pi\) | ||||
−0.248336 | + | 0.968674i | \(0.579884\pi\) | |||||||
\(8\) | 4.74371e7 | − | 1.23295e6i | 0.999662 | − | 0.0259824i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.08553e6 | − | 2.40768e8i | −0.00659504 | − | 0.761375i | ||||
\(11\) | − | 1.97863e8i | − | 0.278308i | −0.990271 | − | 0.139154i | \(-0.955562\pi\) | ||
0.990271 | − | 0.139154i | \(-0.0444384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74981e9i | 1.61495i | 0.589905 | + | 0.807473i | \(0.299165\pi\) | ||||
−0.589905 | + | 0.807473i | \(0.700835\pi\) | |||||||
\(14\) | −2.74247e9 | + | 2.37553e7i | −0.496654 | + | 0.00430202i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.71696e10 | − | 5.95115e8i | 0.999400 | − | 0.0346402i | ||||
\(17\) | −3.37447e10 | −1.17325 | −0.586624 | − | 0.809859i | \(-0.699543\pi\) | ||||
−0.586624 | + | 0.809859i | \(0.699543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00829e11i | − | 1.36201i | −0.732278 | − | 0.681005i | \(-0.761543\pi\) | ||
0.732278 | − | 0.681005i | \(-0.238457\pi\) | |||||||
\(20\) | −1.51003e9 | − | 8.71575e10i | −0.0131896 | − | 0.761290i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.20471e8 | − | 7.16313e10i | −0.00241062 | − | 0.278298i | ||||
\(23\) | −3.16250e11 | −0.842062 | −0.421031 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421031 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.20636e11 | 0.420264 | ||||||||
\(26\) | 1.48948e10 | + | 1.71955e12i | 0.0139881 | + | 1.61489i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.92769e11 | + | 1.72000e10i | −0.496598 | + | 0.00860371i | ||||
\(29\) | − | 3.54291e12i | − | 1.31516i | −0.753386 | − | 0.657578i | \(-0.771581\pi\) | ||
0.753386 | − | 0.657578i | \(-0.228419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.76965e11 | 0.0583245 | 0.0291623 | − | 0.999575i | \(-0.490716\pi\) | ||||
0.0291623 | + | 0.999575i | \(0.490716\pi\) | |||||||
\(32\) | 6.21394e12 | − | 2.69288e11i | 0.999062 | − | 0.0432954i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.22164e13 | + | 1.05819e11i | −1.17320 | + | 0.0101623i | ||||
\(35\) | 5.03806e12i | 0.378168i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.12889e13i | − | 0.996412i | −0.867059 | − | 0.498206i | \(-0.833992\pi\) | ||
0.867059 | − | 0.498206i | \(-0.166008\pi\) | |||||||
\(38\) | −3.16187e11 | − | 3.65027e13i | −0.0117973 | − | 1.36196i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.19983e11 | − | 3.15485e13i | −0.0197831 | − | 0.761147i | ||||
\(41\) | −8.47798e13 | −1.65817 | −0.829086 | − | 0.559121i | \(-0.811139\pi\) | ||||
−0.829086 | + | 0.559121i | \(0.811139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.38239e14i | 1.80363i | 0.432122 | + | 0.901815i | \(0.357765\pi\) | ||||
−0.432122 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(44\) | −4.49252e11 | − | 2.59304e13i | −0.00482106 | − | 0.278267i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.14490e14 | + | 9.91717e11i | −0.842030 | + | 0.00729367i | ||||
\(47\) | −8.21469e13 | −0.503221 | −0.251611 | − | 0.967829i | \(-0.580960\pi\) | ||||
−0.251611 | + | 0.967829i | \(0.580960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.75244e14 | −0.753317 | ||||||||
\(50\) | 1.16078e14 | − | 1.00547e12i | 0.420248 | − | 0.00364019i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.07846e13 | + | 6.22474e14i | 0.0279752 | + | 1.61470i | ||||
\(53\) | − | 3.16386e14i | − | 0.698028i | −0.937118 | − | 0.349014i | \(-0.886517\pi\) | ||
0.937118 | − | 0.349014i | \(-0.113483\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31590e14 | −0.211905 | ||||||||
\(56\) | −3.59353e14 | + | 9.34003e12i | −0.496505 | + | 0.0129048i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.11101e13 | − | 1.28262e15i | −0.0113915 | − | 1.31511i | ||||
\(59\) | 3.29635e14i | 0.292275i | 0.989264 | + | 0.146138i | \(0.0466842\pi\) | ||||
−0.989264 | + | 0.146138i | \(0.953316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.60732e14i | 0.441288i | 0.975354 | + | 0.220644i | \(0.0708159\pi\) | ||||
−0.975354 | + | 0.220644i | \(0.929184\pi\) | |||||||
\(62\) | 1.00268e14 | − | 8.68526e11i | 0.0583223 | − | 0.000505189i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.24876e15 | − | 1.16975e14i | 0.998650 | − | 0.0519474i | ||||
\(65\) | 3.15891e15 | 1.22963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.64311e15i | 1.09607i | 0.836457 | + | 0.548033i | \(0.184623\pi\) | ||||
−0.836457 | + | 0.548033i | \(0.815377\pi\) | |||||||
\(68\) | −4.42232e15 | + | 7.66181e13i | −1.17307 | + | 0.0203238i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.57987e13 | + | 1.82390e15i | 0.00327557 | + | 0.378154i | ||||
\(71\) | −9.19058e15 | −1.68907 | −0.844534 | − | 0.535502i | \(-0.820122\pi\) | ||||
−0.844534 | + | 0.535502i | \(0.820122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.44264e15 | −0.789888 | −0.394944 | − | 0.918705i | \(-0.629236\pi\) | ||||
−0.394944 | + | 0.918705i | \(0.629236\pi\) | |||||||
\(74\) | −6.67591e13 | − | 7.70712e15i | −0.00863060 | − | 0.996374i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.28935e14 | − | 1.32139e16i | −0.0235937 | − | 1.36181i | ||||
\(77\) | 1.49888e15i | 0.138228i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06400e16 | 0.789059 | 0.394529 | − | 0.918883i | \(-0.370908\pi\) | ||||
0.394529 | + | 0.918883i | \(0.370908\pi\) | |||||||
\(80\) | −3.95786e14 | − | 1.14188e16i | −0.0263752 | − | 0.760947i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.06924e16 | + | 2.65858e14i | −1.65811 | + | 0.0143626i | ||||
\(83\) | − | 9.38898e15i | − | 0.457567i | −0.973477 | − | 0.228783i | \(-0.926525\pi\) | ||
0.973477 | − | 0.228783i | \(-0.0734748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24422e16i | 0.893316i | ||||||||
\(86\) | 4.33498e14 | + | 5.00459e16i | 0.0156225 | + | 1.80356i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.43955e14 | − | 9.38604e15i | −0.00723113 | − | 0.278214i | ||||
\(89\) | −2.24169e16 | −0.603616 | −0.301808 | − | 0.953369i | \(-0.597590\pi\) | ||||
−0.301808 | + | 0.953369i | \(0.597590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.59815e16i | − | 0.802099i | ||||||
\(92\) | −4.14453e16 | + | 7.18053e14i | −0.841936 | + | 0.0145868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.97392e16 | + | 2.57601e14i | −0.503203 | + | 0.00435874i | ||||
\(95\) | −6.70573e16 | −1.03704 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.00962e16 | −0.519450 | −0.259725 | − | 0.965683i | \(-0.583632\pi\) | ||||
−0.259725 | + | 0.965683i | \(0.583632\pi\) | |||||||
\(98\) | −6.34429e16 | + | 5.49543e14i | −0.753288 | + | 0.00652499i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.20201e16 | − | 7.28011e14i | 0.420201 | − | 0.00728011i | ||||
\(101\) | 3.80297e16i | 0.349455i | 0.984617 | + | 0.174728i | \(0.0559045\pi\) | ||||
−0.984617 | + | 0.174728i | \(0.944096\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.07629e17 | −1.61500 | −0.807498 | − | 0.589870i | \(-0.799179\pi\) | ||||
−0.807498 | + | 0.589870i | \(0.799179\pi\) | |||||||
\(104\) | 5.85627e15 | + | 2.25317e17i | 0.0419602 | + | 1.61440i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.92144e14 | − | 1.14540e17i | −0.00604609 | − | 0.698001i | ||||
\(107\) | − | 1.68191e17i | − | 0.946325i | −0.880975 | − | 0.473162i | \(-0.843112\pi\) | ||
0.880975 | − | 0.473162i | \(-0.156888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.08973e15i | 0.0196593i | 0.999952 | + | 0.00982967i | \(0.00312893\pi\) | ||||
−0.999952 | + | 0.00982967i | \(0.996871\pi\) | |||||||
\(110\) | −4.76390e16 | + | 4.12650e14i | −0.211897 | + | 0.00183545i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.30066e17 | + | 4.50821e15i | −0.496374 | + | 0.0172048i | ||||
\(113\) | −2.83148e16 | −0.100195 | −0.0500976 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500976 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.10325e17i | 0.641149i | ||||||||
\(116\) | −8.04426e15 | − | 4.64307e17i | −0.0227821 | − | 1.31496i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.03369e15 | + | 1.19336e17i | 0.00253159 | + | 0.292264i | ||||
\(119\) | 2.55628e17 | 0.582720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.66297e17 | 0.922544 | ||||||||
\(122\) | 2.07197e15 | + | 2.39202e17i | 0.00382229 | + | 0.441271i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.62970e16 | − | 6.28856e14i | 0.0583158 | − | 0.00101034i | ||||
\(125\) | − | 7.20642e17i | − | 1.08139i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.04849e17 | −0.137478 | −0.0687388 | − | 0.997635i | \(-0.521898\pi\) | ||||
−0.0687388 | + | 0.997635i | \(0.521898\pi\) | |||||||
\(128\) | 8.13741e17 | − | 4.93997e16i | 0.998162 | − | 0.0605954i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.14360e18 | − | 9.90590e15i | 1.22958 | − | 0.0106506i | ||||
\(131\) | − | 7.82237e17i | − | 0.788011i | −0.919108 | − | 0.394005i | \(-0.871089\pi\) | ||
0.919108 | − | 0.394005i | \(-0.128911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.63817e17i | 0.676473i | ||||||||
\(134\) | 1.14243e16 | + | 1.31890e18i | 0.00949377 | + | 1.09602i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.60075e18 | + | 4.16055e16i | −1.17285 | + | 0.0304839i | ||||
\(137\) | −6.27442e17 | −0.431965 | −0.215983 | − | 0.976397i | \(-0.569295\pi\) | ||||
−0.215983 | + | 0.976397i | \(0.569295\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.57262e17i | − | 0.156585i | −0.996930 | − | 0.0782924i | \(-0.975053\pi\) | ||
0.996930 | − | 0.0782924i | \(-0.0249468\pi\) | |||||||
\(140\) | 1.14390e16 | + | 6.60250e17i | 0.00655090 | + | 0.378112i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.32722e18 | + | 2.88204e16i | −1.68900 | + | 0.0146302i | ||||
\(143\) | 9.39811e17 | 0.449453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.35625e18 | −1.00137 | ||||||||
\(146\) | −1.97037e18 | + | 1.70674e16i | −0.789859 | + | 0.00684176i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.83370e16 | − | 2.78996e18i | −0.0172606 | − | 0.996262i | ||||
\(149\) | 5.12586e18i | 1.72855i | 0.503016 | + | 0.864277i | \(0.332224\pi\) | ||||
−0.503016 | + | 0.864277i | \(0.667776\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51399e18 | −0.455848 | −0.227924 | − | 0.973679i | \(-0.573194\pi\) | ||||
−0.227924 | + | 0.973679i | \(0.573194\pi\) | |||||||
\(152\) | −1.24317e17 | − | 4.78304e18i | −0.0353884 | − | 1.36155i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.70029e15 | + | 5.42633e17i | 0.00119729 | + | 0.138223i | ||||
\(155\) | − | 1.84198e17i | − | 0.0444085i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.31795e18i | 1.36593i | 0.730450 | + | 0.682966i | \(0.239310\pi\) | ||||
−0.730450 | + | 0.682966i | \(0.760690\pi\) | |||||||
\(158\) | 3.85193e18 | − | 3.33654e16i | 0.789029 | − | 0.00683458i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.79092e17 | − | 4.13264e18i | −0.0329653 | − | 0.760690i | ||||
\(161\) | 2.39571e18 | 0.418229 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.62696e18i | − | 1.19883i | −0.800439 | − | 0.599414i | \(-0.795400\pi\) | ||
0.800439 | − | 0.599414i | \(-0.204600\pi\) | |||||||
\(164\) | −1.11106e19 | + | 1.92494e17i | −1.65792 | + | 0.0287240i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.94426e16 | − | 3.39905e18i | −0.00396330 | − | 0.457550i | ||||
\(167\) | −7.60518e18 | −0.972791 | −0.486396 | − | 0.873739i | \(-0.661689\pi\) | ||||
−0.486396 | + | 0.873739i | \(0.661689\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.39103e19 | −1.60805 | ||||||||
\(170\) | 7.03757e16 | + | 8.12465e18i | 0.00773762 | + | 0.893282i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.13874e17 | + | 1.81165e19i | 0.0312438 | + | 1.80336i | ||||
\(173\) | − | 9.85927e18i | − | 0.934228i | −0.884197 | − | 0.467114i | \(-0.845294\pi\) | ||
0.884197 | − | 0.467114i | \(-0.154706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.42893e18 | −0.208734 | ||||||||
\(176\) | −1.17751e17 | − | 3.39722e18i | −0.00964067 | − | 0.278141i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.11549e18 | + | 7.02964e16i | −0.603593 | + | 0.00522833i | ||||
\(179\) | 1.05371e19i | 0.747257i | 0.927578 | + | 0.373628i | \(0.121886\pi\) | ||||
−0.927578 | + | 0.373628i | \(0.878114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.64819e19i | − | 1.70876i | −0.519649 | − | 0.854380i | \(-0.673937\pi\) | ||
0.519649 | − | 0.854380i | \(-0.326063\pi\) | |||||||
\(182\) | −1.12833e17 | − | 1.30262e19i | −0.00694753 | − | 0.802069i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50020e19 | + | 3.89920e17i | −0.841778 | + | 0.0218788i | ||||
\(185\) | −1.41584e19 | −0.758672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.67682e18i | 0.326525i | ||||||||
\(188\) | −1.07655e19 | + | 1.86516e17i | −0.503146 | + | 0.00871716i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.42764e19 | + | 2.10283e17i | −1.03700 | + | 0.00898251i | ||||
\(191\) | −2.32908e19 | −0.951484 | −0.475742 | − | 0.879585i | \(-0.657820\pi\) | ||||
−0.475742 | + | 0.879585i | \(0.657820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.61228e17 | −0.00976748 | −0.00488374 | − | 0.999988i | \(-0.501555\pi\) | ||||
−0.00488374 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(194\) | −1.45158e19 | + | 1.25736e17i | −0.519431 | + | 0.00449931i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.29662e19 | + | 3.97896e17i | −0.753204 | + | 0.0130495i | ||||
\(197\) | 6.46253e18i | 0.202974i | 0.994837 | + | 0.101487i | \(0.0323600\pi\) | ||||
−0.994837 | + | 0.101487i | \(0.967640\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.82250e19 | −0.525311 | −0.262655 | − | 0.964890i | \(-0.584598\pi\) | ||||
−0.262655 | + | 0.964890i | \(0.584598\pi\) | |||||||
\(200\) | 1.52100e19 | − | 3.95328e17i | 0.420122 | − | 0.0109195i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.19256e17 | + | 1.37677e19i | 0.00302687 | + | 0.349442i | ||||
\(203\) | 2.68388e19i | 0.653202i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.63836e19i | 1.26254i | ||||||||
\(206\) | −7.51669e19 | + | 6.51096e17i | −1.61494 | + | 0.0139886i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.82668e18 | + | 8.15522e19i | 0.0559421 | + | 1.61398i | ||||
\(209\) | −1.99503e19 | −0.379059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.73859e19i | − | 1.35600i | −0.735060 | − | 0.678002i | \(-0.762846\pi\) | ||
0.735060 | − | 0.678002i | \(-0.237154\pi\) | |||||||
\(212\) | −7.18362e17 | − | 4.14631e19i | −0.0120917 | − | 0.697923i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.27424e17 | − | 6.08893e19i | −0.00819677 | − | 0.946289i | ||||
\(215\) | 9.19369e19 | 1.37329 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.09811e18 | −0.0289682 | ||||||||
\(218\) | 1.28248e16 | + | 1.48058e18i | 0.000170283 | + | 0.0196586i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.72452e19 | + | 2.98779e17i | −0.211873 | + | 0.00367077i | ||||
\(221\) | − | 1.60281e20i | − | 1.89473i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.34556e20 | −1.47337 | −0.736685 | − | 0.676236i | \(-0.763610\pi\) | ||||
−0.736685 | + | 0.676236i | \(0.763610\pi\) | |||||||
\(224\) | −4.70729e19 | + | 2.03995e18i | −0.496207 | + | 0.0215036i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.02507e19 | + | 8.87915e16i | −0.100192 | + | 0.000867860i | ||||
\(227\) | 7.95558e19i | 0.748949i | 0.927237 | + | 0.374474i | \(0.122177\pi\) | ||||
−0.927237 | + | 0.374474i | \(0.877823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46397e19i | 0.302673i | 0.988482 | + | 0.151336i | \(0.0483576\pi\) | ||||
−0.988482 | + | 0.151336i | \(0.951642\pi\) | |||||||
\(230\) | 6.59550e17 | + | 7.61429e19i | 0.00555343 | + | 0.641125i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.36823e18 | − | 1.68066e20i | −0.0341710 | − | 1.31471i | ||||
\(233\) | 1.21528e20 | 0.916538 | 0.458269 | − | 0.888814i | \(-0.348470\pi\) | ||||
0.458269 | + | 0.888814i | \(0.348470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.46325e19i | 0.383155i | ||||||||
\(236\) | 7.48445e17 | + | 4.31995e19i | 0.00506300 | + | 0.292231i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.25438e19 | − | 8.01616e17i | 0.582698 | − | 0.00504733i | ||||
\(239\) | 2.25849e19 | 0.137226 | 0.0686129 | − | 0.997643i | \(-0.478143\pi\) | ||||
0.0686129 | + | 0.997643i | \(0.478143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.85622e20 | 1.61677 | 0.808383 | − | 0.588657i | \(-0.200343\pi\) | ||||
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(242\) | 1.68811e20 | − | 1.46225e18i | 0.922510 | − | 0.00799079i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.50021e18 | + | 8.65905e19i | 0.00764430 | + | 0.441222i | ||||
\(245\) | 1.16548e20i | 0.573578i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.78920e20 | 2.19957 | ||||||||
\(248\) | 1.31384e19 | − | 3.41484e17i | 0.0583048 | − | 0.00151541i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.25983e18 | − | 2.60890e20i | −0.00936670 | − | 1.08135i | ||||
\(251\) | 1.47186e20i | 0.589713i | 0.955541 | + | 0.294857i | \(0.0952719\pi\) | ||||
−0.955541 | + | 0.294857i | \(0.904728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.25741e19i | 0.234353i | ||||||||
\(254\) | −3.79579e19 | + | 3.28792e17i | −0.137472 | + | 0.00119079i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.94440e20 | − | 2.04357e19i | 0.997600 | − | 0.0692389i | ||||
\(257\) | 3.49632e20 | 1.14599 | 0.572993 | − | 0.819560i | \(-0.305782\pi\) | ||||
0.572993 | + | 0.819560i | \(0.305782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.61271e20i | 0.494890i | ||||||||
\(260\) | 4.13982e20 | − | 7.17237e18i | 1.22944 | − | 0.0213005i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.45299e18 | − | 2.83189e20i | −0.00682550 | − | 0.787981i | ||||
\(263\) | 2.56287e20 | 0.690402 | 0.345201 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345201 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.10415e20 | −0.531481 | ||||||||
\(266\) | 2.39523e18 | + | 2.76521e20i | 0.00585939 | + | 0.676448i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.27177e18 | + | 4.77438e20i | 0.0189868 | + | 1.09590i | ||||
\(269\) | − | 6.85596e20i | − | 1.52466i | −0.647187 | − | 0.762331i | \(-0.724055\pi\) | ||
0.647187 | − | 0.762331i | \(-0.275945\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.06814e20 | 1.05830 | 0.529151 | − | 0.848528i | \(-0.322511\pi\) | ||||
0.529151 | + | 0.848528i | \(0.322511\pi\) | |||||||
\(272\) | −5.79382e20 | + | 2.00820e19i | −1.17254 | + | 0.0406416i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.27150e20 | + | 1.96757e18i | −0.431949 | + | 0.00374154i | ||||
\(275\) | − | 6.34419e19i | − | 0.116963i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.87639e20i | 1.01867i | 0.860569 | + | 0.509334i | \(0.170108\pi\) | ||||
−0.860569 | + | 0.509334i | \(0.829892\pi\) | |||||||
\(278\) | −8.06738e17 | − | 9.31352e19i | −0.00135629 | − | 0.156579i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.21167e18 | + | 2.38991e20i | 0.00982574 | + | 0.378041i | ||||
\(281\) | 5.24336e20 | 0.804647 | 0.402324 | − | 0.915498i | \(-0.368203\pi\) | ||||
0.402324 | + | 0.915498i | \(0.368203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.51546e20i | − | 1.08585i | −0.839780 | − | 0.542927i | \(-0.817316\pi\) | ||
0.839780 | − | 0.542927i | \(-0.182684\pi\) | |||||||
\(284\) | −1.20445e21 | + | 2.08674e19i | −1.68881 | + | 0.0292592i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.40235e20 | − | 2.94712e18i | 0.449436 | − | 0.00389302i | ||||
\(287\) | 6.42237e20 | 0.823568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.11465e20 | 0.376511 | ||||||||
\(290\) | −8.53020e20 | + | 7.38887e18i | −1.00133 | + | 0.00867351i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.13271e20 | + | 1.23576e19i | −0.789770 | + | 0.0136830i | ||||
\(293\) | 7.51033e20i | 0.807764i | 0.914811 | + | 0.403882i | \(0.132339\pi\) | ||||
−0.914811 | + | 0.403882i | \(0.867661\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.19227e20 | 0.222539 | ||||||||
\(296\) | −2.62481e19 | − | 1.00988e21i | −0.0258892 | − | 0.996075i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.60740e19 | + | 1.85569e21i | 0.0149722 | + | 1.72849i | ||||
\(299\) | − | 1.50213e21i | − | 1.35988i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.04721e21i | − | 0.895813i | ||||||
\(302\) | −5.48104e20 | + | 4.74768e18i | −0.455831 | + | 0.00394841i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00049e19 | − | 1.73119e21i | −0.0471804 | − | 1.36119i | ||||
\(305\) | 4.39426e20 | 0.335998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.89249e19i | − | 0.0426209i | −0.999773 | − | 0.0213105i | \(-0.993216\pi\) | ||
0.999773 | − | 0.0213105i | \(-0.00678384\pi\) | |||||||
\(308\) | 3.40325e18 | + | 1.96432e20i | 0.00239449 | + | 0.138207i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.77621e17 | − | 6.66844e19i | −0.000384653 | − | 0.0444069i | ||||
\(311\) | 9.05717e20 | 0.586853 | 0.293427 | − | 0.955982i | \(-0.405204\pi\) | ||||
0.293427 | + | 0.955982i | \(0.405204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.51738e21 | 1.54462 | 0.772311 | − | 0.635245i | \(-0.219101\pi\) | ||||
0.772311 | + | 0.635245i | \(0.219101\pi\) | |||||||
\(314\) | 1.98122e19 | + | 2.28726e21i | 0.0118313 | + | 1.36588i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.39439e21 | − | 2.41583e19i | 0.788940 | − | 0.0136686i | ||||
\(317\) | 1.88675e21i | 1.03923i | 0.854401 | + | 0.519614i | \(0.173924\pi\) | ||||
−0.854401 | + | 0.519614i | \(0.826076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.01010e20 | −0.366019 | ||||||||
\(320\) | −7.77953e19 | − | 1.49556e21i | −0.0395529 | − | 0.760376i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.67307e20 | − | 7.51262e18i | 0.418213 | − | 0.00362257i | ||||
\(323\) | 3.40245e21i | 1.59798i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.52296e21i | 0.678704i | ||||||||
\(326\) | −2.39171e19 | − | 2.76115e21i | −0.0103839 | − | 1.19878i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.02171e21 | + | 1.04529e20i | −1.65761 | + | 0.0430834i | ||||
\(329\) | 6.22292e20 | 0.249936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.03084e21i | − | 0.393236i | −0.980480 | − | 0.196618i | \(-0.937004\pi\) | ||
0.980480 | − | 0.196618i | \(-0.0629959\pi\) | |||||||
\(332\) | −2.13179e19 | − | 1.23045e21i | −0.00792630 | − | 0.457498i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.75327e21 | + | 2.38488e19i | −0.972755 | + | 0.00842601i | ||||
\(335\) | 2.42288e21 | 0.834549 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.14822e21 | 0.703435 | 0.351717 | − | 0.936106i | \(-0.385598\pi\) | ||||
0.351717 | + | 0.936106i | \(0.385598\pi\) | |||||||
\(338\) | −5.03588e21 | + | 4.36208e19i | −1.60799 | + | 0.0139284i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.09556e19 | + | 2.94110e21i | 0.0154747 | + | 0.893181i | ||||
\(341\) | − | 5.48012e19i | − | 0.0162322i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.08980e21 | 0.870824 | ||||||||
\(344\) | 1.70441e20 | + | 6.55764e21i | 0.0468627 | + | 1.80302i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.09173e19 | − | 3.56930e21i | −0.00809199 | − | 0.934193i | ||||
\(347\) | − | 4.67482e21i | − | 1.19389i | −0.802282 | − | 0.596945i | \(-0.796381\pi\) | ||
0.802282 | − | 0.596945i | \(-0.203619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.72313e21i | − | 1.14872i | −0.818603 | − | 0.574360i | \(-0.805251\pi\) | ||
0.818603 | − | 0.574360i | \(-0.194749\pi\) | |||||||
\(350\) | −8.79335e20 | + | 7.61680e18i | −0.208726 | + | 0.00180798i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.32820e19 | − | 1.22951e21i | −0.0120495 | − | 0.278047i | ||||
\(353\) | 4.29922e21 | 0.949084 | 0.474542 | − | 0.880233i | \(-0.342614\pi\) | ||||
0.474542 | + | 0.880233i | \(0.342614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.11228e21i | 1.28606i | ||||||||
\(356\) | −2.93779e21 | + | 5.08981e19i | −0.603525 | + | 0.0104563i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.30429e19 | + | 3.81469e21i | 0.00647250 | + | 0.747229i | ||||
\(359\) | 5.26993e21 | 1.00810 | 0.504048 | − | 0.863675i | \(-0.331843\pi\) | ||||
0.504048 | + | 0.863675i | \(0.331843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.68613e21 | −0.855073 | ||||||||
\(362\) | −8.30436e19 | − | 9.58710e21i | −0.0148007 | − | 1.70870i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.16969e19 | − | 4.71546e21i | −0.0138945 | − | 0.801979i | ||||
\(365\) | 3.61968e21i | 0.601424i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.39416e21 | −1.17281 | −0.586405 | − | 0.810018i | \(-0.699457\pi\) | ||||
−0.586405 | + | 0.810018i | \(0.699457\pi\) | |||||||
\(368\) | −5.42987e21 | + | 1.88205e20i | −0.841557 | + | 0.0291692i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.12569e21 | + | 4.43988e19i | −0.758643 | + | 0.00657137i | ||||
\(371\) | 2.39674e21i | 0.346691i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.45714e21i | − | 0.477740i | −0.971052 | − | 0.238870i | \(-0.923223\pi\) | ||
0.971052 | − | 0.238870i | \(-0.0767769\pi\) | |||||||
\(374\) | 2.09376e19 | + | 2.41718e21i | 0.00282825 | + | 0.326512i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.89681e21 | + | 1.01283e20i | −0.503052 | + | 0.0130749i | ||||
\(377\) | 1.68282e22 | 2.12391 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.17249e21i | 0.382795i | 0.981513 | + | 0.191398i | \(0.0613020\pi\) | ||||
−0.981513 | + | 0.191398i | \(0.938698\pi\) | |||||||
\(380\) | −8.78802e21 | + | 1.52255e20i | −1.03688 | + | 0.0179644i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.43187e21 | + | 7.30369e19i | −0.951448 | + | 0.00824145i | ||||
\(383\) | −3.27971e21 | −0.361947 | −0.180974 | − | 0.983488i | \(-0.557925\pi\) | ||||
−0.180974 | + | 0.983488i | \(0.557925\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.96845e20 | 0.105247 | ||||||||
\(386\) | −9.45711e19 | + | 8.19175e17i | −0.00976711 | + | 8.46028e-5i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.25471e21 | + | 9.10394e19i | −0.519372 | + | 0.00899829i | ||||
\(389\) | − | 1.09936e22i | − | 1.06308i | −0.847032 | − | 0.531542i | \(-0.821613\pi\) | ||
0.847032 | − | 0.531542i | \(-0.178387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06718e22 | 0.987947 | ||||||||
\(392\) | −8.31309e21 | + | 2.16067e20i | −0.753062 | + | 0.0195730i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.02656e19 | + | 2.33960e21i | 0.00175809 | + | 0.202966i | ||||
\(395\) | − | 7.07620e21i | − | 0.600792i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.01100e21i | 0.732915i | 0.930435 | + | 0.366458i | \(0.119430\pi\) | ||||
−0.930435 | + | 0.366458i | \(0.880570\pi\) | |||||||
\(398\) | −6.59791e21 | + | 5.71511e19i | −0.525291 | + | 0.00455008i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.50518e21 | − | 1.90815e20i | 0.420012 | − | 0.0145580i | ||||
\(401\) | −1.05004e22 | −0.784296 | −0.392148 | − | 0.919902i | \(-0.628268\pi\) | ||||
−0.392148 | + | 0.919902i | \(0.628268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.31553e21i | 0.0941910i | ||||||||
\(404\) | 8.63473e19 | + | 4.98388e21i | 0.00605351 | + | 0.349403i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.41629e19 | + | 9.71633e21i | 0.00565783 | + | 0.653177i | ||||
\(407\) | −4.21228e21 | −0.277310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.86541e21 | 0.370382 | 0.185191 | − | 0.982703i | \(-0.440710\pi\) | ||||
0.185191 | + | 0.982703i | \(0.440710\pi\) | |||||||
\(410\) | 1.76811e20 | + | 2.04123e22i | 0.0109357 | + | 1.26249i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.72103e22 | + | 4.71426e20i | −1.61475 | + | 0.0279761i | ||||
\(413\) | − | 2.49711e21i | − | 0.145165i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.24423e21 | −0.348393 | ||||||||
\(416\) | 1.27907e21 | + | 2.95151e22i | 0.0699198 | + | 1.61343i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.22252e21 | + | 6.25615e19i | −0.379045 | + | 0.00328329i | ||||
\(419\) | − | 5.02281e21i | − | 0.258302i | −0.991625 | − | 0.129151i | \(-0.958775\pi\) | ||
0.991625 | − | 0.129151i | \(-0.0412252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.55885e22i | − | 0.769848i | −0.922948 | − | 0.384924i | \(-0.874228\pi\) | ||
0.922948 | − | 0.384924i | \(-0.125772\pi\) | |||||||
\(422\) | −2.42672e20 | − | 2.80156e22i | −0.0117453 | − | 1.35595i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.90088e20 | − | 1.50084e22i | −0.0181365 | − | 0.697792i | ||||
\(425\) | −1.08198e22 | −0.493074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.00528e21i | − | 0.219175i | ||||||
\(428\) | −3.81881e20 | − | 2.20418e22i | −0.0163929 | − | 0.946183i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.32834e22 | − | 2.88301e20i | 1.37324 | − | 0.0118950i | ||||
\(431\) | 2.78561e22 | 1.12684 | 0.563421 | − | 0.826170i | \(-0.309485\pi\) | ||||
0.563421 | + | 0.826170i | \(0.309485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.24470e21 | −0.0484079 | −0.0242040 | − | 0.999707i | \(-0.507705\pi\) | ||||
−0.0242040 | + | 0.999707i | \(0.507705\pi\) | |||||||
\(434\) | −7.59570e20 | + | 6.57940e18i | −0.0289671 | + | 0.000250913i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.28581e18 | + | 5.35968e20i | 0.000340553 | + | 0.0196564i | ||||
\(437\) | 3.18872e22i | 1.14690i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.09614e22 | −0.725224 | −0.362612 | − | 0.931940i | \(-0.618115\pi\) | ||||
−0.362612 | + | 0.931940i | \(0.618115\pi\) | |||||||
\(440\) | −6.24227e21 | + | 1.62244e20i | −0.211834 | + | 0.00550581i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.02619e20 | − | 5.80257e22i | −0.0164116 | − | 1.89466i | ||||
\(443\) | 1.11978e22i | 0.358674i | 0.983788 | + | 0.179337i | \(0.0573952\pi\) | ||||
−0.983788 | + | 0.179337i | \(0.942605\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.49086e22i | 0.459596i | ||||||||
\(446\) | −4.87127e22 | + | 4.21950e20i | −1.47332 | + | 0.0127619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.70352e22 | + | 8.86128e20i | −0.496002 | + | 0.0258008i | ||||
\(449\) | 1.44200e22 | 0.411975 | 0.205987 | − | 0.978555i | \(-0.433959\pi\) | ||||
0.205987 | + | 0.978555i | \(0.433959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.67748e22i | 0.461483i | ||||||||
\(452\) | −3.71072e21 | + | 6.42895e19i | −0.100180 | + | 0.00173565i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.49476e20 | + | 2.88012e22i | 0.00648716 | + | 0.748921i | ||||
\(455\) | −2.39298e22 | −0.610721 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.99851e22 | 0.737254 | 0.368627 | − | 0.929577i | \(-0.379828\pi\) | ||||
0.368627 | + | 0.929577i | \(0.379828\pi\) | |||||||
\(458\) | 1.08626e20 | + | 1.25405e22i | 0.00262165 | + | 0.302661i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.77548e20 | + | 2.75636e22i | 0.0111064 | + | 0.641053i | ||||
\(461\) | − | 4.32706e22i | − | 0.987950i | −0.869476 | − | 0.493975i | \(-0.835544\pi\) | ||
0.869476 | − | 0.493975i | \(-0.164456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.79925e22 | −0.395962 | −0.197981 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197981 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(464\) | −2.10844e21 | − | 6.08302e22i | −0.0455573 | − | 1.31437i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.39961e22 | − | 3.81095e20i | 0.916504 | − | 0.00793876i | ||||
\(467\) | 5.53566e22i | 1.13234i | 0.824289 | + | 0.566169i | \(0.191575\pi\) | ||||
−0.824289 | + | 0.566169i | \(0.808425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.75979e22i | − | 0.544386i | ||||||
\(470\) | 1.71320e20 | + | 1.97783e22i | 0.00331877 | + | 0.383140i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.06424e20 | + | 1.56370e22i | 0.00759402 | + | 0.292176i | ||||
\(473\) | 2.73523e22 | 0.501965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.23295e22i | − | 0.572404i | ||||||
\(476\) | 3.35007e22 | − | 5.80410e20i | 0.582632 | − | 0.0100943i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.17630e21 | − | 7.08232e19i | 0.137221 | − | 0.00118861i | ||||
\(479\) | 1.18108e22 | 0.194727 | 0.0973637 | − | 0.995249i | \(-0.468959\pi\) | ||||
0.0973637 | + | 0.995249i | \(0.468959\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01118e23 | 1.60915 | ||||||||
\(482\) | 1.03402e23 | − | 8.95672e20i | 1.61670 | − | 0.0140039i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.11094e22 | − | 1.05874e21i | 0.922406 | − | 0.0159810i | ||||
\(485\) | 2.66664e22i | 0.395511i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.16692e22 | 0.310347 | 0.155173 | − | 0.987887i | \(-0.450406\pi\) | ||||
0.155173 | + | 0.987887i | \(0.450406\pi\) | |||||||
\(488\) | 8.14649e20 | + | 3.13432e22i | 0.0114657 | + | 0.441139i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.65478e20 | + | 4.21933e22i | 0.00496815 | + | 0.573557i | ||||
\(491\) | − | 1.30265e23i | − | 1.74034i | −0.492749 | − | 0.870172i | \(-0.664008\pi\) | ||
0.492749 | − | 0.870172i | \(-0.335992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.19555e23i | 1.54300i | ||||||||
\(494\) | 1.73381e23 | − | 1.50183e21i | 2.19949 | − | 0.0190520i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.75537e21 | − | 1.64826e20i | 0.0582895 | − | 0.00202038i | ||||
\(497\) | 6.96220e22 | 0.838913 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.17276e22i | − | 0.602376i | −0.953565 | − | 0.301188i | \(-0.902617\pi\) | ||
0.953565 | − | 0.301188i | \(-0.0973832\pi\) | |||||||
\(500\) | −1.63623e21 | − | 9.44418e22i | −0.0187327 | − | 1.08123i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.61556e20 | + | 5.32852e22i | 0.00510791 | + | 0.589691i | ||||
\(503\) | −1.07219e23 | −1.16665 | −0.583327 | − | 0.812237i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812237i | \(0.698249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.52920e22 | 0.266076 | ||||||||
\(506\) | 1.96224e20 | + | 2.26534e22i | 0.00202989 | + | 0.234344i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.37407e22 | + | 2.38062e20i | −0.137457 | + | 0.00238148i | ||||
\(509\) | 1.48328e23i | 1.45922i | 0.683861 | + | 0.729612i | \(0.260299\pi\) | ||||
−0.683861 | + | 0.729612i | \(0.739701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.12300e22 | 0.392316 | ||||||||
\(512\) | 1.06530e23 | − | 8.32156e21i | 0.996963 | − | 0.0778772i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.26576e23 | − | 1.09640e21i | 1.14594 | − | 0.00992617i | ||||
\(515\) | 1.38086e23i | 1.22966i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.62538e22i | 0.140051i | ||||||||
\(518\) | 5.05725e20 | + | 5.83842e22i | 0.00428658 | + | 0.494872i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.49849e23 | − | 3.89477e21i | 1.22921 | − | 0.0319487i | ||||
\(521\) | −7.01242e22 | −0.565910 | −0.282955 | − | 0.959133i | \(-0.591315\pi\) | ||||
−0.282955 | + | 0.959133i | \(0.591315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.14598e23i | − | 1.67634i | −0.545410 | − | 0.838169i | \(-0.683626\pi\) | ||
0.545410 | − | 0.838169i | \(-0.316374\pi\) | |||||||
\(524\) | −1.77609e21 | − | 1.02514e23i | −0.0136505 | − | 0.787893i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.27822e22 | − | 8.03680e20i | 0.690376 | − | 0.00598005i | ||||
\(527\) | −9.34612e21 | −0.0684291 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.10359e22 | −0.290932 | ||||||||
\(530\) | −7.61757e22 | + | 6.59834e20i | −0.531461 | + | 0.00460352i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.73426e21 | + | 1.00100e23i | 0.0117183 | + | 0.676371i | ||||
\(533\) | − | 4.02688e23i | − | 2.67786i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.11857e23 | −0.720536 | ||||||||
\(536\) | 4.49177e21 | + | 1.72819e23i | 0.0284785 | + | 1.09570i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.14993e21 | − | 2.48203e23i | −0.0132061 | − | 1.52460i | ||||
\(539\) | 3.46743e22i | 0.209654i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.34761e23i | − | 0.789565i | −0.918775 | − | 0.394783i | \(-0.870820\pi\) | ||
0.918775 | − | 0.394783i | \(-0.129180\pi\) | |||||||
\(542\) | 1.83479e23 | − | 1.58930e21i | 1.05826 | − | 0.00916667i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.09688e23 | + | 9.08704e21i | −1.17215 | + | 0.0507963i | ||||
\(545\) | 2.71991e21 | 0.0149687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.17960e23i | 1.16274i | 0.813638 | + | 0.581372i | \(0.197484\pi\) | ||||
−0.813638 | + | 0.581372i | \(0.802516\pi\) | |||||||
\(548\) | −8.22277e22 | + | 1.42462e21i | −0.431900 | + | 0.00748281i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.98945e20 | − | 2.29676e22i | −0.00101310 | − | 0.116959i | ||||
\(551\) | −3.57229e23 | −1.79126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.06015e22 | −0.391904 | ||||||||
\(554\) | 1.84276e21 | + | 2.12740e23i | 0.00882337 | + | 1.01863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.84119e20 | − | 3.37148e22i | −0.00271247 | − | 0.156561i | ||||
\(557\) | 7.39588e22i | 0.338237i | 0.985596 | + | 0.169118i | \(0.0540920\pi\) | ||||
−0.985596 | + | 0.169118i | \(0.945908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.56608e23 | −2.91277 | ||||||||
\(560\) | 2.99822e21 | + | 8.65013e22i | 0.0130998 | + | 0.377941i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.89823e23 | − | 1.64424e21i | 0.804617 | − | 0.00696960i | ||||
\(563\) | 6.46778e21i | 0.0270044i | 0.999909 | + | 0.0135022i | \(0.00429801\pi\) | ||||
−0.999909 | + | 0.0135022i | \(0.995702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.88310e22i | 0.0762891i | ||||||||
\(566\) | −2.35675e21 | − | 2.72079e23i | −0.00940532 | − | 1.08581i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.35975e23 | + | 1.13315e22i | −1.68850 | + | 0.0438861i | ||||
\(569\) | −3.40211e23 | −1.29806 | −0.649029 | − | 0.760764i | \(-0.724824\pi\) | ||||
−0.649029 | + | 0.760764i | \(0.724824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.01054e23i | 1.48524i | 0.669715 | + | 0.742619i | \(0.266416\pi\) | ||||
−0.669715 | + | 0.742619i | \(0.733584\pi\) | |||||||
\(572\) | 1.23164e23 | − | 2.13386e21i | 0.449385 | − | 0.00778575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.32506e23 | − | 2.01397e21i | 0.823537 | − | 0.00713348i | ||||
\(575\) | −1.01401e23 | −0.353888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.92304e23 | 0.651619 | 0.325810 | − | 0.945435i | \(-0.394363\pi\) | ||||
0.325810 | + | 0.945435i | \(0.394363\pi\) | |||||||
\(578\) | 1.12758e23 | − | 9.76711e20i | 0.376496 | − | 0.00326121i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.08791e23 | + | 5.34991e21i | −1.00122 | + | 0.0173464i | ||||
\(581\) | 7.11249e22i | 0.227261i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.26010e22 | −0.194267 | ||||||||
\(584\) | −2.58183e23 | + | 6.71050e21i | −0.789622 | + | 0.0205232i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.35514e21 | + | 2.71893e23i | 0.00699659 | + | 0.807733i | ||||
\(587\) | 1.13316e23i | 0.331793i | 0.986143 | + | 0.165896i | \(0.0530517\pi\) | ||||
−0.986143 | + | 0.165896i | \(0.946948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.79262e22i | − | 0.0794386i | ||||||
\(590\) | 7.93657e22 | − | 6.87466e20i | 0.222531 | − | 0.00192757i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.26693e22 | − | 3.65521e23i | −0.0345159 | − | 0.995814i | ||||
\(593\) | −4.06278e23 | −1.09108 | −0.545542 | − | 0.838084i | \(-0.683676\pi\) | ||||
−0.545542 | + | 0.838084i | \(0.683676\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.70008e23i | − | 0.443685i | ||||||
\(596\) | 1.16384e22 | + | 6.71755e23i | 0.0299433 | + | 1.72830i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.71047e21 | − | 5.43808e23i | −0.0117789 | − | 1.35983i | ||||
\(599\) | −5.15444e23 | −1.27073 | −0.635365 | − | 0.772212i | \(-0.719150\pi\) | ||||
−0.635365 | + | 0.772212i | \(0.719150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.97639e23 | 0.952918 | 0.476459 | − | 0.879197i | \(-0.341920\pi\) | ||||
0.476459 | + | 0.879197i | \(0.341920\pi\) | |||||||
\(602\) | −3.28390e21 | − | 3.79115e23i | −0.00775925 | − | 0.895780i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.98413e23 | + | 3.43756e21i | −0.455780 | + | 0.00789653i | ||||
\(605\) | − | 3.10115e23i | − | 0.702429i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.76629e23 | −1.49021 | −0.745104 | − | 0.666948i | \(-0.767600\pi\) | ||||
−0.745104 | + | 0.666948i | \(0.767600\pi\) | |||||||
\(608\) | −2.71521e22 | − | 6.26547e23i | −0.0589688 | − | 1.36073i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.59083e23 | − | 1.37798e21i | 0.335986 | − | 0.00291031i | ||||
\(611\) | − | 3.90182e23i | − | 0.812675i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.69956e23i | 1.35716i | 0.734525 | + | 0.678582i | \(0.237405\pi\) | ||||
−0.734525 | + | 0.678582i | \(0.762595\pi\) | |||||||
\(614\) | −1.84781e20 | − | 2.13323e22i | −0.000369169 | − | 0.0426193i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.84804e21 | + | 7.11026e22i | 0.00359150 | + | 0.138181i | ||||
\(617\) | 2.38236e23 | 0.456649 | 0.228325 | − | 0.973585i | \(-0.426675\pi\) | ||||
0.228325 | + | 0.973585i | \(0.426675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.75944e23i | − | 0.328099i | −0.986452 | − | 0.164049i | \(-0.947544\pi\) | ||
0.986452 | − | 0.164049i | \(-0.0524556\pi\) | |||||||
\(620\) | −4.18227e20 | − | 2.41396e22i | −0.000769276 | − | 0.0444019i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.27892e23 | − | 2.84021e21i | 0.586831 | − | 0.00508314i | ||||
\(623\) | 1.69816e23 | 0.299799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34643e23 | −0.403114 | ||||||||
\(626\) | 9.11355e23 | − | 7.89416e21i | 1.54456 | − | 0.0133790i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.43451e22 | + | 8.27982e23i | 0.0236617 | + | 1.36573i | ||||
\(629\) | 7.18388e23i | 1.16904i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.34532e23 | −0.846689 | −0.423344 | − | 0.905969i | \(-0.639144\pi\) | ||||
−0.423344 | + | 0.905969i | \(0.639144\pi\) | |||||||
\(632\) | 5.04729e23 | − | 1.31185e22i | 0.788792 | − | 0.0205017i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.91659e21 | + | 6.83051e23i | 0.00900146 | + | 1.03919i | ||||
\(635\) | 6.97306e22i | 0.104676i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 8.32378e23i | − | 1.21657i | ||||||
\(638\) | −2.53783e23 | + | 2.19827e21i | −0.366005 | + | 0.00317034i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.28537e22 | − | 5.41185e23i | −0.0461376 | − | 0.760005i | ||||
\(641\) | 1.21663e24 | 1.68603 | 0.843017 | − | 0.537887i | \(-0.180777\pi\) | ||||
0.843017 | + | 0.537887i | \(0.180777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.18465e23i | − | 0.294842i | −0.989074 | − | 0.147421i | \(-0.952903\pi\) | ||
0.989074 | − | 0.147421i | \(-0.0470972\pi\) | |||||||
\(644\) | 3.13963e23 | − | 5.43951e21i | 0.418166 | − | 0.00724486i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.06696e22 | + | 1.23177e24i | 0.0138412 | + | 1.59792i | ||||
\(647\) | −1.14703e24 | −1.46855 | −0.734275 | − | 0.678852i | \(-0.762478\pi\) | ||||
−0.734275 | + | 0.678852i | \(0.762478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.52226e22 | 0.0813426 | ||||||||
\(650\) | 4.77580e21 | + | 5.51350e23i | 0.00587872 | + | 0.678678i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.73172e22 | − | 9.99531e23i | −0.0207670 | − | 1.19865i | ||||
\(653\) | − | 1.50867e23i | − | 0.178580i | −0.996006 | − | 0.0892898i | \(-0.971540\pi\) | ||
0.996006 | − | 0.0892898i | \(-0.0284597\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.20234e23 | −0.599995 | ||||||||
\(656\) | −1.45563e24 | + | 5.04537e22i | −1.65718 | + | 0.0574395i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.25285e23 | − | 1.95142e21i | 0.249927 | − | 0.00216487i | ||||
\(659\) | − | 1.33218e24i | − | 1.45894i | −0.684013 | − | 0.729470i | \(-0.739767\pi\) | ||
0.684013 | − | 0.729470i | \(-0.260233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.50165e24i | − | 1.60272i | −0.598183 | − | 0.801359i | \(-0.704111\pi\) | ||
0.598183 | − | 0.801359i | \(-0.295889\pi\) | |||||||
\(662\) | −3.23257e21 | − | 3.73190e23i | −0.00340609 | − | 0.393221i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.15761e22 | − | 4.45386e23i | −0.0118887 | − | 0.457413i | ||||
\(665\) | 5.07983e23 | 0.515069 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.12045e24i | 1.10744i | ||||||||
\(668\) | −9.96677e23 | + | 1.72677e22i | −0.972645 | + | 0.0168514i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.77145e23 | − | 7.59783e21i | 0.834517 | − | 0.00722860i | ||||
\(671\) | 1.30734e23 | 0.122814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.95354e24 | 1.78935 | 0.894673 | − | 0.446722i | \(-0.147409\pi\) | ||||
0.894673 | + | 0.446722i | \(0.147409\pi\) | |||||||
\(674\) | 7.77708e23 | − | 6.73651e21i | 0.703408 | − | 0.00609293i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82298e24 | + | 3.15837e22i | −1.60781 | + | 0.0278558i | ||||
\(677\) | 1.79219e24i | 1.56092i | 0.625208 | + | 0.780458i | \(0.285014\pi\) | ||||
−0.625208 | + | 0.780458i | \(0.714986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.03743e23 | 0.257997 | ||||||||
\(680\) | 2.76701e22 | + | 1.06459e24i | 0.0232105 | + | 0.893014i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.71849e20 | − | 1.98394e22i | −0.000140598 | − | 0.0162316i | ||||
\(683\) | 2.23745e24i | 1.80791i | 0.427628 | + | 0.903955i | \(0.359349\pi\) | ||||
−0.427628 | + | 0.903955i | \(0.640651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.17286e23i | 0.328900i | ||||||||
\(686\) | 1.11858e24 | − | 9.68919e21i | 0.870791 | − | 0.00754280i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.22678e22 | + | 2.37350e24i | 0.0624782 | + | 1.80255i | ||||
\(689\) | 1.50278e24 | 1.12728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.07548e24i | − | 0.787114i | −0.919300 | − | 0.393557i | \(-0.871244\pi\) | ||
0.919300 | − | 0.393557i | \(-0.128756\pi\) | |||||||
\(692\) | −2.23857e22 | − | 1.29208e24i | −0.0161834 | − | 0.934088i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.46596e22 | − | 1.69240e24i | −0.0103411 | − | 1.19384i | ||||
\(695\) | −1.71094e23 | −0.119224 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.86087e24 | 1.94545 | ||||||||
\(698\) | −1.48111e22 | − | 1.70989e24i | −0.00994985 | − | 1.14868i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.18317e23 | + | 5.51495e21i | −0.208702 | + | 0.00361583i | ||||
\(701\) | − | 4.83049e23i | − | 0.312887i | −0.987687 | − | 0.156444i | \(-0.949997\pi\) | ||
0.987687 | − | 0.156444i | \(-0.0500030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14654e24 | −1.35712 | ||||||||
\(704\) | −2.31450e22 | − | 4.44946e23i | −0.0144574 | − | 0.277933i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.55642e24 | − | 1.34818e22i | 0.949048 | − | 0.00822066i | ||||
\(707\) | − | 2.88089e23i | − | 0.173565i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.46817e23i | 0.380442i | 0.981741 | + | 0.190221i | \(0.0609204\pi\) | ||||
−0.981741 | + | 0.190221i | \(0.939080\pi\) | |||||||
\(710\) | 1.91673e22 | + | 2.21280e24i | 0.0111395 | + | 1.28601i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.06339e24 | + | 2.76389e22i | −0.603412 | + | 0.0156834i | ||||
\(713\) | −8.75904e22 | −0.0491129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 6.25030e23i | − | 0.342215i | ||||||
\(716\) | 2.39247e22 | + | 1.38091e24i | 0.0129445 | + | 0.747145i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.90785e24 | − | 1.65258e22i | 1.00806 | − | 0.00873181i | ||||
\(719\) | 2.08660e24 | 1.08954 | 0.544770 | − | 0.838586i | \(-0.316617\pi\) | ||||
0.544770 | + | 0.838586i | \(0.316617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.57286e24 | 0.802124 | ||||||||
\(722\) | −1.69650e24 | + | 1.46951e22i | −0.855041 | + | 0.00740637i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.01277e22 | − | 3.47051e24i | −0.0296003 | − | 1.70850i | ||||
\(725\) | − | 1.13599e24i | − | 0.552713i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.50710e24 | 1.19160 | 0.595799 | − | 0.803134i | \(-0.296836\pi\) | ||||
0.595799 | + | 0.803134i | \(0.296836\pi\) | |||||||
\(728\) | −4.43634e22 | − | 1.70686e24i | −0.0208405 | − | 0.801828i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.13508e22 | + | 1.31041e24i | 0.00520934 | + | 0.601401i | ||||
\(731\) | − | 4.66482e24i | − | 2.11611i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.50202e24i | 1.10894i | 0.832205 | + | 0.554469i | \(0.187079\pi\) | ||||
−0.832205 | + | 0.554469i | \(0.812921\pi\) | |||||||
\(734\) | −2.67687e24 | + | 2.31871e22i | −1.17277 | + | 0.0101585i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.96516e24 | + | 8.51623e22i | −0.841272 | + | 0.0364574i | ||||
\(737\) | 7.20836e23 | 0.305044 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.98150e24i | 0.819440i | 0.912211 | + | 0.409720i | \(0.134374\pi\) | ||||
−0.912211 | + | 0.409720i | \(0.865626\pi\) | |||||||
\(740\) | −1.85549e24 | + | 3.21469e22i | −0.758558 | + | 0.0131423i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.51585e21 | + | 8.67680e23i | 0.00300293 | + | 0.346678i | ||||
\(743\) | 1.48113e24 | 0.585043 | 0.292521 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292521 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.40900e24 | 1.31613 | ||||||||
\(746\) | −1.08411e22 | − | 1.25157e24i | −0.00413803 | − | 0.477722i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.51599e22 | + | 8.75013e23i | 0.00565629 | + | 0.326476i | ||||
\(749\) | 1.27411e24i | 0.470013i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.06055e24 | −1.82498 | −0.912490 | − | 0.409100i | \(-0.865843\pi\) | ||||
−0.912490 | + | 0.409100i | \(0.865843\pi\) | |||||||
\(752\) | −1.41043e24 | + | 4.88868e22i | −0.502919 | + | 0.0174317i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.09222e24 | − | 5.27709e22i | 2.12383 | − | 0.0183966i | ||||
\(755\) | 1.00690e24i | 0.347085i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.15475e23i | − | 0.0389200i | −0.999811 | − | 0.0194600i | \(-0.993805\pi\) | ||
0.999811 | − | 0.0194600i | \(-0.00619470\pi\) | |||||||
\(758\) | 9.94849e21 | + | 1.14852e24i | 0.00331565 | + | 0.382781i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.18101e24 | + | 8.26782e22i | −1.03669 | + | 0.0269448i | ||||
\(761\) | 3.07347e24 | 0.990510 | 0.495255 | − | 0.868748i | \(-0.335075\pi\) | ||||
0.495255 | + | 0.868748i | \(0.335075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.09811e22i | − | 0.00976425i | ||||||
\(764\) | −3.05232e24 | + | 5.28824e22i | −0.951341 | + | 0.0164823i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.18734e24 | + | 1.02847e22i | −0.361934 | + | 0.00313507i | ||||
\(767\) | −1.56571e24 | −0.472008 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.56828e24 | 0.462434 | 0.231217 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231217 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(770\) | 3.60883e23 | − | 3.12597e21i | 0.105243 | − | 0.000911619i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.42345e22 | + | 5.93124e20i | −0.00976601 | + | 0.000169199i | ||||
\(773\) | − | 3.06812e24i | − | 0.865659i | −0.901476 | − | 0.432830i | \(-0.857515\pi\) | ||
0.901476 | − | 0.432830i | \(-0.142485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.88051e22 | 0.0245117 | ||||||||
\(776\) | −1.90205e24 | + | 4.94366e22i | −0.519275 | + | 0.0134966i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.44744e22 | − | 3.97995e24i | −0.00920810 | − | 1.06304i | ||||
\(779\) | 8.54827e24i | 2.25845i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.81847e24i | 0.470082i | ||||||||
\(782\) | 3.86345e24 | − | 3.34652e22i | 0.987910 | − | 0.00855729i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00887e24 | + | 1.04291e23i | −0.752865 | + | 0.0260951i | ||||
\(785\) | 4.20181e24 | 1.04003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.03196e23i | 0.170330i | 0.996367 | + | 0.0851650i | \(0.0271417\pi\) | ||||
−0.996367 | + | 0.0851650i | \(0.972858\pi\) | |||||||
\(788\) | 1.46733e22 | + | 8.46930e23i | 0.00351606 | + | 0.202943i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.21900e22 | − | 2.56176e24i | −0.00520387 | − | 0.600770i | ||||
\(791\) | 2.14495e23 | 0.0497642 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.13835e24 | −0.712656 | ||||||||
\(794\) | 2.82573e22 | + | 3.26221e24i | 0.00634828 | + | 0.732888i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.38843e24 | + | 4.13803e22i | −0.525232 | + | 0.00909981i | ||||
\(797\) | − | 4.69599e24i | − | 1.02172i | −0.859664 | − | 0.510859i | \(-0.829327\pi\) | ||
0.859664 | − | 0.510859i | \(-0.170673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.77202e24 | 0.590403 | ||||||||
\(800\) | 1.99241e24 | − | 8.63434e22i | 0.419870 | − | 0.0181955i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.80142e24 | + | 3.29279e22i | −0.784267 | + | 0.00679333i | ||||
\(803\) | 1.07690e24i | 0.219832i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.59329e24i | − | 0.318441i | ||||||
\(806\) | 4.12534e21 | + | 4.76256e23i | 0.000815852 | + | 0.0941874i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.68887e22 | + | 1.80402e24i | 0.00907970 | + | 0.349337i | ||||
\(809\) | 4.37783e24 | 0.838873 | 0.419436 | − | 0.907785i | \(-0.362228\pi\) | ||||
0.419436 | + | 0.907785i | \(0.362228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.61180e24i | − | 1.61591i | −0.589245 | − | 0.807954i | \(-0.700575\pi\) | ||
0.589245 | − | 0.807954i | \(-0.299425\pi\) | |||||||
\(812\) | 6.09382e22 | + | 3.51729e24i | 0.0113152 | + | 0.653104i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.52495e24 | + | 1.32091e22i | −0.277299 | + | 0.00240197i | ||||
\(815\) | −5.07238e24 | −0.912793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.39385e25 | 2.45656 | ||||||||
\(818\) | 2.12343e24 | − | 1.83931e22i | 0.370369 | − | 0.00320814i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.28020e23 | + | 7.38920e24i | 0.0218706 | + | 1.26235i | ||||
\(821\) | − | 4.09648e24i | − | 0.692619i | −0.938120 | − | 0.346309i | \(-0.887435\pi\) | ||
0.938120 | − | 0.346309i | \(-0.112565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.02308e24 | −0.666284 | −0.333142 | − | 0.942877i | \(-0.608109\pi\) | ||||
−0.333142 | + | 0.942877i | \(0.608109\pi\) | |||||||
\(824\) | −9.84932e24 | + | 2.55996e23i | −1.61445 | + | 0.0419616i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.83059e21 | − | 9.04015e23i | −0.00125737 | − | 0.145160i | ||||
\(827\) | − | 6.80277e24i | − | 1.08116i | −0.841294 | − | 0.540579i | \(-0.818205\pi\) | ||
0.841294 | − | 0.540579i | \(-0.181795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9.06827e24i | − | 1.41192i | −0.708251 | − | 0.705961i | \(-0.750515\pi\) | ||
0.708251 | − | 0.705961i | \(-0.249485\pi\) | |||||||
\(830\) | −2.26057e24 | + | 1.95810e22i | −0.348380 | + | 0.00301767i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.55610e23 | + | 1.06812e25i | 0.0838922 | + | 1.61277i | ||||
\(833\) | 5.91357e24 | 0.883827 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.05790e24i | 0.740687i | ||||||||
\(836\) | −2.61454e24 | + | 4.52977e22i | −0.379002 | + | 0.00656633i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.57509e22 | − | 1.81838e24i | −0.00223733 | − | 0.258292i | ||||
\(839\) | 2.26281e24 | 0.318179 | 0.159090 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159090 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.29508e24 | −0.729637 | ||||||||
\(842\) | −4.88833e22 | − | 5.64341e24i | −0.00666818 | − | 0.769819i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.75707e23 | − | 1.01416e25i | −0.0234897 | − | 1.35580i | ||||
\(845\) | 9.25117e24i | 1.22438i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.53237e24 | −0.458202 | ||||||||
\(848\) | −1.88286e23 | − | 5.43221e24i | −0.0241798 | − | 0.697609i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.91703e24 | + | 3.39293e22i | −0.493055 | + | 0.00427085i | ||||
\(851\) | 6.73262e24i | 0.839040i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.22743e24i | 1.12723i | 0.826036 | + | 0.563617i | \(0.190591\pi\) | ||||
−0.826036 | + | 0.563617i | \(0.809409\pi\) | |||||||
\(854\) | −1.56959e22 | − | 1.81204e24i | −0.00189843 | − | 0.219167i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.07371e23 | − | 7.97849e24i | −0.0245878 | − | 0.946005i | ||||
\(857\) | −4.23968e24 | −0.497733 | −0.248867 | − | 0.968538i | \(-0.580058\pi\) | ||||
−0.248867 | + | 0.968538i | \(0.580058\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.28165e24i | 0.262608i | 0.991342 | + | 0.131304i | \(0.0419164\pi\) | ||||
−0.991342 | + | 0.131304i | \(0.958084\pi\) | |||||||
\(860\) | 1.20485e25 | − | 2.08745e23i | 1.37309 | − | 0.0237891i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.00846e25 | − | 8.73528e22i | 1.12680 | − | 0.00976034i | ||||
\(863\) | 1.03258e25 | 1.14244 | 0.571220 | − | 0.820797i | \(-0.306470\pi\) | ||||
0.571220 | + | 0.820797i | \(0.306470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.55700e24 | −0.711325 | ||||||||
\(866\) | −4.50612e23 | + | 3.90320e21i | −0.0484061 | + | 0.000419294i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.74963e23 | + | 4.76381e21i | −0.0289638 | + | 0.000501807i | ||||
\(869\) | − | 2.10525e24i | − | 0.219602i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.73041e25 | −1.77009 | ||||||||
\(872\) | 5.04242e21 | + | 1.94005e23i | 0.000510798 | + | 0.0196527i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.99940e22 | + | 1.15440e25i | 0.00993406 | + | 1.14685i | ||||
\(875\) | 5.45912e24i | 0.537099i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.49582e24i | 0.144338i | 0.997392 | + | 0.0721692i | \(0.0229921\pi\) | ||||
−0.997392 | + | 0.0721692i | \(0.977008\pi\) | |||||||
\(878\) | −7.58855e24 | + | 6.57321e22i | −0.725196 | + | 0.00628166i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.25935e24 | + | 7.83114e22i | −0.211778 | + | 0.00734044i | ||||
\(881\) | −9.02128e24 | −0.837477 | −0.418739 | − | 0.908107i | \(-0.637528\pi\) | ||||
−0.418739 | + | 0.908107i | \(0.637528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.61859e24i | − | 0.511636i | −0.966725 | − | 0.255818i | \(-0.917655\pi\) | ||
0.966725 | − | 0.255818i | \(-0.0823448\pi\) | |||||||
\(884\) | −3.63922e23 | − | 2.10052e25i | −0.0328219 | − | 1.89445i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.51146e22 | + | 4.05387e24i | 0.00310672 | + | 0.358660i | ||||
\(887\) | −1.48729e25 | −1.30330 | −0.651649 | − | 0.758521i | \(-0.725922\pi\) | ||||
−0.651649 | + | 0.758521i | \(0.725922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.94267e23 | 0.0682813 | ||||||||
\(890\) | 4.67512e22 | + | 5.39728e24i | 0.00398087 | + | 0.459578i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.76339e25 | + | 3.05513e23i | −1.47315 | + | 0.0255228i | ||||
\(893\) | 8.28280e24i | 0.685393i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.00778e24 | 0.568964 | ||||||||
\(896\) | −6.16438e24 | + | 3.74221e23i | −0.495760 | + | 0.0300961i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.22039e24 | − | 4.52191e22i | 0.411959 | − | 0.00356839i | ||||
\(899\) | − | 9.81264e23i | − | 0.0767059i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.06764e25i | 0.818959i | ||||||||
\(902\) | 5.26034e22 | + | 6.07288e24i | 0.00399722 | + | 0.461466i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.34317e24 | + | 3.49107e22i | −0.100161 | + | 0.00260332i | ||||
\(905\) | −1.76120e25 | −1.30106 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.26650e25i | − | 0.918215i | −0.888381 | − | 0.459107i | \(-0.848169\pi\) | ||
0.888381 | − | 0.459107i | \(-0.151831\pi\) | |||||||
\(908\) | 1.80633e23 | + | 1.04260e25i | 0.0129738 | + | 0.748836i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.66321e24 | + | 7.50407e22i | −0.610698 | + | 0.00528987i | ||||
\(911\) | −2.22052e25 | −1.55077 | −0.775387 | − | 0.631487i | \(-0.782445\pi\) | ||||
−0.775387 | + | 0.631487i | \(0.782445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.85773e24 | −0.127345 | ||||||||
\(914\) | 1.08553e25 | − | 9.40291e22i | 0.737227 | − | 0.00638586i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.86503e22 | + | 4.53962e24i | 0.00524311 | + | 0.302627i | ||||
\(917\) | 5.92572e24i | 0.391383i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.34055e25 | −1.51753 | −0.758763 | − | 0.651367i | \(-0.774196\pi\) | ||||
−0.758763 | + | 0.651367i | \(0.774196\pi\) | |||||||
\(920\) | 2.59320e23 | + | 9.97721e24i | 0.0166586 | + | 0.640933i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.35691e23 | − | 1.56650e25i | −0.00855731 | − | 0.987912i | ||||
\(923\) | − | 4.36536e25i | − | 2.72775i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.82599e24i | − | 0.418756i | ||||||
\(926\) | −6.51374e24 | + | 5.64221e22i | −0.395947 | + | 0.00342970i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.54063e23 | − | 2.20155e25i | −0.0569402 | − | 1.31392i | ||||
\(929\) | −6.30561e24 | −0.372901 | −0.186450 | − | 0.982464i | \(-0.559698\pi\) | ||||
−0.186450 | + | 0.982464i | \(0.559698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76697e25i | 1.02603i | ||||||||
\(932\) | 1.59265e25 | − | 2.75932e23i | 0.916401 | − | 0.0158769i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.73591e23 | + | 2.00405e25i | 0.00980795 | + | 1.13229i | ||||
\(935\) | 4.44048e24 | 0.248617 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.24230e23 | −0.0453171 | −0.0226586 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226586 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(938\) | −8.65432e22 | − | 9.99113e24i | −0.00471529 | − | 0.544365i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.24044e23 | + | 7.15972e24i | 0.00663728 | + | 0.383097i | ||||
\(941\) | 6.73452e24i | 0.357104i | 0.983930 | + | 0.178552i | \(0.0571413\pi\) | ||||
−0.983930 | + | 0.178552i | \(0.942859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.68116e25 | 1.39628 | ||||||||
\(944\) | 1.96171e23 | + | 5.65970e24i | 0.0101245 | + | 0.292100i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.90221e24 | − | 8.57730e22i | 0.501947 | − | 0.00434787i | ||||
\(947\) | 2.19407e25i | 1.10224i | 0.834426 | + | 0.551119i | \(0.185799\pi\) | ||||
−0.834426 | + | 0.551119i | \(0.814201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.58515e25i | − | 1.27563i | ||||||
\(950\) | −1.01381e23 | − | 1.17041e25i | −0.00495798 | − | 0.572383i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.21263e25 | − | 3.15177e23i | 0.582523 | − | 0.0151405i | ||||
\(953\) | −1.04120e25 | −0.495727 | −0.247864 | − | 0.968795i | \(-0.579728\pi\) | ||||
−0.247864 | + | 0.968795i | \(0.579728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.54898e25i | 0.724464i | ||||||||
\(956\) | 2.95980e24 | − | 5.12795e22i | 0.137205 | − | 0.00237712i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.27580e24 | − | 3.70370e22i | 0.194720 | − | 0.00168667i | ||||
\(959\) | 4.75310e24 | 0.214545 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.24734e25 | −0.996598 | ||||||||
\(962\) | 3.66074e25 | − | 3.17093e23i | 1.60909 | − | 0.0139380i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.74315e25 | − | 6.48512e23i | 1.61652 | − | 0.0280068i | ||||
\(965\) | 1.73732e23i | 0.00743700i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.11036e25 | 0.887630 | 0.443815 | − | 0.896118i | \(-0.353625\pi\) | ||||
0.443815 | + | 0.896118i | \(0.353625\pi\) | |||||||
\(968\) | 2.21198e25 | − | 5.74921e23i | 0.922233 | − | 0.0239700i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.36221e22 | + | 9.65389e24i | 0.00342579 | + | 0.395497i | ||||
\(971\) | − | 6.24704e24i | − | 0.253694i | −0.991922 | − | 0.126847i | \(-0.959514\pi\) | ||
0.991922 | − | 0.126847i | \(-0.0404858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.94885e24i | 0.0777713i | ||||||||
\(974\) | 7.84480e24 | − | 6.79517e22i | 0.310335 | − | 0.00268812i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.93211e23 | + | 1.13445e25i | 0.0152863 | + | 0.441023i | ||||
\(977\) | 1.86564e25 | 0.718992 | 0.359496 | − | 0.933147i | \(-0.382949\pi\) | ||||
0.359496 | + | 0.933147i | \(0.382949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.43547e24i | 0.167991i | ||||||||
\(980\) | 2.64625e23 | + | 1.52739e25i | 0.00993593 | + | 0.573492i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.08493e23 | − | 4.71592e25i | −0.0150743 | − | 1.74028i | ||||
\(983\) | 2.39881e25 | 0.877589 | 0.438794 | − | 0.898588i | \(-0.355406\pi\) | ||||
0.438794 | + | 0.898588i | \(0.355406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.29797e24 | 0.154545 | ||||||||
\(986\) | 3.74907e23 | + | 4.32817e25i | 0.0133650 | + | 1.54295i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.27635e25 | − | 1.08740e24i | 2.19924 | − | 0.0381026i | ||||
\(989\) | − | 4.37180e25i | − | 1.51877i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85777e25 | 0.975889 | 0.487945 | − | 0.872875i | \(-0.337747\pi\) | ||||
0.487945 | + | 0.872875i | \(0.337747\pi\) | |||||||
\(992\) | 1.72105e24 | − | 7.45834e22i | 0.0582698 | − | 0.00252518i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.52049e25 | − | 2.18325e23i | 0.838882 | − | 0.00726640i | ||||
\(995\) | 1.21207e25i | 0.399974i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.00050e25i | − | 0.324571i | −0.986744 | − | 0.162285i | \(-0.948113\pi\) | ||
0.986744 | − | 0.162285i | \(-0.0518865\pi\) | |||||||
\(998\) | −1.62211e23 | − | 1.87267e25i | −0.00521759 | − | 0.602353i | ||||
\(999\) | 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 | 72.18.d.b.37.15 | 16 | ||
3.2 | odd | 2 | 8.18.b.a.5.2 | yes | 16 | ||
8.5 | even | 2 | inner | 72.18.d.b.37.16 | 16 | ||
12.11 | even | 2 | 32.18.b.a.17.14 | 16 | |||
24.5 | odd | 2 | 8.18.b.a.5.1 | ✓ | 16 | ||
24.11 | even | 2 | 32.18.b.a.17.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.1 | ✓ | 16 | 24.5 | odd | 2 | ||
8.18.b.a.5.2 | yes | 16 | 3.2 | odd | 2 | ||
32.18.b.a.17.3 | 16 | 24.11 | even | 2 | |||
32.18.b.a.17.14 | 16 | 12.11 | even | 2 | |||
72.18.d.b.37.15 | 16 | 1.1 | even | 1 | trivial | ||
72.18.d.b.37.16 | 16 | 8.5 | even | 2 | inner |