Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,18,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (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: | \(14.6577669876\) |
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: | \( x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} + \cdots + 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{120}\cdot 3^{14}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.15 | ||
Root | \(167.908 + 42.7144i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.18.b.a.5.16 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 351.815 | − | 85.4288i | 0.971761 | − | 0.235966i | ||||
\(3\) | − | 21682.7i | − | 1.90802i | −0.299780 | − | 0.954008i | \(-0.596913\pi\) | ||
0.299780 | − | 0.954008i | \(-0.403087\pi\) | |||||||
\(4\) | 116476. | − | 60110.3i | 0.888640 | − | 0.458605i | ||||
\(5\) | − | 465248.i | − | 0.532647i | −0.963884 | − | 0.266324i | \(-0.914191\pi\) | ||
0.963884 | − | 0.266324i | \(-0.0858090\pi\) | |||||||
\(6\) | −1.85232e6 | − | 7.62829e6i | −0.450227 | − | 1.85414i | ||||
\(7\) | 2.24795e7 | 1.47385 | 0.736926 | − | 0.675973i | \(-0.236276\pi\) | ||||
0.736926 | + | 0.675973i | \(0.236276\pi\) | |||||||
\(8\) | 3.58428e7 | − | 3.10981e7i | 0.755331 | − | 0.655343i | ||||
\(9\) | −3.40998e8 | −2.64053 | ||||||||
\(10\) | −3.97456e7 | − | 1.63681e8i | −0.125687 | − | 0.517606i | ||||
\(11\) | 6.06148e8i | 0.852592i | 0.904584 | + | 0.426296i | \(0.140182\pi\) | ||||
−0.904584 | + | 0.426296i | \(0.859818\pi\) | |||||||
\(12\) | −1.30335e9 | − | 2.52551e9i | −0.875026 | − | 1.69554i | ||||
\(13\) | 2.12768e9i | 0.723417i | 0.932291 | + | 0.361708i | \(0.117806\pi\) | ||||
−0.932291 | + | 0.361708i | \(0.882194\pi\) | |||||||
\(14\) | 7.90864e9 | − | 1.92040e9i | 1.43223 | − | 0.347779i | ||||
\(15\) | −1.00878e10 | −1.01630 | ||||||||
\(16\) | 9.95338e9 | − | 1.40028e10i | 0.579363 | − | 0.815070i | ||||
\(17\) | −5.45139e9 | −0.189536 | −0.0947680 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947680 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(18\) | −1.19968e11 | + | 2.91311e10i | −2.56596 | + | 0.623075i | ||||
\(19\) | 5.72346e9i | 0.0773131i | 0.999253 | + | 0.0386565i | \(0.0123078\pi\) | ||||
−0.999253 | + | 0.0386565i | \(0.987692\pi\) | |||||||
\(20\) | −2.79662e10 | − | 5.41902e10i | −0.244275 | − | 0.473332i | ||||
\(21\) | − | 4.87417e11i | − | 2.81214i | ||||||
\(22\) | 5.17825e10 | + | 2.13252e11i | 0.201183 | + | 0.828515i | ||||
\(23\) | −1.30247e11 | −0.346802 | −0.173401 | − | 0.984851i | \(-0.555476\pi\) | ||||
−0.173401 | + | 0.984851i | \(0.555476\pi\) | |||||||
\(24\) | −6.74290e11 | − | 7.77168e11i | −1.25041 | − | 1.44118i | ||||
\(25\) | 5.46483e11 | 0.716287 | ||||||||
\(26\) | 1.81765e11 | + | 7.48551e11i | 0.170702 | + | 0.702988i | ||||
\(27\) | 4.59365e12i | 3.13016i | ||||||||
\(28\) | 2.61832e12 | − | 1.35125e12i | 1.30972 | − | 0.675916i | ||||
\(29\) | − | 4.23568e11i | − | 0.157232i | −0.996905 | − | 0.0786159i | \(-0.974950\pi\) | ||
0.996905 | − | 0.0786159i | \(-0.0250501\pi\) | |||||||
\(30\) | −3.54905e12 | + | 8.61791e11i | −0.987601 | + | 0.239812i | ||||
\(31\) | 3.83783e12 | 0.808187 | 0.404093 | − | 0.914718i | \(-0.367587\pi\) | ||||
0.404093 | + | 0.914718i | \(0.367587\pi\) | |||||||
\(32\) | 2.30551e12 | − | 5.77670e12i | 0.370674 | − | 0.928763i | ||||
\(33\) | 1.31429e13 | 1.62676 | ||||||||
\(34\) | −1.91788e12 | + | 4.65706e11i | −0.184184 | + | 0.0447240i | ||||
\(35\) | − | 1.04586e13i | − | 0.785044i | ||||||
\(36\) | −3.97181e13 | + | 2.04975e13i | −2.34648 | + | 1.21096i | ||||
\(37\) | 2.39674e13i | 1.12178i | 0.827891 | + | 0.560889i | \(0.189541\pi\) | ||||
−0.827891 | + | 0.560889i | \(0.810459\pi\) | |||||||
\(38\) | 4.88948e11 | + | 2.01360e12i | 0.0182432 | + | 0.0751299i | ||||
\(39\) | 4.61339e13 | 1.38029 | ||||||||
\(40\) | −1.44683e13 | − | 1.66758e13i | −0.349067 | − | 0.402325i | ||||
\(41\) | −5.79528e12 | −0.113347 | −0.0566737 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566737 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(42\) | −4.16394e13 | − | 1.71481e14i | −0.663568 | − | 2.73272i | ||||
\(43\) | − | 4.00069e13i | − | 0.521979i | −0.965342 | − | 0.260989i | \(-0.915951\pi\) | ||
0.965342 | − | 0.260989i | \(-0.0840488\pi\) | |||||||
\(44\) | 3.64357e13 | + | 7.06016e13i | 0.391003 | + | 0.757647i | ||||
\(45\) | 1.58649e14i | 1.40647i | ||||||||
\(46\) | −4.58229e13 | + | 1.11268e13i | −0.337008 | + | 0.0818333i | ||||
\(47\) | −1.56837e14 | −0.960765 | −0.480382 | − | 0.877059i | \(-0.659502\pi\) | ||||
−0.480382 | + | 0.877059i | \(0.659502\pi\) | |||||||
\(48\) | −3.03618e14 | − | 2.15816e14i | −1.55517 | − | 1.10543i | ||||
\(49\) | 2.72699e14 | 1.17224 | ||||||||
\(50\) | 1.92261e14 | − | 4.66854e13i | 0.696060 | − | 0.169019i | ||||
\(51\) | 1.18201e14i | 0.361638i | ||||||||
\(52\) | 1.27896e14 | + | 2.47824e14i | 0.331763 | + | 0.642857i | ||||
\(53\) | − | 6.45318e14i | − | 1.42374i | −0.702314 | − | 0.711868i | \(-0.747850\pi\) | ||
0.702314 | − | 0.711868i | \(-0.252150\pi\) | |||||||
\(54\) | 3.92430e14 | + | 1.61612e15i | 0.738610 | + | 3.04176i | ||||
\(55\) | 2.82010e14 | 0.454131 | ||||||||
\(56\) | 8.05730e14 | − | 6.99071e14i | 1.11325 | − | 0.965880i | ||||
\(57\) | 1.24100e14 | 0.147515 | ||||||||
\(58\) | −3.61849e13 | − | 1.49018e14i | −0.0371013 | − | 0.152792i | ||||
\(59\) | 8.37680e14i | 0.742739i | 0.928485 | + | 0.371369i | \(0.121112\pi\) | ||||
−0.928485 | + | 0.371369i | \(0.878888\pi\) | |||||||
\(60\) | −1.17499e15 | + | 6.06382e14i | −0.903125 | + | 0.466081i | ||||
\(61\) | − | 3.98624e14i | − | 0.266232i | −0.991100 | − | 0.133116i | \(-0.957502\pi\) | ||
0.991100 | − | 0.133116i | \(-0.0424983\pi\) | |||||||
\(62\) | 1.35021e15 | − | 3.27862e14i | 0.785365 | − | 0.190705i | ||||
\(63\) | −7.66548e15 | −3.89175 | ||||||||
\(64\) | 3.17616e14 | − | 2.22929e15i | 0.141050 | − | 0.990002i | ||||
\(65\) | 9.89901e14 | 0.385326 | ||||||||
\(66\) | 4.62388e15 | − | 1.12278e15i | 1.58082 | − | 0.383860i | ||||
\(67\) | − | 5.22273e15i | − | 1.57131i | −0.618665 | − | 0.785655i | \(-0.712326\pi\) | ||
0.618665 | − | 0.785655i | \(-0.287674\pi\) | |||||||
\(68\) | −6.34956e14 | + | 3.27685e14i | −0.168429 | + | 0.0869222i | ||||
\(69\) | 2.82410e15i | 0.661703i | ||||||||
\(70\) | −8.93463e14 | − | 3.67948e15i | −0.185244 | − | 0.762875i | ||||
\(71\) | 5.50116e15 | 1.01102 | 0.505508 | − | 0.862822i | \(-0.331305\pi\) | ||||
0.505508 | + | 0.862822i | \(0.331305\pi\) | |||||||
\(72\) | −1.22223e16 | + | 1.06044e16i | −1.99447 | + | 1.73045i | ||||
\(73\) | 1.47400e15 | 0.213921 | 0.106960 | − | 0.994263i | \(-0.465888\pi\) | ||||
0.106960 | + | 0.994263i | \(0.465888\pi\) | |||||||
\(74\) | 2.04751e15 | + | 8.43211e15i | 0.264701 | + | 1.09010i | ||||
\(75\) | − | 1.18492e16i | − | 1.36669i | ||||||
\(76\) | 3.44039e14 | + | 6.66645e14i | 0.0354562 | + | 0.0687035i | ||||
\(77\) | 1.36259e16i | 1.25659i | ||||||||
\(78\) | 1.62306e16 | − | 3.94116e15i | 1.34131 | − | 0.325702i | ||||
\(79\) | −1.94988e16 | −1.44603 | −0.723015 | − | 0.690833i | \(-0.757244\pi\) | ||||
−0.723015 | + | 0.690833i | \(0.757244\pi\) | |||||||
\(80\) | −6.51478e15 | − | 4.63079e15i | −0.434145 | − | 0.308596i | ||||
\(81\) | 5.55660e16 | 3.33186 | ||||||||
\(82\) | −2.03887e15 | + | 4.95084e14i | −0.110147 | + | 0.0267461i | ||||
\(83\) | 3.36599e16i | 1.64040i | 0.572078 | + | 0.820199i | \(0.306138\pi\) | ||||
−0.572078 | + | 0.820199i | \(0.693862\pi\) | |||||||
\(84\) | −2.92987e16 | − | 5.67723e16i | −1.28966 | − | 2.49898i | ||||
\(85\) | 2.53625e15i | 0.100956i | ||||||||
\(86\) | −3.41774e15 | − | 1.40750e16i | −0.123169 | − | 0.507239i | ||||
\(87\) | −9.18409e15 | −0.300001 | ||||||||
\(88\) | 1.88501e16 | + | 2.17261e16i | 0.558740 | + | 0.643989i | ||||
\(89\) | −1.09831e16 | −0.295740 | −0.147870 | − | 0.989007i | \(-0.547242\pi\) | ||||
−0.147870 | + | 0.989007i | \(0.547242\pi\) | |||||||
\(90\) | 1.35532e16 | + | 5.58151e16i | 0.331879 | + | 1.36675i | ||||
\(91\) | 4.78293e16i | 1.06621i | ||||||||
\(92\) | −1.51706e16 | + | 7.82918e15i | −0.308182 | + | 0.159045i | ||||
\(93\) | − | 8.32145e16i | − | 1.54203i | ||||||
\(94\) | −5.51777e16 | + | 1.33984e16i | −0.933634 | + | 0.226708i | ||||
\(95\) | 2.66283e15 | 0.0411806 | ||||||||
\(96\) | −1.25254e17 | − | 4.99896e16i | −1.77210 | − | 0.707251i | ||||
\(97\) | 6.57395e16 | 0.851660 | 0.425830 | − | 0.904803i | \(-0.359982\pi\) | ||||
0.425830 | + | 0.904803i | \(0.359982\pi\) | |||||||
\(98\) | 9.59397e16 | − | 2.32964e16i | 1.13914 | − | 0.276609i | ||||
\(99\) | − | 2.06695e17i | − | 2.25129i | ||||||
\(100\) | 6.36521e16 | − | 3.28493e16i | 0.636521 | − | 0.328493i | ||||
\(101\) | 7.10748e16i | 0.653106i | 0.945179 | + | 0.326553i | \(0.105887\pi\) | ||||
−0.945179 | + | 0.326553i | \(0.894113\pi\) | |||||||
\(102\) | 1.00977e16 | + | 4.15848e16i | 0.0853342 | + | 0.351426i | ||||
\(103\) | −1.91977e17 | −1.49325 | −0.746624 | − | 0.665246i | \(-0.768327\pi\) | ||||
−0.746624 | + | 0.665246i | \(0.768327\pi\) | |||||||
\(104\) | 6.61669e16 | + | 7.62622e16i | 0.474086 | + | 0.546419i | ||||
\(105\) | −2.26770e17 | −1.49788 | ||||||||
\(106\) | −5.51288e16 | − | 2.27033e17i | −0.335953 | − | 1.38353i | ||||
\(107\) | 5.53132e16i | 0.311220i | 0.987819 | + | 0.155610i | \(0.0497342\pi\) | ||||
−0.987819 | + | 0.155610i | \(0.950266\pi\) | |||||||
\(108\) | 2.76126e17 | + | 5.35049e17i | 1.43551 | + | 2.78158i | ||||
\(109\) | 3.67908e17i | 1.76854i | 0.466978 | + | 0.884269i | \(0.345343\pi\) | ||||
−0.466978 | + | 0.884269i | \(0.654657\pi\) | |||||||
\(110\) | 9.92152e16 | − | 2.40917e16i | 0.441307 | − | 0.107159i | ||||
\(111\) | 5.19678e17 | 2.14037 | ||||||||
\(112\) | 2.23747e17 | − | 3.14776e17i | 0.853895 | − | 1.20129i | ||||
\(113\) | −3.48457e17 | −1.23306 | −0.616528 | − | 0.787333i | \(-0.711461\pi\) | ||||
−0.616528 | + | 0.787333i | \(0.711461\pi\) | |||||||
\(114\) | 4.36602e16 | − | 1.06017e16i | 0.143349 | − | 0.0348084i | ||||
\(115\) | 6.05972e16i | 0.184723i | ||||||||
\(116\) | −2.54608e16 | − | 4.93355e16i | −0.0721073 | − | 0.139723i | ||||
\(117\) | − | 7.25536e17i | − | 1.91020i | ||||||
\(118\) | 7.15620e16 | + | 2.94708e17i | 0.175261 | + | 0.721765i | ||||
\(119\) | −1.22545e17 | −0.279348 | ||||||||
\(120\) | −3.61576e17 | + | 3.13712e17i | −0.767643 | + | 0.666026i | ||||
\(121\) | 1.38031e17 | 0.273088 | ||||||||
\(122\) | −3.40540e16 | − | 1.40242e17i | −0.0628217 | − | 0.258714i | ||||
\(123\) | 1.25657e17i | 0.216269i | ||||||||
\(124\) | 4.47015e17 | − | 2.30693e17i | 0.718187 | − | 0.370639i | ||||
\(125\) | − | 6.09207e17i | − | 0.914176i | ||||||
\(126\) | −2.69683e18 | + | 6.54853e17i | −3.78185 | + | 0.918320i | ||||
\(127\) | 5.29745e17 | 0.694600 | 0.347300 | − | 0.937754i | \(-0.387099\pi\) | ||||
0.347300 | + | 0.937754i | \(0.387099\pi\) | |||||||
\(128\) | −7.87032e16 | − | 8.11431e17i | −0.0965401 | − | 0.995329i | ||||
\(129\) | −8.67456e17 | −0.995944 | ||||||||
\(130\) | 3.48262e17 | − | 8.45661e16i | 0.374445 | − | 0.0909238i | ||||
\(131\) | 1.11774e18i | 1.12599i | 0.826459 | + | 0.562996i | \(0.190351\pi\) | ||||
−0.826459 | + | 0.562996i | \(0.809649\pi\) | |||||||
\(132\) | 1.53083e18 | − | 7.90024e17i | 1.44560 | − | 0.746040i | ||||
\(133\) | 1.28661e17i | 0.113948i | ||||||||
\(134\) | −4.46171e17 | − | 1.83744e18i | −0.370775 | − | 1.52694i | ||||
\(135\) | 2.13719e18 | 1.66727 | ||||||||
\(136\) | −1.95393e17 | + | 1.69528e17i | −0.143162 | + | 0.124211i | ||||
\(137\) | 6.75639e17 | 0.465146 | 0.232573 | − | 0.972579i | \(-0.425285\pi\) | ||||
0.232573 | + | 0.972579i | \(0.425285\pi\) | |||||||
\(138\) | 2.41260e17 | + | 9.93562e17i | 0.156139 | + | 0.643018i | ||||
\(139\) | 1.43378e18i | 0.872686i | 0.899780 | + | 0.436343i | \(0.143727\pi\) | ||||
−0.899780 | + | 0.436343i | \(0.856273\pi\) | |||||||
\(140\) | −6.28668e17 | − | 1.21817e18i | −0.360025 | − | 0.697622i | ||||
\(141\) | 3.40065e18i | 1.83316i | ||||||||
\(142\) | 1.93539e18 | − | 4.69957e17i | 0.982467 | − | 0.238565i | ||||
\(143\) | −1.28969e18 | −0.616779 | ||||||||
\(144\) | −3.39408e18 | + | 4.77493e18i | −1.52982 | + | 2.15221i | ||||
\(145\) | −1.97064e17 | −0.0837491 | ||||||||
\(146\) | 5.18575e17 | − | 1.25922e17i | 0.207880 | − | 0.0504780i | ||||
\(147\) | − | 5.91285e18i | − | 2.23666i | ||||||
\(148\) | 1.44069e18 | + | 2.79163e18i | 0.514453 | + | 0.996857i | ||||
\(149\) | − | 2.92569e18i | − | 0.986608i | −0.869857 | − | 0.493304i | \(-0.835789\pi\) | ||
0.869857 | − | 0.493304i | \(-0.164211\pi\) | |||||||
\(150\) | −1.01226e18 | − | 4.16874e18i | −0.322492 | − | 1.32809i | ||||
\(151\) | 3.38847e18 | 1.02023 | 0.510117 | − | 0.860105i | \(-0.329602\pi\) | ||||
0.510117 | + | 0.860105i | \(0.329602\pi\) | |||||||
\(152\) | 1.77989e17 | + | 2.05145e17i | 0.0506666 | + | 0.0583970i | ||||
\(153\) | 1.85892e18 | 0.500475 | ||||||||
\(154\) | 1.16405e18 | + | 4.79381e18i | 0.296513 | + | 1.22111i | ||||
\(155\) | − | 1.78555e18i | − | 0.430479i | ||||||
\(156\) | 5.37348e18 | − | 2.77312e18i | 1.22658 | − | 0.633009i | ||||
\(157\) | 3.55208e18i | 0.767954i | 0.923343 | + | 0.383977i | \(0.125446\pi\) | ||||
−0.923343 | + | 0.383977i | \(0.874554\pi\) | |||||||
\(158\) | −6.85997e18 | + | 1.66576e18i | −1.40520 | + | 0.341214i | ||||
\(159\) | −1.39922e19 | −2.71651 | ||||||||
\(160\) | −2.68760e18 | − | 1.07263e18i | −0.494703 | − | 0.197438i | ||||
\(161\) | −2.92789e18 | −0.511134 | ||||||||
\(162\) | 1.95490e19 | − | 4.74694e18i | 3.23777 | − | 0.786205i | ||||
\(163\) | 6.81975e18i | 1.07195i | 0.844234 | + | 0.535974i | \(0.180056\pi\) | ||||
−0.844234 | + | 0.535974i | \(0.819944\pi\) | |||||||
\(164\) | −6.75010e17 | + | 3.48356e17i | −0.100725 | + | 0.0519817i | ||||
\(165\) | − | 6.11472e18i | − | 0.866489i | ||||||
\(166\) | 2.87553e18 | + | 1.18421e19i | 0.387078 | + | 1.59408i | ||||
\(167\) | −1.29136e19 | −1.65180 | −0.825899 | − | 0.563819i | \(-0.809332\pi\) | ||||
−0.825899 | + | 0.563819i | \(0.809332\pi\) | |||||||
\(168\) | −1.51577e19 | − | 1.74704e19i | −1.84291 | − | 2.12409i | ||||
\(169\) | 4.12338e18 | 0.476668 | ||||||||
\(170\) | 2.16669e17 | + | 8.92292e17i | 0.0238221 | + | 0.0981050i | ||||
\(171\) | − | 1.95169e18i | − | 0.204147i | ||||||
\(172\) | −2.40483e18 | − | 4.65984e18i | −0.239382 | − | 0.463851i | ||||
\(173\) | − | 2.98078e18i | − | 0.282448i | −0.989978 | − | 0.141224i | \(-0.954896\pi\) | ||
0.989978 | − | 0.141224i | \(-0.0451037\pi\) | |||||||
\(174\) | −3.23110e18 | + | 7.84586e17i | −0.291529 | + | 0.0707900i | ||||
\(175\) | 1.22847e19 | 1.05570 | ||||||||
\(176\) | 8.48777e18 | + | 6.03322e18i | 0.694922 | + | 0.493960i | ||||
\(177\) | 1.81631e19 | 1.41716 | ||||||||
\(178\) | −3.86403e18 | + | 9.38274e17i | −0.287389 | + | 0.0697846i | ||||
\(179\) | 4.00351e18i | 0.283916i | 0.989873 | + | 0.141958i | \(0.0453398\pi\) | ||||
−0.989873 | + | 0.141958i | \(0.954660\pi\) | |||||||
\(180\) | 9.53643e18 | + | 1.84788e19i | 0.645015 | + | 1.24985i | ||||
\(181\) | − | 2.28445e19i | − | 1.47406i | −0.675861 | − | 0.737029i | \(-0.736228\pi\) | ||
0.675861 | − | 0.737029i | \(-0.263772\pi\) | |||||||
\(182\) | 4.08600e18 | + | 1.68271e19i | 0.251589 | + | 1.03610i | ||||
\(183\) | −8.64324e18 | −0.507975 | ||||||||
\(184\) | −4.66842e18 | + | 4.05043e18i | −0.261950 | + | 0.227274i | ||||
\(185\) | 1.11508e19 | 0.597512 | ||||||||
\(186\) | −7.10891e18 | − | 2.92761e19i | −0.363867 | − | 1.49849i | ||||
\(187\) | − | 3.30435e18i | − | 0.161597i | ||||||
\(188\) | −1.82677e19 | + | 9.42753e18i | −0.853774 | + | 0.440612i | ||||
\(189\) | 1.03263e20i | 4.61339i | ||||||||
\(190\) | 9.36824e17 | − | 2.27482e17i | 0.0400177 | − | 0.00971722i | ||||
\(191\) | 3.05570e19 | 1.24832 | 0.624162 | − | 0.781295i | \(-0.285441\pi\) | ||||
0.624162 | + | 0.781295i | \(0.285441\pi\) | |||||||
\(192\) | −4.83369e19 | − | 6.88676e18i | −1.88894 | − | 0.269125i | ||||
\(193\) | 2.24801e19 | 0.840547 | 0.420274 | − | 0.907397i | \(-0.361934\pi\) | ||||
0.420274 | + | 0.907397i | \(0.361934\pi\) | |||||||
\(194\) | 2.31281e19 | − | 5.61604e18i | 0.827611 | − | 0.200963i | ||||
\(195\) | − | 2.14637e19i | − | 0.735209i | ||||||
\(196\) | 3.17629e19 | − | 1.63920e19i | 1.04170 | − | 0.537596i | ||||
\(197\) | − | 5.40141e19i | − | 1.69646i | −0.529625 | − | 0.848232i | \(-0.677667\pi\) | ||
0.529625 | − | 0.848232i | \(-0.322333\pi\) | |||||||
\(198\) | −1.76577e19 | − | 7.27186e19i | −0.531228 | − | 2.18772i | ||||
\(199\) | −3.30197e18 | −0.0951747 | −0.0475874 | − | 0.998867i | \(-0.515153\pi\) | ||||
−0.0475874 | + | 0.998867i | \(0.515153\pi\) | |||||||
\(200\) | 1.95875e19 | − | 1.69946e19i | 0.541034 | − | 0.469414i | ||||
\(201\) | −1.13243e20 | −2.99808 | ||||||||
\(202\) | 6.07183e18 | + | 2.50052e19i | 0.154111 | + | 0.634663i | ||||
\(203\) | − | 9.52162e18i | − | 0.231737i | ||||||
\(204\) | 7.10508e18 | + | 1.37675e19i | 0.165849 | + | 0.321366i | ||||
\(205\) | 2.69624e18i | 0.0603742i | ||||||||
\(206\) | −6.75403e19 | + | 1.64003e19i | −1.45108 | + | 0.352356i | ||||
\(207\) | 4.44140e19 | 0.915739 | ||||||||
\(208\) | 2.97935e19 | + | 2.11776e19i | 0.589635 | + | 0.419121i | ||||
\(209\) | −3.46926e18 | −0.0659165 | ||||||||
\(210\) | −7.97811e19 | + | 1.93727e19i | −1.45558 | + | 0.353448i | ||||
\(211\) | 7.95957e19i | 1.39473i | 0.716718 | + | 0.697363i | \(0.245643\pi\) | ||||
−0.716718 | + | 0.697363i | \(0.754357\pi\) | |||||||
\(212\) | −3.87903e19 | − | 7.51640e19i | −0.652932 | − | 1.26519i | ||||
\(213\) | − | 1.19280e20i | − | 1.92904i | ||||||
\(214\) | 4.72534e18 | + | 1.94600e19i | 0.0734372 | + | 0.302431i | ||||
\(215\) | −1.86131e19 | −0.278031 | ||||||||
\(216\) | 1.42854e20 | + | 1.64649e20i | 2.05133 | + | 2.36430i | ||||
\(217\) | 8.62727e19 | 1.19115 | ||||||||
\(218\) | 3.14300e19 | + | 1.29436e20i | 0.417315 | + | 1.71860i | ||||
\(219\) | − | 3.19603e19i | − | 0.408164i | ||||||
\(220\) | 3.28473e19 | − | 1.69517e19i | 0.403559 | − | 0.208267i | ||||
\(221\) | − | 1.15988e19i | − | 0.137113i | ||||||
\(222\) | 1.82831e20 | − | 4.43955e19i | 2.07993 | − | 0.505055i | ||||
\(223\) | −7.18745e19 | −0.787015 | −0.393508 | − | 0.919321i | \(-0.628739\pi\) | ||||
−0.393508 | + | 0.919321i | \(0.628739\pi\) | |||||||
\(224\) | 5.18267e19 | − | 1.29858e20i | 0.546318 | − | 1.36886i | ||||
\(225\) | −1.86350e20 | −1.89138 | ||||||||
\(226\) | −1.22593e20 | + | 2.97683e19i | −1.19824 | + | 0.290959i | ||||
\(227\) | 1.07253e20i | 1.00969i | 0.863210 | + | 0.504845i | \(0.168450\pi\) | ||||
−0.863210 | + | 0.504845i | \(0.831550\pi\) | |||||||
\(228\) | 1.44546e19 | − | 7.45968e18i | 0.131087 | − | 0.0676510i | ||||
\(229\) | − | 8.55186e19i | − | 0.747238i | −0.927582 | − | 0.373619i | \(-0.878117\pi\) | ||
0.927582 | − | 0.373619i | \(-0.121883\pi\) | |||||||
\(230\) | 5.17674e18 | + | 2.13190e19i | 0.0435883 | + | 0.179507i | ||||
\(231\) | 2.95447e20 | 2.39760 | ||||||||
\(232\) | −1.31722e19 | − | 1.51819e19i | −0.103041 | − | 0.118762i | ||||
\(233\) | −1.65020e20 | −1.24455 | −0.622273 | − | 0.782801i | \(-0.713790\pi\) | ||||
−0.622273 | + | 0.782801i | \(0.713790\pi\) | |||||||
\(234\) | −6.19817e19 | − | 2.55255e20i | −0.450743 | − | 1.85626i | ||||
\(235\) | 7.29682e19i | 0.511749i | ||||||||
\(236\) | 5.03532e19 | + | 9.75695e19i | 0.340624 | + | 0.660027i | ||||
\(237\) | 4.22786e20i | 2.75905i | ||||||||
\(238\) | −4.31131e19 | + | 1.04689e19i | −0.271460 | + | 0.0659166i | ||||
\(239\) | −2.20002e20 | −1.33673 | −0.668367 | − | 0.743832i | \(-0.733006\pi\) | ||||
−0.668367 | + | 0.743832i | \(0.733006\pi\) | |||||||
\(240\) | −1.00408e20 | + | 1.41258e20i | −0.588807 | + | 0.828356i | ||||
\(241\) | 1.65734e19 | 0.0938137 | 0.0469069 | − | 0.998899i | \(-0.485064\pi\) | ||||
0.0469069 | + | 0.998899i | \(0.485064\pi\) | |||||||
\(242\) | 4.85615e19 | − | 1.17919e19i | 0.265376 | − | 0.0644394i | ||||
\(243\) | − | 6.11596e20i | − | 3.22709i | ||||||
\(244\) | −2.39614e19 | − | 4.64301e19i | −0.122095 | − | 0.236584i | ||||
\(245\) | − | 1.26873e20i | − | 0.624392i | ||||||
\(246\) | 1.07347e19 | + | 4.42081e19i | 0.0510320 | + | 0.210162i | ||||
\(247\) | −1.21777e19 | −0.0559296 | ||||||||
\(248\) | 1.37559e20 | − | 1.19349e20i | 0.610449 | − | 0.529640i | ||||
\(249\) | 7.29837e20 | 3.12991 | ||||||||
\(250\) | −5.20438e19 | − | 2.14328e20i | −0.215714 | − | 0.888361i | ||||
\(251\) | 5.13762e19i | 0.205843i | 0.994690 | + | 0.102921i | \(0.0328190\pi\) | ||||
−0.994690 | + | 0.102921i | \(0.967181\pi\) | |||||||
\(252\) | −8.92844e20 | + | 4.60774e20i | −3.45836 | + | 1.78478i | ||||
\(253\) | − | 7.89490e19i | − | 0.295680i | ||||||
\(254\) | 1.86372e20 | − | 4.52554e19i | 0.674986 | − | 0.163902i | ||||
\(255\) | 5.49927e19 | 0.192625 | ||||||||
\(256\) | −9.70085e19 | − | 2.78750e20i | −0.328678 | − | 0.944442i | ||||
\(257\) | −9.03372e19 | −0.296098 | −0.148049 | − | 0.988980i | \(-0.547299\pi\) | ||||
−0.148049 | + | 0.988980i | \(0.547299\pi\) | |||||||
\(258\) | −3.05184e20 | + | 7.41057e19i | −0.967820 | + | 0.235009i | ||||
\(259\) | 5.38777e20i | 1.65334i | ||||||||
\(260\) | 1.15300e20 | − | 5.95033e19i | 0.342416 | − | 0.176713i | ||||
\(261\) | 1.44436e20i | 0.415175i | ||||||||
\(262\) | 9.54873e19 | + | 3.93239e20i | 0.265696 | + | 1.09420i | ||||
\(263\) | −1.92468e20 | −0.518484 | −0.259242 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259242 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(264\) | 4.71079e20 | − | 4.08720e20i | 1.22874 | − | 1.06609i | ||||
\(265\) | −3.00233e20 | −0.758349 | ||||||||
\(266\) | 1.09913e19 | + | 4.52648e19i | 0.0268879 | + | 0.110730i | ||||
\(267\) | 2.38143e20i | 0.564277i | ||||||||
\(268\) | −3.13940e20 | − | 6.08322e20i | −0.720611 | − | 1.39633i | ||||
\(269\) | − | 5.40117e19i | − | 0.120114i | −0.998195 | − | 0.0600569i | \(-0.980872\pi\) | ||
0.998195 | − | 0.0600569i | \(-0.0191282\pi\) | |||||||
\(270\) | 7.51895e20 | − | 1.82577e20i | 1.62019 | − | 0.393419i | ||||
\(271\) | 6.53682e19 | 0.136498 | 0.0682492 | − | 0.997668i | \(-0.478259\pi\) | ||||
0.0682492 | + | 0.997668i | \(0.478259\pi\) | |||||||
\(272\) | −5.42598e19 | + | 7.63347e19i | −0.109810 | + | 0.154485i | ||||
\(273\) | 1.03707e21 | 2.03435 | ||||||||
\(274\) | 2.37700e20 | − | 5.77190e19i | 0.452011 | − | 0.109759i | ||||
\(275\) | 3.31250e20i | 0.610700i | ||||||||
\(276\) | 1.69758e20 | + | 3.28940e20i | 0.303460 | + | 0.588016i | ||||
\(277\) | − | 1.79771e20i | − | 0.311632i | −0.987786 | − | 0.155816i | \(-0.950199\pi\) | ||
0.987786 | − | 0.155816i | \(-0.0498007\pi\) | |||||||
\(278\) | 1.22486e20 | + | 5.04427e20i | 0.205924 | + | 0.848043i | ||||
\(279\) | −1.30869e21 | −2.13404 | ||||||||
\(280\) | −3.25242e20 | − | 3.74865e20i | −0.514473 | − | 0.592968i | ||||
\(281\) | 5.43168e20 | 0.833547 | 0.416774 | − | 0.909010i | \(-0.363161\pi\) | ||||
0.416774 | + | 0.909010i | \(0.363161\pi\) | |||||||
\(282\) | 2.90513e20 | + | 1.19640e21i | 0.432562 | + | 1.78139i | ||||
\(283\) | − | 7.08836e20i | − | 1.02414i | −0.858943 | − | 0.512072i | \(-0.828878\pi\) | ||
0.858943 | − | 0.512072i | \(-0.171122\pi\) | |||||||
\(284\) | 6.40752e20 | − | 3.30676e20i | 0.898430 | − | 0.463657i | ||||
\(285\) | − | 5.77373e19i | − | 0.0785733i | ||||||
\(286\) | −4.53733e20 | + | 1.10177e20i | −0.599362 | + | 0.145539i | ||||
\(287\) | −1.30275e20 | −0.167057 | ||||||||
\(288\) | −7.86174e20 | + | 1.96984e21i | −0.978774 | + | 2.45243i | ||||
\(289\) | −7.97523e20 | −0.964076 | ||||||||
\(290\) | −6.93303e19 | + | 1.68350e19i | −0.0813842 | + | 0.0197619i | ||||
\(291\) | − | 1.42541e21i | − | 1.62498i | ||||||
\(292\) | 1.71685e20 | − | 8.86025e19i | 0.190099 | − | 0.0981052i | ||||
\(293\) | − | 1.02708e20i | − | 0.110467i | −0.998473 | − | 0.0552334i | \(-0.982410\pi\) | ||
0.998473 | − | 0.0552334i | \(-0.0175903\pi\) | |||||||
\(294\) | −5.05127e20 | − | 2.08023e21i | −0.527775 | − | 2.17350i | ||||
\(295\) | 3.89729e20 | 0.395618 | ||||||||
\(296\) | 7.45342e20 | + | 8.59060e20i | 0.735150 | + | 0.847314i | ||||
\(297\) | −2.78443e21 | −2.66874 | ||||||||
\(298\) | −2.49938e20 | − | 1.02930e21i | −0.232806 | − | 0.958747i | ||||
\(299\) | − | 2.77124e20i | − | 0.250882i | ||||||
\(300\) | −7.12260e20 | − | 1.38015e21i | −0.626770 | − | 1.21449i | ||||
\(301\) | − | 8.99336e20i | − | 0.769320i | ||||||
\(302\) | 1.19211e21 | − | 2.89473e20i | 0.991423 | − | 0.240740i | ||||
\(303\) | 1.54109e21 | 1.24614 | ||||||||
\(304\) | 8.01444e19 | + | 5.69677e19i | 0.0630156 | + | 0.0447923i | ||||
\(305\) | −1.85459e20 | −0.141808 | ||||||||
\(306\) | 6.53995e20 | − | 1.58805e20i | 0.486342 | − | 0.118095i | ||||
\(307\) | 6.24758e19i | 0.0451893i | 0.999745 | + | 0.0225946i | \(0.00719271\pi\) | ||||
−0.999745 | + | 0.0225946i | \(0.992807\pi\) | |||||||
\(308\) | 8.19059e20 | + | 1.58709e21i | 0.576281 | + | 1.11666i | ||||
\(309\) | 4.16257e21i | 2.84914i | ||||||||
\(310\) | −1.52537e20 | − | 6.28182e20i | −0.101578 | − | 0.418323i | ||||
\(311\) | −6.19747e20 | −0.401561 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(312\) | 1.65357e21 | − | 1.43468e21i | 1.04258 | − | 0.904565i | ||||
\(313\) | 2.05658e21 | 1.26188 | 0.630942 | − | 0.775830i | \(-0.282669\pi\) | ||||
0.630942 | + | 0.775830i | \(0.282669\pi\) | |||||||
\(314\) | 3.03450e20 | + | 1.24967e21i | 0.181211 | + | 0.746268i | ||||
\(315\) | 3.56635e21i | 2.07293i | ||||||||
\(316\) | −2.27114e21 | + | 1.17208e21i | −1.28500 | + | 0.663156i | ||||
\(317\) | − | 2.76754e21i | − | 1.52437i | −0.647361 | − | 0.762184i | \(-0.724127\pi\) | ||
0.647361 | − | 0.762184i | \(-0.275873\pi\) | |||||||
\(318\) | −4.92268e21 | + | 1.19534e21i | −2.63980 | + | 0.641004i | ||||
\(319\) | 2.56745e20 | 0.134055 | ||||||||
\(320\) | −1.03717e21 | − | 1.47770e20i | −0.527322 | − | 0.0751298i | ||||
\(321\) | 1.19934e21 | 0.593812 | ||||||||
\(322\) | −1.03008e21 | + | 2.50126e20i | −0.496701 | + | 0.120610i | ||||
\(323\) | − | 3.12008e19i | − | 0.0146536i | ||||||
\(324\) | 6.47210e21 | − | 3.34009e21i | 2.96083 | − | 1.52801i | ||||
\(325\) | 1.16274e21i | 0.518174i | ||||||||
\(326\) | 5.82603e20 | + | 2.39929e21i | 0.252943 | + | 1.04168i | ||||
\(327\) | 7.97723e21 | 3.37440 | ||||||||
\(328\) | −2.07719e20 | + | 1.80222e20i | −0.0856148 | + | 0.0742815i | ||||
\(329\) | −3.52563e21 | −1.41603 | ||||||||
\(330\) | −5.22373e20 | − | 2.15125e21i | −0.204462 | − | 0.842021i | ||||
\(331\) | − | 1.62038e21i | − | 0.618128i | −0.951041 | − | 0.309064i | \(-0.899984\pi\) | ||
0.951041 | − | 0.309064i | \(-0.100016\pi\) | |||||||
\(332\) | 2.02331e21 | + | 3.92057e21i | 0.752295 | + | 1.45772i | ||||
\(333\) | − | 8.17285e21i | − | 2.96209i | ||||||
\(334\) | −4.54319e21 | + | 1.10319e21i | −1.60515 | + | 0.389768i | ||||
\(335\) | −2.42987e21 | −0.836954 | ||||||||
\(336\) | −6.82519e21 | − | 4.85144e21i | −2.29209 | − | 1.62925i | ||||
\(337\) | 7.17480e20 | 0.234939 | 0.117470 | − | 0.993076i | \(-0.462522\pi\) | ||||
0.117470 | + | 0.993076i | \(0.462522\pi\) | |||||||
\(338\) | 1.45067e21 | − | 3.52255e20i | 0.463208 | − | 0.112477i | ||||
\(339\) | 7.55549e21i | 2.35269i | ||||||||
\(340\) | 1.52455e20 | + | 2.95412e20i | 0.0462989 | + | 0.0897134i | ||||
\(341\) | 2.32630e21i | 0.689053i | ||||||||
\(342\) | −1.66730e20 | − | 6.86634e20i | −0.0481718 | − | 0.198382i | ||||
\(343\) | 9.00726e20 | 0.253859 | ||||||||
\(344\) | −1.24414e21 | − | 1.43396e21i | −0.342075 | − | 0.394267i | ||||
\(345\) | 1.31391e21 | 0.352455 | ||||||||
\(346\) | −2.54644e20 | − | 1.04868e21i | −0.0666480 | − | 0.274472i | ||||
\(347\) | − | 6.16195e21i | − | 1.57369i | −0.617154 | − | 0.786843i | \(-0.711714\pi\) | ||
0.617154 | − | 0.786843i | \(-0.288286\pi\) | |||||||
\(348\) | −1.06972e21 | + | 5.52058e20i | −0.266593 | + | 0.137582i | ||||
\(349\) | 5.73892e21i | 1.39577i | 0.716210 | + | 0.697885i | \(0.245875\pi\) | ||||
−0.716210 | + | 0.697885i | \(0.754125\pi\) | |||||||
\(350\) | 4.32194e21 | − | 1.04947e21i | 1.02589 | − | 0.249109i | ||||
\(351\) | −9.77383e21 | −2.26441 | ||||||||
\(352\) | 3.50154e21 | + | 1.39748e21i | 0.791856 | + | 0.316033i | ||||
\(353\) | −7.35535e21 | −1.62375 | −0.811873 | − | 0.583834i | \(-0.801552\pi\) | ||||
−0.811873 | + | 0.583834i | \(0.801552\pi\) | |||||||
\(354\) | 6.39007e21 | − | 1.55165e21i | 1.37714 | − | 0.334401i | ||||
\(355\) | − | 2.55941e21i | − | 0.538515i | ||||||
\(356\) | −1.27927e21 | + | 6.60198e20i | −0.262807 | + | 0.135628i | ||||
\(357\) | 2.65710e21i | 0.533001i | ||||||||
\(358\) | 3.42015e20 | + | 1.40849e21i | 0.0669945 | + | 0.275898i | ||||
\(359\) | −1.38050e21 | −0.264079 | −0.132040 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132040 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(360\) | 4.93368e21 | + | 5.68642e21i | 0.921721 | + | 1.06235i | ||||
\(361\) | 5.44763e21 | 0.994023 | ||||||||
\(362\) | −1.95158e21 | − | 8.03706e21i | −0.347827 | − | 1.43243i | ||||
\(363\) | − | 2.99289e21i | − | 0.521056i | ||||||
\(364\) | 2.87504e21 | + | 5.57096e21i | 0.488969 | + | 0.947477i | ||||
\(365\) | − | 6.85776e20i | − | 0.113944i | ||||||
\(366\) | −3.04082e21 | + | 7.38381e20i | −0.493630 | + | 0.119865i | ||||
\(367\) | 9.17912e21 | 1.45593 | 0.727963 | − | 0.685616i | \(-0.240467\pi\) | ||||
0.727963 | + | 0.685616i | \(0.240467\pi\) | |||||||
\(368\) | −1.29640e21 | + | 1.82382e21i | −0.200924 | + | 0.282667i | ||||
\(369\) | 1.97618e21 | 0.299297 | ||||||||
\(370\) | 3.92302e21 | − | 9.52600e20i | 0.580639 | − | 0.140993i | ||||
\(371\) | − | 1.45065e22i | − | 2.09838i | ||||||
\(372\) | −5.00205e21 | − | 9.69248e21i | −0.707185 | − | 1.37031i | ||||
\(373\) | 3.68573e21i | 0.509329i | 0.967029 | + | 0.254665i | \(0.0819651\pi\) | ||||
−0.967029 | + | 0.254665i | \(0.918035\pi\) | |||||||
\(374\) | −2.82287e20 | − | 1.16252e21i | −0.0381313 | − | 0.157033i | ||||
\(375\) | −1.32092e22 | −1.74426 | ||||||||
\(376\) | −5.62149e21 | + | 4.87734e21i | −0.725696 | + | 0.629631i | ||||
\(377\) | 9.01219e20 | 0.113744 | ||||||||
\(378\) | 8.82164e21 | + | 3.63295e22i | 1.08860 | + | 4.48311i | ||||
\(379\) | 9.17543e21i | 1.10712i | 0.832810 | + | 0.553558i | \(0.186730\pi\) | ||||
−0.832810 | + | 0.553558i | \(0.813270\pi\) | |||||||
\(380\) | 3.10155e20 | − | 1.60063e20i | 0.0365947 | − | 0.0188856i | ||||
\(381\) | − | 1.14863e22i | − | 1.32531i | ||||||
\(382\) | 1.07504e22 | − | 2.61045e21i | 1.21307 | − | 0.294562i | ||||
\(383\) | −7.23389e21 | −0.798329 | −0.399165 | − | 0.916879i | \(-0.630700\pi\) | ||||
−0.399165 | + | 0.916879i | \(0.630700\pi\) | |||||||
\(384\) | −1.75940e22 | + | 1.70650e21i | −1.89910 | + | 0.184200i | ||||
\(385\) | 6.33944e21 | 0.669322 | ||||||||
\(386\) | 7.90886e21 | − | 1.92045e21i | 0.816811 | − | 0.198340i | ||||
\(387\) | 1.36423e22i | 1.37830i | ||||||||
\(388\) | 7.65706e21 | − | 3.95162e21i | 0.756820 | − | 0.390576i | ||||
\(389\) | 1.25731e21i | 0.121583i | 0.998150 | + | 0.0607914i | \(0.0193624\pi\) | ||||
−0.998150 | + | 0.0607914i | \(0.980638\pi\) | |||||||
\(390\) | −1.83362e21 | − | 7.55126e21i | −0.173484 | − | 0.714447i | ||||
\(391\) | 7.10027e20 | 0.0657314 | ||||||||
\(392\) | 9.77431e21 | − | 8.48043e21i | 0.885431 | − | 0.768221i | ||||
\(393\) | 2.42356e22 | 2.14841 | ||||||||
\(394\) | −4.61436e21 | − | 1.90030e22i | −0.400308 | − | 1.64856i | ||||
\(395\) | 9.07178e21i | 0.770224i | ||||||||
\(396\) | −1.24245e22 | − | 2.40750e22i | −1.03245 | − | 2.00059i | ||||
\(397\) | 1.07820e22i | 0.876957i | 0.898742 | + | 0.438478i | \(0.144482\pi\) | ||||
−0.898742 | + | 0.438478i | \(0.855518\pi\) | |||||||
\(398\) | −1.16168e21 | + | 2.82083e20i | −0.0924871 | + | 0.0224580i | ||||
\(399\) | 2.78971e21 | 0.217415 | ||||||||
\(400\) | 5.43935e21 | − | 7.65229e21i | 0.414990 | − | 0.583824i | ||||
\(401\) | −1.08434e22 | −0.809915 | −0.404957 | − | 0.914336i | \(-0.632714\pi\) | ||||
−0.404957 | + | 0.914336i | \(0.632714\pi\) | |||||||
\(402\) | −3.98405e22 | + | 9.67419e21i | −2.91342 | + | 0.707446i | ||||
\(403\) | 8.16570e21i | 0.584656i | ||||||||
\(404\) | 4.27233e21 | + | 8.27850e21i | 0.299518 | + | 0.580377i | ||||
\(405\) | − | 2.58520e22i | − | 1.77471i | ||||||
\(406\) | −8.13420e20 | − | 3.34985e21i | −0.0546819 | − | 0.225193i | ||||
\(407\) | −1.45278e22 | −0.956418 | ||||||||
\(408\) | 3.67582e21 | + | 4.23665e21i | 0.236997 | + | 0.273156i | ||||
\(409\) | −2.32714e22 | −1.46951 | −0.734757 | − | 0.678330i | \(-0.762704\pi\) | ||||
−0.734757 | + | 0.678330i | \(0.762704\pi\) | |||||||
\(410\) | 2.30337e20 | + | 9.48580e20i | 0.0142463 | + | 0.0586693i | ||||
\(411\) | − | 1.46497e22i | − | 0.887507i | ||||||
\(412\) | −2.23606e22 | + | 1.15398e22i | −1.32696 | + | 0.684811i | ||||
\(413\) | 1.88307e22i | 1.09469i | ||||||||
\(414\) | 1.56255e22 | − | 3.79423e21i | 0.889880 | − | 0.216083i | ||||
\(415\) | 1.56602e22 | 0.873754 | ||||||||
\(416\) | 1.22910e22 | + | 4.90539e21i | 0.671883 | + | 0.268151i | ||||
\(417\) | 3.10883e22 | 1.66510 | ||||||||
\(418\) | −1.22054e21 | + | 2.96375e20i | −0.0640551 | + | 0.0155540i | ||||
\(419\) | − | 2.64974e22i | − | 1.36265i | −0.731980 | − | 0.681326i | \(-0.761404\pi\) | ||
0.731980 | − | 0.681326i | \(-0.238596\pi\) | |||||||
\(420\) | −2.64132e22 | + | 1.36312e22i | −1.33107 | + | 0.686934i | ||||
\(421\) | 3.52910e21i | 0.174288i | 0.996196 | + | 0.0871438i | \(0.0277739\pi\) | ||||
−0.996196 | + | 0.0871438i | \(0.972226\pi\) | |||||||
\(422\) | 6.79976e21 | + | 2.80030e22i | 0.329108 | + | 1.35534i | ||||
\(423\) | 5.34812e22 | 2.53693 | ||||||||
\(424\) | −2.00682e22 | − | 2.31300e22i | −0.933036 | − | 1.07539i | ||||
\(425\) | −2.97910e21 | −0.135762 | ||||||||
\(426\) | −1.01899e22 | − | 4.19645e22i | −0.455187 | − | 1.87456i | ||||
\(427\) | − | 8.96089e21i | − | 0.392387i | ||||||
\(428\) | 3.32489e21 | + | 6.44266e21i | 0.142727 | + | 0.276562i | ||||
\(429\) | 2.79640e22i | 1.17682i | ||||||||
\(430\) | −6.54839e21 | + | 1.59010e21i | −0.270179 | + | 0.0656058i | ||||
\(431\) | −1.62468e22 | −0.657220 | −0.328610 | − | 0.944466i | \(-0.606580\pi\) | ||||
−0.328610 | + | 0.944466i | \(0.606580\pi\) | |||||||
\(432\) | 6.43239e22 | + | 4.57223e22i | 2.55129 | + | 1.81350i | ||||
\(433\) | −2.11243e22 | −0.821553 | −0.410776 | − | 0.911736i | \(-0.634742\pi\) | ||||
−0.410776 | + | 0.911736i | \(0.634742\pi\) | |||||||
\(434\) | 3.03521e22 | − | 7.37018e21i | 1.15751 | − | 0.281070i | ||||
\(435\) | 4.27288e21i | 0.159795i | ||||||||
\(436\) | 2.21151e22 | + | 4.28524e22i | 0.811060 | + | 1.57159i | ||||
\(437\) | − | 7.45463e20i | − | 0.0268123i | ||||||
\(438\) | −2.73033e21 | − | 1.12441e22i | −0.0963129 | − | 0.396638i | ||||
\(439\) | 3.57810e22 | 1.23795 | 0.618977 | − | 0.785409i | \(-0.287548\pi\) | ||||
0.618977 | + | 0.785409i | \(0.287548\pi\) | |||||||
\(440\) | 1.01080e22 | − | 8.76996e21i | 0.343019 | − | 0.297612i | ||||
\(441\) | −9.29899e22 | −3.09534 | ||||||||
\(442\) | −9.90875e20 | − | 4.08065e21i | −0.0323541 | − | 0.133242i | ||||
\(443\) | 5.46996e22i | 1.75207i | 0.482245 | + | 0.876036i | \(0.339822\pi\) | ||||
−0.482245 | + | 0.876036i | \(0.660178\pi\) | |||||||
\(444\) | 6.05299e22 | − | 3.12380e22i | 1.90202 | − | 0.981585i | ||||
\(445\) | 5.10988e21i | 0.157525i | ||||||||
\(446\) | −2.52865e22 | + | 6.14015e21i | −0.764791 | + | 0.185709i | ||||
\(447\) | −6.34367e22 | −1.88246 | ||||||||
\(448\) | 7.13986e21 | − | 5.01134e22i | 0.207887 | − | 1.45912i | ||||
\(449\) | 1.84591e22 | 0.527371 | 0.263686 | − | 0.964609i | \(-0.415062\pi\) | ||||
0.263686 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(450\) | −6.55607e22 | + | 1.59196e22i | −1.83797 | + | 0.446300i | ||||
\(451\) | − | 3.51280e21i | − | 0.0966390i | ||||||
\(452\) | −4.05869e22 | + | 2.09459e22i | −1.09574 | + | 0.565486i | ||||
\(453\) | − | 7.34711e22i | − | 1.94662i | ||||||
\(454\) | 9.16246e21 | + | 3.77331e22i | 0.238252 | + | 0.981177i | ||||
\(455\) | 2.22525e22 | 0.567914 | ||||||||
\(456\) | 4.44809e21 | − | 3.85927e21i | 0.111422 | − | 0.0966728i | ||||
\(457\) | 2.92054e22 | 0.718085 | 0.359042 | − | 0.933321i | \(-0.383103\pi\) | ||||
0.359042 | + | 0.933321i | \(0.383103\pi\) | |||||||
\(458\) | −7.30575e21 | − | 3.00867e22i | −0.176323 | − | 0.726137i | ||||
\(459\) | − | 2.50418e22i | − | 0.593277i | ||||||
\(460\) | 3.64251e21 | + | 7.05811e21i | 0.0847149 | + | 0.164152i | ||||
\(461\) | − | 4.03608e22i | − | 0.921513i | −0.887527 | − | 0.460756i | \(-0.847578\pi\) | ||
0.887527 | − | 0.460756i | \(-0.152422\pi\) | |||||||
\(462\) | 1.03943e23 | − | 2.52397e22i | 2.32990 | − | 0.565753i | ||||
\(463\) | −6.51927e22 | −1.43470 | −0.717349 | − | 0.696714i | \(-0.754644\pi\) | ||||
−0.717349 | + | 0.696714i | \(0.754644\pi\) | |||||||
\(464\) | −5.93114e21 | − | 4.21593e21i | −0.128155 | − | 0.0910943i | ||||
\(465\) | −3.87154e22 | −0.821361 | ||||||||
\(466\) | −5.80565e22 | + | 1.40974e22i | −1.20940 | + | 0.293670i | ||||
\(467\) | 3.14842e21i | 0.0644021i | 0.999481 | + | 0.0322010i | \(0.0102517\pi\) | ||||
−0.999481 | + | 0.0322010i | \(0.989748\pi\) | |||||||
\(468\) | −4.36122e22 | − | 8.45075e22i | −0.876028 | − | 1.69748i | ||||
\(469\) | − | 1.17405e23i | − | 2.31588i | ||||||
\(470\) | 6.23359e21 | + | 2.56713e22i | 0.120755 | + | 0.497298i | ||||
\(471\) | 7.70185e22 | 1.46527 | ||||||||
\(472\) | 2.60503e22 | + | 3.00248e22i | 0.486749 | + | 0.561013i | ||||
\(473\) | 2.42501e22 | 0.445035 | ||||||||
\(474\) | 3.61181e22 | + | 1.48742e23i | 0.651041 | + | 2.68114i | ||||
\(475\) | 3.12777e21i | 0.0553783i | ||||||||
\(476\) | −1.42735e22 | + | 7.36620e21i | −0.248240 | + | 0.128110i | ||||
\(477\) | 2.20052e23i | 3.75941i | ||||||||
\(478\) | −7.74001e22 | + | 1.87945e22i | −1.29899 | + | 0.315423i | ||||
\(479\) | 5.37771e22 | 0.886637 | 0.443318 | − | 0.896364i | \(-0.353801\pi\) | ||||
0.443318 | + | 0.896364i | \(0.353801\pi\) | |||||||
\(480\) | −2.32576e22 | + | 5.82744e22i | −0.376716 | + | 0.943902i | ||||
\(481\) | −5.09951e22 | −0.811513 | ||||||||
\(482\) | 5.83077e21 | − | 1.41584e21i | 0.0911645 | − | 0.0221368i | ||||
\(483\) | 6.34845e22i | 0.975253i | ||||||||
\(484\) | 1.60773e22 | − | 8.29710e21i | 0.242677 | − | 0.125239i | ||||
\(485\) | − | 3.05852e22i | − | 0.453635i | ||||||
\(486\) | −5.22479e22 | − | 2.15169e23i | −0.761483 | − | 3.13596i | ||||
\(487\) | −1.62097e22 | −0.232155 | −0.116078 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116078 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(488\) | −1.23965e22 | − | 1.42878e22i | −0.174473 | − | 0.201093i | ||||
\(489\) | 1.47870e23 | 2.04530 | ||||||||
\(490\) | −1.08386e22 | − | 4.46358e22i | −0.147335 | − | 0.606760i | ||||
\(491\) | − | 3.89242e22i | − | 0.520028i | −0.965605 | − | 0.260014i | \(-0.916273\pi\) | ||
0.965605 | − | 0.260014i | \(-0.0837273\pi\) | |||||||
\(492\) | 7.55329e21 | + | 1.46360e22i | 0.0991819 | + | 0.192185i | ||||
\(493\) | 2.30904e21i | 0.0298011i | ||||||||
\(494\) | −4.28430e21 | + | 1.04033e21i | −0.0543502 | + | 0.0131975i | ||||
\(495\) | −9.61647e22 | −1.19914 | ||||||||
\(496\) | 3.81994e22 | − | 5.37404e22i | 0.468233 | − | 0.658729i | ||||
\(497\) | 1.23664e23 | 1.49009 | ||||||||
\(498\) | 2.56768e23 | − | 6.23491e22i | 3.04152 | − | 0.738552i | ||||
\(499\) | − | 6.70841e22i | − | 0.781205i | −0.920560 | − | 0.390602i | \(-0.872267\pi\) | ||
0.920560 | − | 0.390602i | \(-0.127733\pi\) | |||||||
\(500\) | −3.66196e22 | − | 7.09579e22i | −0.419246 | − | 0.812373i | ||||
\(501\) | 2.80001e23i | 3.15166i | ||||||||
\(502\) | 4.38901e21 | + | 1.80749e22i | 0.0485718 | + | 0.200030i | ||||
\(503\) | −2.47633e22 | −0.269452 | −0.134726 | − | 0.990883i | \(-0.543015\pi\) | ||||
−0.134726 | + | 0.990883i | \(0.543015\pi\) | |||||||
\(504\) | −2.74753e23 | + | 2.38382e23i | −2.93956 | + | 2.55043i | ||||
\(505\) | 3.30674e22 | 0.347875 | ||||||||
\(506\) | −6.74451e21 | − | 2.77754e22i | −0.0697704 | − | 0.287330i | ||||
\(507\) | − | 8.94059e22i | − | 0.909491i | ||||||
\(508\) | 6.17024e22 | − | 3.18431e22i | 0.617250 | − | 0.318547i | ||||
\(509\) | − | 5.33536e22i | − | 0.524883i | −0.964948 | − | 0.262441i | \(-0.915472\pi\) | ||
0.964948 | − | 0.262441i | \(-0.0845276\pi\) | |||||||
\(510\) | 1.93473e22 | − | 4.69796e21i | 0.187186 | − | 0.0454530i | ||||
\(511\) | 3.31348e22 | 0.315288 | ||||||||
\(512\) | −5.79424e22 | − | 8.97812e22i | −0.542252 | − | 0.840216i | ||||
\(513\) | −2.62916e22 | −0.242002 | ||||||||
\(514\) | −3.17820e22 | + | 7.71740e21i | −0.287736 | + | 0.0698690i | ||||
\(515\) | 8.93169e22i | 0.795375i | ||||||||
\(516\) | −1.01038e23 | + | 5.21430e22i | −0.885036 | + | 0.456745i | ||||
\(517\) | − | 9.50666e22i | − | 0.819140i | ||||||
\(518\) | 4.60271e22 | + | 1.89550e23i | 0.390131 | + | 1.60665i | ||||
\(519\) | −6.46312e22 | −0.538915 | ||||||||
\(520\) | 3.54809e22 | − | 3.07841e22i | 0.291049 | − | 0.252521i | ||||
\(521\) | −2.10097e22 | −0.169551 | −0.0847754 | − | 0.996400i | \(-0.527017\pi\) | ||||
−0.0847754 | + | 0.996400i | \(0.527017\pi\) | |||||||
\(522\) | 1.23390e22 | + | 5.08148e22i | 0.0979671 | + | 0.403451i | ||||
\(523\) | 7.86323e22i | 0.614238i | 0.951671 | + | 0.307119i | \(0.0993650\pi\) | ||||
−0.951671 | + | 0.307119i | \(0.900635\pi\) | |||||||
\(524\) | 6.71878e22 | + | 1.30190e23i | 0.516386 | + | 1.00060i | ||||
\(525\) | − | 2.66365e23i | − | 2.01430i | ||||||
\(526\) | −6.77132e22 | + | 1.64423e22i | −0.503842 | + | 0.122344i | ||||
\(527\) | −2.09215e22 | −0.153180 | ||||||||
\(528\) | 1.30816e23 | − | 1.84038e23i | 0.942484 | − | 1.32592i | ||||
\(529\) | −1.24086e23 | −0.879729 | ||||||||
\(530\) | −1.05627e23 | + | 2.56486e22i | −0.736934 | + | 0.178944i | ||||
\(531\) | − | 2.85647e23i | − | 1.96122i | ||||||
\(532\) | 7.73383e21 | + | 1.49859e22i | 0.0522572 | + | 0.101259i | ||||
\(533\) | − | 1.23305e22i | − | 0.0819974i | ||||||
\(534\) | 2.03443e22 | + | 8.37824e22i | 0.133150 | + | 0.548343i | ||||
\(535\) | 2.57344e22 | 0.165770 | ||||||||
\(536\) | −1.62417e23 | − | 1.87197e23i | −1.02975 | − | 1.18686i | ||||
\(537\) | 8.68067e22 | 0.541716 | ||||||||
\(538\) | −4.61415e21 | − | 1.90021e22i | −0.0283428 | − | 0.116722i | ||||
\(539\) | 1.65296e23i | 0.999443i | ||||||||
\(540\) | 2.48931e23 | − | 1.28467e23i | 1.48160 | − | 0.764618i | ||||
\(541\) | − | 8.46969e22i | − | 0.496239i | −0.968729 | − | 0.248120i | \(-0.920187\pi\) | ||
0.968729 | − | 0.248120i | \(-0.0798126\pi\) | |||||||
\(542\) | 2.29975e22 | − | 5.58433e21i | 0.132644 | − | 0.0322090i | ||||
\(543\) | −4.95331e23 | −2.81253 | ||||||||
\(544\) | −1.25682e22 | + | 3.14911e22i | −0.0702560 | + | 0.176034i | ||||
\(545\) | 1.71169e23 | 0.942007 | ||||||||
\(546\) | 3.64856e23 | − | 8.85955e22i | 1.97690 | − | 0.480036i | ||||
\(547\) | 3.22585e23i | 1.72088i | 0.509548 | + | 0.860442i | \(0.329813\pi\) | ||||
−0.509548 | + | 0.860442i | \(0.670187\pi\) | |||||||
\(548\) | 7.86956e22 | − | 4.06128e22i | 0.413348 | − | 0.213318i | ||||
\(549\) | 1.35930e23i | 0.702993i | ||||||||
\(550\) | 2.82983e22 | + | 1.16539e23i | 0.144104 | + | 0.593455i | ||||
\(551\) | 2.42428e21 | 0.0121561 | ||||||||
\(552\) | 8.78242e22 | + | 1.01224e23i | 0.433643 | + | 0.499805i | ||||
\(553\) | −4.38324e23 | −2.13123 | ||||||||
\(554\) | −1.53576e22 | − | 6.32462e22i | −0.0735345 | − | 0.302832i | ||||
\(555\) | − | 2.41779e23i | − | 1.14006i | ||||||
\(556\) | 8.61852e22 | + | 1.67001e23i | 0.400218 | + | 0.775504i | ||||
\(557\) | 1.27684e23i | 0.583937i | 0.956428 | + | 0.291968i | \(0.0943102\pi\) | ||||
−0.956428 | + | 0.291968i | \(0.905690\pi\) | |||||||
\(558\) | −4.60419e23 | + | 1.11800e23i | −2.07378 | + | 0.503561i | ||||
\(559\) | 8.51220e22 | 0.377608 | ||||||||
\(560\) | −1.46449e23 | − | 1.04098e23i | −0.639866 | − | 0.454825i | ||||
\(561\) | −7.16472e22 | −0.308329 | ||||||||
\(562\) | 1.91095e23 | − | 4.64022e22i | 0.810009 | − | 0.196689i | ||||
\(563\) | 3.00272e23i | 1.25370i | 0.779141 | + | 0.626849i | \(0.215656\pi\) | ||||
−0.779141 | + | 0.626849i | \(0.784344\pi\) | |||||||
\(564\) | 2.04414e23 | + | 3.96093e23i | 0.840694 | + | 1.62902i | ||||
\(565\) | 1.62119e23i | 0.656785i | ||||||||
\(566\) | −6.05550e22 | − | 2.49379e23i | −0.241663 | − | 0.995223i | ||||
\(567\) | 1.24910e24 | 4.91067 | ||||||||
\(568\) | 1.97177e23 | − | 1.71076e23i | 0.763652 | − | 0.662563i | ||||
\(569\) | 1.90009e23 | 0.724969 | 0.362485 | − | 0.931990i | \(-0.381929\pi\) | ||||
0.362485 | + | 0.931990i | \(0.381929\pi\) | |||||||
\(570\) | −4.93243e21 | − | 2.03129e22i | −0.0185406 | − | 0.0763545i | ||||
\(571\) | − | 1.14724e23i | − | 0.424862i | −0.977176 | − | 0.212431i | \(-0.931862\pi\) | ||
0.977176 | − | 0.212431i | \(-0.0681381\pi\) | |||||||
\(572\) | −1.50218e23 | + | 7.75237e22i | −0.548095 | + | 0.282858i | ||||
\(573\) | − | 6.62557e23i | − | 2.38182i | ||||||
\(574\) | −4.58328e22 | + | 1.11293e22i | −0.162340 | + | 0.0394198i | ||||
\(575\) | −7.11778e22 | −0.248409 | ||||||||
\(576\) | −1.08306e23 | + | 7.60183e23i | −0.372446 | + | 2.61413i | ||||
\(577\) | −3.30120e23 | −1.11861 | −0.559303 | − | 0.828963i | \(-0.688931\pi\) | ||||
−0.559303 | + | 0.828963i | \(0.688931\pi\) | |||||||
\(578\) | −2.80581e23 | + | 6.81314e22i | −0.936852 | + | 0.227489i | ||||
\(579\) | − | 4.87430e23i | − | 1.60378i | ||||||
\(580\) | −2.29533e22 | + | 1.18456e22i | −0.0744228 | + | 0.0384078i | ||||
\(581\) | 7.56660e23i | 2.41771i | ||||||||
\(582\) | −1.21771e23 | − | 5.01480e23i | −0.383440 | − | 1.57909i | ||||
\(583\) | 3.91159e23 | 1.21386 | ||||||||
\(584\) | 5.28323e22 | − | 4.58386e22i | 0.161581 | − | 0.140192i | ||||
\(585\) | −3.37555e23 | −1.01746 | ||||||||
\(586\) | −8.77426e21 | − | 3.61344e22i | −0.0260664 | − | 0.107347i | ||||
\(587\) | − | 4.63905e23i | − | 1.35833i | −0.733985 | − | 0.679166i | \(-0.762342\pi\) | ||
0.733985 | − | 0.679166i | \(-0.237658\pi\) | |||||||
\(588\) | −3.55423e23 | − | 6.88704e23i | −1.02574 | − | 1.98758i | ||||
\(589\) | 2.19657e22i | 0.0624834i | ||||||||
\(590\) | 1.37113e23 | − | 3.32941e22i | 0.384446 | − | 0.0933523i | ||||
\(591\) | −1.17117e24 | −3.23688 | ||||||||
\(592\) | 3.35611e23 | + | 2.38557e23i | 0.914327 | + | 0.649916i | ||||
\(593\) | 6.61931e23 | 1.77766 | 0.888829 | − | 0.458240i | \(-0.151520\pi\) | ||||
0.888829 | + | 0.458240i | \(0.151520\pi\) | |||||||
\(594\) | −9.79606e23 | + | 2.37871e23i | −2.59338 | + | 0.629733i | ||||
\(595\) | 5.70138e22i | 0.148794i | ||||||||
\(596\) | −1.75864e23 | − | 3.40772e23i | −0.452463 | − | 0.876739i | ||||
\(597\) | 7.15955e22i | 0.181595i | ||||||||
\(598\) | −2.36744e22 | − | 9.74965e22i | −0.0591996 | − | 0.243797i | ||||
\(599\) | 3.11969e23 | 0.769102 | 0.384551 | − | 0.923104i | \(-0.374356\pi\) | ||||
0.384551 | + | 0.923104i | \(0.374356\pi\) | |||||||
\(600\) | −3.68488e23 | − | 4.24710e23i | −0.895649 | − | 1.03230i | ||||
\(601\) | −2.76234e22 | −0.0661978 | −0.0330989 | − | 0.999452i | \(-0.510538\pi\) | ||||
−0.0330989 | + | 0.999452i | \(0.510538\pi\) | |||||||
\(602\) | −7.68292e22 | − | 3.16400e23i | −0.181533 | − | 0.747595i | ||||
\(603\) | 1.78094e24i | 4.14909i | ||||||||
\(604\) | 3.94675e23 | − | 2.03682e23i | 0.906620 | − | 0.467884i | ||||
\(605\) | − | 6.42189e22i | − | 0.145459i | ||||||
\(606\) | 5.42179e23 | − | 1.31654e23i | 1.21095 | − | 0.294046i | ||||
\(607\) | 5.72816e23 | 1.26157 | 0.630785 | − | 0.775958i | \(-0.282733\pi\) | ||||
0.630785 | + | 0.775958i | \(0.282733\pi\) | |||||||
\(608\) | 3.30627e22 | + | 1.31955e22i | 0.0718055 | + | 0.0286579i | ||||
\(609\) | −2.06454e23 | −0.442157 | ||||||||
\(610\) | −6.52474e22 | + | 1.58436e22i | −0.137803 | + | 0.0334618i | ||||
\(611\) | − | 3.33700e23i | − | 0.695033i | ||||||
\(612\) | 2.16519e23 | − | 1.11740e23i | 0.444742 | − | 0.229520i | ||||
\(613\) | − | 5.83184e23i | − | 1.18139i | −0.806896 | − | 0.590693i | \(-0.798854\pi\) | ||
0.806896 | − | 0.590693i | \(-0.201146\pi\) | |||||||
\(614\) | 5.33723e21 | + | 2.19799e22i | 0.0106631 | + | 0.0439132i | ||||
\(615\) | 5.84618e22 | 0.115195 | ||||||||
\(616\) | 4.23741e23 | + | 4.88392e23i | 0.823501 | + | 0.949145i | ||||
\(617\) | −5.87532e23 | −1.12618 | −0.563090 | − | 0.826396i | \(-0.690388\pi\) | ||||
−0.563090 | + | 0.826396i | \(0.690388\pi\) | |||||||
\(618\) | 3.55603e23 | + | 1.46445e24i | 0.672301 | + | 2.76869i | ||||
\(619\) | − | 1.26636e23i | − | 0.236150i | −0.993005 | − | 0.118075i | \(-0.962328\pi\) | ||
0.993005 | − | 0.118075i | \(-0.0376723\pi\) | |||||||
\(620\) | −1.07330e23 | − | 2.07973e23i | −0.197420 | − | 0.382541i | ||||
\(621\) | − | 5.98309e23i | − | 1.08554i | ||||||
\(622\) | −2.18037e23 | + | 5.29443e22i | −0.390221 | + | 0.0947547i | ||||
\(623\) | −2.46895e23 | −0.435878 | ||||||||
\(624\) | 4.59188e23 | − | 6.46003e23i | 0.799689 | − | 1.12503i | ||||
\(625\) | 1.33501e23 | 0.229353 | ||||||||
\(626\) | 7.23537e23 | − | 1.75691e23i | 1.22625 | − | 0.297762i | ||||
\(627\) | 7.52229e22i | 0.125770i | ||||||||
\(628\) | 2.13516e23 | + | 4.13731e23i | 0.352188 | + | 0.682435i | ||||
\(629\) | − | 1.30656e23i | − | 0.212617i | ||||||
\(630\) | 3.04669e23 | + | 1.25470e24i | 0.489141 | + | 2.01439i | ||||
\(631\) | 9.95923e22 | 0.157753 | 0.0788763 | − | 0.996884i | \(-0.474867\pi\) | ||||
0.0788763 | + | 0.996884i | \(0.474867\pi\) | |||||||
\(632\) | −6.98891e23 | + | 6.06375e23i | −1.09223 | + | 0.947646i | ||||
\(633\) | 1.72585e24 | 2.66116 | ||||||||
\(634\) | −2.36427e23 | − | 9.73661e23i | −0.359699 | − | 1.48132i | ||||
\(635\) | − | 2.46463e23i | − | 0.369977i | ||||||
\(636\) | −1.62976e24 | + | 8.41077e23i | −2.41400 | + | 1.24581i | ||||
\(637\) | 5.80218e23i | 0.848019i | ||||||||
\(638\) | 9.03268e22 | − | 2.19334e22i | 0.130269 | − | 0.0316323i | ||||
\(639\) | −1.87589e24 | −2.66962 | ||||||||
\(640\) | −3.77517e23 | + | 3.66165e22i | −0.530160 | + | 0.0514218i | ||||
\(641\) | 8.64785e22 | 0.119844 | 0.0599218 | − | 0.998203i | \(-0.480915\pi\) | ||||
0.0599218 | + | 0.998203i | \(0.480915\pi\) | |||||||
\(642\) | 4.21946e23 | − | 1.02458e23i | 0.577044 | − | 0.140119i | ||||
\(643\) | − | 5.63561e22i | − | 0.0760585i | −0.999277 | − | 0.0380292i | \(-0.987892\pi\) | ||
0.999277 | − | 0.0380292i | \(-0.0121080\pi\) | |||||||
\(644\) | −3.41029e23 | + | 1.75996e23i | −0.454215 | + | 0.234409i | ||||
\(645\) | 4.03583e23i | 0.530487i | ||||||||
\(646\) | −2.66545e21 | − | 1.09769e22i | −0.00345775 | − | 0.0142398i | ||||
\(647\) | −8.85704e23 | −1.13397 | −0.566986 | − | 0.823728i | \(-0.691890\pi\) | ||||
−0.566986 | + | 0.823728i | \(0.691890\pi\) | |||||||
\(648\) | 1.99164e24 | − | 1.72800e24i | 2.51666 | − | 2.18351i | ||||
\(649\) | −5.07758e23 | −0.633253 | ||||||||
\(650\) | 9.93318e22 | + | 4.09071e23i | 0.122271 | + | 0.503541i | ||||
\(651\) | − | 1.87062e24i | − | 2.27273i | ||||||
\(652\) | 4.09937e23 | + | 7.94337e23i | 0.491601 | + | 0.952577i | ||||
\(653\) | − | 3.56939e23i | − | 0.422505i | −0.977432 | − | 0.211252i | \(-0.932246\pi\) | ||
0.977432 | − | 0.211252i | \(-0.0677542\pi\) | |||||||
\(654\) | 2.80651e24 | − | 6.81485e23i | 3.27911 | − | 0.796243i | ||||
\(655\) | 5.20028e23 | 0.599757 | ||||||||
\(656\) | −5.76826e22 | + | 8.11501e22i | −0.0656693 | + | 0.0923860i | ||||
\(657\) | −5.02631e23 | −0.564864 | ||||||||
\(658\) | −1.24037e24 | + | 3.01190e23i | −1.37604 | + | 0.334134i | ||||
\(659\) | − | 6.90655e23i | − | 0.756372i | −0.925730 | − | 0.378186i | \(-0.876548\pi\) | ||
0.925730 | − | 0.378186i | \(-0.123452\pi\) | |||||||
\(660\) | −3.67558e23 | − | 7.12217e23i | −0.397376 | − | 0.769997i | ||||
\(661\) | 1.43884e24i | 1.53567i | 0.640645 | + | 0.767837i | \(0.278667\pi\) | ||||
−0.640645 | + | 0.767837i | \(0.721333\pi\) | |||||||
\(662\) | −1.38427e23 | − | 5.70074e23i | −0.145857 | − | 0.600673i | ||||
\(663\) | −2.51494e23 | −0.261615 | ||||||||
\(664\) | 1.04676e24 | + | 1.20647e24i | 1.07502 | + | 1.23904i | ||||
\(665\) | 5.98592e22 | 0.0606942 | ||||||||
\(666\) | −6.98197e23 | − | 2.87533e24i | −0.698951 | − | 2.87844i | ||||
\(667\) | 5.51685e22i | 0.0545282i | ||||||||
\(668\) | −1.50412e24 | + | 7.76239e23i | −1.46785 | + | 0.757523i | ||||
\(669\) | 1.55843e24i | 1.50164i | ||||||||
\(670\) | −8.54864e23 | + | 2.07581e23i | −0.813320 | + | 0.197493i | ||||
\(671\) | 2.41625e23 | 0.226987 | ||||||||
\(672\) | −2.81566e24 | − | 1.12374e24i | −2.61181 | − | 1.04238i | ||||
\(673\) | −1.28567e24 | −1.17761 | −0.588806 | − | 0.808275i | \(-0.700402\pi\) | ||||
−0.588806 | + | 0.808275i | \(0.700402\pi\) | |||||||
\(674\) | 2.52420e23 | − | 6.12935e22i | 0.228305 | − | 0.0554377i | ||||
\(675\) | 2.51035e24i | 2.24209i | ||||||||
\(676\) | 4.80274e23 | − | 2.47858e23i | 0.423587 | − | 0.218603i | ||||
\(677\) | − | 7.83643e23i | − | 0.682519i | −0.939969 | − | 0.341259i | \(-0.889147\pi\) | ||
0.939969 | − | 0.341259i | \(-0.110853\pi\) | |||||||
\(678\) | 6.45456e23 | + | 2.65814e24i | 0.555155 | + | 2.28626i | ||||
\(679\) | 1.47779e24 | 1.25522 | ||||||||
\(680\) | 7.88726e22 | + | 9.09064e22i | 0.0661608 | + | 0.0762551i | ||||
\(681\) | 2.32552e24 | 1.92650 | ||||||||
\(682\) | 1.98733e23 | + | 8.18426e23i | 0.162593 | + | 0.669595i | ||||
\(683\) | − | 7.52256e23i | − | 0.607841i | −0.952697 | − | 0.303920i | \(-0.901704\pi\) | ||
0.952697 | − | 0.303920i | \(-0.0982957\pi\) | |||||||
\(684\) | −1.17317e23 | − | 2.27325e23i | −0.0936230 | − | 0.181414i | ||||
\(685\) | − | 3.14340e23i | − | 0.247759i | ||||||
\(686\) | 3.16889e23 | − | 7.69479e22i | 0.246690 | − | 0.0599021i | ||||
\(687\) | −1.85427e24 | −1.42574 | ||||||||
\(688\) | −5.60208e23 | − | 3.98204e23i | −0.425449 | − | 0.302415i | ||||
\(689\) | 1.37303e24 | 1.02995 | ||||||||
\(690\) | 4.62253e23 | − | 1.12246e23i | 0.342502 | − | 0.0831672i | ||||
\(691\) | − | 1.95452e24i | − | 1.43046i | −0.698888 | − | 0.715231i | \(-0.746321\pi\) | ||
0.698888 | − | 0.715231i | \(-0.253679\pi\) | |||||||
\(692\) | −1.79175e23 | − | 3.47189e23i | −0.129532 | − | 0.250994i | ||||
\(693\) | − | 4.64642e24i | − | 3.31807i | ||||||
\(694\) | −5.26408e23 | − | 2.16787e24i | −0.371336 | − | 1.52925i | ||||
\(695\) | 6.67066e23 | 0.464834 | ||||||||
\(696\) | −3.29184e23 | + | 2.85608e23i | −0.226600 | + | 0.196604i | ||||
\(697\) | 3.15923e22 | 0.0214834 | ||||||||
\(698\) | 4.90269e23 | + | 2.01904e24i | 0.329354 | + | 1.35636i | ||||
\(699\) | 3.57807e24i | 2.37461i | ||||||||
\(700\) | 1.43087e24 | − | 7.38437e23i | 0.938138 | − | 0.484150i | ||||
\(701\) | 2.08668e24i | 1.35162i | 0.737078 | + | 0.675808i | \(0.236205\pi\) | ||||
−0.737078 | + | 0.675808i | \(0.763795\pi\) | |||||||
\(702\) | −3.43858e24 | + | 8.34967e23i | −2.20046 | + | 0.534323i | ||||
\(703\) | −1.37177e23 | −0.0867281 | ||||||||
\(704\) | 1.35128e24 | + | 1.92522e23i | 0.844068 | + | 0.120258i | ||||
\(705\) | 1.58215e24 | 0.976426 | ||||||||
\(706\) | −2.58772e24 | + | 6.28358e23i | −1.57789 | + | 0.383149i | ||||
\(707\) | 1.59773e24i | 0.962583i | ||||||||
\(708\) | 2.11557e24 | − | 1.09179e24i | 1.25934 | − | 0.649916i | ||||
\(709\) | − | 1.76067e24i | − | 1.03558i | −0.855508 | − | 0.517790i | \(-0.826755\pi\) | ||
0.855508 | − | 0.517790i | \(-0.173245\pi\) | |||||||
\(710\) | −2.18647e23 | − | 9.00438e23i | −0.127071 | − | 0.523308i | ||||
\(711\) | 6.64905e24 | 3.81828 | ||||||||
\(712\) | −3.93666e23 | + | 3.41554e23i | −0.223382 | + | 0.193811i | ||||
\(713\) | −4.99866e23 | −0.280280 | ||||||||
\(714\) | 2.26993e23 | + | 9.34808e23i | 0.125770 | + | 0.517950i | ||||
\(715\) | 6.00027e23i | 0.328526i | ||||||||
\(716\) | 2.40652e23 | + | 4.66312e23i | 0.130205 | + | 0.252299i | ||||
\(717\) | 4.77023e24i | 2.55051i | ||||||||
\(718\) | −4.85682e23 | + | 1.17935e23i | −0.256622 | + | 0.0623137i | ||||
\(719\) | −3.64140e24 | −1.90140 | −0.950698 | − | 0.310118i | \(-0.899631\pi\) | ||||
−0.950698 | + | 0.310118i | \(0.899631\pi\) | |||||||
\(720\) | 2.22153e24 | + | 1.57909e24i | 1.14637 | + | 0.814857i | ||||
\(721\) | −4.31555e24 | −2.20083 | ||||||||
\(722\) | 1.91656e24 | − | 4.65384e23i | 0.965953 | − | 0.234555i | ||||
\(723\) | − | 3.59355e23i | − | 0.178998i | ||||||
\(724\) | −1.37319e24 | − | 2.66084e24i | −0.676010 | − | 1.30991i | ||||
\(725\) | − | 2.31473e23i | − | 0.112623i | ||||||
\(726\) | −2.55679e23 | − | 1.05294e24i | −0.122951 | − | 0.506342i | ||||
\(727\) | 2.16795e24 | 1.03040 | 0.515201 | − | 0.857069i | \(-0.327717\pi\) | ||||
0.515201 | + | 0.857069i | \(0.327717\pi\) | |||||||
\(728\) | 1.48740e24 | + | 1.71434e24i | 0.698734 | + | 0.805341i | ||||
\(729\) | −6.08522e24 | −2.82548 | ||||||||
\(730\) | −5.85850e22 | − | 2.41266e23i | −0.0268870 | − | 0.110727i | ||||
\(731\) | 2.18093e23i | 0.0989338i | ||||||||
\(732\) | −1.00673e24 | + | 5.19548e23i | −0.451407 | + | 0.232960i | ||||
\(733\) | − | 2.91223e24i | − | 1.29075i | −0.763866 | − | 0.645375i | \(-0.776701\pi\) | ||
0.763866 | − | 0.645375i | \(-0.223299\pi\) | |||||||
\(734\) | 3.22935e24 | − | 7.84161e23i | 1.41481 | − | 0.343549i | ||||
\(735\) | −2.75094e24 | −1.19135 | ||||||||
\(736\) | −3.00285e23 | + | 7.52398e23i | −0.128550 | + | 0.322096i | ||||
\(737\) | 3.16575e24 | 1.33969 | ||||||||
\(738\) | 6.95250e23 | − | 1.68823e23i | 0.290845 | − | 0.0706239i | ||||
\(739\) | − | 2.56079e23i | − | 0.105900i | −0.998597 | − | 0.0529500i | \(-0.983138\pi\) | ||
0.998597 | − | 0.0529500i | \(-0.0168624\pi\) | |||||||
\(740\) | 1.29880e24 | − | 6.70278e23i | 0.530973 | − | 0.274022i | ||||
\(741\) | 2.64045e23i | 0.106715i | ||||||||
\(742\) | −1.23927e24 | − | 5.10359e24i | −0.495145 | − | 2.03912i | ||||
\(743\) | −1.24281e24 | −0.490907 | −0.245453 | − | 0.969408i | \(-0.578937\pi\) | ||||
−0.245453 | + | 0.969408i | \(0.578937\pi\) | |||||||
\(744\) | −2.58781e24 | − | 2.98264e24i | −1.01056 | − | 1.16475i | ||||
\(745\) | −1.36117e24 | −0.525514 | ||||||||
\(746\) | 3.14868e23 | + | 1.29670e24i | 0.120184 | + | 0.494947i | ||||
\(747\) | − | 1.14780e25i | − | 4.33152i | ||||||
\(748\) | −1.98626e23 | − | 3.84877e23i | −0.0741091 | − | 0.143601i | ||||
\(749\) | 1.24342e24i | 0.458692i | ||||||||
\(750\) | −4.64721e24 | + | 1.12845e24i | −1.69501 | + | 0.411587i | ||||
\(751\) | 4.22804e24 | 1.52475 | 0.762376 | − | 0.647134i | \(-0.224032\pi\) | ||||
0.762376 | + | 0.647134i | \(0.224032\pi\) | |||||||
\(752\) | −1.56106e24 | + | 2.19616e24i | −0.556631 | + | 0.783090i | ||||
\(753\) | 1.11397e24 | 0.392751 | ||||||||
\(754\) | 3.17063e23 | − | 7.69901e22i | 0.110532 | − | 0.0268397i | ||||
\(755\) | − | 1.57648e24i | − | 0.543425i | ||||||
\(756\) | 6.20718e24 | + | 1.20277e25i | 2.11572 | + | 4.09964i | ||||
\(757\) | − | 1.18946e24i | − | 0.400899i | −0.979704 | − | 0.200449i | \(-0.935760\pi\) | ||
0.979704 | − | 0.200449i | \(-0.0642402\pi\) | |||||||
\(758\) | 7.83846e23 | + | 3.22806e24i | 0.261242 | + | 1.07585i | ||||
\(759\) | −1.71182e24 | −0.564162 | ||||||||
\(760\) | 9.54433e22 | − | 8.28090e22i | 0.0311050 | − | 0.0269874i | ||||
\(761\) | −5.41223e24 | −1.74424 | −0.872120 | − | 0.489291i | \(-0.837255\pi\) | ||||
−0.872120 | + | 0.489291i | \(0.837255\pi\) | |||||||
\(762\) | −9.81259e23 | − | 4.04105e24i | −0.312728 | − | 1.28788i | ||||
\(763\) | 8.27041e24i | 2.60656i | ||||||||
\(764\) | 3.55915e24 | − | 1.83679e24i | 1.10931 | − | 0.572487i | ||||
\(765\) | − | 8.64857e23i | − | 0.266577i | ||||||
\(766\) | −2.54499e24 | + | 6.17982e23i | −0.775785 | + | 0.188378i | ||||
\(767\) | −1.78232e24 | −0.537309 | ||||||||
\(768\) | −6.04405e24 | + | 2.10340e24i | −1.80201 | + | 0.627122i | ||||
\(769\) | −2.19062e24 | −0.645942 | −0.322971 | − | 0.946409i | \(-0.604682\pi\) | ||||
−0.322971 | + | 0.946409i | \(0.604682\pi\) | |||||||
\(770\) | 2.23031e24 | − | 5.41571e23i | 0.650421 | − | 0.157937i | ||||
\(771\) | 1.95875e24i | 0.564959i | ||||||||
\(772\) | 2.61839e24 | − | 1.35129e24i | 0.746944 | − | 0.385479i | ||||
\(773\) | − | 1.32708e24i | − | 0.374431i | −0.982319 | − | 0.187216i | \(-0.940054\pi\) | ||
0.982319 | − | 0.187216i | \(-0.0599463\pi\) | |||||||
\(774\) | 1.16544e24 | + | 4.79956e24i | 0.325232 | + | 1.33938i | ||||
\(775\) | 2.09731e24 | 0.578893 | ||||||||
\(776\) | 2.35629e24 | − | 2.04437e24i | 0.643285 | − | 0.558130i | ||||
\(777\) | 1.16821e25 | 3.15459 | ||||||||
\(778\) | 1.07411e23 | + | 4.42342e23i | 0.0286894 | + | 0.118149i | ||||
\(779\) | − | 3.31690e22i | − | 0.00876324i | ||||||
\(780\) | −1.29019e24 | − | 2.50000e24i | −0.337170 | − | 0.653336i | ||||
\(781\) | 3.33452e24i | 0.861984i | ||||||||
\(782\) | 2.49798e23 | − | 6.06568e22i | 0.0638752 | − | 0.0155104i | ||||
\(783\) | 1.94572e24 | 0.492160 | ||||||||
\(784\) | 2.71428e24 | − | 3.81855e24i | 0.679153 | − | 0.955459i | ||||
\(785\) | 1.65260e24 | 0.409049 | ||||||||
\(786\) | 8.52646e24 | − | 2.07042e24i | 2.08774 | − | 0.506952i | ||||
\(787\) | 2.81620e24i | 0.682146i | 0.940037 | + | 0.341073i | \(0.110790\pi\) | ||||
−0.940037 | + | 0.341073i | \(0.889210\pi\) | |||||||
\(788\) | −3.24681e24 | − | 6.29134e24i | −0.778007 | − | 1.50755i | ||||
\(789\) | 4.17322e24i | 0.989276i | ||||||||
\(790\) | 7.74991e23 | + | 3.19159e24i | 0.181747 | + | 0.748474i | ||||
\(791\) | −7.83316e24 | −1.81734 | ||||||||
\(792\) | −6.42784e24 | − | 7.40855e24i | −1.47537 | − | 1.70047i | ||||
\(793\) | 8.48146e23 | 0.192597 | ||||||||
\(794\) | 9.21089e23 | + | 3.79326e24i | 0.206932 | + | 0.852193i | ||||
\(795\) | 6.50986e24i | 1.44694i | ||||||||
\(796\) | −3.84600e23 | + | 1.98482e23i | −0.0845761 | + | 0.0436476i | ||||
\(797\) | − | 6.52060e24i | − | 1.41870i | −0.704854 | − | 0.709352i | \(-0.748988\pi\) | ||
0.704854 | − | 0.709352i | \(-0.251012\pi\) | |||||||
\(798\) | 9.81462e23 | − | 2.38321e23i | 0.211275 | − | 0.0513025i | ||||
\(799\) | 8.54981e23 | 0.182100 | ||||||||
\(800\) | 1.25992e24 | − | 3.15687e24i | 0.265509 | − | 0.665261i | ||||
\(801\) | 3.74522e24 | 0.780910 | ||||||||
\(802\) | −3.81488e24 | + | 9.26340e23i | −0.787044 | + | 0.191112i | ||||
\(803\) | 8.93462e23i | 0.182387i | ||||||||
\(804\) | −1.31900e25 | + | 6.80705e24i | −2.66422 | + | 1.37494i | ||||
\(805\) | 1.36220e24i | 0.272254i | ||||||||
\(806\) | 6.97585e23 | + | 2.87282e24i | 0.137959 | + | 0.568146i | ||||
\(807\) | −1.17112e24 | −0.229179 | ||||||||
\(808\) | 2.21029e24 | + | 2.54752e24i | 0.428009 | + | 0.493311i | ||||
\(809\) | 8.81198e23 | 0.168854 | 0.0844269 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844269 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(810\) | −2.20851e24 | − | 9.09513e24i | −0.418770 | − | 1.72459i | ||||
\(811\) | − | 3.57272e24i | − | 0.670381i | −0.942150 | − | 0.335191i | \(-0.891199\pi\) | ||
0.942150 | − | 0.335191i | \(-0.108801\pi\) | |||||||
\(812\) | −5.72347e23 | − | 1.10904e24i | −0.106276 | − | 0.205930i | ||||
\(813\) | − | 1.41736e24i | − | 0.260441i | ||||||
\(814\) | −5.11111e24 | + | 1.24109e24i | −0.929410 | + | 0.225682i | ||||
\(815\) | 3.17288e24 | 0.570971 | ||||||||
\(816\) | 1.65514e24 | + | 1.17650e24i | 0.294760 | + | 0.209519i | ||||
\(817\) | 2.28978e23 | 0.0403558 | ||||||||
\(818\) | −8.18722e24 | + | 1.98804e24i | −1.42802 | + | 0.346755i | ||||
\(819\) | − | 1.63097e25i | − | 2.81536i | ||||||
\(820\) | 1.62072e23 | + | 3.14047e23i | 0.0276879 | + | 0.0536509i | ||||
\(821\) | 1.46618e24i | 0.247896i | 0.992289 | + | 0.123948i | \(0.0395556\pi\) | ||||
−0.992289 | + | 0.123948i | \(0.960444\pi\) | |||||||
\(822\) | −1.25150e24 | − | 5.15397e24i | −0.209421 | − | 0.862445i | ||||
\(823\) | −2.89883e24 | −0.480091 | −0.240046 | − | 0.970762i | \(-0.577162\pi\) | ||||
−0.240046 | + | 0.970762i | \(0.577162\pi\) | |||||||
\(824\) | −6.88099e24 | + | 5.97011e24i | −1.12790 | + | 0.978591i | ||||
\(825\) | 7.18238e24 | 1.16523 | ||||||||
\(826\) | 1.60868e24 | + | 6.62491e24i | 0.258309 | + | 1.06377i | ||||
\(827\) | 4.06842e24i | 0.646590i | 0.946298 | + | 0.323295i | \(0.104791\pi\) | ||||
−0.946298 | + | 0.323295i | \(0.895209\pi\) | |||||||
\(828\) | 5.17316e24 | − | 2.66974e24i | 0.813763 | − | 0.419963i | ||||
\(829\) | − | 7.02644e24i | − | 1.09401i | −0.837129 | − | 0.547005i | \(-0.815768\pi\) | ||
0.837129 | − | 0.547005i | \(-0.184232\pi\) | |||||||
\(830\) | 5.50951e24 | − | 1.33783e24i | 0.849081 | − | 0.206176i | ||||
\(831\) | −3.89792e24 | −0.594599 | ||||||||
\(832\) | 4.74322e24 | + | 6.75786e23i | 0.716184 | + | 0.102038i | ||||
\(833\) | −1.48659e24 | −0.222182 | ||||||||
\(834\) | 1.09373e25 | − | 2.65583e24i | 1.61808 | − | 0.392907i | ||||
\(835\) | 6.00802e24i | 0.879826i | ||||||||
\(836\) | −4.04085e23 | + | 2.08538e23i | −0.0585760 | + | 0.0302296i | ||||
\(837\) | 1.76297e25i | 2.52975i | ||||||||
\(838\) | −2.26364e24 | − | 9.32220e24i | −0.321539 | − | 1.32417i | ||||
\(839\) | −3.75744e24 | −0.528342 | −0.264171 | − | 0.964476i | \(-0.585098\pi\) | ||||
−0.264171 | + | 0.964476i | \(0.585098\pi\) | |||||||
\(840\) | −8.12807e24 | + | 7.05211e24i | −1.13139 | + | 0.981624i | ||||
\(841\) | 7.07774e24 | 0.975278 | ||||||||
\(842\) | 3.01487e23 | + | 1.24159e24i | 0.0411259 | + | 0.169366i | ||||
\(843\) | − | 1.17773e25i | − | 1.59042i | ||||||
\(844\) | 4.78452e24 | + | 9.27097e24i | 0.639628 | + | 1.23941i | ||||
\(845\) | − | 1.91840e24i | − | 0.253896i | ||||||
\(846\) | 1.88155e25 | − | 4.56883e24i | 2.46529 | − | 0.598628i | ||||
\(847\) | 3.10288e24 | 0.402491 | ||||||||
\(848\) | −9.03626e24 | − | 6.42310e24i | −1.16044 | − | 0.824859i | ||||
\(849\) | −1.53695e25 | −1.95408 | ||||||||
\(850\) | −1.04809e24 | + | 2.54500e23i | −0.131928 | + | 0.0320352i | ||||
\(851\) | − | 3.12169e24i | − | 0.389034i | ||||||
\(852\) | −7.16994e24 | − | 1.38932e25i | −0.884666 | − | 1.71422i | ||||
\(853\) | 8.76545e24i | 1.07080i | 0.844599 | + | 0.535399i | \(0.179839\pi\) | ||||
−0.844599 | + | 0.535399i | \(0.820161\pi\) | |||||||
\(854\) | −7.65518e23 | − | 3.15258e24i | −0.0925899 | − | 0.381306i | ||||
\(855\) | −9.08020e23 | −0.108739 | ||||||||
\(856\) | 1.72014e24 | + | 1.98258e24i | 0.203956 | + | 0.235074i | ||||
\(857\) | −7.03954e24 | −0.826432 | −0.413216 | − | 0.910633i | \(-0.635595\pi\) | ||||
−0.413216 | + | 0.910633i | \(0.635595\pi\) | |||||||
\(858\) | 2.38893e24 | + | 9.83815e24i | 0.277690 | + | 1.14359i | ||||
\(859\) | 5.42420e24i | 0.624301i | 0.950033 | + | 0.312151i | \(0.101049\pi\) | ||||
−0.950033 | + | 0.312151i | \(0.898951\pi\) | |||||||
\(860\) | −2.16798e24 | + | 1.11884e24i | −0.247069 | + | 0.127506i | ||||
\(861\) | 2.82471e24i | 0.318748i | ||||||||
\(862\) | −5.71587e24 | + | 1.38794e24i | −0.638661 | + | 0.155082i | ||||
\(863\) | −4.27768e24 | −0.473278 | −0.236639 | − | 0.971598i | \(-0.576046\pi\) | ||||
−0.236639 | + | 0.971598i | \(0.576046\pi\) | |||||||
\(864\) | 2.65361e25 | + | 1.05907e25i | 2.90717 | + | 1.16027i | ||||
\(865\) | −1.38680e24 | −0.150445 | ||||||||
\(866\) | −7.43186e24 | + | 1.80462e24i | −0.798353 | + | 0.193858i | ||||
\(867\) | 1.72924e25i | 1.83947i | ||||||||
\(868\) | 1.00487e25 | − | 5.18588e24i | 1.05850 | − | 0.546267i | ||||
\(869\) | − | 1.18192e25i | − | 1.23287i | ||||||
\(870\) | 3.65027e23 | + | 1.50327e24i | 0.0377061 | + | 0.155282i | ||||
\(871\) | 1.11123e25 | 1.13671 | ||||||||
\(872\) | 1.14412e25 | + | 1.31869e25i | 1.15900 | + | 1.33583i | ||||
\(873\) | −2.24170e25 | −2.24883 | ||||||||
\(874\) | −6.36840e22 | − | 2.62265e23i | −0.00632679 | − | 0.0260551i | ||||
\(875\) | − | 1.36947e25i | − | 1.34736i | ||||||
\(876\) | −1.92114e24 | − | 3.72260e24i | −0.187186 | − | 0.362711i | ||||
\(877\) | − | 1.78456e25i | − | 1.72201i | −0.508597 | − | 0.861005i | \(-0.669836\pi\) | ||
0.508597 | − | 0.861005i | \(-0.330164\pi\) | |||||||
\(878\) | 1.25883e25 | − | 3.05673e24i | 1.20300 | − | 0.292115i | ||||
\(879\) | −2.22699e24 | −0.210772 | ||||||||
\(880\) | 2.80695e24 | − | 3.94892e24i | 0.263106 | − | 0.370148i | ||||
\(881\) | 2.01186e25 | 1.86768 | 0.933841 | − | 0.357688i | \(-0.116435\pi\) | ||||
0.933841 | + | 0.357688i | \(0.116435\pi\) | |||||||
\(882\) | −3.27153e25 | + | 7.94402e24i | −3.00793 | + | 0.730394i | ||||
\(883\) | − | 9.33262e24i | − | 0.849841i | −0.905231 | − | 0.424921i | \(-0.860302\pi\) | ||
0.905231 | − | 0.424921i | \(-0.139698\pi\) | |||||||
\(884\) | −6.97209e23 | − | 1.35098e24i | −0.0628809 | − | 0.121845i | ||||
\(885\) | − | 8.45037e24i | − | 0.754845i | ||||||
\(886\) | 4.67292e24 | + | 1.92441e25i | 0.413429 | + | 1.70260i | ||||
\(887\) | 1.53656e25 | 1.34647 | 0.673237 | − | 0.739426i | \(-0.264903\pi\) | ||||
0.673237 | + | 0.739426i | \(0.264903\pi\) | |||||||
\(888\) | 1.86267e25 | − | 1.61610e25i | 1.61669 | − | 1.40268i | ||||
\(889\) | 1.19084e25 | 1.02374 | ||||||||
\(890\) | 4.36531e23 | + | 1.79773e24i | 0.0371706 | + | 0.153077i | ||||
\(891\) | 3.36813e25i | 2.84072i | ||||||||
\(892\) | −8.37164e24 | + | 4.32039e24i | −0.699373 | + | 0.360929i | ||||
\(893\) | − | 8.97651e23i | − | 0.0742797i | ||||||
\(894\) | −2.23180e25 | + | 5.41932e24i | −1.82931 | + | 0.444197i | ||||
\(895\) | 1.86262e24 | 0.151227 | ||||||||
\(896\) | −1.76921e24 | − | 1.82406e25i | −0.142286 | − | 1.46697i | ||||
\(897\) | −6.00880e24 | −0.478687 | ||||||||
\(898\) | 6.49419e24 | − | 1.57694e24i | 0.512479 | − | 0.124442i | ||||
\(899\) | − | 1.62558e24i | − | 0.127073i | ||||||
\(900\) | −2.17053e25 | + | 1.12015e25i | −1.68075 | + | 0.867394i | ||||
\(901\) | 3.51788e24i | 0.269849i | ||||||||
\(902\) | −3.00094e23 | − | 1.23586e24i | −0.0228035 | − | 0.0939101i | ||||
\(903\) | −1.95000e25 | −1.46788 | ||||||||
\(904\) | −1.24897e25 | + | 1.08364e25i | −0.931366 | + | 0.808076i | ||||
\(905\) | −1.06284e25 | −0.785153 | ||||||||
\(906\) | −6.27654e24 | − | 2.58482e25i | −0.459336 | − | 1.89165i | ||||
\(907\) | − | 1.19285e25i | − | 0.864818i | −0.901678 | − | 0.432409i | \(-0.857664\pi\) | ||
0.901678 | − | 0.432409i | \(-0.142336\pi\) | |||||||
\(908\) | 6.44698e24 | + | 1.24923e25i | 0.463049 | + | 0.897251i | ||||
\(909\) | − | 2.42364e25i | − | 1.72455i | ||||||
\(910\) | 7.82878e24 | − | 1.90101e24i | 0.551877 | − | 0.134008i | ||||
\(911\) | 2.47178e24 | 0.172625 | 0.0863124 | − | 0.996268i | \(-0.472492\pi\) | ||||
0.0863124 | + | 0.996268i | \(0.472492\pi\) | |||||||
\(912\) | 1.23521e24 | − | 1.73775e24i | 0.0854645 | − | 0.120235i | ||||
\(913\) | −2.04029e25 | −1.39859 | ||||||||
\(914\) | 1.02749e25 | − | 2.49498e24i | 0.697807 | − | 0.169443i | ||||
\(915\) | 4.02125e24i | 0.270572i | ||||||||
\(916\) | −5.14054e24 | − | 9.96085e24i | −0.342687 | − | 0.664025i | ||||
\(917\) | 2.51263e25i | 1.65955i | ||||||||
\(918\) | −2.13929e24 | − | 8.81008e24i | −0.139993 | − | 0.576524i | ||||
\(919\) | 2.69765e24 | 0.174905 | 0.0874527 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874527 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(920\) | 1.88446e24 | + | 2.17197e24i | 0.121057 | + | 0.139527i | ||||
\(921\) | 1.35464e24 | 0.0862219 | ||||||||
\(922\) | −3.44797e24 | − | 1.41995e25i | −0.217446 | − | 0.895491i | ||||
\(923\) | 1.17047e25i | 0.731386i | ||||||||
\(924\) | 3.44124e25 | − | 1.77594e25i | 2.13061 | − | 1.09955i | ||||
\(925\) | 1.30978e25i | 0.803515i | ||||||||
\(926\) | −2.29358e25 | + | 5.56933e24i | −1.39418 | + | 0.338540i | ||||
\(927\) | 6.54637e25 | 3.94296 | ||||||||
\(928\) | −2.44683e24 | − | 9.76540e23i | −0.146031 | − | 0.0582817i | ||||
\(929\) | 1.73143e24 | 0.102393 | 0.0511967 | − | 0.998689i | \(-0.483696\pi\) | ||||
0.0511967 | + | 0.998689i | \(0.483696\pi\) | |||||||
\(930\) | −1.36207e25 | + | 3.30741e24i | −0.798167 | + | 0.193813i | ||||
\(931\) | 1.56078e24i | 0.0906296i | ||||||||
\(932\) | −1.92208e25 | + | 9.91939e24i | −1.10595 | + | 0.570755i | ||||
\(933\) | 1.34378e25i | 0.766185i | ||||||||
\(934\) | 2.68966e23 | + | 1.10766e24i | 0.0151967 | + | 0.0625834i | ||||
\(935\) | −1.53734e24 | −0.0860741 | ||||||||
\(936\) | −2.25628e25 | − | 2.60053e25i | −1.25184 | − | 1.44283i | ||||
\(937\) | −1.92274e25 | −1.05714 | −0.528572 | − | 0.848888i | \(-0.677272\pi\) | ||||
−0.528572 | + | 0.848888i | \(0.677272\pi\) | |||||||
\(938\) | −1.00297e25 | − | 4.13047e25i | −0.546468 | − | 2.25048i | ||||
\(939\) | − | 4.45922e25i | − | 2.40770i | ||||||
\(940\) | 4.38614e24 | + | 8.49904e24i | 0.234691 | + | 0.454761i | ||||
\(941\) | 2.50201e25i | 1.32671i | 0.748303 | + | 0.663357i | \(0.230869\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(942\) | 2.70963e25 | − | 6.57960e24i | 1.42389 | − | 0.345754i | ||||
\(943\) | 7.54817e23 | 0.0393090 | ||||||||
\(944\) | 1.17299e25 | + | 8.33774e24i | 0.605384 | + | 0.430315i | ||||
\(945\) | 4.80430e25 | 2.45731 | ||||||||
\(946\) | 8.53155e24 | − | 2.07166e24i | 0.432468 | − | 0.105013i | ||||
\(947\) | 2.84634e25i | 1.42992i | 0.699165 | + | 0.714961i | \(0.253555\pi\) | ||||
−0.699165 | + | 0.714961i | \(0.746445\pi\) | |||||||
\(948\) | 2.54138e25 | + | 4.92443e25i | 1.26531 | + | 2.45180i | ||||
\(949\) | 3.13620e24i | 0.154754i | ||||||||
\(950\) | 2.67202e23 | + | 1.10040e24i | 0.0130674 | + | 0.0538145i | ||||
\(951\) | −6.00076e25 | −2.90852 | ||||||||
\(952\) | −4.39235e24 | + | 3.81091e24i | −0.211000 | + | 0.183069i | ||||
\(953\) | 3.20703e25 | 1.52691 | 0.763455 | − | 0.645862i | \(-0.223502\pi\) | ||||
0.763455 | + | 0.645862i | \(0.223502\pi\) | |||||||
\(954\) | 1.87988e25 | + | 7.74178e25i | 0.887093 | + | 3.65325i | ||||
\(955\) | − | 1.42166e25i | − | 0.664916i | ||||||
\(956\) | −2.56249e25 | + | 1.32244e25i | −1.18787 | + | 0.613033i | ||||
\(957\) | − | 5.56692e24i | − | 0.255778i | ||||||
\(958\) | 1.89196e25 | − | 4.59412e24i | 0.861599 | − | 0.209216i | ||||
\(959\) | 1.51880e25 | 0.685557 | ||||||||
\(960\) | −3.20406e24 | + | 2.24887e25i | −0.143349 | + | 1.00614i | ||||
\(961\) | −7.82115e24 | −0.346834 | ||||||||
\(962\) | −1.79409e25 | + | 4.35645e24i | −0.788597 | + | 0.191489i | ||||
\(963\) | − | 1.88617e25i | − | 0.821784i | ||||||
\(964\) | 1.93040e24 | − | 9.96231e23i | 0.0833666 | − | 0.0430234i | ||||
\(965\) | − | 1.04589e25i | − | 0.447715i | ||||||
\(966\) | 5.42341e24 | + | 2.23348e25i | 0.230126 | + | 0.947713i | ||||
\(967\) | −4.41829e25 | −1.85836 | −0.929178 | − | 0.369633i | \(-0.879483\pi\) | ||||
−0.929178 | + | 0.369633i | \(0.879483\pi\) | |||||||
\(968\) | 4.94743e24 | − | 4.29251e24i | 0.206272 | − | 0.178966i | ||||
\(969\) | −6.76517e23 | −0.0279593 | ||||||||
\(970\) | −2.61286e24 | − | 1.07603e25i | −0.107042 | − | 0.440825i | ||||
\(971\) | − | 5.97199e24i | − | 0.242524i | −0.992621 | − | 0.121262i | \(-0.961306\pi\) | ||
0.992621 | − | 0.121262i | \(-0.0386942\pi\) | |||||||
\(972\) | −3.67632e25 | − | 7.12361e25i | −1.47996 | − | 2.86772i | ||||
\(973\) | 3.22308e25i | 1.28621i | ||||||||
\(974\) | −5.70281e24 | + | 1.38477e24i | −0.225599 | + | 0.0547807i | ||||
\(975\) | 2.52114e25 | 0.988684 | ||||||||
\(976\) | −5.58185e24 | − | 3.96766e24i | −0.216998 | − | 0.154245i | ||||
\(977\) | 1.23801e25 | 0.477112 | 0.238556 | − | 0.971129i | \(-0.423326\pi\) | ||||
0.238556 | + | 0.971129i | \(0.423326\pi\) | |||||||
\(978\) | 5.20231e25 | − | 1.26324e25i | 1.98754 | − | 0.482620i | ||||
\(979\) | − | 6.65740e24i | − | 0.252146i | ||||||
\(980\) | −7.62637e24 | − | 1.47776e25i | −0.286349 | − | 0.554860i | ||||
\(981\) | − | 1.25456e26i | − | 4.66987i | ||||||
\(982\) | −3.32525e24 | − | 1.36941e25i | −0.122709 | − | 0.505344i | ||||
\(983\) | 1.37346e25 | 0.502471 | 0.251235 | − | 0.967926i | \(-0.419163\pi\) | ||||
0.251235 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(984\) | 3.90770e24 | + | 4.50391e24i | 0.141730 | + | 0.163354i | ||||
\(985\) | −2.51300e25 | −0.903617 | ||||||||
\(986\) | 1.97258e23 | + | 8.12354e23i | 0.00703204 | + | 0.0289595i | ||||
\(987\) | 7.64450e25i | 2.70180i | ||||||||
\(988\) | −1.41841e24 | + | 7.32006e23i | −0.0497013 | + | 0.0256496i | ||||
\(989\) | 5.21078e24i | 0.181023i | ||||||||
\(990\) | −3.38322e25 | + | 8.21524e24i | −1.16528 | + | 0.282957i | ||||
\(991\) | −3.74894e25 | −1.28021 | −0.640106 | − | 0.768286i | \(-0.721110\pi\) | ||||
−0.640106 | + | 0.768286i | \(0.721110\pi\) | |||||||
\(992\) | 8.84815e24 | − | 2.21700e25i | 0.299574 | − | 0.750614i | ||||
\(993\) | −3.51341e25 | −1.17940 | ||||||||
\(994\) | 4.35067e25 | − | 1.05644e25i | 1.44801 | − | 0.351610i | ||||
\(995\) | 1.53624e24i | 0.0506946i | ||||||||
\(996\) | 8.50084e25 | − | 4.38707e25i | 2.78136 | − | 1.43539i | ||||
\(997\) | − | 1.39329e25i | − | 0.451993i | −0.974128 | − | 0.225997i | \(-0.927436\pi\) | ||
0.974128 | − | 0.225997i | \(-0.0725638\pi\) | |||||||
\(998\) | −5.73091e24 | − | 2.36012e25i | −0.184338 | − | 0.759144i | ||||
\(999\) | −1.10098e26 | −3.51134 |
(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 | 8.18.b.a.5.15 | ✓ | 16 | |
3.2 | odd | 2 | 72.18.d.b.37.2 | 16 | |||
4.3 | odd | 2 | 32.18.b.a.17.16 | 16 | |||
8.3 | odd | 2 | 32.18.b.a.17.1 | 16 | |||
8.5 | even | 2 | inner | 8.18.b.a.5.16 | yes | 16 | |
24.5 | odd | 2 | 72.18.d.b.37.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.18.b.a.5.15 | ✓ | 16 | 1.1 | even | 1 | trivial | |
8.18.b.a.5.16 | yes | 16 | 8.5 | even | 2 | inner | |
32.18.b.a.17.1 | 16 | 8.3 | odd | 2 | |||
32.18.b.a.17.16 | 16 | 4.3 | odd | 2 | |||
72.18.d.b.37.1 | 16 | 24.5 | odd | 2 | |||
72.18.d.b.37.2 | 16 | 3.2 | odd | 2 |