Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,17,Mod(3,8)]
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([1, 1]))
N = Newforms(chi, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(12.9859635085\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} + \cdots + 27\!\cdots\!20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{91}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(109.380 - 40.6323i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.17.d.b.3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −242.759 | + | 81.2647i | −0.948278 | + | 0.317440i | ||||
\(3\) | −7667.81 | −1.16869 | −0.584347 | − | 0.811504i | \(-0.698649\pi\) | ||||
−0.584347 | + | 0.811504i | \(0.698649\pi\) | |||||||
\(4\) | 52328.1 | − | 39455.5i | 0.798464 | − | 0.602043i | ||||
\(5\) | 557358.i | 1.42684i | 0.700739 | + | 0.713418i | \(0.252854\pi\) | ||||
−0.700739 | + | 0.713418i | \(0.747146\pi\) | |||||||
\(6\) | 1.86143e6 | − | 623122.i | 1.10825 | − | 0.370991i | ||||
\(7\) | 8.55454e6i | 1.48393i | 0.670441 | + | 0.741963i | \(0.266105\pi\) | ||||
−0.670441 | + | 0.741963i | \(0.733895\pi\) | |||||||
\(8\) | −9.49679e6 | + | 1.38306e7i | −0.566053 | + | 0.824369i | ||||
\(9\) | 1.57485e7 | 0.365847 | ||||||||
\(10\) | −4.52935e7 | − | 1.35304e8i | −0.452935 | − | 1.35304i | ||||
\(11\) | 1.51024e8 | 0.704536 | 0.352268 | − | 0.935899i | \(-0.385410\pi\) | ||||
0.352268 | + | 0.935899i | \(0.385410\pi\) | |||||||
\(12\) | −4.01242e8 | + | 3.02537e8i | −0.933160 | + | 0.703605i | ||||
\(13\) | 3.64901e8i | 0.447330i | 0.974666 | + | 0.223665i | \(0.0718021\pi\) | ||||
−0.974666 | + | 0.223665i | \(0.928198\pi\) | |||||||
\(14\) | −6.95181e8 | − | 2.07669e9i | −0.471057 | − | 1.40717i | ||||
\(15\) | − | 4.27371e9i | − | 1.66754i | ||||||
\(16\) | 1.18149e9 | − | 4.12926e9i | 0.275088 | − | 0.961419i | ||||
\(17\) | −1.29368e10 | −1.85454 | −0.927271 | − | 0.374390i | \(-0.877852\pi\) | ||||
−0.927271 | + | 0.374390i | \(0.877852\pi\) | |||||||
\(18\) | −3.82310e9 | + | 1.27980e9i | −0.346925 | + | 0.116135i | ||||
\(19\) | 2.11348e9 | 0.124442 | 0.0622212 | − | 0.998062i | \(-0.480182\pi\) | ||||
0.0622212 | + | 0.998062i | \(0.480182\pi\) | |||||||
\(20\) | 2.19908e10 | + | 2.91655e10i | 0.859017 | + | 1.13928i | ||||
\(21\) | − | 6.55945e10i | − | 1.73426i | ||||||
\(22\) | −3.66624e10 | + | 1.22729e10i | −0.668097 | + | 0.223648i | ||||
\(23\) | 7.33433e10i | 0.936564i | 0.883579 | + | 0.468282i | \(0.155127\pi\) | ||||
−0.883579 | + | 0.468282i | \(0.844873\pi\) | |||||||
\(24\) | 7.28196e10 | − | 1.06050e11i | 0.661543 | − | 0.963435i | ||||
\(25\) | −1.58060e11 | −1.03586 | ||||||||
\(26\) | −2.96535e10 | − | 8.85830e10i | −0.142000 | − | 0.424193i | ||||
\(27\) | 2.09317e11 | 0.741131 | ||||||||
\(28\) | 3.37523e11 | + | 4.47643e11i | 0.893387 | + | 1.18486i | ||||
\(29\) | 2.80131e11i | 0.559985i | 0.960002 | + | 0.279993i | \(0.0903320\pi\) | ||||
−0.960002 | + | 0.279993i | \(0.909668\pi\) | |||||||
\(30\) | 3.47302e11 | + | 1.03748e12i | 0.529343 | + | 1.58129i | ||||
\(31\) | − | 9.63483e11i | − | 1.12967i | −0.825205 | − | 0.564834i | \(-0.808940\pi\) | ||
0.825205 | − | 0.564834i | \(-0.191060\pi\) | |||||||
\(32\) | 4.87445e10 | + | 1.09843e12i | 0.0443329 | + | 0.999017i | ||||
\(33\) | −1.15802e12 | −0.823388 | ||||||||
\(34\) | 3.14054e12 | − | 1.05131e12i | 1.75862 | − | 0.588706i | ||||
\(35\) | −4.76794e12 | −2.11732 | ||||||||
\(36\) | 8.24090e11 | − | 6.21366e11i | 0.292116 | − | 0.220256i | ||||
\(37\) | − | 5.53641e12i | − | 1.57621i | −0.615540 | − | 0.788106i | \(-0.711062\pi\) | ||
0.615540 | − | 0.788106i | \(-0.288938\pi\) | |||||||
\(38\) | −5.13066e11 | + | 1.71751e11i | −0.118006 | + | 0.0395030i | ||||
\(39\) | − | 2.79799e12i | − | 0.522792i | ||||||
\(40\) | −7.70860e12 | − | 5.29311e12i | −1.17624 | − | 0.807665i | ||||
\(41\) | −1.80493e11 | −0.0226042 | −0.0113021 | − | 0.999936i | \(-0.503598\pi\) | ||||
−0.0113021 | + | 0.999936i | \(0.503598\pi\) | |||||||
\(42\) | 5.33052e12 | + | 1.59237e13i | 0.550522 | + | 1.64456i | ||||
\(43\) | 2.29216e12 | 0.196109 | 0.0980544 | − | 0.995181i | \(-0.468738\pi\) | ||||
0.0980544 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(44\) | 7.90278e12 | − | 5.95871e12i | 0.562547 | − | 0.424161i | ||||
\(45\) | 8.77757e12i | 0.522004i | ||||||||
\(46\) | −5.96022e12 | − | 1.78048e13i | −0.297303 | − | 0.888124i | ||||
\(47\) | 1.12569e13i | 0.472757i | 0.971661 | + | 0.236378i | \(0.0759604\pi\) | ||||
−0.971661 | + | 0.236378i | \(0.924040\pi\) | |||||||
\(48\) | −9.05947e12 | + | 3.16624e13i | −0.321494 | + | 1.12361i | ||||
\(49\) | −3.99471e13 | −1.20204 | ||||||||
\(50\) | 3.83705e13 | − | 1.28447e13i | 0.982286 | − | 0.328824i | ||||
\(51\) | 9.91972e13 | 2.16739 | ||||||||
\(52\) | 1.43973e13 | + | 1.90946e13i | 0.269312 | + | 0.357177i | ||||
\(53\) | − | 8.73423e12i | − | 0.140287i | −0.997537 | − | 0.0701435i | \(-0.977654\pi\) | ||
0.997537 | − | 0.0701435i | \(-0.0223457\pi\) | |||||||
\(54\) | −5.08137e13 | + | 1.70101e13i | −0.702798 | + | 0.235265i | ||||
\(55\) | 8.41742e13i | 1.00526i | ||||||||
\(56\) | −1.18314e14 | − | 8.12407e13i | −1.22330 | − | 0.839981i | ||||
\(57\) | −1.62057e13 | −0.145435 | ||||||||
\(58\) | −2.27647e13 | − | 6.80043e13i | −0.177762 | − | 0.531022i | ||||
\(59\) | 2.07936e14 | 1.41616 | 0.708082 | − | 0.706131i | \(-0.249561\pi\) | ||||
0.708082 | + | 0.706131i | \(0.249561\pi\) | |||||||
\(60\) | −1.68621e14 | − | 2.23635e14i | −1.00393 | − | 1.33147i | ||||
\(61\) | 8.30772e12i | 0.0433354i | 0.999765 | + | 0.0216677i | \(0.00689759\pi\) | ||||
−0.999765 | + | 0.0216677i | \(0.993102\pi\) | |||||||
\(62\) | 7.82971e13 | + | 2.33894e14i | 0.358602 | + | 1.07124i | ||||
\(63\) | 1.34721e14i | 0.542890i | ||||||||
\(64\) | −1.01097e14 | − | 2.62693e14i | −0.359168 | − | 0.933273i | ||||
\(65\) | −2.03380e14 | −0.638267 | ||||||||
\(66\) | 2.81120e14 | − | 9.41061e13i | 0.780801 | − | 0.261376i | ||||
\(67\) | −8.80887e13 | −0.216931 | −0.108466 | − | 0.994100i | \(-0.534594\pi\) | ||||
−0.108466 | + | 0.994100i | \(0.534594\pi\) | |||||||
\(68\) | −6.76960e14 | + | 5.10429e14i | −1.48078 | + | 1.11651i | ||||
\(69\) | − | 5.62382e14i | − | 1.09456i | ||||||
\(70\) | 1.15746e15 | − | 3.87465e14i | 2.00781 | − | 0.672122i | ||||
\(71\) | − | 6.03023e14i | − | 0.933829i | −0.884302 | − | 0.466915i | \(-0.845366\pi\) | ||
0.884302 | − | 0.466915i | \(-0.154634\pi\) | |||||||
\(72\) | −1.49560e14 | + | 2.17812e14i | −0.207089 | + | 0.301593i | ||||
\(73\) | −1.18912e15 | −1.47449 | −0.737244 | − | 0.675627i | \(-0.763873\pi\) | ||||
−0.737244 | + | 0.675627i | \(0.763873\pi\) | |||||||
\(74\) | 4.49915e14 | + | 1.34401e15i | 0.500353 | + | 1.49469i | ||||
\(75\) | 1.21197e15 | 1.21061 | ||||||||
\(76\) | 1.10594e14 | − | 8.33882e13i | 0.0993627 | − | 0.0749197i | ||||
\(77\) | 1.29194e15i | 1.04548i | ||||||||
\(78\) | 2.27378e14 | + | 6.79238e14i | 0.165955 | + | 0.495752i | ||||
\(79\) | 1.98915e15i | 1.31115i | 0.755132 | + | 0.655573i | \(0.227573\pi\) | ||||
−0.755132 | + | 0.655573i | \(0.772427\pi\) | |||||||
\(80\) | 2.30148e15 | + | 6.58515e14i | 1.37179 | + | 0.392506i | ||||
\(81\) | −2.28293e15 | −1.23200 | ||||||||
\(82\) | 4.38164e13 | − | 1.46677e13i | 0.0214351 | − | 0.00717549i | ||||
\(83\) | 1.65008e15 | 0.732621 | 0.366311 | − | 0.930493i | \(-0.380621\pi\) | ||||
0.366311 | + | 0.930493i | \(0.380621\pi\) | |||||||
\(84\) | −2.58806e15 | − | 3.43244e15i | −1.04410 | − | 1.38474i | ||||
\(85\) | − | 7.21045e15i | − | 2.64613i | ||||||
\(86\) | −5.56443e14 | + | 1.86272e14i | −0.185966 | + | 0.0622528i | ||||
\(87\) | − | 2.14799e15i | − | 0.654452i | ||||||
\(88\) | −1.43424e15 | + | 2.08875e15i | −0.398805 | + | 0.580798i | ||||
\(89\) | −2.34380e15 | −0.595389 | −0.297695 | − | 0.954661i | \(-0.596218\pi\) | ||||
−0.297695 | + | 0.954661i | \(0.596218\pi\) | |||||||
\(90\) | −7.13306e14 | − | 2.13084e15i | −0.165705 | − | 0.495005i | ||||
\(91\) | −3.12156e15 | −0.663804 | ||||||||
\(92\) | 2.89380e15 | + | 3.83791e15i | 0.563852 | + | 0.747812i | ||||
\(93\) | 7.38780e15i | 1.32024i | ||||||||
\(94\) | −9.14792e14 | − | 2.73273e15i | −0.150072 | − | 0.448305i | ||||
\(95\) | 1.17796e15i | 0.177559i | ||||||||
\(96\) | −3.73763e14 | − | 8.42255e15i | −0.0518116 | − | 1.16755i | ||||
\(97\) | 1.05424e16 | 1.34513 | 0.672566 | − | 0.740038i | \(-0.265192\pi\) | ||||
0.672566 | + | 0.740038i | \(0.265192\pi\) | |||||||
\(98\) | 9.69754e15 | − | 3.24629e15i | 1.13986 | − | 0.381574i | ||||
\(99\) | 2.37840e15 | 0.257753 | ||||||||
\(100\) | −8.27098e15 | + | 6.23634e15i | −0.827098 | + | 0.623634i | ||||
\(101\) | 1.99013e16i | 1.83785i | 0.394431 | + | 0.918926i | \(0.370942\pi\) | ||||
−0.394431 | + | 0.918926i | \(0.629058\pi\) | |||||||
\(102\) | −2.40810e16 | + | 8.06123e15i | −2.05529 | + | 0.688018i | ||||
\(103\) | − | 6.97952e15i | − | 0.550970i | −0.961305 | − | 0.275485i | \(-0.911162\pi\) | ||
0.961305 | − | 0.275485i | \(-0.0888384\pi\) | |||||||
\(104\) | −5.04680e15 | − | 3.46539e15i | −0.368765 | − | 0.253212i | ||||
\(105\) | 3.65596e16 | 2.47450 | ||||||||
\(106\) | 7.09784e14 | + | 2.12031e15i | 0.0445327 | + | 0.133031i | ||||
\(107\) | −1.15042e16 | −0.669555 | −0.334777 | − | 0.942297i | \(-0.608661\pi\) | ||||
−0.334777 | + | 0.942297i | \(0.608661\pi\) | |||||||
\(108\) | 1.09532e16 | − | 8.25872e15i | 0.591766 | − | 0.446193i | ||||
\(109\) | − | 2.34185e16i | − | 1.17530i | −0.809116 | − | 0.587648i | \(-0.800054\pi\) | ||
0.809116 | − | 0.587648i | \(-0.199946\pi\) | |||||||
\(110\) | −6.84039e15 | − | 2.04341e16i | −0.319109 | − | 0.953265i | ||||
\(111\) | 4.24521e16i | 1.84211i | ||||||||
\(112\) | 3.53239e16 | + | 1.01071e16i | 1.42667 | + | 0.408210i | ||||
\(113\) | −1.76133e16 | −0.662542 | −0.331271 | − | 0.943536i | \(-0.607477\pi\) | ||||
−0.331271 | + | 0.943536i | \(0.607477\pi\) | |||||||
\(114\) | 3.93409e15 | − | 1.31695e15i | 0.137913 | − | 0.0461670i | ||||
\(115\) | −4.08785e16 | −1.33632 | ||||||||
\(116\) | 1.10527e16 | + | 1.46587e16i | 0.337135 | + | 0.447128i | ||||
\(117\) | 5.74665e15i | 0.163654i | ||||||||
\(118\) | −5.04784e16 | + | 1.68978e16i | −1.34292 | + | 0.449547i | ||||
\(119\) | − | 1.10669e17i | − | 2.75200i | ||||||
\(120\) | 5.91081e16 | + | 4.05866e16i | 1.37466 | + | 0.943914i | ||||
\(121\) | −2.31416e16 | −0.503628 | ||||||||
\(122\) | −6.75124e14 | − | 2.01678e15i | −0.0137564 | − | 0.0410940i | ||||
\(123\) | 1.38399e15 | 0.0264174 | ||||||||
\(124\) | −3.80147e16 | − | 5.04173e16i | −0.680108 | − | 0.901998i | ||||
\(125\) | − | 3.04994e15i | − | 0.0511695i | ||||||
\(126\) | −1.09481e16 | − | 3.27048e16i | −0.172335 | − | 0.514811i | ||||
\(127\) | − | 1.43339e15i | − | 0.0211805i | −0.999944 | − | 0.0105902i | \(-0.996629\pi\) | ||
0.999944 | − | 0.0105902i | \(-0.00337104\pi\) | |||||||
\(128\) | 4.58898e16 | + | 5.55556e16i | 0.636849 | + | 0.770988i | ||||
\(129\) | −1.75758e16 | −0.229191 | ||||||||
\(130\) | 4.93725e16 | − | 1.65276e16i | 0.605254 | − | 0.202611i | ||||
\(131\) | −3.24094e16 | −0.373681 | −0.186840 | − | 0.982390i | \(-0.559825\pi\) | ||||
−0.186840 | + | 0.982390i | \(0.559825\pi\) | |||||||
\(132\) | −6.05970e16 | + | 4.56903e16i | −0.657445 | + | 0.495715i | ||||
\(133\) | 1.80798e16i | 0.184663i | ||||||||
\(134\) | 2.13843e16 | − | 7.15850e15i | 0.205711 | − | 0.0688626i | ||||
\(135\) | 1.16665e17i | 1.05747i | ||||||||
\(136\) | 1.22859e17 | − | 1.78924e17i | 1.04977 | − | 1.52883i | ||||
\(137\) | 1.75284e17 | 1.41246 | 0.706231 | − | 0.707982i | \(-0.250394\pi\) | ||||
0.706231 | + | 0.707982i | \(0.250394\pi\) | |||||||
\(138\) | 4.57018e16 | + | 1.36523e17i | 0.347456 | + | 1.03795i | ||||
\(139\) | −6.24449e16 | −0.448104 | −0.224052 | − | 0.974577i | \(-0.571928\pi\) | ||||
−0.224052 | + | 0.974577i | \(0.571928\pi\) | |||||||
\(140\) | −2.49497e17 | + | 1.88121e17i | −1.69060 | + | 1.27472i | ||||
\(141\) | − | 8.63160e16i | − | 0.552508i | ||||||
\(142\) | 4.90045e16 | + | 1.46390e17i | 0.296435 | + | 0.885530i | ||||
\(143\) | 5.51086e16i | 0.315160i | ||||||||
\(144\) | 1.86068e16 | − | 6.50298e16i | 0.100640 | − | 0.351733i | ||||
\(145\) | −1.56133e17 | −0.799008 | ||||||||
\(146\) | 2.88669e17 | − | 9.66330e16i | 1.39822 | − | 0.468061i | ||||
\(147\) | 3.06307e17 | 1.40481 | ||||||||
\(148\) | −2.18442e17 | − | 2.89710e17i | −0.948947 | − | 1.25855i | ||||
\(149\) | 1.99108e17i | 0.819593i | 0.912177 | + | 0.409796i | \(0.134400\pi\) | ||||
−0.912177 | + | 0.409796i | \(0.865600\pi\) | |||||||
\(150\) | −2.94218e17 | + | 9.84906e16i | −1.14799 | + | 0.384295i | ||||
\(151\) | − | 9.45575e16i | − | 0.349849i | −0.984582 | − | 0.174924i | \(-0.944032\pi\) | ||
0.984582 | − | 0.174924i | \(-0.0559681\pi\) | |||||||
\(152\) | −2.00712e16 | + | 2.92307e16i | −0.0704410 | + | 0.102586i | ||||
\(153\) | −2.03736e17 | −0.678479 | ||||||||
\(154\) | −1.04989e17 | − | 3.13630e17i | −0.331877 | − | 0.991406i | ||||
\(155\) | 5.37005e17 | 1.61185 | ||||||||
\(156\) | −1.10396e17 | − | 1.46413e17i | −0.314743 | − | 0.417430i | ||||
\(157\) | − | 7.05881e16i | − | 0.191220i | −0.995419 | − | 0.0956102i | \(-0.969520\pi\) | ||
0.995419 | − | 0.0956102i | \(-0.0304802\pi\) | |||||||
\(158\) | −1.61648e17 | − | 4.82885e17i | −0.416211 | − | 1.24333i | ||||
\(159\) | 6.69724e16i | 0.163953i | ||||||||
\(160\) | −6.12219e17 | + | 2.71681e16i | −1.42543 | + | 0.0632558i | ||||
\(161\) | −6.27418e17 | −1.38979 | ||||||||
\(162\) | 5.54202e17 | − | 1.85521e17i | 1.16828 | − | 0.391087i | ||||
\(163\) | 2.34479e17 | 0.470547 | 0.235274 | − | 0.971929i | \(-0.424401\pi\) | ||||
0.235274 | + | 0.971929i | \(0.424401\pi\) | |||||||
\(164\) | −9.44486e15 | + | 7.12144e15i | −0.0180487 | + | 0.0136087i | ||||
\(165\) | − | 6.45432e17i | − | 1.17484i | ||||||
\(166\) | −4.00571e17 | + | 1.34093e17i | −0.694729 | + | 0.232563i | ||||
\(167\) | 9.91844e17i | 1.63950i | 0.572721 | + | 0.819751i | \(0.305888\pi\) | ||||
−0.572721 | + | 0.819751i | \(0.694112\pi\) | |||||||
\(168\) | 9.07212e17 | + | 6.22938e17i | 1.42967 | + | 0.981681i | ||||
\(169\) | 5.32264e17 | 0.799896 | ||||||||
\(170\) | 5.85955e17 | + | 1.75040e18i | 0.839987 | + | 2.50927i | ||||
\(171\) | 3.32841e16 | 0.0455269 | ||||||||
\(172\) | 1.19944e17 | − | 9.04383e16i | 0.156586 | − | 0.118066i | ||||
\(173\) | 4.60112e17i | 0.573449i | 0.958013 | + | 0.286724i | \(0.0925664\pi\) | ||||
−0.958013 | + | 0.286724i | \(0.907434\pi\) | |||||||
\(174\) | 1.74555e17 | + | 5.21444e17i | 0.207749 | + | 0.620603i | ||||
\(175\) | − | 1.35213e18i | − | 1.53714i | ||||||
\(176\) | 1.78434e17 | − | 6.23616e17i | 0.193810 | − | 0.677355i | ||||
\(177\) | −1.59441e18 | −1.65506 | ||||||||
\(178\) | 5.68980e17 | − | 1.90468e17i | 0.564595 | − | 0.189000i | ||||
\(179\) | −1.47277e18 | −1.39737 | −0.698683 | − | 0.715431i | \(-0.746230\pi\) | ||||
−0.698683 | + | 0.715431i | \(0.746230\pi\) | |||||||
\(180\) | 3.46323e17 | + | 4.59313e17i | 0.314269 | + | 0.416801i | ||||
\(181\) | − | 6.60815e17i | − | 0.573655i | −0.957982 | − | 0.286828i | \(-0.907399\pi\) | ||
0.957982 | − | 0.286828i | \(-0.0926007\pi\) | |||||||
\(182\) | 7.57787e17 | − | 2.53672e17i | 0.629471 | − | 0.210718i | ||||
\(183\) | − | 6.37020e16i | − | 0.0506459i | ||||||
\(184\) | −1.01438e18 | − | 6.96526e17i | −0.772074 | − | 0.530145i | ||||
\(185\) | 3.08576e18 | 2.24900 | ||||||||
\(186\) | −6.00367e17 | − | 1.79346e18i | −0.419096 | − | 1.25195i | ||||
\(187\) | −1.95377e18 | −1.30659 | ||||||||
\(188\) | 4.44148e17 | + | 5.89054e17i | 0.284620 | + | 0.377479i | ||||
\(189\) | 1.79061e18i | 1.09978i | ||||||||
\(190\) | −9.57267e16 | − | 2.85961e17i | −0.0563643 | − | 0.168375i | ||||
\(191\) | − | 1.53435e18i | − | 0.866280i | −0.901327 | − | 0.433140i | \(-0.857406\pi\) | ||
0.901327 | − | 0.433140i | \(-0.142594\pi\) | |||||||
\(192\) | 7.75190e17 | + | 2.01428e18i | 0.419758 | + | 1.09071i | ||||
\(193\) | 7.58207e16 | 0.0393849 | 0.0196924 | − | 0.999806i | \(-0.493731\pi\) | ||||
0.0196924 | + | 0.999806i | \(0.493731\pi\) | |||||||
\(194\) | −2.55926e18 | + | 8.56723e17i | −1.27556 | + | 0.426999i | ||||
\(195\) | 1.55948e18 | 0.745939 | ||||||||
\(196\) | −2.09036e18 | + | 1.57613e18i | −0.959781 | + | 0.723677i | ||||
\(197\) | − | 9.73556e17i | − | 0.429172i | −0.976705 | − | 0.214586i | \(-0.931160\pi\) | ||
0.976705 | − | 0.214586i | \(-0.0688402\pi\) | |||||||
\(198\) | −5.77379e17 | + | 1.93280e17i | −0.244421 | + | 0.0818211i | ||||
\(199\) | 8.87051e17i | 0.360681i | 0.983604 | + | 0.180341i | \(0.0577200\pi\) | ||||
−0.983604 | + | 0.180341i | \(0.942280\pi\) | |||||||
\(200\) | 1.50106e18 | − | 2.18607e18i | 0.586353 | − | 0.853932i | ||||
\(201\) | 6.75447e17 | 0.253526 | ||||||||
\(202\) | −1.61727e18 | − | 4.83122e18i | −0.583408 | − | 1.74279i | ||||
\(203\) | −2.39639e18 | −0.830977 | ||||||||
\(204\) | 5.19080e18 | − | 3.91387e18i | 1.73059 | − | 1.30486i | ||||
\(205\) | − | 1.00599e17i | − | 0.0322525i | ||||||
\(206\) | 5.67188e17 | + | 1.69434e18i | 0.174900 | + | 0.522473i | ||||
\(207\) | 1.15505e18i | 0.342639i | ||||||||
\(208\) | 1.50677e18 | + | 4.31128e17i | 0.430072 | + | 0.123055i | ||||
\(209\) | 3.19185e17 | 0.0876742 | ||||||||
\(210\) | −8.87519e18 | + | 2.97101e18i | −2.34651 | + | 0.785505i | ||||
\(211\) | 1.81860e17 | 0.0462890 | 0.0231445 | − | 0.999732i | \(-0.492632\pi\) | ||||
0.0231445 | + | 0.999732i | \(0.492632\pi\) | |||||||
\(212\) | −3.44613e17 | − | 4.57046e17i | −0.0844588 | − | 0.112014i | ||||
\(213\) | 4.62387e18i | 1.09136i | ||||||||
\(214\) | 2.79275e18 | − | 9.34885e17i | 0.634924 | − | 0.212544i | ||||
\(215\) | 1.27755e18i | 0.279815i | ||||||||
\(216\) | −1.98784e18 | + | 2.89499e18i | −0.419519 | + | 0.610965i | ||||
\(217\) | 8.24215e18 | 1.67634 | ||||||||
\(218\) | 1.90310e18 | + | 5.68506e18i | 0.373086 | + | 1.11451i | ||||
\(219\) | 9.11790e18 | 1.72323 | ||||||||
\(220\) | 3.32114e18 | + | 4.40468e18i | 0.605209 | + | 0.802662i | ||||
\(221\) | − | 4.72066e18i | − | 0.829592i | ||||||
\(222\) | −3.44986e18 | − | 1.03056e19i | −0.584760 | − | 1.74683i | ||||
\(223\) | 4.73123e18i | 0.773633i | 0.922157 | + | 0.386816i | \(0.126425\pi\) | ||||
−0.922157 | + | 0.386816i | \(0.873575\pi\) | |||||||
\(224\) | −9.39656e18 | + | 4.16987e17i | −1.48247 | + | 0.0657867i | ||||
\(225\) | −2.48921e18 | −0.378967 | ||||||||
\(226\) | 4.27579e18 | − | 1.43134e18i | 0.628274 | − | 0.210317i | ||||
\(227\) | −1.01230e19 | −1.43583 | −0.717913 | − | 0.696133i | \(-0.754902\pi\) | ||||
−0.717913 | + | 0.696133i | \(0.754902\pi\) | |||||||
\(228\) | −8.48015e17 | + | 6.39405e17i | −0.116125 | + | 0.0875582i | ||||
\(229\) | 1.24157e19i | 1.64168i | 0.571159 | + | 0.820840i | \(0.306494\pi\) | ||||
−0.571159 | + | 0.820840i | \(0.693506\pi\) | |||||||
\(230\) | 9.92362e18 | − | 3.32197e18i | 1.26721 | − | 0.424203i | ||||
\(231\) | − | 9.90632e18i | − | 1.22185i | ||||||
\(232\) | −3.87438e18 | − | 2.66034e18i | −0.461634 | − | 0.316981i | ||||
\(233\) | −9.63007e18 | −1.10862 | −0.554309 | − | 0.832311i | \(-0.687018\pi\) | ||||
−0.554309 | + | 0.832311i | \(0.687018\pi\) | |||||||
\(234\) | −4.67000e17 | − | 1.39505e18i | −0.0519505 | − | 0.155190i | ||||
\(235\) | −6.27415e18 | −0.674546 | ||||||||
\(236\) | 1.08809e19 | − | 8.20421e18i | 1.13075 | − | 0.852591i | ||||
\(237\) | − | 1.52524e19i | − | 1.53233i | ||||||
\(238\) | 8.99345e18 | + | 2.68658e19i | 0.873596 | + | 2.60967i | ||||
\(239\) | − | 1.17222e19i | − | 1.10109i | −0.834804 | − | 0.550547i | \(-0.814419\pi\) | ||
0.834804 | − | 0.550547i | \(-0.185581\pi\) | |||||||
\(240\) | −1.76473e19 | − | 5.04937e18i | −1.60320 | − | 0.458719i | ||||
\(241\) | −8.99136e18 | −0.790112 | −0.395056 | − | 0.918657i | \(-0.629275\pi\) | ||||
−0.395056 | + | 0.918657i | \(0.629275\pi\) | |||||||
\(242\) | 5.61783e18 | − | 1.88059e18i | 0.477580 | − | 0.159872i | ||||
\(243\) | 8.49461e18 | 0.698704 | ||||||||
\(244\) | 3.27785e17 | + | 4.34727e17i | 0.0260898 | + | 0.0346018i | ||||
\(245\) | − | 2.22649e19i | − | 1.71511i | ||||||
\(246\) | −3.35975e17 | + | 1.12469e17i | −0.0250511 | + | 0.00838596i | ||||
\(247\) | 7.71209e17i | 0.0556668i | ||||||||
\(248\) | 1.33256e19 | + | 9.15000e18i | 0.931263 | + | 0.639452i | ||||
\(249\) | −1.26525e19 | −0.856210 | ||||||||
\(250\) | 2.47852e17 | + | 7.40401e17i | 0.0162432 | + | 0.0485229i | ||||
\(251\) | −8.44272e17 | −0.0535911 | −0.0267955 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267955 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(252\) | 5.31550e18 | + | 7.04971e18i | 0.326843 | + | 0.433478i | ||||
\(253\) | 1.10766e19i | 0.659844i | ||||||||
\(254\) | 1.16484e17 | + | 3.47969e17i | 0.00672353 | + | 0.0200850i | ||||
\(255\) | 5.52883e19i | 3.09252i | ||||||||
\(256\) | −1.56549e19 | − | 9.75740e18i | −0.848653 | − | 0.528950i | ||||
\(257\) | −1.12539e19 | −0.591343 | −0.295672 | − | 0.955290i | \(-0.595543\pi\) | ||||
−0.295672 | + | 0.955290i | \(0.595543\pi\) | |||||||
\(258\) | 4.26670e18 | − | 1.42829e18i | 0.217337 | − | 0.0727546i | ||||
\(259\) | 4.73614e19 | 2.33898 | ||||||||
\(260\) | −1.06425e19 | + | 8.02447e18i | −0.509633 | + | 0.384264i | ||||
\(261\) | 4.41164e18i | 0.204869i | ||||||||
\(262\) | 7.86768e18 | − | 2.63374e18i | 0.354353 | − | 0.118621i | ||||
\(263\) | − | 2.11514e19i | − | 0.924046i | −0.886868 | − | 0.462023i | \(-0.847124\pi\) | ||
0.886868 | − | 0.462023i | \(-0.152876\pi\) | |||||||
\(264\) | 1.09975e19 | − | 1.60161e19i | 0.466081 | − | 0.678775i | ||||
\(265\) | 4.86809e18 | 0.200167 | ||||||||
\(266\) | −1.46925e18 | − | 4.38904e18i | −0.0586195 | − | 0.175112i | ||||
\(267\) | 1.79718e19 | 0.695828 | ||||||||
\(268\) | −4.60951e18 | + | 3.47558e18i | −0.173212 | + | 0.130602i | ||||
\(269\) | 3.46645e19i | 1.26435i | 0.774826 | + | 0.632174i | \(0.217837\pi\) | ||||
−0.774826 | + | 0.632174i | \(0.782163\pi\) | |||||||
\(270\) | −9.48071e18 | − | 2.83214e19i | −0.335684 | − | 1.00278i | ||||
\(271\) | − | 1.79486e19i | − | 0.616986i | −0.951227 | − | 0.308493i | \(-0.900175\pi\) | ||
0.951227 | − | 0.308493i | \(-0.0998246\pi\) | |||||||
\(272\) | −1.52848e19 | + | 5.34196e19i | −0.510163 | + | 1.78299i | ||||
\(273\) | 2.39355e19 | 0.775785 | ||||||||
\(274\) | −4.25517e19 | + | 1.42444e19i | −1.33941 | + | 0.448372i | ||||
\(275\) | −2.38708e19 | −0.729803 | ||||||||
\(276\) | −2.21891e19 | − | 2.94284e19i | −0.658971 | − | 0.873964i | ||||
\(277\) | − | 1.89220e19i | − | 0.545920i | −0.962025 | − | 0.272960i | \(-0.911997\pi\) | ||
0.962025 | − | 0.272960i | \(-0.0880027\pi\) | |||||||
\(278\) | 1.51591e19 | − | 5.07456e18i | 0.424927 | − | 0.142246i | ||||
\(279\) | − | 1.51734e19i | − | 0.413286i | ||||||
\(280\) | 4.52801e19 | − | 6.59435e19i | 1.19851 | − | 1.74545i | ||||
\(281\) | −2.99742e19 | −0.771077 | −0.385538 | − | 0.922692i | \(-0.625984\pi\) | ||||
−0.385538 | + | 0.922692i | \(0.625984\pi\) | |||||||
\(282\) | 7.01444e18 | + | 2.09540e19i | 0.175388 | + | 0.523931i | ||||
\(283\) | −2.97748e19 | −0.723697 | −0.361849 | − | 0.932237i | \(-0.617854\pi\) | ||||
−0.361849 | + | 0.932237i | \(0.617854\pi\) | |||||||
\(284\) | −2.37926e19 | − | 3.15551e19i | −0.562205 | − | 0.745629i | ||||
\(285\) | − | 9.03239e18i | − | 0.207512i | ||||||
\(286\) | −4.47839e18 | − | 1.33781e19i | −0.100045 | − | 0.298860i | ||||
\(287\) | − | 1.54403e18i | − | 0.0335430i | ||||||
\(288\) | 7.67654e17 | + | 1.72987e19i | 0.0162191 | + | 0.365488i | ||||
\(289\) | 1.18701e20 | 2.43933 | ||||||||
\(290\) | 3.79027e19 | − | 1.26881e19i | 0.757681 | − | 0.253637i | ||||
\(291\) | −8.08369e19 | −1.57205 | ||||||||
\(292\) | −6.22241e19 | + | 4.69171e19i | −1.17732 | + | 0.887705i | ||||
\(293\) | − | 3.21807e18i | − | 0.0592453i | −0.999561 | − | 0.0296227i | \(-0.990569\pi\) | ||
0.999561 | − | 0.0296227i | \(-0.00943057\pi\) | |||||||
\(294\) | −7.43589e19 | + | 2.48919e19i | −1.33215 | + | 0.445944i | ||||
\(295\) | 1.15895e20i | 2.02063i | ||||||||
\(296\) | 7.65720e19 | + | 5.25782e19i | 1.29938 | + | 0.892219i | ||||
\(297\) | 3.16119e19 | 0.522154 | ||||||||
\(298\) | −1.61804e19 | − | 4.83353e19i | −0.260172 | − | 0.777202i | ||||
\(299\) | −2.67630e19 | −0.418953 | ||||||||
\(300\) | 6.34203e19 | − | 4.78190e19i | 0.966625 | − | 0.728837i | ||||
\(301\) | 1.96084e19i | 0.291011i | ||||||||
\(302\) | 7.68418e18 | + | 2.29547e19i | 0.111056 | + | 0.331754i | ||||
\(303\) | − | 1.52599e20i | − | 2.14789i | ||||||
\(304\) | 2.49706e18 | − | 8.72710e18i | 0.0342326 | − | 0.119641i | ||||
\(305\) | −4.63037e18 | −0.0618326 | ||||||||
\(306\) | 4.94588e19 | − | 1.65565e19i | 0.643387 | − | 0.215377i | ||||
\(307\) | 5.81978e19 | 0.737564 | 0.368782 | − | 0.929516i | \(-0.379775\pi\) | ||||
0.368782 | + | 0.929516i | \(0.379775\pi\) | |||||||
\(308\) | 5.09740e19 | + | 6.76046e19i | 0.629424 | + | 0.834777i | ||||
\(309\) | 5.35176e19i | 0.643915i | ||||||||
\(310\) | −1.30363e20 | + | 4.36395e19i | −1.52848 | + | 0.511666i | ||||
\(311\) | − | 1.04256e20i | − | 1.19129i | −0.803248 | − | 0.595645i | \(-0.796896\pi\) | ||
0.803248 | − | 0.595645i | \(-0.203104\pi\) | |||||||
\(312\) | 3.86979e19 | + | 2.65719e19i | 0.430974 | + | 0.295928i | ||||
\(313\) | −1.60356e20 | −1.74073 | −0.870365 | − | 0.492407i | \(-0.836117\pi\) | ||||
−0.870365 | + | 0.492407i | \(0.836117\pi\) | |||||||
\(314\) | 5.73632e18 | + | 1.71359e19i | 0.0607010 | + | 0.181330i | ||||
\(315\) | −7.50880e19 | −0.774615 | ||||||||
\(316\) | 7.84830e19 | + | 1.04089e20i | 0.789367 | + | 1.04690i | ||||
\(317\) | − | 1.13662e19i | − | 0.111466i | −0.998446 | − | 0.0557329i | \(-0.982250\pi\) | ||
0.998446 | − | 0.0557329i | \(-0.0177495\pi\) | |||||||
\(318\) | −5.44249e18 | − | 1.62582e19i | −0.0520452 | − | 0.155473i | ||||
\(319\) | 4.23064e19i | 0.394530i | ||||||||
\(320\) | 1.46414e20 | − | 5.63471e19i | 1.33163 | − | 0.512474i | ||||
\(321\) | 8.82120e19 | 0.782505 | ||||||||
\(322\) | 1.52311e20 | − | 5.09869e19i | 1.31791 | − | 0.441176i | ||||
\(323\) | −2.73417e19 | −0.230784 | ||||||||
\(324\) | −1.19461e20 | + | 9.00740e19i | −0.983710 | + | 0.741719i | ||||
\(325\) | − | 5.76762e19i | − | 0.463372i | ||||||
\(326\) | −5.69220e19 | + | 1.90549e19i | −0.446210 | + | 0.149371i | ||||
\(327\) | 1.79569e20i | 1.37356i | ||||||||
\(328\) | 1.71411e18 | − | 2.49633e18i | 0.0127952 | − | 0.0186342i | ||||
\(329\) | −9.62979e19 | −0.701535 | ||||||||
\(330\) | 5.24508e19 | + | 1.56685e20i | 0.372941 | + | 1.11408i | ||||
\(331\) | 4.34350e18 | 0.0301450 | 0.0150725 | − | 0.999886i | \(-0.495202\pi\) | ||||
0.0150725 | + | 0.999886i | \(0.495202\pi\) | |||||||
\(332\) | 8.63454e19 | − | 6.51046e19i | 0.584971 | − | 0.441070i | ||||
\(333\) | − | 8.71903e19i | − | 0.576653i | ||||||
\(334\) | −8.06019e19 | − | 2.40779e20i | −0.520443 | − | 1.55470i | ||||
\(335\) | − | 4.90969e19i | − | 0.309525i | ||||||
\(336\) | −2.70857e20 | − | 7.74996e19i | −1.66735 | − | 0.477073i | ||||
\(337\) | 5.38785e19 | 0.323874 | 0.161937 | − | 0.986801i | \(-0.448226\pi\) | ||||
0.161937 | + | 0.986801i | \(0.448226\pi\) | |||||||
\(338\) | −1.29212e20 | + | 4.32543e19i | −0.758524 | + | 0.253919i | ||||
\(339\) | 1.35055e20 | 0.774309 | ||||||||
\(340\) | −2.84492e20 | − | 3.77309e20i | −1.59308 | − | 2.11284i | ||||
\(341\) | − | 1.45509e20i | − | 0.795892i | ||||||
\(342\) | −8.08003e18 | + | 2.70482e18i | −0.0431722 | + | 0.0144521i | ||||
\(343\) | − | 5.74370e19i | − | 0.299805i | ||||||
\(344\) | −2.17682e19 | + | 3.17020e19i | −0.111008 | + | 0.161666i | ||||
\(345\) | 3.13448e20 | 1.56175 | ||||||||
\(346\) | −3.73908e19 | − | 1.11696e20i | −0.182036 | − | 0.543789i | ||||
\(347\) | 1.01011e18 | 0.00480544 | 0.00240272 | − | 0.999997i | \(-0.499235\pi\) | ||||
0.00240272 | + | 0.999997i | \(0.499235\pi\) | |||||||
\(348\) | −8.47499e19 | − | 1.12400e20i | −0.394008 | − | 0.522556i | ||||
\(349\) | 1.68723e20i | 0.766602i | 0.923624 | + | 0.383301i | \(0.125213\pi\) | ||||
−0.923624 | + | 0.383301i | \(0.874787\pi\) | |||||||
\(350\) | 1.09880e20 | + | 3.28242e20i | 0.487951 | + | 1.45764i | ||||
\(351\) | 7.63800e19i | 0.331530i | ||||||||
\(352\) | 7.36157e18 | + | 1.65889e20i | 0.0312341 | + | 0.703844i | ||||
\(353\) | −2.84133e20 | −1.17849 | −0.589243 | − | 0.807956i | \(-0.700574\pi\) | ||||
−0.589243 | + | 0.807956i | \(0.700574\pi\) | |||||||
\(354\) | 3.87058e20 | − | 1.29569e20i | 1.56946 | − | 0.525383i | ||||
\(355\) | 3.36100e20 | 1.33242 | ||||||||
\(356\) | −1.22647e20 | + | 9.24759e19i | −0.475397 | + | 0.358450i | ||||
\(357\) | 8.48586e20i | 3.21625i | ||||||||
\(358\) | 3.57528e20 | − | 1.19684e20i | 1.32509 | − | 0.443580i | ||||
\(359\) | 2.04614e20i | 0.741617i | 0.928709 | + | 0.370809i | \(0.120919\pi\) | ||||
−0.928709 | + | 0.370809i | \(0.879081\pi\) | |||||||
\(360\) | −1.21399e20 | − | 8.33587e19i | −0.430324 | − | 0.295482i | ||||
\(361\) | −2.83975e20 | −0.984514 | ||||||||
\(362\) | 5.37009e19 | + | 1.60419e20i | 0.182101 | + | 0.543985i | ||||
\(363\) | 1.77445e20 | 0.588588 | ||||||||
\(364\) | −1.63345e20 | + | 1.23163e20i | −0.530024 | + | 0.399639i | ||||
\(365\) | − | 6.62763e20i | − | 2.10385i | ||||||
\(366\) | 5.17672e18 | + | 1.54642e19i | 0.0160770 | + | 0.0480264i | ||||
\(367\) | − | 1.00923e20i | − | 0.306664i | −0.988175 | − | 0.153332i | \(-0.951000\pi\) | ||
0.988175 | − | 0.153332i | \(-0.0490004\pi\) | |||||||
\(368\) | 3.02854e20 | + | 8.66547e19i | 0.900431 | + | 0.257638i | ||||
\(369\) | −2.84250e18 | −0.00826970 | ||||||||
\(370\) | −7.49097e20 | + | 2.50763e20i | −2.13267 | + | 0.713922i | ||||
\(371\) | 7.47173e19 | 0.208176 | ||||||||
\(372\) | 2.91489e20 | + | 3.86590e20i | 0.794839 | + | 1.05416i | ||||
\(373\) | − | 6.48351e20i | − | 1.73037i | −0.501451 | − | 0.865186i | \(-0.667200\pi\) | ||
0.501451 | − | 0.865186i | \(-0.332800\pi\) | |||||||
\(374\) | 4.74295e20 | − | 1.58772e20i | 1.23901 | − | 0.414765i | ||||
\(375\) | 2.33863e19i | 0.0598015i | ||||||||
\(376\) | −1.55690e20 | − | 1.06905e20i | −0.389726 | − | 0.267605i | ||||
\(377\) | −1.02220e20 | −0.250498 | ||||||||
\(378\) | −1.45513e20 | − | 4.34688e20i | −0.349115 | − | 1.04290i | ||||
\(379\) | 4.49795e18 | 0.0105658 | 0.00528288 | − | 0.999986i | \(-0.498318\pi\) | ||||
0.00528288 | + | 0.999986i | \(0.498318\pi\) | |||||||
\(380\) | 4.64771e19 | + | 6.16405e19i | 0.106898 | + | 0.141774i | ||||
\(381\) | 1.09910e19i | 0.0247535i | ||||||||
\(382\) | 1.24689e20 | + | 3.72478e20i | 0.274992 | + | 0.821474i | ||||
\(383\) | 5.53477e20i | 1.19539i | 0.801724 | + | 0.597694i | \(0.203916\pi\) | ||||
−0.801724 | + | 0.597694i | \(0.796084\pi\) | |||||||
\(384\) | −3.51874e20 | − | 4.25989e20i | −0.744283 | − | 0.901050i | ||||
\(385\) | −7.20072e20 | −1.49173 | ||||||||
\(386\) | −1.84062e19 | + | 6.16155e18i | −0.0373478 | + | 0.0125023i | ||||
\(387\) | 3.60981e19 | 0.0717459 | ||||||||
\(388\) | 5.51663e20 | − | 4.15955e20i | 1.07404 | − | 0.809827i | ||||
\(389\) | 1.51215e19i | 0.0288402i | 0.999896 | + | 0.0144201i | \(0.00459022\pi\) | ||||
−0.999896 | + | 0.0144201i | \(0.995410\pi\) | |||||||
\(390\) | −3.78578e20 | + | 1.26731e20i | −0.707358 | + | 0.236791i | ||||
\(391\) | − | 9.48830e20i | − | 1.73690i | ||||||
\(392\) | 3.79370e20 | − | 5.52494e20i | 0.680416 | − | 0.990920i | ||||
\(393\) | 2.48509e20 | 0.436719 | ||||||||
\(394\) | 7.91157e19 | + | 2.36340e20i | 0.136236 | + | 0.406974i | ||||
\(395\) | −1.10867e21 | −1.87079 | ||||||||
\(396\) | 1.24457e20 | − | 9.38409e19i | 0.205806 | − | 0.155178i | ||||
\(397\) | 6.46671e20i | 1.04800i | 0.851720 | + | 0.523998i | \(0.175560\pi\) | ||||
−0.851720 | + | 0.523998i | \(0.824440\pi\) | |||||||
\(398\) | −7.20859e19 | − | 2.15340e20i | −0.114495 | − | 0.342026i | ||||
\(399\) | − | 1.38632e20i | − | 0.215815i | ||||||
\(400\) | −1.86747e20 | + | 6.52671e20i | −0.284953 | + | 0.995898i | ||||
\(401\) | 2.36360e20 | 0.353524 | 0.176762 | − | 0.984254i | \(-0.443438\pi\) | ||||
0.176762 | + | 0.984254i | \(0.443438\pi\) | |||||||
\(402\) | −1.63971e20 | + | 5.48900e19i | −0.240413 | + | 0.0804794i | ||||
\(403\) | 3.51576e20 | 0.505334 | ||||||||
\(404\) | 7.85216e20 | + | 1.04140e21i | 1.10647 | + | 1.46746i | ||||
\(405\) | − | 1.27241e21i | − | 1.75787i | ||||||
\(406\) | 5.81745e20 | − | 1.94742e20i | 0.787997 | − | 0.263785i | ||||
\(407\) | − | 8.36129e20i | − | 1.11050i | ||||||
\(408\) | −9.42055e20 | + | 1.37196e21i | −1.22686 | + | 1.78673i | ||||
\(409\) | 1.09893e21 | 1.40341 | 0.701706 | − | 0.712467i | \(-0.252422\pi\) | ||||
0.701706 | + | 0.712467i | \(0.252422\pi\) | |||||||
\(410\) | 8.17517e18 | + | 2.44214e19i | 0.0102382 | + | 0.0305844i | ||||
\(411\) | −1.34404e21 | −1.65074 | ||||||||
\(412\) | −2.75380e20 | − | 3.65225e20i | −0.331708 | − | 0.439929i | ||||
\(413\) | 1.77879e21i | 2.10148i | ||||||||
\(414\) | −9.38646e19 | − | 2.80399e20i | −0.108767 | − | 0.324918i | ||||
\(415\) | 9.19684e20i | 1.04533i | ||||||||
\(416\) | −4.00818e20 | + | 1.77869e19i | −0.446890 | + | 0.0198314i | ||||
\(417\) | 4.78815e20 | 0.523696 | ||||||||
\(418\) | −7.74851e19 | + | 2.59384e19i | −0.0831395 | + | 0.0278313i | ||||
\(419\) | −5.87615e19 | −0.0618559 | −0.0309279 | − | 0.999522i | \(-0.509846\pi\) | ||||
−0.0309279 | + | 0.999522i | \(0.509846\pi\) | |||||||
\(420\) | 1.91310e21 | − | 1.44248e21i | 1.97580 | − | 1.48976i | ||||
\(421\) | 8.68806e20i | 0.880372i | 0.897907 | + | 0.440186i | \(0.145087\pi\) | ||||
−0.897907 | + | 0.440186i | \(0.854913\pi\) | |||||||
\(422\) | −4.41483e19 | + | 1.47788e19i | −0.0438949 | + | 0.0146940i | ||||
\(423\) | 1.77280e20i | 0.172957i | ||||||||
\(424\) | 1.20800e20 | + | 8.29472e19i | 0.115648 | + | 0.0794099i | ||||
\(425\) | 2.04480e21 | 1.92105 | ||||||||
\(426\) | −3.75757e20 | − | 1.12249e21i | −0.346442 | − | 1.03491i | ||||
\(427\) | −7.10687e19 | −0.0643065 | ||||||||
\(428\) | −6.01993e20 | + | 4.53904e20i | −0.534615 | + | 0.403101i | ||||
\(429\) | − | 4.22562e20i | − | 0.368326i | ||||||
\(430\) | −1.03820e20 | − | 3.10138e20i | −0.0888246 | − | 0.265343i | ||||
\(431\) | − | 1.92605e20i | − | 0.161752i | −0.996724 | − | 0.0808758i | \(-0.974228\pi\) | ||
0.996724 | − | 0.0808758i | \(-0.0257717\pi\) | |||||||
\(432\) | 2.47307e20 | − | 8.64326e20i | 0.203876 | − | 0.712537i | ||||
\(433\) | −2.34786e20 | −0.190006 | −0.0950032 | − | 0.995477i | \(-0.530286\pi\) | ||||
−0.0950032 | + | 0.995477i | \(0.530286\pi\) | |||||||
\(434\) | −2.00086e21 | + | 6.69796e20i | −1.58964 | + | 0.532138i | ||||
\(435\) | 1.19720e21 | 0.933796 | ||||||||
\(436\) | −9.23990e20 | − | 1.22545e21i | −0.707579 | − | 0.938432i | ||||
\(437\) | 1.55009e20i | 0.116548i | ||||||||
\(438\) | −2.21346e21 | + | 7.40963e20i | −1.63410 | + | 0.547021i | ||||
\(439\) | 2.18515e21i | 1.58404i | 0.610497 | + | 0.792018i | \(0.290970\pi\) | ||||
−0.610497 | + | 0.792018i | \(0.709030\pi\) | |||||||
\(440\) | −1.16418e21 | − | 7.99385e20i | −0.828704 | − | 0.569030i | ||||
\(441\) | −6.29109e20 | −0.439761 | ||||||||
\(442\) | 3.83623e20 | + | 1.14598e21i | 0.263346 | + | 0.786685i | ||||
\(443\) | 1.07184e21 | 0.722602 | 0.361301 | − | 0.932449i | \(-0.382333\pi\) | ||||
0.361301 | + | 0.932449i | \(0.382333\pi\) | |||||||
\(444\) | 1.67497e21 | + | 2.22144e21i | 1.10903 | + | 1.47086i | ||||
\(445\) | − | 1.30634e21i | − | 0.849523i | ||||||
\(446\) | −3.84481e20 | − | 1.14855e21i | −0.245582 | − | 0.733619i | ||||
\(447\) | − | 1.52672e21i | − | 0.957854i | ||||||
\(448\) | 2.24722e21 | − | 8.64836e20i | 1.38491 | − | 0.532978i | ||||
\(449\) | −1.09657e21 | −0.663842 | −0.331921 | − | 0.943307i | \(-0.607697\pi\) | ||||
−0.331921 | + | 0.943307i | \(0.607697\pi\) | |||||||
\(450\) | 6.04279e20 | − | 2.02285e20i | 0.359367 | − | 0.120299i | ||||
\(451\) | −2.72587e19 | −0.0159255 | ||||||||
\(452\) | −9.21671e20 | + | 6.94942e20i | −0.529016 | + | 0.398879i | ||||
\(453\) | 7.25048e20i | 0.408866i | ||||||||
\(454\) | 2.45745e21 | − | 8.22641e20i | 1.36156 | − | 0.455789i | ||||
\(455\) | − | 1.73982e21i | − | 0.947140i | ||||||
\(456\) | 1.53902e20 | − | 2.24135e20i | 0.0823240 | − | 0.119892i | ||||
\(457\) | −6.92574e20 | −0.364030 | −0.182015 | − | 0.983296i | \(-0.558262\pi\) | ||||
−0.182015 | + | 0.983296i | \(0.558262\pi\) | |||||||
\(458\) | −1.00896e21 | − | 3.01403e21i | −0.521135 | − | 1.55677i | ||||
\(459\) | −2.70790e21 | −1.37446 | ||||||||
\(460\) | −2.13909e21 | + | 1.61288e21i | −1.06701 | + | 0.804525i | ||||
\(461\) | − | 1.76325e21i | − | 0.864384i | −0.901782 | − | 0.432192i | \(-0.857740\pi\) | ||
0.901782 | − | 0.432192i | \(-0.142260\pi\) | |||||||
\(462\) | 8.05034e20 | + | 2.40485e21i | 0.387863 | + | 1.15865i | ||||
\(463\) | 8.88321e20i | 0.420651i | 0.977631 | + | 0.210325i | \(0.0674524\pi\) | ||||
−0.977631 | + | 0.210325i | \(0.932548\pi\) | |||||||
\(464\) | 1.15673e21 | + | 3.30973e20i | 0.538381 | + | 0.154045i | ||||
\(465\) | −4.11765e21 | −1.88376 | ||||||||
\(466\) | 2.33779e21 | − | 7.82585e20i | 1.05128 | − | 0.351920i | ||||
\(467\) | 2.42168e21 | 1.07049 | 0.535244 | − | 0.844697i | \(-0.320220\pi\) | ||||
0.535244 | + | 0.844697i | \(0.320220\pi\) | |||||||
\(468\) | 2.26737e20 | + | 3.00711e20i | 0.0985270 | + | 0.130672i | ||||
\(469\) | − | 7.53558e20i | − | 0.321910i | ||||||
\(470\) | 1.52311e21 | − | 5.09866e20i | 0.639658 | − | 0.214128i | ||||
\(471\) | 5.41256e20i | 0.223478i | ||||||||
\(472\) | −1.97472e21 | + | 2.87588e21i | −0.801624 | + | 1.16744i | ||||
\(473\) | 3.46170e20 | 0.138166 | ||||||||
\(474\) | 1.23948e21 | + | 3.70267e21i | 0.486423 | + | 1.45308i | ||||
\(475\) | −3.34056e20 | −0.128905 | ||||||||
\(476\) | −4.36649e21 | − | 5.79108e21i | −1.65682 | − | 2.19737i | ||||
\(477\) | − | 1.37551e20i | − | 0.0513236i | ||||||
\(478\) | 9.52597e20 | + | 2.84566e21i | 0.349531 | + | 1.04414i | ||||
\(479\) | − | 2.90885e21i | − | 1.04963i | −0.851215 | − | 0.524817i | \(-0.824134\pi\) | ||
0.851215 | − | 0.524817i | \(-0.175866\pi\) | |||||||
\(480\) | 4.69438e21 | − | 2.08320e20i | 1.66590 | − | 0.0739267i | ||||
\(481\) | 2.02024e21 | 0.705087 | ||||||||
\(482\) | 2.18274e21 | − | 7.30680e20i | 0.749247 | − | 0.250813i | ||||
\(483\) | 4.81092e21 | 1.62424 | ||||||||
\(484\) | −1.21096e21 | + | 9.13063e20i | −0.402129 | + | 0.303206i | ||||
\(485\) | 5.87588e21i | 1.91928i | ||||||||
\(486\) | −2.06215e21 | + | 6.90312e20i | −0.662566 | + | 0.221797i | ||||
\(487\) | 3.94387e21i | 1.24650i | 0.782024 | + | 0.623249i | \(0.214187\pi\) | ||||
−0.782024 | + | 0.623249i | \(0.785813\pi\) | |||||||
\(488\) | −1.14901e20 | − | 7.88967e19i | −0.0357244 | − | 0.0245301i | ||||
\(489\) | −1.79794e21 | −0.549926 | ||||||||
\(490\) | 1.80935e21 | + | 5.40500e21i | 0.544444 | + | 1.62640i | ||||
\(491\) | −6.54682e21 | −1.93811 | −0.969056 | − | 0.246842i | \(-0.920607\pi\) | ||||
−0.969056 | + | 0.246842i | \(0.920607\pi\) | |||||||
\(492\) | 7.24214e19 | − | 5.46059e19i | 0.0210934 | − | 0.0159044i | ||||
\(493\) | − | 3.62401e21i | − | 1.03852i | ||||||
\(494\) | −6.26720e19 | − | 1.87218e20i | −0.0176709 | − | 0.0527876i | ||||
\(495\) | 1.32562e21i | 0.367771i | ||||||||
\(496\) | −3.97848e21 | − | 1.13835e21i | −1.08608 | − | 0.310758i | ||||
\(497\) | 5.15859e21 | 1.38573 | ||||||||
\(498\) | 3.07150e21 | − | 1.02820e21i | 0.811926 | − | 0.271796i | ||||
\(499\) | 5.84564e21 | 1.52064 | 0.760322 | − | 0.649546i | \(-0.225041\pi\) | ||||
0.760322 | + | 0.649546i | \(0.225041\pi\) | |||||||
\(500\) | −1.20337e20 | − | 1.59598e20i | −0.0308062 | − | 0.0408570i | ||||
\(501\) | − | 7.60527e21i | − | 1.91608i | ||||||
\(502\) | 2.04955e20 | − | 6.86095e19i | 0.0508192 | − | 0.0170120i | ||||
\(503\) | 5.16336e21i | 1.26005i | 0.776574 | + | 0.630026i | \(0.216956\pi\) | ||||
−0.776574 | + | 0.630026i | \(0.783044\pi\) | |||||||
\(504\) | −1.86328e21 | − | 1.27942e21i | −0.447542 | − | 0.307305i | ||||
\(505\) | −1.10921e22 | −2.62231 | ||||||||
\(506\) | −9.00134e20 | − | 2.68894e21i | −0.209461 | − | 0.625715i | ||||
\(507\) | −4.08130e21 | −0.934834 | ||||||||
\(508\) | −5.65552e19 | − | 7.50067e19i | −0.0127516 | − | 0.0169118i | ||||
\(509\) | 1.25680e21i | 0.278948i | 0.990226 | + | 0.139474i | \(0.0445412\pi\) | ||||
−0.990226 | + | 0.139474i | \(0.955459\pi\) | |||||||
\(510\) | −4.49299e21 | − | 1.34218e22i | −0.981689 | − | 2.93257i | ||||
\(511\) | − | 1.01723e22i | − | 2.18803i | ||||||
\(512\) | 4.59330e21 | + | 1.09651e21i | 0.972669 | + | 0.232195i | ||||
\(513\) | 4.42387e20 | 0.0922281 | ||||||||
\(514\) | 2.73200e21 | − | 9.14548e20i | 0.560758 | − | 0.187716i | ||||
\(515\) | 3.89009e21 | 0.786144 | ||||||||
\(516\) | −9.19710e20 | + | 6.93463e20i | −0.183001 | + | 0.137983i | ||||
\(517\) | 1.70006e21i | 0.333074i | ||||||||
\(518\) | −1.14974e22 | + | 3.84881e21i | −2.21800 | + | 0.742486i | ||||
\(519\) | − | 3.52805e21i | − | 0.670186i | ||||||
\(520\) | 1.93146e21 | − | 2.81288e21i | 0.361293 | − | 0.526167i | ||||
\(521\) | 4.04183e21 | 0.744520 | 0.372260 | − | 0.928129i | \(-0.378583\pi\) | ||||
0.372260 | + | 0.928129i | \(0.378583\pi\) | |||||||
\(522\) | −3.58511e20 | − | 1.07097e21i | −0.0650337 | − | 0.194273i | ||||
\(523\) | 5.82231e21 | 1.04012 | 0.520058 | − | 0.854131i | \(-0.325910\pi\) | ||||
0.520058 | + | 0.854131i | \(0.325910\pi\) | |||||||
\(524\) | −1.69592e21 | + | 1.27873e21i | −0.298371 | + | 0.224972i | ||||
\(525\) | 1.03679e22i | 1.79645i | ||||||||
\(526\) | 1.71886e21 | + | 5.13470e21i | 0.293329 | + | 0.876253i | ||||
\(527\) | 1.24644e22i | 2.09502i | ||||||||
\(528\) | −1.36819e21 | + | 4.78177e21i | −0.226504 | + | 0.791621i | ||||
\(529\) | 7.53376e20 | 0.122848 | ||||||||
\(530\) | −1.18177e21 | + | 3.95604e20i | −0.189814 | + | 0.0635409i | ||||
\(531\) | 3.27468e21 | 0.518099 | ||||||||
\(532\) | 7.13347e20 | + | 9.46082e20i | 0.111175 | + | 0.147447i | ||||
\(533\) | − | 6.58621e19i | − | 0.0101115i | ||||||
\(534\) | −4.36283e21 | + | 1.46047e21i | −0.659839 | + | 0.220884i | ||||
\(535\) | − | 6.41196e21i | − | 0.955345i | ||||||
\(536\) | 8.36560e20 | − | 1.21832e21i | 0.122794 | − | 0.178831i | ||||
\(537\) | 1.12929e22 | 1.63309 | ||||||||
\(538\) | −2.81700e21 | − | 8.41513e21i | −0.401355 | − | 1.19895i | ||||
\(539\) | −6.03296e21 | −0.846878 | ||||||||
\(540\) | 4.60306e21 | + | 6.10484e21i | 0.636644 | + | 0.844353i | ||||
\(541\) | 3.05007e21i | 0.415654i | 0.978166 | + | 0.207827i | \(0.0666391\pi\) | ||||
−0.978166 | + | 0.207827i | \(0.933361\pi\) | |||||||
\(542\) | 1.45858e21 | + | 4.35718e21i | 0.195856 | + | 0.585074i | ||||
\(543\) | 5.06700e21i | 0.670428i | ||||||||
\(544\) | −6.30600e20 | − | 1.42102e22i | −0.0822172 | − | 1.85272i | ||||
\(545\) | 1.30525e22 | 1.67696 | ||||||||
\(546\) | −5.81056e21 | + | 1.94511e21i | −0.735660 | + | 0.246265i | ||||
\(547\) | −9.94165e21 | −1.24039 | −0.620197 | − | 0.784446i | \(-0.712947\pi\) | ||||
−0.620197 | + | 0.784446i | \(0.712947\pi\) | |||||||
\(548\) | 9.17225e21 | − | 6.91590e21i | 1.12780 | − | 0.850363i | ||||
\(549\) | 1.30834e20i | 0.0158541i | ||||||||
\(550\) | 5.79486e21 | − | 1.93985e21i | 0.692056 | − | 0.231669i | ||||
\(551\) | 5.92049e20i | 0.0696859i | ||||||||
\(552\) | 7.77809e21 | + | 5.34083e21i | 0.902319 | + | 0.619578i | ||||
\(553\) | −1.70163e22 | −1.94564 | ||||||||
\(554\) | 1.53769e21 | + | 4.59350e21i | 0.173297 | + | 0.517685i | ||||
\(555\) | −2.36610e22 | −2.62839 | ||||||||
\(556\) | −3.26762e21 | + | 2.46379e21i | −0.357794 | + | 0.269778i | ||||
\(557\) | − | 1.20851e22i | − | 1.30440i | −0.758048 | − | 0.652199i | \(-0.773847\pi\) | ||
0.758048 | − | 0.652199i | \(-0.226153\pi\) | |||||||
\(558\) | 1.23306e21 | + | 3.68349e21i | 0.131193 | + | 0.391910i | ||||
\(559\) | 8.36411e20i | 0.0877254i | ||||||||
\(560\) | −5.63329e21 | + | 1.96881e22i | −0.582449 | + | 2.03563i | ||||
\(561\) | 1.49811e22 | 1.52701 | ||||||||
\(562\) | 7.27652e21 | − | 2.43585e21i | 0.731195 | − | 0.244771i | ||||
\(563\) | 1.12872e22 | 1.11820 | 0.559100 | − | 0.829100i | \(-0.311147\pi\) | ||||
0.559100 | + | 0.829100i | \(0.311147\pi\) | |||||||
\(564\) | −3.40564e21 | − | 4.51675e21i | −0.332634 | − | 0.441158i | ||||
\(565\) | − | 9.81692e21i | − | 0.945339i | ||||||
\(566\) | 7.22810e21 | − | 2.41964e21i | 0.686266 | − | 0.229731i | ||||
\(567\) | − | 1.95294e22i | − | 1.82820i | ||||||
\(568\) | 8.34018e21 | + | 5.72679e21i | 0.769820 | + | 0.528597i | ||||
\(569\) | 5.86823e21 | 0.534083 | 0.267042 | − | 0.963685i | \(-0.413954\pi\) | ||||
0.267042 | + | 0.963685i | \(0.413954\pi\) | |||||||
\(570\) | 7.34014e20 | + | 2.19270e21i | 0.0658727 | + | 0.196779i | ||||
\(571\) | −1.37932e22 | −1.22061 | −0.610304 | − | 0.792168i | \(-0.708953\pi\) | ||||
−0.610304 | + | 0.792168i | \(0.708953\pi\) | |||||||
\(572\) | 2.17434e21 | + | 2.88373e21i | 0.189740 | + | 0.251644i | ||||
\(573\) | 1.17651e22i | 1.01242i | ||||||||
\(574\) | 1.25475e20 | + | 3.74829e20i | 0.0106479 | + | 0.0318081i | ||||
\(575\) | − | 1.15926e22i | − | 0.970151i | ||||||
\(576\) | −1.59213e21 | − | 4.13703e21i | −0.131401 | − | 0.341435i | ||||
\(577\) | −2.09216e22 | −1.70290 | −0.851449 | − | 0.524437i | \(-0.824276\pi\) | ||||
−0.851449 | + | 0.524437i | \(0.824276\pi\) | |||||||
\(578\) | −2.88157e22 | + | 9.64617e21i | −2.31316 | + | 0.774341i | ||||
\(579\) | −5.81379e20 | −0.0460289 | ||||||||
\(580\) | −8.17015e21 | + | 6.16031e21i | −0.637978 | + | 0.481037i | ||||
\(581\) | 1.41156e22i | 1.08716i | ||||||||
\(582\) | 1.96239e22 | − | 6.56918e21i | 1.49074 | − | 0.499031i | ||||
\(583\) | − | 1.31907e21i | − | 0.0988373i | ||||||
\(584\) | 1.12928e22 | − | 1.64462e22i | 0.834638 | − | 1.21552i | ||||
\(585\) | −3.20294e21 | −0.233508 | ||||||||
\(586\) | 2.61515e20 | + | 7.81216e20i | 0.0188068 | + | 0.0561811i | ||||
\(587\) | −1.05244e22 | −0.746608 | −0.373304 | − | 0.927709i | \(-0.621775\pi\) | ||||
−0.373304 | + | 0.927709i | \(0.621775\pi\) | |||||||
\(588\) | 1.60285e22 | − | 1.20855e22i | 1.12169 | − | 0.845757i | ||||
\(589\) | − | 2.03630e21i | − | 0.140579i | ||||||
\(590\) | −9.41815e21 | − | 2.81345e22i | −0.641430 | − | 1.91612i | ||||
\(591\) | 7.46504e21i | 0.501571i | ||||||||
\(592\) | −2.28613e22 | − | 6.54124e21i | −1.51540 | − | 0.433597i | ||||
\(593\) | −1.40079e22 | −0.916085 | −0.458042 | − | 0.888930i | \(-0.651449\pi\) | ||||
−0.458042 | + | 0.888930i | \(0.651449\pi\) | |||||||
\(594\) | −7.67407e21 | + | 2.56893e21i | −0.495147 | + | 0.165753i | ||||
\(595\) | 6.16821e22 | 3.92666 | ||||||||
\(596\) | 7.85590e21 | + | 1.04189e22i | 0.493430 | + | 0.654415i | ||||
\(597\) | − | 6.80173e21i | − | 0.421526i | ||||||
\(598\) | 6.49697e21 | − | 2.17489e21i | 0.397284 | − | 0.132993i | ||||
\(599\) | 1.63288e22i | 0.985233i | 0.870247 | + | 0.492616i | \(0.163959\pi\) | ||||
−0.870247 | + | 0.492616i | \(0.836041\pi\) | |||||||
\(600\) | −1.15099e22 | + | 1.67623e22i | −0.685268 | + | 0.997986i | ||||
\(601\) | −9.56729e20 | −0.0562074 | −0.0281037 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281037 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(602\) | −1.59347e21 | − | 4.76011e21i | −0.0923786 | − | 0.275959i | ||||
\(603\) | −1.38727e21 | −0.0793636 | ||||||||
\(604\) | −3.73081e21 | − | 4.94801e21i | −0.210624 | − | 0.279341i | ||||
\(605\) | − | 1.28981e22i | − | 0.718595i | ||||||
\(606\) | 1.24009e22 | + | 3.70449e22i | 0.681825 | + | 2.03679i | ||||
\(607\) | 3.42389e22i | 1.85785i | 0.370273 | + | 0.928923i | \(0.379264\pi\) | ||||
−0.370273 | + | 0.928923i | \(0.620736\pi\) | |||||||
\(608\) | 1.03020e20 | + | 2.32151e21i | 0.00551689 | + | 0.124320i | ||||
\(609\) | 1.83750e22 | 0.971158 | ||||||||
\(610\) | 1.12407e21 | − | 3.76286e20i | 0.0586345 | − | 0.0196281i | ||||
\(611\) | −4.10767e21 | −0.211478 | ||||||||
\(612\) | −1.06611e22 | + | 8.03851e21i | −0.541741 | + | 0.408474i | ||||
\(613\) | − | 3.27644e22i | − | 1.64330i | −0.569990 | − | 0.821652i | \(-0.693053\pi\) | ||
0.569990 | − | 0.821652i | \(-0.306947\pi\) | |||||||
\(614\) | −1.41281e22 | + | 4.72942e21i | −0.699416 | + | 0.234132i | ||||
\(615\) | 7.71376e20i | 0.0376934i | ||||||||
\(616\) | −1.78683e22 | − | 1.22693e22i | −0.861861 | − | 0.591797i | ||||
\(617\) | −2.90372e21 | −0.138253 | −0.0691264 | − | 0.997608i | \(-0.522021\pi\) | ||||
−0.0691264 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(618\) | −4.34909e21 | − | 1.29919e22i | −0.204405 | − | 0.610611i | ||||
\(619\) | 2.23150e22 | 1.03531 | 0.517657 | − | 0.855588i | \(-0.326804\pi\) | ||||
0.517657 | + | 0.855588i | \(0.326804\pi\) | |||||||
\(620\) | 2.81005e22 | − | 2.11878e22i | 1.28700 | − | 0.970404i | ||||
\(621\) | 1.53520e22i | 0.694117i | ||||||||
\(622\) | 8.47233e21 | + | 2.53091e22i | 0.378163 | + | 1.12968i | ||||
\(623\) | − | 2.00501e22i | − | 0.883513i | ||||||
\(624\) | −1.15536e22 | − | 3.30581e21i | −0.502622 | − | 0.143814i | ||||
\(625\) | −2.24181e22 | −0.962852 | ||||||||
\(626\) | 3.89280e22 | − | 1.30313e22i | 1.65070 | − | 0.552578i | ||||
\(627\) | −2.44745e21 | −0.102464 | ||||||||
\(628\) | −2.78509e21 | − | 3.69374e21i | −0.115123 | − | 0.152683i | ||||
\(629\) | 7.16237e22i | 2.92315i | ||||||||
\(630\) | 1.82283e22 | − | 6.10200e21i | 0.734551 | − | 0.245894i | ||||
\(631\) | 2.79894e22i | 1.11368i | 0.830621 | + | 0.556838i | \(0.187986\pi\) | ||||
−0.830621 | + | 0.556838i | \(0.812014\pi\) | |||||||
\(632\) | −2.75112e22 | − | 1.88906e22i | −1.08087 | − | 0.742179i | ||||
\(633\) | −1.39447e21 | −0.0540977 | ||||||||
\(634\) | 9.23672e20 | + | 2.75925e21i | 0.0353837 | + | 0.105701i | ||||
\(635\) | 7.98913e20 | 0.0302211 | ||||||||
\(636\) | 2.64243e21 | + | 3.50454e21i | 0.0987066 | + | 0.130910i | ||||
\(637\) | − | 1.45767e22i | − | 0.537706i | ||||||
\(638\) | −3.43801e21 | − | 1.02703e22i | −0.125240 | − | 0.374124i | ||||
\(639\) | − | 9.49673e21i | − | 0.341639i | ||||||
\(640\) | −3.09643e22 | + | 2.55771e22i | −1.10007 | + | 0.908680i | ||||
\(641\) | −2.28901e21 | −0.0803125 | −0.0401563 | − | 0.999193i | \(-0.512786\pi\) | ||||
−0.0401563 | + | 0.999193i | \(0.512786\pi\) | |||||||
\(642\) | −2.14143e22 | + | 7.16852e21i | −0.742033 | + | 0.248399i | ||||
\(643\) | 3.53144e22 | 1.20855 | 0.604274 | − | 0.796777i | \(-0.293463\pi\) | ||||
0.604274 | + | 0.796777i | \(0.293463\pi\) | |||||||
\(644\) | −3.28316e22 | + | 2.47551e22i | −1.10970 | + | 0.836714i | ||||
\(645\) | − | 9.79603e21i | − | 0.327019i | ||||||
\(646\) | 6.63745e21 | − | 2.22191e21i | 0.218847 | − | 0.0732600i | ||||
\(647\) | − | 5.78292e22i | − | 1.88327i | −0.336634 | − | 0.941636i | \(-0.609288\pi\) | ||
0.336634 | − | 0.941636i | \(-0.390712\pi\) | |||||||
\(648\) | 2.16805e22 | − | 3.15743e22i | 0.697379 | − | 1.01562i | ||||
\(649\) | 3.14032e22 | 0.997739 | ||||||||
\(650\) | 4.68704e21 | + | 1.40014e22i | 0.147093 | + | 0.439406i | ||||
\(651\) | −6.31992e22 | −1.95913 | ||||||||
\(652\) | 1.22698e22 | − | 9.25149e21i | 0.375715 | − | 0.283290i | ||||
\(653\) | − | 4.75473e22i | − | 1.43820i | −0.694904 | − | 0.719102i | \(-0.744553\pi\) | ||
0.694904 | − | 0.719102i | \(-0.255447\pi\) | |||||||
\(654\) | −1.45926e22 | − | 4.35920e22i | −0.436024 | − | 1.30252i | ||||
\(655\) | − | 1.80636e22i | − | 0.533181i | ||||||
\(656\) | −2.13252e20 | + | 7.45303e20i | −0.00621815 | + | 0.0217321i | ||||
\(657\) | −1.87268e22 | −0.539437 | ||||||||
\(658\) | 2.33772e22 | − | 7.82562e21i | 0.665251 | − | 0.222695i | ||||
\(659\) | 1.20594e22 | 0.339035 | 0.169517 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169517 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(660\) | −2.54658e22 | − | 3.37742e22i | −0.707304 | − | 0.938067i | ||||
\(661\) | 1.63382e22i | 0.448326i | 0.974552 | + | 0.224163i | \(0.0719648\pi\) | ||||
−0.974552 | + | 0.224163i | \(0.928035\pi\) | |||||||
\(662\) | −1.05442e21 | + | 3.52973e20i | −0.0285859 | + | 0.00956924i | ||||
\(663\) | 3.61971e22i | 0.969540i | ||||||||
\(664\) | −1.56704e22 | + | 2.28216e22i | −0.414702 | + | 0.603950i | ||||
\(665\) | −1.00769e22 | −0.263484 | ||||||||
\(666\) | 7.08549e21 | + | 2.11663e22i | 0.183053 | + | 0.546827i | ||||
\(667\) | −2.05457e22 | −0.524462 | ||||||||
\(668\) | 3.91337e22 | + | 5.19013e22i | 0.987050 | + | 1.30908i | ||||
\(669\) | − | 3.62781e22i | − | 0.904140i | ||||||
\(670\) | 3.98985e21 | + | 1.19187e22i | 0.0982557 | + | 0.293516i | ||||
\(671\) | 1.25466e21i | 0.0305314i | ||||||||
\(672\) | 7.20510e22 | − | 3.19737e21i | 1.73255 | − | 0.0768845i | ||||
\(673\) | −6.92380e22 | −1.64522 | −0.822610 | − | 0.568607i | \(-0.807483\pi\) | ||||
−0.822610 | + | 0.568607i | \(0.807483\pi\) | |||||||
\(674\) | −1.30795e22 | + | 4.37842e21i | −0.307123 | + | 0.102811i | ||||
\(675\) | −3.30847e22 | −0.767710 | ||||||||
\(676\) | 2.78524e22 | − | 2.10007e22i | 0.638688 | − | 0.481572i | ||||
\(677\) | − | 5.05127e22i | − | 1.14470i | −0.820010 | − | 0.572350i | \(-0.806032\pi\) | ||
0.820010 | − | 0.572350i | \(-0.193968\pi\) | |||||||
\(678\) | −3.27859e22 | + | 1.09752e22i | −0.734261 | + | 0.245797i | ||||
\(679\) | 9.01851e22i | 1.99607i | ||||||||
\(680\) | 9.97250e22 | + | 6.84762e22i | 2.18139 | + | 1.49785i | ||||
\(681\) | 7.76211e22 | 1.67804 | ||||||||
\(682\) | 1.18247e22 | + | 3.53236e22i | 0.252648 | + | 0.754727i | ||||
\(683\) | −6.89980e22 | −1.45704 | −0.728519 | − | 0.685025i | \(-0.759791\pi\) | ||||
−0.728519 | + | 0.685025i | \(0.759791\pi\) | |||||||
\(684\) | 1.74169e21 | − | 1.31324e21i | 0.0363516 | − | 0.0274092i | ||||
\(685\) | 9.76957e22i | 2.01535i | ||||||||
\(686\) | 4.66760e21 | + | 1.39434e22i | 0.0951701 | + | 0.284299i | ||||
\(687\) | − | 9.52014e22i | − | 1.91862i | ||||||
\(688\) | 2.70817e21 | − | 9.46493e21i | 0.0539472 | − | 0.188543i | ||||
\(689\) | 3.18713e21 | 0.0627546 | ||||||||
\(690\) | −7.60924e22 | + | 2.54723e22i | −1.48098 | + | 0.495764i | ||||
\(691\) | 1.01417e23 | 1.95114 | 0.975569 | − | 0.219694i | \(-0.0705059\pi\) | ||||
0.975569 | + | 0.219694i | \(0.0705059\pi\) | |||||||
\(692\) | 1.81539e22 | + | 2.40768e22i | 0.345241 | + | 0.457878i | ||||
\(693\) | 2.03461e22i | 0.382486i | ||||||||
\(694\) | −2.45214e20 | + | 8.20863e19i | −0.00455690 | + | 0.00152544i | ||||
\(695\) | − | 3.48041e22i | − | 0.639370i | ||||||
\(696\) | 2.97080e22 | + | 2.03990e22i | 0.539510 | + | 0.370454i | ||||
\(697\) | 2.33501e21 | 0.0419205 | ||||||||
\(698\) | −1.37112e22 | − | 4.09590e22i | −0.243350 | − | 0.726952i | ||||
\(699\) | 7.38415e22 | 1.29564 | ||||||||
\(700\) | −5.33490e22 | − | 7.07544e22i | −0.925426 | − | 1.22735i | ||||
\(701\) | 3.43490e22i | 0.589075i | 0.955640 | + | 0.294537i | \(0.0951655\pi\) | ||||
−0.955640 | + | 0.294537i | \(0.904834\pi\) | |||||||
\(702\) | −6.20700e21 | − | 1.85420e22i | −0.105241 | − | 0.314383i | ||||
\(703\) | − | 1.17011e22i | − | 0.196148i | ||||||
\(704\) | −1.52680e22 | − | 3.96729e22i | −0.253047 | − | 0.657525i | ||||
\(705\) | 4.81089e22 | 0.788339 | ||||||||
\(706\) | 6.89760e22 | − | 2.30900e22i | 1.11753 | − | 0.374099i | ||||
\(707\) | −1.70246e23 | −2.72723 | ||||||||
\(708\) | −8.34326e22 | + | 6.29083e22i | −1.32151 | + | 0.996419i | ||||
\(709\) | − | 5.45976e22i | − | 0.855074i | −0.903998 | − | 0.427537i | \(-0.859381\pi\) | ||
0.903998 | − | 0.427537i | \(-0.140619\pi\) | |||||||
\(710\) | −8.15914e22 | + | 2.73130e22i | −1.26351 | + | 0.422964i | ||||
\(711\) | 3.13262e22i | 0.479679i | ||||||||
\(712\) | 2.22586e22 | − | 3.24162e22i | 0.337022 | − | 0.490820i | ||||
\(713\) | 7.06650e22 | 1.05801 | ||||||||
\(714\) | −6.89600e22 | − | 2.06002e23i | −1.02097 | − | 3.04990i | ||||
\(715\) | −3.07152e22 | −0.449682 | ||||||||
\(716\) | −7.70672e22 | + | 5.81088e22i | −1.11575 | + | 0.841275i | ||||
\(717\) | 8.98832e22i | 1.28684i | ||||||||
\(718\) | −1.66279e22 | − | 4.96719e22i | −0.235419 | − | 0.703260i | ||||
\(719\) | 3.00804e22i | 0.421165i | 0.977576 | + | 0.210583i | \(0.0675361\pi\) | ||||
−0.977576 | + | 0.210583i | \(0.932464\pi\) | |||||||
\(720\) | 3.62449e22 | + | 1.03706e22i | 0.501865 | + | 0.143597i | ||||
\(721\) | 5.97065e22 | 0.817598 | ||||||||
\(722\) | 6.89375e22 | − | 2.30771e22i | 0.933593 | − | 0.312524i | ||||
\(723\) | 6.89440e22 | 0.923400 | ||||||||
\(724\) | −2.60728e22 | − | 3.45792e22i | −0.345365 | − | 0.458043i | ||||
\(725\) | − | 4.42775e22i | − | 0.580068i | ||||||
\(726\) | −4.30765e22 | + | 1.44200e22i | −0.558145 | + | 0.186841i | ||||
\(727\) | − | 1.19550e23i | − | 1.53206i | −0.642806 | − | 0.766029i | \(-0.722230\pi\) | ||
0.642806 | − | 0.766029i | \(-0.277770\pi\) | |||||||
\(728\) | 2.96448e22 | − | 4.31730e22i | 0.375748 | − | 0.547220i | ||||
\(729\) | 3.31374e22 | 0.415431 | ||||||||
\(730\) | 5.38592e22 | + | 1.60892e23i | 0.667847 | + | 1.99504i | ||||
\(731\) | −2.96533e22 | −0.363692 | ||||||||
\(732\) | −2.51339e21 | − | 3.33340e21i | −0.0304910 | − | 0.0404389i | ||||
\(733\) | 3.41068e22i | 0.409270i | 0.978838 | + | 0.204635i | \(0.0656007\pi\) | ||||
−0.978838 | + | 0.204635i | \(0.934399\pi\) | |||||||
\(734\) | 8.20149e21 | + | 2.45000e22i | 0.0973474 | + | 0.290803i | ||||
\(735\) | 1.70723e23i | 2.00444i | ||||||||
\(736\) | −8.05625e22 | + | 3.57508e21i | −0.935643 | + | 0.0415206i | ||||
\(737\) | −1.33035e22 | −0.152836 | ||||||||
\(738\) | 6.90043e20 | − | 2.30995e20i | 0.00784197 | − | 0.00262513i | ||||
\(739\) | −4.42548e22 | −0.497513 | −0.248757 | − | 0.968566i | \(-0.580022\pi\) | ||||
−0.248757 | + | 0.968566i | \(0.580022\pi\) | |||||||
\(740\) | 1.61472e23 | − | 1.21750e23i | 1.79574 | − | 1.35399i | ||||
\(741\) | − | 5.91348e21i | − | 0.0650575i | ||||||
\(742\) | −1.81383e22 | + | 6.07187e21i | −0.197408 | + | 0.0660833i | ||||
\(743\) | − | 6.24045e21i | − | 0.0671901i | −0.999436 | − | 0.0335951i | \(-0.989304\pi\) | ||
0.999436 | − | 0.0335951i | \(-0.0106957\pi\) | |||||||
\(744\) | −1.02178e23 | − | 7.01604e22i | −1.08836 | − | 0.747324i | ||||
\(745\) | −1.10974e23 | −1.16942 | ||||||||
\(746\) | 5.26880e22 | + | 1.57393e23i | 0.549289 | + | 1.64087i | ||||
\(747\) | 2.59863e22 | 0.268027 | ||||||||
\(748\) | −1.02237e23 | + | 7.70869e22i | −1.04327 | + | 0.786625i | ||||
\(749\) | − | 9.84131e22i | − | 0.993570i | ||||||
\(750\) | −1.90048e21 | − | 5.67725e21i | −0.0189834 | − | 0.0567085i | ||||
\(751\) | − | 3.46827e22i | − | 0.342762i | −0.985205 | − | 0.171381i | \(-0.945177\pi\) | ||
0.985205 | − | 0.171381i | \(-0.0548229\pi\) | |||||||
\(752\) | 4.64829e22 | + | 1.33000e22i | 0.454517 | + | 0.130050i | ||||
\(753\) | 6.47371e21 | 0.0626316 | ||||||||
\(754\) | 2.48148e22 | − | 8.30687e21i | 0.237542 | − | 0.0795182i | ||||
\(755\) | 5.27024e22 | 0.499177 | ||||||||
\(756\) | 7.06495e22 | + | 9.36993e22i | 0.662117 | + | 0.878137i | ||||
\(757\) | 3.91438e22i | 0.362991i | 0.983392 | + | 0.181495i | \(0.0580938\pi\) | ||||
−0.983392 | + | 0.181495i | \(0.941906\pi\) | |||||||
\(758\) | −1.09192e21 | + | 3.65524e20i | −0.0100193 | + | 0.00335400i | ||||
\(759\) | − | 8.49330e22i | − | 0.771156i | ||||||
\(760\) | −1.62919e22 | − | 1.11869e22i | −0.146374 | − | 0.100508i | ||||
\(761\) | −7.00706e22 | −0.622958 | −0.311479 | − | 0.950253i | \(-0.600824\pi\) | ||||
−0.311479 | + | 0.950253i | \(0.600824\pi\) | |||||||
\(762\) | −8.93178e20 | − | 2.66816e21i | −0.00785775 | − | 0.0234732i | ||||
\(763\) | 2.00335e23 | 1.74405 | ||||||||
\(764\) | −6.05386e22 | − | 8.02898e22i | −0.521538 | − | 0.691693i | ||||
\(765\) | − | 1.13554e23i | − | 0.968079i | ||||||
\(766\) | −4.49781e22 | − | 1.34362e23i | −0.379464 | − | 1.13356i | ||||
\(767\) | 7.58760e22i | 0.633492i | ||||||||
\(768\) | 1.20039e23 | + | 7.48179e22i | 0.991816 | + | 0.618181i | ||||
\(769\) | −3.23281e22 | −0.264344 | −0.132172 | − | 0.991227i | \(-0.542195\pi\) | ||||
−0.132172 | + | 0.991227i | \(0.542195\pi\) | |||||||
\(770\) | 1.74804e23 | − | 5.85164e22i | 1.41457 | − | 0.473534i | ||||
\(771\) | 8.62930e22 | 0.691100 | ||||||||
\(772\) | 3.96756e21 | − | 2.99154e21i | 0.0314474 | − | 0.0237114i | ||||
\(773\) | 1.25542e23i | 0.984809i | 0.870366 | + | 0.492405i | \(0.163882\pi\) | ||||
−0.870366 | + | 0.492405i | \(0.836118\pi\) | |||||||
\(774\) | −8.76316e21 | + | 2.93350e21i | −0.0680351 | + | 0.0227750i | ||||
\(775\) | 1.52288e23i | 1.17018i | ||||||||
\(776\) | −1.00119e23 | + | 1.45808e23i | −0.761416 | + | 1.10888i | ||||
\(777\) | −3.63158e23 | −2.73355 | ||||||||
\(778\) | −1.22884e21 | − | 3.67088e21i | −0.00915503 | − | 0.0273485i | ||||
\(779\) | −3.81468e20 | −0.00281292 | ||||||||
\(780\) | 8.16047e22 | − | 6.15301e22i | 0.595605 | − | 0.449087i | ||||
\(781\) | − | 9.10708e22i | − | 0.657917i | ||||||
\(782\) | 7.71064e22 | + | 2.30337e23i | 0.551361 | + | 1.64706i | ||||
\(783\) | 5.86362e22i | 0.415022i | ||||||||
\(784\) | −4.71973e22 | + | 1.64952e23i | −0.330666 | + | 1.15566i | ||||
\(785\) | 3.93428e22 | 0.272840 | ||||||||
\(786\) | −6.03279e22 | + | 2.01950e22i | −0.414131 | + | 0.138632i | ||||
\(787\) | 1.23669e22 | 0.0840353 | 0.0420176 | − | 0.999117i | \(-0.486621\pi\) | ||||
0.0420176 | + | 0.999117i | \(0.486621\pi\) | |||||||
\(788\) | −3.84121e22 | − | 5.09443e22i | −0.258380 | − | 0.342678i | ||||
\(789\) | 1.62185e23i | 1.07993i | ||||||||
\(790\) | 2.69140e23 | − | 9.00957e22i | 1.77403 | − | 0.593864i | ||||
\(791\) | − | 1.50674e23i | − | 0.983163i | ||||||
\(792\) | −2.25872e22 | + | 3.28947e22i | −0.145902 | + | 0.212483i | ||||
\(793\) | −3.03149e21 | −0.0193852 | ||||||||
\(794\) | −5.25515e22 | − | 1.56985e23i | −0.332676 | − | 0.993791i | ||||
\(795\) | −3.73276e22 | −0.233934 | ||||||||
\(796\) | 3.49990e22 | + | 4.64177e22i | 0.217146 | + | 0.287991i | ||||
\(797\) | − | 2.33288e23i | − | 1.43294i | −0.697620 | − | 0.716468i | \(-0.745758\pi\) | ||
0.697620 | − | 0.716468i | \(-0.254242\pi\) | |||||||
\(798\) | 1.12659e22 | + | 3.36543e22i | 0.0685083 | + | 0.204653i | ||||
\(799\) | − | 1.45629e23i | − | 0.876747i | ||||||
\(800\) | −7.70456e21 | − | 1.73618e23i | −0.0459227 | − | 1.03484i | ||||
\(801\) | −3.69114e22 | −0.217821 | ||||||||
\(802\) | −5.73786e22 | + | 1.92077e22i | −0.335239 | + | 0.112223i | ||||
\(803\) | −1.79585e23 | −1.03883 | ||||||||
\(804\) | 3.53449e22 | − | 2.66501e22i | 0.202431 | − | 0.152634i | ||||
\(805\) | − | 3.49696e23i | − | 1.98301i | ||||||
\(806\) | −8.53483e22 | + | 2.85707e22i | −0.479197 | + | 0.160413i | ||||
\(807\) | − | 2.65801e23i | − | 1.47764i | ||||||
\(808\) | −2.75247e23 | − | 1.88999e23i | −1.51507 | − | 1.04032i | ||||
\(809\) | 1.68226e22 | 0.0916865 | 0.0458433 | − | 0.998949i | \(-0.485403\pi\) | ||||
0.0458433 | + | 0.998949i | \(0.485403\pi\) | |||||||
\(810\) | 1.03402e23 | + | 3.08889e23i | 0.558017 | + | 1.66695i | ||||
\(811\) | −2.04733e22 | −0.109401 | −0.0547004 | − | 0.998503i | \(-0.517420\pi\) | ||||
−0.0547004 | + | 0.998503i | \(0.517420\pi\) | |||||||
\(812\) | −1.25398e23 | + | 9.45507e22i | −0.663505 | + | 0.500284i | ||||
\(813\) | 1.37626e23i | 0.721068i | ||||||||
\(814\) | 6.79477e22 | + | 2.02978e23i | 0.352517 | + | 1.05306i | ||||
\(815\) | 1.30689e23i | 0.671394i | ||||||||
\(816\) | 1.17201e23 | − | 4.09611e23i | 0.596224 | − | 2.08377i | ||||
\(817\) | 4.84442e21 | 0.0244043 | ||||||||
\(818\) | −2.66776e23 | + | 8.93045e22i | −1.33082 | + | 0.445499i | ||||
\(819\) | −4.91599e22 | −0.242851 | ||||||||
\(820\) | −3.96919e21 | − | 5.26417e21i | −0.0194174 | − | 0.0257525i | ||||
\(821\) | 2.90138e23i | 1.40559i | 0.711392 | + | 0.702795i | \(0.248065\pi\) | ||||
−0.711392 | + | 0.702795i | \(0.751935\pi\) | |||||||
\(822\) | 3.26278e23 | − | 1.09223e23i | 1.56536 | − | 0.524010i | ||||
\(823\) | 3.39906e23i | 1.61495i | 0.589900 | + | 0.807476i | \(0.299167\pi\) | ||||
−0.589900 | + | 0.807476i | \(0.700833\pi\) | |||||||
\(824\) | 9.65310e22 | + | 6.62831e22i | 0.454202 | + | 0.311878i | ||||
\(825\) | 1.83037e23 | 0.852917 | ||||||||
\(826\) | −1.44553e23 | − | 4.31819e23i | −0.667094 | − | 1.99279i | ||||
\(827\) | 2.71198e23 | 1.23949 | 0.619745 | − | 0.784803i | \(-0.287236\pi\) | ||||
0.619745 | + | 0.784803i | \(0.287236\pi\) | |||||||
\(828\) | 4.55730e22 | + | 6.04415e22i | 0.206284 | + | 0.273585i | ||||
\(829\) | 2.18126e23i | 0.977848i | 0.872326 | + | 0.488924i | \(0.162611\pi\) | ||||
−0.872326 | + | 0.488924i | \(0.837389\pi\) | |||||||
\(830\) | −7.47378e22 | − | 2.23262e23i | −0.331830 | − | 0.991264i | ||||
\(831\) | 1.45090e23i | 0.638014i | ||||||||
\(832\) | 9.58569e22 | − | 3.68903e22i | 0.417481 | − | 0.160667i | ||||
\(833\) | 5.16790e23 | 2.22923 | ||||||||
\(834\) | −1.16237e23 | + | 3.89108e22i | −0.496610 | + | 0.166242i | ||||
\(835\) | −5.52812e23 | −2.33930 | ||||||||
\(836\) | 1.67023e22 | − | 1.25936e22i | 0.0700047 | − | 0.0527837i | ||||
\(837\) | − | 2.01674e23i | − | 0.837231i | ||||||
\(838\) | 1.42649e22 | − | 4.77524e21i | 0.0586566 | − | 0.0196355i | ||||
\(839\) | 9.38513e22i | 0.382248i | 0.981566 | + | 0.191124i | \(0.0612132\pi\) | ||||
−0.981566 | + | 0.191124i | \(0.938787\pi\) | |||||||
\(840\) | −3.47199e23 | + | 5.05642e23i | −1.40070 | + | 2.03990i | ||||
\(841\) | 1.71773e23 | 0.686416 | ||||||||
\(842\) | −7.06032e22 | − | 2.10911e23i | −0.279465 | − | 0.834837i | ||||
\(843\) | 2.29837e23 | 0.901153 | ||||||||
\(844\) | 9.51640e21 | − | 7.17539e21i | 0.0369601 | − | 0.0278680i | ||||
\(845\) | 2.96662e23i | 1.14132i | ||||||||
\(846\) | −1.44066e22 | − | 4.30364e22i | −0.0549034 | − | 0.164011i | ||||
\(847\) | − | 1.97966e23i | − | 0.747347i | ||||||
\(848\) | −3.60659e22 | − | 1.03194e22i | −0.134875 | − | 0.0385913i | ||||
\(849\) | 2.28307e23 | 0.845781 | ||||||||
\(850\) | −4.96393e23 | + | 1.66170e23i | −1.82169 | + | 0.609819i | ||||
\(851\) | 4.06058e23 | 1.47622 | ||||||||
\(852\) | 1.82437e23 | + | 2.41958e23i | 0.657047 | + | 0.871412i | ||||
\(853\) | 1.61571e23i | 0.576462i | 0.957561 | + | 0.288231i | \(0.0930670\pi\) | ||||
−0.957561 | + | 0.288231i | \(0.906933\pi\) | |||||||
\(854\) | 1.72526e22 | − | 5.77537e21i | 0.0609805 | − | 0.0204135i | ||||
\(855\) | 1.85512e22i | 0.0649594i | ||||||||
\(856\) | 1.09253e23 | − | 1.59110e23i | 0.379004 | − | 0.551960i | ||||
\(857\) | −3.29920e23 | −1.13387 | −0.566933 | − | 0.823764i | \(-0.691870\pi\) | ||||
−0.566933 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(858\) | 3.43394e22 | + | 1.02581e23i | 0.116921 | + | 0.349276i | ||||
\(859\) | 3.82694e23 | 1.29094 | 0.645470 | − | 0.763785i | \(-0.276661\pi\) | ||||
0.645470 | + | 0.763785i | \(0.276661\pi\) | |||||||
\(860\) | 5.04065e22 | + | 6.68520e22i | 0.168461 | + | 0.223422i | ||||
\(861\) | 1.18394e22i | 0.0392015i | ||||||||
\(862\) | 1.56519e22 | + | 4.67565e22i | 0.0513464 | + | 0.153385i | ||||
\(863\) | − | 4.07008e23i | − | 1.32287i | −0.750003 | − | 0.661435i | \(-0.769948\pi\) | ||
0.750003 | − | 0.661435i | \(-0.230052\pi\) | |||||||
\(864\) | 1.02031e22 | + | 2.29920e23i | 0.0328565 | + | 0.740402i | ||||
\(865\) | −2.56447e23 | −0.818217 | ||||||||
\(866\) | 5.69964e22 | − | 1.90798e22i | 0.180179 | − | 0.0603156i | ||||
\(867\) | −9.10173e23 | −2.85083 | ||||||||
\(868\) | 4.31296e23 | − | 3.25198e23i | 1.33850 | − | 1.00923i | ||||
\(869\) | 3.00409e23i | 0.923751i | ||||||||
\(870\) | −2.90631e23 | + | 9.72899e22i | −0.885498 | + | 0.296424i | ||||
\(871\) | − | 3.21436e22i | − | 0.0970398i | ||||||
\(872\) | 3.23893e23 | + | 2.22401e23i | 0.968878 | + | 0.665280i | ||||
\(873\) | 1.66027e23 | 0.492113 | ||||||||
\(874\) | −1.25968e22 | − | 3.76299e22i | −0.0369971 | − | 0.110520i | ||||
\(875\) | 2.60908e22 | 0.0759317 | ||||||||
\(876\) | 4.77123e23 | − | 3.59751e23i | 1.37593 | − | 1.03746i | ||||
\(877\) | − | 4.28239e23i | − | 1.22374i | −0.790958 | − | 0.611871i | \(-0.790417\pi\) | ||
0.790958 | − | 0.611871i | \(-0.209583\pi\) | |||||||
\(878\) | −1.77576e23 | − | 5.30466e23i | −0.502837 | − | 1.50211i | ||||
\(879\) | 2.46755e22i | 0.0692397i | ||||||||
\(880\) | 3.47578e23 | + | 9.94514e22i | 0.966474 | + | 0.276535i | ||||
\(881\) | −3.65451e23 | −1.00698 | −0.503491 | − | 0.864000i | \(-0.667951\pi\) | ||||
−0.503491 | + | 0.864000i | \(0.667951\pi\) | |||||||
\(882\) | 1.52722e23 | − | 5.11243e22i | 0.417016 | − | 0.139598i | ||||
\(883\) | −4.78165e23 | −1.29387 | −0.646937 | − | 0.762543i | \(-0.723950\pi\) | ||||
−0.646937 | + | 0.762543i | \(0.723950\pi\) | |||||||
\(884\) | −1.86256e23 | − | 2.47023e23i | −0.499450 | − | 0.662399i | ||||
\(885\) | − | 8.88658e23i | − | 2.36150i | ||||||
\(886\) | −2.60198e23 | + | 8.71025e22i | −0.685227 | + | 0.229383i | ||||
\(887\) | 4.68950e23i | 1.22388i | 0.790905 | + | 0.611939i | \(0.209610\pi\) | ||||
−0.790905 | + | 0.611939i | \(0.790390\pi\) | |||||||
\(888\) | −5.87139e23 | − | 4.03159e23i | −1.51858 | − | 1.04273i | ||||
\(889\) | 1.22620e22 | 0.0314302 | ||||||||
\(890\) | 1.06159e23 | + | 3.17125e23i | 0.269673 | + | 0.805584i | ||||
\(891\) | −3.44776e23 | −0.867991 | ||||||||
\(892\) | 1.86673e23 | + | 2.47576e23i | 0.465760 | + | 0.617717i | ||||
\(893\) | 2.37913e22i | 0.0588310i | ||||||||
\(894\) | 1.24068e23 | + | 3.70625e23i | 0.304061 | + | 0.908312i | ||||
\(895\) | − | 8.20860e23i | − | 1.99381i | ||||||
\(896\) | −4.75252e23 | + | 3.92566e23i | −1.14409 | + | 0.945037i | ||||
\(897\) | 2.05214e23 | 0.489628 | ||||||||
\(898\) | 2.66202e23 | − | 8.91123e22i | 0.629507 | − | 0.210730i | ||||
\(899\) | 2.69901e23 | 0.632597 | ||||||||
\(900\) | −1.30256e23 | + | 9.82131e22i | −0.302592 | + | 0.228155i | ||||
\(901\) | 1.12993e23i | 0.260168i | ||||||||
\(902\) | 6.61731e21 | − | 2.21517e21i | 0.0151018 | − | 0.00505539i | ||||
\(903\) | − | 1.50353e23i | − | 0.340103i | ||||||
\(904\) | 1.67270e23 | − | 2.43603e23i | 0.375034 | − | 0.546179i | ||||
\(905\) | 3.68310e23 | 0.818513 | ||||||||
\(906\) | −5.89208e22 | − | 1.76012e23i | −0.129791 | − | 0.387719i | ||||
\(907\) | −2.76998e22 | −0.0604810 | −0.0302405 | − | 0.999543i | \(-0.509627\pi\) | ||||
−0.0302405 | + | 0.999543i | \(0.509627\pi\) | |||||||
\(908\) | −5.29717e23 | + | 3.99407e23i | −1.14645 | + | 0.864429i | ||||
\(909\) | 3.13416e23i | 0.672373i | ||||||||
\(910\) | 1.41386e23 | + | 4.22358e23i | 0.300660 | + | 0.898153i | ||||
\(911\) | 6.80989e23i | 1.43547i | 0.696318 | + | 0.717734i | \(0.254820\pi\) | ||||
−0.696318 | + | 0.717734i | \(0.745180\pi\) | |||||||
\(912\) | −1.91470e22 | + | 6.69177e22i | −0.0400075 | + | 0.139824i | ||||
\(913\) | 2.49201e23 | 0.516158 | ||||||||
\(914\) | 1.68129e23 | − | 5.62818e22i | 0.345201 | − | 0.115558i | ||||
\(915\) | 3.55048e22 | 0.0722634 | ||||||||
\(916\) | 4.89869e23 | + | 6.49691e23i | 0.988362 | + | 1.31082i | ||||
\(917\) | − | 2.77247e23i | − | 0.554515i | ||||||
\(918\) | 6.57369e23 | − | 2.20057e23i | 1.30337 | − | 0.436308i | ||||
\(919\) | 4.10602e23i | 0.807043i | 0.914970 | + | 0.403522i | \(0.132214\pi\) | ||||
−0.914970 | + | 0.403522i | \(0.867786\pi\) | |||||||
\(920\) | 3.88214e23 | − | 5.65374e23i | 0.756430 | − | 1.10162i | ||||
\(921\) | −4.46249e23 | −0.861987 | ||||||||
\(922\) | 1.43290e23 | + | 4.28045e23i | 0.274390 | + | 0.819676i | ||||
\(923\) | 2.20044e23 | 0.417730 | ||||||||
\(924\) | −3.90859e23 | − | 5.18379e23i | −0.735604 | − | 0.975600i | ||||
\(925\) | 8.75085e23i | 1.63274i | ||||||||
\(926\) | −7.21891e22 | − | 2.15648e23i | −0.133531 | − | 0.398894i | ||||
\(927\) | − | 1.09917e23i | − | 0.201571i | ||||||
\(928\) | −3.07704e23 | + | 1.36548e22i | −0.559435 | + | 0.0248258i | ||||
\(929\) | −5.97517e23 | −1.07702 | −0.538511 | − | 0.842618i | \(-0.681013\pi\) | ||||
−0.538511 | + | 0.842618i | \(0.681013\pi\) | |||||||
\(930\) | 9.99598e23 | − | 3.34619e23i | 1.78633 | − | 0.597981i | ||||
\(931\) | −8.44273e22 | −0.149584 | ||||||||
\(932\) | −5.03923e23 | + | 3.79959e23i | −0.885192 | + | 0.667436i | ||||
\(933\) | 7.99414e23i | 1.39226i | ||||||||
\(934\) | −5.87886e23 | + | 1.96797e23i | −1.01512 | + | 0.339816i | ||||
\(935\) | − | 1.08895e24i | − | 1.86429i | ||||||
\(936\) | −7.94797e22 | − | 5.45747e22i | −0.134912 | − | 0.0926371i | ||||
\(937\) | 7.64808e22 | 0.128717 | 0.0643585 | − | 0.997927i | \(-0.479500\pi\) | ||||
0.0643585 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(938\) | 6.12376e22 | + | 1.82933e23i | 0.102187 | + | 0.305260i | ||||
\(939\) | 1.22958e24 | 2.03438 | ||||||||
\(940\) | −3.28314e23 | + | 2.47550e23i | −0.538601 | + | 0.406106i | ||||
\(941\) | − | 9.30929e23i | − | 1.51426i | −0.653266 | − | 0.757129i | \(-0.726601\pi\) | ||
0.653266 | − | 0.757129i | \(-0.273399\pi\) | |||||||
\(942\) | −4.39850e22 | − | 1.31395e23i | −0.0709410 | − | 0.211920i | ||||
\(943\) | − | 1.32380e22i | − | 0.0211703i | ||||||
\(944\) | 2.45675e23 | − | 8.58622e23i | 0.389570 | − | 1.36153i | ||||
\(945\) | −9.98012e23 | −1.56921 | ||||||||
\(946\) | −8.40361e22 | + | 2.81314e22i | −0.131020 | + | 0.0438594i | ||||
\(947\) | −2.38672e23 | −0.368979 | −0.184489 | − | 0.982835i | \(-0.559063\pi\) | ||||
−0.184489 | + | 0.982835i | \(0.559063\pi\) | |||||||
\(948\) | −6.01792e23 | − | 7.98131e23i | −0.922529 | − | 1.22351i | ||||
\(949\) | − | 4.33909e23i | − | 0.659582i | ||||||
\(950\) | 8.10952e22 | − | 2.71469e22i | 0.122238 | − | 0.0409197i | ||||
\(951\) | 8.71539e22i | 0.130270i | ||||||||
\(952\) | 1.53062e24 | + | 1.05100e24i | 2.26867 | + | 1.55778i | ||||
\(953\) | 8.09862e23 | 1.19033 | 0.595166 | − | 0.803603i | \(-0.297086\pi\) | ||||
0.595166 | + | 0.803603i | \(0.297086\pi\) | |||||||
\(954\) | 1.11781e22 | + | 3.33918e22i | 0.0162922 | + | 0.0486691i | ||||
\(955\) | 8.55184e23 | 1.23604 | ||||||||
\(956\) | −4.62504e23 | − | 6.13398e23i | −0.662906 | − | 0.879183i | ||||
\(957\) | − | 3.24397e23i | − | 0.461085i | ||||||
\(958\) | 2.36387e23 | + | 7.06151e23i | 0.333196 | + | 0.995344i | ||||
\(959\) | 1.49947e24i | 2.09599i | ||||||||
\(960\) | −1.12267e24 | + | 4.32059e23i | −1.55627 | + | 0.598925i | ||||
\(961\) | −2.00877e23 | −0.276148 | ||||||||
\(962\) | −4.90432e23 | + | 1.64174e23i | −0.668618 | + | 0.223823i | ||||
\(963\) | −1.81174e23 | −0.244955 | ||||||||
\(964\) | −4.70501e23 | + | 3.54758e23i | −0.630876 | + | 0.475682i | ||||
\(965\) | 4.22593e22i | 0.0561958i | ||||||||
\(966\) | −1.16789e24 | + | 3.90957e23i | −1.54023 | + | 0.515600i | ||||
\(967\) | 1.42829e24i | 1.86812i | 0.357120 | + | 0.934059i | \(0.383759\pi\) | ||||
−0.357120 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(968\) | 2.19771e23 | − | 3.20062e23i | 0.285080 | − | 0.415176i | ||||
\(969\) | 2.09651e23 | 0.269716 | ||||||||
\(970\) | −4.77501e23 | − | 1.42642e24i | −0.609257 | − | 1.82001i | ||||
\(971\) | 1.39310e24 | 1.76290 | 0.881451 | − | 0.472276i | \(-0.156568\pi\) | ||||
0.881451 | + | 0.472276i | \(0.156568\pi\) | |||||||
\(972\) | 4.44507e23 | − | 3.35159e23i | 0.557890 | − | 0.420650i | ||||
\(973\) | − | 5.34187e23i | − | 0.664952i | ||||||
\(974\) | −3.20498e23 | − | 9.57412e23i | −0.395688 | − | 1.18203i | ||||
\(975\) | 4.42250e23i | 0.541541i | ||||||||
\(976\) | 3.43048e22 | + | 9.81552e21i | 0.0416635 | + | 0.0119211i | ||||
\(977\) | −1.28434e24 | −1.54712 | −0.773561 | − | 0.633722i | \(-0.781526\pi\) | ||||
−0.773561 | + | 0.633722i | \(0.781526\pi\) | |||||||
\(978\) | 4.36467e23 | − | 1.46109e23i | 0.521483 | − | 0.174569i | ||||
\(979\) | −3.53970e23 | −0.419473 | ||||||||
\(980\) | −8.78471e23 | − | 1.16508e24i | −1.03257 | − | 1.36945i | ||||
\(981\) | − | 3.68807e23i | − | 0.429979i | ||||||
\(982\) | 1.58930e24 | − | 5.32025e23i | 1.83787 | − | 0.615234i | ||||
\(983\) | − | 6.92489e23i | − | 0.794300i | −0.917754 | − | 0.397150i | \(-0.869999\pi\) | ||
0.917754 | − | 0.397150i | \(-0.130001\pi\) | |||||||
\(984\) | −1.31434e22 | + | 1.91414e22i | −0.0149537 | + | 0.0217777i | ||||
\(985\) | 5.42619e23 | 0.612358 | ||||||||
\(986\) | 2.94504e23 | + | 8.79761e23i | 0.329667 | + | 0.984803i | ||||
\(987\) | 7.38394e23 | 0.819881 | ||||||||
\(988\) | 3.04284e22 | + | 4.03559e22i | 0.0335138 | + | 0.0444479i | ||||
\(989\) | 1.68114e23i | 0.183669i | ||||||||
\(990\) | −1.07726e23 | − | 3.21807e23i | −0.116745 | − | 0.348749i | ||||
\(991\) | − | 1.54253e24i | − | 1.65823i | −0.559075 | − | 0.829117i | \(-0.688844\pi\) | ||
0.559075 | − | 0.829117i | \(-0.311156\pi\) | |||||||
\(992\) | 1.05832e24 | − | 4.69645e22i | 1.12856 | − | 0.0500814i | ||||
\(993\) | −3.33051e22 | −0.0352303 | ||||||||
\(994\) | −1.25229e24 | + | 4.19211e23i | −1.31406 | + | 0.439887i | ||||
\(995\) | −4.94405e23 | −0.514633 | ||||||||
\(996\) | −6.62080e23 | + | 4.99210e23i | −0.683653 | + | 0.515476i | ||||
\(997\) | 1.85521e24i | 1.90034i | 0.311726 | + | 0.950172i | \(0.399093\pi\) | ||||
−0.311726 | + | 0.950172i | \(0.600907\pi\) | |||||||
\(998\) | −1.41908e24 | + | 4.75044e23i | −1.44199 | + | 0.482714i | ||||
\(999\) | − | 1.15887e24i | − | 1.16818i |
(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 | 8.17.d.b.3.2 | yes | 14 | |
3.2 | odd | 2 | 72.17.b.b.19.13 | 14 | |||
4.3 | odd | 2 | 32.17.d.b.15.12 | 14 | |||
8.3 | odd | 2 | inner | 8.17.d.b.3.1 | ✓ | 14 | |
8.5 | even | 2 | 32.17.d.b.15.11 | 14 | |||
24.11 | even | 2 | 72.17.b.b.19.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.17.d.b.3.1 | ✓ | 14 | 8.3 | odd | 2 | inner | |
8.17.d.b.3.2 | yes | 14 | 1.1 | even | 1 | trivial | |
32.17.d.b.15.11 | 14 | 8.5 | even | 2 | |||
32.17.d.b.15.12 | 14 | 4.3 | odd | 2 | |||
72.17.b.b.19.13 | 14 | 3.2 | odd | 2 | |||
72.17.b.b.19.14 | 14 | 24.11 | even | 2 |