Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,35,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 35, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 35);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 35 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.6128270213\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.11 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.35.c.a.3.11 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 67956.3 | + | 67956.3i | 0.518465 | + | 0.518465i | 0.917107 | − | 0.398642i | \(-0.130518\pi\) |
−0.398642 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(3\) | −7.73822e7 | + | 7.73822e7i | −0.599211 | + | 0.599211i | −0.940103 | − | 0.340892i | \(-0.889271\pi\) |
0.340892 | + | 0.940103i | \(0.389271\pi\) | |||||||
\(4\) | − | 7.94376e9i | − | 0.462388i | ||||||
\(5\) | −6.92309e11 | + | 3.20600e11i | −0.907423 | + | 0.420217i | ||||
\(6\) | −1.05172e13 | −0.621340 | ||||||||
\(7\) | −2.59708e14 | − | 2.59708e14i | −1.11640 | − | 1.11640i | −0.992266 | − | 0.124130i | \(-0.960386\pi\) |
−0.124130 | − | 0.992266i | \(-0.539614\pi\) | |||||||
\(8\) | 1.70731e15 | − | 1.70731e15i | 0.758197 | − | 0.758197i | ||||
\(9\) | 4.70118e15i | 0.281893i | ||||||||
\(10\) | −6.88336e16 | − | 2.52599e16i | −0.688336 | − | 0.252599i | ||||
\(11\) | −8.17717e16 | −0.161781 | −0.0808904 | − | 0.996723i | \(-0.525776\pi\) | ||||
−0.0808904 | + | 0.996723i | \(0.525776\pi\) | |||||||
\(12\) | 6.14706e17 | + | 6.14706e17i | 0.277068 | + | 0.277068i | ||||
\(13\) | 1.39558e18 | − | 1.39558e18i | 0.161331 | − | 0.161331i | −0.621825 | − | 0.783156i | \(-0.713609\pi\) |
0.783156 | + | 0.621825i | \(0.213609\pi\) | |||||||
\(14\) | − | 3.52975e19i | − | 1.15762i | ||||||
\(15\) | 2.87636e19 | − | 7.83812e19i | 0.291939 | − | 0.795537i | ||||
\(16\) | 9.55718e19 | 0.323810 | ||||||||
\(17\) | 3.22164e20 | + | 3.22164e20i | 0.389444 | + | 0.389444i | 0.874489 | − | 0.485045i | \(-0.161197\pi\) |
−0.485045 | + | 0.874489i | \(0.661197\pi\) | |||||||
\(18\) | −3.19474e20 | + | 3.19474e20i | −0.146152 | + | 0.146152i | ||||
\(19\) | 2.60332e21i | 0.475025i | 0.971385 | + | 0.237512i | \(0.0763320\pi\) | ||||
−0.971385 | + | 0.237512i | \(0.923668\pi\) | |||||||
\(20\) | 2.54677e21 | + | 5.49954e21i | 0.194303 | + | 0.419582i | ||||
\(21\) | 4.01935e22 | 1.33791 | ||||||||
\(22\) | −5.55690e21 | − | 5.55690e21i | −0.0838777 | − | 0.0838777i | ||||
\(23\) | 5.14001e22 | − | 5.14001e22i | 0.364410 | − | 0.364410i | −0.501023 | − | 0.865434i | \(-0.667043\pi\) |
0.865434 | + | 0.501023i | \(0.167043\pi\) | |||||||
\(24\) | 2.64230e23i | 0.908640i | ||||||||
\(25\) | 3.76507e23 | − | 4.43909e23i | 0.646835 | − | 0.762630i | ||||
\(26\) | 1.89677e23 | 0.167289 | ||||||||
\(27\) | −1.65430e24 | − | 1.65430e24i | −0.768124 | − | 0.768124i | ||||
\(28\) | −2.06306e24 | + | 2.06306e24i | −0.516208 | + | 0.516208i | ||||
\(29\) | 1.01031e25i | 1.39215i | 0.717967 | + | 0.696077i | \(0.245073\pi\) | ||||
−0.717967 | + | 0.696077i | \(0.754927\pi\) | |||||||
\(30\) | 7.28116e24 | − | 3.37182e24i | 0.563818 | − | 0.261098i | ||||
\(31\) | −9.26973e24 | −0.411072 | −0.205536 | − | 0.978650i | \(-0.565894\pi\) | ||||
−0.205536 | + | 0.978650i | \(0.565894\pi\) | |||||||
\(32\) | −2.28366e25 | − | 2.28366e25i | −0.590313 | − | 0.590313i | ||||
\(33\) | 6.32767e24 | − | 6.32767e24i | 0.0969408 | − | 0.0969408i | ||||
\(34\) | 4.37861e25i | 0.403826i | ||||||||
\(35\) | 2.63061e26 | + | 9.65356e25i | 1.48217 | + | 0.543915i | ||||
\(36\) | 3.73450e25 | 0.130344 | ||||||||
\(37\) | 4.80955e26 | + | 4.80955e26i | 1.05360 | + | 1.05360i | 0.998480 | + | 0.0551194i | \(0.0175539\pi\) |
0.0551194 | + | 0.998480i | \(0.482446\pi\) | |||||||
\(38\) | −1.76912e26 | + | 1.76912e26i | −0.246284 | + | 0.246284i | ||||
\(39\) | 2.15986e26i | 0.193342i | ||||||||
\(40\) | −6.34621e26 | + | 1.72935e27i | −0.369398 | + | 1.00661i | ||||
\(41\) | 2.99041e27 | 1.14395 | 0.571973 | − | 0.820273i | \(-0.306178\pi\) | ||||
0.571973 | + | 0.820273i | \(0.306178\pi\) | |||||||
\(42\) | 2.73140e27 | + | 2.73140e27i | 0.693661 | + | 0.693661i | ||||
\(43\) | −3.50684e27 | + | 3.50684e27i | −0.596969 | + | 0.596969i | −0.939505 | − | 0.342536i | \(-0.888714\pi\) |
0.342536 | + | 0.939505i | \(0.388714\pi\) | |||||||
\(44\) | 6.49575e26i | 0.0748055i | ||||||||
\(45\) | −1.50720e27 | − | 3.25467e27i | −0.118456 | − | 0.255796i | ||||
\(46\) | 6.98591e27 | 0.377868 | ||||||||
\(47\) | 3.01254e28 | + | 3.01254e28i | 1.13050 | + | 1.13050i | 0.990094 | + | 0.140403i | \(0.0448399\pi\) |
0.140403 | + | 0.990094i | \(0.455160\pi\) | |||||||
\(48\) | −7.39555e27 | + | 7.39555e27i | −0.194030 | + | 0.194030i | ||||
\(49\) | 8.07793e28i | 1.49268i | ||||||||
\(50\) | 5.57524e28 | − | 4.58039e27i | 0.730758 | − | 0.0600361i | ||||
\(51\) | −4.98594e28 | −0.466718 | ||||||||
\(52\) | −1.10861e28 | − | 1.10861e28i | −0.0745974 | − | 0.0745974i | ||||
\(53\) | 1.96696e29 | − | 1.96696e29i | 0.957426 | − | 0.957426i | −0.0417044 | − | 0.999130i | \(-0.513279\pi\) |
0.999130 | + | 0.0417044i | \(0.0132788\pi\) | |||||||
\(54\) | − | 2.24841e29i | − | 0.796491i | ||||||
\(55\) | 5.66113e28 | − | 2.62160e28i | 0.146804 | − | 0.0679832i | ||||
\(56\) | −8.86802e29 | −1.69290 | ||||||||
\(57\) | −2.01451e29 | − | 2.01451e29i | −0.284640 | − | 0.284640i | ||||
\(58\) | −6.86567e29 | + | 6.86567e29i | −0.721784 | + | 0.721784i | ||||
\(59\) | − | 1.74853e30i | − | 1.37464i | −0.726354 | − | 0.687321i | \(-0.758786\pi\) | ||
0.726354 | − | 0.687321i | \(-0.241214\pi\) | |||||||
\(60\) | −6.22641e29 | − | 2.28491e29i | −0.367846 | − | 0.134989i | ||||
\(61\) | 2.76233e29 | 0.123216 | 0.0616081 | − | 0.998100i | \(-0.480377\pi\) | ||||
0.0616081 | + | 0.998100i | \(0.480377\pi\) | |||||||
\(62\) | −6.29936e29 | − | 6.29936e29i | −0.213127 | − | 0.213127i | ||||
\(63\) | 1.22093e30 | − | 1.22093e30i | 0.314704 | − | 0.314704i | ||||
\(64\) | − | 4.74569e30i | − | 0.935923i | ||||||
\(65\) | −5.18749e29 | + | 1.41360e30i | −0.0786013 | + | 0.214189i | ||||
\(66\) | 8.60010e29 | 0.100521 | ||||||||
\(67\) | 6.56107e30 | + | 6.56107e30i | 0.593886 | + | 0.593886i | 0.938679 | − | 0.344793i | \(-0.112051\pi\) |
−0.344793 | + | 0.938679i | \(0.612051\pi\) | |||||||
\(68\) | 2.55919e30 | − | 2.55919e30i | 0.180074 | − | 0.180074i | ||||
\(69\) | 7.95490e30i | 0.436717i | ||||||||
\(70\) | 1.13164e31 | + | 2.44368e31i | 0.486454 | + | 1.05046i | ||||
\(71\) | −4.26783e31 | −1.44150 | −0.720751 | − | 0.693194i | \(-0.756203\pi\) | ||||
−0.720751 | + | 0.693194i | \(0.756203\pi\) | |||||||
\(72\) | 8.02636e30 | + | 8.02636e30i | 0.213730 | + | 0.213730i | ||||
\(73\) | 4.46612e31 | − | 4.46612e31i | 0.940680 | − | 0.940680i | −0.0576567 | − | 0.998336i | \(-0.518363\pi\) |
0.998336 | + | 0.0576567i | \(0.0183629\pi\) | |||||||
\(74\) | 6.53678e31i | 1.09251i | ||||||||
\(75\) | 5.21572e30 | + | 6.34856e31i | 0.0693861 | + | 0.844567i | ||||
\(76\) | 2.06802e31 | 0.219646 | ||||||||
\(77\) | 2.12367e31 | + | 2.12367e31i | 0.180612 | + | 0.180612i | ||||
\(78\) | −1.46776e31 | + | 1.46776e31i | −0.100241 | + | 0.100241i | ||||
\(79\) | − | 2.33726e32i | − | 1.28542i | −0.766108 | − | 0.642712i | \(-0.777809\pi\) | ||
0.766108 | − | 0.642712i | \(-0.222191\pi\) | |||||||
\(80\) | −6.61652e31 | + | 3.06404e31i | −0.293833 | + | 0.136071i | ||||
\(81\) | 1.77625e32 | 0.638644 | ||||||||
\(82\) | 2.03217e32 | + | 2.03217e32i | 0.593096 | + | 0.593096i | ||||
\(83\) | −1.29241e32 | + | 1.29241e32i | −0.306953 | + | 0.306953i | −0.843727 | − | 0.536773i | \(-0.819643\pi\) |
0.536773 | + | 0.843727i | \(0.319643\pi\) | |||||||
\(84\) | − | 3.19288e32i | − | 0.618635i | ||||||
\(85\) | −3.26323e32 | − | 1.19751e32i | −0.517041 | − | 0.189739i | ||||
\(86\) | −4.76623e32 | −0.619015 | ||||||||
\(87\) | −7.81798e32 | − | 7.81798e32i | −0.834194 | − | 0.834194i | ||||
\(88\) | −1.39609e32 | + | 1.39609e32i | −0.122662 | + | 0.122662i | ||||
\(89\) | − | 1.79750e33i | − | 1.30328i | −0.758527 | − | 0.651641i | \(-0.774081\pi\) | ||
0.758527 | − | 0.651641i | \(-0.225919\pi\) | |||||||
\(90\) | 1.18751e32 | − | 3.23599e32i | 0.0712059 | − | 0.194037i | ||||
\(91\) | −7.24885e32 | −0.360218 | ||||||||
\(92\) | −4.08310e32 | − | 4.08310e32i | −0.168499 | − | 0.168499i | ||||
\(93\) | 7.17312e32 | − | 7.17312e32i | 0.246319 | − | 0.246319i | ||||
\(94\) | 4.09442e33i | 1.17225i | ||||||||
\(95\) | −8.34626e32 | − | 1.80230e33i | −0.199614 | − | 0.431049i | ||||
\(96\) | 3.53430e33 | 0.707444 | ||||||||
\(97\) | 8.38959e33 | + | 8.38959e33i | 1.40806 | + | 1.40806i | 0.769924 | + | 0.638136i | \(0.220294\pi\) |
0.638136 | + | 0.769924i | \(0.279706\pi\) | |||||||
\(98\) | −5.48946e33 | + | 5.48946e33i | −0.773903 | + | 0.773903i | ||||
\(99\) | − | 3.84423e32i | − | 0.0456049i | ||||||
\(100\) | −3.52631e33 | − | 2.99088e33i | −0.352631 | − | 0.299088i | ||||
\(101\) | 2.15841e34 | 1.82252 | 0.911258 | − | 0.411837i | \(-0.135113\pi\) | ||||
0.911258 | + | 0.411837i | \(0.135113\pi\) | |||||||
\(102\) | −3.38826e33 | − | 3.38826e33i | −0.241977 | − | 0.241977i | ||||
\(103\) | −6.33700e33 | + | 6.33700e33i | −0.383399 | + | 0.383399i | −0.872325 | − | 0.488926i | \(-0.837389\pi\) |
0.488926 | + | 0.872325i | \(0.337389\pi\) | |||||||
\(104\) | − | 4.76537e33i | − | 0.244641i | ||||||
\(105\) | −2.78263e34 | + | 1.28861e34i | −1.21405 | + | 0.562214i | ||||
\(106\) | 2.67334e34 | 0.992784 | ||||||||
\(107\) | 1.25797e34 | + | 1.25797e34i | 0.398243 | + | 0.398243i | 0.877613 | − | 0.479370i | \(-0.159135\pi\) |
−0.479370 | + | 0.877613i | \(0.659135\pi\) | |||||||
\(108\) | −1.31414e34 | + | 1.31414e34i | −0.355171 | + | 0.355171i | ||||
\(109\) | − | 4.98129e34i | − | 1.15104i | −0.817787 | − | 0.575521i | \(-0.804799\pi\) | ||
0.817787 | − | 0.575521i | \(-0.195201\pi\) | |||||||
\(110\) | 5.62863e33 | + | 2.06555e33i | 0.111360 | + | 0.0408657i | ||||
\(111\) | −7.44347e34 | −1.26266 | ||||||||
\(112\) | −2.48207e34 | − | 2.48207e34i | −0.361500 | − | 0.361500i | ||||
\(113\) | 2.32442e34 | − | 2.32442e34i | 0.291059 | − | 0.291059i | −0.546440 | − | 0.837498i | \(-0.684017\pi\) |
0.837498 | + | 0.546440i | \(0.184017\pi\) | |||||||
\(114\) | − | 2.73797e34i | − | 0.295152i | ||||||
\(115\) | −1.91059e34 | + | 5.20636e34i | −0.177543 | + | 0.483806i | ||||
\(116\) | 8.02564e34 | 0.643715 | ||||||||
\(117\) | 6.56086e33 | + | 6.56086e33i | 0.0454780 | + | 0.0454780i | ||||
\(118\) | 1.18824e35 | − | 1.18824e35i | 0.712704 | − | 0.712704i | ||||
\(119\) | − | 1.67337e35i | − | 0.869547i | ||||||
\(120\) | −8.47124e34 | − | 1.82929e35i | −0.381826 | − | 0.824521i | ||||
\(121\) | −2.48790e35 | −0.973827 | ||||||||
\(122\) | 1.87717e34 | + | 1.87717e34i | 0.0638833 | + | 0.0638833i | ||||
\(123\) | −2.31405e35 | + | 2.31405e35i | −0.685465 | + | 0.685465i | ||||
\(124\) | 7.36365e34i | 0.190075i | ||||||||
\(125\) | −1.18342e35 | + | 4.28031e35i | −0.266482 | + | 0.963840i | ||||
\(126\) | 1.65940e35 | 0.326326 | ||||||||
\(127\) | 7.98848e35 | + | 7.98848e35i | 1.37341 | + | 1.37341i | 0.855332 | + | 0.518080i | \(0.173353\pi\) |
0.518080 | + | 0.855332i | \(0.326647\pi\) | |||||||
\(128\) | −6.98307e34 | + | 6.98307e34i | −0.105070 | + | 0.105070i | ||||
\(129\) | − | 5.42733e35i | − | 0.715421i | ||||||
\(130\) | −1.31315e35 | + | 6.08104e34i | −0.151802 | + | 0.0702977i | ||||
\(131\) | 2.04340e34 | 0.0207368 | 0.0103684 | − | 0.999946i | \(-0.496700\pi\) | ||||
0.0103684 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(132\) | −5.02655e34 | − | 5.02655e34i | −0.0448243 | − | 0.0448243i | ||||
\(133\) | 6.76102e35 | − | 6.76102e35i | 0.530316 | − | 0.530316i | ||||
\(134\) | 8.91732e35i | 0.615818i | ||||||||
\(135\) | 1.67566e36 | + | 6.14919e35i | 1.01979 | + | 0.374235i | ||||
\(136\) | 1.10006e36 | 0.590550 | ||||||||
\(137\) | −9.31467e35 | − | 9.31467e35i | −0.441487 | − | 0.441487i | 0.451025 | − | 0.892512i | \(-0.351059\pi\) |
−0.892512 | + | 0.451025i | \(0.851059\pi\) | |||||||
\(138\) | −5.40585e35 | + | 5.40585e35i | −0.226423 | + | 0.226423i | ||||
\(139\) | 3.44082e36i | 1.27471i | 0.770572 | + | 0.637353i | \(0.219971\pi\) | ||||
−0.770572 | + | 0.637353i | \(0.780029\pi\) | |||||||
\(140\) | 7.66856e35 | − | 2.08969e36i | 0.251500 | − | 0.685339i | ||||
\(141\) | −4.66234e36 | −1.35481 | ||||||||
\(142\) | −2.90026e36 | − | 2.90026e36i | −0.747369 | − | 0.747369i | ||||
\(143\) | −1.14119e35 | + | 1.14119e35i | −0.0261002 | + | 0.0261002i | ||||
\(144\) | 4.49300e35i | 0.0912796i | ||||||||
\(145\) | −3.23905e36 | − | 6.99445e36i | −0.585008 | − | 1.26327i | ||||
\(146\) | 6.07002e36 | 0.975419 | ||||||||
\(147\) | −6.25088e36 | − | 6.25088e36i | −0.894430 | − | 0.894430i | ||||
\(148\) | 3.82059e36 | − | 3.82059e36i | 0.487171 | − | 0.487171i | ||||
\(149\) | 9.17060e35i | 0.104287i | 0.998640 | + | 0.0521436i | \(0.0166054\pi\) | ||||
−0.998640 | + | 0.0521436i | \(0.983395\pi\) | |||||||
\(150\) | −3.95981e36 | + | 4.66869e36i | −0.401904 | + | 0.473853i | ||||
\(151\) | −4.13188e36 | −0.374576 | −0.187288 | − | 0.982305i | \(-0.559970\pi\) | ||||
−0.187288 | + | 0.982305i | \(0.559970\pi\) | |||||||
\(152\) | 4.44467e36 | + | 4.44467e36i | 0.360162 | + | 0.360162i | ||||
\(153\) | −1.51455e36 | + | 1.51455e36i | −0.109781 | + | 0.109781i | ||||
\(154\) | 2.88634e36i | 0.187282i | ||||||||
\(155\) | 6.41752e36 | − | 2.97188e36i | 0.373017 | − | 0.172740i | ||||
\(156\) | 1.71574e36 | 0.0893991 | ||||||||
\(157\) | 1.51944e37 | + | 1.51944e37i | 0.710214 | + | 0.710214i | 0.966580 | − | 0.256366i | \(-0.0825253\pi\) |
−0.256366 | + | 0.966580i | \(0.582525\pi\) | |||||||
\(158\) | 1.58831e37 | − | 1.58831e37i | 0.666447 | − | 0.666447i | ||||
\(159\) | 3.04415e37i | 1.14740i | ||||||||
\(160\) | 2.31314e37 | + | 8.48857e36i | 0.783724 | + | 0.287604i | ||||
\(161\) | −2.66980e37 | −0.813652 | ||||||||
\(162\) | 1.20707e37 | + | 1.20707e37i | 0.331114 | + | 0.331114i | ||||
\(163\) | −3.02315e37 | + | 3.02315e37i | −0.746914 | + | 0.746914i | −0.973898 | − | 0.226984i | \(-0.927113\pi\) |
0.226984 | + | 0.973898i | \(0.427113\pi\) | |||||||
\(164\) | − | 2.37551e37i | − | 0.528946i | ||||||
\(165\) | −2.35205e36 | + | 6.40936e36i | −0.0472302 | + | 0.128703i | ||||
\(166\) | −1.75654e37 | −0.318289 | ||||||||
\(167\) | −2.14424e37 | − | 2.14424e37i | −0.350828 | − | 0.350828i | 0.509590 | − | 0.860418i | \(-0.329797\pi\) |
−0.860418 | + | 0.509590i | \(0.829797\pi\) | |||||||
\(168\) | 6.86227e37 | − | 6.86227e37i | 1.01440 | − | 1.01440i | ||||
\(169\) | 7.09344e37i | 0.947945i | ||||||||
\(170\) | −1.40378e37 | − | 3.03135e37i | −0.169695 | − | 0.366441i | ||||
\(171\) | −1.22387e37 | −0.133906 | ||||||||
\(172\) | 2.78575e37 | + | 2.78575e37i | 0.276031 | + | 0.276031i | ||||
\(173\) | −1.65984e34 | + | 1.65984e34i | −0.000149033 | + | 0.000149033i | −0.707181 | − | 0.707032i | \(-0.750034\pi\) |
0.707032 | + | 0.707181i | \(0.250034\pi\) | |||||||
\(174\) | − | 1.06256e38i | − | 0.865001i | ||||||
\(175\) | −2.13069e38 | + | 1.75048e37i | −1.57352 | + | 0.129274i | ||||
\(176\) | −7.81506e36 | −0.0523862 | ||||||||
\(177\) | 1.35305e38 | + | 1.35305e38i | 0.823701 | + | 0.823701i | ||||
\(178\) | 1.22151e38 | − | 1.22151e38i | 0.675707 | − | 0.675707i | ||||
\(179\) | − | 1.55792e38i | − | 0.783508i | −0.920070 | − | 0.391754i | \(-0.871868\pi\) | ||
0.920070 | − | 0.391754i | \(-0.128132\pi\) | |||||||
\(180\) | −2.58543e37 | + | 1.19728e37i | −0.118277 | + | 0.0547727i | ||||
\(181\) | −5.58045e37 | −0.232345 | −0.116172 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116172 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(182\) | −4.92605e37 | − | 4.92605e37i | −0.186761 | − | 0.186761i | ||||
\(183\) | −2.13755e37 | + | 2.13755e37i | −0.0738325 | + | 0.0738325i | ||||
\(184\) | − | 1.75512e38i | − | 0.552589i | ||||||
\(185\) | −4.87164e38 | − | 1.78775e38i | −1.39880 | − | 0.513320i | ||||
\(186\) | 9.74916e37 | 0.255416 | ||||||||
\(187\) | −2.63438e37 | − | 2.63438e37i | −0.0630046 | − | 0.0630046i | ||||
\(188\) | 2.39309e38 | − | 2.39309e38i | 0.522728 | − | 0.522728i | ||||
\(189\) | 8.59271e38i | 1.71506i | ||||||||
\(190\) | 6.57597e37 | − | 1.79196e38i | 0.119991 | − | 0.326976i | ||||
\(191\) | 1.97226e38 | 0.329152 | 0.164576 | − | 0.986364i | \(-0.447374\pi\) | ||||
0.164576 | + | 0.986364i | \(0.447374\pi\) | |||||||
\(192\) | 3.67232e38 | + | 3.67232e38i | 0.560815 | + | 0.560815i | ||||
\(193\) | −3.25332e38 | + | 3.25332e38i | −0.454834 | + | 0.454834i | −0.896955 | − | 0.442121i | \(-0.854226\pi\) |
0.442121 | + | 0.896955i | \(0.354226\pi\) | |||||||
\(194\) | 1.14025e39i | 1.46006i | ||||||||
\(195\) | −6.92452e37 | − | 1.49529e38i | −0.0812458 | − | 0.175443i | ||||
\(196\) | 6.41692e38 | 0.690197 | ||||||||
\(197\) | 3.17547e38 | + | 3.17547e38i | 0.313243 | + | 0.313243i | 0.846165 | − | 0.532921i | \(-0.178906\pi\) |
−0.532921 | + | 0.846165i | \(0.678906\pi\) | |||||||
\(198\) | 2.61240e37 | − | 2.61240e37i | 0.0236445 | − | 0.0236445i | ||||
\(199\) | − | 9.44538e36i | − | 0.00784725i | −0.999992 | − | 0.00392362i | \(-0.998751\pi\) | ||
0.999992 | − | 0.00392362i | \(-0.00124893\pi\) | |||||||
\(200\) | −1.15076e38 | − | 1.40070e39i | −0.0877960 | − | 1.06865i | ||||
\(201\) | −1.01542e39 | −0.711726 | ||||||||
\(202\) | 1.46678e39 | + | 1.46678e39i | 0.944911 | + | 0.944911i | ||||
\(203\) | 2.62385e39 | − | 2.62385e39i | 1.55420 | − | 1.55420i | ||||
\(204\) | 3.96071e38i | 0.215805i | ||||||||
\(205\) | −2.07029e39 | + | 9.58727e38i | −1.03804 | + | 0.480706i | ||||
\(206\) | −8.61278e38 | −0.397558 | ||||||||
\(207\) | 2.41641e38 | + | 2.41641e38i | 0.102725 | + | 0.102725i | ||||
\(208\) | 1.33378e38 | − | 1.33378e38i | 0.0522405 | − | 0.0522405i | ||||
\(209\) | − | 2.12878e38i | − | 0.0768499i | ||||||
\(210\) | −2.76666e39 | − | 1.01529e39i | −0.920933 | − | 0.337956i | ||||
\(211\) | −5.32019e39 | −1.63352 | −0.816762 | − | 0.576975i | \(-0.804233\pi\) | ||||
−0.816762 | + | 0.576975i | \(0.804233\pi\) | |||||||
\(212\) | −1.56250e39 | − | 1.56250e39i | −0.442702 | − | 0.442702i | ||||
\(213\) | 3.30254e39 | − | 3.30254e39i | 0.863764 | − | 0.863764i | ||||
\(214\) | 1.70975e39i | 0.412950i | ||||||||
\(215\) | 1.30352e39 | − | 3.55211e39i | 0.290847 | − | 0.792560i | ||||
\(216\) | −5.64881e39 | −1.16478 | ||||||||
\(217\) | 2.40742e39 | + | 2.40742e39i | 0.458919 | + | 0.458919i | ||||
\(218\) | 3.38510e39 | − | 3.38510e39i | 0.596775 | − | 0.596775i | ||||
\(219\) | 6.91196e39i | 1.12733i | ||||||||
\(220\) | −2.08254e38 | − | 4.49706e38i | −0.0314346 | − | 0.0678803i | ||||
\(221\) | 8.99209e38 | 0.125659 | ||||||||
\(222\) | −5.05831e39 | − | 5.05831e39i | −0.654643 | − | 0.654643i | ||||
\(223\) | 1.12852e40 | − | 1.12852e40i | 1.35309 | − | 1.35309i | 0.470912 | − | 0.882180i | \(-0.343925\pi\) |
0.882180 | − | 0.470912i | \(-0.156075\pi\) | |||||||
\(224\) | 1.18617e40i | 1.31805i | ||||||||
\(225\) | 2.08690e39 | + | 1.77003e39i | 0.214980 | + | 0.182338i | ||||
\(226\) | 3.15917e39 | 0.301807 | ||||||||
\(227\) | 5.35193e39 | + | 5.35193e39i | 0.474319 | + | 0.474319i | 0.903309 | − | 0.428990i | \(-0.141130\pi\) |
−0.428990 | + | 0.903309i | \(0.641130\pi\) | |||||||
\(228\) | −1.60028e39 | + | 1.60028e39i | −0.131614 | + | 0.131614i | ||||
\(229\) | 7.90446e39i | 0.603489i | 0.953389 | + | 0.301744i | \(0.0975689\pi\) | ||||
−0.953389 | + | 0.301744i | \(0.902431\pi\) | |||||||
\(230\) | −4.83641e39 | + | 2.23969e39i | −0.342886 | + | 0.158787i | ||||
\(231\) | −3.28669e39 | −0.216449 | ||||||||
\(232\) | 1.72491e40 | + | 1.72491e40i | 1.05553 | + | 1.05553i | ||||
\(233\) | −3.09113e39 | + | 3.09113e39i | −0.175819 | + | 0.175819i | −0.789531 | − | 0.613711i | \(-0.789676\pi\) |
0.613711 | + | 0.789531i | \(0.289676\pi\) | |||||||
\(234\) | 8.91704e38i | 0.0471575i | ||||||||
\(235\) | −3.05143e40 | − | 1.11979e40i | −1.50089 | − | 0.550785i | ||||
\(236\) | −1.38899e40 | −0.635618 | ||||||||
\(237\) | 1.80862e40 | + | 1.80862e40i | 0.770240 | + | 0.770240i | ||||
\(238\) | 1.13716e40 | − | 1.13716e40i | 0.450830 | − | 0.450830i | ||||
\(239\) | 2.93007e39i | 0.108172i | 0.998536 | + | 0.0540859i | \(0.0172245\pi\) | ||||
−0.998536 | + | 0.0540859i | \(0.982776\pi\) | |||||||
\(240\) | 2.74899e39 | − | 7.49102e39i | 0.0945327 | − | 0.257603i | ||||
\(241\) | 2.60118e40 | 0.833454 | 0.416727 | − | 0.909032i | \(-0.363177\pi\) | ||||
0.416727 | + | 0.909032i | \(0.363177\pi\) | |||||||
\(242\) | −1.69068e40 | − | 1.69068e40i | −0.504895 | − | 0.504895i | ||||
\(243\) | 1.38441e40 | − | 1.38441e40i | 0.385442 | − | 0.385442i | ||||
\(244\) | − | 2.19433e39i | − | 0.0569736i | ||||||
\(245\) | −2.58979e40 | − | 5.59243e40i | −0.627250 | − | 1.35449i | ||||
\(246\) | −3.14508e40 | −0.710779 | ||||||||
\(247\) | 3.63314e39 | + | 3.63314e39i | 0.0766361 | + | 0.0766361i | ||||
\(248\) | −1.58263e40 | + | 1.58263e40i | −0.311674 | + | 0.311674i | ||||
\(249\) | − | 2.00019e40i | − | 0.367859i | ||||||
\(250\) | −3.71295e40 | + | 2.10453e40i | −0.637879 | + | 0.361556i | ||||
\(251\) | 8.73238e40 | 1.40178 | 0.700889 | − | 0.713270i | \(-0.252787\pi\) | ||||
0.700889 | + | 0.713270i | \(0.252787\pi\) | |||||||
\(252\) | −9.69880e39 | − | 9.69880e39i | −0.145515 | − | 0.145515i | ||||
\(253\) | −4.20307e39 | + | 4.20307e39i | −0.0589546 | + | 0.0589546i | ||||
\(254\) | 1.08573e41i | 1.42413i | ||||||||
\(255\) | 3.45181e40 | − | 1.59850e40i | 0.423511 | − | 0.196123i | ||||
\(256\) | −9.10213e40 | −1.04487 | ||||||||
\(257\) | −6.78066e39 | − | 6.78066e39i | −0.0728465 | − | 0.0728465i | 0.669745 | − | 0.742591i | \(-0.266403\pi\) |
−0.742591 | + | 0.669745i | \(0.766403\pi\) | |||||||
\(258\) | 3.68821e40 | − | 3.68821e40i | 0.370921 | − | 0.370921i | ||||
\(259\) | − | 2.49816e41i | − | 2.35247i | ||||||
\(260\) | 1.12293e40 | + | 4.12082e39i | 0.0990386 | + | 0.0363443i | ||||
\(261\) | −4.74963e40 | −0.392438 | ||||||||
\(262\) | 1.38862e39 | + | 1.38862e39i | 0.0107513 | + | 0.0107513i | ||||
\(263\) | −7.96532e40 | + | 7.96532e40i | −0.578037 | + | 0.578037i | −0.934362 | − | 0.356325i | \(-0.884030\pi\) |
0.356325 | + | 0.934362i | \(0.384030\pi\) | |||||||
\(264\) | − | 2.16066e40i | − | 0.147001i | ||||||
\(265\) | −7.31135e40 | + | 1.99235e41i | −0.466463 | + | 1.27112i | ||||
\(266\) | 9.18908e40 | 0.549900 | ||||||||
\(267\) | 1.39094e41 | + | 1.39094e41i | 0.780941 | + | 0.780941i | ||||
\(268\) | 5.21196e40 | − | 5.21196e40i | 0.274606 | − | 0.274606i | ||||
\(269\) | 1.79805e41i | 0.889228i | 0.895722 | + | 0.444614i | \(0.146659\pi\) | ||||
−0.895722 | + | 0.444614i | \(0.853341\pi\) | |||||||
\(270\) | 7.20840e40 | + | 1.55659e41i | 0.334699 | + | 0.722755i | ||||
\(271\) | 1.01536e41 | 0.442733 | 0.221366 | − | 0.975191i | \(-0.428948\pi\) | ||||
0.221366 | + | 0.975191i | \(0.428948\pi\) | |||||||
\(272\) | 3.07897e40 | + | 3.07897e40i | 0.126106 | + | 0.126106i | ||||
\(273\) | 5.60932e40 | − | 5.60932e40i | 0.215847 | − | 0.215847i | ||||
\(274\) | − | 1.26598e41i | − | 0.457791i | ||||||
\(275\) | −3.07876e40 | + | 3.62992e40i | −0.104645 | + | 0.123379i | ||||
\(276\) | 6.31918e40 | 0.201933 | ||||||||
\(277\) | −4.75876e40 | − | 4.75876e40i | −0.143001 | − | 0.143001i | 0.631982 | − | 0.774983i | \(-0.282242\pi\) |
−0.774983 | + | 0.631982i | \(0.782242\pi\) | |||||||
\(278\) | −2.33825e41 | + | 2.33825e41i | −0.660891 | + | 0.660891i | ||||
\(279\) | − | 4.35786e40i | − | 0.115878i | ||||||
\(280\) | 6.13941e41 | − | 2.84309e41i | 1.53617 | − | 0.711385i | ||||
\(281\) | −1.19477e41 | −0.281370 | −0.140685 | − | 0.990054i | \(-0.544930\pi\) | ||||
−0.140685 | + | 0.990054i | \(0.544930\pi\) | |||||||
\(282\) | −3.16835e41 | − | 3.16835e41i | −0.702423 | − | 0.702423i | ||||
\(283\) | −1.19388e41 | + | 1.19388e41i | −0.249225 | + | 0.249225i | −0.820652 | − | 0.571428i | \(-0.806390\pi\) |
0.571428 | + | 0.820652i | \(0.306390\pi\) | |||||||
\(284\) | 3.39026e41i | 0.666533i | ||||||||
\(285\) | 2.04051e41 | + | 7.48809e40i | 0.377900 | + | 0.138678i | ||||
\(286\) | −1.55102e40 | −0.0270641 | ||||||||
\(287\) | −7.76633e41 | − | 7.76633e41i | −1.27710 | − | 1.27710i | ||||
\(288\) | 1.07359e41 | − | 1.07359e41i | 0.166405 | − | 0.166405i | ||||
\(289\) | − | 4.76748e41i | − | 0.696667i | ||||||
\(290\) | 2.55203e41 | − | 6.95430e41i | 0.351657 | − | 0.958269i | ||||
\(291\) | −1.29841e42 | −1.68745 | ||||||||
\(292\) | −3.54778e41 | − | 3.54778e41i | −0.434959 | − | 0.434959i | ||||
\(293\) | −9.44709e41 | + | 9.44709e41i | −1.09282 | + | 1.09282i | −0.0975934 | + | 0.995226i | \(0.531114\pi\) |
−0.995226 | + | 0.0975934i | \(0.968886\pi\) | |||||||
\(294\) | − | 8.49573e41i | − | 0.927462i | ||||||
\(295\) | 5.60581e41 | + | 1.21053e42i | 0.577649 | + | 1.24738i | ||||
\(296\) | 1.64228e42 | 1.59767 | ||||||||
\(297\) | 1.35275e41 | + | 1.35275e41i | 0.124268 | + | 0.124268i | ||||
\(298\) | −6.23200e40 | + | 6.23200e40i | −0.0540693 | + | 0.0540693i | ||||
\(299\) | − | 1.43466e41i | − | 0.117581i | ||||||
\(300\) | 5.04315e41 | − | 4.14324e40i | 0.390517 | − | 0.0320833i | ||||
\(301\) | 1.82151e42 | 1.33291 | ||||||||
\(302\) | −2.80787e41 | − | 2.80787e41i | −0.194205 | − | 0.194205i | ||||
\(303\) | −1.67023e42 | + | 1.67023e42i | −1.09207 | + | 1.09207i | ||||
\(304\) | 2.48804e41i | 0.153818i | ||||||||
\(305\) | −1.91238e41 | + | 8.85603e40i | −0.111809 | + | 0.0517776i | ||||
\(306\) | −2.05846e41 | −0.113836 | ||||||||
\(307\) | 6.13445e41 | + | 6.13445e41i | 0.320939 | + | 0.320939i | 0.849127 | − | 0.528188i | \(-0.177128\pi\) |
−0.528188 | + | 0.849127i | \(0.677128\pi\) | |||||||
\(308\) | 1.68700e41 | − | 1.68700e41i | 0.0835126 | − | 0.0835126i | ||||
\(309\) | − | 9.80742e41i | − | 0.459474i | ||||||
\(310\) | 6.38068e41 | + | 2.34153e41i | 0.282956 | + | 0.103837i | ||||
\(311\) | 2.97928e42 | 1.25079 | 0.625395 | − | 0.780308i | \(-0.284938\pi\) | ||||
0.625395 | + | 0.780308i | \(0.284938\pi\) | |||||||
\(312\) | 3.68754e41 | + | 3.68754e41i | 0.146592 | + | 0.146592i | ||||
\(313\) | 8.83692e41 | − | 8.83692e41i | 0.332696 | − | 0.332696i | −0.520914 | − | 0.853609i | \(-0.674409\pi\) |
0.853609 | + | 0.520914i | \(0.174409\pi\) | |||||||
\(314\) | 2.06511e42i | 0.736442i | ||||||||
\(315\) | −4.53831e41 | + | 1.23669e42i | −0.153326 | + | 0.417814i | ||||
\(316\) | −1.85666e42 | −0.594364 | ||||||||
\(317\) | −1.41949e42 | − | 1.41949e42i | −0.430652 | − | 0.430652i | 0.458198 | − | 0.888850i | \(-0.348495\pi\) |
−0.888850 | + | 0.458198i | \(0.848495\pi\) | |||||||
\(318\) | −2.06869e42 | + | 2.06869e42i | −0.594887 | + | 0.594887i | ||||
\(319\) | − | 8.26145e41i | − | 0.225224i | ||||||
\(320\) | 1.52147e42 | + | 3.28549e42i | 0.393291 | + | 0.849279i | ||||
\(321\) | −1.94690e42 | −0.477263 | ||||||||
\(322\) | −1.81430e42 | − | 1.81430e42i | −0.421850 | − | 0.421850i | ||||
\(323\) | −8.38695e41 | + | 8.38695e41i | −0.184995 | + | 0.184995i | ||||
\(324\) | − | 1.41101e42i | − | 0.295301i | ||||||
\(325\) | −9.40648e40 | − | 1.14496e42i | −0.0186814 | − | 0.227390i | ||||
\(326\) | −4.10884e42 | −0.774498 | ||||||||
\(327\) | 3.85463e42 | + | 3.85463e42i | 0.689717 | + | 0.689717i | ||||
\(328\) | 5.10555e42 | − | 5.10555e42i | 0.867336 | − | 0.867336i | ||||
\(329\) | − | 1.56476e43i | − | 2.52417i | ||||||
\(330\) | −5.95392e41 | + | 2.75719e41i | −0.0912150 | + | 0.0422406i | ||||
\(331\) | 1.64418e42 | 0.239262 | 0.119631 | − | 0.992818i | \(-0.461829\pi\) | ||||
0.119631 | + | 0.992818i | \(0.461829\pi\) | |||||||
\(332\) | 1.02666e42 | + | 1.02666e42i | 0.141931 | + | 0.141931i | ||||
\(333\) | −2.26106e42 | + | 2.26106e42i | −0.297002 | + | 0.297002i | ||||
\(334\) | − | 2.91430e42i | − | 0.363784i | ||||||
\(335\) | −6.64577e42 | − | 2.43881e42i | −0.788467 | − | 0.289345i | ||||
\(336\) | 3.84136e42 | 0.433229 | ||||||||
\(337\) | 5.88430e41 | + | 5.88430e41i | 0.0630938 | + | 0.0630938i | 0.737950 | − | 0.674856i | \(-0.235794\pi\) |
−0.674856 | + | 0.737950i | \(0.735794\pi\) | |||||||
\(338\) | −4.82044e42 | + | 4.82044e42i | −0.491476 | + | 0.491476i | ||||
\(339\) | 3.59737e42i | 0.348811i | ||||||||
\(340\) | −9.51273e41 | + | 2.59223e42i | −0.0877331 | + | 0.239074i | ||||
\(341\) | 7.58001e41 | 0.0665036 | ||||||||
\(342\) | −8.31694e41 | − | 8.31694e41i | −0.0694256 | − | 0.0694256i | ||||
\(343\) | 6.92442e42 | − | 6.92442e42i | 0.550026 | − | 0.550026i | ||||
\(344\) | 1.19745e43i | 0.905240i | ||||||||
\(345\) | −2.55034e42 | − | 5.50725e42i | −0.183516 | − | 0.396287i | ||||
\(346\) | −2.25593e39 | −0.000154537 | ||||||||
\(347\) | 3.62955e42 | + | 3.62955e42i | 0.236729 | + | 0.236729i | 0.815494 | − | 0.578765i | \(-0.196465\pi\) |
−0.578765 | + | 0.815494i | \(0.696465\pi\) | |||||||
\(348\) | −6.21041e42 | + | 6.21041e42i | −0.385721 | + | 0.385721i | ||||
\(349\) | 2.41730e43i | 1.42988i | 0.699187 | + | 0.714939i | \(0.253545\pi\) | ||||
−0.699187 | + | 0.714939i | \(0.746455\pi\) | |||||||
\(350\) | −1.56689e43 | − | 1.32898e43i | −0.882840 | − | 0.748792i | ||||
\(351\) | −4.61742e42 | −0.247844 | ||||||||
\(352\) | 1.86739e42 | + | 1.86739e42i | 0.0955014 | + | 0.0955014i | ||||
\(353\) | 1.84650e43 | − | 1.84650e43i | 0.899870 | − | 0.899870i | −0.0955541 | − | 0.995424i | \(-0.530462\pi\) |
0.995424 | + | 0.0955541i | \(0.0304623\pi\) | |||||||
\(354\) | 1.83897e43i | 0.854120i | ||||||||
\(355\) | 2.95466e43 | − | 1.36827e43i | 1.30805 | − | 0.605745i | ||||
\(356\) | −1.42789e43 | −0.602622 | ||||||||
\(357\) | 1.29489e43 | + | 1.29489e43i | 0.521042 | + | 0.521042i | ||||
\(358\) | 1.05870e43 | − | 1.05870e43i | 0.406222 | − | 0.406222i | ||||
\(359\) | 3.14832e43i | 1.15205i | 0.817431 | + | 0.576027i | \(0.195398\pi\) | ||||
−0.817431 | + | 0.576027i | \(0.804602\pi\) | |||||||
\(360\) | −8.12998e42 | − | 2.98347e42i | −0.283757 | − | 0.104131i | ||||
\(361\) | 2.32574e43 | 0.774351 | ||||||||
\(362\) | −3.79226e42 | − | 3.79226e42i | −0.120463 | − | 0.120463i | ||||
\(363\) | 1.92519e43 | − | 1.92519e43i | 0.583528 | − | 0.583528i | ||||
\(364\) | 5.75832e42i | 0.166561i | ||||||||
\(365\) | −1.66010e43 | + | 4.52378e43i | −0.458305 | + | 1.24888i | ||||
\(366\) | −2.90520e42 | −0.0765591 | ||||||||
\(367\) | −1.46395e43 | − | 1.46395e43i | −0.368300 | − | 0.368300i | 0.498557 | − | 0.866857i | \(-0.333863\pi\) |
−0.866857 | + | 0.498557i | \(0.833863\pi\) | |||||||
\(368\) | 4.91240e42 | − | 4.91240e42i | 0.118000 | − | 0.118000i | ||||
\(369\) | 1.40585e43i | 0.322470i | ||||||||
\(370\) | −2.09570e43 | − | 4.52548e43i | −0.459091 | − | 0.991368i | ||||
\(371\) | −1.02167e44 | −2.13773 | ||||||||
\(372\) | −5.69815e42 | − | 5.69815e42i | −0.113895 | − | 0.113895i | ||||
\(373\) | 4.34650e43 | − | 4.34650e43i | 0.830022 | − | 0.830022i | −0.157498 | − | 0.987519i | \(-0.550343\pi\) |
0.987519 | + | 0.157498i | \(0.0503427\pi\) | |||||||
\(374\) | − | 3.58046e42i | − | 0.0653313i | ||||||
\(375\) | −2.39644e43 | − | 4.22795e43i | −0.417864 | − | 0.737222i | ||||
\(376\) | 1.02867e44 | 1.71428 | ||||||||
\(377\) | 1.40996e43 | + | 1.40996e43i | 0.224597 | + | 0.224597i | ||||
\(378\) | −5.83929e43 | + | 5.83929e43i | −0.889199 | + | 0.889199i | ||||
\(379\) | − | 9.45767e43i | − | 1.37695i | −0.725261 | − | 0.688474i | \(-0.758281\pi\) | ||
0.725261 | − | 0.688474i | \(-0.241719\pi\) | |||||||
\(380\) | −1.43171e43 | + | 6.63007e42i | −0.199312 | + | 0.0922989i | ||||
\(381\) | −1.23633e44 | −1.64593 | ||||||||
\(382\) | 1.34027e43 | + | 1.34027e43i | 0.170654 | + | 0.170654i | ||||
\(383\) | 4.75065e43 | − | 4.75065e43i | 0.578594 | − | 0.578594i | −0.355922 | − | 0.934516i | \(-0.615833\pi\) |
0.934516 | + | 0.355922i | \(0.115833\pi\) | |||||||
\(384\) | − | 1.08073e43i | − | 0.125918i | ||||||
\(385\) | −2.15109e43 | − | 7.89388e42i | −0.239787 | − | 0.0879950i | ||||
\(386\) | −4.42167e43 | −0.471631 | ||||||||
\(387\) | −1.64863e43 | − | 1.64863e43i | −0.168281 | − | 0.168281i | ||||
\(388\) | 6.66449e43 | − | 6.66449e43i | 0.651070 | − | 0.651070i | ||||
\(389\) | 1.20858e44i | 1.13014i | 0.825042 | + | 0.565072i | \(0.191152\pi\) | ||||
−0.825042 | + | 0.565072i | \(0.808848\pi\) | |||||||
\(390\) | 5.45579e42 | − | 1.48671e43i | 0.0488381 | − | 0.133084i | ||||
\(391\) | 3.31185e43 | 0.283835 | ||||||||
\(392\) | 1.37915e44 | + | 1.37915e44i | 1.13175 | + | 1.13175i | ||||
\(393\) | −1.58123e42 | + | 1.58123e42i | −0.0124257 | + | 0.0124257i | ||||
\(394\) | 4.31586e43i | 0.324811i | ||||||||
\(395\) | 7.49326e43 | + | 1.61811e44i | 0.540158 | + | 1.16642i | ||||
\(396\) | −3.05377e42 | −0.0210871 | ||||||||
\(397\) | 8.26372e43 | + | 8.26372e43i | 0.546685 | + | 0.546685i | 0.925480 | − | 0.378796i | \(-0.123662\pi\) |
−0.378796 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(398\) | 6.41873e41 | − | 6.41873e41i | 0.00406852 | − | 0.00406852i | ||||
\(399\) | 1.04637e44i | 0.635542i | ||||||||
\(400\) | 3.59835e43 | − | 4.24252e43i | 0.209451 | − | 0.246947i | ||||
\(401\) | −3.35129e43 | −0.186964 | −0.0934819 | − | 0.995621i | \(-0.529800\pi\) | ||||
−0.0934819 | + | 0.995621i | \(0.529800\pi\) | |||||||
\(402\) | −6.90041e43 | − | 6.90041e43i | −0.369005 | − | 0.369005i | ||||
\(403\) | −1.29366e43 | + | 1.29366e43i | −0.0663186 | + | 0.0663186i | ||||
\(404\) | − | 1.71459e44i | − | 0.842709i | ||||||
\(405\) | −1.22971e44 | + | 5.69466e43i | −0.579520 | + | 0.268369i | ||||
\(406\) | 3.56614e44 | 1.61159 | ||||||||
\(407\) | −3.93285e43 | − | 3.93285e43i | −0.170452 | − | 0.170452i | ||||
\(408\) | −8.51254e43 | + | 8.51254e43i | −0.353864 | + | 0.353864i | ||||
\(409\) | − | 3.95351e44i | − | 1.57647i | −0.615372 | − | 0.788236i | \(-0.710994\pi\) | ||
0.615372 | − | 0.788236i | \(-0.289006\pi\) | |||||||
\(410\) | −2.05841e44 | − | 7.55376e43i | −0.787418 | − | 0.288960i | ||||
\(411\) | 1.44158e44 | 0.529088 | ||||||||
\(412\) | 5.03396e43 | + | 5.03396e43i | 0.177279 | + | 0.177279i | ||||
\(413\) | −4.54108e44 | + | 4.54108e44i | −1.53465 | + | 1.53465i | ||||
\(414\) | 3.28420e43i | 0.106518i | ||||||||
\(415\) | 4.80399e43 | − | 1.30909e44i | 0.149549 | − | 0.407524i | ||||
\(416\) | −6.37406e43 | −0.190471 | ||||||||
\(417\) | −2.66258e44 | − | 2.66258e44i | −0.763817 | − | 0.763817i | ||||
\(418\) | 1.44664e43 | − | 1.44664e43i | 0.0398440 | − | 0.0398440i | ||||
\(419\) | 2.10092e44i | 0.555611i | 0.960637 | + | 0.277805i | \(0.0896071\pi\) | ||||
−0.960637 | + | 0.277805i | \(0.910393\pi\) | |||||||
\(420\) | 1.02364e44 | + | 2.21046e44i | 0.259961 | + | 0.561364i | ||||
\(421\) | 3.76106e44 | 0.917306 | 0.458653 | − | 0.888615i | \(-0.348332\pi\) | ||||
0.458653 | + | 0.888615i | \(0.348332\pi\) | |||||||
\(422\) | −3.61540e44 | − | 3.61540e44i | −0.846925 | − | 0.846925i | ||||
\(423\) | −1.41625e44 | + | 1.41625e44i | −0.318679 | + | 0.318679i | ||||
\(424\) | − | 6.71640e44i | − | 1.45183i | ||||||
\(425\) | 2.64308e44 | − | 2.17145e43i | 0.548907 | − | 0.0450959i | ||||
\(426\) | 4.48857e44 | 0.895663 | ||||||||
\(427\) | −7.17397e43 | − | 7.17397e43i | −0.137558 | − | 0.137558i | ||||
\(428\) | 9.99305e43 | − | 9.99305e43i | 0.184143 | − | 0.184143i | ||||
\(429\) | − | 1.76615e43i | − | 0.0312791i | ||||||
\(430\) | 3.29970e44 | − | 1.52806e44i | 0.561709 | − | 0.260121i | ||||
\(431\) | −1.11882e45 | −1.83082 | −0.915411 | − | 0.402520i | \(-0.868134\pi\) | ||||
−0.915411 | + | 0.402520i | \(0.868134\pi\) | |||||||
\(432\) | −1.58105e44 | − | 1.58105e44i | −0.248726 | − | 0.248726i | ||||
\(433\) | 2.89363e44 | − | 2.89363e44i | 0.437672 | − | 0.437672i | −0.453556 | − | 0.891228i | \(-0.649845\pi\) |
0.891228 | + | 0.453556i | \(0.149845\pi\) | |||||||
\(434\) | 3.27199e44i | 0.475867i | ||||||||
\(435\) | 7.91890e44 | + | 2.90601e44i | 1.10751 | + | 0.406424i | ||||
\(436\) | −3.95702e44 | −0.532228 | ||||||||
\(437\) | 1.33811e44 | + | 1.33811e44i | 0.173104 | + | 0.173104i | ||||
\(438\) | −4.69711e44 | + | 4.69711e44i | −0.584482 | + | 0.584482i | ||||
\(439\) | 1.29055e44i | 0.154483i | 0.997012 | + | 0.0772413i | \(0.0246112\pi\) | ||||
−0.997012 | + | 0.0772413i | \(0.975389\pi\) | |||||||
\(440\) | 5.18940e43 | − | 1.41412e44i | 0.0597616 | − | 0.162851i | ||||
\(441\) | −3.79758e44 | −0.420776 | ||||||||
\(442\) | 6.11069e43 | + | 6.11069e43i | 0.0651496 | + | 0.0651496i | ||||
\(443\) | 1.58949e44 | − | 1.58949e44i | 0.163077 | − | 0.163077i | −0.620851 | − | 0.783928i | \(-0.713213\pi\) |
0.783928 | + | 0.620851i | \(0.213213\pi\) | |||||||
\(444\) | 5.91292e44i | 0.583837i | ||||||||
\(445\) | 5.76279e44 | + | 1.24443e45i | 0.547662 | + | 1.18263i | ||||
\(446\) | 1.53380e45 | 1.40306 | ||||||||
\(447\) | −7.09641e43 | − | 7.09641e43i | −0.0624900 | − | 0.0624900i | ||||
\(448\) | −1.23249e45 | + | 1.23249e45i | −1.04486 | + | 1.04486i | ||||
\(449\) | − | 1.53129e45i | − | 1.24988i | −0.780672 | − | 0.624941i | \(-0.785123\pi\) | ||
0.780672 | − | 0.624941i | \(-0.214877\pi\) | |||||||
\(450\) | 2.15332e43 | + | 2.62102e44i | 0.0169237 | + | 0.205996i | ||||
\(451\) | −2.44531e44 | −0.185069 | ||||||||
\(452\) | −1.84646e44 | − | 1.84646e44i | −0.134582 | − | 0.134582i | ||||
\(453\) | 3.19734e44 | − | 3.19734e44i | 0.224450 | − | 0.224450i | ||||
\(454\) | 7.27394e44i | 0.491836i | ||||||||
\(455\) | 5.01845e44 | − | 2.32399e44i | 0.326870 | − | 0.151370i | ||||
\(456\) | −6.87876e44 | −0.431626 | ||||||||
\(457\) | 8.16319e44 | + | 8.16319e44i | 0.493497 | + | 0.493497i | 0.909406 | − | 0.415909i | \(-0.136537\pi\) |
−0.415909 | + | 0.909406i | \(0.636537\pi\) | |||||||
\(458\) | −5.37158e44 | + | 5.37158e44i | −0.312888 | + | 0.312888i | ||||
\(459\) | − | 1.06591e45i | − | 0.598282i | ||||||
\(460\) | 4.13581e44 | + | 1.51772e44i | 0.223706 | + | 0.0820936i | ||||
\(461\) | 1.96054e45 | 1.02202 | 0.511011 | − | 0.859574i | \(-0.329271\pi\) | ||||
0.511011 | + | 0.859574i | \(0.329271\pi\) | |||||||
\(462\) | −2.23351e44 | − | 2.23351e44i | −0.112221 | − | 0.112221i | ||||
\(463\) | 1.13717e45 | − | 1.13717e45i | 0.550741 | − | 0.550741i | −0.375914 | − | 0.926655i | \(-0.622671\pi\) |
0.926655 | + | 0.375914i | \(0.122671\pi\) | |||||||
\(464\) | 9.65568e44i | 0.450793i | ||||||||
\(465\) | −2.66631e44 | + | 7.26572e44i | −0.120008 | + | 0.327023i | ||||
\(466\) | −4.20124e44 | −0.182313 | ||||||||
\(467\) | −1.08103e45 | − | 1.08103e45i | −0.452326 | − | 0.452326i | 0.443800 | − | 0.896126i | \(-0.353630\pi\) |
−0.896126 | + | 0.443800i | \(0.853630\pi\) | |||||||
\(468\) | 5.21179e43 | − | 5.21179e43i | 0.0210285 | − | 0.0210285i | ||||
\(469\) | − | 3.40792e45i | − | 1.32602i | ||||||
\(470\) | −1.31267e45 | − | 2.83461e45i | −0.492599 | − | 1.06372i | ||||
\(471\) | −2.35155e45 | −0.851135 | ||||||||
\(472\) | −2.98529e45 | − | 2.98529e45i | −1.04225 | − | 1.04225i | ||||
\(473\) | 2.86760e44 | − | 2.86760e44i | 0.0965782 | − | 0.0965782i | ||||
\(474\) | 2.45814e45i | 0.798685i | ||||||||
\(475\) | 1.15564e45 | + | 9.80169e44i | 0.362268 | + | 0.307262i | ||||
\(476\) | −1.32928e45 | −0.402068 | ||||||||
\(477\) | 9.24701e44 | + | 9.24701e44i | 0.269891 | + | 0.269891i | ||||
\(478\) | −1.99117e44 | + | 1.99117e44i | −0.0560833 | + | 0.0560833i | ||||
\(479\) | 2.62021e45i | 0.712250i | 0.934438 | + | 0.356125i | \(0.115902\pi\) | ||||
−0.934438 | + | 0.356125i | \(0.884098\pi\) | |||||||
\(480\) | −2.44683e45 | + | 1.13310e45i | −0.641951 | + | 0.297280i | ||||
\(481\) | 1.34242e45 | 0.339956 | ||||||||
\(482\) | 1.76767e45 | + | 1.76767e45i | 0.432117 | + | 0.432117i | ||||
\(483\) | 2.06595e45 | − | 2.06595e45i | 0.487549 | − | 0.487549i | ||||
\(484\) | 1.97633e45i | 0.450286i | ||||||||
\(485\) | −8.49789e45 | − | 3.11848e45i | −1.86940 | − | 0.686015i | ||||
\(486\) | 1.88159e45 | 0.399676 | ||||||||
\(487\) | 1.15951e45 | + | 1.15951e45i | 0.237838 | + | 0.237838i | 0.815954 | − | 0.578116i | \(-0.196212\pi\) |
−0.578116 | + | 0.815954i | \(0.696212\pi\) | |||||||
\(488\) | 4.71614e44 | − | 4.71614e44i | 0.0934221 | − | 0.0934221i | ||||
\(489\) | − | 4.67876e45i | − | 0.895118i | ||||||
\(490\) | 2.04048e45 | − | 5.56033e45i | 0.377050 | − | 1.02746i | ||||
\(491\) | 5.34078e45 | 0.953278 | 0.476639 | − | 0.879099i | \(-0.341855\pi\) | ||||
0.476639 | + | 0.879099i | \(0.341855\pi\) | |||||||
\(492\) | 1.83822e45 | + | 1.83822e45i | 0.316950 | + | 0.316950i | ||||
\(493\) | −3.25484e45 | + | 3.25484e45i | −0.542166 | + | 0.542166i | ||||
\(494\) | 4.93789e44i | 0.0794663i | ||||||||
\(495\) | 1.23246e44 | + | 2.66140e44i | 0.0191640 | + | 0.0413829i | ||||
\(496\) | −8.85924e44 | −0.133109 | ||||||||
\(497\) | 1.10839e46 | + | 1.10839e46i | 1.60929 | + | 1.60929i | ||||
\(498\) | 1.35925e45 | − | 1.35925e45i | 0.190722 | − | 0.190722i | ||||
\(499\) | 9.42765e45i | 1.27848i | 0.769007 | + | 0.639240i | \(0.220751\pi\) | ||||
−0.769007 | + | 0.639240i | \(0.779249\pi\) | |||||||
\(500\) | 3.40018e45 | + | 9.40080e44i | 0.445668 | + | 0.123218i | ||||
\(501\) | 3.31852e45 | 0.420440 | ||||||||
\(502\) | 5.93420e45 | + | 5.93420e45i | 0.726773 | + | 0.726773i | ||||
\(503\) | 1.78441e44 | − | 1.78441e44i | 0.0211271 | − | 0.0211271i | −0.696464 | − | 0.717591i | \(-0.745245\pi\) |
0.717591 | + | 0.696464i | \(0.245245\pi\) | |||||||
\(504\) | − | 4.16902e45i | − | 0.477215i | ||||||
\(505\) | −1.49429e46 | + | 6.91988e45i | −1.65379 | + | 0.765853i | ||||
\(506\) | −5.71250e44 | −0.0611318 | ||||||||
\(507\) | −5.48906e45 | − | 5.48906e45i | −0.568019 | − | 0.568019i | ||||
\(508\) | 6.34586e45 | − | 6.34586e45i | 0.635049 | − | 0.635049i | ||||
\(509\) | 4.99224e45i | 0.483162i | 0.970381 | + | 0.241581i | \(0.0776659\pi\) | ||||
−0.970381 | + | 0.241581i | \(0.922334\pi\) | |||||||
\(510\) | 3.43200e45 | + | 1.25945e45i | 0.321258 | + | 0.117893i | ||||
\(511\) | −2.31977e46 | −2.10034 | ||||||||
\(512\) | −4.98578e45 | − | 4.98578e45i | −0.436661 | − | 0.436661i | ||||
\(513\) | 4.30668e45 | − | 4.30668e45i | 0.364878 | − | 0.364878i | ||||
\(514\) | − | 9.21576e44i | − | 0.0755368i | ||||||
\(515\) | 2.35552e45 | − | 6.41881e45i | 0.186794 | − | 0.509016i | ||||
\(516\) | −4.31134e45 | −0.330802 | ||||||||
\(517\) | −2.46341e45 | − | 2.46341e45i | −0.182893 | − | 0.182893i | ||||
\(518\) | 1.69765e46 | − | 1.69765e46i | 1.21967 | − | 1.21967i | ||||
\(519\) | − | 2.56884e42i | − | 0.000178604i | ||||||
\(520\) | 1.52778e45 | + | 3.29911e45i | 0.102802 | + | 0.221993i | ||||
\(521\) | −1.29314e46 | −0.842177 | −0.421088 | − | 0.907020i | \(-0.638352\pi\) | ||||
−0.421088 | + | 0.907020i | \(0.638352\pi\) | |||||||
\(522\) | −3.22767e45 | − | 3.22767e45i | −0.203466 | − | 0.203466i | ||||
\(523\) | 6.06529e44 | − | 6.06529e44i | 0.0370103 | − | 0.0370103i | −0.688359 | − | 0.725370i | \(-0.741669\pi\) |
0.725370 | + | 0.688359i | \(0.241669\pi\) | |||||||
\(524\) | − | 1.62323e44i | − | 0.00958845i | ||||||
\(525\) | 1.51331e46 | − | 1.78423e46i | 0.865408 | − | 1.02033i | ||||
\(526\) | −1.08259e46 | −0.599384 | ||||||||
\(527\) | −2.98637e45 | − | 2.98637e45i | −0.160089 | − | 0.160089i | ||||
\(528\) | 6.04747e44 | − | 6.04747e44i | 0.0313904 | − | 0.0313904i | ||||
\(529\) | 1.46112e46i | 0.734410i | ||||||||
\(530\) | −1.85078e46 | + | 8.57074e45i | −0.900875 | + | 0.417185i | ||||
\(531\) | 8.22017e45 | 0.387502 | ||||||||
\(532\) | −5.37080e45 | − | 5.37080e45i | −0.245212 | − | 0.245212i | ||||
\(533\) | 4.17335e45 | − | 4.17335e45i | 0.184554 | − | 0.184554i | ||||
\(534\) | 1.89047e46i | 0.809781i | ||||||||
\(535\) | −1.27421e46 | − | 4.67600e45i | −0.528723 | − | 0.194026i | ||||
\(536\) | 2.24035e46 | 0.900565 | ||||||||
\(537\) | 1.20555e46 | + | 1.20555e46i | 0.469486 | + | 0.469486i | ||||
\(538\) | −1.22189e46 | + | 1.22189e46i | −0.461033 | + | 0.461033i | ||||
\(539\) | − | 6.60546e45i | − | 0.241487i | ||||||
\(540\) | 4.88477e45 | − | 1.33110e46i | 0.173042 | − | 0.471540i | ||||
\(541\) | 2.24150e46 | 0.769458 | 0.384729 | − | 0.923029i | \(-0.374295\pi\) | ||||
0.384729 | + | 0.923029i | \(0.374295\pi\) | |||||||
\(542\) | 6.90000e45 | + | 6.90000e45i | 0.229541 | + | 0.229541i | ||||
\(543\) | 4.31827e45 | − | 4.31827e45i | 0.139224 | − | 0.139224i | ||||
\(544\) | − | 1.47143e46i | − | 0.459787i | ||||||
\(545\) | 1.59700e46 | + | 3.44859e46i | 0.483688 | + | 1.04448i | ||||
\(546\) | 7.62377e45 | 0.223818 | ||||||||
\(547\) | −2.35640e46 | − | 2.35640e46i | −0.670602 | − | 0.670602i | 0.287253 | − | 0.957855i | \(-0.407258\pi\) |
−0.957855 | + | 0.287253i | \(0.907258\pi\) | |||||||
\(548\) | −7.39935e45 | + | 7.39935e45i | −0.204138 | + | 0.204138i | ||||
\(549\) | 1.29862e45i | 0.0347338i | ||||||||
\(550\) | −4.55897e45 | + | 3.74546e44i | −0.118223 | + | 0.00971269i | ||||
\(551\) | −2.63015e46 | −0.661308 | ||||||||
\(552\) | 1.35815e46 | + | 1.35815e46i | 0.331118 | + | 0.331118i | ||||
\(553\) | −6.07004e46 | + | 6.07004e46i | −1.43504 | + | 1.43504i | ||||
\(554\) | − | 6.46776e45i | − | 0.148282i | ||||||
\(555\) | 5.15319e46 | − | 2.38638e46i | 1.14576 | − | 0.530590i | ||||
\(556\) | 2.73330e46 | 0.589408 | ||||||||
\(557\) | 5.56372e45 | + | 5.56372e45i | 0.116366 | + | 0.116366i | 0.762892 | − | 0.646526i | \(-0.223779\pi\) |
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(558\) | 2.96144e45 | − | 2.96144e45i | 0.0600789 | − | 0.0600789i | ||||
\(559\) | 9.78813e45i | 0.192619i | ||||||||
\(560\) | 2.51412e46 | + | 9.22608e45i | 0.479942 | + | 0.176125i | ||||
\(561\) | 4.07709e45 | 0.0755060 | ||||||||
\(562\) | −8.11922e45 | − | 8.11922e45i | −0.145880 | − | 0.145880i | ||||
\(563\) | 2.94138e46 | − | 2.94138e46i | 0.512754 | − | 0.512754i | −0.402615 | − | 0.915369i | \(-0.631899\pi\) |
0.915369 | + | 0.402615i | \(0.131899\pi\) | |||||||
\(564\) | 3.70365e46i | 0.626449i | ||||||||
\(565\) | −8.64006e45 | + | 2.35442e46i | −0.141805 | + | 0.386421i | ||||
\(566\) | −1.62263e46 | −0.258429 | ||||||||
\(567\) | −4.61306e46 | − | 4.61306e46i | −0.712979 | − | 0.712979i | ||||
\(568\) | −7.28650e46 | + | 7.28650e46i | −1.09294 | + | 1.09294i | ||||
\(569\) | − | 6.94152e46i | − | 1.01052i | −0.862966 | − | 0.505261i | \(-0.831396\pi\) | ||
0.862966 | − | 0.505261i | \(-0.168604\pi\) | |||||||
\(570\) | 8.77793e45 | + | 1.89552e46i | 0.124028 | + | 0.267828i | ||||
\(571\) | 6.43763e46 | 0.882901 | 0.441450 | − | 0.897286i | \(-0.354464\pi\) | ||||
0.441450 | + | 0.897286i | \(0.354464\pi\) | |||||||
\(572\) | 9.06533e44 | + | 9.06533e44i | 0.0120684 | + | 0.0120684i | ||||
\(573\) | −1.52617e46 | + | 1.52617e46i | −0.197231 | + | 0.197231i | ||||
\(574\) | − | 1.05554e47i | − | 1.32426i | ||||||
\(575\) | −3.46447e45 | − | 4.21695e46i | −0.0421972 | − | 0.513623i | ||||
\(576\) | 2.23104e46 | 0.263830 | ||||||||
\(577\) | 5.14827e46 | + | 5.14827e46i | 0.591116 | + | 0.591116i | 0.937933 | − | 0.346817i | \(-0.112738\pi\) |
−0.346817 | + | 0.937933i | \(0.612738\pi\) | |||||||
\(578\) | 3.23980e46 | − | 3.23980e46i | 0.361198 | − | 0.361198i | ||||
\(579\) | − | 5.03498e46i | − | 0.545083i | ||||||
\(580\) | −5.55622e46 | + | 2.57302e46i | −0.584122 | + | 0.270500i | ||||
\(581\) | 6.71297e46 | 0.685363 | ||||||||
\(582\) | −8.82350e46 | − | 8.82350e46i | −0.874884 | − | 0.874884i | ||||
\(583\) | −1.60841e46 | + | 1.60841e46i | −0.154893 | + | 0.154893i | ||||
\(584\) | − | 1.52501e47i | − | 1.42644i | ||||||
\(585\) | −6.64556e45 | − | 2.43873e45i | −0.0603785 | − | 0.0221572i | ||||
\(586\) | −1.28398e47 | −1.13318 | ||||||||
\(587\) | −3.00344e46 | − | 3.00344e46i | −0.257496 | − | 0.257496i | 0.566539 | − | 0.824035i | \(-0.308282\pi\) |
−0.824035 | + | 0.566539i | \(0.808282\pi\) | |||||||
\(588\) | −4.96555e46 | + | 4.96555e46i | −0.413574 | + | 0.413574i | ||||
\(589\) | − | 2.41321e46i | − | 0.195269i | ||||||
\(590\) | −4.41678e46 | + | 1.20358e47i | −0.347234 | + | 0.946215i | ||||
\(591\) | −4.91449e46 | −0.375398 | ||||||||
\(592\) | 4.59657e46 | + | 4.59657e46i | 0.341166 | + | 0.341166i | ||||
\(593\) | −3.43717e46 | + | 3.43717e46i | −0.247897 | + | 0.247897i | −0.820107 | − | 0.572210i | \(-0.806086\pi\) |
0.572210 | + | 0.820107i | \(0.306086\pi\) | |||||||
\(594\) | 1.83856e46i | 0.128857i | ||||||||
\(595\) | 5.36482e46 | + | 1.15849e47i | 0.365399 | + | 0.789047i | ||||
\(596\) | 7.28490e45 | 0.0482211 | ||||||||
\(597\) | 7.30904e44 | + | 7.30904e44i | 0.00470215 | + | 0.00470215i | ||||
\(598\) | 9.74939e45 | − | 9.74939e45i | 0.0609617 | − | 0.0609617i | ||||
\(599\) | − | 3.14444e46i | − | 0.191112i | −0.995424 | − | 0.0955558i | \(-0.969537\pi\) | ||
0.995424 | − | 0.0955558i | \(-0.0304628\pi\) | |||||||
\(600\) | 1.17294e47 | + | 9.94847e46i | 0.692956 | + | 0.587740i | ||||
\(601\) | 2.76387e47 | 1.58728 | 0.793638 | − | 0.608391i | \(-0.208185\pi\) | ||||
0.793638 | + | 0.608391i | \(0.208185\pi\) | |||||||
\(602\) | 1.23783e47 | + | 1.23783e47i | 0.691066 | + | 0.691066i | ||||
\(603\) | −3.08448e46 | + | 3.08448e46i | −0.167412 | + | 0.167412i | ||||
\(604\) | 3.28227e46i | 0.173199i | ||||||||
\(605\) | 1.72240e47 | − | 7.97622e46i | 0.883673 | − | 0.409219i | ||||
\(606\) | −2.27005e47 | −1.13240 | ||||||||
\(607\) | −1.32824e47 | − | 1.32824e47i | −0.644272 | − | 0.644272i | 0.307330 | − | 0.951603i | \(-0.400564\pi\) |
−0.951603 | + | 0.307330i | \(0.900564\pi\) | |||||||
\(608\) | 5.94510e46 | − | 5.94510e46i | 0.280413 | − | 0.280413i | ||||
\(609\) | 4.06078e47i | 1.86258i | ||||||||
\(610\) | −1.90141e46 | − | 6.97762e45i | −0.0848141 | − | 0.0311243i | ||||
\(611\) | 8.40848e46 | 0.364768 | ||||||||
\(612\) | 1.20312e46 | + | 1.20312e46i | 0.0507616 | + | 0.0507616i | ||||
\(613\) | 1.22216e47 | − | 1.22216e47i | 0.501532 | − | 0.501532i | −0.410382 | − | 0.911914i | \(-0.634605\pi\) |
0.911914 | + | 0.410382i | \(0.134605\pi\) | |||||||
\(614\) | 8.33748e46i | 0.332792i | ||||||||
\(615\) | 8.60151e46 | − | 2.34392e47i | 0.333962 | − | 0.910051i | ||||
\(616\) | 7.25153e46 | 0.273878 | ||||||||
\(617\) | −8.48498e46 | − | 8.48498e46i | −0.311747 | − | 0.311747i | 0.533839 | − | 0.845586i | \(-0.320749\pi\) |
−0.845586 | + | 0.533839i | \(0.820749\pi\) | |||||||
\(618\) | 6.66476e46 | − | 6.66476e46i | 0.238221 | − | 0.238221i | ||||
\(619\) | 2.29897e45i | 0.00799451i | 0.999992 | + | 0.00399726i | \(0.00127237\pi\) | ||||
−0.999992 | + | 0.00399726i | \(0.998728\pi\) | |||||||
\(620\) | −2.36079e46 | − | 5.09792e46i | −0.0798727 | − | 0.172478i | ||||
\(621\) | −1.70063e47 | −0.559824 | ||||||||
\(622\) | 2.02461e47 | + | 2.02461e47i | 0.648491 | + | 0.648491i | ||||
\(623\) | −4.66825e47 | + | 4.66825e47i | −1.45498 | + | 1.45498i | ||||
\(624\) | 2.06421e46i | 0.0626061i | ||||||||
\(625\) | −5.52977e46 | − | 3.34270e47i | −0.163210 | − | 0.986591i | ||||
\(626\) | 1.20105e47 | 0.344982 | ||||||||
\(627\) | 1.64729e46 | + | 1.64729e46i | 0.0460493 | + | 0.0460493i | ||||
\(628\) | 1.20701e47 | − | 1.20701e47i | 0.328394 | − | 0.328394i | ||||
\(629\) | 3.09893e47i | 0.820635i | ||||||||
\(630\) | −1.14882e47 | + | 5.32005e46i | −0.296116 | + | 0.137128i | ||||
\(631\) | −5.04387e47 | −1.26551 | −0.632754 | − | 0.774353i | \(-0.718075\pi\) | ||||
−0.632754 | + | 0.774353i | \(0.718075\pi\) | |||||||
\(632\) | −3.99042e47 | − | 3.99042e47i | −0.974605 | − | 0.974605i | ||||
\(633\) | 4.11688e47 | − | 4.11688e47i | 0.978825 | − | 0.978825i | ||||
\(634\) | − | 1.92927e47i | − | 0.446556i | ||||||
\(635\) | −8.09161e47 | − | 2.96939e47i | −1.82340 | − | 0.669135i | ||||
\(636\) | 2.41820e47 | 0.530544 | ||||||||
\(637\) | 1.12734e47 | + | 1.12734e47i | 0.240815 | + | 0.240815i | ||||
\(638\) | 5.61417e46 | − | 5.61417e46i | 0.116771 | − | 0.116771i | ||||
\(639\) | − | 2.00638e47i | − | 0.406349i | ||||||
\(640\) | 2.59567e46 | − | 7.07321e46i | 0.0511905 | − | 0.139495i | ||||
\(641\) | −1.85685e47 | −0.356608 | −0.178304 | − | 0.983975i | \(-0.557061\pi\) | ||||
−0.178304 | + | 0.983975i | \(0.557061\pi\) | |||||||
\(642\) | −1.32304e47 | − | 1.32304e47i | −0.247444 | − | 0.247444i | ||||
\(643\) | 5.80223e47 | − | 5.80223e47i | 1.05684 | − | 1.05684i | 0.0585541 | − | 0.998284i | \(-0.481351\pi\) |
0.998284 | − | 0.0585541i | \(-0.0186490\pi\) | |||||||
\(644\) | 2.12083e47i | 0.376223i | ||||||||
\(645\) | 1.74001e47 | + | 3.75739e47i | 0.300632 | + | 0.649189i | ||||
\(646\) | −1.13989e47 | −0.191827 | ||||||||
\(647\) | 4.69490e47 | + | 4.69490e47i | 0.769580 | + | 0.769580i | 0.978032 | − | 0.208453i | \(-0.0668427\pi\) |
−0.208453 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(648\) | 3.03260e47 | − | 3.03260e47i | 0.484218 | − | 0.484218i | ||||
\(649\) | 1.42981e47i | 0.222391i | ||||||||
\(650\) | 7.14146e46 | − | 8.41992e46i | 0.108208 | − | 0.127580i | ||||
\(651\) | −3.72583e47 | −0.549979 | ||||||||
\(652\) | 2.40152e47 | + | 2.40152e47i | 0.345364 | + | 0.345364i | ||||
\(653\) | −8.67113e47 | + | 8.67113e47i | −1.21493 | + | 1.21493i | −0.245547 | + | 0.969385i | \(0.578968\pi\) |
−0.969385 | + | 0.245547i | \(0.921032\pi\) | |||||||
\(654\) | 5.23893e47i | 0.715189i | ||||||||
\(655\) | −1.41467e46 | + | 6.55116e45i | −0.0188171 | + | 0.00871397i | ||||
\(656\) | 2.85799e47 | 0.370421 | ||||||||
\(657\) | 2.09960e47 | + | 2.09960e47i | 0.265171 | + | 0.265171i | ||||
\(658\) | 1.06335e48 | − | 1.06335e48i | 1.30869 | − | 1.30869i | ||||
\(659\) | − | 3.34007e47i | − | 0.400593i | −0.979735 | − | 0.200296i | \(-0.935810\pi\) | ||
0.979735 | − | 0.200296i | \(-0.0641905\pi\) | |||||||
\(660\) | 5.09144e46 | + | 1.86841e46i | 0.0595105 | + | 0.0218386i | ||||
\(661\) | 1.20808e47 | 0.137617 | 0.0688084 | − | 0.997630i | \(-0.478080\pi\) | ||||
0.0688084 | + | 0.997630i | \(0.478080\pi\) | |||||||
\(662\) | 1.11732e47 | + | 1.11732e47i | 0.124049 | + | 0.124049i | ||||
\(663\) | −6.95828e46 | + | 6.95828e46i | −0.0752960 | + | 0.0752960i | ||||
\(664\) | 4.41308e47i | 0.465462i | ||||||||
\(665\) | −2.51313e47 | + | 6.84831e47i | −0.258373 | + | 0.704069i | ||||
\(666\) | −3.07306e47 | −0.307970 | ||||||||
\(667\) | 5.19299e47 | + | 5.19299e47i | 0.507315 | + | 0.507315i | ||||
\(668\) | −1.70334e47 | + | 1.70334e47i | −0.162219 | + | 0.162219i | ||||
\(669\) | 1.74655e48i | 1.62158i | ||||||||
\(670\) | −2.85890e47 | − | 6.17354e47i | −0.258778 | − | 0.558808i | ||||
\(671\) | −2.25880e46 | −0.0199340 | ||||||||
\(672\) | −9.17884e47 | − | 9.17884e47i | −0.789788 | − | 0.789788i | ||||
\(673\) | 4.39107e46 | − | 4.39107e46i | 0.0368396 | − | 0.0368396i | −0.688447 | − | 0.725287i | \(-0.741707\pi\) |
0.725287 | + | 0.688447i | \(0.241707\pi\) | |||||||
\(674\) | 7.99750e46i | 0.0654238i | ||||||||
\(675\) | −1.35722e48 | + | 1.11503e47i | −1.08264 | + | 0.0889455i | ||||
\(676\) | 5.63486e47 | 0.438318 | ||||||||
\(677\) | 1.83676e48 | + | 1.83676e48i | 1.39330 | + | 1.39330i | 0.817807 | + | 0.575493i | \(0.195190\pi\) |
0.575493 | + | 0.817807i | \(0.304810\pi\) | |||||||
\(678\) | −2.44464e47 | + | 2.44464e47i | −0.180846 | + | 0.180846i | ||||
\(679\) | − | 4.35768e48i | − | 3.14390i | ||||||
\(680\) | −7.61585e47 | + | 3.52681e47i | −0.535879 | + | 0.248160i | ||||
\(681\) | −8.28287e47 | −0.568434 | ||||||||
\(682\) | 5.15109e46 | + | 5.15109e46i | 0.0344798 | + | 0.0344798i | ||||
\(683\) | 9.42364e47 | − | 9.42364e47i | 0.615272 | − | 0.615272i | −0.329043 | − | 0.944315i | \(-0.606726\pi\) |
0.944315 | + | 0.329043i | \(0.106726\pi\) | |||||||
\(684\) | 9.72211e46i | 0.0619165i | ||||||||
\(685\) | 9.43492e47 | + | 3.46234e47i | 0.586136 | + | 0.215095i | ||||
\(686\) | 9.41116e47 | 0.570339 | ||||||||
\(687\) | −6.11665e47 | − | 6.11665e47i | −0.361617 | − | 0.361617i | ||||
\(688\) | −3.35155e47 | + | 3.35155e47i | −0.193304 | + | 0.193304i | ||||
\(689\) | − | 5.49009e47i | − | 0.308925i | ||||||
\(690\) | 2.00940e47 | − | 5.47564e47i | 0.110314 | − | 0.300608i | ||||
\(691\) | 5.66789e47 | 0.303595 | 0.151797 | − | 0.988412i | \(-0.451494\pi\) | ||||
0.151797 | + | 0.988412i | \(0.451494\pi\) | |||||||
\(692\) | 1.31854e44 | + | 1.31854e44i | 6.89110e−5 | + | 6.89110e-5i | ||||
\(693\) | −9.98377e46 | + | 9.98377e46i | −0.0509131 | + | 0.0509131i | ||||
\(694\) | 4.93301e47i | 0.245472i | ||||||||
\(695\) | −1.10313e48 | − | 2.38211e48i | −0.535654 | − | 1.15670i | ||||
\(696\) | −2.66954e48 | −1.26497 | ||||||||
\(697\) | 9.63402e47 | + | 9.63402e47i | 0.445502 | + | 0.445502i | ||||
\(698\) | −1.64271e48 | + | 1.64271e48i | −0.741342 | + | 0.741342i | ||||
\(699\) | − | 4.78397e47i | − | 0.210706i | ||||||
\(700\) | 1.39054e47 | + | 1.69257e48i | 0.0597747 | + | 0.727577i | ||||
\(701\) | 5.58939e47 | 0.234508 | 0.117254 | − | 0.993102i | \(-0.462591\pi\) | ||||
0.117254 | + | 0.993102i | \(0.462591\pi\) | |||||||
\(702\) | −3.13783e47 | − | 3.13783e47i | −0.128499 | − | 0.128499i | ||||
\(703\) | −1.25208e48 | + | 1.25208e48i | −0.500486 | + | 0.500486i | ||||
\(704\) | 3.88063e47i | 0.151414i | ||||||||
\(705\) | 3.22778e48 | − | 1.49475e48i | 1.22939 | − | 0.569316i | ||||
\(706\) | 2.50963e48 | 0.933103 | ||||||||
\(707\) | −5.60557e48 | − | 5.60557e48i | −2.03465 | − | 2.03465i | ||||
\(708\) | 1.07483e48 | − | 1.07483e48i | 0.380869 | − | 0.380869i | ||||
\(709\) | 2.87907e48i | 0.996016i | 0.867172 | + | 0.498008i | \(0.165935\pi\) | ||||
−0.867172 | + | 0.498008i | \(0.834065\pi\) | |||||||
\(710\) | 2.93770e48 | + | 1.07805e48i | 0.992237 | + | 0.364123i | ||||
\(711\) | 1.09879e48 | 0.362352 | ||||||||
\(712\) | −3.06888e48 | − | 3.06888e48i | −0.988145 | − | 0.988145i | ||||
\(713\) | −4.76465e47 | + | 4.76465e47i | −0.149799 | + | 0.149799i | ||||
\(714\) | 1.75992e48i | 0.540284i | ||||||||
\(715\) | 4.24189e46 | − | 1.15592e47i | 0.0127162 | − | 0.0346517i | ||||
\(716\) | −1.23757e48 | −0.362285 | ||||||||
\(717\) | −2.26735e47 | − | 2.26735e47i | −0.0648177 | − | 0.0648177i | ||||
\(718\) | −2.13948e48 | + | 2.13948e48i | −0.597300 | + | 0.597300i | ||||
\(719\) | − | 3.82883e48i | − | 1.04394i | −0.852964 | − | 0.521969i | \(-0.825198\pi\) | ||
0.852964 | − | 0.521969i | \(-0.174802\pi\) | |||||||
\(720\) | −1.44046e47 | − | 3.11054e47i | −0.0383573 | − | 0.0828293i | ||||
\(721\) | 3.29154e48 | 0.856050 | ||||||||
\(722\) | 1.58048e48 | + | 1.58048e48i | 0.401474 | + | 0.401474i | ||||
\(723\) | −2.01285e48 | + | 2.01285e48i | −0.499414 | + | 0.499414i | ||||
\(724\) | 4.43297e47i | 0.107433i | ||||||||
\(725\) | 4.48485e48 | + | 3.80388e48i | 1.06170 | + | 0.900494i | ||||
\(726\) | 2.61658e48 | 0.605077 | ||||||||
\(727\) | 6.09193e48 | + | 6.09193e48i | 1.37616 | + | 1.37616i | 0.851004 | + | 0.525160i | \(0.175994\pi\) |
0.525160 | + | 0.851004i | \(0.324006\pi\) | |||||||
\(728\) | −1.23760e48 | + | 1.23760e48i | −0.273116 | + | 0.273116i | ||||
\(729\) | 5.10486e48i | 1.10057i | ||||||||
\(730\) | −4.20233e48 | + | 1.94605e48i | −0.885118 | + | 0.409888i | ||||
\(731\) | −2.25955e48 | −0.464972 | ||||||||
\(732\) | 1.69802e47 | + | 1.69802e47i | 0.0341392 | + | 0.0341392i | ||||
\(733\) | 2.81523e48 | − | 2.81523e48i | 0.553026 | − | 0.553026i | −0.374287 | − | 0.927313i | \(-0.622112\pi\) |
0.927313 | + | 0.374287i | \(0.122112\pi\) | |||||||
\(734\) | − | 1.98968e48i | − | 0.381901i | ||||||
\(735\) | 6.33158e48 | + | 2.32351e48i | 1.18748 | + | 0.435772i | ||||
\(736\) | −2.34761e48 | −0.430232 | ||||||||
\(737\) | −5.36510e47 | − | 5.36510e47i | −0.0960794 | − | 0.0960794i | ||||
\(738\) | −9.55360e47 | + | 9.55360e47i | −0.167189 | + | 0.167189i | ||||
\(739\) | − | 7.58569e48i | − | 1.29730i | −0.761088 | − | 0.648649i | \(-0.775334\pi\) | ||
0.761088 | − | 0.648649i | \(-0.224666\pi\) | |||||||
\(740\) | −1.42015e48 | + | 3.86992e48i | −0.237353 | + | 0.646789i | ||||
\(741\) | −5.62280e47 | −0.0918424 | ||||||||
\(742\) | −6.94287e48 | − | 6.94287e48i | −1.10834 | − | 1.10834i | ||||
\(743\) | 3.35478e48 | − | 3.35478e48i | 0.523425 | − | 0.523425i | −0.395179 | − | 0.918604i | \(-0.629317\pi\) |
0.918604 | + | 0.395179i | \(0.129317\pi\) | |||||||
\(744\) | − | 2.44934e48i | − | 0.373517i | ||||||
\(745\) | −2.94010e47 | − | 6.34889e47i | −0.0438233 | − | 0.0946327i | ||||
\(746\) | 5.90744e48 | 0.860674 | ||||||||
\(747\) | −6.07584e47 | − | 6.07584e47i | −0.0865279 | − | 0.0865279i | ||||
\(748\) | −2.09269e47 | + | 2.09269e47i | −0.0291325 | + | 0.0291325i | ||||
\(749\) | − | 6.53412e48i | − | 0.889193i | ||||||
\(750\) | 1.24463e48 | − | 4.50169e48i | 0.165576 | − | 0.598872i | ||||
\(751\) | −1.49177e49 | −1.94010 | −0.970048 | − | 0.242913i | \(-0.921897\pi\) | ||||
−0.970048 | + | 0.242913i | \(0.921897\pi\) | |||||||
\(752\) | 2.87914e48 | + | 2.87914e48i | 0.366066 | + | 0.366066i | ||||
\(753\) | −6.75730e48 | + | 6.75730e48i | −0.839960 | + | 0.839960i | ||||
\(754\) | 1.91632e48i | 0.232892i | ||||||||
\(755\) | 2.86054e48 | − | 1.32468e48i | 0.339899 | − | 0.157403i | ||||
\(756\) | 6.82585e48 | 0.793023 | ||||||||
\(757\) | 7.60388e47 | + | 7.60388e47i | 0.0863785 | + | 0.0863785i | 0.748976 | − | 0.662597i | \(-0.230546\pi\) |
−0.662597 | + | 0.748976i | \(0.730546\pi\) | |||||||
\(758\) | 6.42708e48 | − | 6.42708e48i | 0.713899 | − | 0.713899i | ||||
\(759\) | − | 6.50485e47i | − | 0.0706525i | ||||||
\(760\) | −4.50205e48 | − | 1.65212e48i | −0.478166 | − | 0.175473i | ||||
\(761\) | −1.43211e49 | −1.48744 | −0.743718 | − | 0.668494i | \(-0.766939\pi\) | ||||
−0.743718 | + | 0.668494i | \(0.766939\pi\) | |||||||
\(762\) | −8.40165e48 | − | 8.40165e48i | −0.853356 | − | 0.853356i | ||||
\(763\) | −1.29368e49 | + | 1.29368e49i | −1.28502 | + | 1.28502i | ||||
\(764\) | − | 1.56671e48i | − | 0.152196i | ||||||
\(765\) | 5.62971e47 | − | 1.53410e48i | 0.0534862 | − | 0.145750i | ||||
\(766\) | 6.45673e48 | 0.599962 | ||||||||
\(767\) | −2.44022e48 | − | 2.44022e48i | −0.221772 | − | 0.221772i | ||||
\(768\) | 7.04342e48 | − | 7.04342e48i | 0.626099 | − | 0.626099i | ||||
\(769\) | 1.10209e48i | 0.0958225i | 0.998852 | + | 0.0479112i | \(0.0152565\pi\) | ||||
−0.998852 | + | 0.0479112i | \(0.984744\pi\) | |||||||
\(770\) | −9.25362e47 | − | 1.99824e48i | −0.0786990 | − | 0.169944i | ||||
\(771\) | 1.04940e48 | 0.0873008 | ||||||||
\(772\) | 2.58436e48 | + | 2.58436e48i | 0.210310 | + | 0.210310i | ||||
\(773\) | 3.85327e47 | − | 3.85327e47i | 0.0306746 | − | 0.0306746i | −0.691603 | − | 0.722278i | \(-0.743095\pi\) |
0.722278 | + | 0.691603i | \(0.243095\pi\) | |||||||
\(774\) | − | 2.24069e48i | − | 0.174496i | ||||||
\(775\) | −3.49012e48 | + | 4.11492e48i | −0.265896 | + | 0.313496i | ||||
\(776\) | 2.86472e49 | 2.13517 | ||||||||
\(777\) | 1.93313e49 | + | 1.93313e49i | 1.40962 | + | 1.40962i | ||||
\(778\) | −8.21309e48 | + | 8.21309e48i | −0.585940 | + | 0.585940i | ||||
\(779\) | 7.78500e48i | 0.543403i | ||||||||
\(780\) | −1.18782e48 | + | 5.50067e47i | −0.0811229 | + | 0.0375671i | ||||
\(781\) | 3.48988e48 | 0.233208 | ||||||||
\(782\) | 2.25061e48 | + | 2.25061e48i | 0.147158 | + | 0.147158i | ||||
\(783\) | 1.67136e49 | − | 1.67136e49i | 1.06935 | − | 1.06935i | ||||
\(784\) | 7.72022e48i | 0.483344i | ||||||||
\(785\) | −1.53905e49 | − | 5.64788e48i | −0.942909 | − | 0.346020i | ||||
\(786\) | −2.14909e47 | −0.0128846 | ||||||||
\(787\) | 9.94569e47 | + | 9.94569e47i | 0.0583532 | + | 0.0583532i | 0.735681 | − | 0.677328i | \(-0.236862\pi\) |
−0.677328 | + | 0.735681i | \(0.736862\pi\) | |||||||
\(788\) | 2.52252e48 | − | 2.52252e48i | 0.144840 | − | 0.144840i | ||||
\(789\) | − | 1.23275e49i | − | 0.692732i | ||||||
\(790\) | −5.90390e48 | + | 1.60882e49i | −0.324697 | + | 0.884803i | ||||
\(791\) | −1.20734e49 | −0.649873 | ||||||||
\(792\) | −6.56329e47 | − | 6.56329e47i | −0.0345775 | − | 0.0345775i | ||||
\(793\) | 3.85504e47 | − | 3.85504e47i | 0.0198786 | − | 0.0198786i | ||||
\(794\) | 1.12314e49i | 0.566874i | ||||||||
\(795\) | −9.75955e48 | − | 2.10749e49i | −0.482157 | − | 1.04118i | ||||
\(796\) | −7.50319e46 | −0.00362847 | ||||||||
\(797\) | 2.49194e49 | + | 2.49194e49i | 1.17963 | + | 1.17963i | 0.979838 | + | 0.199794i | \(0.0640274\pi\) |
0.199794 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(798\) | −7.11071e48 | + | 7.11071e48i | −0.329506 | + | 0.329506i | ||||
\(799\) | 1.94106e49i | 0.880530i | ||||||||
\(800\) | −1.87355e49 | + | 1.53924e48i | −0.832026 | + | 0.0683558i | ||||
\(801\) | 8.45036e48 | 0.367386 | ||||||||
\(802\) | −2.27741e48 | − | 2.27741e48i | −0.0969342 | − | 0.0969342i | ||||
\(803\) | −3.65202e48 | + | 3.65202e48i | −0.152184 | + | 0.152184i | ||||
\(804\) | 8.06625e48i | 0.329093i | ||||||||
\(805\) | 1.84833e49 | − | 8.55939e48i | 0.738327 | − | 0.341911i | ||||
\(806\) | −1.75825e48 | −0.0687678 | ||||||||
\(807\) | −1.39137e49 | − | 1.39137e49i | −0.532835 | − | 0.532835i | ||||
\(808\) | 3.68508e49 | − | 3.68508e49i | 1.38183 | − | 1.38183i | ||||
\(809\) | 2.87976e49i | 1.05738i | 0.848815 | + | 0.528690i | \(0.177316\pi\) | ||||
−0.848815 | + | 0.528690i | \(0.822684\pi\) | |||||||
\(810\) | −1.22266e49 | − | 4.48679e48i | −0.439601 | − | 0.161321i | ||||
\(811\) | −5.08727e49 | −1.79114 | −0.895572 | − | 0.444917i | \(-0.853233\pi\) | ||||
−0.895572 | + | 0.444917i | \(0.853233\pi\) | |||||||
\(812\) | −2.08432e49 | − | 2.08432e49i | −0.718641 | − | 0.718641i | ||||
\(813\) | −7.85707e48 | + | 7.85707e48i | −0.265290 | + | 0.265290i | ||||
\(814\) | − | 5.34524e48i | − | 0.176747i | ||||||
\(815\) | 1.12373e49 | − | 3.06218e49i | 0.363901 | − | 0.991634i | ||||
\(816\) | −4.76515e48 | −0.151128 | ||||||||
\(817\) | −9.12942e48 | − | 9.12942e48i | −0.283575 | − | 0.283575i | ||||
\(818\) | 2.68666e49 | − | 2.68666e49i | 0.817346 | − | 0.817346i | ||||
\(819\) | − | 3.40781e48i | − | 0.101543i | ||||||
\(820\) | 7.61590e48 | + | 1.64459e49i | 0.222273 | + | 0.479978i | ||||
\(821\) | 2.26744e49 | 0.648190 | 0.324095 | − | 0.946024i | \(-0.394940\pi\) | ||||
0.324095 | + | 0.946024i | \(0.394940\pi\) | |||||||
\(822\) | 9.79643e48 | + | 9.79643e48i | 0.274313 | + | 0.274313i | ||||
\(823\) | 2.80478e49 | − | 2.80478e49i | 0.769310 | − | 0.769310i | −0.208675 | − | 0.977985i | \(-0.566915\pi\) |
0.977985 | + | 0.208675i | \(0.0669150\pi\) | |||||||
\(824\) | 2.16384e49i | 0.581384i | ||||||||
\(825\) | −4.26498e47 | − | 5.19132e48i | −0.0112253 | − | 0.136635i | ||||
\(826\) | −6.17189e49 | −1.59132 | ||||||||
\(827\) | 1.06712e48 | + | 1.06712e48i | 0.0269539 | + | 0.0269539i | 0.720455 | − | 0.693501i | \(-0.243933\pi\) |
−0.693501 | + | 0.720455i | \(0.743933\pi\) | |||||||
\(828\) | 1.91954e48 | − | 1.91954e48i | 0.0474986 | − | 0.0474986i | ||||
\(829\) | − | 3.21095e49i | − | 0.778407i | −0.921152 | − | 0.389203i | \(-0.872750\pi\) | ||
0.921152 | − | 0.389203i | \(-0.127250\pi\) | |||||||
\(830\) | 1.21607e49 | − | 5.63149e48i | 0.288823 | − | 0.133751i | ||||
\(831\) | 7.36487e48 | 0.171375 | ||||||||
\(832\) | −6.62299e48 | − | 6.62299e48i | −0.150993 | − | 0.150993i | ||||
\(833\) | −2.60242e49 | + | 2.60242e49i | −0.581315 | + | 0.581315i | ||||
\(834\) | − | 3.61878e49i | − | 0.792025i | ||||||
\(835\) | 2.17193e49 | + | 7.97034e48i | 0.465773 | + | 0.170925i | ||||
\(836\) | −1.69105e48 | −0.0355345 | ||||||||
\(837\) | 1.53349e49 | + | 1.53349e49i | 0.315754 | + | 0.315754i | ||||
\(838\) | −1.42771e49 | + | 1.42771e49i | −0.288065 | + | 0.288065i | ||||
\(839\) | 1.26696e49i | 0.250501i | 0.992125 | + | 0.125250i | \(0.0399734\pi\) | ||||
−0.992125 | + | 0.125250i | \(0.960027\pi\) | |||||||
\(840\) | −2.55077e49 | + | 6.95086e49i | −0.494223 | + | 1.34676i | ||||
\(841\) | −4.94058e49 | −0.938094 | ||||||||
\(842\) | 2.55587e49 | + | 2.55587e49i | 0.475591 | + | 0.475591i | ||||
\(843\) | 9.24540e48 | − | 9.24540e48i | 0.168600 | − | 0.168600i | ||||
\(844\) | 4.22623e49i | 0.755322i | ||||||||
\(845\) | −2.27416e49 | − | 4.91085e49i | −0.398343 | − | 0.860187i | ||||
\(846\) | −1.92486e49 | −0.330448 | ||||||||
\(847\) | 6.46127e49 | + | 6.46127e49i | 1.08718 | + | 1.08718i | ||||
\(848\) | 1.87986e49 | − | 1.87986e49i | 0.310024 | − | 0.310024i | ||||
\(849\) | − | 1.84770e49i | − | 0.298676i | ||||||
\(850\) | 1.94370e49 | + | 1.64858e49i | 0.307970 | + | 0.261209i | ||||
\(851\) | 4.94423e49 | 0.767885 | ||||||||
\(852\) | −2.62346e49 | − | 2.62346e49i | −0.399394 | − | 0.399394i | ||||
\(853\) | −1.42058e49 | + | 1.42058e49i | −0.211998 | + | 0.211998i | −0.805116 | − | 0.593117i | \(-0.797897\pi\) |
0.593117 | + | 0.805116i | \(0.297897\pi\) | |||||||
\(854\) | − | 9.75033e48i | − | 0.142638i | ||||||
\(855\) | 8.47294e48 | − | 3.92372e48i | 0.121510 | − | 0.0562697i | ||||
\(856\) | 4.29550e49 | 0.603893 | ||||||||
\(857\) | −2.55442e49 | − | 2.55442e49i | −0.352061 | − | 0.352061i | 0.508815 | − | 0.860876i | \(-0.330084\pi\) |
−0.860876 | + | 0.508815i | \(0.830084\pi\) | |||||||
\(858\) | 1.20021e48 | − | 1.20021e48i | 0.0162171 | − | 0.0162171i | ||||
\(859\) | 1.28561e49i | 0.170304i | 0.996368 | + | 0.0851520i | \(0.0271376\pi\) | ||||
−0.996368 | + | 0.0851520i | \(0.972862\pi\) | |||||||
\(860\) | −2.82171e49 | − | 1.03549e49i | −0.366470 | − | 0.134484i | ||||
\(861\) | 1.20195e50 | 1.53050 | ||||||||
\(862\) | −7.60307e49 | − | 7.60307e49i | −0.949217 | − | 0.949217i | ||||
\(863\) | −7.57613e49 | + | 7.57613e49i | −0.927393 | + | 0.927393i | −0.997537 | − | 0.0701438i | \(-0.977654\pi\) |
0.0701438 | + | 0.997537i | \(0.477654\pi\) | |||||||
\(864\) | 7.55575e49i | 0.906867i | ||||||||
\(865\) | 6.16976e45 | − | 1.68127e46i | 7.26097e−5 | − | 0.000197862i | ||||
\(866\) | 3.93280e49 | 0.453835 | ||||||||
\(867\) | 3.68918e49 | + | 3.68918e49i | 0.417450 | + | 0.417450i | ||||
\(868\) | 1.91240e49 | − | 1.91240e49i | 0.212199 | − | 0.212199i | ||||
\(869\) | 1.91122e49i | 0.207957i | ||||||||
\(870\) | 3.40658e49 | + | 7.35621e49i | 0.363489 | + | 0.784922i | ||||
\(871\) | 1.83130e49 | 0.191624 | ||||||||
\(872\) | −8.50460e49 | − | 8.50460e49i | −0.872717 | − | 0.872717i | ||||
\(873\) | −3.94409e49 | + | 3.94409e49i | −0.396922 | + | 0.396922i | ||||
\(874\) | 1.81866e49i | 0.179497i | ||||||||
\(875\) | 1.41897e50 | − | 8.04286e49i | 1.37353 | − | 0.778527i | ||||
\(876\) | 5.49070e49 | 0.521264 | ||||||||
\(877\) | 6.44344e49 | + | 6.44344e49i | 0.599963 | + | 0.599963i | 0.940303 | − | 0.340340i | \(-0.110542\pi\) |
−0.340340 | + | 0.940303i | \(0.610542\pi\) | |||||||
\(878\) | −8.77012e48 | + | 8.77012e48i | −0.0800938 | + | 0.0800938i | ||||
\(879\) | − | 1.46207e50i | − | 1.30966i | ||||||
\(880\) | 5.41044e48 | − | 2.50551e48i | 0.0475365 | − | 0.0220136i | ||||
\(881\) | −1.19713e50 | −1.03170 | −0.515848 | − | 0.856680i | \(-0.672523\pi\) | ||||
−0.515848 | + | 0.856680i | \(0.672523\pi\) | |||||||
\(882\) | −2.58069e49 | − | 2.58069e49i | −0.218158 | − | 0.218158i | ||||
\(883\) | −2.74430e49 | + | 2.74430e49i | −0.227562 | + | 0.227562i | −0.811674 | − | 0.584111i | \(-0.801443\pi\) |
0.584111 | + | 0.811674i | \(0.301443\pi\) | |||||||
\(884\) | − | 7.14310e48i | − | 0.0581030i | ||||||
\(885\) | −1.37052e50 | − | 5.02942e49i | −1.09358 | − | 0.401312i | ||||
\(886\) | 2.16031e49 | 0.169100 | ||||||||
\(887\) | −6.34355e49 | − | 6.34355e49i | −0.487114 | − | 0.487114i | 0.420280 | − | 0.907394i | \(-0.361932\pi\) |
−0.907394 | + | 0.420280i | \(0.861932\pi\) | |||||||
\(888\) | −1.27083e50 | + | 1.27083e50i | −0.957342 | + | 0.957342i | ||||
\(889\) | − | 4.14934e50i | − | 3.06654i | ||||||
\(890\) | −4.54047e49 | + | 1.23728e50i | −0.329208 | + | 0.897096i | ||||
\(891\) | −1.45247e49 | −0.103320 | ||||||||
\(892\) | −8.96471e49 | − | 8.96471e49i | −0.625653 | − | 0.625653i | ||||
\(893\) | −7.84261e49 | + | 7.84261e49i | −0.537014 | + | 0.537014i | ||||
\(894\) | − | 9.64491e48i | − | 0.0647978i | ||||||
\(895\) | 4.99470e49 | + | 1.07856e50i | 0.329244 | + | 0.710973i | ||||
\(896\) | 3.62711e49 | 0.234598 | ||||||||
\(897\) | 1.11017e49 | + | 1.11017e49i | 0.0704559 | + | 0.0704559i | ||||
\(898\) | 1.04061e50 | − | 1.04061e50i | 0.648021 | − | 0.648021i | ||||
\(899\) | − | 9.36527e49i | − | 0.572276i | ||||||
\(900\) | 1.40607e49 | − | 1.65778e49i | 0.0843109 | − | 0.0994041i | ||||
\(901\) | 1.26736e50 | 0.745727 | ||||||||
\(902\) | −1.66174e49 | − | 1.66174e49i | −0.0959516 | − | 0.0959516i | ||||
\(903\) | −1.40952e50 | + | 1.40952e50i | −0.798693 | + | 0.798693i | ||||
\(904\) | − | 7.93699e49i | − | 0.441360i | ||||||
\(905\) | 3.86339e49 | − | 1.78909e49i | 0.210835 | − | 0.0976354i | ||||
\(906\) | 4.34559e49 | 0.232739 | ||||||||
\(907\) | 2.10353e50 | + | 2.10353e50i | 1.10567 | + | 1.10567i | 0.993713 | + | 0.111956i | \(0.0357114\pi\) |
0.111956 | + | 0.993713i | \(0.464289\pi\) | |||||||
\(908\) | 4.25144e49 | − | 4.25144e49i | 0.219319 | − | 0.219319i | ||||
\(909\) | 1.01471e50i | 0.513754i | ||||||||
\(910\) | 4.98964e49 | + | 1.83106e49i | 0.247951 | + | 0.0909909i | ||||
\(911\) | −1.88897e50 | −0.921325 | −0.460662 | − | 0.887575i | \(-0.652388\pi\) | ||||
−0.460662 | + | 0.887575i | \(0.652388\pi\) | |||||||
\(912\) | −1.92530e49 | − | 1.92530e49i | −0.0921692 | − | 0.0921692i | ||||
\(913\) | 1.05682e49 | − | 1.05682e49i | 0.0496592 | − | 0.0496592i | ||||
\(914\) | 1.10948e50i | 0.511722i | ||||||||
\(915\) | 7.94545e48 | − | 2.16514e49i | 0.0359716 | − | 0.0980230i | ||||
\(916\) | 6.27912e49 | 0.279046 | ||||||||
\(917\) | −5.30688e48 | − | 5.30688e48i | −0.0231505 | − | 0.0231505i | ||||
\(918\) | 7.24355e49 | − | 7.24355e49i | 0.310188 | − | 0.310188i | ||||
\(919\) | 3.19012e50i | 1.34105i | 0.741889 | + | 0.670523i | \(0.233930\pi\) | ||||
−0.741889 | + | 0.670523i | \(0.766070\pi\) | |||||||
\(920\) | 5.62691e49 | + | 1.21508e50i | 0.232208 | + | 0.501433i | ||||
\(921\) | −9.49394e49 | −0.384621 | ||||||||
\(922\) | 1.33231e50 | + | 1.33231e50i | 0.529883 | + | 0.529883i | ||||
\(923\) | −5.95610e49 | + | 5.95610e49i | −0.232559 | + | 0.232559i | ||||
\(924\) | 2.61087e49i | 0.100083i | ||||||||
\(925\) | 3.94584e50 | − | 3.24174e49i | 1.48501 | − | 0.122002i | ||||
\(926\) | 1.54555e50 | 0.571080 | ||||||||
\(927\) | −2.97914e49 | − | 2.97914e49i | −0.108077 | − | 0.108077i | ||||
\(928\) | 2.30720e50 | − | 2.30720e50i | 0.821807 | − | 0.821807i | ||||
\(929\) | 2.61825e50i | 0.915681i | 0.889034 | + | 0.457841i | \(0.151377\pi\) | ||||
−0.889034 | + | 0.457841i | \(0.848623\pi\) | |||||||
\(930\) | −6.74943e49 | + | 3.12559e49i | −0.231770 | + | 0.107330i | ||||
\(931\) | −2.10294e50 | −0.709060 | ||||||||
\(932\) | 2.45552e49 | + | 2.45552e49i | 0.0812968 | + | 0.0812968i | ||||
\(933\) | −2.30543e50 | + | 2.30543e50i | −0.749487 | + | 0.749487i | ||||
\(934\) | − | 1.46926e50i | − | 0.469030i | ||||||
\(935\) | 2.66839e49 | + | 9.79224e48i | 0.0836474 | + | 0.0306962i | ||||
\(936\) | 2.24028e49 | 0.0689626 | ||||||||
\(937\) | −3.42945e50 | − | 3.42945e50i | −1.03670 | − | 1.03670i | −0.999301 | − | 0.0373952i | \(-0.988094\pi\) |
−0.0373952 | − | 0.999301i | \(-0.511906\pi\) | |||||||
\(938\) | 2.31590e50 | − | 2.31590e50i | 0.687497 | − | 0.687497i | ||||
\(939\) | 1.36764e50i | 0.398710i | ||||||||
\(940\) | −8.89533e49 | + | 2.42399e50i | −0.254676 | + | 0.693995i | ||||
\(941\) | −4.56648e50 | −1.28398 | −0.641989 | − | 0.766714i | \(-0.721891\pi\) | ||||
−0.641989 | + | 0.766714i | \(0.721891\pi\) | |||||||
\(942\) | −1.59802e50 | − | 1.59802e50i | −0.441284 | − | 0.441284i | ||||
\(943\) | 1.53707e50 | − | 1.53707e50i | 0.416865 | − | 0.416865i | ||||
\(944\) | − | 1.67110e50i | − | 0.445123i | ||||||
\(945\) | −2.75483e50 | − | 5.94881e50i | −0.720699 | − | 1.55629i | ||||
\(946\) | 3.89743e49 | 0.100145 | ||||||||
\(947\) | 2.44821e50 | + | 2.44821e50i | 0.617874 | + | 0.617874i | 0.944986 | − | 0.327112i | \(-0.106075\pi\) |
−0.327112 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(948\) | 1.43673e50 | − | 1.43673e50i | 0.356149 | − | 0.356149i | ||||
\(949\) | − | 1.24656e50i | − | 0.303521i | ||||||
\(950\) | 1.19242e49 | + | 1.45141e50i | 0.0285186 | + | 0.347128i | ||||
\(951\) | 2.19687e50 | 0.516102 | ||||||||
\(952\) | −2.85695e50 | − | 2.85695e50i | −0.659288 | − | 0.659288i | ||||
\(953\) | 4.71306e49 | − | 4.71306e49i | 0.106837 | − | 0.106837i | −0.651667 | − | 0.758505i | \(-0.725930\pi\) |
0.758505 | + | 0.651667i | \(0.225930\pi\) | |||||||
\(954\) | 1.25678e50i | 0.279859i | ||||||||
\(955\) | −1.36541e50 | + | 6.32306e49i | −0.298680 | + | 0.138315i | ||||
\(956\) | 2.32758e49 | 0.0500173 | ||||||||
\(957\) | 6.39289e49 | + | 6.39289e49i | 0.134957 | + | 0.134957i | ||||
\(958\) | −1.78060e50 | + | 1.78060e50i | −0.369277 | + | 0.369277i | ||||
\(959\) | 4.83819e50i | 0.985749i | ||||||||
\(960\) | −3.71973e50 | − | 1.36503e50i | −0.744561 | − | 0.273233i | ||||
\(961\) | −4.22580e50 | −0.831020 | ||||||||
\(962\) | 9.12260e49 | + | 9.12260e49i | 0.176255 | + | 0.176255i | ||||
\(963\) | −5.91396e49 | + | 5.91396e49i | −0.112262 | + | 0.112262i | ||||
\(964\) | − | 2.06632e50i | − | 0.385379i | ||||||
\(965\) | 1.20929e50 | − | 3.29532e50i | 0.221598 | − | 0.603856i | ||||
\(966\) | 2.80788e50 | 0.505555 | ||||||||
\(967\) | 5.66212e50 | + | 5.66212e50i | 1.00168 | + | 1.00168i | 0.999999 | + | 0.00168064i | \(0.000534965\pi\) |
0.00168064 | + | 0.999999i | \(0.499465\pi\) | |||||||
\(968\) | −4.24761e50 | + | 4.24761e50i | −0.738353 | + | 0.738353i | ||||
\(969\) | − | 1.29800e50i | − | 0.221703i | ||||||
\(970\) | −3.65565e50 | − | 7.89405e50i | −0.613543 | − | 1.32489i | ||||
\(971\) | 6.69164e50 | 1.10358 | 0.551792 | − | 0.833981i | \(-0.313944\pi\) | ||||
0.551792 | + | 0.833981i | \(0.313944\pi\) | |||||||
\(972\) | −1.09974e50 | − | 1.09974e50i | −0.178224 | − | 0.178224i | ||||
\(973\) | 8.93607e50 | − | 8.93607e50i | 1.42308 | − | 1.42308i | ||||
\(974\) | 1.57591e50i | 0.246621i | ||||||||
\(975\) | 9.58781e49 | + | 8.13202e49i | 0.147449 | + | 0.125061i | ||||
\(976\) | 2.64000e49 | 0.0398986 | ||||||||
\(977\) | −6.93643e50 | − | 6.93643e50i | −1.03022 | − | 1.03022i | −0.999529 | − | 0.0306880i | \(-0.990230\pi\) |
−0.0306880 | − | 0.999529i | \(-0.509770\pi\) | |||||||
\(978\) | 3.17951e50 | − | 3.17951e50i | 0.464088 | − | 0.464088i | ||||
\(979\) | 1.46984e50i | 0.210846i | ||||||||
\(980\) | −4.44249e50 | + | 2.05727e50i | −0.626301 | + | 0.290033i | ||||
\(981\) | 2.34179e50 | 0.324471 | ||||||||
\(982\) | 3.62939e50 | + | 3.62939e50i | 0.494241 | + | 0.494241i | ||||
\(983\) | 1.01850e50 | − | 1.01850e50i | 0.136318 | − | 0.136318i | −0.635655 | − | 0.771973i | \(-0.719270\pi\) |
0.771973 | + | 0.635655i | \(0.219270\pi\) | |||||||
\(984\) | 7.90158e50i | 1.03943i | ||||||||
\(985\) | −3.21646e50 | − | 1.18035e50i | −0.415875 | − | 0.152614i | ||||
\(986\) | −4.42374e50 | −0.562188 | ||||||||
\(987\) | 1.21085e51 | + | 1.21085e51i | 1.51251 | + | 1.51251i | ||||
\(988\) | 2.88608e49 | − | 2.88608e49i | 0.0354356 | − | 0.0354356i | ||||
\(989\) | 3.60503e50i | 0.435083i | ||||||||
\(990\) | −9.71050e48 | + | 2.64612e49i | −0.0115198 | + | 0.0313915i | ||||
\(991\) | −1.37291e51 | −1.60100 | −0.800498 | − | 0.599335i | \(-0.795432\pi\) | ||||
−0.800498 | + | 0.599335i | \(0.795432\pi\) | |||||||
\(992\) | 2.11689e50 | + | 2.11689e50i | 0.242661 | + | 0.242661i | ||||
\(993\) | −1.27230e50 | + | 1.27230e50i | −0.143368 | + | 0.143368i | ||||
\(994\) | 1.50644e51i | 1.66872i | ||||||||
\(995\) | 3.02819e48 | + | 6.53912e48i | 0.00329755 | + | 0.00712077i | ||||
\(996\) | −1.58890e50 | −0.170094 | ||||||||
\(997\) | 4.57054e49 | + | 4.57054e49i | 0.0481005 | + | 0.0481005i | 0.730748 | − | 0.682647i | \(-0.239172\pi\) |
−0.682647 | + | 0.730748i | \(0.739172\pi\) | |||||||
\(998\) | −6.40668e50 | + | 6.40668e50i | −0.662848 | + | 0.662848i | ||||
\(999\) | − | 1.59129e51i | − | 1.61859i |
(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 | 5.35.c.a.2.11 | ✓ | 32 | |
5.2 | odd | 4 | 25.35.c.b.18.6 | 32 | |||
5.3 | odd | 4 | inner | 5.35.c.a.3.11 | yes | 32 | |
5.4 | even | 2 | 25.35.c.b.7.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.35.c.a.2.11 | ✓ | 32 | 1.1 | even | 1 | trivial | |
5.35.c.a.3.11 | yes | 32 | 5.3 | odd | 4 | inner | |
25.35.c.b.7.6 | 32 | 5.4 | even | 2 | |||
25.35.c.b.18.6 | 32 | 5.2 | odd | 4 |