Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,67,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 67, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 67);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 67 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(82.7604085389\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + \cdots + 56\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{216}\cdot 3^{291}\cdot 5^{20}\cdot 7^{10}\cdot 11^{6}\cdot 13^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.17 | ||
Root | \(3.39530e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.67.b.b.2.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22231e10i | 1.42296i | 0.702709 | + | 0.711478i | \(0.251974\pi\) | ||||
−0.702709 | + | 0.711478i | \(0.748026\pi\) | |||||||
\(3\) | 1.27232e15 | + | 5.41150e15i | 0.228873 | + | 0.973456i | ||||
\(4\) | −7.56171e19 | −1.02480 | ||||||||
\(5\) | − | 1.11898e23i | − | 0.961197i | −0.876941 | − | 0.480599i | \(-0.840419\pi\) | ||
0.876941 | − | 0.480599i | \(-0.159581\pi\) | |||||||
\(6\) | −6.61453e25 | + | 1.55517e25i | −1.38519 | + | 0.325676i | ||||
\(7\) | −1.34063e28 | −1.73410 | −0.867051 | − | 0.498219i | \(-0.833988\pi\) | ||||
−0.867051 | + | 0.498219i | \(0.833988\pi\) | |||||||
\(8\) | − | 2.23699e28i | − | 0.0352935i | ||||||
\(9\) | −2.76656e31 | + | 1.37703e31i | −0.895234 | + | 0.445596i | ||||
\(10\) | 1.36774e33 | 1.36774 | ||||||||
\(11\) | − | 2.93013e34i | − | 1.26162i | −0.775938 | − | 0.630810i | \(-0.782723\pi\) | ||
0.775938 | − | 0.630810i | \(-0.217277\pi\) | |||||||
\(12\) | −9.62092e34 | − | 4.09202e35i | −0.234550 | − | 0.997601i | ||||
\(13\) | 3.87614e36 | 0.673394 | 0.336697 | − | 0.941613i | \(-0.390690\pi\) | ||||
0.336697 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(14\) | − | 1.63867e38i | − | 2.46755i | ||||||
\(15\) | 6.05537e38 | − | 1.42370e38i | 0.935683 | − | 0.219992i | ||||
\(16\) | −5.30613e39 | −0.974582 | ||||||||
\(17\) | 2.37940e40i | 0.591090i | 0.955329 | + | 0.295545i | \(0.0955012\pi\) | ||||
−0.955329 | + | 0.295545i | \(0.904499\pi\) | |||||||
\(18\) | −1.68316e41 | − | 3.38159e41i | −0.634064 | − | 1.27388i | ||||
\(19\) | −1.19889e42 | −0.758422 | −0.379211 | − | 0.925310i | \(-0.623804\pi\) | ||||
−0.379211 | + | 0.925310i | \(0.623804\pi\) | |||||||
\(20\) | 8.46141e42i | 0.985038i | ||||||||
\(21\) | −1.70571e43 | − | 7.25484e43i | −0.396890 | − | 1.68807i | ||||
\(22\) | 3.58153e44 | 1.79523 | ||||||||
\(23\) | − | 1.09383e45i | − | 1.26453i | −0.774751 | − | 0.632267i | \(-0.782125\pi\) | ||
0.774751 | − | 0.632267i | \(-0.217875\pi\) | |||||||
\(24\) | 1.21055e44 | − | 2.84617e43i | 0.0343566 | − | 0.00807773i | ||||
\(25\) | 1.03135e45 | 0.0761002 | ||||||||
\(26\) | 4.73785e46i | 0.958209i | ||||||||
\(27\) | −1.09718e47 | − | 1.32192e47i | −0.638663 | − | 0.769486i | ||||
\(28\) | 1.01375e48 | 1.77711 | ||||||||
\(29\) | 2.55829e48i | 1.40869i | 0.709856 | + | 0.704347i | \(0.248760\pi\) | ||||
−0.709856 | + | 0.704347i | \(0.751240\pi\) | |||||||
\(30\) | 1.74020e48 | + | 7.40153e48i | 0.313039 | + | 1.33144i | ||||
\(31\) | 1.47668e49 | 0.900223 | 0.450112 | − | 0.892972i | \(-0.351384\pi\) | ||||
0.450112 | + | 0.892972i | \(0.351384\pi\) | |||||||
\(32\) | − | 6.65079e49i | − | 1.42208i | ||||||
\(33\) | 1.58564e50 | − | 3.72806e49i | 1.22813 | − | 0.288751i | ||||
\(34\) | −2.90837e50 | −0.841095 | ||||||||
\(35\) | 1.50014e51i | 1.66681i | ||||||||
\(36\) | 2.09199e51 | − | 1.04127e51i | 0.917439 | − | 0.456648i | ||||
\(37\) | −5.97408e51 | −1.06075 | −0.530376 | − | 0.847762i | \(-0.677949\pi\) | ||||
−0.530376 | + | 0.847762i | \(0.677949\pi\) | |||||||
\(38\) | − | 1.46542e52i | − | 1.07920i | ||||||
\(39\) | 4.93169e51 | + | 2.09758e52i | 0.154122 | + | 0.655519i | ||||
\(40\) | −2.50315e51 | −0.0339240 | ||||||||
\(41\) | 4.97073e52i | 0.298231i | 0.988820 | + | 0.149115i | \(0.0476426\pi\) | ||||
−0.988820 | + | 0.149115i | \(0.952357\pi\) | |||||||
\(42\) | 8.86766e53 | − | 2.08491e53i | 2.40205 | − | 0.564756i | ||||
\(43\) | 1.15764e54 | 1.44249 | 0.721247 | − | 0.692678i | \(-0.243569\pi\) | ||||
0.721247 | + | 0.692678i | \(0.243569\pi\) | |||||||
\(44\) | 2.21568e54i | 1.29291i | ||||||||
\(45\) | 1.54087e54 | + | 3.09572e54i | 0.428306 | + | 0.860496i | ||||
\(46\) | 1.33700e55 | 1.79938 | ||||||||
\(47\) | 2.00509e54i | 0.132710i | 0.997796 | + | 0.0663552i | \(0.0211371\pi\) | ||||
−0.997796 | + | 0.0663552i | \(0.978863\pi\) | |||||||
\(48\) | −6.75109e54 | − | 2.87141e55i | −0.223056 | − | 0.948713i | ||||
\(49\) | 1.19962e56 | 2.00711 | ||||||||
\(50\) | 1.26063e55i | 0.108287i | ||||||||
\(51\) | −1.28761e56 | + | 3.02736e55i | −0.575400 | + | 0.135285i | ||||
\(52\) | −2.93103e56 | −0.690096 | ||||||||
\(53\) | 1.00051e57i | 1.25637i | 0.778065 | + | 0.628184i | \(0.216201\pi\) | ||||
−0.778065 | + | 0.628184i | \(0.783799\pi\) | |||||||
\(54\) | 1.61580e57 | − | 1.34109e57i | 1.09494 | − | 0.908790i | ||||
\(55\) | −3.27876e57 | −1.21267 | ||||||||
\(56\) | 2.99898e56i | 0.0612025i | ||||||||
\(57\) | −1.52537e57 | − | 6.48780e57i | −0.173582 | − | 0.738290i | ||||
\(58\) | −3.12703e58 | −2.00451 | ||||||||
\(59\) | − | 1.54437e58i | − | 0.563165i | −0.959537 | − | 0.281583i | \(-0.909141\pi\) | ||
0.959537 | − | 0.281583i | \(-0.0908594\pi\) | |||||||
\(60\) | −4.57889e58 | + | 1.07656e58i | −0.958891 | + | 0.225449i | ||||
\(61\) | 2.11015e58 | 0.256111 | 0.128056 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128056 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(62\) | 1.80496e59i | 1.28098i | ||||||||
\(63\) | 3.70894e59 | − | 1.84610e59i | 1.55243 | − | 0.772709i | ||||
\(64\) | 4.21410e59 | 1.04898 | ||||||||
\(65\) | − | 4.33733e59i | − | 0.647264i | ||||||
\(66\) | 4.55685e59 | + | 1.93814e60i | 0.410880 | + | 1.74758i | ||||
\(67\) | 7.76951e59 | 0.426506 | 0.213253 | − | 0.976997i | \(-0.431594\pi\) | ||||
0.213253 | + | 0.976997i | \(0.431594\pi\) | |||||||
\(68\) | − | 1.79924e60i | − | 0.605751i | ||||||
\(69\) | 5.91925e60 | − | 1.39170e60i | 1.23097 | − | 0.289418i | ||||
\(70\) | −1.83364e61 | −2.37180 | ||||||||
\(71\) | 1.19531e61i | 0.968174i | 0.875020 | + | 0.484087i | \(0.160848\pi\) | ||||
−0.875020 | + | 0.484087i | \(0.839152\pi\) | |||||||
\(72\) | 3.08041e59 | + | 6.18875e59i | 0.0157266 | + | 0.0315959i | ||||
\(73\) | −4.94610e61 | −1.60180 | −0.800900 | − | 0.598798i | \(-0.795645\pi\) | ||||
−0.800900 | + | 0.598798i | \(0.795645\pi\) | |||||||
\(74\) | − | 7.30217e61i | − | 1.50940i | ||||||
\(75\) | 1.31221e60 | + | 5.58115e60i | 0.0174173 | + | 0.0740802i | ||||
\(76\) | 9.06566e61 | 0.777233 | ||||||||
\(77\) | 3.92823e62i | 2.18778i | ||||||||
\(78\) | −2.56389e62 | + | 6.02806e61i | −0.932775 | + | 0.219308i | ||||
\(79\) | 3.63937e62 | 0.869626 | 0.434813 | − | 0.900521i | \(-0.356815\pi\) | ||||
0.434813 | + | 0.900521i | \(0.356815\pi\) | |||||||
\(80\) | 5.93746e62i | 0.936765i | ||||||||
\(81\) | 5.75761e62 | − | 7.61928e62i | 0.602888 | − | 0.797826i | ||||
\(82\) | −6.07577e62 | −0.424369 | ||||||||
\(83\) | − | 6.01832e62i | − | 0.281772i | −0.990026 | − | 0.140886i | \(-0.955005\pi\) | ||
0.990026 | − | 0.140886i | \(-0.0449952\pi\) | |||||||
\(84\) | 1.28981e63 | + | 5.48590e63i | 0.406734 | + | 1.72994i | ||||
\(85\) | 2.66251e63 | 0.568154 | ||||||||
\(86\) | 1.41499e64i | 2.05260i | ||||||||
\(87\) | −1.38442e64 | + | 3.25497e63i | −1.37130 | + | 0.322412i | ||||
\(88\) | −6.55467e62 | −0.0445269 | ||||||||
\(89\) | − | 3.58687e63i | − | 0.167820i | −0.996473 | − | 0.0839102i | \(-0.973259\pi\) | ||
0.996473 | − | 0.0839102i | \(-0.0267409\pi\) | |||||||
\(90\) | −3.78393e64 | + | 1.88342e64i | −1.22445 | + | 0.609460i | ||||
\(91\) | −5.19649e64 | −1.16773 | ||||||||
\(92\) | 8.27121e64i | 1.29590i | ||||||||
\(93\) | 1.87881e64 | + | 7.99105e64i | 0.206037 | + | 0.876328i | ||||
\(94\) | −2.45084e64 | −0.188841 | ||||||||
\(95\) | 1.34154e65i | 0.728993i | ||||||||
\(96\) | 3.59908e65 | − | 8.46194e64i | 1.38433 | − | 0.325476i | ||||
\(97\) | −2.58963e64 | −0.0707571 | −0.0353785 | − | 0.999374i | \(-0.511264\pi\) | ||||
−0.0353785 | + | 0.999374i | \(0.511264\pi\) | |||||||
\(98\) | 1.46630e66i | 2.85603i | ||||||||
\(99\) | 4.03489e65 | + | 8.10637e65i | 0.562173 | + | 1.12944i | ||||
\(100\) | −7.79877e64 | −0.0779877 | ||||||||
\(101\) | − | 1.64889e66i | − | 1.18737i | −0.804698 | − | 0.593684i | \(-0.797673\pi\) | ||
0.804698 | − | 0.593684i | \(-0.202327\pi\) | |||||||
\(102\) | −3.70038e65 | − | 1.57386e66i | −0.192504 | − | 0.818769i | ||||
\(103\) | 1.63871e65 | 0.0617836 | 0.0308918 | − | 0.999523i | \(-0.490165\pi\) | ||||
0.0308918 | + | 0.999523i | \(0.490165\pi\) | |||||||
\(104\) | − | 8.67089e64i | − | 0.0237664i | ||||||
\(105\) | −8.11803e66 | + | 1.90866e66i | −1.62257 | + | 0.381489i | ||||
\(106\) | −1.22293e67 | −1.78776 | ||||||||
\(107\) | − | 8.01513e66i | − | 0.859500i | −0.902948 | − | 0.429750i | \(-0.858602\pi\) | ||
0.902948 | − | 0.429750i | \(-0.141398\pi\) | |||||||
\(108\) | 8.29653e66 | + | 9.99597e66i | 0.654504 | + | 0.788572i | ||||
\(109\) | 3.05399e67 | 1.77743 | 0.888716 | − | 0.458458i | \(-0.151598\pi\) | ||||
0.888716 | + | 0.458458i | \(0.151598\pi\) | |||||||
\(110\) | − | 4.00766e67i | − | 1.72557i | ||||||
\(111\) | −7.60094e66 | − | 3.23287e67i | −0.242778 | − | 1.03260i | ||||
\(112\) | 7.11357e67 | 1.69002 | ||||||||
\(113\) | 1.94618e67i | 0.344822i | 0.985025 | + | 0.172411i | \(0.0551557\pi\) | ||||
−0.985025 | + | 0.172411i | \(0.944844\pi\) | |||||||
\(114\) | 7.93010e67 | − | 1.86448e67i | 1.05055 | − | 0.247000i | ||||
\(115\) | −1.22397e68 | −1.21547 | ||||||||
\(116\) | − | 1.93451e68i | − | 1.44363i | ||||||
\(117\) | −1.07236e68 | + | 5.33757e67i | −0.602845 | + | 0.300062i | ||||
\(118\) | 1.88770e68 | 0.801360 | ||||||||
\(119\) | − | 3.18991e68i | − | 1.02501i | ||||||
\(120\) | −3.18480e66 | − | 1.35458e67i | −0.00776429 | − | 0.0330235i | ||||
\(121\) | −3.19159e68 | −0.591684 | ||||||||
\(122\) | 2.57926e68i | 0.364435i | ||||||||
\(123\) | −2.68991e68 | + | 6.32436e67i | −0.290315 | + | 0.0682571i | ||||
\(124\) | −1.11662e69 | −0.922551 | ||||||||
\(125\) | − | 1.63191e69i | − | 1.03434i | ||||||
\(126\) | 2.25650e69 | + | 4.53347e69i | 1.09953 | + | 2.20904i | ||||
\(127\) | −2.01001e69 | −0.754528 | −0.377264 | − | 0.926106i | \(-0.623135\pi\) | ||||
−0.377264 | + | 0.926106i | \(0.623135\pi\) | |||||||
\(128\) | 2.43512e68i | 0.0705652i | ||||||||
\(129\) | 1.47289e69 | + | 6.26456e69i | 0.330148 | + | 1.40420i | ||||
\(130\) | 5.30156e69 | 0.921028 | ||||||||
\(131\) | − | 5.66022e68i | − | 0.0763625i | −0.999271 | − | 0.0381813i | \(-0.987844\pi\) | ||
0.999271 | − | 0.0381813i | \(-0.0121564\pi\) | |||||||
\(132\) | −1.19902e70 | + | 2.81905e69i | −1.25859 | + | 0.295913i | ||||
\(133\) | 1.60727e70 | 1.31518 | ||||||||
\(134\) | 9.49674e69i | 0.606899i | ||||||||
\(135\) | −1.47920e70 | + | 1.22772e70i | −0.739628 | + | 0.613881i | ||||
\(136\) | 5.32270e68 | 0.0208616 | ||||||||
\(137\) | − | 3.11806e70i | − | 0.959635i | −0.877368 | − | 0.479817i | \(-0.840703\pi\) | ||
0.877368 | − | 0.479817i | \(-0.159297\pi\) | |||||||
\(138\) | 1.70109e70 | + | 7.23516e70i | 0.411829 | + | 1.75161i | ||||
\(139\) | −6.89209e70 | −1.31481 | −0.657404 | − | 0.753538i | \(-0.728345\pi\) | ||||
−0.657404 | + | 0.753538i | \(0.728345\pi\) | |||||||
\(140\) | − | 1.13436e71i | − | 1.70816i | ||||||
\(141\) | −1.08506e70 | + | 2.55112e69i | −0.129188 | + | 0.0303739i | ||||
\(142\) | −1.46103e71 | −1.37767 | ||||||||
\(143\) | − | 1.13576e71i | − | 0.849567i | ||||||
\(144\) | 1.46797e71 | − | 7.30671e70i | 0.872479 | − | 0.434270i | ||||
\(145\) | 2.86268e71 | 1.35403 | ||||||||
\(146\) | − | 6.04567e71i | − | 2.27929i | ||||||
\(147\) | 1.52629e71 | + | 6.49172e71i | 0.459374 | + | 1.95383i | ||||
\(148\) | 4.51743e71 | 1.08706 | ||||||||
\(149\) | − | 2.05968e71i | − | 0.396874i | −0.980114 | − | 0.198437i | \(-0.936413\pi\) | ||
0.980114 | − | 0.198437i | \(-0.0635866\pi\) | |||||||
\(150\) | −6.82190e70 | + | 1.60392e70i | −0.105413 | + | 0.0247840i | ||||
\(151\) | 8.60865e71 | 1.06831 | 0.534153 | − | 0.845388i | \(-0.320631\pi\) | ||||
0.534153 | + | 0.845388i | \(0.320631\pi\) | |||||||
\(152\) | 2.68190e70i | 0.0267673i | ||||||||
\(153\) | −3.27652e71 | − | 6.58275e71i | −0.263387 | − | 0.529164i | ||||
\(154\) | −4.80152e72 | −3.11311 | ||||||||
\(155\) | − | 1.65238e72i | − | 0.865292i | ||||||
\(156\) | −3.72920e71 | − | 1.58613e72i | −0.157944 | − | 0.671778i | ||||
\(157\) | 4.73363e72 | 1.62370 | 0.811850 | − | 0.583866i | \(-0.198461\pi\) | ||||
0.811850 | + | 0.583866i | \(0.198461\pi\) | |||||||
\(158\) | 4.44844e72i | 1.23744i | ||||||||
\(159\) | −5.41425e72 | + | 1.27297e72i | −1.22302 | + | 0.287549i | ||||
\(160\) | −7.44211e72 | −1.36690 | ||||||||
\(161\) | 1.46642e73i | 2.19283i | ||||||||
\(162\) | 9.31311e72 | + | 7.03758e72i | 1.13527 | + | 0.857883i | ||||
\(163\) | 1.63451e73 | 1.62629 | 0.813145 | − | 0.582062i | \(-0.197754\pi\) | ||||
0.813145 | + | 0.582062i | \(0.197754\pi\) | |||||||
\(164\) | − | 3.75872e72i | − | 0.305628i | ||||||
\(165\) | −4.17163e72 | − | 1.77430e73i | −0.277547 | − | 1.18048i | ||||
\(166\) | 7.35626e72 | 0.400950 | ||||||||
\(167\) | 3.15012e73i | 1.40826i | 0.710071 | + | 0.704131i | \(0.248663\pi\) | ||||
−0.710071 | + | 0.704131i | \(0.751337\pi\) | |||||||
\(168\) | −1.62290e72 | + | 3.81566e71i | −0.0595779 | + | 0.0140076i | ||||
\(169\) | −1.81086e73 | −0.546541 | ||||||||
\(170\) | 3.25441e73i | 0.808458i | ||||||||
\(171\) | 3.31680e73 | − | 1.65091e73i | 0.678965 | − | 0.337950i | ||||
\(172\) | −8.75373e73 | −1.47827 | ||||||||
\(173\) | − | 7.33202e73i | − | 1.02259i | −0.859405 | − | 0.511296i | \(-0.829166\pi\) | ||
0.859405 | − | 0.511296i | \(-0.170834\pi\) | |||||||
\(174\) | −3.97858e73 | − | 1.69219e74i | −0.458778 | − | 1.95130i | ||||
\(175\) | −1.38266e73 | −0.131965 | ||||||||
\(176\) | 1.55477e74i | 1.22955i | ||||||||
\(177\) | 8.35738e73 | − | 1.96494e73i | 0.548217 | − | 0.128894i | ||||
\(178\) | 4.38426e73 | 0.238801 | ||||||||
\(179\) | − | 8.52176e73i | − | 0.385815i | −0.981217 | − | 0.192908i | \(-0.938208\pi\) | ||
0.981217 | − | 0.192908i | \(-0.0617918\pi\) | |||||||
\(180\) | −1.16516e74 | − | 2.34090e74i | −0.438929 | − | 0.881839i | ||||
\(181\) | 5.82996e74 | 1.82925 | 0.914625 | − | 0.404304i | \(-0.132486\pi\) | ||||
0.914625 | + | 0.404304i | \(0.132486\pi\) | |||||||
\(182\) | − | 6.35171e74i | − | 1.66163i | ||||||
\(183\) | 2.68479e73 | + | 1.14191e74i | 0.0586170 | + | 0.249313i | ||||
\(184\) | −2.44688e73 | −0.0446298 | ||||||||
\(185\) | 6.68488e74i | 1.01959i | ||||||||
\(186\) | −9.76754e74 | + | 2.29649e74i | −1.24698 | + | 0.293182i | ||||
\(187\) | 6.97196e74 | 0.745731 | ||||||||
\(188\) | − | 1.51619e74i | − | 0.136002i | ||||||
\(189\) | 1.47091e75 | + | 1.77221e75i | 1.10751 | + | 1.33437i | ||||
\(190\) | −1.63977e75 | −1.03732 | ||||||||
\(191\) | − | 2.33048e75i | − | 1.23978i | −0.784688 | − | 0.619891i | \(-0.787177\pi\) | ||
0.784688 | − | 0.619891i | \(-0.212823\pi\) | |||||||
\(192\) | 5.36168e74 | + | 2.28046e75i | 0.240082 | + | 1.02113i | ||||
\(193\) | −2.03031e75 | −0.765899 | −0.382949 | − | 0.923769i | \(-0.625092\pi\) | ||||
−0.382949 | + | 0.923769i | \(0.625092\pi\) | |||||||
\(194\) | − | 3.16532e74i | − | 0.100684i | ||||||
\(195\) | 2.34715e75 | − | 5.51847e74i | 0.630083 | − | 0.148141i | ||||
\(196\) | −9.07114e75 | −2.05689 | ||||||||
\(197\) | 8.50392e75i | 1.63017i | 0.579340 | + | 0.815086i | \(0.303310\pi\) | ||||
−0.579340 | + | 0.815086i | \(0.696690\pi\) | |||||||
\(198\) | −9.90849e75 | + | 4.93188e75i | −1.60715 | + | 0.799947i | ||||
\(199\) | 1.04884e76 | 1.44065 | 0.720326 | − | 0.693636i | \(-0.243992\pi\) | ||||
0.720326 | + | 0.693636i | \(0.243992\pi\) | |||||||
\(200\) | − | 2.30712e73i | − | 0.00268584i | ||||||
\(201\) | 9.88530e74 | + | 4.20447e75i | 0.0976158 | + | 0.415185i | ||||
\(202\) | 2.01545e76 | 1.68957 | ||||||||
\(203\) | − | 3.42973e76i | − | 2.44282i | ||||||
\(204\) | 9.73657e75 | − | 2.28920e75i | 0.589672 | − | 0.138640i | ||||
\(205\) | 5.56215e75 | 0.286659 | ||||||||
\(206\) | 2.00301e75i | 0.0879154i | ||||||||
\(207\) | 1.50624e76 | + | 3.02614e76i | 0.563471 | + | 1.13205i | ||||
\(208\) | −2.05673e76 | −0.656277 | ||||||||
\(209\) | 3.51291e76i | 0.956840i | ||||||||
\(210\) | −2.33298e76 | − | 9.92274e76i | −0.542842 | − | 2.30885i | ||||
\(211\) | −2.83385e76 | −0.563709 | −0.281855 | − | 0.959457i | \(-0.590950\pi\) | ||||
−0.281855 | + | 0.959457i | \(0.590950\pi\) | |||||||
\(212\) | − | 7.56555e76i | − | 1.28753i | ||||||
\(213\) | −6.46840e76 | + | 1.52081e76i | −0.942475 | + | 0.221589i | ||||
\(214\) | 9.79698e76 | 1.22303 | ||||||||
\(215\) | − | 1.29537e77i | − | 1.38652i | ||||||
\(216\) | −2.95712e75 | + | 2.45437e75i | −0.0271578 | + | 0.0225406i | ||||
\(217\) | −1.97969e77 | −1.56108 | ||||||||
\(218\) | 3.73292e77i | 2.52921i | ||||||||
\(219\) | −6.29302e76 | − | 2.67658e77i | −0.366609 | − | 1.55928i | ||||
\(220\) | 2.47930e77 | 1.24274 | ||||||||
\(221\) | 9.22291e76i | 0.398036i | ||||||||
\(222\) | 3.95157e77 | − | 9.29070e76i | 1.46934 | − | 0.345462i | ||||
\(223\) | 2.30583e77 | 0.739209 | 0.369605 | − | 0.929189i | \(-0.379493\pi\) | ||||
0.369605 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(224\) | 8.91627e77i | 2.46603i | ||||||||
\(225\) | −2.85329e76 | + | 1.42020e76i | −0.0681275 | + | 0.0339099i | ||||
\(226\) | −2.37884e77 | −0.490666 | ||||||||
\(227\) | 3.50513e77i | 0.624958i | 0.949925 | + | 0.312479i | \(0.101159\pi\) | ||||
−0.949925 | + | 0.312479i | \(0.898841\pi\) | |||||||
\(228\) | 1.15344e77 | + | 4.90589e77i | 0.177888 | + | 0.756602i | ||||
\(229\) | −4.45168e77 | −0.594228 | −0.297114 | − | 0.954842i | \(-0.596024\pi\) | ||||
−0.297114 | + | 0.954842i | \(0.596024\pi\) | |||||||
\(230\) | − | 1.49607e78i | − | 1.72955i | ||||||
\(231\) | −2.12576e78 | + | 4.99797e77i | −2.12971 | + | 0.500724i | ||||
\(232\) | 5.72287e76 | 0.0497177 | ||||||||
\(233\) | − | 9.03528e76i | − | 0.0681077i | −0.999420 | − | 0.0340539i | \(-0.989158\pi\) | ||
0.999420 | − | 0.0340539i | \(-0.0108418\pi\) | |||||||
\(234\) | −6.52417e77 | − | 1.31075e78i | −0.426974 | − | 0.857822i | ||||
\(235\) | 2.24366e77 | 0.127561 | ||||||||
\(236\) | 1.16781e78i | 0.577134i | ||||||||
\(237\) | 4.63045e77 | + | 1.96945e78i | 0.199034 | + | 0.846543i | ||||
\(238\) | 3.89906e78 | 1.45854 | ||||||||
\(239\) | − | 2.90634e78i | − | 0.946706i | −0.880873 | − | 0.473353i | \(-0.843044\pi\) | ||
0.880873 | − | 0.473353i | \(-0.156956\pi\) | |||||||
\(240\) | −3.21306e78 | + | 7.55434e77i | −0.911900 | + | 0.214400i | ||||
\(241\) | 5.13136e78 | 1.26961 | 0.634804 | − | 0.772673i | \(-0.281081\pi\) | ||||
0.634804 | + | 0.772673i | \(0.281081\pi\) | |||||||
\(242\) | − | 3.90111e78i | − | 0.841940i | ||||||
\(243\) | 4.85572e78 | + | 2.14632e78i | 0.914633 | + | 0.404284i | ||||
\(244\) | −1.59563e78 | −0.262464 | ||||||||
\(245\) | − | 1.34235e79i | − | 1.92923i | ||||||
\(246\) | −7.73032e77 | − | 3.28790e78i | −0.0971268 | − | 0.413105i | ||||
\(247\) | −4.64707e78 | −0.510716 | ||||||||
\(248\) | − | 3.30331e77i | − | 0.0317720i | ||||||
\(249\) | 3.25682e78 | − | 7.65723e77i | 0.274293 | − | 0.0644902i | ||||
\(250\) | 1.99470e79 | 1.47183 | ||||||||
\(251\) | 1.41302e79i | 0.913937i | 0.889483 | + | 0.456969i | \(0.151065\pi\) | ||||
−0.889483 | + | 0.456969i | \(0.848935\pi\) | |||||||
\(252\) | −2.80459e79 | + | 1.39596e79i | −1.59093 | + | 0.791875i | ||||
\(253\) | −3.20506e79 | −1.59536 | ||||||||
\(254\) | − | 2.45686e79i | − | 1.07366i | ||||||
\(255\) | 3.38756e78 | + | 1.44082e79i | 0.130035 | + | 0.553073i | ||||
\(256\) | 2.81181e79 | 0.948564 | ||||||||
\(257\) | 2.72517e79i | 0.808352i | 0.914681 | + | 0.404176i | \(0.132442\pi\) | ||||
−0.914681 | + | 0.404176i | \(0.867558\pi\) | |||||||
\(258\) | −7.65723e79 | + | 1.80032e79i | −1.99812 | + | 0.469786i | ||||
\(259\) | 8.00905e79 | 1.83945 | ||||||||
\(260\) | 3.27976e79i | 0.663318i | ||||||||
\(261\) | −3.52285e79 | − | 7.07766e79i | −0.627708 | − | 1.26111i | ||||
\(262\) | 6.91854e78 | 0.108660 | ||||||||
\(263\) | 6.05932e79i | 0.839236i | 0.907701 | + | 0.419618i | \(0.137836\pi\) | ||||
−0.907701 | + | 0.419618i | \(0.862164\pi\) | |||||||
\(264\) | −8.33964e77 | − | 3.54706e78i | −0.0101910 | − | 0.0433450i | ||||
\(265\) | 1.11955e80 | 1.20762 | ||||||||
\(266\) | 1.96458e80i | 1.87144i | ||||||||
\(267\) | 1.94103e79 | − | 4.56364e78i | 0.163366 | − | 0.0384096i | ||||
\(268\) | −5.87508e79 | −0.437084 | ||||||||
\(269\) | 1.65958e79i | 0.109188i | 0.998509 | + | 0.0545939i | \(0.0173864\pi\) | ||||
−0.998509 | + | 0.0545939i | \(0.982614\pi\) | |||||||
\(270\) | −1.50065e80 | − | 1.80804e80i | −0.873526 | − | 1.05246i | ||||
\(271\) | 1.68420e80 | 0.867773 | 0.433887 | − | 0.900967i | \(-0.357142\pi\) | ||||
0.433887 | + | 0.900967i | \(0.357142\pi\) | |||||||
\(272\) | − | 1.26254e80i | − | 0.576066i | ||||||
\(273\) | −6.61159e79 | − | 2.81208e80i | −0.267263 | − | 1.13674i | ||||
\(274\) | 3.81124e80 | 1.36552 | ||||||||
\(275\) | − | 3.02199e79i | − | 0.0960095i | ||||||
\(276\) | −4.47597e80 | + | 1.05236e80i | −1.26150 | + | 0.296596i | ||||
\(277\) | −1.61975e80 | −0.405150 | −0.202575 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202575 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(278\) | − | 8.42426e80i | − | 1.87091i | ||||||
\(279\) | −4.08532e80 | + | 2.03344e80i | −0.805911 | + | 0.401136i | ||||
\(280\) | 3.35580e79 | 0.0588276 | ||||||||
\(281\) | 4.07271e80i | 0.634710i | 0.948307 | + | 0.317355i | \(0.102795\pi\) | ||||
−0.948307 | + | 0.317355i | \(0.897205\pi\) | |||||||
\(282\) | −3.11826e79 | − | 1.32628e80i | −0.0432207 | − | 0.183829i | ||||
\(283\) | 6.34627e80 | 0.782647 | 0.391323 | − | 0.920253i | \(-0.372017\pi\) | ||||
0.391323 | + | 0.920253i | \(0.372017\pi\) | |||||||
\(284\) | − | 9.03856e80i | − | 0.992188i | ||||||
\(285\) | −7.25972e80 | + | 1.70686e80i | −0.709642 | + | 0.166847i | ||||
\(286\) | 1.38825e81 | 1.20890 | ||||||||
\(287\) | − | 6.66392e80i | − | 0.517163i | ||||||
\(288\) | 9.15836e80 | + | 1.83998e81i | 0.633674 | + | 1.27309i | ||||
\(289\) | 1.05427e81 | 0.650612 | ||||||||
\(290\) | 3.49908e81i | 1.92673i | ||||||||
\(291\) | −3.29483e79 | − | 1.40138e80i | −0.0161944 | − | 0.0688789i | ||||
\(292\) | 3.74010e81 | 1.64153 | ||||||||
\(293\) | − | 1.98609e81i | − | 0.778695i | −0.921091 | − | 0.389347i | \(-0.872701\pi\) | ||
0.921091 | − | 0.389347i | \(-0.127299\pi\) | |||||||
\(294\) | −7.93489e81 | + | 1.86560e81i | −2.78022 | + | 0.653669i | ||||
\(295\) | −1.72812e81 | −0.541313 | ||||||||
\(296\) | 1.33639e80i | 0.0374376i | ||||||||
\(297\) | −3.87340e81 | + | 3.21487e81i | −0.970799 | + | 0.805750i | ||||
\(298\) | 2.51757e81 | 0.564735 | ||||||||
\(299\) | − | 4.23983e81i | − | 0.851529i | ||||||
\(300\) | −9.92253e79 | − | 4.22031e80i | −0.0178493 | − | 0.0759176i | ||||
\(301\) | −1.55197e82 | −2.50143 | ||||||||
\(302\) | 1.05224e82i | 1.52015i | ||||||||
\(303\) | 8.92296e81 | − | 2.09791e81i | 1.15585 | − | 0.271757i | ||||
\(304\) | 6.36147e81 | 0.739144 | ||||||||
\(305\) | − | 2.36122e81i | − | 0.246174i | ||||||
\(306\) | 8.04616e81 | − | 4.00492e81i | 0.752977 | − | 0.374789i | ||||
\(307\) | 1.04478e82 | 0.877928 | 0.438964 | − | 0.898505i | \(-0.355346\pi\) | ||||
0.438964 | + | 0.898505i | \(0.355346\pi\) | |||||||
\(308\) | − | 2.97042e82i | − | 2.24204i | ||||||
\(309\) | 2.08496e80 | + | 8.86788e80i | 0.0141406 | + | 0.0601437i | ||||
\(310\) | 2.01971e82 | 1.23127 | ||||||||
\(311\) | 8.64391e81i | 0.473824i | 0.971531 | + | 0.236912i | \(0.0761354\pi\) | ||||
−0.971531 | + | 0.236912i | \(0.923865\pi\) | |||||||
\(312\) | 4.69225e80 | − | 1.10321e80i | 0.0231355 | − | 0.00543949i | ||||
\(313\) | −2.19377e81 | −0.0973258 | −0.0486629 | − | 0.998815i | \(-0.515496\pi\) | ||||
−0.0486629 | + | 0.998815i | \(0.515496\pi\) | |||||||
\(314\) | 5.78596e82i | 2.31045i | ||||||||
\(315\) | −2.06575e82 | − | 4.15023e82i | −0.742726 | − | 1.49219i | ||||
\(316\) | −2.75199e82 | −0.891195 | ||||||||
\(317\) | − | 3.95328e81i | − | 0.115346i | −0.998336 | − | 0.0576730i | \(-0.981632\pi\) | ||
0.998336 | − | 0.0576730i | \(-0.0183681\pi\) | |||||||
\(318\) | −1.55596e82 | − | 6.61789e82i | −0.409169 | − | 1.74030i | ||||
\(319\) | 7.49614e82 | 1.77724 | ||||||||
\(320\) | − | 4.71549e82i | − | 1.00827i | ||||||
\(321\) | 4.33739e82 | − | 1.01978e82i | 0.836686 | − | 0.196717i | ||||
\(322\) | −1.79242e83 | −3.12030 | ||||||||
\(323\) | − | 2.85264e82i | − | 0.448296i | ||||||
\(324\) | −4.35374e82 | + | 5.76148e82i | −0.617842 | + | 0.817614i | ||||
\(325\) | 3.99766e81 | 0.0512454 | ||||||||
\(326\) | 1.99788e83i | 2.31414i | ||||||||
\(327\) | 3.88565e82 | + | 1.65267e83i | 0.406807 | + | 1.73025i | ||||
\(328\) | 1.11195e81 | 0.0105256 | ||||||||
\(329\) | − | 2.68809e82i | − | 0.230134i | ||||||
\(330\) | 2.16875e83 | − | 5.09903e82i | 1.67977 | − | 0.394936i | ||||
\(331\) | 5.80049e82 | 0.406575 | 0.203288 | − | 0.979119i | \(-0.434837\pi\) | ||||
0.203288 | + | 0.979119i | \(0.434837\pi\) | |||||||
\(332\) | 4.55088e82i | 0.288761i | ||||||||
\(333\) | 1.65276e83 | − | 8.22650e82i | 0.949622 | − | 0.472667i | ||||
\(334\) | −3.85042e83 | −2.00389 | ||||||||
\(335\) | − | 8.69393e82i | − | 0.409956i | ||||||
\(336\) | 9.05074e82 | + | 3.84951e83i | 0.386801 | + | 1.64517i | ||||
\(337\) | 1.39279e83 | 0.539633 | 0.269816 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269816 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(338\) | − | 2.21343e83i | − | 0.777704i | ||||||
\(339\) | −1.05318e83 | + | 2.47617e82i | −0.335669 | + | 0.0789205i | ||||
\(340\) | −2.01331e83 | −0.582246 | ||||||||
\(341\) | − | 4.32686e83i | − | 1.13574i | ||||||
\(342\) | 2.01793e83 | + | 4.05415e83i | 0.480888 | + | 0.966137i | ||||
\(343\) | −8.06971e83 | −1.74643 | ||||||||
\(344\) | − | 2.58962e82i | − | 0.0509106i | ||||||
\(345\) | −1.55728e83 | − | 6.62353e83i | −0.278188 | − | 1.18320i | ||||
\(346\) | 8.96200e83 | 1.45510 | ||||||||
\(347\) | − | 1.03739e82i | − | 0.0153133i | −0.999971 | − | 0.00765665i | \(-0.997563\pi\) | ||
0.999971 | − | 0.00765665i | \(-0.00243721\pi\) | |||||||
\(348\) | 1.04686e84 | − | 2.46131e83i | 1.40531 | − | 0.330409i | ||||
\(349\) | −3.78947e83 | −0.462742 | −0.231371 | − | 0.972866i | \(-0.574321\pi\) | ||||
−0.231371 | + | 0.972866i | \(0.574321\pi\) | |||||||
\(350\) | − | 1.69004e83i | − | 0.187781i | ||||||
\(351\) | −4.25281e83 | − | 5.12395e83i | −0.430072 | − | 0.518167i | ||||
\(352\) | −1.94877e84 | −1.79412 | ||||||||
\(353\) | − | 1.31899e84i | − | 1.10580i | −0.833248 | − | 0.552900i | \(-0.813521\pi\) | ||
0.833248 | − | 0.552900i | \(-0.186479\pi\) | |||||||
\(354\) | 2.40176e83 | + | 1.02153e84i | 0.183410 | + | 0.780088i | ||||
\(355\) | 1.33752e84 | 0.930606 | ||||||||
\(356\) | 2.71228e83i | 0.171983i | ||||||||
\(357\) | 1.72622e84 | − | 4.05858e83i | 0.997803 | − | 0.234598i | ||||
\(358\) | 1.04162e84 | 0.548998 | ||||||||
\(359\) | − | 1.63953e84i | − | 0.788137i | −0.919081 | − | 0.394069i | \(-0.871067\pi\) | ||
0.919081 | − | 0.394069i | \(-0.128933\pi\) | |||||||
\(360\) | 6.92510e82 | − | 3.44692e82i | 0.0303699 | − | 0.0151164i | ||||
\(361\) | −1.06150e84 | −0.424797 | ||||||||
\(362\) | 7.12602e84i | 2.60294i | ||||||||
\(363\) | −4.06072e83 | − | 1.72713e84i | −0.135421 | − | 0.575978i | ||||
\(364\) | 3.92943e84 | 1.19670 | ||||||||
\(365\) | 5.53459e84i | 1.53965i | ||||||||
\(366\) | −1.39577e84 | + | 3.28164e83i | −0.354762 | + | 0.0834094i | ||||
\(367\) | −5.86884e84 | −1.36324 | −0.681620 | − | 0.731706i | \(-0.738724\pi\) | ||||
−0.681620 | + | 0.731706i | \(0.738724\pi\) | |||||||
\(368\) | 5.80399e84i | 1.23239i | ||||||||
\(369\) | −6.84485e83 | − | 1.37518e84i | −0.132891 | − | 0.266987i | ||||
\(370\) | −8.17099e84 | −1.45083 | ||||||||
\(371\) | − | 1.34131e85i | − | 2.17867i | ||||||
\(372\) | −1.42070e84 | − | 6.04260e84i | −0.211147 | − | 0.898063i | ||||
\(373\) | 1.59521e84 | 0.216983 | 0.108492 | − | 0.994097i | \(-0.465398\pi\) | ||||
0.108492 | + | 0.994097i | \(0.465398\pi\) | |||||||
\(374\) | 8.52190e84i | 1.06114i | ||||||||
\(375\) | 8.83107e84 | − | 2.07631e84i | 1.00689 | − | 0.236734i | ||||
\(376\) | 4.48537e82 | 0.00468381 | ||||||||
\(377\) | 9.91631e84i | 0.948605i | ||||||||
\(378\) | −2.16619e85 | + | 1.79791e85i | −1.89875 | + | 1.57593i | ||||
\(379\) | 1.29573e85 | 1.04093 | 0.520463 | − | 0.853884i | \(-0.325759\pi\) | ||||
0.520463 | + | 0.853884i | \(0.325759\pi\) | |||||||
\(380\) | − | 1.01443e85i | − | 0.747074i | ||||||
\(381\) | −2.55738e84 | − | 1.08772e85i | −0.172691 | − | 0.734500i | ||||
\(382\) | 2.84857e85 | 1.76415 | ||||||||
\(383\) | − | 1.99600e85i | − | 1.13397i | −0.823730 | − | 0.566983i | \(-0.808111\pi\) | ||
0.823730 | − | 0.566983i | \(-0.191889\pi\) | |||||||
\(384\) | −1.31776e84 | + | 3.09825e83i | −0.0686921 | + | 0.0161505i | ||||
\(385\) | 4.39562e85 | 2.10289 | ||||||||
\(386\) | − | 2.48167e85i | − | 1.08984i | ||||||
\(387\) | −3.20267e85 | + | 1.59411e85i | −1.29137 | + | 0.642769i | ||||
\(388\) | 1.95820e84 | 0.0725120 | ||||||||
\(389\) | − | 4.04352e85i | − | 1.37538i | −0.726004 | − | 0.687691i | \(-0.758625\pi\) | ||
0.726004 | − | 0.687691i | \(-0.241375\pi\) | |||||||
\(390\) | 6.74528e84 | + | 2.86894e85i | 0.210799 | + | 0.896581i | ||||
\(391\) | 2.60266e85 | 0.747453 | ||||||||
\(392\) | − | 2.68353e84i | − | 0.0708379i | ||||||
\(393\) | 3.06303e84 | − | 7.20161e83i | 0.0743356 | − | 0.0174773i | ||||
\(394\) | −1.03944e86 | −2.31966 | ||||||||
\(395\) | − | 4.07239e85i | − | 0.835882i | ||||||
\(396\) | −3.05106e85 | − | 6.12980e85i | −0.576116 | − | 1.15746i | ||||
\(397\) | −4.80321e85 | −0.834536 | −0.417268 | − | 0.908784i | \(-0.637012\pi\) | ||||
−0.417268 | + | 0.908784i | \(0.637012\pi\) | |||||||
\(398\) | 1.28201e86i | 2.04998i | ||||||||
\(399\) | 2.04497e85 | + | 8.69776e85i | 0.301010 | + | 1.28027i | ||||
\(400\) | −5.47247e84 | −0.0741659 | ||||||||
\(401\) | − | 1.05588e86i | − | 1.31780i | −0.752230 | − | 0.658901i | \(-0.771022\pi\) | ||
0.752230 | − | 0.658901i | \(-0.228978\pi\) | |||||||
\(402\) | −5.13916e85 | + | 1.20829e85i | −0.590789 | + | 0.138903i | ||||
\(403\) | 5.72382e85 | 0.606205 | ||||||||
\(404\) | 1.24684e86i | 1.21682i | ||||||||
\(405\) | −8.52582e85 | − | 6.44266e85i | −0.766868 | − | 0.579494i | ||||
\(406\) | 4.19220e86 | 3.47602 | ||||||||
\(407\) | 1.75048e86i | 1.33827i | ||||||||
\(408\) | 6.77218e83 | + | 2.88038e84i | 0.00477467 | + | 0.0203079i | ||||
\(409\) | −5.38262e85 | −0.350045 | −0.175023 | − | 0.984564i | \(-0.556000\pi\) | ||||
−0.175023 | + | 0.984564i | \(0.556000\pi\) | |||||||
\(410\) | 6.79867e85i | 0.407903i | ||||||||
\(411\) | 1.68734e86 | − | 3.96717e85i | 0.934162 | − | 0.219635i | ||||
\(412\) | −1.23914e85 | −0.0633160 | ||||||||
\(413\) | 2.07044e86i | 0.976587i | ||||||||
\(414\) | −3.69887e86 | + | 1.84109e86i | −1.61086 | + | 0.801795i | ||||
\(415\) | −6.73439e85 | −0.270839 | ||||||||
\(416\) | − | 2.57794e86i | − | 0.957620i | ||||||
\(417\) | −8.76894e85 | − | 3.72965e86i | −0.300924 | − | 1.27991i | ||||
\(418\) | −4.29386e86 | −1.36154 | ||||||||
\(419\) | − | 5.52553e85i | − | 0.161924i | −0.996717 | − | 0.0809620i | \(-0.974201\pi\) | ||
0.996717 | − | 0.0809620i | \(-0.0257992\pi\) | |||||||
\(420\) | 6.13862e86 | − | 1.44328e86i | 1.66282 | − | 0.390951i | ||||
\(421\) | −2.74501e86 | −0.687440 | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(422\) | − | 3.46384e86i | − | 0.802133i | ||||||
\(423\) | −2.76108e85 | − | 5.54720e85i | −0.0591353 | − | 0.118807i | ||||
\(424\) | 2.23812e85 | 0.0443416 | ||||||||
\(425\) | 2.45400e85i | 0.0449821i | ||||||||
\(426\) | −1.85890e86 | − | 7.90639e86i | −0.315312 | − | 1.34110i | ||||
\(427\) | −2.82894e86 | −0.444123 | ||||||||
\(428\) | 6.06081e86i | 0.880819i | ||||||||
\(429\) | 6.14617e86 | − | 1.44505e86i | 0.827016 | − | 0.194443i | ||||
\(430\) | 1.58335e87 | 1.97296 | ||||||||
\(431\) | 7.36293e85i | 0.0849769i | 0.999097 | + | 0.0424884i | \(0.0135286\pi\) | ||||
−0.999097 | + | 0.0424884i | \(0.986471\pi\) | |||||||
\(432\) | 5.82176e86 | + | 7.01428e86i | 0.622430 | + | 0.749927i | ||||
\(433\) | −1.31665e87 | −1.30428 | −0.652138 | − | 0.758100i | \(-0.726128\pi\) | ||||
−0.652138 | + | 0.758100i | \(0.726128\pi\) | |||||||
\(434\) | − | 2.41979e87i | − | 2.22135i | ||||||
\(435\) | 3.64225e86 | + | 1.54914e87i | 0.309902 | + | 1.31809i | ||||
\(436\) | −2.30934e87 | −1.82152 | ||||||||
\(437\) | 1.31138e87i | 0.959050i | ||||||||
\(438\) | 3.27161e87 | − | 7.69202e86i | 2.21879 | − | 0.521669i | ||||
\(439\) | 1.74404e87 | 1.09705 | 0.548526 | − | 0.836134i | \(-0.315189\pi\) | ||||
0.548526 | + | 0.836134i | \(0.315189\pi\) | |||||||
\(440\) | 7.33455e85i | 0.0427991i | ||||||||
\(441\) | −3.31880e87 | + | 1.65191e87i | −1.79683 | + | 0.894361i | ||||
\(442\) | −1.12732e87 | −0.566388 | ||||||||
\(443\) | − | 2.32567e87i | − | 1.08449i | −0.840221 | − | 0.542244i | \(-0.817575\pi\) | ||
0.840221 | − | 0.542244i | \(-0.182425\pi\) | |||||||
\(444\) | 5.74761e86 | + | 2.44461e87i | 0.248799 | + | 1.05821i | ||||
\(445\) | −4.01363e86 | −0.161309 | ||||||||
\(446\) | 2.81844e87i | 1.05186i | ||||||||
\(447\) | 1.11460e87 | − | 2.62057e86i | 0.386340 | − | 0.0908339i | ||||
\(448\) | −5.64956e87 | −1.81903 | ||||||||
\(449\) | − | 7.28143e86i | − | 0.217815i | −0.994052 | − | 0.108907i | \(-0.965265\pi\) | ||
0.994052 | − | 0.108907i | \(-0.0347352\pi\) | |||||||
\(450\) | −1.73593e86 | − | 3.48760e86i | −0.0482524 | − | 0.0969424i | ||||
\(451\) | 1.45649e87 | 0.376254 | ||||||||
\(452\) | − | 1.47165e87i | − | 0.353374i | ||||||
\(453\) | 1.09530e87 | + | 4.65857e87i | 0.244507 | + | 1.03995i | ||||
\(454\) | −4.28436e87 | −0.889288 | ||||||||
\(455\) | 5.81477e87i | 1.12242i | ||||||||
\(456\) | −1.45131e86 | + | 3.41224e85i | −0.0260568 | + | 0.00612632i | ||||
\(457\) | 4.04717e87 | 0.675954 | 0.337977 | − | 0.941154i | \(-0.390257\pi\) | ||||
0.337977 | + | 0.941154i | \(0.390257\pi\) | |||||||
\(458\) | − | 5.44134e87i | − | 0.845561i | ||||||
\(459\) | 3.14538e87 | − | 2.61062e87i | 0.454836 | − | 0.377508i | ||||
\(460\) | 9.25532e87 | 1.24561 | ||||||||
\(461\) | 7.39518e87i | 0.926442i | 0.886243 | + | 0.463221i | \(0.153306\pi\) | ||||
−0.886243 | + | 0.463221i | \(0.846694\pi\) | |||||||
\(462\) | −6.10906e87 | − | 2.59834e88i | −0.712508 | − | 3.03048i | ||||
\(463\) | −3.70147e86 | −0.0401978 | −0.0200989 | − | 0.999798i | \(-0.506398\pi\) | ||||
−0.0200989 | + | 0.999798i | \(0.506398\pi\) | |||||||
\(464\) | − | 1.35746e88i | − | 1.37289i | ||||||
\(465\) | 8.94183e87 | − | 2.10235e87i | 0.842324 | − | 0.198042i | ||||
\(466\) | 1.10439e87 | 0.0969143 | ||||||||
\(467\) | 2.02503e88i | 1.65568i | 0.560967 | + | 0.827838i | \(0.310429\pi\) | ||||
−0.560967 | + | 0.827838i | \(0.689571\pi\) | |||||||
\(468\) | 8.10885e87 | − | 4.03612e87i | 0.617797 | − | 0.307504i | ||||
\(469\) | −1.04161e88 | −0.739605 | ||||||||
\(470\) | 2.74245e87i | 0.181514i | ||||||||
\(471\) | 6.02269e87 | + | 2.56160e88i | 0.371621 | + | 1.58060i | ||||
\(472\) | −3.45475e86 | −0.0198761 | ||||||||
\(473\) | − | 3.39203e88i | − | 1.81988i | ||||||
\(474\) | −2.40727e88 | + | 5.65984e87i | −1.20459 | + | 0.283217i | ||||
\(475\) | −1.23648e87 | −0.0577160 | ||||||||
\(476\) | 2.41212e88i | 1.05043i | ||||||||
\(477\) | −1.37773e88 | − | 2.76796e88i | −0.559833 | − | 1.12474i | ||||
\(478\) | 3.55244e88 | 1.34712 | ||||||||
\(479\) | − | 2.97840e88i | − | 1.05417i | −0.849812 | − | 0.527085i | \(-0.823285\pi\) | ||
0.849812 | − | 0.527085i | \(-0.176715\pi\) | |||||||
\(480\) | −9.46874e87 | − | 4.02730e88i | −0.312847 | − | 1.33062i | ||||
\(481\) | −2.31564e88 | −0.714304 | ||||||||
\(482\) | 6.27211e88i | 1.80660i | ||||||||
\(483\) | −7.93555e88 | + | 1.86576e88i | −2.13462 | + | 0.501880i | ||||
\(484\) | 2.41339e88 | 0.606359 | ||||||||
\(485\) | 2.89774e87i | 0.0680115i | ||||||||
\(486\) | −2.62346e88 | + | 5.93520e88i | −0.575279 | + | 1.30148i | ||||
\(487\) | 3.36136e88 | 0.688746 | 0.344373 | − | 0.938833i | \(-0.388091\pi\) | ||||
0.344373 | + | 0.938833i | \(0.388091\pi\) | |||||||
\(488\) | − | 4.72038e86i | − | 0.00903906i | ||||||
\(489\) | 2.07963e88 | + | 8.84518e88i | 0.372214 | + | 1.58312i | ||||
\(490\) | 1.64076e89 | 2.74521 | ||||||||
\(491\) | 6.16349e88i | 0.964133i | 0.876135 | + | 0.482067i | \(0.160114\pi\) | ||||
−0.876135 | + | 0.482067i | \(0.839886\pi\) | |||||||
\(492\) | 2.03403e88 | − | 4.78230e87i | 0.297515 | − | 0.0699501i | ||||
\(493\) | −6.08721e88 | −0.832665 | ||||||||
\(494\) | − | 5.68016e88i | − | 0.726727i | ||||||
\(495\) | 9.07087e88 | − | 4.51496e88i | 1.08562 | − | 0.540359i | ||||
\(496\) | −7.83545e88 | −0.877341 | ||||||||
\(497\) | − | 1.60247e89i | − | 1.67891i | ||||||
\(498\) | 9.35951e87 | + | 3.98084e88i | 0.0917667 | + | 0.390307i | ||||
\(499\) | 6.71565e88 | 0.616269 | 0.308134 | − | 0.951343i | \(-0.400295\pi\) | ||||
0.308134 | + | 0.951343i | \(0.400295\pi\) | |||||||
\(500\) | 1.23400e89i | 1.06000i | ||||||||
\(501\) | −1.70469e89 | + | 4.00796e88i | −1.37088 | + | 0.322313i | ||||
\(502\) | −1.72715e89 | −1.30049 | ||||||||
\(503\) | − | 5.22801e88i | − | 0.368632i | −0.982867 | − | 0.184316i | \(-0.940993\pi\) | ||
0.982867 | − | 0.184316i | \(-0.0590069\pi\) | |||||||
\(504\) | −4.12970e87 | − | 8.29685e87i | −0.0272716 | − | 0.0547905i | ||||
\(505\) | −1.84507e89 | −1.14130 | ||||||||
\(506\) | − | 3.91757e89i | − | 2.27013i | ||||||
\(507\) | −2.30399e88 | − | 9.79945e88i | −0.125089 | − | 0.532034i | ||||
\(508\) | 1.51991e89 | 0.773243 | ||||||||
\(509\) | − | 2.87661e89i | − | 1.37150i | −0.727839 | − | 0.685748i | \(-0.759475\pi\) | ||
0.727839 | − | 0.685748i | \(-0.240525\pi\) | |||||||
\(510\) | −1.76112e89 | + | 4.14065e88i | −0.786999 | + | 0.185034i | ||||
\(511\) | 6.63091e89 | 2.77769 | ||||||||
\(512\) | 3.61658e89i | 1.42033i | ||||||||
\(513\) | 1.31539e89 | + | 1.58484e89i | 0.484376 | + | 0.583595i | ||||
\(514\) | −3.33100e89 | −1.15025 | ||||||||
\(515\) | − | 1.83368e88i | − | 0.0593862i | ||||||
\(516\) | −1.11375e89 | − | 4.73708e89i | −0.338337 | − | 1.43903i | ||||
\(517\) | 5.87519e88 | 0.167430 | ||||||||
\(518\) | 9.78954e89i | 2.61746i | ||||||||
\(519\) | 3.96772e89 | − | 9.32867e88i | 0.995448 | − | 0.234044i | ||||
\(520\) | −9.70255e87 | −0.0228442 | ||||||||
\(521\) | − | 2.17928e89i | − | 0.481581i | −0.970577 | − | 0.240790i | \(-0.922593\pi\) | ||
0.970577 | − | 0.240790i | \(-0.0774066\pi\) | |||||||
\(522\) | 8.65109e89 | − | 4.30602e89i | 1.79450 | − | 0.893201i | ||||
\(523\) | 9.29637e88 | 0.181033 | 0.0905165 | − | 0.995895i | \(-0.471148\pi\) | ||||
0.0905165 | + | 0.995895i | \(0.471148\pi\) | |||||||
\(524\) | 4.28009e88i | 0.0782565i | ||||||||
\(525\) | −1.75919e88 | − | 7.48228e88i | −0.0302034 | − | 0.128463i | ||||
\(526\) | −7.40636e89 | −1.19420 | ||||||||
\(527\) | 3.51362e89i | 0.532113i | ||||||||
\(528\) | −8.41361e89 | + | 1.97816e89i | −1.19691 | + | 0.281411i | ||||
\(529\) | −4.48226e89 | −0.599045 | ||||||||
\(530\) | 1.36844e90i | 1.71839i | ||||||||
\(531\) | 2.12665e89 | + | 4.27260e89i | 0.250944 | + | 0.504165i | ||||
\(532\) | −1.21537e90 | −1.34780 | ||||||||
\(533\) | 1.92672e89i | 0.200827i | ||||||||
\(534\) | 5.57818e88 | + | 2.37254e89i | 0.0546552 | + | 0.232462i | ||||
\(535\) | −8.96878e89 | −0.826149 | ||||||||
\(536\) | − | 1.73803e88i | − | 0.0150529i | ||||||
\(537\) | 4.61155e89 | − | 1.08424e89i | 0.375574 | − | 0.0883028i | ||||
\(538\) | −2.02853e89 | −0.155369 | ||||||||
\(539\) | − | 3.51503e90i | − | 2.53221i | ||||||
\(540\) | 1.11853e90 | − | 9.28365e89i | 0.757973 | − | 0.629108i | ||||
\(541\) | −2.16785e88 | −0.0138204 | −0.00691020 | − | 0.999976i | \(-0.502200\pi\) | ||||
−0.00691020 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(542\) | 2.05861e90i | 1.23480i | ||||||||
\(543\) | 7.41758e89 | + | 3.15489e90i | 0.418666 | + | 1.78069i | ||||
\(544\) | 1.58249e90 | 0.840578 | ||||||||
\(545\) | − | 3.41735e90i | − | 1.70846i | ||||||
\(546\) | 3.43723e90 | − | 8.08141e89i | 1.61753 | − | 0.380303i | ||||
\(547\) | −1.88414e88 | −0.00834701 | −0.00417351 | − | 0.999991i | \(-0.501328\pi\) | ||||
−0.00417351 | + | 0.999991i | \(0.501328\pi\) | |||||||
\(548\) | 2.35779e90i | 0.983436i | ||||||||
\(549\) | −5.83785e89 | + | 2.90575e89i | −0.229280 | + | 0.114122i | ||||
\(550\) | 3.69381e89 | 0.136617 | ||||||||
\(551\) | − | 3.06711e90i | − | 1.06838i | ||||||
\(552\) | −3.11322e88 | − | 1.32413e89i | −0.0102146 | − | 0.0434451i | ||||
\(553\) | −4.87906e90 | −1.50802 | ||||||||
\(554\) | − | 1.97984e90i | − | 0.576511i | ||||||
\(555\) | −3.61752e90 | + | 8.50531e89i | −0.992528 | + | 0.233357i | ||||
\(556\) | 5.21160e90 | 1.34742 | ||||||||
\(557\) | − | 1.07089e90i | − | 0.260929i | −0.991453 | − | 0.130465i | \(-0.958353\pi\) | ||
0.991453 | − | 0.130465i | \(-0.0416469\pi\) | |||||||
\(558\) | −2.48549e90 | − | 4.99352e90i | −0.570799 | − | 1.14678i | ||||
\(559\) | 4.48717e90 | 0.971366 | ||||||||
\(560\) | − | 7.95995e90i | − | 1.62445i | ||||||
\(561\) | 8.87057e89 | + | 3.77288e90i | 0.170678 | + | 0.725936i | ||||
\(562\) | −4.97811e90 | −0.903164 | ||||||||
\(563\) | 4.06558e90i | 0.695577i | 0.937573 | + | 0.347789i | \(0.113067\pi\) | ||||
−0.937573 | + | 0.347789i | \(0.886933\pi\) | |||||||
\(564\) | 8.20488e89 | − | 1.92908e89i | 0.132392 | − | 0.0311272i | ||||
\(565\) | 2.17774e90 | 0.331442 | ||||||||
\(566\) | 7.75710e90i | 1.11367i | ||||||||
\(567\) | −7.71885e90 | + | 1.02147e91i | −1.04547 | + | 1.38351i | ||||
\(568\) | 2.67389e89 | 0.0341702 | ||||||||
\(569\) | 4.32914e90i | 0.522031i | 0.965335 | + | 0.261016i | \(0.0840574\pi\) | ||||
−0.965335 | + | 0.261016i | \(0.915943\pi\) | |||||||
\(570\) | −2.08631e90 | − | 8.87363e90i | −0.237416 | − | 1.00979i | ||||
\(571\) | −1.15273e91 | −1.23805 | −0.619023 | − | 0.785373i | \(-0.712471\pi\) | ||||
−0.619023 | + | 0.785373i | \(0.712471\pi\) | |||||||
\(572\) | 8.58829e90i | 0.870638i | ||||||||
\(573\) | 1.26114e91 | − | 2.96512e90i | 1.20687 | − | 0.283753i | ||||
\(574\) | 8.14538e90 | 0.735900 | ||||||||
\(575\) | − | 1.12812e90i | − | 0.0962312i | ||||||
\(576\) | −1.16585e91 | + | 5.80295e90i | −0.939079 | + | 0.467419i | ||||
\(577\) | 1.94270e91 | 1.47776 | 0.738878 | − | 0.673839i | \(-0.235356\pi\) | ||||
0.738878 | + | 0.673839i | \(0.235356\pi\) | |||||||
\(578\) | 1.28864e91i | 0.925793i | ||||||||
\(579\) | −2.58320e90 | − | 1.09870e91i | −0.175294 | − | 0.745569i | ||||
\(580\) | −2.16468e91 | −1.38762 | ||||||||
\(581\) | 8.06837e90i | 0.488622i | ||||||||
\(582\) | 1.71292e90 | − | 4.02731e89i | 0.0980116 | − | 0.0230439i | ||||
\(583\) | 2.93162e91 | 1.58506 | ||||||||
\(584\) | 1.10644e90i | 0.0565331i | ||||||||
\(585\) | 5.97264e90 | + | 1.19995e91i | 0.288418 | + | 0.579453i | ||||
\(586\) | 2.42762e91 | 1.10805 | ||||||||
\(587\) | 6.18587e90i | 0.266897i | 0.991056 | + | 0.133448i | \(0.0426051\pi\) | ||||
−0.991056 | + | 0.133448i | \(0.957395\pi\) | |||||||
\(588\) | −1.15414e91 | − | 4.90885e91i | −0.470768 | − | 2.00230i | ||||
\(589\) | −1.77038e91 | −0.682749 | ||||||||
\(590\) | − | 2.11230e91i | − | 0.770264i | ||||||
\(591\) | −4.60190e91 | + | 1.08197e91i | −1.58690 | + | 0.373103i | ||||
\(592\) | 3.16992e91 | 1.03379 | ||||||||
\(593\) | 2.76895e91i | 0.854103i | 0.904227 | + | 0.427051i | \(0.140448\pi\) | ||||
−0.904227 | + | 0.427051i | \(0.859552\pi\) | |||||||
\(594\) | −3.92957e91 | − | 4.73449e91i | −1.14655 | − | 1.38140i | ||||
\(595\) | −3.56945e91 | −0.985237 | ||||||||
\(596\) | 1.55747e91i | 0.406718i | ||||||||
\(597\) | 1.33446e91 | + | 5.67582e91i | 0.329727 | + | 1.40241i | ||||
\(598\) | 5.18239e91 | 1.21169 | ||||||||
\(599\) | − | 8.44653e91i | − | 1.86893i | −0.356055 | − | 0.934465i | \(-0.615879\pi\) | ||
0.356055 | − | 0.934465i | \(-0.384121\pi\) | |||||||
\(600\) | 1.24850e89 | − | 2.93539e88i | 0.00261455 | − | 0.000614717i | ||||
\(601\) | 1.42953e91 | 0.283358 | 0.141679 | − | 0.989913i | \(-0.454750\pi\) | ||||
0.141679 | + | 0.989913i | \(0.454750\pi\) | |||||||
\(602\) | − | 1.89699e92i | − | 3.55943i | ||||||
\(603\) | −2.14948e91 | + | 1.06989e91i | −0.381823 | + | 0.190049i | ||||
\(604\) | −6.50961e91 | −1.09480 | ||||||||
\(605\) | 3.57133e91i | 0.568725i | ||||||||
\(606\) | 2.56430e91 | + | 1.09066e92i | 0.386698 | + | 1.64473i | ||||
\(607\) | 3.12704e91 | 0.446587 | 0.223294 | − | 0.974751i | \(-0.428319\pi\) | ||||
0.223294 | + | 0.974751i | \(0.428319\pi\) | |||||||
\(608\) | 7.97357e91i | 1.07854i | ||||||||
\(609\) | 1.85600e92 | − | 4.36372e91i | 2.37798 | − | 0.559096i | ||||
\(610\) | 2.88614e91 | 0.350294 | ||||||||
\(611\) | 7.77203e90i | 0.0893664i | ||||||||
\(612\) | 2.47761e91 | + | 4.97769e91i | 0.269920 | + | 0.542289i | ||||
\(613\) | −1.80195e92 | −1.86015 | −0.930073 | − | 0.367376i | \(-0.880256\pi\) | ||||
−0.930073 | + | 0.367376i | \(0.880256\pi\) | |||||||
\(614\) | 1.27705e92i | 1.24925i | ||||||||
\(615\) | 7.07683e90 | + | 3.00996e91i | 0.0656085 | + | 0.279050i | ||||
\(616\) | 8.78741e90 | 0.0772142 | ||||||||
\(617\) | − | 9.03100e91i | − | 0.752186i | −0.926582 | − | 0.376093i | \(-0.877267\pi\) | ||
0.926582 | − | 0.376093i | \(-0.122733\pi\) | |||||||
\(618\) | −1.08393e91 | + | 2.54847e90i | −0.0855818 | + | 0.0201215i | ||||
\(619\) | 2.02351e92 | 1.51465 | 0.757327 | − | 0.653036i | \(-0.226505\pi\) | ||||
0.757327 | + | 0.653036i | \(0.226505\pi\) | |||||||
\(620\) | 1.24948e92i | 0.886754i | ||||||||
\(621\) | −1.44595e92 | + | 1.20012e92i | −0.973041 | + | 0.807611i | ||||
\(622\) | −1.05655e92 | −0.674231 | ||||||||
\(623\) | 4.80867e91i | 0.291018i | ||||||||
\(624\) | −2.61682e91 | − | 1.11300e92i | −0.150204 | − | 0.638857i | ||||
\(625\) | −1.68630e92 | −0.918109 | ||||||||
\(626\) | − | 2.68147e91i | − | 0.138490i | ||||||
\(627\) | −1.90101e92 | + | 4.46954e91i | −0.931441 | + | 0.218995i | ||||
\(628\) | −3.57943e92 | −1.66397 | ||||||||
\(629\) | − | 1.42147e92i | − | 0.627000i | ||||||
\(630\) | 5.07286e92 | − | 2.52498e92i | 2.12332 | − | 1.05687i | ||||
\(631\) | −2.57647e92 | −1.02342 | −0.511712 | − | 0.859157i | \(-0.670989\pi\) | ||||
−0.511712 | + | 0.859157i | \(0.670989\pi\) | |||||||
\(632\) | − | 8.14123e90i | − | 0.0306921i | ||||||
\(633\) | −3.60556e91 | − | 1.53354e92i | −0.129018 | − | 0.548746i | ||||
\(634\) | 4.83214e91 | 0.164132 | ||||||||
\(635\) | 2.24916e92i | 0.725251i | ||||||||
\(636\) | 4.09410e92 | − | 9.62580e91i | 1.25335 | − | 0.294681i | ||||
\(637\) | 4.64988e92 | 1.35158 | ||||||||
\(638\) | 9.16260e92i | 2.52893i | ||||||||
\(639\) | −1.64598e92 | − | 3.30688e92i | −0.431415 | − | 0.866743i | ||||
\(640\) | 2.72485e91 | 0.0678271 | ||||||||
\(641\) | − | 3.91266e92i | − | 0.925032i | −0.886611 | − | 0.462516i | \(-0.846947\pi\) | ||
0.886611 | − | 0.462516i | \(-0.153053\pi\) | |||||||
\(642\) | 1.24649e92 | + | 5.30164e92i | 0.279919 | + | 1.19057i | ||||
\(643\) | 3.48247e92 | 0.742892 | 0.371446 | − | 0.928455i | \(-0.378862\pi\) | ||||
0.371446 | + | 0.928455i | \(0.378862\pi\) | |||||||
\(644\) | − | 1.10887e93i | − | 2.24722i | ||||||
\(645\) | 7.00992e92 | − | 1.64813e92i | 1.34972 | − | 0.317337i | ||||
\(646\) | 3.48681e92 | 0.637905 | ||||||||
\(647\) | − | 4.47442e92i | − | 0.777849i | −0.921270 | − | 0.388924i | \(-0.872847\pi\) | ||
0.921270 | − | 0.388924i | \(-0.127153\pi\) | |||||||
\(648\) | −1.70442e91 | − | 1.28797e91i | −0.0281580 | − | 0.0212780i | ||||
\(649\) | −4.52522e92 | −0.710501 | ||||||||
\(650\) | 4.88638e91i | 0.0729199i | ||||||||
\(651\) | −2.51879e92 | − | 1.07131e93i | −0.357289 | − | 1.51964i | ||||
\(652\) | −1.23597e93 | −1.66663 | ||||||||
\(653\) | 7.54715e92i | 0.967493i | 0.875208 | + | 0.483746i | \(0.160724\pi\) | ||||
−0.875208 | + | 0.483746i | \(0.839276\pi\) | |||||||
\(654\) | −2.02007e93 | + | 4.74947e92i | −2.46207 | + | 0.578868i | ||||
\(655\) | −6.33367e91 | −0.0733994 | ||||||||
\(656\) | − | 2.63753e92i | − | 0.290650i | ||||||
\(657\) | 1.36837e93 | − | 6.81094e92i | 1.43399 | − | 0.713756i | ||||
\(658\) | 3.28568e92 | 0.327470 | ||||||||
\(659\) | 1.82446e93i | 1.72948i | 0.502220 | + | 0.864740i | \(0.332517\pi\) | ||||
−0.502220 | + | 0.864740i | \(0.667483\pi\) | |||||||
\(660\) | 3.15447e92 | + | 1.34168e93i | 0.284431 | + | 1.20976i | ||||
\(661\) | −1.64655e93 | −1.41230 | −0.706150 | − | 0.708063i | \(-0.749569\pi\) | ||||
−0.706150 | + | 0.708063i | \(0.749569\pi\) | |||||||
\(662\) | 7.08999e92i | 0.578538i | ||||||||
\(663\) | −4.99098e92 | + | 1.17345e92i | −0.387471 | + | 0.0910999i | ||||
\(664\) | −1.34629e91 | −0.00994472 | ||||||||
\(665\) | − | 1.79851e93i | − | 1.26415i | ||||||
\(666\) | 1.00553e93 | + | 2.02019e93i | 0.672585 | + | 1.35127i | ||||
\(667\) | 2.79833e93 | 1.78134 | ||||||||
\(668\) | − | 2.38203e93i | − | 1.44319i | ||||||
\(669\) | 2.93376e92 | + | 1.24780e93i | 0.169185 | + | 0.719588i | ||||
\(670\) | 1.06267e93 | 0.583349 | ||||||||
\(671\) | − | 6.18302e92i | − | 0.323115i | ||||||
\(672\) | −4.82504e93 | + | 1.13444e93i | −2.40057 | + | 0.564409i | ||||
\(673\) | 2.33912e93 | 1.10804 | 0.554019 | − | 0.832504i | \(-0.313093\pi\) | ||||
0.554019 | + | 0.832504i | \(0.313093\pi\) | |||||||
\(674\) | 1.70242e93i | 0.767874i | ||||||||
\(675\) | −1.13157e92 | − | 1.36336e92i | −0.0486024 | − | 0.0585580i | ||||
\(676\) | 1.36932e93 | 0.560097 | ||||||||
\(677\) | 3.69813e93i | 1.44064i | 0.693640 | + | 0.720321i | \(0.256006\pi\) | ||||
−0.693640 | + | 0.720321i | \(0.743994\pi\) | |||||||
\(678\) | −3.02664e92 | − | 1.28731e93i | −0.112300 | − | 0.477642i | ||||
\(679\) | 3.47174e92 | 0.122700 | ||||||||
\(680\) | − | 5.95600e91i | − | 0.0200521i | ||||||
\(681\) | −1.89680e93 | + | 4.45965e92i | −0.608369 | + | 0.143036i | ||||
\(682\) | 5.28877e93 | 1.61611 | ||||||||
\(683\) | − | 4.78206e93i | − | 1.39230i | −0.717899 | − | 0.696148i | \(-0.754896\pi\) | ||
0.717899 | − | 0.696148i | \(-0.245104\pi\) | |||||||
\(684\) | −2.50807e93 | + | 1.24837e93i | −0.695805 | + | 0.346332i | ||||
\(685\) | −3.48905e93 | −0.922398 | ||||||||
\(686\) | − | 9.86368e93i | − | 2.48510i | ||||||
\(687\) | −5.66397e92 | − | 2.40903e93i | −0.136003 | − | 0.578455i | ||||
\(688\) | −6.14258e93 | −1.40583 | ||||||||
\(689\) | 3.87811e93i | 0.846030i | ||||||||
\(690\) | 8.09600e93 | − | 1.90348e93i | 1.68365 | − | 0.395849i | ||||
\(691\) | 9.45872e92 | 0.187524 | 0.0937620 | − | 0.995595i | \(-0.470111\pi\) | ||||
0.0937620 | + | 0.995595i | \(0.470111\pi\) | |||||||
\(692\) | 5.54426e93i | 1.04795i | ||||||||
\(693\) | −5.40930e93 | − | 1.08677e94i | −0.974865 | − | 1.95857i | ||||
\(694\) | 1.26801e92 | 0.0217902 | ||||||||
\(695\) | 7.71211e93i | 1.26379i | ||||||||
\(696\) | 7.28133e91 | + | 3.09693e92i | 0.0113790 | + | 0.0483980i | ||||
\(697\) | −1.18274e93 | −0.176281 | ||||||||
\(698\) | − | 4.63190e93i | − | 0.658462i | ||||||
\(699\) | 4.88945e92 | − | 1.14958e92i | 0.0662999 | − | 0.0155880i | ||||
\(700\) | 1.04553e93 | 0.135239 | ||||||||
\(701\) | 4.29448e93i | 0.529927i | 0.964258 | + | 0.264964i | \(0.0853599\pi\) | ||||
−0.964258 | + | 0.264964i | \(0.914640\pi\) | |||||||
\(702\) | 6.26305e93 | − | 5.19825e93i | 0.737329 | − | 0.611973i | ||||
\(703\) | 7.16227e93 | 0.804498 | ||||||||
\(704\) | − | 1.23479e94i | − | 1.32341i | ||||||
\(705\) | 2.85465e92 | + | 1.21416e93i | 0.0291953 | + | 0.124175i | ||||
\(706\) | 1.61222e94 | 1.57350 | ||||||||
\(707\) | 2.21055e94i | 2.05902i | ||||||||
\(708\) | −6.31961e93 | + | 1.48583e93i | −0.561814 | + | 0.132090i | ||||
\(709\) | −1.78704e94 | −1.51638 | −0.758190 | − | 0.652033i | \(-0.773916\pi\) | ||||
−0.758190 | + | 0.652033i | \(0.773916\pi\) | |||||||
\(710\) | 1.63487e94i | 1.32421i | ||||||||
\(711\) | −1.00685e94 | + | 5.01153e93i | −0.778519 | + | 0.387502i | ||||
\(712\) | −8.02378e91 | −0.00592296 | ||||||||
\(713\) | − | 1.61523e94i | − | 1.13836i | ||||||
\(714\) | 4.96085e93 | + | 2.10997e94i | 0.333822 | + | 1.41983i | ||||
\(715\) | −1.27089e94 | −0.816601 | ||||||||
\(716\) | 6.44391e93i | 0.395385i | ||||||||
\(717\) | 1.57276e94 | − | 3.69779e93i | 0.921577 | − | 0.216676i | ||||
\(718\) | 2.00401e94 | 1.12148 | ||||||||
\(719\) | − | 8.06091e93i | − | 0.430855i | −0.976520 | − | 0.215427i | \(-0.930886\pi\) | ||
0.976520 | − | 0.215427i | \(-0.0691144\pi\) | |||||||
\(720\) | −8.17607e93 | − | 1.64263e94i | −0.417419 | − | 0.838624i | ||||
\(721\) | −2.19691e93 | −0.107139 | ||||||||
\(722\) | − | 1.29748e94i | − | 0.604467i | ||||||
\(723\) | 6.52873e93 | + | 2.77684e94i | 0.290580 | + | 1.23591i | ||||
\(724\) | −4.40845e94 | −1.87462 | ||||||||
\(725\) | 2.63850e93i | 0.107202i | ||||||||
\(726\) | 2.11109e94 | − | 4.96346e93i | 0.819592 | − | 0.192698i | ||||
\(727\) | 3.76356e92 | 0.0139625 | 0.00698124 | − | 0.999976i | \(-0.497778\pi\) | ||||
0.00698124 | + | 0.999976i | \(0.497778\pi\) | |||||||
\(728\) | 1.16245e93i | 0.0412134i | ||||||||
\(729\) | −5.43676e93 | + | 2.90076e94i | −0.184218 | + | 0.982885i | ||||
\(730\) | −6.76498e94 | −2.19085 | ||||||||
\(731\) | 2.75449e94i | 0.852644i | ||||||||
\(732\) | −2.03016e93 | − | 8.63478e93i | −0.0600709 | − | 0.255497i | ||||
\(733\) | 1.65121e94 | 0.467059 | 0.233530 | − | 0.972350i | \(-0.424972\pi\) | ||||
0.233530 | + | 0.972350i | \(0.424972\pi\) | |||||||
\(734\) | − | 7.17354e94i | − | 1.93983i | ||||||
\(735\) | 7.26411e94 | − | 1.70789e94i | 1.87802 | − | 0.441549i | ||||
\(736\) | −7.27482e94 | −1.79827 | ||||||||
\(737\) | − | 2.27657e94i | − | 0.538088i | ||||||
\(738\) | 1.68090e94 | − | 8.36653e93i | 0.379910 | − | 0.189097i | ||||
\(739\) | 5.89743e94 | 1.27467 | 0.637333 | − | 0.770589i | \(-0.280038\pi\) | ||||
0.637333 | + | 0.770589i | \(0.280038\pi\) | |||||||
\(740\) | − | 5.05491e94i | − | 1.04488i | ||||||
\(741\) | −5.91256e93 | − | 2.51476e94i | −0.116889 | − | 0.497160i | ||||
\(742\) | 1.63950e95 | 3.10015 | ||||||||
\(743\) | − | 2.89608e94i | − | 0.523817i | −0.965093 | − | 0.261908i | \(-0.915648\pi\) | ||
0.965093 | − | 0.261908i | \(-0.0843518\pi\) | |||||||
\(744\) | 1.78759e93 | − | 4.20287e92i | 0.0309286 | − | 0.00727176i | ||||
\(745\) | −2.30474e94 | −0.381474 | ||||||||
\(746\) | 1.94984e94i | 0.308758i | ||||||||
\(747\) | 8.28743e93 | + | 1.66500e94i | 0.125557 | + | 0.252252i | ||||
\(748\) | −5.27200e94 | −0.764227 | ||||||||
\(749\) | 1.07454e95i | 1.49046i | ||||||||
\(750\) | 2.53789e94 | + | 1.07943e95i | 0.336862 | + | 1.43276i | ||||
\(751\) | 1.57997e94 | 0.200692 | 0.100346 | − | 0.994953i | \(-0.468005\pi\) | ||||
0.100346 | + | 0.994953i | \(0.468005\pi\) | |||||||
\(752\) | − | 1.06393e94i | − | 0.129337i | ||||||
\(753\) | −7.64658e94 | + | 1.79782e94i | −0.889678 | + | 0.209176i | ||||
\(754\) | −1.21208e95 | −1.34982 | ||||||||
\(755\) | − | 9.63292e94i | − | 1.02685i | ||||||
\(756\) | −1.11226e95 | − | 1.34009e95i | −1.13498 | − | 1.36746i | ||||
\(757\) | 8.08015e94 | 0.789325 | 0.394662 | − | 0.918826i | \(-0.370862\pi\) | ||||
0.394662 | + | 0.918826i | \(0.370862\pi\) | |||||||
\(758\) | 1.58378e95i | 1.48119i | ||||||||
\(759\) | −4.07786e94 | − | 1.73442e95i | −0.365135 | − | 1.55301i | ||||
\(760\) | 3.00100e93 | 0.0257287 | ||||||||
\(761\) | 1.81683e94i | 0.149149i | 0.997215 | + | 0.0745746i | \(0.0237599\pi\) | ||||
−0.997215 | + | 0.0745746i | \(0.976240\pi\) | |||||||
\(762\) | 1.32953e95 | − | 3.12591e94i | 1.04516 | − | 0.245732i | ||||
\(763\) | −4.09428e95 | −3.08225 | ||||||||
\(764\) | 1.76224e95i | 1.27053i | ||||||||
\(765\) | −7.36597e94 | + | 3.66636e94i | −0.508631 | + | 0.253167i | ||||
\(766\) | 2.43972e95 | 1.61358 | ||||||||
\(767\) | − | 5.98621e94i | − | 0.379232i | ||||||
\(768\) | 3.57752e94 | + | 1.52161e95i | 0.217101 | + | 0.923386i | ||||
\(769\) | 2.56981e95 | 1.49393 | 0.746966 | − | 0.664862i | \(-0.231510\pi\) | ||||
0.746966 | + | 0.664862i | \(0.231510\pi\) | |||||||
\(770\) | 5.37280e95i | 2.99231i | ||||||||
\(771\) | −1.47473e95 | + | 3.46729e94i | −0.786895 | + | 0.185010i | ||||
\(772\) | 1.53526e95 | 0.784895 | ||||||||
\(773\) | − | 3.10010e95i | − | 1.51863i | −0.650722 | − | 0.759316i | \(-0.725534\pi\) | ||
0.650722 | − | 0.759316i | \(-0.274466\pi\) | |||||||
\(774\) | −1.94849e95 | − | 3.91466e95i | −0.914633 | − | 1.83756i | ||||
\(775\) | 1.52297e94 | 0.0685072 | ||||||||
\(776\) | 5.79296e92i | 0.00249726i | ||||||||
\(777\) | 1.01901e95 | + | 4.33410e95i | 0.421002 | + | 1.79063i | ||||
\(778\) | 4.94244e95 | 1.95711 | ||||||||
\(779\) | − | 5.95936e94i | − | 0.226185i | ||||||
\(780\) | −1.77484e95 | + | 4.17291e94i | −0.645711 | + | 0.151816i | ||||
\(781\) | 3.50240e95 | 1.22147 | ||||||||
\(782\) | 3.18125e95i | 1.06359i | ||||||||
\(783\) | 3.38186e95 | − | 2.80690e95i | 1.08397 | − | 0.899681i | ||||
\(784\) | −6.36531e95 | −1.95609 | ||||||||
\(785\) | − | 5.29684e95i | − | 1.56070i | ||||||
\(786\) | 8.80259e93 | + | 3.74397e94i | 0.0248695 | + | 0.105776i | ||||
\(787\) | −6.03069e95 | −1.63381 | −0.816904 | − | 0.576774i | \(-0.804311\pi\) | ||||
−0.816904 | + | 0.576774i | \(0.804311\pi\) | |||||||
\(788\) | − | 6.43042e95i | − | 1.67061i | ||||||
\(789\) | −3.27900e95 | + | 7.70939e94i | −0.816959 | + | 0.192079i | ||||
\(790\) | 4.97772e95 | 1.18942 | ||||||||
\(791\) | − | 2.60912e95i | − | 0.597956i | ||||||
\(792\) | 1.81339e94 | − | 9.02599e93i | 0.0398620 | − | 0.0198410i | ||||
\(793\) | 8.17924e94 | 0.172464 | ||||||||
\(794\) | − | 5.87101e95i | − | 1.18751i | ||||||
\(795\) | 1.42442e95 | + | 6.05844e95i | 0.276391 | + | 1.17556i | ||||
\(796\) | −7.93105e95 | −1.47638 | ||||||||
\(797\) | − | 8.65932e95i | − | 1.54653i | −0.634081 | − | 0.773267i | \(-0.718621\pi\) | ||
0.634081 | − | 0.773267i | \(-0.281379\pi\) | |||||||
\(798\) | −1.06314e96 | + | 2.49958e95i | −1.82177 | + | 0.428323i | ||||
\(799\) | −4.77093e94 | −0.0784439 | ||||||||
\(800\) | − | 6.85929e94i | − | 0.108221i | ||||||
\(801\) | 4.93923e94 | + | 9.92326e94i | 0.0747801 | + | 0.150239i | ||||
\(802\) | 1.29061e96 | 1.87517 | ||||||||
\(803\) | 1.44927e96i | 2.02086i | ||||||||
\(804\) | −7.47498e94 | − | 3.17930e95i | −0.100037 | − | 0.425483i | ||||
\(805\) | 1.64090e96 | 2.10774 | ||||||||
\(806\) | 6.99628e95i | 0.862602i | ||||||||
\(807\) | −8.98084e94 | + | 2.11152e94i | −0.106290 | + | 0.0249902i | ||||
\(808\) | −3.68854e94 | −0.0419063 | ||||||||
\(809\) | − | 1.08403e95i | − | 0.118234i | −0.998251 | − | 0.0591168i | \(-0.981172\pi\) | ||
0.998251 | − | 0.0591168i | \(-0.0188284\pi\) | |||||||
\(810\) | 7.87492e95 | − | 1.04212e96i | 0.824595 | − | 1.09122i | ||||
\(811\) | 4.30165e95 | 0.432461 | 0.216230 | − | 0.976342i | \(-0.430624\pi\) | ||||
0.216230 | + | 0.976342i | \(0.430624\pi\) | |||||||
\(812\) | 2.59347e96i | 2.50341i | ||||||||
\(813\) | 2.14284e95 | + | 9.11403e95i | 0.198610 | + | 0.844739i | ||||
\(814\) | −2.13963e96 | −1.90429 | ||||||||
\(815\) | − | 1.82899e96i | − | 1.56318i | ||||||
\(816\) | 6.83225e95 | − | 1.60636e95i | 0.560775 | − | 0.131846i | ||||
\(817\) | −1.38788e96 | −1.09402 | ||||||||
\(818\) | − | 6.57922e95i | − | 0.498099i | ||||||
\(819\) | 1.43764e96 | − | 7.15573e95i | 1.04539 | − | 0.520338i | ||||
\(820\) | −4.20594e95 | −0.293769 | ||||||||
\(821\) | 1.29186e96i | 0.866747i | 0.901214 | + | 0.433374i | \(0.142677\pi\) | ||||
−0.901214 | + | 0.433374i | \(0.857323\pi\) | |||||||
\(822\) | 4.84911e95 | + | 2.06245e96i | 0.312530 | + | 1.32927i | ||||
\(823\) | −1.66682e96 | −1.03203 | −0.516016 | − | 0.856579i | \(-0.672586\pi\) | ||||
−0.516016 | + | 0.856579i | \(0.672586\pi\) | |||||||
\(824\) | − | 3.66577e93i | − | 0.00218056i | ||||||
\(825\) | 1.63535e95 | − | 3.84494e94i | 0.0934610 | − | 0.0219740i | ||||
\(826\) | −2.53072e96 | −1.38964 | ||||||||
\(827\) | 2.74780e96i | 1.44979i | 0.688862 | + | 0.724893i | \(0.258111\pi\) | ||||
−0.688862 | + | 0.724893i | \(0.741889\pi\) | |||||||
\(828\) | −1.13897e96 | − | 2.28828e96i | −0.577447 | − | 1.16013i | ||||
\(829\) | −2.06929e96 | −1.00814 | −0.504070 | − | 0.863663i | \(-0.668165\pi\) | ||||
−0.504070 | + | 0.863663i | \(0.668165\pi\) | |||||||
\(830\) | − | 8.23151e95i | − | 0.385392i | ||||||
\(831\) | −2.06084e95 | − | 8.76529e95i | −0.0927280 | − | 0.394396i | ||||
\(832\) | 1.63344e96 | 0.706373 | ||||||||
\(833\) | 2.85437e96i | 1.18638i | ||||||||
\(834\) | 4.55879e96 | − | 1.07184e96i | 1.82125 | − | 0.428202i | ||||
\(835\) | 3.52492e96 | 1.35362 | ||||||||
\(836\) | − | 2.65636e96i | − | 0.980572i | ||||||
\(837\) | −1.62018e96 | − | 1.95205e96i | −0.574940 | − | 0.692709i | ||||
\(838\) | 6.75391e95 | 0.230411 | ||||||||
\(839\) | − | 2.95428e96i | − | 0.968964i | −0.874801 | − | 0.484482i | \(-0.839008\pi\) | ||
0.874801 | − | 0.484482i | \(-0.160992\pi\) | |||||||
\(840\) | 4.26966e94 | + | 1.81599e95i | 0.0134641 | + | 0.0572661i | ||||
\(841\) | −3.24674e96 | −0.984417 | ||||||||
\(842\) | − | 3.35525e96i | − | 0.978197i | ||||||
\(843\) | −2.20395e96 | + | 5.18179e95i | −0.617862 | + | 0.145268i | ||||
\(844\) | 2.14287e96 | 0.577691 | ||||||||
\(845\) | 2.02631e96i | 0.525334i | ||||||||
\(846\) | 6.78040e95 | − | 3.37489e95i | 0.169057 | − | 0.0841469i | ||||
\(847\) | 4.27875e96 | 1.02604 | ||||||||
\(848\) | − | 5.30882e96i | − | 1.22443i | ||||||
\(849\) | 8.07448e95 | + | 3.43428e96i | 0.179127 | + | 0.761872i | ||||
\(850\) | −2.99954e95 | −0.0640075 | ||||||||
\(851\) | 6.53461e96i | 1.34136i | ||||||||
\(852\) | 4.89122e96 | − | 1.14999e96i | 0.965851 | − | 0.227085i | ||||
\(853\) | −2.17566e96 | −0.413307 | −0.206653 | − | 0.978414i | \(-0.566257\pi\) | ||||
−0.206653 | + | 0.978414i | \(0.566257\pi\) | |||||||
\(854\) | − | 3.45784e96i | − | 0.631968i | ||||||
\(855\) | −1.84734e96 | − | 3.71143e96i | −0.324836 | − | 0.652619i | ||||
\(856\) | −1.79298e95 | −0.0303347 | ||||||||
\(857\) | − | 4.42484e96i | − | 0.720328i | −0.932889 | − | 0.360164i | \(-0.882721\pi\) | ||
0.932889 | − | 0.360164i | \(-0.117279\pi\) | |||||||
\(858\) | 1.76630e96 | + | 7.51252e96i | 0.276684 | + | 1.17681i | ||||
\(859\) | −5.20225e96 | −0.784183 | −0.392091 | − | 0.919926i | \(-0.628248\pi\) | ||||
−0.392091 | + | 0.919926i | \(0.628248\pi\) | |||||||
\(860\) | 9.79525e96i | 1.42091i | ||||||||
\(861\) | 3.60618e96 | − | 8.47864e95i | 0.503436 | − | 0.118365i | ||||
\(862\) | −8.99978e95 | −0.120918 | ||||||||
\(863\) | 1.69983e96i | 0.219811i | 0.993942 | + | 0.109905i | \(0.0350548\pi\) | ||||
−0.993942 | + | 0.109905i | \(0.964945\pi\) | |||||||
\(864\) | −8.79181e96 | + | 7.29709e96i | −1.09427 | + | 0.908231i | ||||
\(865\) | −8.20439e96 | −0.982912 | ||||||||
\(866\) | − | 1.60935e97i | − | 1.85593i | ||||||
\(867\) | 1.34137e96 | + | 5.70518e96i | 0.148908 | + | 0.633343i | ||||
\(868\) | 1.49698e97 | 1.59980 | ||||||||
\(869\) | − | 1.06638e97i | − | 1.09714i | ||||||
\(870\) | −1.89353e97 | + | 4.45195e96i | −1.87558 | + | 0.440976i | ||||
\(871\) | 3.01157e96 | 0.287206 | ||||||||
\(872\) | − | 6.83174e95i | − | 0.0627317i | ||||||
\(873\) | 7.16434e95 | − | 3.56600e95i | 0.0633441 | − | 0.0315291i | ||||
\(874\) | −1.60291e97 | −1.36469 | ||||||||
\(875\) | 2.18779e97i | 1.79366i | ||||||||
\(876\) | 4.75860e96 | + | 2.02395e97i | 0.375702 | + | 1.59796i | ||||
\(877\) | −1.84878e96 | −0.140572 | −0.0702859 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702859 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(878\) | 2.13176e97i | 1.56106i | ||||||||
\(879\) | 1.07477e97 | − | 2.52694e96i | 0.758025 | − | 0.178222i | ||||
\(880\) | 1.73975e97 | 1.18184 | ||||||||
\(881\) | 3.70612e96i | 0.242501i | 0.992622 | + | 0.121251i | \(0.0386905\pi\) | ||||
−0.992622 | + | 0.121251i | \(0.961310\pi\) | |||||||
\(882\) | −2.01914e97 | − | 4.05660e97i | −1.27264 | − | 2.55682i | ||||
\(883\) | 1.61100e97 | 0.978117 | 0.489059 | − | 0.872251i | \(-0.337340\pi\) | ||||
0.489059 | + | 0.872251i | \(0.337340\pi\) | |||||||
\(884\) | − | 6.97409e96i | − | 0.407909i | ||||||
\(885\) | −2.19873e96 | − | 9.35175e96i | −0.123892 | − | 0.526945i | ||||
\(886\) | 2.84269e97 | 1.54318 | ||||||||
\(887\) | − | 7.71534e96i | − | 0.403530i | −0.979434 | − | 0.201765i | \(-0.935332\pi\) | ||
0.979434 | − | 0.201765i | \(-0.0646677\pi\) | |||||||
\(888\) | −7.23190e95 | + | 1.70032e95i | −0.0364439 | + | 0.00856847i | ||||
\(889\) | 2.69469e97 | 1.30843 | ||||||||
\(890\) | − | 4.90590e96i | − | 0.229535i | ||||||
\(891\) | −2.23255e97 | − | 1.68706e97i | −1.00655 | − | 0.760615i | ||||
\(892\) | −1.74360e97 | −0.757544 | ||||||||
\(893\) | − | 2.40389e96i | − | 0.100651i | ||||||
\(894\) | 3.20315e96 | + | 1.36238e97i | 0.129253 | + | 0.549744i | ||||
\(895\) | −9.53569e96 | −0.370844 | ||||||||
\(896\) | − | 3.26460e96i | − | 0.122367i | ||||||
\(897\) | 2.29439e97 | − | 5.39442e96i | 0.828926 | − | 0.194892i | ||||
\(898\) | 8.90017e96 | 0.309941 | ||||||||
\(899\) | 3.77778e97i | 1.26814i | ||||||||
\(900\) | 2.15757e96 | − | 1.07392e96i | 0.0698172 | − | 0.0347510i | ||||
\(901\) | −2.38061e97 | −0.742626 | ||||||||
\(902\) | 1.78028e97i | 0.535393i | ||||||||
\(903\) | −1.97460e97 | − | 8.39848e97i | −0.572511 | − | 2.43503i | ||||
\(904\) | 4.35359e95 | 0.0121700 | ||||||||
\(905\) | − | 6.52362e97i | − | 1.75827i | ||||||
\(906\) | −5.69422e97 | + | 1.33879e97i | −1.47980 | + | 0.347922i | ||||
\(907\) | 2.01602e97 | 0.505189 | 0.252595 | − | 0.967572i | \(-0.418716\pi\) | ||||
0.252595 | + | 0.967572i | \(0.418716\pi\) | |||||||
\(908\) | − | 2.65048e97i | − | 0.640459i | ||||||
\(909\) | 2.27057e97 | + | 4.56174e97i | 0.529087 | + | 1.06297i | ||||
\(910\) | −7.10745e97 | −1.59716 | ||||||||
\(911\) | − | 2.00570e97i | − | 0.434669i | −0.976097 | − | 0.217335i | \(-0.930264\pi\) | ||
0.976097 | − | 0.217335i | \(-0.0697363\pi\) | |||||||
\(912\) | 8.09382e96 | + | 3.44251e97i | 0.169170 | + | 0.719524i | ||||
\(913\) | −1.76345e97 | −0.355490 | ||||||||
\(914\) | 4.94690e97i | 0.961852i | ||||||||
\(915\) | 1.27777e97 | − | 3.00422e96i | 0.239639 | − | 0.0563425i | ||||
\(916\) | 3.36624e97 | 0.608967 | ||||||||
\(917\) | 7.58827e96i | 0.132420i | ||||||||
\(918\) | 3.19099e97 | + | 3.84463e97i | 0.537177 | + | 0.647211i | ||||
\(919\) | 7.20468e97 | 1.17005 | 0.585023 | − | 0.811017i | \(-0.301085\pi\) | ||||
0.585023 | + | 0.811017i | \(0.301085\pi\) | |||||||
\(920\) | 2.73801e96i | 0.0428980i | ||||||||
\(921\) | 1.32930e97 | + | 5.65384e97i | 0.200934 | + | 0.854625i | ||||
\(922\) | −9.03921e97 | −1.31829 | ||||||||
\(923\) | 4.63318e97i | 0.651962i | ||||||||
\(924\) | 1.60744e98 | − | 3.77932e97i | 2.18253 | − | 0.513143i | ||||
\(925\) | −6.16136e96 | −0.0807235 | ||||||||
\(926\) | − | 4.52435e96i | − | 0.0571996i | ||||||
\(927\) | −4.53358e96 | + | 2.25656e96i | −0.0553108 | + | 0.0275305i | ||||
\(928\) | 1.70147e98 | 2.00328 | ||||||||
\(929\) | 7.02283e97i | 0.797983i | 0.916955 | + | 0.398992i | \(0.130640\pi\) | ||||
−0.916955 | + | 0.398992i | \(0.869360\pi\) | |||||||
\(930\) | 2.56972e97 | + | 1.09297e98i | 0.281805 | + | 1.19859i | ||||
\(931\) | −1.43821e98 | −1.52224 | ||||||||
\(932\) | 6.83222e96i | 0.0697970i | ||||||||
\(933\) | −4.67765e97 | + | 1.09978e97i | −0.461247 | + | 0.108446i | ||||
\(934\) | −2.47522e98 | −2.35595 | ||||||||
\(935\) | − | 7.80149e97i | − | 0.716794i | ||||||
\(936\) | 1.19401e96 | + | 2.39885e96i | 0.0105902 | + | 0.0212765i | ||||
\(937\) | −1.05965e98 | −0.907309 | −0.453655 | − | 0.891178i | \(-0.649880\pi\) | ||||
−0.453655 | + | 0.891178i | \(0.649880\pi\) | |||||||
\(938\) | − | 1.27316e98i | − | 1.05242i | ||||||
\(939\) | −2.79118e96 | − | 1.18716e97i | −0.0222753 | − | 0.0947424i | ||||
\(940\) | −1.69659e97 | −0.130725 | ||||||||
\(941\) | − | 8.09811e97i | − | 0.602457i | −0.953552 | − | 0.301228i | \(-0.902603\pi\) | ||
0.953552 | − | 0.301228i | \(-0.0973967\pi\) | |||||||
\(942\) | −3.13107e98 | + | 7.36160e97i | −2.24913 | + | 0.528801i | ||||
\(943\) | 5.43712e97 | 0.377123 | ||||||||
\(944\) | 8.19465e97i | 0.548851i | ||||||||
\(945\) | 1.98307e98 | − | 1.64592e98i | 1.28259 | − | 1.06453i | ||||
\(946\) | 4.14611e98 | 2.58961 | ||||||||
\(947\) | − | 2.17413e98i | − | 1.31140i | −0.755021 | − | 0.655701i | \(-0.772373\pi\) | ||
0.755021 | − | 0.655701i | \(-0.227627\pi\) | |||||||
\(948\) | −3.50141e97 | − | 1.48924e98i | −0.203971 | − | 0.867539i | ||||
\(949\) | −1.91718e98 | −1.07864 | ||||||||
\(950\) | − | 1.51136e97i | − | 0.0821273i | ||||||
\(951\) | 2.13932e97 | − | 5.02984e96i | 0.112284 | − | 0.0263996i | ||||
\(952\) | −7.13579e96 | −0.0361762 | ||||||||
\(953\) | − | 1.22952e98i | − | 0.602102i | −0.953608 | − | 0.301051i | \(-0.902663\pi\) | ||
0.953608 | − | 0.301051i | \(-0.0973374\pi\) | |||||||
\(954\) | 3.38330e98 | − | 1.68401e98i | 1.60046 | − | 0.796617i | ||||
\(955\) | −2.60777e98 | −1.19167 | ||||||||
\(956\) | 2.19769e98i | 0.970187i | ||||||||
\(957\) | 9.53748e97 | + | 4.05654e98i | 0.406762 | + | 1.73006i | ||||
\(958\) | 3.64052e98 | 1.50004 | ||||||||
\(959\) | 4.18018e98i | 1.66410i | ||||||||
\(960\) | 2.55179e98 | − | 5.99962e97i | 0.981509 | − | 0.230766i | ||||
\(961\) | −5.10159e97 | −0.189598 | ||||||||
\(962\) | − | 2.83043e98i | − | 1.01642i | ||||||
\(963\) | 1.10371e98 | + | 2.21743e98i | 0.382990 | + | 0.769454i | ||||
\(964\) | −3.88019e98 | −1.30110 | ||||||||
\(965\) | 2.27188e98i | 0.736179i | ||||||||
\(966\) | −2.28053e98 | − | 9.69970e98i | −0.714153 | − | 3.03748i | ||||
\(967\) | −1.05764e98 | −0.320083 | −0.160042 | − | 0.987110i | \(-0.551163\pi\) | ||||
−0.160042 | + | 0.987110i | \(0.551163\pi\) | |||||||
\(968\) | 7.13955e96i | 0.0208826i | ||||||||
\(969\) | 1.54371e98 | − | 3.62948e97i | 0.436396 | − | 0.102603i | ||||
\(970\) | −3.54194e97 | −0.0967773 | ||||||||
\(971\) | − | 1.72623e98i | − | 0.455895i | −0.973673 | − | 0.227948i | \(-0.926799\pi\) | ||
0.973673 | − | 0.227948i | \(-0.0732015\pi\) | |||||||
\(972\) | −3.67176e98 | − | 1.62298e98i | −0.937319 | − | 0.414312i | ||||
\(973\) | 9.23976e98 | 2.28001 | ||||||||
\(974\) | 4.10862e98i | 0.980055i | ||||||||
\(975\) | 5.08630e96 | + | 2.16333e97i | 0.0117287 | + | 0.0498851i | ||||
\(976\) | −1.11967e98 | −0.249602 | ||||||||
\(977\) | 1.30299e97i | 0.0280815i | 0.999901 | + | 0.0140408i | \(0.00446946\pi\) | ||||
−0.999901 | + | 0.0140408i | \(0.995531\pi\) | |||||||
\(978\) | −1.08115e99 | + | 2.54195e98i | −2.25271 | + | 0.529644i | ||||
\(979\) | −1.05100e98 | −0.211726 | ||||||||
\(980\) | 1.01504e99i | 1.97708i | ||||||||
\(981\) | −8.44903e98 | + | 4.20544e98i | −1.59122 | + | 0.792017i | ||||
\(982\) | −7.53369e98 | −1.37192 | ||||||||
\(983\) | 9.87142e98i | 1.73826i | 0.494587 | + | 0.869128i | \(0.335319\pi\) | ||||
−0.494587 | + | 0.869128i | \(0.664681\pi\) | |||||||
\(984\) | 1.41475e96 | + | 6.01730e96i | 0.00240903 | + | 0.0102462i | ||||
\(985\) | 9.51572e98 | 1.56692 | ||||||||
\(986\) | − | 7.44046e98i | − | 1.18485i | ||||||
\(987\) | 1.45466e98 | − | 3.42012e97i | 0.224025 | − | 0.0526714i | ||||
\(988\) | 3.51398e98 | 0.523384 | ||||||||
\(989\) | − | 1.26626e99i | − | 1.82408i | ||||||
\(990\) | 5.51868e98 | + | 1.10874e99i | 0.768907 | + | 1.54479i | ||||
\(991\) | −4.06315e98 | −0.547560 | −0.273780 | − | 0.961792i | \(-0.588274\pi\) | ||||
−0.273780 | + | 0.961792i | \(0.588274\pi\) | |||||||
\(992\) | − | 9.82109e98i | − | 1.28019i | ||||||
\(993\) | 7.38008e97 | + | 3.13894e98i | 0.0930541 | + | 0.395783i | ||||
\(994\) | 1.95871e99 | 2.38902 | ||||||||
\(995\) | − | 1.17364e99i | − | 1.38475i | ||||||
\(996\) | −2.46271e98 | + | 5.79018e97i | −0.281096 | + | 0.0660897i | ||||
\(997\) | −6.76976e98 | −0.747538 | −0.373769 | − | 0.927522i | \(-0.621935\pi\) | ||||
−0.373769 | + | 0.927522i | \(0.621935\pi\) | |||||||
\(998\) | 8.20861e98i | 0.876923i | ||||||||
\(999\) | 6.55462e98 | + | 7.89725e98i | 0.677464 | + | 0.816234i |
(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 | 3.67.b.b.2.17 | yes | 20 | |
3.2 | odd | 2 | inner | 3.67.b.b.2.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.67.b.b.2.4 | ✓ | 20 | 3.2 | odd | 2 | inner | |
3.67.b.b.2.17 | yes | 20 | 1.1 | even | 1 | trivial |