Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,37,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 37, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(32.8365034637\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + \cdots + 51\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.13 | ||
Root | \(-2.71780e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.37.b.b.3.14 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 194816. | − | 175403.i | 0.743164 | − | 0.669110i | ||||
\(3\) | − | 4.34848e8i | − | 1.12242i | −0.827674 | − | 0.561210i | \(-0.810336\pi\) | ||
0.827674 | − | 0.561210i | \(-0.189664\pi\) | |||||||
\(4\) | 7.18697e9 | − | 6.83426e10i | 0.104584 | − | 0.994516i | ||||
\(5\) | −7.52461e12 | −1.97253 | −0.986266 | − | 0.165163i | \(-0.947185\pi\) | ||||
−0.986266 | + | 0.165163i | \(0.947185\pi\) | |||||||
\(6\) | −7.62737e13 | − | 8.47153e13i | −0.751022 | − | 0.834141i | ||||
\(7\) | − | 2.26538e15i | − | 1.39115i | −0.718451 | − | 0.695577i | \(-0.755149\pi\) | ||
0.718451 | − | 0.695577i | \(-0.244851\pi\) | |||||||
\(8\) | −1.05874e16 | − | 1.45748e16i | −0.587717 | − | 0.809066i | ||||
\(9\) | −3.89984e16 | −0.259825 | ||||||||
\(10\) | −1.46591e18 | + | 1.31984e18i | −1.46591 | + | 1.31984i | ||||
\(11\) | − | 3.43277e17i | − | 0.0617413i | −0.999523 | − | 0.0308707i | \(-0.990172\pi\) | ||
0.999523 | − | 0.0308707i | \(-0.00982799\pi\) | |||||||
\(12\) | −2.97187e19 | − | 3.12524e18i | −1.11626 | − | 0.117387i | ||||
\(13\) | 4.11380e19 | 0.365816 | 0.182908 | − | 0.983130i | \(-0.441449\pi\) | ||||
0.182908 | + | 0.983130i | \(0.441449\pi\) | |||||||
\(14\) | −3.97354e20 | − | 4.41331e20i | −0.930835 | − | 1.03386i | ||||
\(15\) | 3.27207e21i | 2.21401i | ||||||||
\(16\) | −4.61906e21 | − | 9.82353e20i | −0.978124 | − | 0.208021i | ||||
\(17\) | 1.36790e22 | 0.972686 | 0.486343 | − | 0.873768i | \(-0.338331\pi\) | ||||
0.486343 | + | 0.873768i | \(0.338331\pi\) | |||||||
\(18\) | −7.59750e21 | + | 6.84044e21i | −0.193093 | + | 0.173852i | ||||
\(19\) | 6.68442e21i | 0.0641947i | 0.999485 | + | 0.0320973i | \(0.0102187\pi\) | ||||
−0.999485 | + | 0.0320973i | \(0.989781\pi\) | |||||||
\(20\) | −5.40792e22 | + | 5.14252e23i | −0.206296 | + | 1.96172i | ||||
\(21\) | −9.85095e23 | −1.56146 | ||||||||
\(22\) | −6.02118e22 | − | 6.68757e22i | −0.0413117 | − | 0.0458839i | ||||
\(23\) | − | 3.00330e24i | − | 0.925760i | −0.886421 | − | 0.462880i | \(-0.846816\pi\) | ||
0.886421 | − | 0.462880i | \(-0.153184\pi\) | |||||||
\(24\) | −6.33785e24 | + | 4.60390e24i | −0.908112 | + | 0.659665i | ||||
\(25\) | 4.20679e25 | 2.89088 | ||||||||
\(26\) | 8.01434e24 | − | 7.21574e24i | 0.271861 | − | 0.244771i | ||||
\(27\) | − | 4.83100e25i | − | 0.830786i | ||||||
\(28\) | −1.54822e26 | − | 1.62812e25i | −1.38353 | − | 0.145493i | ||||
\(29\) | −1.64857e26 | −0.783329 | −0.391665 | − | 0.920108i | \(-0.628101\pi\) | ||||
−0.391665 | + | 0.920108i | \(0.628101\pi\) | |||||||
\(30\) | 5.73930e26 | + | 6.37450e26i | 1.48141 | + | 1.64537i | ||||
\(31\) | 4.32456e26i | 0.618631i | 0.950960 | + | 0.309315i | \(0.100100\pi\) | ||||
−0.950960 | + | 0.309315i | \(0.899900\pi\) | |||||||
\(32\) | −1.07217e27 | + | 6.18820e26i | −0.866095 | + | 0.499879i | ||||
\(33\) | −1.49273e26 | −0.0692996 | ||||||||
\(34\) | 2.66488e27 | − | 2.39933e27i | 0.722865 | − | 0.650834i | ||||
\(35\) | 1.70461e28i | 2.74410i | ||||||||
\(36\) | −2.80280e26 | + | 2.66525e27i | −0.0271736 | + | 0.258400i | ||||
\(37\) | −2.47476e27 | −0.146522 | −0.0732609 | − | 0.997313i | \(-0.523341\pi\) | ||||
−0.0732609 | + | 0.997313i | \(0.523341\pi\) | |||||||
\(38\) | 1.17247e27 | + | 1.30223e27i | 0.0429533 | + | 0.0477071i | ||||
\(39\) | − | 1.78888e28i | − | 0.410599i | ||||||
\(40\) | 7.96659e28 | + | 1.09670e29i | 1.15929 | + | 1.59591i | ||||
\(41\) | 3.98388e28 | 0.371704 | 0.185852 | − | 0.982578i | \(-0.440496\pi\) | ||||
0.185852 | + | 0.982578i | \(0.440496\pi\) | |||||||
\(42\) | −1.91912e29 | + | 1.72789e29i | −1.16042 | + | 1.04479i | ||||
\(43\) | 3.42354e29i | 1.35533i | 0.735373 | + | 0.677663i | \(0.237007\pi\) | ||||
−0.735373 | + | 0.677663i | \(0.762993\pi\) | |||||||
\(44\) | −2.34604e28 | − | 2.46712e27i | −0.0614027 | − | 0.00645716i | ||||
\(45\) | 2.93448e29 | 0.512514 | ||||||||
\(46\) | −5.26789e29 | − | 5.85091e29i | −0.619435 | − | 0.687991i | ||||
\(47\) | − | 7.98074e29i | − | 0.637208i | −0.947888 | − | 0.318604i | \(-0.896786\pi\) | ||
0.947888 | − | 0.318604i | \(-0.103214\pi\) | |||||||
\(48\) | −4.27174e29 | + | 2.00859e30i | −0.233487 | + | 1.09787i | ||||
\(49\) | −2.48020e30 | −0.935312 | ||||||||
\(50\) | 8.19549e30 | − | 7.37884e30i | 2.14840 | − | 1.93432i | ||||
\(51\) | − | 5.94827e30i | − | 1.09176i | ||||||
\(52\) | 2.95658e29 | − | 2.81148e30i | 0.0382586 | − | 0.363810i | ||||
\(53\) | −1.60293e30 | −0.147214 | −0.0736070 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736070 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(54\) | −8.47373e30 | − | 9.41156e30i | −0.555887 | − | 0.617410i | ||||
\(55\) | 2.58302e30i | 0.121787i | ||||||||
\(56\) | −3.30175e31 | + | 2.39844e31i | −1.12554 | + | 0.817606i | ||||
\(57\) | 2.90671e30 | 0.0720533 | ||||||||
\(58\) | −3.21168e31 | + | 2.89165e31i | −0.582142 | + | 0.524133i | ||||
\(59\) | − | 8.75336e31i | − | 1.16638i | −0.812337 | − | 0.583188i | \(-0.801805\pi\) | ||
0.812337 | − | 0.583188i | \(-0.198195\pi\) | |||||||
\(60\) | 2.23622e32 | + | 2.35162e31i | 2.20187 | + | 0.231550i | ||||
\(61\) | −3.85746e31 | −0.282075 | −0.141037 | − | 0.990004i | \(-0.545044\pi\) | ||||
−0.141037 | + | 0.990004i | \(0.545044\pi\) | |||||||
\(62\) | 7.58541e31 | + | 8.42493e31i | 0.413932 | + | 0.459744i | ||||
\(63\) | 8.83460e31i | 0.361457i | ||||||||
\(64\) | −1.00334e32 | + | 3.08619e32i | −0.309177 | + | 0.951005i | ||||
\(65\) | −3.09548e32 | −0.721584 | ||||||||
\(66\) | −2.90808e31 | + | 2.61830e31i | −0.0515010 | + | 0.0463691i | ||||
\(67\) | 7.88595e32i | 1.06539i | 0.846308 | + | 0.532694i | \(0.178820\pi\) | ||||
−0.846308 | + | 0.532694i | \(0.821180\pi\) | |||||||
\(68\) | 9.83103e31 | − | 9.34856e32i | 0.101728 | − | 0.967352i | ||||
\(69\) | −1.30598e33 | −1.03909 | ||||||||
\(70\) | 2.98994e33 | + | 3.32085e33i | 1.83610 | + | 2.03931i | ||||
\(71\) | − | 3.14638e33i | − | 1.49679i | −0.663254 | − | 0.748395i | \(-0.730825\pi\) | ||
0.663254 | − | 0.748395i | \(-0.269175\pi\) | |||||||
\(72\) | 4.12890e32 | + | 5.68395e32i | 0.152704 | + | 0.210216i | ||||
\(73\) | −3.43035e33 | −0.989755 | −0.494877 | − | 0.868963i | \(-0.664787\pi\) | ||||
−0.494877 | + | 0.868963i | \(0.664787\pi\) | |||||||
\(74\) | −4.82122e32 | + | 4.34081e32i | −0.108890 | + | 0.0980391i | ||||
\(75\) | − | 1.82932e34i | − | 3.24478i | ||||||
\(76\) | 4.56831e32 | + | 4.80407e31i | 0.0638426 | + | 0.00671375i | ||||
\(77\) | −7.77650e32 | −0.0858917 | ||||||||
\(78\) | −3.13775e33 | − | 3.48502e33i | −0.274736 | − | 0.305142i | ||||
\(79\) | 9.73086e33i | 0.677429i | 0.940889 | + | 0.338714i | \(0.109992\pi\) | ||||
−0.940889 | + | 0.338714i | \(0.890008\pi\) | |||||||
\(80\) | 3.47567e34 | + | 7.39182e33i | 1.92938 | + | 0.410329i | ||||
\(81\) | −2.68610e34 | −1.19232 | ||||||||
\(82\) | 7.76123e33 | − | 6.98785e33i | 0.276237 | − | 0.248711i | ||||
\(83\) | − | 3.05582e34i | − | 0.874424i | −0.899359 | − | 0.437212i | \(-0.855966\pi\) | ||
0.899359 | − | 0.437212i | \(-0.144034\pi\) | |||||||
\(84\) | −7.07985e33 | + | 6.73240e34i | −0.163304 | + | 1.55290i | ||||
\(85\) | −1.02929e35 | −1.91865 | ||||||||
\(86\) | 6.00500e34 | + | 6.66961e34i | 0.906862 | + | 1.00723i | ||||
\(87\) | 7.16879e34i | 0.879224i | ||||||||
\(88\) | −5.00320e33 | + | 3.63440e33i | −0.0499528 | + | 0.0362864i | ||||
\(89\) | 1.54289e35 | 1.25694 | 0.628471 | − | 0.777833i | \(-0.283681\pi\) | ||||
0.628471 | + | 0.777833i | \(0.283681\pi\) | |||||||
\(90\) | 5.71683e34 | − | 5.14717e34i | 0.380882 | − | 0.342928i | ||||
\(91\) | − | 9.31931e34i | − | 0.508907i | ||||||
\(92\) | −2.05254e35 | − | 2.15847e34i | −0.920683 | − | 0.0968198i | ||||
\(93\) | 1.88053e35 | 0.694363 | ||||||||
\(94\) | −1.39985e35 | − | 1.55477e35i | −0.426362 | − | 0.473550i | ||||
\(95\) | − | 5.02977e34i | − | 0.126626i | ||||||
\(96\) | 2.69093e35 | + | 4.66233e35i | 0.561074 | + | 0.972122i | ||||
\(97\) | −2.22436e35 | −0.384870 | −0.192435 | − | 0.981310i | \(-0.561638\pi\) | ||||
−0.192435 | + | 0.981310i | \(0.561638\pi\) | |||||||
\(98\) | −4.83181e35 | + | 4.35034e35i | −0.695090 | + | 0.625826i | ||||
\(99\) | 1.33872e34i | 0.0160420i | ||||||||
\(100\) | 3.02341e35 | − | 2.87503e36i | 0.302341 | − | 2.87503i | ||||
\(101\) | −8.23756e35 | −0.688674 | −0.344337 | − | 0.938846i | \(-0.611896\pi\) | ||||
−0.344337 | + | 0.938846i | \(0.611896\pi\) | |||||||
\(102\) | −1.04335e36 | − | 1.15882e36i | −0.730508 | − | 0.811357i | ||||
\(103\) | 2.38014e36i | 1.39808i | 0.715081 | + | 0.699042i | \(0.246390\pi\) | ||||
−0.715081 | + | 0.699042i | \(0.753610\pi\) | |||||||
\(104\) | −4.35544e35 | − | 5.99580e35i | −0.214997 | − | 0.295970i | ||||
\(105\) | 7.41246e36 | 3.08003 | ||||||||
\(106\) | −3.12276e35 | + | 2.81159e35i | −0.109404 | + | 0.0985023i | ||||
\(107\) | − | 5.96349e34i | − | 0.0176438i | −0.999961 | − | 0.00882190i | \(-0.997192\pi\) | ||
0.999961 | − | 0.00882190i | \(-0.00280814\pi\) | |||||||
\(108\) | −3.30163e36 | − | 3.47203e35i | −0.826230 | − | 0.0868871i | ||||
\(109\) | −2.46758e36 | −0.523111 | −0.261555 | − | 0.965188i | \(-0.584235\pi\) | ||||
−0.261555 | + | 0.965188i | \(0.584235\pi\) | |||||||
\(110\) | 4.53070e35 | + | 5.03214e35i | 0.0814887 | + | 0.0905075i | ||||
\(111\) | 1.07614e36i | 0.164459i | ||||||||
\(112\) | −2.22540e36 | + | 1.04639e37i | −0.289390 | + | 1.36072i | ||||
\(113\) | −1.13641e35 | −0.0125928 | −0.00629639 | − | 0.999980i | \(-0.502004\pi\) | ||||
−0.00629639 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(114\) | 5.66273e35 | − | 5.09846e35i | 0.0535474 | − | 0.0482116i | ||||
\(115\) | 2.25987e37i | 1.82609i | ||||||||
\(116\) | −1.18482e36 | + | 1.12668e37i | −0.0819238 | + | 0.779033i | ||||
\(117\) | −1.60432e36 | −0.0950483 | ||||||||
\(118\) | −1.53537e37 | − | 1.70529e37i | −0.780434 | − | 0.866808i | ||||
\(119\) | − | 3.09880e37i | − | 1.35316i | ||||||
\(120\) | 4.76898e37 | − | 3.46426e37i | 1.79128 | − | 1.30121i | ||||
\(121\) | 3.07948e37 | 0.996188 | ||||||||
\(122\) | −7.51494e36 | + | 6.76610e36i | −0.209628 | + | 0.188739i | ||||
\(123\) | − | 1.73238e37i | − | 0.417208i | ||||||
\(124\) | 2.95552e37 | + | 3.10805e36i | 0.615238 | + | 0.0646990i | ||||
\(125\) | −2.07047e38 | −3.72983 | ||||||||
\(126\) | 1.54962e37 | + | 1.72112e37i | 0.241855 | + | 0.268622i | ||||
\(127\) | − | 1.29608e38i | − | 1.75455i | −0.479992 | − | 0.877273i | \(-0.659361\pi\) | ||
0.479992 | − | 0.877273i | \(-0.340639\pi\) | |||||||
\(128\) | 3.45861e37 | + | 7.77226e37i | 0.406558 | + | 0.913625i | ||||
\(129\) | 1.48872e38 | 1.52124 | ||||||||
\(130\) | −6.03048e37 | + | 5.42956e37i | −0.536255 | + | 0.482819i | ||||
\(131\) | − | 9.30311e37i | − | 0.720684i | −0.932820 | − | 0.360342i | \(-0.882660\pi\) | ||
0.932820 | − | 0.360342i | \(-0.117340\pi\) | |||||||
\(132\) | −1.07282e36 | + | 1.02017e37i | −0.00724764 | + | 0.0689196i | ||||
\(133\) | 1.51427e37 | 0.0893047 | ||||||||
\(134\) | 1.38322e38 | + | 1.53631e38i | 0.712861 | + | 0.791757i | ||||
\(135\) | 3.63514e38i | 1.63875i | ||||||||
\(136\) | −1.44824e38 | − | 1.99369e38i | −0.571664 | − | 0.786967i | ||||
\(137\) | −2.21131e38 | −0.765031 | −0.382515 | − | 0.923949i | \(-0.624942\pi\) | ||||
−0.382515 | + | 0.923949i | \(0.624942\pi\) | |||||||
\(138\) | −2.54426e38 | + | 2.29073e38i | −0.772214 | + | 0.695266i | ||||
\(139\) | − | 5.94068e37i | − | 0.158332i | −0.996861 | − | 0.0791661i | \(-0.974774\pi\) | ||
0.996861 | − | 0.0791661i | \(-0.0252258\pi\) | |||||||
\(140\) | 1.16497e39 | + | 1.22510e38i | 2.72905 | + | 0.286989i | ||||
\(141\) | −3.47041e38 | −0.715215 | ||||||||
\(142\) | −5.51885e38 | − | 6.12964e38i | −1.00152 | − | 1.11236i | ||||
\(143\) | − | 1.41217e37i | − | 0.0225860i | ||||||
\(144\) | 1.80136e38 | + | 3.83102e37i | 0.254141 | + | 0.0540492i | ||||
\(145\) | 1.24049e39 | 1.54514 | ||||||||
\(146\) | −6.68287e38 | + | 6.01695e38i | −0.735550 | + | 0.662254i | ||||
\(147\) | 1.07851e39i | 1.04981i | ||||||||
\(148\) | −1.77860e37 | + | 1.69132e38i | −0.0153239 | + | 0.145718i | ||||
\(149\) | 8.40830e38 | 0.641734 | 0.320867 | − | 0.947124i | \(-0.396026\pi\) | ||||
0.320867 | + | 0.947124i | \(0.396026\pi\) | |||||||
\(150\) | −3.20868e39 | − | 3.56380e39i | −2.17112 | − | 2.41141i | ||||
\(151\) | 1.55416e38i | 0.0933061i | 0.998911 | + | 0.0466530i | \(0.0148555\pi\) | ||||
−0.998911 | + | 0.0466530i | \(0.985144\pi\) | |||||||
\(152\) | 9.74244e37 | − | 7.07704e37i | 0.0519377 | − | 0.0377283i | ||||
\(153\) | −5.33457e38 | −0.252728 | ||||||||
\(154\) | −1.51499e38 | + | 1.36402e38i | −0.0638316 | + | 0.0574710i | ||||
\(155\) | − | 3.25406e39i | − | 1.22027i | ||||||
\(156\) | −1.22257e39 | − | 1.28566e38i | −0.408348 | − | 0.0429422i | ||||
\(157\) | 5.36842e39 | 1.59828 | 0.799140 | − | 0.601145i | \(-0.205289\pi\) | ||||
0.799140 | + | 0.601145i | \(0.205289\pi\) | |||||||
\(158\) | 1.70682e39 | + | 1.89573e39i | 0.453274 | + | 0.503440i | ||||
\(159\) | 6.97031e38i | 0.165236i | ||||||||
\(160\) | 8.06770e39 | − | 4.65638e39i | 1.70840 | − | 0.986027i | ||||
\(161\) | −6.80361e39 | −1.28788 | ||||||||
\(162\) | −5.23294e39 | + | 4.71150e39i | −0.886086 | + | 0.797790i | ||||
\(163\) | 1.12696e40i | 1.70817i | 0.520134 | + | 0.854085i | \(0.325882\pi\) | ||||
−0.520134 | + | 0.854085i | \(0.674118\pi\) | |||||||
\(164\) | 2.86320e38 | − | 2.72269e39i | 0.0388743 | − | 0.369665i | ||||
\(165\) | 1.12322e39 | 0.136696 | ||||||||
\(166\) | −5.36000e39 | − | 5.95322e39i | −0.585085 | − | 0.649840i | ||||
\(167\) | 4.42541e39i | 0.433568i | 0.976220 | + | 0.216784i | \(0.0695567\pi\) | ||||
−0.976220 | + | 0.216784i | \(0.930443\pi\) | |||||||
\(168\) | 1.04296e40 | + | 1.43576e40i | 0.917697 | + | 1.26332i | ||||
\(169\) | −1.09539e40 | −0.866178 | ||||||||
\(170\) | −2.00522e40 | + | 1.80541e40i | −1.42587 | + | 1.28379i | ||||
\(171\) | − | 2.60682e38i | − | 0.0166794i | ||||||
\(172\) | 2.33974e40 | + | 2.46049e39i | 1.34789 | + | 0.141746i | ||||
\(173\) | 1.15750e40 | 0.600747 | 0.300373 | − | 0.953822i | \(-0.402889\pi\) | ||||
0.300373 | + | 0.953822i | \(0.402889\pi\) | |||||||
\(174\) | 1.25743e40 | + | 1.39659e40i | 0.588297 | + | 0.653407i | ||||
\(175\) | − | 9.52996e40i | − | 4.02167i | ||||||
\(176\) | −3.37219e38 | + | 1.58562e39i | −0.0128435 | + | 0.0603907i | ||||
\(177\) | −3.80638e40 | −1.30916 | ||||||||
\(178\) | 3.00580e40 | − | 2.70628e40i | 0.934114 | − | 0.841032i | ||||
\(179\) | 3.56882e40i | 1.00270i | 0.865245 | + | 0.501349i | \(0.167163\pi\) | ||||
−0.865245 | + | 0.501349i | \(0.832837\pi\) | |||||||
\(180\) | 2.10900e39 | − | 2.00550e40i | 0.0536008 | − | 0.509703i | ||||
\(181\) | 2.34751e39 | 0.0539999 | 0.0269999 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269999 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(182\) | −1.63464e40 | − | 1.81555e40i | −0.340515 | − | 0.378201i | ||||
\(183\) | 1.67741e40i | 0.316606i | ||||||||
\(184\) | −4.37727e40 | + | 3.17971e40i | −0.749001 | + | 0.544085i | ||||
\(185\) | 1.86216e40 | 0.289019 | ||||||||
\(186\) | 3.66357e40 | − | 3.29850e40i | 0.516025 | − | 0.464605i | ||||
\(187\) | − | 4.69567e39i | − | 0.0600549i | ||||||
\(188\) | −5.45424e40 | − | 5.73573e39i | −0.633714 | − | 0.0666419i | ||||
\(189\) | −1.09440e41 | −1.15575 | ||||||||
\(190\) | −8.82237e39 | − | 9.79879e39i | −0.0847267 | − | 0.0941039i | ||||
\(191\) | 8.12961e40i | 0.710344i | 0.934801 | + | 0.355172i | \(0.115578\pi\) | ||||
−0.934801 | + | 0.355172i | \(0.884422\pi\) | |||||||
\(192\) | 1.34202e41 | + | 4.36299e40i | 1.06743 | + | 0.347026i | ||||
\(193\) | 1.55906e41 | 1.12936 | 0.564680 | − | 0.825310i | \(-0.309000\pi\) | ||||
0.564680 | + | 0.825310i | \(0.309000\pi\) | |||||||
\(194\) | −4.33341e40 | + | 3.90160e40i | −0.286021 | + | 0.257520i | ||||
\(195\) | 1.34606e41i | 0.809920i | ||||||||
\(196\) | −1.78251e40 | + | 1.69503e41i | −0.0978188 | + | 0.930183i | ||||
\(197\) | 2.26219e41 | 1.13276 | 0.566379 | − | 0.824145i | \(-0.308344\pi\) | ||||
0.566379 | + | 0.824145i | \(0.308344\pi\) | |||||||
\(198\) | 2.34816e39 | + | 2.60804e39i | 0.0107338 | + | 0.0119218i | ||||
\(199\) | − | 1.03550e41i | − | 0.432310i | −0.976359 | − | 0.216155i | \(-0.930648\pi\) | ||
0.976359 | − | 0.216155i | \(-0.0693517\pi\) | |||||||
\(200\) | −4.45389e41 | − | 6.13133e41i | −1.69902 | − | 2.33892i | ||||
\(201\) | 3.42919e41 | 1.19581 | ||||||||
\(202\) | −1.60481e41 | + | 1.44489e41i | −0.511798 | + | 0.460799i | ||||
\(203\) | 3.73464e41i | 1.08973i | ||||||||
\(204\) | −4.06521e41 | − | 4.27501e40i | −1.08577 | − | 0.114181i | ||||
\(205\) | −2.99772e41 | −0.733198 | ||||||||
\(206\) | 4.17485e41 | + | 4.63690e41i | 0.935472 | + | 1.03901i | ||||
\(207\) | 1.17124e41i | 0.240536i | ||||||||
\(208\) | −1.90019e41 | − | 4.04120e40i | −0.357814 | − | 0.0760976i | ||||
\(209\) | 2.29460e39 | 0.00396346 | ||||||||
\(210\) | 1.44406e42 | − | 1.30017e42i | 2.28897 | − | 2.06088i | ||||
\(211\) | 1.91579e40i | 0.0278781i | 0.999903 | + | 0.0139391i | \(0.00443708\pi\) | ||||
−0.999903 | + | 0.0139391i | \(0.995563\pi\) | |||||||
\(212\) | −1.15202e40 | + | 1.09548e41i | −0.0153962 | + | 0.146407i | ||||
\(213\) | −1.36820e42 | −1.68003 | ||||||||
\(214\) | −1.04601e40 | − | 1.16178e40i | −0.0118056 | − | 0.0131122i | ||||
\(215\) | − | 2.57608e42i | − | 2.67342i | ||||||
\(216\) | −7.04111e41 | + | 5.11476e41i | −0.672161 | + | 0.488268i | ||||
\(217\) | 9.79675e41 | 0.860611 | ||||||||
\(218\) | −4.80723e41 | + | 4.32821e41i | −0.388757 | + | 0.350018i | ||||
\(219\) | 1.49168e42i | 1.11092i | ||||||||
\(220\) | 1.76531e41 | + | 1.85641e40i | 0.121119 | + | 0.0127370i | ||||
\(221\) | 5.62725e41 | 0.355824 | ||||||||
\(222\) | 1.88759e41 | + | 2.09650e41i | 0.110041 | + | 0.122220i | ||||
\(223\) | − | 4.31584e41i | − | 0.232048i | −0.993246 | − | 0.116024i | \(-0.962985\pi\) | ||
0.993246 | − | 0.116024i | \(-0.0370149\pi\) | |||||||
\(224\) | 1.40186e42 | + | 2.42888e42i | 0.695409 | + | 1.20487i | ||||
\(225\) | −1.64058e42 | −0.751125 | ||||||||
\(226\) | −2.21390e40 | + | 1.99329e40i | −0.00935850 | + | 0.00842595i | ||||
\(227\) | − | 1.08048e42i | − | 0.421842i | −0.977503 | − | 0.210921i | \(-0.932354\pi\) | ||
0.977503 | − | 0.210921i | \(-0.0676464\pi\) | |||||||
\(228\) | 2.08904e40 | − | 1.98652e41i | 0.00753564 | − | 0.0716582i | ||||
\(229\) | −4.35291e41 | −0.145124 | −0.0725622 | − | 0.997364i | \(-0.523118\pi\) | ||||
−0.0725622 | + | 0.997364i | \(0.523118\pi\) | |||||||
\(230\) | 3.96388e42 | + | 4.40259e42i | 1.22186 | + | 1.35708i | ||||
\(231\) | 3.38160e41i | 0.0964065i | ||||||||
\(232\) | 1.74541e42 | + | 2.40277e42i | 0.460376 | + | 0.633765i | ||||
\(233\) | −6.81668e42 | −1.66405 | −0.832025 | − | 0.554738i | \(-0.812819\pi\) | ||||
−0.832025 | + | 0.554738i | \(0.812819\pi\) | |||||||
\(234\) | −3.12546e41 | + | 2.81402e41i | −0.0706364 | + | 0.0635978i | ||||
\(235\) | 6.00520e42i | 1.25691i | ||||||||
\(236\) | −5.98228e42 | − | 6.29102e41i | −1.15998 | − | 0.121985i | ||||
\(237\) | 4.23145e42 | 0.760359 | ||||||||
\(238\) | −5.43539e42 | − | 6.03695e42i | −0.905410 | − | 1.00562i | ||||
\(239\) | − | 7.79042e42i | − | 1.20337i | −0.798734 | − | 0.601684i | \(-0.794497\pi\) | ||
0.798734 | − | 0.601684i | \(-0.205503\pi\) | |||||||
\(240\) | 3.21432e42 | − | 1.51139e43i | 0.460561 | − | 2.16558i | ||||
\(241\) | 4.71741e42 | 0.627186 | 0.313593 | − | 0.949557i | \(-0.398467\pi\) | ||||
0.313593 | + | 0.949557i | \(0.398467\pi\) | |||||||
\(242\) | 5.99932e42 | − | 5.40151e42i | 0.740331 | − | 0.666559i | ||||
\(243\) | 4.42937e42i | 0.507492i | ||||||||
\(244\) | −2.77234e41 | + | 2.63629e42i | −0.0295005 | + | 0.280528i | ||||
\(245\) | 1.86625e43 | 1.84493 | ||||||||
\(246\) | −3.03866e42 | − | 3.37496e42i | −0.279158 | − | 0.310053i | ||||
\(247\) | 2.74984e41i | 0.0234835i | ||||||||
\(248\) | 6.30298e42 | − | 4.57857e42i | 0.500513 | − | 0.363580i | ||||
\(249\) | −1.32882e43 | −0.981470 | ||||||||
\(250\) | −4.03361e43 | + | 3.63167e43i | −2.77187 | + | 2.49567i | ||||
\(251\) | − | 2.11996e43i | − | 1.35581i | −0.735148 | − | 0.677907i | \(-0.762887\pi\) | ||
0.735148 | − | 0.677907i | \(-0.237113\pi\) | |||||||
\(252\) | 6.03780e42 | + | 6.34940e41i | 0.359475 | + | 0.0378027i | ||||
\(253\) | −1.03096e42 | −0.0571576 | ||||||||
\(254\) | −2.27336e43 | − | 2.52497e43i | −1.17398 | − | 1.30391i | ||||
\(255\) | 4.47585e43i | 2.15353i | ||||||||
\(256\) | 2.03707e43 | + | 9.07509e42i | 0.913454 | + | 0.406941i | ||||
\(257\) | 1.72260e43 | 0.720093 | 0.360046 | − | 0.932934i | \(-0.382761\pi\) | ||||
0.360046 | + | 0.932934i | \(0.382761\pi\) | |||||||
\(258\) | 2.90027e43 | − | 2.61126e43i | 1.13053 | − | 1.01788i | ||||
\(259\) | 5.60626e42i | 0.203834i | ||||||||
\(260\) | −2.22471e42 | + | 2.11553e43i | −0.0754663 | + | 0.717627i | ||||
\(261\) | 6.42917e42 | 0.203529 | ||||||||
\(262\) | −1.63179e43 | − | 1.81239e43i | −0.482216 | − | 0.535586i | ||||
\(263\) | 6.57982e43i | 1.81556i | 0.419447 | + | 0.907780i | \(0.362224\pi\) | ||||
−0.419447 | + | 0.907780i | \(0.637776\pi\) | |||||||
\(264\) | 1.58041e42 | + | 2.17563e42i | 0.0407286 | + | 0.0560680i | ||||
\(265\) | 1.20614e43 | 0.290384 | ||||||||
\(266\) | 2.95004e42 | − | 2.65608e42i | 0.0663680 | − | 0.0597547i | ||||
\(267\) | − | 6.70924e43i | − | 1.41082i | ||||||
\(268\) | 5.38947e43 | + | 5.66761e42i | 1.05955 | + | 0.111423i | ||||
\(269\) | −7.40548e43 | −1.36148 | −0.680742 | − | 0.732523i | \(-0.738342\pi\) | ||||
−0.680742 | + | 0.732523i | \(0.738342\pi\) | |||||||
\(270\) | 6.37615e43 | + | 7.08183e43i | 1.09651 | + | 1.21786i | ||||
\(271\) | − | 1.10364e44i | − | 1.77574i | −0.460093 | − | 0.887871i | \(-0.652184\pi\) | ||
0.460093 | − | 0.887871i | \(-0.347816\pi\) | |||||||
\(272\) | −6.31840e43 | − | 1.34376e43i | −0.951408 | − | 0.202339i | ||||
\(273\) | −4.05248e43 | −0.571207 | ||||||||
\(274\) | −4.30798e43 | + | 3.87870e43i | −0.568543 | + | 0.511889i | ||||
\(275\) | − | 1.44409e43i | − | 0.178487i | ||||||
\(276\) | −9.38605e42 | + | 8.92542e43i | −0.108672 | + | 1.03339i | ||||
\(277\) | −9.72478e43 | −1.05498 | −0.527490 | − | 0.849561i | \(-0.676867\pi\) | ||||
−0.527490 | + | 0.849561i | \(0.676867\pi\) | |||||||
\(278\) | −1.04201e43 | − | 1.15734e43i | −0.105942 | − | 0.117667i | ||||
\(279\) | − | 1.68651e43i | − | 0.160736i | ||||||
\(280\) | 2.48444e44 | − | 1.80473e44i | 2.22016 | − | 1.61275i | ||||
\(281\) | 1.73479e44 | 1.45390 | 0.726948 | − | 0.686693i | \(-0.240938\pi\) | ||||
0.726948 | + | 0.686693i | \(0.240938\pi\) | |||||||
\(282\) | −6.76091e43 | + | 6.08721e43i | −0.531522 | + | 0.478557i | ||||
\(283\) | − | 7.44370e43i | − | 0.549077i | −0.961576 | − | 0.274538i | \(-0.911475\pi\) | ||
0.961576 | − | 0.274538i | \(-0.0885250\pi\) | |||||||
\(284\) | −2.15032e44 | − | 2.26129e43i | −1.48858 | − | 0.156540i | ||||
\(285\) | −2.18719e43 | −0.142128 | ||||||||
\(286\) | −2.47699e42 | − | 2.75113e42i | −0.0151125 | − | 0.0167851i | ||||
\(287\) | − | 9.02499e43i | − | 0.517098i | ||||||
\(288\) | 4.18131e43 | − | 2.41330e43i | 0.225033 | − | 0.129881i | ||||
\(289\) | −1.06563e43 | −0.0538822 | ||||||||
\(290\) | 2.41667e44 | − | 2.17585e44i | 1.14829 | − | 1.03387i | ||||
\(291\) | 9.67260e43i | 0.431986i | ||||||||
\(292\) | −2.46539e43 | + | 2.34439e44i | −0.103513 | + | 0.984327i | ||||
\(293\) | −2.78417e44 | −1.09921 | −0.549603 | − | 0.835426i | \(-0.685221\pi\) | ||||
−0.549603 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(294\) | 1.89174e44 | + | 2.10111e44i | 0.702440 | + | 0.780182i | ||||
\(295\) | 6.58657e44i | 2.30072i | ||||||||
\(296\) | 2.62012e43 | + | 3.60692e43i | 0.0861133 | + | 0.118546i | ||||
\(297\) | −1.65837e43 | −0.0512938 | ||||||||
\(298\) | 1.63807e44 | − | 1.47484e44i | 0.476913 | − | 0.429391i | ||||
\(299\) | − | 1.23550e44i | − | 0.338658i | ||||||
\(300\) | −1.25020e45 | − | 1.31472e44i | −3.22699 | − | 0.339353i | ||||
\(301\) | 7.75561e44 | 1.88547 | ||||||||
\(302\) | 2.72604e43 | + | 3.02775e43i | 0.0624320 | + | 0.0693417i | ||||
\(303\) | 3.58209e44i | 0.772981i | ||||||||
\(304\) | 6.56646e42 | − | 3.08757e43i | 0.0133539 | − | 0.0627904i | ||||
\(305\) | 2.90259e44 | 0.556401 | ||||||||
\(306\) | −1.03926e44 | + | 9.35701e43i | −0.187819 | + | 0.169103i | ||||
\(307\) | 2.16030e44i | 0.368149i | 0.982912 | + | 0.184074i | \(0.0589287\pi\) | ||||
−0.982912 | + | 0.184074i | \(0.941071\pi\) | |||||||
\(308\) | −5.58895e42 | + | 5.31467e43i | −0.00898291 | + | 0.0854207i | ||||
\(309\) | 1.03500e45 | 1.56924 | ||||||||
\(310\) | −5.70773e44 | − | 6.33943e44i | −0.816494 | − | 0.906860i | ||||
\(311\) | − | 9.39975e44i | − | 1.26891i | −0.772962 | − | 0.634453i | \(-0.781226\pi\) | ||
0.772962 | − | 0.634453i | \(-0.218774\pi\) | |||||||
\(312\) | −2.60726e44 | + | 1.89395e44i | −0.332202 | + | 0.241316i | ||||
\(313\) | −1.04146e45 | −1.25269 | −0.626344 | − | 0.779547i | \(-0.715449\pi\) | ||||
−0.626344 | + | 0.779547i | \(0.715449\pi\) | |||||||
\(314\) | 1.04585e45 | − | 9.41638e44i | 1.18778 | − | 1.06942i | ||||
\(315\) | − | 6.64769e44i | − | 0.712986i | ||||||
\(316\) | 6.65033e44 | + | 6.99354e43i | 0.673714 | + | 0.0708483i | ||||
\(317\) | −1.66259e45 | −1.59118 | −0.795589 | − | 0.605837i | \(-0.792838\pi\) | ||||
−0.795589 | + | 0.605837i | \(0.792838\pi\) | |||||||
\(318\) | 1.22261e44 | + | 1.35793e44i | 0.110561 | + | 0.122797i | ||||
\(319\) | 5.65917e43i | 0.0483638i | ||||||||
\(320\) | 7.54972e44 | − | 2.32224e45i | 0.609861 | − | 1.87589i | ||||
\(321\) | −2.59321e43 | −0.0198038 | ||||||||
\(322\) | −1.32545e45 | + | 1.19338e45i | −0.957102 | + | 0.861730i | ||||
\(323\) | 9.14359e43i | 0.0624412i | ||||||||
\(324\) | −1.93049e44 | + | 1.83575e45i | −0.124697 | + | 1.18578i | ||||
\(325\) | 1.73059e45 | 1.05753 | ||||||||
\(326\) | 1.97672e45 | + | 2.19549e45i | 1.14295 | + | 1.26945i | ||||
\(327\) | 1.07302e45i | 0.587150i | ||||||||
\(328\) | −4.21788e44 | − | 5.80645e44i | −0.218457 | − | 0.300733i | ||||
\(329\) | −1.80794e45 | −0.886456 | ||||||||
\(330\) | 2.18822e44 | − | 1.97017e44i | 0.101587 | − | 0.0914645i | ||||
\(331\) | 1.91416e45i | 0.841540i | 0.907167 | + | 0.420770i | \(0.138240\pi\) | ||||
−0.907167 | + | 0.420770i | \(0.861760\pi\) | |||||||
\(332\) | −2.08843e45 | − | 2.19621e44i | −0.869628 | − | 0.0914509i | ||||
\(333\) | 9.65116e43 | 0.0380700 | ||||||||
\(334\) | 7.76231e44 | + | 8.62140e44i | 0.290104 | + | 0.322212i | ||||
\(335\) | − | 5.93387e45i | − | 2.10151i | ||||||
\(336\) | 4.55021e45 | + | 9.67710e44i | 1.52730 | + | 0.324817i | ||||
\(337\) | −4.37726e45 | −1.39272 | −0.696361 | − | 0.717692i | \(-0.745199\pi\) | ||||
−0.696361 | + | 0.717692i | \(0.745199\pi\) | |||||||
\(338\) | −2.13399e45 | + | 1.92135e45i | −0.643712 | + | 0.579568i | ||||
\(339\) | 4.94164e43i | 0.0141344i | ||||||||
\(340\) | −7.39747e44 | + | 7.03443e45i | −0.200661 | + | 1.90813i | ||||
\(341\) | 1.48452e44 | 0.0381951 | ||||||||
\(342\) | −4.57244e43 | − | 5.07849e43i | −0.0111603 | − | 0.0123955i | ||||
\(343\) | − | 3.88592e44i | − | 0.0899910i | ||||||
\(344\) | 4.98976e45 | − | 3.62463e45i | 1.09655 | − | 0.796548i | ||||
\(345\) | 9.82701e45 | 2.04964 | ||||||||
\(346\) | 2.25500e45 | − | 2.03029e45i | 0.446453 | − | 0.401966i | ||||
\(347\) | − | 8.28743e42i | − | 0.00155772i | −1.00000 | 0.000778859i | \(-0.999752\pi\) | |||
1.00000 | 0.000778859i | \(-0.000247919\pi\) | ||||||||
\(348\) | 4.89934e45 | + | 5.15219e44i | 0.874402 | + | 0.0919529i | ||||
\(349\) | −7.11793e45 | −1.20641 | −0.603207 | − | 0.797585i | \(-0.706111\pi\) | ||||
−0.603207 | + | 0.797585i | \(0.706111\pi\) | |||||||
\(350\) | −1.67158e46 | − | 1.85659e46i | −2.69094 | − | 2.98876i | ||||
\(351\) | − | 1.98738e45i | − | 0.303915i | ||||||
\(352\) | 2.12426e44 | + | 3.68052e44i | 0.0308632 | + | 0.0534739i | ||||
\(353\) | 4.99214e45 | 0.689195 | 0.344597 | − | 0.938751i | \(-0.388015\pi\) | ||||
0.344597 | + | 0.938751i | \(0.388015\pi\) | |||||||
\(354\) | −7.41544e45 | + | 6.67652e45i | −0.972923 | + | 0.875974i | ||||
\(355\) | 2.36753e46i | 2.95247i | ||||||||
\(356\) | 1.10887e45 | − | 1.05445e46i | 0.131456 | − | 1.25005i | ||||
\(357\) | −1.34751e46 | −1.51881 | ||||||||
\(358\) | 6.25983e45 | + | 6.95263e45i | 0.670915 | + | 0.745169i | ||||
\(359\) | − | 8.91149e45i | − | 0.908344i | −0.890914 | − | 0.454172i | \(-0.849935\pi\) | ||
0.890914 | − | 0.454172i | \(-0.150065\pi\) | |||||||
\(360\) | −3.10684e45 | − | 4.27696e45i | −0.301213 | − | 0.414658i | ||||
\(361\) | 1.07978e46 | 0.995879 | ||||||||
\(362\) | 4.57332e44 | − | 4.11760e44i | 0.0401308 | − | 0.0361319i | ||||
\(363\) | − | 1.33911e46i | − | 1.11814i | ||||||
\(364\) | −6.36906e45 | − | 6.69776e44i | −0.506116 | − | 0.0532236i | ||||
\(365\) | 2.58121e46 | 1.95232 | ||||||||
\(366\) | 2.94223e45 | + | 3.26786e45i | 0.211844 | + | 0.235290i | ||||
\(367\) | − | 1.18171e46i | − | 0.810069i | −0.914301 | − | 0.405034i | \(-0.867260\pi\) | ||
0.914301 | − | 0.405034i | \(-0.132740\pi\) | |||||||
\(368\) | −2.95030e45 | + | 1.38724e46i | −0.192578 | + | 0.905508i | ||||
\(369\) | −1.55365e45 | −0.0965781 | ||||||||
\(370\) | 3.62779e45 | − | 3.26629e45i | 0.214788 | − | 0.193385i | ||||
\(371\) | 3.63124e45i | 0.204797i | ||||||||
\(372\) | 1.35153e45 | − | 1.28520e46i | 0.0726194 | − | 0.690555i | ||||
\(373\) | 8.97723e45 | 0.459604 | 0.229802 | − | 0.973237i | \(-0.426192\pi\) | ||||
0.229802 | + | 0.973237i | \(0.426192\pi\) | |||||||
\(374\) | −8.23635e44 | − | 9.14790e44i | −0.0401833 | − | 0.0446306i | ||||
\(375\) | 9.00341e46i | 4.18643i | ||||||||
\(376\) | −1.16318e46 | + | 8.44950e45i | −0.515544 | + | 0.374498i | ||||
\(377\) | −6.78190e45 | −0.286555 | ||||||||
\(378\) | −2.13207e46 | + | 1.91962e46i | −0.858913 | + | 0.773325i | ||||
\(379\) | − | 3.46979e46i | − | 1.33290i | −0.745550 | − | 0.666450i | \(-0.767813\pi\) | ||
0.745550 | − | 0.666450i | \(-0.232187\pi\) | |||||||
\(380\) | −3.43748e45 | − | 3.61488e44i | −0.125932 | − | 0.0132431i | ||||
\(381\) | −5.63598e46 | −1.96934 | ||||||||
\(382\) | 1.42596e46 | + | 1.58378e46i | 0.475298 | + | 0.527902i | ||||
\(383\) | − | 3.27569e46i | − | 1.04166i | −0.853661 | − | 0.520828i | \(-0.825623\pi\) | ||
0.853661 | − | 0.520828i | \(-0.174377\pi\) | |||||||
\(384\) | 3.37976e46 | − | 1.50397e46i | 1.02547 | − | 0.456328i | ||||
\(385\) | 5.85152e45 | 0.169424 | ||||||||
\(386\) | 3.03730e46 | − | 2.73465e46i | 0.839299 | − | 0.755666i | ||||
\(387\) | − | 1.33513e46i | − | 0.352148i | ||||||
\(388\) | −1.59864e45 | + | 1.52019e46i | −0.0402513 | + | 0.382759i | ||||
\(389\) | −9.40263e45 | −0.226025 | −0.113013 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113013 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(390\) | 2.36104e46 | + | 2.62234e46i | 0.541926 | + | 0.601903i | ||||
\(391\) | − | 4.10821e46i | − | 0.900474i | ||||||
\(392\) | 2.62588e46 | + | 3.61485e46i | 0.549699 | + | 0.756729i | ||||
\(393\) | −4.04544e46 | −0.808909 | ||||||||
\(394\) | 4.40710e46 | − | 3.96795e46i | 0.841824 | − | 0.757939i | ||||
\(395\) | − | 7.32210e46i | − | 1.33625i | ||||||
\(396\) | 9.14918e44 | + | 9.62136e43i | 0.0159540 | + | 0.00167773i | ||||
\(397\) | 6.27686e46 | 1.04596 | 0.522978 | − | 0.852346i | \(-0.324821\pi\) | ||||
0.522978 | + | 0.852346i | \(0.324821\pi\) | |||||||
\(398\) | −1.81630e46 | − | 2.01732e46i | −0.289263 | − | 0.321277i | ||||
\(399\) | − | 6.58479e45i | − | 0.100237i | ||||||
\(400\) | −1.94314e47 | − | 4.13255e46i | −2.82764 | − | 0.601365i | ||||
\(401\) | −1.33162e47 | −1.85260 | −0.926298 | − | 0.376792i | \(-0.877027\pi\) | ||||
−0.926298 | + | 0.376792i | \(0.877027\pi\) | |||||||
\(402\) | 6.68061e46 | − | 6.01491e46i | 0.888684 | − | 0.800129i | ||||
\(403\) | 1.77904e46i | 0.226305i | ||||||||
\(404\) | −5.92031e45 | + | 5.62976e46i | −0.0720244 | + | 0.684898i | ||||
\(405\) | 2.02118e47 | 2.35188 | ||||||||
\(406\) | 6.55067e46 | + | 7.27567e46i | 0.729151 | + | 0.809849i | ||||
\(407\) | 8.49527e44i | 0.00904644i | ||||||||
\(408\) | −8.66952e46 | + | 6.29766e46i | −0.883308 | + | 0.641647i | ||||
\(409\) | 4.14628e46 | 0.404240 | 0.202120 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202120 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(410\) | −5.84003e46 | + | 5.25809e46i | −0.544886 | + | 0.490590i | ||||
\(411\) | 9.61583e46i | 0.858685i | ||||||||
\(412\) | 1.62665e47 | + | 1.71060e46i | 1.39042 | + | 0.146217i | ||||
\(413\) | −1.98297e47 | −1.62261 | ||||||||
\(414\) | 2.05439e46 | + | 2.28176e46i | 0.160945 | + | 0.178757i | ||||
\(415\) | 2.29939e47i | 1.72483i | ||||||||
\(416\) | −4.41071e46 | + | 2.54570e46i | −0.316832 | + | 0.182864i | ||||
\(417\) | −2.58329e46 | −0.177715 | ||||||||
\(418\) | 4.47025e44 | − | 4.02481e44i | 0.00294550 | − | 0.00265199i | ||||
\(419\) | − | 1.13757e46i | − | 0.0718000i | −0.999355 | − | 0.0359000i | \(-0.988570\pi\) | ||
0.999355 | − | 0.0359000i | \(-0.0114298\pi\) | |||||||
\(420\) | 5.32731e46 | − | 5.06587e47i | 0.322122 | − | 3.06314i | ||||
\(421\) | 3.96082e45 | 0.0229460 | 0.0114730 | − | 0.999934i | \(-0.496348\pi\) | ||||
0.0114730 | + | 0.999934i | \(0.496348\pi\) | |||||||
\(422\) | 3.36035e45 | + | 3.73226e45i | 0.0186535 | + | 0.0207180i | ||||
\(423\) | 3.11236e46i | 0.165563i | ||||||||
\(424\) | 1.69708e46 | + | 2.33625e46i | 0.0865202 | + | 0.119106i | ||||
\(425\) | 5.75445e47 | 2.81192 | ||||||||
\(426\) | −2.66547e47 | + | 2.39986e47i | −1.24853 | + | 1.12412i | ||||
\(427\) | 8.73859e46i | 0.392410i | ||||||||
\(428\) | −4.07560e45 | − | 4.28594e44i | −0.0175471 | − | 0.00184526i | ||||
\(429\) | −6.14080e45 | −0.0253509 | ||||||||
\(430\) | −4.51853e47 | − | 5.01862e47i | −1.78881 | − | 1.98679i | ||||
\(431\) | 1.09299e47i | 0.414977i | 0.978237 | + | 0.207488i | \(0.0665289\pi\) | ||||
−0.978237 | + | 0.207488i | \(0.933471\pi\) | |||||||
\(432\) | −4.74575e46 | + | 2.23147e47i | −0.172821 | + | 0.812612i | ||||
\(433\) | −1.57783e47 | −0.551161 | −0.275580 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275580 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(434\) | 1.90856e47 | − | 1.71838e47i | 0.639575 | − | 0.575843i | ||||
\(435\) | − | 5.39424e47i | − | 1.73430i | ||||||
\(436\) | −1.77344e46 | + | 1.68641e47i | −0.0547091 | + | 0.520242i | ||||
\(437\) | 2.00754e46 | 0.0594288 | ||||||||
\(438\) | 2.61646e47 | + | 2.90604e47i | 0.743327 | + | 0.825595i | ||||
\(439\) | − | 5.16564e47i | − | 1.40852i | −0.709942 | − | 0.704260i | \(-0.751279\pi\) | ||
0.709942 | − | 0.704260i | \(-0.248721\pi\) | |||||||
\(440\) | 3.76472e46 | − | 2.73474e46i | 0.0985335 | − | 0.0715762i | ||||
\(441\) | 9.67236e46 | 0.243018 | ||||||||
\(442\) | 1.09628e47 | − | 9.87038e46i | 0.264436 | − | 0.238086i | ||||
\(443\) | 6.09572e47i | 1.41175i | 0.708336 | + | 0.705875i | \(0.249446\pi\) | ||||
−0.708336 | + | 0.705875i | \(0.750554\pi\) | |||||||
\(444\) | 7.35466e46 | + | 7.73422e45i | 0.163557 | + | 0.0171998i | ||||
\(445\) | −1.16097e48 | −2.47936 | ||||||||
\(446\) | −7.57011e46 | − | 8.40794e46i | −0.155265 | − | 0.172450i | ||||
\(447\) | − | 3.65633e47i | − | 0.720295i | ||||||
\(448\) | 6.99137e47 | + | 2.27293e47i | 1.32299 | + | 0.430113i | ||||
\(449\) | 3.24553e47 | 0.590000 | 0.295000 | − | 0.955497i | \(-0.404680\pi\) | ||||
0.295000 | + | 0.955497i | \(0.404680\pi\) | |||||||
\(450\) | −3.19611e47 | + | 2.87763e47i | −0.558209 | + | 0.502585i | ||||
\(451\) | − | 1.36757e46i | − | 0.0229495i | ||||||
\(452\) | −8.16732e44 | + | 7.76650e45i | −0.00131701 | + | 0.0125237i | ||||
\(453\) | 6.75823e46 | 0.104729 | ||||||||
\(454\) | −1.89519e47 | − | 2.10494e47i | −0.282259 | − | 0.313498i | ||||
\(455\) | 7.01242e47i | 1.00384i | ||||||||
\(456\) | −3.07744e46 | − | 4.23648e46i | −0.0423470 | − | 0.0582959i | ||||
\(457\) | 4.95004e47 | 0.654813 | 0.327406 | − | 0.944884i | \(-0.393825\pi\) | ||||
0.327406 | + | 0.944884i | \(0.393825\pi\) | |||||||
\(458\) | −8.48015e46 | + | 7.63513e46i | −0.107851 | + | 0.0971042i | ||||
\(459\) | − | 6.60831e47i | − | 0.808094i | ||||||
\(460\) | 1.54446e48 | + | 1.62416e47i | 1.81608 | + | 0.190980i | ||||
\(461\) | −9.17912e47 | −1.03797 | −0.518984 | − | 0.854784i | \(-0.673690\pi\) | ||||
−0.518984 | + | 0.854784i | \(0.673690\pi\) | |||||||
\(462\) | 5.93143e46 | + | 6.58789e46i | 0.0645065 | + | 0.0716458i | ||||
\(463\) | 2.97206e47i | 0.310885i | 0.987845 | + | 0.155442i | \(0.0496803\pi\) | ||||
−0.987845 | + | 0.155442i | \(0.950320\pi\) | |||||||
\(464\) | 7.61486e47 | + | 1.61948e47i | 0.766193 | + | 0.162949i | ||||
\(465\) | −1.41502e48 | −1.36965 | ||||||||
\(466\) | −1.32800e48 | + | 1.19567e48i | −1.23666 | + | 1.11343i | ||||
\(467\) | 8.45631e47i | 0.757665i | 0.925465 | + | 0.378832i | \(0.123674\pi\) | ||||
−0.925465 | + | 0.378832i | \(0.876326\pi\) | |||||||
\(468\) | −1.15302e46 | + | 1.09643e47i | −0.00994055 | + | 0.0945271i | ||||
\(469\) | 1.78646e48 | 1.48212 | ||||||||
\(470\) | 1.05333e48 | + | 1.16991e48i | 0.841014 | + | 0.934093i | ||||
\(471\) | − | 2.33445e48i | − | 1.79394i | ||||||
\(472\) | −1.27579e48 | + | 9.26751e47i | −0.943676 | + | 0.685500i | ||||
\(473\) | 1.17522e47 | 0.0836796 | ||||||||
\(474\) | 8.24353e47 | − | 7.42209e47i | 0.565071 | − | 0.508764i | ||||
\(475\) | 2.81200e47i | 0.185579i | ||||||||
\(476\) | −2.11780e48 | − | 2.22710e47i | −1.34574 | − | 0.141519i | ||||
\(477\) | 6.25117e46 | 0.0382499 | ||||||||
\(478\) | −1.36646e48 | − | 1.51770e48i | −0.805186 | − | 0.894300i | ||||
\(479\) | − | 9.59845e47i | − | 0.544706i | −0.962197 | − | 0.272353i | \(-0.912198\pi\) | ||
0.962197 | − | 0.272353i | \(-0.0878018\pi\) | |||||||
\(480\) | −2.02482e48 | − | 3.50822e48i | −1.10674 | − | 1.91754i | ||||
\(481\) | −1.01807e47 | −0.0536000 | ||||||||
\(482\) | 9.19025e47 | − | 8.27448e47i | 0.466102 | − | 0.419656i | ||||
\(483\) | 2.95854e48i | 1.44554i | ||||||||
\(484\) | 2.21322e47 | − | 2.10460e48i | 0.104185 | − | 0.990725i | ||||
\(485\) | 1.67375e48 | 0.759169 | ||||||||
\(486\) | 7.76926e47 | + | 8.62912e47i | 0.339568 | + | 0.377150i | ||||
\(487\) | − | 4.05452e47i | − | 0.170772i | −0.996348 | − | 0.0853862i | \(-0.972788\pi\) | ||
0.996348 | − | 0.0853862i | \(-0.0272124\pi\) | |||||||
\(488\) | 4.08403e47 | + | 5.62218e47i | 0.165780 | + | 0.228217i | ||||
\(489\) | 4.90056e48 | 1.91728 | ||||||||
\(490\) | 3.63575e48 | − | 3.27346e48i | 1.37109 | − | 1.23446i | ||||
\(491\) | 3.18556e48i | 1.15803i | 0.815317 | + | 0.579014i | \(0.196562\pi\) | ||||
−0.815317 | + | 0.579014i | \(0.803438\pi\) | |||||||
\(492\) | −1.18396e48 | − | 1.24506e47i | −0.414920 | − | 0.0436333i | ||||
\(493\) | −2.25508e48 | −0.761933 | ||||||||
\(494\) | 4.82330e46 | + | 5.35712e46i | 0.0157130 | + | 0.0174520i | ||||
\(495\) | − | 1.00734e47i | − | 0.0316433i | ||||||
\(496\) | 4.24824e47 | − | 1.99754e48i | 0.128688 | − | 0.605098i | ||||
\(497\) | −7.12773e48 | −2.08227 | ||||||||
\(498\) | −2.58875e48 | + | 2.33079e48i | −0.729393 | + | 0.656711i | ||||
\(499\) | − | 4.13407e48i | − | 1.12349i | −0.827312 | − | 0.561743i | \(-0.810131\pi\) | ||
0.827312 | − | 0.561743i | \(-0.189869\pi\) | |||||||
\(500\) | −1.48804e48 | + | 1.41501e49i | −0.390081 | + | 3.70938i | ||||
\(501\) | 1.92438e48 | 0.486645 | ||||||||
\(502\) | −3.71847e48 | − | 4.13001e48i | −0.907188 | − | 1.00759i | ||||
\(503\) | 3.40859e48i | 0.802325i | 0.916007 | + | 0.401163i | \(0.131394\pi\) | ||||
−0.916007 | + | 0.401163i | \(0.868606\pi\) | |||||||
\(504\) | 1.28763e48 | − | 9.35352e47i | 0.292443 | − | 0.212435i | ||||
\(505\) | 6.19845e48 | 1.35843 | ||||||||
\(506\) | −2.00848e47 | + | 1.80834e47i | −0.0424775 | + | 0.0382447i | ||||
\(507\) | 4.76328e48i | 0.972216i | ||||||||
\(508\) | −8.85775e48 | − | 9.31488e47i | −1.74492 | − | 0.183498i | ||||
\(509\) | −1.48385e48 | −0.282143 | −0.141071 | − | 0.989999i | \(-0.545055\pi\) | ||||
−0.141071 | + | 0.989999i | \(0.545055\pi\) | |||||||
\(510\) | 7.85077e48 | + | 8.71966e48i | 1.44095 | + | 1.60043i | ||||
\(511\) | 7.77104e48i | 1.37690i | ||||||||
\(512\) | 5.56034e48 | − | 1.80511e48i | 0.951134 | − | 0.308777i | ||||
\(513\) | 3.22924e47 | 0.0533321 | ||||||||
\(514\) | 3.35590e48 | − | 3.02150e48i | 0.535147 | − | 0.481821i | ||||
\(515\) | − | 1.79097e49i | − | 2.75777i | ||||||
\(516\) | 1.06994e48 | − | 1.01743e49i | 0.159098 | − | 1.51290i | ||||
\(517\) | −2.73960e47 | −0.0393421 | ||||||||
\(518\) | 9.83356e47 | + | 1.09219e48i | 0.136388 | + | 0.151482i | ||||
\(519\) | − | 5.03337e48i | − | 0.674290i | ||||||
\(520\) | 3.27730e48 | + | 4.51161e48i | 0.424088 | + | 0.583810i | ||||
\(521\) | 9.01266e48 | 1.12661 | 0.563305 | − | 0.826249i | \(-0.309529\pi\) | ||||
0.563305 | + | 0.826249i | \(0.309529\pi\) | |||||||
\(522\) | 1.25250e48 | − | 1.12770e48i | 0.151255 | − | 0.136183i | ||||
\(523\) | − | 1.22155e49i | − | 1.42522i | −0.701560 | − | 0.712611i | \(-0.747513\pi\) | ||
0.701560 | − | 0.712611i | \(-0.252487\pi\) | |||||||
\(524\) | −6.35799e48 | − | 6.68611e47i | −0.716731 | − | 0.0753721i | ||||
\(525\) | −4.14409e49 | −4.51400 | ||||||||
\(526\) | 1.15412e49 | + | 1.28185e49i | 1.21481 | + | 1.34926i | ||||
\(527\) | 5.91555e48i | 0.601733i | ||||||||
\(528\) | 6.89502e47 | + | 1.46639e47i | 0.0677837 | + | 0.0144158i | ||||
\(529\) | 1.50468e48 | 0.142969 | ||||||||
\(530\) | 2.34976e48 | − | 2.11561e48i | 0.215803 | − | 0.194299i | ||||
\(531\) | 3.41367e48i | 0.303054i | ||||||||
\(532\) | 1.08830e47 | − | 1.03489e48i | 0.00933986 | − | 0.0888150i | ||||
\(533\) | 1.63889e48 | 0.135975 | ||||||||
\(534\) | −1.17682e49 | − | 1.30707e49i | −0.943991 | − | 1.04847i | ||||
\(535\) | 4.48729e47i | 0.0348030i | ||||||||
\(536\) | 1.14937e49 | − | 8.34915e48i | 0.861969 | − | 0.626147i | ||||
\(537\) | 1.55190e49 | 1.12545 | ||||||||
\(538\) | −1.44271e49 | + | 1.29895e49i | −1.01181 | + | 0.910982i | ||||
\(539\) | 8.51393e47i | 0.0577474i | ||||||||
\(540\) | 2.48435e49 | + | 2.61257e48i | 1.62977 | + | 0.171388i | ||||
\(541\) | 7.20733e48 | 0.457324 | 0.228662 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228662 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(542\) | −1.93582e49 | − | 2.15006e49i | −1.18817 | − | 1.31967i | ||||
\(543\) | − | 1.02081e48i | − | 0.0606105i | ||||||
\(544\) | −1.46662e49 | + | 8.46481e48i | −0.842439 | + | 0.486225i | ||||
\(545\) | 1.85676e49 | 1.03185 | ||||||||
\(546\) | −7.89488e48 | + | 7.10818e48i | −0.424500 | + | 0.382200i | ||||
\(547\) | 2.03419e49i | 1.05833i | 0.848520 | + | 0.529164i | \(0.177494\pi\) | ||||
−0.848520 | + | 0.529164i | \(0.822506\pi\) | |||||||
\(548\) | −1.58926e48 | + | 1.51127e49i | −0.0800101 | + | 0.760835i | ||||
\(549\) | 1.50435e48 | 0.0732901 | ||||||||
\(550\) | −2.53298e48 | − | 2.81332e48i | −0.119427 | − | 0.132645i | ||||
\(551\) | − | 1.10198e48i | − | 0.0502856i | ||||||
\(552\) | 1.38269e49 | + | 1.90345e49i | 0.610692 | + | 0.840693i | ||||
\(553\) | 2.20441e49 | 0.942408 | ||||||||
\(554\) | −1.89454e49 | + | 1.70576e49i | −0.784022 | + | 0.705897i | ||||
\(555\) | − | 8.09758e48i | − | 0.324400i | ||||||
\(556\) | −4.06001e48 | − | 4.26955e47i | −0.157464 | − | 0.0165590i | ||||
\(557\) | −3.28864e49 | −1.23487 | −0.617437 | − | 0.786620i | \(-0.711829\pi\) | ||||
−0.617437 | + | 0.786620i | \(0.711829\pi\) | |||||||
\(558\) | −2.95819e48 | − | 3.28559e48i | −0.107550 | − | 0.119453i | ||||
\(559\) | 1.40838e49i | 0.495800i | ||||||||
\(560\) | 1.67453e49 | − | 7.87369e49i | 0.570831 | − | 2.68407i | ||||
\(561\) | −2.04190e48 | −0.0674068 | ||||||||
\(562\) | 3.37965e49 | − | 3.04288e49i | 1.08048 | − | 0.972816i | ||||
\(563\) | 1.93623e49i | 0.599524i | 0.954014 | + | 0.299762i | \(0.0969072\pi\) | ||||
−0.954014 | + | 0.299762i | \(0.903093\pi\) | |||||||
\(564\) | −2.49417e48 | + | 2.37177e49i | −0.0748002 | + | 0.711293i | ||||
\(565\) | 8.55102e47 | 0.0248397 | ||||||||
\(566\) | −1.30565e49 | − | 1.45015e49i | −0.367393 | − | 0.408054i | ||||
\(567\) | 6.08502e49i | 1.65870i | ||||||||
\(568\) | −4.58580e49 | + | 3.33119e49i | −1.21100 | + | 0.879689i | ||||
\(569\) | 3.77299e49 | 0.965307 | 0.482653 | − | 0.875811i | \(-0.339673\pi\) | ||||
0.482653 | + | 0.875811i | \(0.339673\pi\) | |||||||
\(570\) | −4.26099e48 | + | 3.83639e48i | −0.105624 | + | 0.0950989i | ||||
\(571\) | 4.20874e49i | 1.01089i | 0.862860 | + | 0.505443i | \(0.168671\pi\) | ||||
−0.862860 | + | 0.505443i | \(0.831329\pi\) | |||||||
\(572\) | −9.65115e47 | − | 1.01492e47i | −0.0224621 | − | 0.00236214i | ||||
\(573\) | 3.53515e49 | 0.797304 | ||||||||
\(574\) | −1.58301e49 | − | 1.75821e49i | −0.345995 | − | 0.384288i | ||||
\(575\) | − | 1.26343e50i | − | 2.67626i | ||||||
\(576\) | 3.91285e48 | − | 1.20356e49i | 0.0803320 | − | 0.247095i | ||||
\(577\) | −4.53491e49 | −0.902410 | −0.451205 | − | 0.892420i | \(-0.649006\pi\) | ||||
−0.451205 | + | 0.892420i | \(0.649006\pi\) | |||||||
\(578\) | −2.07601e48 | + | 1.86915e48i | −0.0400433 | + | 0.0360531i | ||||
\(579\) | − | 6.77956e49i | − | 1.26762i | ||||||
\(580\) | 8.91535e48 | − | 8.47782e49i | 0.161597 | − | 1.53667i | ||||
\(581\) | −6.92258e49 | −1.21646 | ||||||||
\(582\) | 1.69660e49 | + | 1.88438e49i | 0.289046 | + | 0.321036i | ||||
\(583\) | 5.50248e47i | 0.00908918i | ||||||||
\(584\) | 3.63184e49 | + | 4.99969e49i | 0.581696 | + | 0.800777i | ||||
\(585\) | 1.20719e49 | 0.187486 | ||||||||
\(586\) | −5.42401e49 | + | 4.88352e49i | −0.816890 | + | 0.735489i | ||||
\(587\) | − | 8.51700e49i | − | 1.24394i | −0.783039 | − | 0.621972i | \(-0.786332\pi\) | ||
0.783039 | − | 0.621972i | \(-0.213668\pi\) | |||||||
\(588\) | 7.37081e49 | + | 7.75121e48i | 1.04406 | + | 0.109794i | ||||
\(589\) | −2.89072e48 | −0.0397128 | ||||||||
\(590\) | 1.15530e50 | + | 1.28317e50i | 1.53943 | + | 1.70981i | ||||
\(591\) | − | 9.83709e49i | − | 1.27143i | ||||||
\(592\) | 1.14311e49 | + | 2.43109e48i | 0.143316 | + | 0.0304796i | ||||
\(593\) | −1.87931e49 | −0.228567 | −0.114284 | − | 0.993448i | \(-0.536457\pi\) | ||||
−0.114284 | + | 0.993448i | \(0.536457\pi\) | |||||||
\(594\) | −3.23077e48 | + | 2.90883e48i | −0.0381197 | + | 0.0343212i | ||||
\(595\) | 2.33173e50i | 2.66915i | ||||||||
\(596\) | 6.04302e48 | − | 5.74645e49i | 0.0671152 | − | 0.638215i | ||||
\(597\) | −4.50286e49 | −0.485233 | ||||||||
\(598\) | −2.16711e49 | − | 2.40695e49i | −0.226599 | − | 0.251678i | ||||
\(599\) | 8.39840e48i | 0.0852145i | 0.999092 | + | 0.0426073i | \(0.0135664\pi\) | ||||
−0.999092 | + | 0.0426073i | \(0.986434\pi\) | |||||||
\(600\) | −2.66620e50 | + | 1.93676e50i | −2.62525 | + | 1.90702i | ||||
\(601\) | 1.20630e50 | 1.15269 | 0.576346 | − | 0.817205i | \(-0.304478\pi\) | ||||
0.576346 | + | 0.817205i | \(0.304478\pi\) | |||||||
\(602\) | 1.51092e50 | − | 1.36036e50i | 1.40121 | − | 1.26158i | ||||
\(603\) | − | 3.07539e49i | − | 0.276815i | ||||||
\(604\) | 1.06215e49 | + | 1.11697e48i | 0.0927944 | + | 0.00975834i | ||||
\(605\) | −2.31719e50 | −1.96501 | ||||||||
\(606\) | 6.28309e49 | + | 6.97848e49i | 0.517209 | + | 0.574452i | ||||
\(607\) | 1.57546e50i | 1.25896i | 0.777018 | + | 0.629478i | \(0.216731\pi\) | ||||
−0.777018 | + | 0.629478i | \(0.783269\pi\) | |||||||
\(608\) | −4.13645e48 | − | 7.16686e48i | −0.0320895 | − | 0.0555987i | ||||
\(609\) | 1.62400e50 | 1.22314 | ||||||||
\(610\) | 5.65470e49 | − | 5.09123e49i | 0.413497 | − | 0.372294i | ||||
\(611\) | − | 3.28312e49i | − | 0.233101i | ||||||
\(612\) | −3.83394e48 | + | 3.64579e49i | −0.0264314 | + | 0.251342i | ||||
\(613\) | −1.31538e50 | −0.880566 | −0.440283 | − | 0.897859i | \(-0.645122\pi\) | ||||
−0.440283 | + | 0.897859i | \(0.645122\pi\) | |||||||
\(614\) | 3.78923e49 | + | 4.20861e49i | 0.246332 | + | 0.273595i | ||||
\(615\) | 1.30355e50i | 0.822955i | ||||||||
\(616\) | 8.23327e48 | + | 1.13341e49i | 0.0504800 | + | 0.0694921i | ||||
\(617\) | −9.52767e49 | −0.567354 | −0.283677 | − | 0.958920i | \(-0.591554\pi\) | ||||
−0.283677 | + | 0.958920i | \(0.591554\pi\) | |||||||
\(618\) | 2.01635e50 | − | 1.81543e50i | 1.16620 | − | 1.04999i | ||||
\(619\) | − | 2.21171e50i | − | 1.24250i | −0.783612 | − | 0.621250i | \(-0.786625\pi\) | ||
0.783612 | − | 0.621250i | \(-0.213375\pi\) | |||||||
\(620\) | −2.22391e50 | − | 2.33869e49i | −1.21358 | − | 0.127621i | ||||
\(621\) | −1.45090e50 | −0.769109 | ||||||||
\(622\) | −1.64875e50 | − | 1.83122e50i | −0.849037 | − | 0.943004i | ||||
\(623\) | − | 3.49523e50i | − | 1.74860i | ||||||
\(624\) | −1.75731e49 | + | 8.26294e49i | −0.0854134 | + | 0.401617i | ||||
\(625\) | 9.45782e50 | 4.46633 | ||||||||
\(626\) | −2.02892e50 | + | 1.82675e50i | −0.930952 | + | 0.838185i | ||||
\(627\) | − | 9.97805e47i | − | 0.00444867i | ||||||
\(628\) | 3.85827e49 | − | 3.66892e50i | 0.167155 | − | 1.58952i | ||||
\(629\) | −3.38521e49 | −0.142520 | ||||||||
\(630\) | −1.16603e50 | − | 1.29508e50i | −0.477066 | − | 0.529865i | ||||
\(631\) | − | 1.60389e50i | − | 0.637745i | −0.947798 | − | 0.318873i | \(-0.896696\pi\) | ||
0.947798 | − | 0.318873i | \(-0.103304\pi\) | |||||||
\(632\) | 1.41826e50 | − | 1.03024e50i | 0.548085 | − | 0.398137i | ||||
\(633\) | 8.33077e48 | 0.0312909 | ||||||||
\(634\) | −3.23899e50 | + | 2.91624e50i | −1.18250 | + | 1.06467i | ||||
\(635\) | 9.75250e50i | 3.46090i | ||||||||
\(636\) | 4.76369e49 | + | 5.00954e48i | 0.164330 | + | 0.0172810i | ||||
\(637\) | −1.02030e50 | −0.342152 | ||||||||
\(638\) | 9.92635e48 | + | 1.10250e49i | 0.0323607 | + | 0.0359422i | ||||
\(639\) | 1.22704e50i | 0.388904i | ||||||||
\(640\) | −2.60247e50 | − | 5.84833e50i | −0.801948 | − | 1.80216i | ||||
\(641\) | 2.25422e50 | 0.675384 | 0.337692 | − | 0.941257i | \(-0.390354\pi\) | ||||
0.337692 | + | 0.941257i | \(0.390354\pi\) | |||||||
\(642\) | −5.05199e48 | + | 4.54858e48i | −0.0147174 | + | 0.0132509i | ||||
\(643\) | − | 2.07340e50i | − | 0.587336i | −0.955907 | − | 0.293668i | \(-0.905124\pi\) | ||
0.955907 | − | 0.293668i | \(-0.0948760\pi\) | |||||||
\(644\) | −4.88974e49 | + | 4.64977e50i | −0.134691 | + | 1.28081i | ||||
\(645\) | −1.12021e51 | −3.00070 | ||||||||
\(646\) | 1.60381e49 | + | 1.78132e49i | 0.0417800 | + | 0.0464041i | ||||
\(647\) | 1.51911e50i | 0.384869i | 0.981310 | + | 0.192435i | \(0.0616383\pi\) | ||||
−0.981310 | + | 0.192435i | \(0.938362\pi\) | |||||||
\(648\) | 2.84387e50 | + | 3.91495e50i | 0.700745 | + | 0.964663i | ||||
\(649\) | −3.00482e49 | −0.0720136 | ||||||||
\(650\) | 3.37146e50 | − | 3.03551e50i | 0.785920 | − | 0.707605i | ||||
\(651\) | − | 4.26010e50i | − | 0.965967i | ||||||
\(652\) | 7.70193e50 | + | 8.09942e49i | 1.69880 | + | 0.178648i | ||||
\(653\) | 7.75913e50 | 1.66485 | 0.832427 | − | 0.554135i | \(-0.186951\pi\) | ||||
0.832427 | + | 0.554135i | \(0.186951\pi\) | |||||||
\(654\) | 1.88211e50 | + | 2.09042e50i | 0.392868 | + | 0.436348i | ||||
\(655\) | 7.00023e50i | 1.42157i | ||||||||
\(656\) | −1.84018e50 | − | 3.91358e49i | −0.363573 | − | 0.0773223i | ||||
\(657\) | 1.33778e50 | 0.257163 | ||||||||
\(658\) | −3.52215e50 | + | 3.17118e50i | −0.658781 | + | 0.593136i | ||||
\(659\) | − | 8.46566e50i | − | 1.54072i | −0.637610 | − | 0.770359i | \(-0.720077\pi\) | ||
0.637610 | − | 0.770359i | \(-0.279923\pi\) | |||||||
\(660\) | 8.07257e48 | − | 7.67640e49i | 0.0142962 | − | 0.135946i | ||||
\(661\) | −2.43111e50 | −0.418965 | −0.209483 | − | 0.977812i | \(-0.567178\pi\) | ||||
−0.209483 | + | 0.977812i | \(0.567178\pi\) | |||||||
\(662\) | 3.35750e50 | + | 3.72909e50i | 0.563082 | + | 0.625402i | ||||
\(663\) | − | 2.44700e50i | − | 0.399384i | ||||||
\(664\) | −4.45381e50 | + | 3.23531e50i | −0.707467 | + | 0.513914i | ||||
\(665\) | −1.13943e50 | −0.176156 | ||||||||
\(666\) | 1.88020e49 | − | 1.69284e49i | 0.0282923 | − | 0.0254730i | ||||
\(667\) | 4.95117e50i | 0.725175i | ||||||||
\(668\) | 3.02444e50 | + | 3.18053e49i | 0.431190 | + | 0.0453443i | ||||
\(669\) | −1.87673e50 | −0.260455 | ||||||||
\(670\) | −1.04082e51 | − | 1.15601e51i | −1.40614 | − | 1.56177i | ||||
\(671\) | 1.32417e49i | 0.0174157i | ||||||||
\(672\) | 1.05619e51 | − | 6.09596e50i | 1.35237 | − | 0.780540i | ||||
\(673\) | −9.90164e49 | −0.123434 | −0.0617172 | − | 0.998094i | \(-0.519658\pi\) | ||||
−0.0617172 | + | 0.998094i | \(0.519658\pi\) | |||||||
\(674\) | −8.52760e50 | + | 7.67785e50i | −1.03502 | + | 0.931883i | ||||
\(675\) | − | 2.03230e51i | − | 2.40171i | ||||||
\(676\) | −7.87252e49 | + | 7.48617e50i | −0.0905886 | + | 0.861428i | ||||
\(677\) | −1.49122e51 | −1.67088 | −0.835439 | − | 0.549584i | \(-0.814786\pi\) | ||||
−0.835439 | + | 0.549584i | \(0.814786\pi\) | |||||||
\(678\) | 8.66780e48 | + | 9.62711e48i | 0.00945745 | + | 0.0105042i | ||||
\(679\) | 5.03901e50i | 0.535414i | ||||||||
\(680\) | 1.08975e51 | + | 1.50017e51i | 1.12763 | + | 1.55232i | ||||
\(681\) | −4.69844e50 | −0.473484 | ||||||||
\(682\) | 2.89208e49 | − | 2.60389e49i | 0.0283852 | − | 0.0255567i | ||||
\(683\) | − | 1.19203e51i | − | 1.13950i | −0.821819 | − | 0.569749i | \(-0.807040\pi\) | ||
0.821819 | − | 0.569749i | \(-0.192960\pi\) | |||||||
\(684\) | −1.78157e49 | − | 1.87351e48i | −0.0165879 | − | 0.00174440i | ||||
\(685\) | 1.66392e51 | 1.50905 | ||||||||
\(686\) | −6.81602e49 | − | 7.57038e49i | −0.0602139 | − | 0.0668781i | ||||
\(687\) | 1.89285e50i | 0.162891i | ||||||||
\(688\) | 3.36313e50 | − | 1.58136e51i | 0.281937 | − | 1.32568i | ||||
\(689\) | −6.59414e49 | −0.0538532 | ||||||||
\(690\) | 1.91446e51 | − | 1.72369e51i | 1.52322 | − | 1.37143i | ||||
\(691\) | 1.05725e51i | 0.819548i | 0.912187 | + | 0.409774i | \(0.134392\pi\) | ||||
−0.912187 | + | 0.409774i | \(0.865608\pi\) | |||||||
\(692\) | 8.31892e49 | − | 7.91066e50i | 0.0628286 | − | 0.597452i | ||||
\(693\) | 3.03271e49 | 0.0223168 | ||||||||
\(694\) | −1.45364e48 | − | 1.61452e48i | −0.00104228 | − | 0.00115764i | ||||
\(695\) | 4.47013e50i | 0.312316i | ||||||||
\(696\) | 1.04484e51 | − | 7.58987e50i | 0.711351 | − | 0.516735i | ||||
\(697\) | 5.44954e50 | 0.361551 | ||||||||
\(698\) | −1.38669e51 | + | 1.24851e51i | −0.896562 | + | 0.807223i | ||||
\(699\) | 2.96422e51i | 1.86776i | ||||||||
\(700\) | −6.51302e51 | − | 6.84915e50i | −3.99961 | − | 0.420603i | ||||
\(701\) | −1.10197e51 | −0.659548 | −0.329774 | − | 0.944060i | \(-0.606973\pi\) | ||||
−0.329774 | + | 0.944060i | \(0.606973\pi\) | |||||||
\(702\) | −3.48592e50 | − | 3.87173e50i | −0.203353 | − | 0.225859i | ||||
\(703\) | − | 1.65423e49i | − | 0.00940591i | ||||||
\(704\) | 1.05942e50 | + | 3.44422e49i | 0.0587163 | + | 0.0190890i | ||||
\(705\) | 2.61135e51 | 1.41078 | ||||||||
\(706\) | 9.72548e50 | − | 8.75637e50i | 0.512184 | − | 0.461147i | ||||
\(707\) | 1.86612e51i | 0.958053i | ||||||||
\(708\) | −2.73564e50 | + | 2.60138e51i | −0.136918 | + | 1.30198i | ||||
\(709\) | 1.97821e51 | 0.965251 | 0.482625 | − | 0.875827i | \(-0.339683\pi\) | ||||
0.482625 | + | 0.875827i | \(0.339683\pi\) | |||||||
\(710\) | 4.15272e51 | + | 4.61232e51i | 1.97552 | + | 2.19416i | ||||
\(711\) | − | 3.79488e50i | − | 0.176013i | ||||||
\(712\) | −1.63352e51 | − | 2.24874e51i | −0.738727 | − | 1.01695i | ||||
\(713\) | 1.29880e51 | 0.572703 | ||||||||
\(714\) | −2.62516e51 | + | 2.36357e51i | −1.12872 | + | 1.01625i | ||||
\(715\) | 1.06260e50i | 0.0445516i | ||||||||
\(716\) | 2.43903e51 | + | 2.56490e50i | 0.997200 | + | 0.104866i | ||||
\(717\) | −3.38765e51 | −1.35068 | ||||||||
\(718\) | −1.56310e51 | − | 1.73610e51i | −0.607782 | − | 0.675048i | ||||
\(719\) | − | 3.36013e51i | − | 1.27419i | −0.770784 | − | 0.637097i | \(-0.780135\pi\) | ||
0.770784 | − | 0.637097i | \(-0.219865\pi\) | |||||||
\(720\) | −1.35545e51 | − | 2.88269e50i | −0.501302 | − | 0.106614i | ||||
\(721\) | 5.39192e51 | 1.94495 | ||||||||
\(722\) | 2.10359e51 | − | 1.89397e51i | 0.740101 | − | 0.666352i | ||||
\(723\) | − | 2.05136e51i | − | 0.703966i | ||||||
\(724\) | 1.68715e49 | − | 1.60435e50i | 0.00564753 | − | 0.0537038i | ||||
\(725\) | −6.93520e51 | −2.26451 | ||||||||
\(726\) | −2.34884e51 | − | 2.60880e51i | −0.748159 | − | 0.830961i | ||||
\(727\) | 4.47646e51i | 1.39096i | 0.718545 | + | 0.695480i | \(0.244808\pi\) | ||||
−0.718545 | + | 0.695480i | \(0.755192\pi\) | |||||||
\(728\) | −1.35827e51 | + | 9.86670e50i | −0.411740 | + | 0.299093i | ||||
\(729\) | −2.10558e51 | −0.622697 | ||||||||
\(730\) | 5.02861e51 | − | 4.52752e51i | 1.45090 | − | 1.30632i | ||||
\(731\) | 4.68305e51i | 1.31831i | ||||||||
\(732\) | 1.14638e51 | + | 1.20555e50i | 0.314870 | + | 0.0331120i | ||||
\(733\) | 3.81951e51 | 1.02361 | 0.511807 | − | 0.859100i | \(-0.328976\pi\) | ||||
0.511807 | + | 0.859100i | \(0.328976\pi\) | |||||||
\(734\) | −2.07276e51 | − | 2.30216e51i | −0.542025 | − | 0.602013i | ||||
\(735\) | − | 8.11536e51i | − | 2.07079i | ||||||
\(736\) | 1.85850e51 | + | 3.22007e51i | 0.462768 | + | 0.801796i | ||||
\(737\) | 2.70706e50 | 0.0657784 | ||||||||
\(738\) | −3.02676e50 | + | 2.72515e50i | −0.0717733 | + | 0.0646213i | ||||
\(739\) | − | 3.07723e51i | − | 0.712132i | −0.934461 | − | 0.356066i | \(-0.884118\pi\) | ||
0.934461 | − | 0.356066i | \(-0.115882\pi\) | |||||||
\(740\) | 1.33833e50 | − | 1.27265e51i | 0.0302268 | − | 0.287434i | ||||
\(741\) | 1.19576e50 | 0.0263583 | ||||||||
\(742\) | 6.36931e50 | + | 7.07423e50i | 0.137032 | + | 0.152198i | ||||
\(743\) | − | 5.84492e51i | − | 1.22738i | −0.789546 | − | 0.613691i | \(-0.789684\pi\) | ||
0.789546 | − | 0.613691i | \(-0.210316\pi\) | |||||||
\(744\) | −1.99098e51 | − | 2.74084e51i | −0.408089 | − | 0.561786i | ||||
\(745\) | −6.32692e51 | −1.26584 | ||||||||
\(746\) | 1.74891e51 | − | 1.57463e51i | 0.341561 | − | 0.307525i | ||||
\(747\) | 1.19172e51i | 0.227197i | ||||||||
\(748\) | −3.20914e50 | − | 3.37476e49i | −0.0597256 | − | 0.00628079i | ||||
\(749\) | −1.35095e50 | −0.0245453 | ||||||||
\(750\) | 1.57923e52 | + | 1.75401e52i | 2.80118 | + | 3.11121i | ||||
\(751\) | 4.22629e51i | 0.731881i | 0.930638 | + | 0.365941i | \(0.119253\pi\) | ||||
−0.930638 | + | 0.365941i | \(0.880747\pi\) | |||||||
\(752\) | −7.83990e50 | + | 3.68635e51i | −0.132553 | + | 0.623269i | ||||
\(753\) | −9.21859e51 | −1.52179 | ||||||||
\(754\) | −1.32122e51 | + | 1.18957e51i | −0.212957 | + | 0.191736i | ||||
\(755\) | − | 1.16944e51i | − | 0.184049i | ||||||
\(756\) | −7.86544e50 | + | 7.47944e51i | −0.120873 | + | 1.14941i | ||||
\(757\) | −4.22243e50 | −0.0633631 | −0.0316815 | − | 0.999498i | \(-0.510086\pi\) | ||||
−0.0316815 | + | 0.999498i | \(0.510086\pi\) | |||||||
\(758\) | −6.08612e51 | − | 6.75970e51i | −0.891856 | − | 0.990562i | ||||
\(759\) | 4.48313e50i | 0.0641548i | ||||||||
\(760\) | −7.33081e50 | + | 5.32520e50i | −0.102449 | + | 0.0744203i | ||||
\(761\) | 7.10752e51 | 0.970050 | 0.485025 | − | 0.874500i | \(-0.338811\pi\) | ||||
0.485025 | + | 0.874500i | \(0.338811\pi\) | |||||||
\(762\) | −1.09798e52 | + | 9.88568e51i | −1.46354 | + | 1.31770i | ||||
\(763\) | 5.58999e51i | 0.727728i | ||||||||
\(764\) | 5.55599e51 | + | 5.84272e50i | 0.706449 | + | 0.0742908i | ||||
\(765\) | 4.01406e51 | 0.498515 | ||||||||
\(766\) | −5.74566e51 | − | 6.38156e51i | −0.696983 | − | 0.774121i | ||||
\(767\) | − | 3.60096e51i | − | 0.426679i | ||||||
\(768\) | 3.94629e51 | − | 8.85817e51i | 0.456759 | − | 1.02528i | ||||
\(769\) | 2.79923e51 | 0.316493 | 0.158246 | − | 0.987400i | \(-0.449416\pi\) | ||||
0.158246 | + | 0.987400i | \(0.449416\pi\) | |||||||
\(770\) | 1.13997e51 | − | 1.02637e51i | 0.125910 | − | 0.113363i | ||||
\(771\) | − | 7.49070e51i | − | 0.808246i | ||||||
\(772\) | 1.12049e51 | − | 1.06551e52i | 0.118113 | − | 1.12317i | ||||
\(773\) | 1.10985e52 | 1.14296 | 0.571482 | − | 0.820615i | \(-0.306369\pi\) | ||||
0.571482 | + | 0.820615i | \(0.306369\pi\) | |||||||
\(774\) | −2.34185e51 | − | 2.60104e51i | −0.235626 | − | 0.261703i | ||||
\(775\) | 1.81925e52i | 1.78839i | ||||||||
\(776\) | 2.35501e51 | + | 3.24197e51i | 0.226195 | + | 0.311385i | ||||
\(777\) | 2.43787e51 | 0.228788 | ||||||||
\(778\) | −1.83178e51 | + | 1.64925e51i | −0.167974 | + | 0.151236i | ||||
\(779\) | 2.66299e50i | 0.0238614i | ||||||||
\(780\) | 9.19935e51 | + | 9.67411e50i | 0.805479 | + | 0.0847048i | ||||
\(781\) | −1.08008e51 | −0.0924137 | ||||||||
\(782\) | −7.20593e51 | − | 8.00344e51i | −0.602516 | − | 0.669199i | ||||
\(783\) | 7.96426e51i | 0.650779i | ||||||||
\(784\) | 1.14562e52 | + | 2.43643e51i | 0.914851 | + | 0.194565i | ||||
\(785\) | −4.03953e52 | −3.15266 | ||||||||
\(786\) | −7.88116e51 | + | 7.09583e51i | −0.601152 | + | 0.541249i | ||||
\(787\) | − | 8.81768e51i | − | 0.657369i | −0.944440 | − | 0.328684i | \(-0.893395\pi\) | ||
0.944440 | − | 0.328684i | \(-0.106605\pi\) | |||||||
\(788\) | 1.62583e51 | − | 1.54604e52i | 0.118469 | − | 1.12655i | ||||
\(789\) | 2.86122e52 | 2.03782 | ||||||||
\(790\) | −1.28432e52 | − | 1.42646e52i | −0.894098 | − | 0.993052i | ||||
\(791\) | 2.57439e50i | 0.0175185i | ||||||||
\(792\) | 1.95117e50 | − | 1.41736e50i | 0.0129790 | − | 0.00942813i | ||||
\(793\) | −1.58688e51 | −0.103187 | ||||||||
\(794\) | 1.22283e52 | − | 1.10098e52i | 0.777316 | − | 0.699859i | ||||
\(795\) | − | 5.24489e51i | − | 0.325933i | ||||||
\(796\) | −7.07689e51 | − | 7.44212e50i | −0.429939 | − | 0.0452128i | ||||
\(797\) | 1.28642e52 | 0.764067 | 0.382033 | − | 0.924148i | \(-0.375224\pi\) | ||||
0.382033 | + | 0.924148i | \(0.375224\pi\) | |||||||
\(798\) | −1.15499e51 | − | 1.28282e51i | −0.0670698 | − | 0.0744927i | ||||
\(799\) | − | 1.09168e52i | − | 0.619804i | ||||||
\(800\) | −4.51041e52 | + | 2.60325e52i | −2.50378 | + | 1.44509i | ||||
\(801\) | −6.01703e51 | −0.326585 | ||||||||
\(802\) | −2.59420e52 | + | 2.33570e52i | −1.37678 | + | 1.23959i | ||||
\(803\) | 1.17756e51i | 0.0611087i | ||||||||
\(804\) | 2.46455e51 | − | 2.34360e52i | 0.125063 | − | 1.18925i | ||||
\(805\) | 5.11946e52 | 2.54038 | ||||||||
\(806\) | 3.12049e51 | + | 3.46585e51i | 0.151423 | + | 0.168182i | ||||
\(807\) | 3.22026e52i | 1.52816i | ||||||||
\(808\) | 8.72141e51 | + | 1.20061e52i | 0.404746 | + | 0.557183i | ||||
\(809\) | 7.12246e51 | 0.323263 | 0.161632 | − | 0.986851i | \(-0.448324\pi\) | ||||
0.161632 | + | 0.986851i | \(0.448324\pi\) | |||||||
\(810\) | 3.93759e52 | − | 3.54522e52i | 1.74783 | − | 1.57367i | ||||
\(811\) | 2.94632e52i | 1.27910i | 0.768749 | + | 0.639550i | \(0.220879\pi\) | ||||
−0.768749 | + | 0.639550i | \(0.779121\pi\) | |||||||
\(812\) | 2.55235e52 | + | 2.68407e51i | 1.08376 | + | 0.113969i | ||||
\(813\) | −4.79915e52 | −1.99313 | ||||||||
\(814\) | 1.49010e50 | + | 1.65501e50i | 0.00605306 | + | 0.00672299i | ||||
\(815\) | − | 8.47993e52i | − | 3.36942i | ||||||
\(816\) | −5.84330e51 | + | 2.74754e52i | −0.227110 | + | 1.06788i | ||||
\(817\) | −2.28844e51 | −0.0870047 | ||||||||
\(818\) | 8.07761e51 | − | 7.27270e51i | 0.300416 | − | 0.270481i | ||||
\(819\) | 3.63438e51i | 0.132227i | ||||||||
\(820\) | −2.15445e51 | + | 2.04872e52i | −0.0766809 | + | 0.729177i | ||||
\(821\) | −2.51774e52 | −0.876664 | −0.438332 | − | 0.898813i | \(-0.644431\pi\) | ||||
−0.438332 | + | 0.898813i | \(0.644431\pi\) | |||||||
\(822\) | 1.68665e52 | + | 1.87332e52i | 0.574555 | + | 0.638144i | ||||
\(823\) | 4.49416e52i | 1.49779i | 0.662687 | + | 0.748896i | \(0.269416\pi\) | ||||
−0.662687 | + | 0.748896i | \(0.730584\pi\) | |||||||
\(824\) | 3.46902e52 | − | 2.51995e52i | 1.13114 | − | 0.821678i | ||||
\(825\) | −6.27961e51 | −0.200337 | ||||||||
\(826\) | −3.86313e52 | + | 3.47818e52i | −1.20586 | + | 1.08570i | ||||
\(827\) | − | 2.24802e52i | − | 0.686597i | −0.939226 | − | 0.343299i | \(-0.888456\pi\) | ||
0.939226 | − | 0.343299i | \(-0.111544\pi\) | |||||||
\(828\) | 8.00456e51 | + | 8.41767e50i | 0.239217 | + | 0.0251562i | ||||
\(829\) | −3.39012e52 | −0.991364 | −0.495682 | − | 0.868504i | \(-0.665082\pi\) | ||||
−0.495682 | + | 0.868504i | \(0.665082\pi\) | |||||||
\(830\) | 4.03319e52 | + | 4.47957e52i | 1.15410 | + | 1.28183i | ||||
\(831\) | 4.22880e52i | 1.18413i | ||||||||
\(832\) | −4.12753e51 | + | 1.26960e52i | −0.113102 | + | 0.347893i | ||||
\(833\) | −3.39265e52 | −0.909765 | ||||||||
\(834\) | −5.03266e51 | + | 4.53118e51i | −0.132071 | + | 0.118911i | ||||
\(835\) | − | 3.32995e52i | − | 0.855226i | ||||||
\(836\) | 1.64913e49 | − | 1.56819e50i | 0.000414515 | − | 0.00394173i | ||||
\(837\) | 2.08920e52 | 0.513950 | ||||||||
\(838\) | −1.99533e51 | − | 2.21616e51i | −0.0480421 | − | 0.0533592i | ||||
\(839\) | 3.59773e52i | 0.847839i | 0.905700 | + | 0.423919i | \(0.139346\pi\) | ||||
−0.905700 | + | 0.423919i | \(0.860654\pi\) | |||||||
\(840\) | −7.84784e52 | − | 1.08035e53i | −1.81019 | − | 2.49195i | ||||
\(841\) | −1.71143e52 | −0.386395 | ||||||||
\(842\) | 7.71631e50 | − | 6.94741e50i | 0.0170527 | − | 0.0153534i | ||||
\(843\) | − | 7.54371e52i | − | 1.63188i | ||||||
\(844\) | 1.30930e51 | + | 1.37687e50i | 0.0277252 | + | 0.00291561i | ||||
\(845\) | 8.24237e52 | 1.70857 | ||||||||
\(846\) | 5.45917e51 | + | 6.06337e51i | 0.110780 | + | 0.123040i | ||||
\(847\) | − | 6.97619e52i | − | 1.38585i | ||||||
\(848\) | 7.40403e51 | + | 1.57464e51i | 0.143994 | + | 0.0306236i | ||||
\(849\) | −3.23688e52 | −0.616294 | ||||||||
\(850\) | 1.12106e53 | − | 1.00935e53i | 2.08972 | − | 1.88148i | ||||
\(851\) | 7.43246e51i | 0.135644i | ||||||||
\(852\) | −9.83319e51 | + | 9.35062e52i | −0.175704 | + | 1.67081i | ||||
\(853\) | 2.48028e52 | 0.433928 | 0.216964 | − | 0.976180i | \(-0.430385\pi\) | ||||
0.216964 | + | 0.976180i | \(0.430385\pi\) | |||||||
\(854\) | 1.53278e52 | + | 1.70242e52i | 0.262565 | + | 0.291624i | ||||
\(855\) | 1.96153e51i | 0.0329006i | ||||||||
\(856\) | −8.69169e50 | + | 6.31377e50i | −0.0142750 | + | 0.0103696i | ||||
\(857\) | 8.00448e52 | 1.28730 | 0.643648 | − | 0.765322i | \(-0.277420\pi\) | ||||
0.643648 | + | 0.765322i | \(0.277420\pi\) | |||||||
\(858\) | −1.19633e51 | + | 1.07712e51i | −0.0188399 | + | 0.0169626i | ||||
\(859\) | − | 9.48414e51i | − | 0.146259i | −0.997322 | − | 0.0731293i | \(-0.976701\pi\) | ||
0.997322 | − | 0.0731293i | \(-0.0232986\pi\) | |||||||
\(860\) | −1.76056e53 | − | 1.85142e52i | −2.65876 | − | 0.279598i | ||||
\(861\) | −3.92450e52 | −0.580400 | ||||||||
\(862\) | 1.91713e52 | + | 2.12931e52i | 0.277665 | + | 0.308396i | ||||
\(863\) | − | 3.61750e52i | − | 0.513114i | −0.966529 | − | 0.256557i | \(-0.917412\pi\) | ||
0.966529 | − | 0.256557i | \(-0.0825881\pi\) | |||||||
\(864\) | 2.98952e52 | + | 5.17968e52i | 0.415292 | + | 0.719540i | ||||
\(865\) | −8.70975e52 | −1.18499 | ||||||||
\(866\) | −3.07386e52 | + | 2.76756e52i | −0.409603 | + | 0.368787i | ||||
\(867\) | 4.63387e51i | 0.0604784i | ||||||||
\(868\) | 7.04090e51 | − | 6.69536e52i | 0.0900063 | − | 0.855892i | ||||
\(869\) | 3.34038e51 | 0.0418253 | ||||||||
\(870\) | −9.46167e52 | − | 1.05088e53i | −1.16044 | − | 1.28887i | ||||
\(871\) | 3.24412e52i | 0.389736i | ||||||||
\(872\) | 2.61251e52 | + | 3.59645e52i | 0.307441 | + | 0.423231i | ||||
\(873\) | 8.67465e51 | 0.0999990 | ||||||||
\(874\) | 3.91100e51 | − | 3.52128e51i | 0.0441654 | − | 0.0397644i | ||||
\(875\) | 4.69040e53i | 5.18877i | ||||||||
\(876\) | 1.01946e53 | + | 1.07207e52i | 1.10483 | + | 0.116185i | ||||
\(877\) | 1.41377e53 | 1.50101 | 0.750507 | − | 0.660863i | \(-0.229809\pi\) | ||||
0.750507 | + | 0.660863i | \(0.229809\pi\) | |||||||
\(878\) | −9.06070e52 | − | 1.00635e53i | −0.942455 | − | 1.04676i | ||||
\(879\) | 1.21069e53i | 1.23377i | ||||||||
\(880\) | 2.53744e51 | − | 1.19311e52i | 0.0253342 | − | 0.119123i | ||||
\(881\) | −7.35045e51 | −0.0719031 | −0.0359516 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359516 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(882\) | 1.88433e52 | − | 1.69656e52i | 0.180602 | − | 0.162606i | ||||
\(883\) | − | 1.87248e53i | − | 1.75843i | −0.476424 | − | 0.879216i | \(-0.658067\pi\) | ||
0.476424 | − | 0.879216i | \(-0.341933\pi\) | |||||||
\(884\) | 4.04429e51 | − | 3.84581e52i | 0.0372136 | − | 0.353873i | ||||
\(885\) | 2.86416e53 | 2.58237 | ||||||||
\(886\) | 1.06921e53 | + | 1.18754e53i | 0.944616 | + | 1.04916i | ||||
\(887\) | − | 3.87380e52i | − | 0.335361i | −0.985841 | − | 0.167680i | \(-0.946372\pi\) | ||
0.985841 | − | 0.167680i | \(-0.0536277\pi\) | |||||||
\(888\) | 1.56846e52 | − | 1.13935e52i | 0.133058 | − | 0.0966553i | ||||
\(889\) | −2.93611e53 | −2.44084 | ||||||||
\(890\) | −2.26175e53 | + | 2.03637e53i | −1.84257 | + | 1.65896i | ||||
\(891\) | 9.22074e51i | 0.0736151i | ||||||||
\(892\) | −2.94956e52 | − | 3.10178e51i | −0.230775 | − | 0.0242685i | ||||
\(893\) | 5.33466e51 | 0.0409054 | ||||||||
\(894\) | −6.41332e52 | − | 7.12312e52i | −0.481956 | − | 0.535297i | ||||
\(895\) | − | 2.68540e53i | − | 1.97786i | ||||||
\(896\) | 1.76071e53 | − | 7.83505e52i | 1.27099 | − | 0.565585i | ||||
\(897\) | −5.37255e52 | −0.380116 | ||||||||
\(898\) | 6.32281e52 | − | 5.69277e52i | 0.438466 | − | 0.394775i | ||||
\(899\) | − | 7.12936e52i | − | 0.484591i | ||||||
\(900\) | −1.17908e52 | + | 1.12122e53i | −0.0785558 | + | 0.747006i | ||||
\(901\) | −2.19264e52 | −0.143193 | ||||||||
\(902\) | −2.39877e51 | − | 2.66425e51i | −0.0153557 | − | 0.0170552i | ||||
\(903\) | − | 3.37251e53i | − | 2.11629i | ||||||
\(904\) | 1.20316e51 | + | 1.65629e51i | 0.00740100 | + | 0.0101884i | ||||
\(905\) | −1.76641e52 | −0.106517 | ||||||||
\(906\) | 1.31661e52 | − | 1.18541e52i | 0.0778305 | − | 0.0700749i | ||||
\(907\) | 9.02603e52i | 0.523077i | 0.965193 | + | 0.261538i | \(0.0842298\pi\) | ||||
−0.965193 | + | 0.261538i | \(0.915770\pi\) | |||||||
\(908\) | −7.38427e52 | − | 7.76536e51i | −0.419529 | − | 0.0441180i | ||||
\(909\) | 3.21251e52 | 0.178935 | ||||||||
\(910\) | 1.23000e53 | + | 1.36613e53i | 0.671676 | + | 0.746014i | ||||
\(911\) | 2.92851e53i | 1.56789i | 0.620829 | + | 0.783946i | \(0.286796\pi\) | ||||
−0.620829 | + | 0.783946i | \(0.713204\pi\) | |||||||
\(912\) | −1.34263e52 | − | 2.85541e51i | −0.0704771 | − | 0.0149886i | ||||
\(913\) | −1.04899e52 | −0.0539881 | ||||||||
\(914\) | 9.64347e52 | − | 8.68253e52i | 0.486633 | − | 0.438142i | ||||
\(915\) | − | 1.26219e53i | − | 0.624516i | ||||||
\(916\) | −3.12842e51 | + | 2.97489e52i | −0.0151777 | + | 0.144329i | ||||
\(917\) | −2.10750e53 | −1.00258 | ||||||||
\(918\) | −1.15912e53 | − | 1.28740e53i | −0.540704 | − | 0.600546i | ||||
\(919\) | 6.20645e52i | 0.283899i | 0.989874 | + | 0.141950i | \(0.0453371\pi\) | ||||
−0.989874 | + | 0.141950i | \(0.954663\pi\) | |||||||
\(920\) | 3.29373e53 | − | 2.39261e53i | 1.47743 | − | 1.07323i | ||||
\(921\) | 9.39403e52 | 0.413217 | ||||||||
\(922\) | −1.78824e53 | + | 1.61005e53i | −0.771380 | + | 0.694515i | ||||
\(923\) | − | 1.29436e53i | − | 0.547550i | ||||||
\(924\) | 2.31107e52 | + | 2.43034e51i | 0.0958778 | + | 0.0100826i | ||||
\(925\) | −1.04108e53 | −0.423577 | ||||||||
\(926\) | 5.21308e52 | + | 5.79004e52i | 0.208016 | + | 0.231038i | ||||
\(927\) | − | 9.28218e52i | − | 0.363258i | ||||||
\(928\) | 1.76756e53 | − | 1.02017e53i | 0.678438 | − | 0.391570i | ||||
\(929\) | −3.77823e52 | −0.142235 | −0.0711173 | − | 0.997468i | \(-0.522656\pi\) | ||||
−0.0711173 | + | 0.997468i | \(0.522656\pi\) | |||||||
\(930\) | −2.75669e53 | + | 2.48200e53i | −1.01788 | + | 0.916449i | ||||
\(931\) | − | 1.65787e52i | − | 0.0600420i | ||||||
\(932\) | −4.89913e52 | + | 4.65870e53i | −0.174033 | + | 1.65492i | ||||
\(933\) | −4.08746e53 | −1.42424 | ||||||||
\(934\) | 1.48326e53 | + | 1.64742e53i | 0.506961 | + | 0.563069i | ||||
\(935\) | 3.53331e52i | 0.118460i | ||||||||
\(936\) | 1.69855e52 | + | 2.33827e52i | 0.0558615 | + | 0.0769004i | ||||
\(937\) | −3.94855e53 | −1.27387 | −0.636934 | − | 0.770918i | \(-0.719798\pi\) | ||||
−0.636934 | + | 0.770918i | \(0.719798\pi\) | |||||||
\(938\) | 3.48032e53 | − | 3.13351e53i | 1.10146 | − | 0.991700i | ||||
\(939\) | 4.52875e53i | 1.40604i | ||||||||
\(940\) | 4.10411e53 | + | 4.31592e52i | 1.25002 | + | 0.131453i | ||||
\(941\) | 4.23837e53 | 1.26644 | 0.633222 | − | 0.773970i | \(-0.281732\pi\) | ||||
0.633222 | + | 0.773970i | \(0.281732\pi\) | |||||||
\(942\) | −4.09470e53 | − | 4.54788e53i | −1.20034 | − | 1.33319i | ||||
\(943\) | − | 1.19648e53i | − | 0.344109i | ||||||
\(944\) | −8.59889e52 | + | 4.04323e53i | −0.242631 | + | 1.14086i | ||||
\(945\) | 8.23496e53 | 2.27976 | ||||||||
\(946\) | 2.28952e52 | − | 2.06138e52i | 0.0621876 | − | 0.0559908i | ||||
\(947\) | − | 2.93453e53i | − | 0.782058i | −0.920378 | − | 0.391029i | \(-0.872119\pi\) | ||
0.920378 | − | 0.391029i | \(-0.127881\pi\) | |||||||
\(948\) | 3.04113e52 | − | 2.89188e53i | 0.0795215 | − | 0.756189i | ||||
\(949\) | −1.41118e53 | −0.362068 | ||||||||
\(950\) | 4.93233e52 | + | 5.47821e52i | 0.124173 | + | 0.137916i | ||||
\(951\) | 7.22974e53i | 1.78597i | ||||||||
\(952\) | −4.51645e53 | + | 3.28081e53i | −1.09479 | + | 0.795274i | ||||
\(953\) | 8.04997e53 | 1.91479 | 0.957396 | − | 0.288777i | \(-0.0932485\pi\) | ||||
0.957396 | + | 0.288777i | \(0.0932485\pi\) | |||||||
\(954\) | 1.21783e52 | − | 1.09647e52i | 0.0284259 | − | 0.0255934i | ||||
\(955\) | − | 6.11722e53i | − | 1.40118i | ||||||
\(956\) | −5.32418e53 | − | 5.59895e52i | −1.19677 | − | 0.125853i | ||||
\(957\) | 2.46088e52 | 0.0542844 | ||||||||
\(958\) | −1.68360e53 | − | 1.86993e53i | −0.364468 | − | 0.404805i | ||||
\(959\) | 5.00944e53i | 1.06428i | ||||||||
\(960\) | −1.00982e54 | − | 3.28298e53i | −2.10553 | − | 0.684520i | ||||
\(961\) | 3.01658e53 | 0.617296 | ||||||||
\(962\) | −1.98336e52 | + | 1.78572e52i | −0.0398336 | + | 0.0358643i | ||||
\(963\) | 2.32566e51i | 0.00458431i | ||||||||
\(964\) | 3.39039e52 | − | 3.22400e53i | 0.0655937 | − | 0.623747i | ||||
\(965\) | −1.17314e54 | −2.22770 | ||||||||
\(966\) | 5.18937e53 | + | 5.76370e53i | 0.967223 | + | 1.07427i | ||||
\(967\) | 9.47185e53i | 1.73284i | 0.499316 | + | 0.866420i | \(0.333585\pi\) | ||||
−0.499316 | + | 0.866420i | \(0.666415\pi\) | |||||||
\(968\) | −3.26036e53 | − | 4.48830e53i | −0.585477 | − | 0.805982i | ||||
\(969\) | 3.97608e52 | 0.0700853 | ||||||||
\(970\) | 3.26072e53 | − | 2.93580e53i | 0.564186 | − | 0.507967i | ||||
\(971\) | − | 5.98851e53i | − | 1.01712i | −0.861026 | − | 0.508561i | \(-0.830178\pi\) | ||
0.861026 | − | 0.508561i | \(-0.169822\pi\) | |||||||
\(972\) | 3.02715e53 | + | 3.18338e52i | 0.504709 | + | 0.0530757i | ||||
\(973\) | −1.34579e53 | −0.220265 | ||||||||
\(974\) | −7.11175e52 | − | 7.89884e52i | −0.114266 | − | 0.126912i | ||||
\(975\) | − | 7.52544e53i | − | 1.18699i | ||||||
\(976\) | 1.78178e53 | + | 3.78938e52i | 0.275904 | + | 0.0586775i | ||||
\(977\) | 6.85985e53 | 1.04283 | 0.521413 | − | 0.853304i | \(-0.325405\pi\) | ||||
0.521413 | + | 0.853304i | \(0.325405\pi\) | |||||||
\(978\) | 9.54707e53 | − | 8.59573e53i | 1.42485 | − | 1.28287i | ||||
\(979\) | − | 5.29639e52i | − | 0.0776053i | ||||||
\(980\) | 1.34127e53 | − | 1.27545e54i | 0.192951 | − | 1.83482i | ||||
\(981\) | 9.62315e52 | 0.135917 | ||||||||
\(982\) | 5.58758e53 | + | 6.20598e53i | 0.774848 | + | 0.860605i | ||||
\(983\) | − | 6.74599e53i | − | 0.918507i | −0.888305 | − | 0.459254i | \(-0.848117\pi\) | ||
0.888305 | − | 0.459254i | \(-0.151883\pi\) | |||||||
\(984\) | −2.52492e53 | + | 1.83414e53i | −0.337549 | + | 0.245200i | ||||
\(985\) | −1.70221e54 | −2.23440 | ||||||||
\(986\) | −4.39325e53 | + | 3.95548e53i | −0.566241 | + | 0.509817i | ||||
\(987\) | 7.86178e53i | 0.994975i | ||||||||
\(988\) | 1.87931e52 | + | 1.97630e51i | 0.0233547 | + | 0.00245600i | ||||
\(989\) | 1.02819e54 | 1.25471 | ||||||||
\(990\) | −1.76690e52 | − | 1.96245e52i | −0.0211728 | − | 0.0235161i | ||||
\(991\) | − | 5.23328e52i | − | 0.0615812i | −0.999526 | − | 0.0307906i | \(-0.990198\pi\) | ||
0.999526 | − | 0.0307906i | \(-0.00980250\pi\) | |||||||
\(992\) | −2.67612e53 | − | 4.63668e53i | −0.309240 | − | 0.535793i | ||||
\(993\) | 8.32370e53 | 0.944560 | ||||||||
\(994\) | −1.38859e54 | + | 1.25023e54i | −1.54746 | + | 1.39326i | ||||
\(995\) | 7.79175e53i | 0.852746i | ||||||||
\(996\) | −9.55017e52 | + | 9.08149e53i | −0.102646 | + | 0.976088i | ||||
\(997\) | 1.02177e54 | 1.07855 | 0.539275 | − | 0.842130i | \(-0.318698\pi\) | ||||
0.539275 | + | 0.842130i | \(0.318698\pi\) | |||||||
\(998\) | −7.25129e53 | − | 8.05382e53i | −0.751736 | − | 0.834934i | ||||
\(999\) | 1.19556e53i | 0.121728i |
(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 | 4.37.b.b.3.13 | ✓ | 16 | |
4.3 | odd | 2 | inner | 4.37.b.b.3.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.37.b.b.3.13 | ✓ | 16 | 1.1 | even | 1 | trivial | |
4.37.b.b.3.14 | yes | 16 | 4.3 | odd | 2 | inner |