Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,31,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 31, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 31);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 31 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(34.2085571416\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + \cdots + 17\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{104}\cdot 3^{53}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Root | \(-1.58422e9i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.31.b.a.5.10 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 23170.5i | − | 0.707107i | ||||||
\(3\) | 1.42278e7 | + | 1.86071e6i | 0.991556 | + | 0.129676i | ||||
\(4\) | −5.36871e8 | −0.500000 | ||||||||
\(5\) | − | 3.80214e10i | − | 1.24588i | −0.782268 | − | 0.622942i | \(-0.785937\pi\) | ||
0.782268 | − | 0.622942i | \(-0.214063\pi\) | |||||||
\(6\) | 4.31134e10 | − | 3.29664e11i | 0.0916946 | − | 0.701136i | ||||
\(7\) | 7.78024e12 | 1.63879 | 0.819393 | − | 0.573232i | \(-0.194311\pi\) | ||||
0.819393 | + | 0.573232i | \(0.194311\pi\) | |||||||
\(8\) | 1.24396e13i | 0.353553i | ||||||||
\(9\) | 1.98967e14 | + | 5.29473e13i | 0.966368 | + | 0.257162i | ||||
\(10\) | −8.80973e14 | −0.880973 | ||||||||
\(11\) | − | 2.27578e15i | − | 0.544803i | −0.962184 | − | 0.272402i | \(-0.912182\pi\) | ||
0.962184 | − | 0.272402i | \(-0.0878179\pi\) | |||||||
\(12\) | −7.63847e15 | − | 9.98958e14i | −0.495778 | − | 0.0648379i | ||||
\(13\) | 1.13538e16 | 0.221815 | 0.110908 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110908 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(14\) | − | 1.80272e17i | − | 1.15880i | ||||||
\(15\) | 7.07466e16 | − | 5.40959e17i | 0.161561 | − | 1.23536i | ||||
\(16\) | 2.88230e17 | 0.250000 | ||||||||
\(17\) | 4.86602e18i | 1.69996i | 0.526811 | + | 0.849982i | \(0.323387\pi\) | ||||
−0.526811 | + | 0.849982i | \(0.676613\pi\) | |||||||
\(18\) | 1.22681e18 | − | 4.61015e18i | 0.181841 | − | 0.683326i | ||||
\(19\) | 1.09576e19 | 0.721788 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(20\) | 2.04126e19i | 0.622942i | ||||||||
\(21\) | 1.10695e20 | + | 1.44767e19i | 1.62495 | + | 0.212511i | ||||
\(22\) | −5.27308e19 | −0.385234 | ||||||||
\(23\) | − | 4.33263e20i | − | 1.62493i | −0.583011 | − | 0.812464i | \(-0.698126\pi\) | ||
0.583011 | − | 0.812464i | \(-0.301874\pi\) | |||||||
\(24\) | −2.31463e19 | + | 1.76987e20i | −0.0458473 | + | 0.350568i | ||||
\(25\) | −5.14303e20 | −0.552229 | ||||||||
\(26\) | − | 2.63073e20i | − | 0.156847i | ||||||
\(27\) | 2.73233e21 | + | 1.12354e21i | 0.924861 | + | 0.380305i | ||||
\(28\) | −4.17698e21 | −0.819393 | ||||||||
\(29\) | − | 1.37646e21i | − | 0.159512i | −0.996814 | − | 0.0797559i | \(-0.974586\pi\) | ||
0.996814 | − | 0.0797559i | \(-0.0254141\pi\) | |||||||
\(30\) | −1.25343e22 | − | 1.63923e21i | −0.873535 | − | 0.114241i | ||||
\(31\) | −7.68233e21 | −0.327392 | −0.163696 | − | 0.986511i | \(-0.552342\pi\) | ||||
−0.163696 | + | 0.986511i | \(0.552342\pi\) | |||||||
\(32\) | − | 6.67843e21i | − | 0.176777i | ||||||
\(33\) | 4.23455e21 | − | 3.23792e22i | 0.0706477 | − | 0.540203i | ||||
\(34\) | 1.12748e23 | 1.20206 | ||||||||
\(35\) | − | 2.95815e23i | − | 2.04174i | ||||||
\(36\) | −1.06819e23 | − | 2.84259e22i | −0.483184 | − | 0.128581i | ||||
\(37\) | −8.83896e22 | −0.265079 | −0.132539 | − | 0.991178i | \(-0.542313\pi\) | ||||
−0.132539 | + | 0.991178i | \(0.542313\pi\) | |||||||
\(38\) | − | 2.53892e23i | − | 0.510382i | ||||||
\(39\) | 1.61539e23 | + | 2.11261e22i | 0.219942 | + | 0.0287641i | ||||
\(40\) | 4.72969e23 | 0.440487 | ||||||||
\(41\) | − | 1.91086e24i | − | 1.22877i | −0.789005 | − | 0.614387i | \(-0.789403\pi\) | ||
0.789005 | − | 0.614387i | \(-0.210597\pi\) | |||||||
\(42\) | 3.35433e23 | − | 2.56486e24i | 0.150268 | − | 1.14901i | ||||
\(43\) | −5.27890e24 | −1.66156 | −0.830781 | − | 0.556599i | \(-0.812106\pi\) | ||||
−0.830781 | + | 0.556599i | \(0.812106\pi\) | |||||||
\(44\) | 1.22180e24i | 0.272402i | ||||||||
\(45\) | 2.01313e24 | − | 7.56499e24i | 0.320394 | − | 1.20398i | ||||
\(46\) | −1.00389e25 | −1.14900 | ||||||||
\(47\) | − | 1.59051e25i | − | 1.31847i | −0.751938 | − | 0.659234i | \(-0.770881\pi\) | ||
0.751938 | − | 0.659234i | \(-0.229119\pi\) | |||||||
\(48\) | 4.10087e24 | + | 5.36312e23i | 0.247889 | + | 0.0324189i | ||||
\(49\) | 3.79928e25 | 1.68562 | ||||||||
\(50\) | 1.19166e25i | 0.390485i | ||||||||
\(51\) | −9.05422e24 | + | 6.92325e25i | −0.220444 | + | 1.68561i | ||||
\(52\) | −6.09553e24 | −0.110908 | ||||||||
\(53\) | 6.96076e24i | 0.0951741i | 0.998867 | + | 0.0475871i | \(0.0151532\pi\) | ||||
−0.998867 | + | 0.0475871i | \(0.984847\pi\) | |||||||
\(54\) | 2.60329e25 | − | 6.33094e25i | 0.268916 | − | 0.653976i | ||||
\(55\) | −8.65282e25 | −0.678762 | ||||||||
\(56\) | 9.67827e25i | 0.579398i | ||||||||
\(57\) | 1.55901e26 | + | 2.03888e25i | 0.715694 | + | 0.0935985i | ||||
\(58\) | −3.18932e25 | −0.112792 | ||||||||
\(59\) | 5.40161e26i | 1.47823i | 0.673577 | + | 0.739117i | \(0.264757\pi\) | ||||
−0.673577 | + | 0.739117i | \(0.735243\pi\) | |||||||
\(60\) | −3.79818e25 | + | 2.90425e26i | −0.0807805 | + | 0.617682i | ||||
\(61\) | −9.06733e26 | −1.50498 | −0.752492 | − | 0.658601i | \(-0.771148\pi\) | ||||
−0.752492 | + | 0.658601i | \(0.771148\pi\) | |||||||
\(62\) | 1.78003e26i | 0.231501i | ||||||||
\(63\) | 1.54801e27 | + | 4.11943e26i | 1.58367 | + | 0.421433i | ||||
\(64\) | −1.54743e26 | −0.125000 | ||||||||
\(65\) | − | 4.31688e26i | − | 0.276356i | ||||||
\(66\) | −7.50241e26 | − | 9.81166e25i | −0.381981 | − | 0.0499555i | ||||
\(67\) | 2.89531e27 | 1.17645 | 0.588225 | − | 0.808698i | \(-0.299827\pi\) | ||||
0.588225 | + | 0.808698i | \(0.299827\pi\) | |||||||
\(68\) | − | 2.61242e27i | − | 0.849982i | ||||||
\(69\) | 8.06175e26 | − | 6.16436e27i | 0.210714 | − | 1.61121i | ||||
\(70\) | −6.85418e27 | −1.44373 | ||||||||
\(71\) | − | 2.12041e27i | − | 0.361031i | −0.983572 | − | 0.180516i | \(-0.942223\pi\) | ||
0.983572 | − | 0.180516i | \(-0.0577767\pi\) | |||||||
\(72\) | −6.58641e26 | + | 2.47506e27i | −0.0909204 | + | 0.341663i | ||||
\(73\) | 5.48943e27 | 0.616147 | 0.308073 | − | 0.951363i | \(-0.400316\pi\) | ||||
0.308073 | + | 0.951363i | \(0.400316\pi\) | |||||||
\(74\) | 2.04803e27i | 0.187439i | ||||||||
\(75\) | −7.31737e27 | − | 9.56966e26i | −0.547566 | − | 0.0716106i | ||||
\(76\) | −5.88280e27 | −0.360894 | ||||||||
\(77\) | − | 1.77061e28i | − | 0.892816i | ||||||
\(78\) | 4.89502e26 | − | 3.74294e27i | 0.0203393 | − | 0.155523i | ||||
\(79\) | 1.73705e27 | 0.0596220 | 0.0298110 | − | 0.999556i | \(-0.490509\pi\) | ||||
0.0298110 | + | 0.999556i | \(0.490509\pi\) | |||||||
\(80\) | − | 1.09589e28i | − | 0.311471i | ||||||
\(81\) | 3.67843e28 | + | 2.10695e28i | 0.867736 | + | 0.497026i | ||||
\(82\) | −4.42756e28 | −0.868874 | ||||||||
\(83\) | 4.74090e28i | 0.775692i | 0.921724 | + | 0.387846i | \(0.126781\pi\) | ||||
−0.921724 | + | 0.387846i | \(0.873219\pi\) | |||||||
\(84\) | −5.94291e28 | − | 7.77213e27i | −0.812475 | − | 0.106255i | ||||
\(85\) | 1.85013e29 | 2.11796 | ||||||||
\(86\) | 1.22315e29i | 1.17490i | ||||||||
\(87\) | 2.56118e27 | − | 1.95839e28i | 0.0206848 | − | 0.158165i | ||||
\(88\) | 2.83097e28 | 0.192617 | ||||||||
\(89\) | 2.15151e29i | 1.23564i | 0.786318 | + | 0.617822i | \(0.211985\pi\) | ||||
−0.786318 | + | 0.617822i | \(0.788015\pi\) | |||||||
\(90\) | −1.75284e29 | − | 4.66452e28i | −0.851345 | − | 0.226553i | ||||
\(91\) | 8.83354e28 | 0.363508 | ||||||||
\(92\) | 2.32606e29i | 0.812464i | ||||||||
\(93\) | −1.09302e29 | − | 1.42945e28i | −0.324627 | − | 0.0424547i | ||||
\(94\) | −3.68530e29 | −0.932298 | ||||||||
\(95\) | − | 4.16622e29i | − | 0.899265i | ||||||
\(96\) | 1.24266e28 | − | 9.50191e28i | 0.0229236 | − | 0.175284i | ||||
\(97\) | 2.31086e29 | 0.364920 | 0.182460 | − | 0.983213i | \(-0.441594\pi\) | ||||
0.182460 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(98\) | − | 8.80310e29i | − | 1.19191i | ||||||
\(99\) | 1.20496e29 | − | 4.52804e29i | 0.140102 | − | 0.526480i | ||||
\(100\) | 2.76114e29 | 0.276114 | ||||||||
\(101\) | 5.36165e29i | 0.461825i | 0.972975 | + | 0.230913i | \(0.0741711\pi\) | ||||
−0.972975 | + | 0.230913i | \(0.925829\pi\) | |||||||
\(102\) | 1.60415e30 | + | 2.09791e29i | 1.19191 | + | 0.155878i | ||||
\(103\) | −2.11607e30 | −1.35823 | −0.679113 | − | 0.734033i | \(-0.737636\pi\) | ||||
−0.679113 | + | 0.734033i | \(0.737636\pi\) | |||||||
\(104\) | 1.41236e29i | 0.0784236i | ||||||||
\(105\) | 5.50425e29 | − | 4.20879e30i | 0.264764 | − | 2.02450i | ||||
\(106\) | 1.61284e29 | 0.0672983 | ||||||||
\(107\) | 2.33057e30i | 0.844705i | 0.906432 | + | 0.422353i | \(0.138796\pi\) | ||||
−0.906432 | + | 0.422353i | \(0.861204\pi\) | |||||||
\(108\) | −1.46691e30 | − | 6.03196e29i | −0.462431 | − | 0.190152i | ||||
\(109\) | 1.56872e30 | 0.430674 | 0.215337 | − | 0.976540i | \(-0.430915\pi\) | ||||
0.215337 | + | 0.976540i | \(0.430915\pi\) | |||||||
\(110\) | 2.00490e30i | 0.479957i | ||||||||
\(111\) | −1.25758e30 | − | 1.64467e29i | −0.262841 | − | 0.0343743i | ||||
\(112\) | 2.24250e30 | 0.409697 | ||||||||
\(113\) | 3.55407e30i | 0.568263i | 0.958785 | + | 0.284132i | \(0.0917053\pi\) | ||||
−0.958785 | + | 0.284132i | \(0.908295\pi\) | |||||||
\(114\) | 4.72418e29 | − | 3.61231e30i | 0.0661841 | − | 0.506072i | ||||
\(115\) | −1.64733e31 | −2.02447 | ||||||||
\(116\) | 7.38980e29i | 0.0797559i | ||||||||
\(117\) | 2.25903e30 | + | 6.01154e29i | 0.214355 | + | 0.0570424i | ||||
\(118\) | 1.25158e31 | 1.04527 | ||||||||
\(119\) | 3.78588e31i | 2.78588i | ||||||||
\(120\) | 6.72929e30 | + | 8.80056e29i | 0.436767 | + | 0.0571204i | ||||
\(121\) | 1.22702e31 | 0.703190 | ||||||||
\(122\) | 2.10094e31i | 1.06418i | ||||||||
\(123\) | 3.55556e30 | − | 2.71873e31i | 0.159342 | − | 1.21840i | ||||
\(124\) | 4.12442e30 | 0.163696 | ||||||||
\(125\) | − | 1.58557e31i | − | 0.557872i | ||||||
\(126\) | 9.54491e30 | − | 3.58681e31i | 0.297998 | − | 1.11982i | ||||
\(127\) | −1.99255e31 | −0.552528 | −0.276264 | − | 0.961082i | \(-0.589096\pi\) | ||||
−0.276264 | + | 0.961082i | \(0.589096\pi\) | |||||||
\(128\) | 3.58546e30i | 0.0883883i | ||||||||
\(129\) | −7.51069e31 | − | 9.82248e30i | −1.64753 | − | 0.215464i | ||||
\(130\) | −1.00024e31 | −0.195413 | ||||||||
\(131\) | − | 2.03315e31i | − | 0.354079i | −0.984204 | − | 0.177040i | \(-0.943348\pi\) | ||
0.984204 | − | 0.177040i | \(-0.0566521\pi\) | |||||||
\(132\) | −2.27341e30 | + | 1.73834e31i | −0.0353239 | + | 0.270101i | ||||
\(133\) | 8.52524e31 | 1.18286 | ||||||||
\(134\) | − | 6.70857e31i | − | 0.831875i | ||||||
\(135\) | 4.27185e31 | − | 1.03887e32i | 0.473816 | − | 1.15227i | ||||
\(136\) | −6.05311e31 | −0.601028 | ||||||||
\(137\) | 1.46014e32i | 1.29893i | 0.760390 | + | 0.649467i | \(0.225008\pi\) | ||||
−0.760390 | + | 0.649467i | \(0.774992\pi\) | |||||||
\(138\) | −1.42831e32 | − | 1.86795e31i | −1.13930 | − | 0.148997i | ||||
\(139\) | 9.21852e31 | 0.659841 | 0.329921 | − | 0.944009i | \(-0.392978\pi\) | ||||
0.329921 | + | 0.944009i | \(0.392978\pi\) | |||||||
\(140\) | 1.58815e32i | 1.02087i | ||||||||
\(141\) | 2.95948e31 | − | 2.26294e32i | 0.170973 | − | 1.30734i | ||||
\(142\) | −4.91310e31 | −0.255288 | ||||||||
\(143\) | − | 2.58388e31i | − | 0.120846i | ||||||
\(144\) | 5.73482e31 | + | 1.52610e31i | 0.241592 | + | 0.0642904i | ||||
\(145\) | −5.23348e31 | −0.198733 | ||||||||
\(146\) | − | 1.27193e32i | − | 0.435682i | ||||||
\(147\) | 5.40552e32 | + | 7.06933e31i | 1.67139 | + | 0.218584i | ||||
\(148\) | 4.74538e31 | 0.132539 | ||||||||
\(149\) | 4.01131e32i | 1.01273i | 0.862320 | + | 0.506363i | \(0.169010\pi\) | ||||
−0.862320 | + | 0.506363i | \(0.830990\pi\) | |||||||
\(150\) | −2.21734e31 | + | 1.69547e32i | −0.0506364 | + | 0.387187i | ||||
\(151\) | −3.75341e32 | −0.775840 | −0.387920 | − | 0.921693i | \(-0.626806\pi\) | ||||
−0.387920 | + | 0.921693i | \(0.626806\pi\) | |||||||
\(152\) | 1.36307e32i | 0.255191i | ||||||||
\(153\) | −2.57642e32 | + | 9.68175e32i | −0.437166 | + | 1.64279i | ||||
\(154\) | −4.10259e32 | −0.631316 | ||||||||
\(155\) | 2.92093e32i | 0.407892i | ||||||||
\(156\) | −8.67257e31 | − | 1.13420e31i | −0.109971 | − | 0.0143820i | ||||
\(157\) | 4.70110e32 | 0.541633 | 0.270816 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270816 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(158\) | − | 4.02483e31i | − | 0.0421591i | ||||||
\(159\) | −1.29519e31 | + | 9.90360e31i | −0.0123418 | + | 0.0943705i | ||||
\(160\) | −2.53923e32 | −0.220243 | ||||||||
\(161\) | − | 3.37089e33i | − | 2.66291i | ||||||
\(162\) | 4.88190e32 | − | 8.52310e32i | 0.351450 | − | 0.613582i | ||||
\(163\) | 7.58294e32 | 0.497764 | 0.248882 | − | 0.968534i | \(-0.419937\pi\) | ||||
0.248882 | + | 0.968534i | \(0.419937\pi\) | |||||||
\(164\) | 1.02589e33i | 0.614387i | ||||||||
\(165\) | −1.23110e33 | − | 1.61003e32i | −0.673031 | − | 0.0880189i | ||||
\(166\) | 1.09849e33 | 0.548497 | ||||||||
\(167\) | − | 3.37257e32i | − | 0.153891i | −0.997035 | − | 0.0769456i | \(-0.975483\pi\) | ||
0.997035 | − | 0.0769456i | \(-0.0245168\pi\) | |||||||
\(168\) | −1.80084e32 | + | 1.37700e33i | −0.0751339 | + | 0.574506i | ||||
\(169\) | −2.49109e33 | −0.950798 | ||||||||
\(170\) | − | 4.28683e33i | − | 1.49762i | ||||||
\(171\) | 2.18019e33 | + | 5.80173e32i | 0.697514 | + | 0.185616i | ||||
\(172\) | 2.83409e33 | 0.830781 | ||||||||
\(173\) | − | 1.70291e33i | − | 0.457616i | −0.973472 | − | 0.228808i | \(-0.926517\pi\) | ||
0.973472 | − | 0.228808i | \(-0.0734828\pi\) | |||||||
\(174\) | −4.53768e32 | − | 5.93438e31i | −0.111839 | − | 0.0146264i | ||||
\(175\) | −4.00140e33 | −0.904984 | ||||||||
\(176\) | − | 6.55948e32i | − | 0.136201i | ||||||
\(177\) | −1.00508e33 | + | 7.68528e33i | −0.191691 | + | 1.46575i | ||||
\(178\) | 4.98516e33 | 0.873733 | ||||||||
\(179\) | − | 2.93722e33i | − | 0.473305i | −0.971594 | − | 0.236652i | \(-0.923950\pi\) | ||
0.971594 | − | 0.236652i | \(-0.0760502\pi\) | |||||||
\(180\) | −1.08079e33 | + | 4.06142e33i | −0.160197 | + | 0.601992i | ||||
\(181\) | −5.16473e33 | −0.704480 | −0.352240 | − | 0.935910i | \(-0.614580\pi\) | ||||
−0.352240 | + | 0.935910i | \(0.614580\pi\) | |||||||
\(182\) | − | 2.04677e33i | − | 0.257039i | ||||||
\(183\) | −1.29008e34 | − | 1.68716e33i | −1.49228 | − | 0.195160i | ||||
\(184\) | 5.38960e33 | 0.574499 | ||||||||
\(185\) | 3.36069e33i | 0.330258i | ||||||||
\(186\) | −3.31212e32 | + | 2.53259e33i | −0.0300200 | + | 0.229546i | ||||
\(187\) | 1.10740e34 | 0.926146 | ||||||||
\(188\) | 8.53901e33i | 0.659234i | ||||||||
\(189\) | 2.12582e34 | + | 8.74140e33i | 1.51565 | + | 0.623238i | ||||
\(190\) | −9.65332e33 | −0.635877 | ||||||||
\(191\) | 1.93599e34i | 1.17870i | 0.807878 | + | 0.589350i | \(0.200616\pi\) | ||||
−0.807878 | + | 0.589350i | \(0.799384\pi\) | |||||||
\(192\) | −2.20164e33 | − | 2.87930e32i | −0.123945 | − | 0.0162095i | ||||
\(193\) | 2.42851e34 | 1.26468 | 0.632339 | − | 0.774692i | \(-0.282095\pi\) | ||||
0.632339 | + | 0.774692i | \(0.282095\pi\) | |||||||
\(194\) | − | 5.35437e33i | − | 0.258037i | ||||||
\(195\) | 8.03244e32 | − | 6.14195e33i | 0.0358367 | − | 0.274023i | ||||
\(196\) | −2.03972e34 | −0.842810 | ||||||||
\(197\) | − | 3.38838e34i | − | 1.29717i | −0.761140 | − | 0.648587i | \(-0.775360\pi\) | ||
0.761140 | − | 0.648587i | \(-0.224640\pi\) | |||||||
\(198\) | −1.04917e34 | − | 2.79196e33i | −0.372278 | − | 0.0990674i | ||||
\(199\) | −4.61962e34 | −1.51988 | −0.759941 | − | 0.649992i | \(-0.774772\pi\) | ||||
−0.759941 | + | 0.649992i | \(0.774772\pi\) | |||||||
\(200\) | − | 6.39770e33i | − | 0.195242i | ||||||
\(201\) | 4.11938e34 | + | 5.38732e33i | 1.16652 | + | 0.152557i | ||||
\(202\) | 1.24232e34 | 0.326560 | ||||||||
\(203\) | − | 1.07092e34i | − | 0.261406i | ||||||
\(204\) | 4.86095e33 | − | 3.71689e34i | 0.110222 | − | 0.842805i | ||||
\(205\) | −7.26537e34 | −1.53091 | ||||||||
\(206\) | 4.90304e34i | 0.960411i | ||||||||
\(207\) | 2.29401e34 | − | 8.62049e34i | 0.417869 | − | 1.57028i | ||||
\(208\) | 3.27251e33 | 0.0554538 | ||||||||
\(209\) | − | 2.49370e34i | − | 0.393233i | ||||||
\(210\) | −9.75196e34 | − | 1.27536e34i | −1.43154 | − | 0.187216i | ||||
\(211\) | 1.17815e35 | 1.61051 | 0.805256 | − | 0.592928i | \(-0.202028\pi\) | ||||
0.805256 | + | 0.592928i | \(0.202028\pi\) | |||||||
\(212\) | − | 3.73703e33i | − | 0.0475871i | ||||||
\(213\) | 3.94546e33 | − | 3.01687e34i | 0.0468170 | − | 0.357983i | ||||
\(214\) | 5.40004e34 | 0.597297 | ||||||||
\(215\) | 2.00711e35i | 2.07012i | ||||||||
\(216\) | −1.39763e34 | + | 3.39890e34i | −0.134458 | + | 0.326988i | ||||
\(217\) | −5.97704e34 | −0.536525 | ||||||||
\(218\) | − | 3.63481e34i | − | 0.304533i | ||||||
\(219\) | 7.81022e34 | + | 1.02142e34i | 0.610944 | + | 0.0798993i | ||||
\(220\) | 4.64545e34 | 0.339381 | ||||||||
\(221\) | 5.52479e34i | 0.377078i | ||||||||
\(222\) | −3.81078e33 | + | 2.91388e34i | −0.0243063 | + | 0.185856i | ||||
\(223\) | 3.92453e34 | 0.234000 | 0.117000 | − | 0.993132i | \(-0.462672\pi\) | ||||
0.117000 | + | 0.993132i | \(0.462672\pi\) | |||||||
\(224\) | − | 5.19598e34i | − | 0.289699i | ||||||
\(225\) | −1.02329e35 | − | 2.72309e34i | −0.533656 | − | 0.142012i | ||||
\(226\) | 8.23496e34 | 0.401823 | ||||||||
\(227\) | 6.36451e34i | 0.290655i | 0.989384 | + | 0.145327i | \(0.0464235\pi\) | ||||
−0.989384 | + | 0.145327i | \(0.953576\pi\) | |||||||
\(228\) | −8.36990e34 | − | 1.09461e34i | −0.357847 | − | 0.0467992i | ||||
\(229\) | −1.18324e35 | −0.473739 | −0.236870 | − | 0.971541i | \(-0.576121\pi\) | ||||
−0.236870 | + | 0.971541i | \(0.576121\pi\) | |||||||
\(230\) | 3.81693e35i | 1.43152i | ||||||||
\(231\) | 3.29458e34 | − | 2.51918e35i | 0.115777 | − | 0.885277i | ||||
\(232\) | 1.71225e34 | 0.0563959 | ||||||||
\(233\) | 5.79194e35i | 1.78849i | 0.447583 | + | 0.894243i | \(0.352285\pi\) | ||||
−0.447583 | + | 0.894243i | \(0.647715\pi\) | |||||||
\(234\) | 1.39290e34 | − | 5.23428e34i | 0.0403351 | − | 0.151572i | ||||
\(235\) | −6.04736e35 | −1.64266 | ||||||||
\(236\) | − | 2.89997e35i | − | 0.739117i | ||||||
\(237\) | 2.47143e34 | + | 3.23214e33i | 0.0591186 | + | 0.00773153i | ||||
\(238\) | 8.77206e35 | 1.96991 | ||||||||
\(239\) | − | 4.01382e35i | − | 0.846426i | −0.906030 | − | 0.423213i | \(-0.860902\pi\) | ||
0.906030 | − | 0.423213i | \(-0.139098\pi\) | |||||||
\(240\) | 2.03913e34 | − | 1.55921e35i | 0.0403903 | − | 0.308841i | ||||
\(241\) | −4.24885e35 | −0.790707 | −0.395353 | − | 0.918529i | \(-0.629378\pi\) | ||||
−0.395353 | + | 0.918529i | \(0.629378\pi\) | |||||||
\(242\) | − | 2.84307e35i | − | 0.497230i | ||||||
\(243\) | 4.84154e35 | + | 3.68216e35i | 0.795957 | + | 0.605353i | ||||
\(244\) | 4.86799e35 | 0.752492 | ||||||||
\(245\) | − | 1.44454e36i | − | 2.10009i | ||||||
\(246\) | −6.29943e35 | − | 8.23839e34i | −0.861538 | − | 0.112672i | ||||
\(247\) | 1.24410e35 | 0.160104 | ||||||||
\(248\) | − | 9.55648e34i | − | 0.115750i | ||||||
\(249\) | −8.82142e34 | + | 6.74524e35i | −0.100588 | + | 0.769143i | ||||
\(250\) | −3.67383e35 | −0.394475 | ||||||||
\(251\) | − | 1.65303e36i | − | 1.67176i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) | ||
0.548911 | − | 0.835881i | \(-0.315043\pi\) | |||||||
\(252\) | −8.31081e35 | − | 2.21160e35i | −0.791836 | − | 0.210716i | ||||
\(253\) | −9.86011e35 | −0.885266 | ||||||||
\(254\) | 4.61684e35i | 0.390696i | ||||||||
\(255\) | 2.63231e36 | + | 3.44254e35i | 2.10008 | + | 0.274648i | ||||
\(256\) | 8.30767e34 | 0.0625000 | ||||||||
\(257\) | 1.80039e36i | 1.27752i | 0.769405 | + | 0.638762i | \(0.220553\pi\) | ||||
−0.769405 | + | 0.638762i | \(0.779447\pi\) | |||||||
\(258\) | −2.27592e35 | + | 1.74026e36i | −0.152356 | + | 1.16498i | ||||
\(259\) | −6.87692e35 | −0.434408 | ||||||||
\(260\) | 2.31761e35i | 0.138178i | ||||||||
\(261\) | 7.28797e34 | − | 2.73869e35i | 0.0410203 | − | 0.154147i | ||||
\(262\) | −4.71091e35 | −0.250372 | ||||||||
\(263\) | 1.84926e36i | 0.928243i | 0.885772 | + | 0.464122i | \(0.153630\pi\) | ||||
−0.885772 | + | 0.464122i | \(0.846370\pi\) | |||||||
\(264\) | 4.02783e35 | + | 5.26759e34i | 0.190991 | + | 0.0249777i | ||||
\(265\) | 2.64658e35 | 0.118576 | ||||||||
\(266\) | − | 1.97534e36i | − | 0.836406i | ||||||
\(267\) | −4.00333e35 | + | 3.06112e36i | −0.160233 | + | 1.22521i | ||||
\(268\) | −1.55441e36 | −0.588225 | ||||||||
\(269\) | − | 3.50145e36i | − | 1.25304i | −0.779406 | − | 0.626519i | \(-0.784479\pi\) | ||
0.779406 | − | 0.626519i | \(-0.215521\pi\) | |||||||
\(270\) | −2.40711e36 | − | 9.89808e35i | −0.814778 | − | 0.335038i | ||||
\(271\) | 2.98225e36 | 0.955004 | 0.477502 | − | 0.878631i | \(-0.341542\pi\) | ||||
0.477502 | + | 0.878631i | \(0.341542\pi\) | |||||||
\(272\) | 1.40253e36i | 0.424991i | ||||||||
\(273\) | 1.25681e36 | + | 1.64366e35i | 0.360439 | + | 0.0471381i | ||||
\(274\) | 3.38322e36 | 0.918485 | ||||||||
\(275\) | 1.17044e36i | 0.300856i | ||||||||
\(276\) | −4.32812e35 | + | 3.30947e36i | −0.105357 | + | 0.805604i | ||||
\(277\) | 3.69874e36 | 0.852820 | 0.426410 | − | 0.904530i | \(-0.359778\pi\) | ||||
0.426410 | + | 0.904530i | \(0.359778\pi\) | |||||||
\(278\) | − | 2.13598e36i | − | 0.466578i | ||||||
\(279\) | −1.52853e36 | − | 4.06759e35i | −0.316381 | − | 0.0841926i | ||||
\(280\) | 3.67981e36 | 0.721864 | ||||||||
\(281\) | 2.72349e36i | 0.506443i | 0.967408 | + | 0.253222i | \(0.0814902\pi\) | ||||
−0.967408 | + | 0.253222i | \(0.918510\pi\) | |||||||
\(282\) | −5.24335e36 | − | 6.85725e35i | −0.924426 | − | 0.120896i | ||||
\(283\) | −5.44695e36 | −0.910660 | −0.455330 | − | 0.890323i | \(-0.650479\pi\) | ||||
−0.455330 | + | 0.890323i | \(0.650479\pi\) | |||||||
\(284\) | 1.13839e36i | 0.180516i | ||||||||
\(285\) | 7.75210e35 | − | 5.92759e36i | 0.116613 | − | 0.891672i | ||||
\(286\) | −5.98696e35 | −0.0854508 | ||||||||
\(287\) | − | 1.48670e37i | − | 2.01370i | ||||||
\(288\) | 3.53605e35 | − | 1.32879e36i | 0.0454602 | − | 0.170831i | ||||
\(289\) | −1.54847e37 | −1.88988 | ||||||||
\(290\) | 1.21262e36i | 0.140526i | ||||||||
\(291\) | 3.28783e36 | + | 4.29982e35i | 0.361838 | + | 0.0473212i | ||||
\(292\) | −2.94711e36 | −0.308073 | ||||||||
\(293\) | 9.85499e36i | 0.978682i | 0.872092 | + | 0.489341i | \(0.162763\pi\) | ||||
−0.872092 | + | 0.489341i | \(0.837237\pi\) | |||||||
\(294\) | 1.63800e36 | − | 1.25248e37i | 0.154562 | − | 1.18185i | ||||
\(295\) | 2.05377e37 | 1.84171 | ||||||||
\(296\) | − | 1.09953e36i | − | 0.0937196i | ||||||
\(297\) | 2.55693e36 | − | 6.21817e36i | 0.207191 | − | 0.503867i | ||||
\(298\) | 9.29439e36 | 0.716106 | ||||||||
\(299\) | − | 4.91919e36i | − | 0.360434i | ||||||
\(300\) | 3.92849e36 | + | 5.13767e35i | 0.273783 | + | 0.0358053i | ||||
\(301\) | −4.10711e37 | −2.72295 | ||||||||
\(302\) | 8.69683e36i | 0.548601i | ||||||||
\(303\) | −9.97644e35 | + | 7.62842e36i | −0.0598875 | + | 0.457926i | ||||
\(304\) | 3.15830e36 | 0.180447 | ||||||||
\(305\) | 3.44752e37i | 1.87504i | ||||||||
\(306\) | 2.24331e37 | + | 5.96970e36i | 1.16163 | + | 0.309123i | ||||
\(307\) | 3.55895e37 | 1.75487 | 0.877437 | − | 0.479692i | \(-0.159251\pi\) | ||||
0.877437 | + | 0.479692i | \(0.159251\pi\) | |||||||
\(308\) | 9.50589e36i | 0.446408i | ||||||||
\(309\) | −3.01070e37 | − | 3.93739e36i | −1.34676 | − | 0.176129i | ||||
\(310\) | 6.76793e36 | 0.288423 | ||||||||
\(311\) | 3.42711e37i | 1.39162i | 0.718224 | + | 0.695812i | \(0.244955\pi\) | ||||
−0.718224 | + | 0.695812i | \(0.755045\pi\) | |||||||
\(312\) | −2.62799e35 | + | 2.00948e36i | −0.0101696 | + | 0.0777614i | ||||
\(313\) | −1.06099e37 | −0.391332 | −0.195666 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195666 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(314\) | − | 1.08927e37i | − | 0.382992i | ||||||
\(315\) | 1.56626e37 | − | 5.88574e37i | 0.525057 | − | 1.97307i | ||||
\(316\) | −9.32573e35 | −0.0298110 | ||||||||
\(317\) | − | 6.66930e36i | − | 0.203325i | −0.994819 | − | 0.101663i | \(-0.967584\pi\) | ||
0.994819 | − | 0.101663i | \(-0.0324162\pi\) | |||||||
\(318\) | 2.29471e36 | + | 3.00102e35i | 0.0667300 | + | 0.00872695i | ||||
\(319\) | −3.13251e36 | −0.0869025 | ||||||||
\(320\) | 5.88352e36i | 0.155736i | ||||||||
\(321\) | −4.33650e36 | + | 3.31587e37i | −0.109538 | + | 0.837573i | ||||
\(322\) | −7.81051e37 | −1.88296 | ||||||||
\(323\) | 5.33197e37i | 1.22701i | ||||||||
\(324\) | −1.97484e37 | − | 1.13116e37i | −0.433868 | − | 0.248513i | ||||
\(325\) | −5.83930e36 | −0.122493 | ||||||||
\(326\) | − | 1.75700e37i | − | 0.351972i | ||||||
\(327\) | 2.23194e37 | + | 2.91893e36i | 0.427038 | + | 0.0558480i | ||||
\(328\) | 2.37703e37 | 0.434437 | ||||||||
\(329\) | − | 1.23746e38i | − | 2.16069i | ||||||
\(330\) | −3.73053e36 | + | 2.85252e37i | −0.0622388 | + | 0.475904i | ||||
\(331\) | 1.18046e38 | 1.88205 | 0.941026 | − | 0.338336i | \(-0.109864\pi\) | ||||
0.941026 | + | 0.338336i | \(0.109864\pi\) | |||||||
\(332\) | − | 2.54525e37i | − | 0.387846i | ||||||
\(333\) | −1.75866e37 | − | 4.67999e36i | −0.256164 | − | 0.0681681i | ||||
\(334\) | −7.81440e36 | −0.108817 | ||||||||
\(335\) | − | 1.10084e38i | − | 1.46572i | ||||||
\(336\) | 3.19057e37 | + | 4.17263e36i | 0.406237 | + | 0.0531277i | ||||
\(337\) | 9.88992e36 | 0.120433 | 0.0602163 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602163 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(338\) | 5.77197e37i | 0.672316i | ||||||||
\(339\) | −6.61308e36 | + | 5.05665e37i | −0.0736900 | + | 0.563465i | ||||
\(340\) | −9.93279e37 | −1.05898 | ||||||||
\(341\) | 1.74833e37i | 0.178364i | ||||||||
\(342\) | 1.34429e37 | − | 5.05160e37i | 0.131251 | − | 0.493217i | ||||
\(343\) | 1.20231e38 | 1.12358 | ||||||||
\(344\) | − | 6.56672e37i | − | 0.587451i | ||||||
\(345\) | −2.34378e38 | − | 3.06519e37i | −2.00738 | − | 0.262525i | ||||
\(346\) | −3.94573e37 | −0.323583 | ||||||||
\(347\) | − | 1.26069e37i | − | 0.0990069i | −0.998774 | − | 0.0495034i | \(-0.984236\pi\) | ||
0.998774 | − | 0.0495034i | \(-0.0157639\pi\) | |||||||
\(348\) | −1.37502e36 | + | 1.05140e37i | −0.0103424 | + | 0.0790824i | ||||
\(349\) | 9.26991e37 | 0.667873 | 0.333937 | − | 0.942596i | \(-0.391623\pi\) | ||||
0.333937 | + | 0.942596i | \(0.391623\pi\) | |||||||
\(350\) | 9.27143e37i | 0.639921i | ||||||||
\(351\) | 3.10224e37 | + | 1.27565e37i | 0.205148 | + | 0.0843574i | ||||
\(352\) | −1.51986e37 | −0.0963085 | ||||||||
\(353\) | 8.73770e37i | 0.530612i | 0.964164 | + | 0.265306i | \(0.0854729\pi\) | ||||
−0.964164 | + | 0.265306i | \(0.914527\pi\) | |||||||
\(354\) | 1.78072e38 | + | 2.32882e37i | 1.03644 | + | 0.135546i | ||||
\(355\) | −8.06210e37 | −0.449804 | ||||||||
\(356\) | − | 1.15508e38i | − | 0.617822i | ||||||
\(357\) | −7.04440e37 | + | 5.38645e38i | −0.361261 | + | 2.76236i | ||||
\(358\) | −6.80567e37 | −0.334677 | ||||||||
\(359\) | − | 2.48400e37i | − | 0.117148i | −0.998283 | − | 0.0585739i | \(-0.981345\pi\) | ||
0.998283 | − | 0.0585739i | \(-0.0186553\pi\) | |||||||
\(360\) | 9.41051e37 | + | 2.50424e37i | 0.425672 | + | 0.113276i | ||||
\(361\) | −1.10398e38 | −0.479021 | ||||||||
\(362\) | 1.19669e38i | 0.498143i | ||||||||
\(363\) | 1.74578e38 | + | 2.28313e37i | 0.697252 | + | 0.0911866i | ||||
\(364\) | −4.74247e37 | −0.181754 | ||||||||
\(365\) | − | 2.08716e38i | − | 0.767648i | ||||||
\(366\) | −3.90924e37 | + | 2.98917e38i | −0.137999 | + | 1.05520i | ||||
\(367\) | 5.68207e37 | 0.192538 | 0.0962688 | − | 0.995355i | \(-0.469309\pi\) | ||||
0.0962688 | + | 0.995355i | \(0.469309\pi\) | |||||||
\(368\) | − | 1.24880e38i | − | 0.406232i | ||||||
\(369\) | 1.01175e38 | − | 3.80198e38i | 0.315994 | − | 1.18745i | ||||
\(370\) | 7.78689e37 | 0.233528 | ||||||||
\(371\) | 5.41564e37i | 0.155970i | ||||||||
\(372\) | 5.86812e37 | + | 7.67433e36i | 0.162314 | + | 0.0212274i | ||||
\(373\) | −1.02713e38 | −0.272893 | −0.136446 | − | 0.990647i | \(-0.543568\pi\) | ||||
−0.136446 | + | 0.990647i | \(0.543568\pi\) | |||||||
\(374\) | − | 2.56589e38i | − | 0.654884i | ||||||
\(375\) | 2.95027e37 | − | 2.25590e38i | 0.0723424 | − | 0.553161i | ||||
\(376\) | 1.97853e38 | 0.466149 | ||||||||
\(377\) | − | 1.56280e37i | − | 0.0353821i | ||||||
\(378\) | 2.02542e38 | − | 4.92562e38i | 0.440696 | − | 1.07173i | ||||
\(379\) | −5.04928e38 | −1.05594 | −0.527972 | − | 0.849262i | \(-0.677048\pi\) | ||||
−0.527972 | + | 0.849262i | \(0.677048\pi\) | |||||||
\(380\) | 2.23672e38i | 0.449633i | ||||||||
\(381\) | −2.83496e38 | − | 3.70755e37i | −0.547863 | − | 0.0716495i | ||||
\(382\) | 4.48579e38 | 0.833467 | ||||||||
\(383\) | 2.52753e38i | 0.451560i | 0.974178 | + | 0.225780i | \(0.0724930\pi\) | ||||
−0.974178 | + | 0.225780i | \(0.927507\pi\) | |||||||
\(384\) | −6.67148e36 | + | 5.10130e37i | −0.0114618 | + | 0.0876420i | ||||
\(385\) | −6.73210e38 | −1.11235 | ||||||||
\(386\) | − | 5.62697e38i | − | 0.894262i | ||||||
\(387\) | −1.05033e39 | − | 2.79504e38i | −1.60568 | − | 0.427290i | ||||
\(388\) | −1.24063e38 | −0.182460 | ||||||||
\(389\) | 9.46333e37i | 0.133906i | 0.997756 | + | 0.0669530i | \(0.0213278\pi\) | ||||
−0.997756 | + | 0.0669530i | \(0.978672\pi\) | |||||||
\(390\) | −1.42312e38 | − | 1.86115e37i | −0.193763 | − | 0.0253404i | ||||
\(391\) | 2.10827e39 | 2.76232 | ||||||||
\(392\) | 4.72613e38i | 0.595957i | ||||||||
\(393\) | 3.78310e37 | − | 2.89272e38i | 0.0459155 | − | 0.351089i | ||||
\(394\) | −7.85103e38 | −0.917241 | ||||||||
\(395\) | − | 6.60451e37i | − | 0.0742821i | ||||||
\(396\) | −6.46909e37 | + | 2.43097e38i | −0.0700512 | + | 0.263240i | ||||
\(397\) | −2.35941e38 | −0.246006 | −0.123003 | − | 0.992406i | \(-0.539252\pi\) | ||||
−0.123003 | + | 0.992406i | \(0.539252\pi\) | |||||||
\(398\) | 1.07039e39i | 1.07472i | ||||||||
\(399\) | 1.21295e39 | + | 1.58630e38i | 1.17287 | + | 0.153388i | ||||
\(400\) | −1.48238e38 | −0.138057 | ||||||||
\(401\) | 2.91357e38i | 0.261372i | 0.991424 | + | 0.130686i | \(0.0417180\pi\) | ||||
−0.991424 | + | 0.130686i | \(0.958282\pi\) | |||||||
\(402\) | 1.24827e38 | − | 9.54479e38i | 0.107874 | − | 0.824851i | ||||
\(403\) | −8.72237e37 | −0.0726205 | ||||||||
\(404\) | − | 2.87851e38i | − | 0.230913i | ||||||
\(405\) | 8.01091e38 | − | 1.39859e39i | 0.619237 | − | 1.08110i | ||||
\(406\) | −2.48136e38 | −0.184842 | ||||||||
\(407\) | 2.01155e38i | 0.144416i | ||||||||
\(408\) | −8.61221e38 | − | 1.12631e38i | −0.595953 | − | 0.0779388i | ||||
\(409\) | 1.29846e38 | 0.0866120 | 0.0433060 | − | 0.999062i | \(-0.486211\pi\) | ||||
0.0433060 | + | 0.999062i | \(0.486211\pi\) | |||||||
\(410\) | 1.68342e39i | 1.08252i | ||||||||
\(411\) | −2.71690e38 | + | 2.07745e39i | −0.168440 | + | 1.28797i | ||||
\(412\) | 1.13606e39 | 0.679113 | ||||||||
\(413\) | 4.20258e39i | 2.42251i | ||||||||
\(414\) | −1.99741e39 | − | 5.31533e38i | −1.11036 | − | 0.295478i | ||||
\(415\) | 1.80256e39 | 0.966423 | ||||||||
\(416\) | − | 7.58257e37i | − | 0.0392118i | ||||||
\(417\) | 1.31159e39 | + | 1.71530e38i | 0.654270 | + | 0.0855654i | ||||
\(418\) | −5.77802e38 | −0.278057 | ||||||||
\(419\) | − | 9.93091e38i | − | 0.461083i | −0.973063 | − | 0.230541i | \(-0.925950\pi\) | ||
0.973063 | − | 0.230541i | \(-0.0740497\pi\) | |||||||
\(420\) | −2.95507e38 | + | 2.25958e39i | −0.132382 | + | 1.01225i | ||||
\(421\) | −1.22865e39 | −0.531125 | −0.265562 | − | 0.964094i | \(-0.585558\pi\) | ||||
−0.265562 | + | 0.964094i | \(0.585558\pi\) | |||||||
\(422\) | − | 2.72983e39i | − | 1.13880i | ||||||
\(423\) | 8.42135e38 | − | 3.16459e39i | 0.339060 | − | 1.27413i | ||||
\(424\) | −8.65888e37 | −0.0336491 | ||||||||
\(425\) | − | 2.50261e39i | − | 0.938769i | ||||||
\(426\) | −6.99023e38 | − | 9.14182e37i | −0.253132 | − | 0.0331046i | ||||
\(427\) | −7.05460e39 | −2.46635 | ||||||||
\(428\) | − | 1.25121e39i | − | 0.422353i | ||||||
\(429\) | 4.80783e37 | − | 3.67627e38i | 0.0156707 | − | 0.119825i | ||||
\(430\) | 4.65057e39 | 1.46379 | ||||||||
\(431\) | − | 1.55422e39i | − | 0.472448i | −0.971699 | − | 0.236224i | \(-0.924090\pi\) | ||
0.971699 | − | 0.236224i | \(-0.0759099\pi\) | |||||||
\(432\) | 7.87540e38 | + | 3.23838e38i | 0.231215 | + | 0.0950762i | ||||
\(433\) | 2.46856e39 | 0.700045 | 0.350022 | − | 0.936741i | \(-0.386174\pi\) | ||||
0.350022 | + | 0.936741i | \(0.386174\pi\) | |||||||
\(434\) | 1.38491e39i | 0.379380i | ||||||||
\(435\) | −7.44606e38 | − | 9.73796e37i | −0.197055 | − | 0.0257709i | ||||
\(436\) | −8.42202e38 | −0.215337 | ||||||||
\(437\) | − | 4.74751e39i | − | 1.17285i | ||||||
\(438\) | 2.36668e38 | − | 1.80967e39i | 0.0564973 | − | 0.432003i | ||||
\(439\) | −7.41940e39 | −1.71160 | −0.855798 | − | 0.517310i | \(-0.826933\pi\) | ||||
−0.855798 | + | 0.517310i | \(0.826933\pi\) | |||||||
\(440\) | − | 1.07637e39i | − | 0.239979i | ||||||
\(441\) | 7.55929e39 | + | 2.01161e39i | 1.62893 | + | 0.433477i | ||||
\(442\) | 1.28012e39 | 0.266635 | ||||||||
\(443\) | − | 1.68756e38i | − | 0.0339784i | −0.999856 | − | 0.0169892i | \(-0.994592\pi\) | ||
0.999856 | − | 0.0169892i | \(-0.00540810\pi\) | |||||||
\(444\) | 6.75161e38 | + | 8.82975e37i | 0.131420 | + | 0.0171872i | ||||
\(445\) | 8.18035e39 | 1.53947 | ||||||||
\(446\) | − | 9.09333e38i | − | 0.165463i | ||||||
\(447\) | −7.46386e38 | + | 5.70719e39i | −0.131326 | + | 1.00418i | ||||
\(448\) | −1.20393e39 | −0.204848 | ||||||||
\(449\) | 5.79376e39i | 0.953378i | 0.879072 | + | 0.476689i | \(0.158163\pi\) | ||||
−0.879072 | + | 0.476689i | \(0.841837\pi\) | |||||||
\(450\) | −6.30954e38 | + | 2.37101e39i | −0.100418 | + | 0.377352i | ||||
\(451\) | −4.34870e39 | −0.669440 | ||||||||
\(452\) | − | 1.90808e39i | − | 0.284132i | ||||||
\(453\) | −5.34026e39 | − | 6.98399e38i | −0.769289 | − | 0.100608i | ||||
\(454\) | 1.47469e39 | 0.205524 | ||||||||
\(455\) | − | 3.35863e39i | − | 0.452889i | ||||||
\(456\) | −2.53627e38 | + | 1.93934e39i | −0.0330921 | + | 0.253036i | ||||
\(457\) | −5.48984e39 | −0.693134 | −0.346567 | − | 0.938025i | \(-0.612653\pi\) | ||||
−0.346567 | + | 0.938025i | \(0.612653\pi\) | |||||||
\(458\) | 2.74162e39i | 0.334984i | ||||||||
\(459\) | −5.46716e39 | + | 1.32956e40i | −0.646505 | + | 1.57223i | ||||
\(460\) | 8.84402e39 | 1.01224 | ||||||||
\(461\) | − | 1.79816e40i | − | 1.99211i | −0.0887186 | − | 0.996057i | \(-0.528277\pi\) | ||
0.0887186 | − | 0.996057i | \(-0.471723\pi\) | |||||||
\(462\) | −5.83706e39 | − | 7.63370e38i | −0.625985 | − | 0.0818664i | ||||
\(463\) | −1.00133e40 | −1.03959 | −0.519794 | − | 0.854292i | \(-0.673991\pi\) | ||||
−0.519794 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(464\) | − | 3.96737e38i | − | 0.0398779i | ||||||
\(465\) | −5.43499e38 | + | 4.15582e39i | −0.0528937 | + | 0.404448i | ||||
\(466\) | 1.34202e40 | 1.26465 | ||||||||
\(467\) | 1.11131e40i | 1.01410i | 0.861916 | + | 0.507050i | \(0.169264\pi\) | ||||
−0.861916 | + | 0.507050i | \(0.830736\pi\) | |||||||
\(468\) | −1.21281e39 | − | 3.22742e38i | −0.107178 | − | 0.0285212i | ||||
\(469\) | 2.25262e40 | 1.92795 | ||||||||
\(470\) | 1.40120e40i | 1.16154i | ||||||||
\(471\) | 6.68861e39 | + | 8.74737e38i | 0.537060 | + | 0.0702366i | ||||
\(472\) | −6.71937e39 | −0.522635 | ||||||||
\(473\) | 1.20136e40i | 0.905225i | ||||||||
\(474\) | 7.48903e37 | − | 5.72643e38i | 0.00546701 | − | 0.0418031i | ||||
\(475\) | −5.63551e39 | −0.398592 | ||||||||
\(476\) | − | 2.03253e40i | − | 1.39294i | ||||||
\(477\) | −3.68554e38 | + | 1.38496e39i | −0.0244751 | + | 0.0919732i | ||||
\(478\) | −9.30020e39 | −0.598514 | ||||||||
\(479\) | 4.87641e39i | 0.304135i | 0.988370 | + | 0.152068i | \(0.0485932\pi\) | ||||
−0.988370 | + | 0.152068i | \(0.951407\pi\) | |||||||
\(480\) | −3.61276e39 | − | 4.72476e38i | −0.218384 | − | 0.0285602i | ||||
\(481\) | −1.00356e39 | −0.0587986 | ||||||||
\(482\) | 9.84478e39i | 0.559114i | ||||||||
\(483\) | 6.27223e39 | − | 4.79602e40i | 0.345315 | − | 2.64043i | ||||
\(484\) | −6.58753e39 | −0.351595 | ||||||||
\(485\) | − | 8.78620e39i | − | 0.454648i | ||||||
\(486\) | 8.53175e39 | − | 1.12181e40i | 0.428049 | − | 0.562826i | ||||
\(487\) | 1.98513e40 | 0.965729 | 0.482864 | − | 0.875695i | \(-0.339596\pi\) | ||||
0.482864 | + | 0.875695i | \(0.339596\pi\) | |||||||
\(488\) | − | 1.12794e40i | − | 0.532092i | ||||||
\(489\) | 1.07888e40 | + | 1.41096e39i | 0.493561 | + | 0.0645479i | ||||
\(490\) | −3.34706e40 | −1.48499 | ||||||||
\(491\) | − | 6.87806e39i | − | 0.295967i | −0.988990 | − | 0.147983i | \(-0.952722\pi\) | ||
0.988990 | − | 0.147983i | \(-0.0472783\pi\) | |||||||
\(492\) | −1.90887e39 | + | 1.45961e40i | −0.0796711 | + | 0.609199i | ||||
\(493\) | 6.69786e39 | 0.271164 | ||||||||
\(494\) | − | 2.88264e39i | − | 0.113210i | ||||||
\(495\) | −1.72162e40 | − | 4.58143e39i | −0.655934 | − | 0.174551i | ||||
\(496\) | −2.21428e39 | −0.0818479 | ||||||||
\(497\) | − | 1.64973e40i | − | 0.591653i | ||||||
\(498\) | 1.56290e40 | + | 2.04396e39i | 0.543866 | + | 0.0711268i | ||||
\(499\) | −1.42438e40 | −0.480969 | −0.240484 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240484 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(500\) | 8.51245e39i | 0.278936i | ||||||||
\(501\) | 6.27535e38 | − | 4.79841e39i | 0.0199559 | − | 0.152592i | ||||
\(502\) | −3.83015e40 | −1.18211 | ||||||||
\(503\) | 8.74553e39i | 0.261979i | 0.991384 | + | 0.130989i | \(0.0418154\pi\) | ||||
−0.991384 | + | 0.130989i | \(0.958185\pi\) | |||||||
\(504\) | −5.12438e39 | + | 1.92565e40i | −0.148999 | + | 0.559912i | ||||
\(505\) | 2.03857e40 | 0.575381 | ||||||||
\(506\) | 2.28463e40i | 0.625978i | ||||||||
\(507\) | −3.54426e40 | − | 4.63518e39i | −0.942770 | − | 0.123295i | ||||
\(508\) | 1.06974e40 | 0.276264 | ||||||||
\(509\) | 6.83043e40i | 1.71270i | 0.516396 | + | 0.856350i | \(0.327273\pi\) | ||||
−0.516396 | + | 0.856350i | \(0.672727\pi\) | |||||||
\(510\) | 7.97653e39 | − | 6.09920e40i | 0.194205 | − | 1.48498i | ||||
\(511\) | 4.27091e40 | 1.00973 | ||||||||
\(512\) | − | 1.92493e39i | − | 0.0441942i | ||||||
\(513\) | 2.99397e40 | + | 1.23113e40i | 0.667554 | + | 0.274500i | ||||
\(514\) | 4.17158e40 | 0.903346 | ||||||||
\(515\) | 8.04560e40i | 1.69219i | ||||||||
\(516\) | 4.03227e40 | + | 5.27340e39i | 0.823767 | + | 0.107732i | ||||
\(517\) | −3.61966e40 | −0.718306 | ||||||||
\(518\) | 1.59342e40i | 0.307173i | ||||||||
\(519\) | 3.16862e39 | − | 2.42286e40i | 0.0593417 | − | 0.453752i | ||||
\(520\) | 5.37000e39 | 0.0977067 | ||||||||
\(521\) | − | 2.60437e40i | − | 0.460401i | −0.973143 | − | 0.230201i | \(-0.926062\pi\) | ||
0.973143 | − | 0.230201i | \(-0.0739382\pi\) | |||||||
\(522\) | −6.34568e39 | − | 1.68866e39i | −0.108998 | − | 0.0290057i | ||||
\(523\) | 4.72362e39 | 0.0788405 | 0.0394202 | − | 0.999223i | \(-0.487449\pi\) | ||||
0.0394202 | + | 0.999223i | \(0.487449\pi\) | |||||||
\(524\) | 1.09154e40i | 0.177040i | ||||||||
\(525\) | −5.69309e40 | − | 7.44542e39i | −0.897343 | − | 0.117355i | ||||
\(526\) | 4.28482e40 | 0.656367 | ||||||||
\(527\) | − | 3.73824e40i | − | 0.556554i | ||||||
\(528\) | 1.22053e39 | − | 9.33267e39i | 0.0176619 | − | 0.135051i | ||||
\(529\) | −1.16623e41 | −1.64039 | ||||||||
\(530\) | − | 6.13225e39i | − | 0.0838459i | ||||||
\(531\) | −2.86001e40 | + | 1.07474e41i | −0.380145 | + | 1.42852i | ||||
\(532\) | −4.57696e40 | −0.591429 | ||||||||
\(533\) | − | 2.16956e40i | − | 0.272561i | ||||||
\(534\) | 7.09275e40 | + | 9.27590e39i | 0.866355 | + | 0.113302i | ||||
\(535\) | 8.86114e40 | 1.05241 | ||||||||
\(536\) | 3.60164e40i | 0.415938i | ||||||||
\(537\) | 5.46530e39 | − | 4.17900e40i | 0.0613761 | − | 0.469308i | ||||
\(538\) | −8.11303e40 | −0.886032 | ||||||||
\(539\) | − | 8.64631e40i | − | 0.918331i | ||||||
\(540\) | −2.29343e40 | + | 5.57739e40i | −0.236908 | + | 0.576135i | ||||
\(541\) | 1.34102e41 | 1.34734 | 0.673668 | − | 0.739034i | \(-0.264718\pi\) | ||||
0.673668 | + | 0.739034i | \(0.264718\pi\) | |||||||
\(542\) | − | 6.91002e40i | − | 0.675290i | ||||||
\(543\) | −7.34825e40 | − | 9.61004e39i | −0.698532 | − | 0.0913540i | ||||
\(544\) | 3.24974e40 | 0.300514 | ||||||||
\(545\) | − | 5.96450e40i | − | 0.536570i | ||||||
\(546\) | 3.80844e39 | − | 2.91210e40i | 0.0333317 | − | 0.254869i | ||||
\(547\) | −1.55528e40 | −0.132433 | −0.0662167 | − | 0.997805i | \(-0.521093\pi\) | ||||
−0.0662167 | + | 0.997805i | \(0.521093\pi\) | |||||||
\(548\) | − | 7.83908e40i | − | 0.649467i | ||||||
\(549\) | −1.80410e41 | − | 4.80091e40i | −1.45437 | − | 0.387024i | ||||
\(550\) | 2.71196e40 | 0.212737 | ||||||||
\(551\) | − | 1.50826e40i | − | 0.115134i | ||||||
\(552\) | 7.66819e40 | + | 1.00285e40i | 0.569648 | + | 0.0744986i | ||||
\(553\) | 1.35147e40 | 0.0977077 | ||||||||
\(554\) | − | 8.57016e40i | − | 0.603035i | ||||||
\(555\) | −6.25326e39 | + | 4.78151e40i | −0.0428264 | + | 0.327469i | ||||
\(556\) | −4.94916e40 | −0.329921 | ||||||||
\(557\) | 9.55049e40i | 0.619723i | 0.950782 | + | 0.309862i | \(0.100283\pi\) | ||||
−0.950782 | + | 0.309862i | \(0.899717\pi\) | |||||||
\(558\) | −9.42479e39 | + | 3.54167e40i | −0.0595331 | + | 0.223715i | ||||
\(559\) | −5.99357e40 | −0.368560 | ||||||||
\(560\) | − | 8.52630e40i | − | 0.510435i | ||||||
\(561\) | 1.57558e41 | + | 2.06054e40i | 0.918326 | + | 0.120099i | ||||
\(562\) | 6.31045e40 | 0.358110 | ||||||||
\(563\) | − | 3.04520e41i | − | 1.68263i | −0.540543 | − | 0.841317i | \(-0.681781\pi\) | ||
0.540543 | − | 0.841317i | \(-0.318219\pi\) | |||||||
\(564\) | −1.58886e40 | + | 1.21491e41i | −0.0854867 | + | 0.653668i | ||||
\(565\) | 1.35131e41 | 0.707991 | ||||||||
\(566\) | 1.26208e41i | 0.643934i | ||||||||
\(567\) | 2.86191e41 | + | 1.63926e41i | 1.42203 | + | 0.814519i | ||||
\(568\) | 2.63770e40 | 0.127644 | ||||||||
\(569\) | − | 8.74730e40i | − | 0.412278i | −0.978523 | − | 0.206139i | \(-0.933910\pi\) | ||
0.978523 | − | 0.206139i | \(-0.0660899\pi\) | |||||||
\(570\) | −1.37345e41 | − | 1.79620e40i | −0.630507 | − | 0.0824578i | ||||
\(571\) | −2.67782e40 | −0.119740 | −0.0598700 | − | 0.998206i | \(-0.519069\pi\) | ||||
−0.0598700 | + | 0.998206i | \(0.519069\pi\) | |||||||
\(572\) | 1.38721e40i | 0.0604228i | ||||||||
\(573\) | −3.60231e40 | + | 2.75448e41i | −0.152849 | + | 1.16875i | ||||
\(574\) | −3.44475e41 | −1.42390 | ||||||||
\(575\) | 2.22829e41i | 0.897332i | ||||||||
\(576\) | −3.07886e40 | − | 8.19320e39i | −0.120796 | − | 0.0321452i | ||||
\(577\) | −4.58861e41 | −1.75406 | −0.877028 | − | 0.480439i | \(-0.840477\pi\) | ||||
−0.877028 | + | 0.480439i | \(0.840477\pi\) | |||||||
\(578\) | 3.58787e41i | 1.33635i | ||||||||
\(579\) | 3.45522e41 | + | 4.51873e40i | 1.25400 | + | 0.163998i | ||||
\(580\) | 2.80970e40 | 0.0993666 | ||||||||
\(581\) | 3.68853e41i | 1.27119i | ||||||||
\(582\) | 9.96290e39 | − | 7.61806e40i | 0.0334611 | − | 0.255858i | ||||
\(583\) | 1.58411e40 | 0.0518511 | ||||||||
\(584\) | 6.82860e40i | 0.217841i | ||||||||
\(585\) | 2.28567e40 | − | 8.58915e40i | 0.0710682 | − | 0.267062i | ||||
\(586\) | 2.28345e41 | 0.692033 | ||||||||
\(587\) | − | 1.12440e41i | − | 0.332160i | −0.986112 | − | 0.166080i | \(-0.946889\pi\) | ||
0.986112 | − | 0.166080i | \(-0.0531110\pi\) | |||||||
\(588\) | −2.90206e41 | − | 3.79532e40i | −0.835694 | − | 0.109292i | ||||
\(589\) | −8.41796e40 | −0.236307 | ||||||||
\(590\) | − | 4.75868e41i | − | 1.30229i | ||||||
\(591\) | 6.30477e40 | − | 4.82090e41i | 0.168212 | − | 1.28622i | ||||
\(592\) | −2.54766e40 | −0.0662697 | ||||||||
\(593\) | − | 1.84371e40i | − | 0.0467598i | −0.999727 | − | 0.0233799i | \(-0.992557\pi\) | ||
0.999727 | − | 0.0233799i | \(-0.00744272\pi\) | |||||||
\(594\) | −1.44078e41 | − | 5.92452e40i | −0.356288 | − | 0.146506i | ||||
\(595\) | 1.43944e42 | 3.47088 | ||||||||
\(596\) | − | 2.15356e41i | − | 0.506363i | ||||||
\(597\) | −6.57267e41 | − | 8.59574e40i | −1.50705 | − | 0.197092i | ||||
\(598\) | −1.13980e41 | −0.254865 | ||||||||
\(599\) | − | 7.70925e40i | − | 0.168116i | −0.996461 | − | 0.0840582i | \(-0.973212\pi\) | ||
0.996461 | − | 0.0840582i | \(-0.0267882\pi\) | |||||||
\(600\) | 1.19042e40 | − | 9.10249e40i | 0.0253182 | − | 0.193594i | ||||
\(601\) | −7.35174e41 | −1.52501 | −0.762505 | − | 0.646982i | \(-0.776031\pi\) | ||||
−0.762505 | + | 0.646982i | \(0.776031\pi\) | |||||||
\(602\) | 9.51637e41i | 1.92541i | ||||||||
\(603\) | 5.76071e41 | + | 1.53299e41i | 1.13688 | + | 0.302538i | ||||
\(604\) | 2.01510e41 | 0.387920 | ||||||||
\(605\) | − | 4.66531e41i | − | 0.876093i | ||||||
\(606\) | 1.76754e41 | + | 2.31159e40i | 0.323802 | + | 0.0423469i | ||||
\(607\) | −8.50614e41 | −1.52020 | −0.760102 | − | 0.649804i | \(-0.774851\pi\) | ||||
−0.760102 | + | 0.649804i | \(0.774851\pi\) | |||||||
\(608\) | − | 7.31794e40i | − | 0.127595i | ||||||
\(609\) | 1.99266e40 | − | 1.52367e41i | 0.0338980 | − | 0.259198i | ||||
\(610\) | 7.98808e41 | 1.32585 | ||||||||
\(611\) | − | 1.80584e41i | − | 0.292457i | ||||||
\(612\) | 1.38321e41 | − | 5.19785e41i | 0.218583 | − | 0.821396i | ||||
\(613\) | −1.68060e40 | −0.0259154 | −0.0129577 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129577 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(614\) | − | 8.24625e41i | − | 1.24088i | ||||||
\(615\) | −1.03370e42 | − | 1.35187e41i | −1.51798 | − | 0.198522i | ||||
\(616\) | 2.20256e41 | 0.315658 | ||||||||
\(617\) | 6.31789e41i | 0.883679i | 0.897094 | + | 0.441840i | \(0.145674\pi\) | ||||
−0.897094 | + | 0.441840i | \(0.854326\pi\) | |||||||
\(618\) | −9.12312e40 | + | 6.97593e41i | −0.124542 | + | 0.952302i | ||||
\(619\) | −3.35846e41 | −0.447487 | −0.223744 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223744 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(620\) | − | 1.56816e41i | − | 0.203946i | ||||||
\(621\) | 4.86788e41 | − | 1.18382e42i | 0.617968 | − | 1.50283i | ||||
\(622\) | 7.94077e41 | 0.984027 | ||||||||
\(623\) | 1.67393e42i | 2.02496i | ||||||||
\(624\) | 4.65605e40 | + | 6.08918e39i | 0.0549856 | + | 0.00719102i | ||||
\(625\) | −1.08184e42 | −1.24727 | ||||||||
\(626\) | 2.45836e41i | 0.276714i | ||||||||
\(627\) | 4.64004e40 | − | 3.54797e41i | 0.0509927 | − | 0.389912i | ||||
\(628\) | −2.52389e41 | −0.270816 | ||||||||
\(629\) | − | 4.30105e41i | − | 0.450625i | ||||||
\(630\) | −1.36375e42 | − | 3.62911e41i | −1.39517 | − | 0.371271i | ||||
\(631\) | −4.78635e41 | −0.478150 | −0.239075 | − | 0.971001i | \(-0.576844\pi\) | ||||
−0.239075 | + | 0.971001i | \(0.576844\pi\) | |||||||
\(632\) | 2.16082e40i | 0.0210796i | ||||||||
\(633\) | 1.67624e42 | + | 2.19219e41i | 1.59691 | + | 0.208844i | ||||
\(634\) | −1.54531e41 | −0.143773 | ||||||||
\(635\) | 7.57596e41i | 0.688386i | ||||||||
\(636\) | 6.95351e39 | − | 5.31695e40i | 0.00617089 | − | 0.0471852i | ||||
\(637\) | 4.31363e41 | 0.373896 | ||||||||
\(638\) | 7.25817e40i | 0.0614493i | ||||||||
\(639\) | 1.12270e41 | − | 4.21891e41i | 0.0928434 | − | 0.348889i | ||||
\(640\) | 1.36324e41 | 0.110122 | ||||||||
\(641\) | 2.07742e42i | 1.63928i | 0.572879 | + | 0.819640i | \(0.305827\pi\) | ||||
−0.572879 | + | 0.819640i | \(0.694173\pi\) | |||||||
\(642\) | 7.68304e41 | + | 1.00479e41i | 0.592253 | + | 0.0774549i | ||||
\(643\) | 9.51151e41 | 0.716283 | 0.358142 | − | 0.933667i | \(-0.383411\pi\) | ||||
0.358142 | + | 0.933667i | \(0.383411\pi\) | |||||||
\(644\) | 1.80973e42i | 1.33146i | ||||||||
\(645\) | −3.73464e41 | + | 2.85567e42i | −0.268444 | + | 2.05264i | ||||
\(646\) | 1.23544e42 | 0.867631 | ||||||||
\(647\) | − | 1.62594e42i | − | 1.11568i | −0.829948 | − | 0.557841i | \(-0.811630\pi\) | ||
0.829948 | − | 0.557841i | \(-0.188370\pi\) | |||||||
\(648\) | −2.62095e41 | + | 4.57581e41i | −0.175725 | + | 0.306791i | ||||
\(649\) | 1.22929e42 | 0.805347 | ||||||||
\(650\) | 1.35299e41i | 0.0866154i | ||||||||
\(651\) | −8.50398e41 | − | 1.11215e41i | −0.531995 | − | 0.0695743i | ||||
\(652\) | −4.07106e41 | −0.248882 | ||||||||
\(653\) | − | 2.70001e42i | − | 1.61312i | −0.591150 | − | 0.806562i | \(-0.701326\pi\) | ||
0.591150 | − | 0.806562i | \(-0.298674\pi\) | |||||||
\(654\) | 6.76330e40 | − | 5.17151e41i | 0.0394905 | − | 0.301961i | ||||
\(655\) | −7.73032e41 | −0.441142 | ||||||||
\(656\) | − | 5.50769e41i | − | 0.307194i | ||||||
\(657\) | 1.09221e42 | + | 2.90650e41i | 0.595425 | + | 0.158449i | ||||
\(658\) | −2.86725e42 | −1.52784 | ||||||||
\(659\) | − | 1.32042e42i | − | 0.687749i | −0.939016 | − | 0.343875i | \(-0.888261\pi\) | ||
0.939016 | − | 0.343875i | \(-0.111739\pi\) | |||||||
\(660\) | 6.60943e41 | + | 8.64381e40i | 0.336515 | + | 0.0440095i | ||||
\(661\) | −1.08335e42 | −0.539195 | −0.269598 | − | 0.962973i | \(-0.586891\pi\) | ||||
−0.269598 | + | 0.962973i | \(0.586891\pi\) | |||||||
\(662\) | − | 2.73518e42i | − | 1.33081i | ||||||
\(663\) | −1.02800e41 | + | 7.86053e41i | −0.0488979 | + | 0.373894i | ||||
\(664\) | −5.89747e41 | −0.274249 | ||||||||
\(665\) | − | 3.24142e42i | − | 1.47370i | ||||||
\(666\) | −1.08438e41 | + | 4.07489e41i | −0.0482021 | + | 0.181135i | ||||
\(667\) | −5.96368e41 | −0.259195 | ||||||||
\(668\) | 1.81063e41i | 0.0769456i | ||||||||
\(669\) | 5.58373e41 | + | 7.30240e40i | 0.232024 | + | 0.0303441i | ||||
\(670\) | −2.55069e42 | −1.03642 | ||||||||
\(671\) | 2.06352e42i | 0.819920i | ||||||||
\(672\) | 9.66819e40 | − | 7.39271e41i | 0.0375670 | − | 0.287253i | ||||
\(673\) | 1.69638e42 | 0.644610 | 0.322305 | − | 0.946636i | \(-0.395542\pi\) | ||||
0.322305 | + | 0.946636i | \(0.395542\pi\) | |||||||
\(674\) | − | 2.29154e41i | − | 0.0851587i | ||||||
\(675\) | −1.40524e42 | − | 5.77840e41i | −0.510735 | − | 0.210015i | ||||
\(676\) | 1.33739e42 | 0.475399 | ||||||||
\(677\) | − | 1.13146e42i | − | 0.393379i | −0.980466 | − | 0.196689i | \(-0.936981\pi\) | ||
0.980466 | − | 0.196689i | \(-0.0630190\pi\) | |||||||
\(678\) | 1.17165e42 | + | 1.53228e41i | 0.398430 | + | 0.0521067i | ||||
\(679\) | 1.79790e42 | 0.598025 | ||||||||
\(680\) | 2.30148e42i | 0.748812i | ||||||||
\(681\) | −1.18425e41 | + | 9.05527e41i | −0.0376908 | + | 0.288200i | ||||
\(682\) | 4.05096e41 | 0.126122 | ||||||||
\(683\) | − | 9.51949e41i | − | 0.289937i | −0.989436 | − | 0.144968i | \(-0.953692\pi\) | ||
0.989436 | − | 0.144968i | \(-0.0463080\pi\) | |||||||
\(684\) | −1.17048e42 | − | 3.11478e41i | −0.348757 | − | 0.0928082i | ||||
\(685\) | 5.55166e42 | 1.61832 | ||||||||
\(686\) | − | 2.78582e42i | − | 0.794495i | ||||||
\(687\) | −1.68348e42 | − | 2.20165e41i | −0.469739 | − | 0.0614325i | ||||
\(688\) | −1.52154e42 | −0.415391 | ||||||||
\(689\) | 7.90312e40i | 0.0211111i | ||||||||
\(690\) | −7.10219e41 | + | 5.43064e42i | −0.185633 | + | 1.41943i | ||||
\(691\) | −5.40021e42 | −1.38115 | −0.690574 | − | 0.723262i | \(-0.742642\pi\) | ||||
−0.690574 | + | 0.723262i | \(0.742642\pi\) | |||||||
\(692\) | 9.14245e41i | 0.228808i | ||||||||
\(693\) | 9.37490e41 | − | 3.52292e42i | 0.229598 | − | 0.862789i | ||||
\(694\) | −2.92107e41 | −0.0700084 | ||||||||
\(695\) | − | 3.50501e42i | − | 0.822086i | ||||||
\(696\) | 2.43615e41 | + | 3.18599e40i | 0.0559197 | + | 0.00731318i | ||||
\(697\) | 9.29830e42 | 2.08887 | ||||||||
\(698\) | − | 2.14788e42i | − | 0.472258i | ||||||
\(699\) | −1.07771e42 | + | 8.24063e42i | −0.231923 | + | 1.77338i | ||||
\(700\) | 2.14823e42 | 0.452492 | ||||||||
\(701\) | 6.67700e42i | 1.37661i | 0.725421 | + | 0.688306i | \(0.241645\pi\) | ||||
−0.725421 | + | 0.688306i | \(0.758355\pi\) | |||||||
\(702\) | 2.95573e41 | − | 7.18803e41i | 0.0596497 | − | 0.145062i | ||||
\(703\) | −9.68534e41 | −0.191331 | ||||||||
\(704\) | 3.52160e41i | 0.0681004i | ||||||||
\(705\) | −8.60403e42 | − | 1.12523e42i | −1.62879 | − | 0.213013i | ||||
\(706\) | 2.02457e42 | 0.375199 | ||||||||
\(707\) | 4.17149e42i | 0.756833i | ||||||||
\(708\) | 5.39599e41 | − | 4.12600e42i | 0.0958456 | − | 0.732876i | ||||
\(709\) | −4.33459e42 | −0.753797 | −0.376899 | − | 0.926255i | \(-0.623009\pi\) | ||||
−0.376899 | + | 0.926255i | \(0.623009\pi\) | |||||||
\(710\) | 1.86803e42i | 0.318059i | ||||||||
\(711\) | 3.45616e41 | + | 9.19722e40i | 0.0576168 | + | 0.0153325i | ||||
\(712\) | −2.67638e42 | −0.436866 | ||||||||
\(713\) | 3.32847e42i | 0.531988i | ||||||||
\(714\) | 1.24807e43 | + | 1.63222e42i | 1.95328 | + | 0.255450i | ||||
\(715\) | −9.82425e41 | −0.150560 | ||||||||
\(716\) | 1.57691e42i | 0.236652i | ||||||||
\(717\) | 7.46853e41 | − | 5.71076e42i | 0.109761 | − | 0.839279i | ||||
\(718\) | −5.75554e41 | −0.0828361 | ||||||||
\(719\) | 9.64399e42i | 1.35933i | 0.733525 | + | 0.679663i | \(0.237874\pi\) | ||||
−0.733525 | + | 0.679663i | \(0.762126\pi\) | |||||||
\(720\) | 5.80245e41 | − | 2.18046e42i | 0.0800984 | − | 0.300996i | ||||
\(721\) | −1.64636e43 | −2.22584 | ||||||||
\(722\) | 2.55798e42i | 0.338719i | ||||||||
\(723\) | −6.04516e42 | − | 7.90585e41i | −0.784031 | − | 0.102536i | ||||
\(724\) | 2.77279e42 | 0.352240 | ||||||||
\(725\) | 7.07916e41i | 0.0880869i | ||||||||
\(726\) | 5.29012e41 | − | 4.04505e42i | 0.0644787 | − | 0.493032i | ||||
\(727\) | 8.03630e42 | 0.959489 | 0.479744 | − | 0.877408i | \(-0.340729\pi\) | ||||
0.479744 | + | 0.877408i | \(0.340729\pi\) | |||||||
\(728\) | 1.09885e42i | 0.128519i | ||||||||
\(729\) | 6.20328e42 | + | 6.13976e42i | 0.710737 | + | 0.703458i | ||||
\(730\) | −4.83604e42 | −0.542809 | ||||||||
\(731\) | − | 2.56872e43i | − | 2.82460i | ||||||
\(732\) | 6.92605e42 | + | 9.05788e41i | 0.746138 | + | 0.0975799i | ||||
\(733\) | 7.56873e42 | 0.798847 | 0.399424 | − | 0.916767i | \(-0.369210\pi\) | ||||
0.399424 | + | 0.916767i | \(0.369210\pi\) | |||||||
\(734\) | − | 1.31656e42i | − | 0.136145i | ||||||
\(735\) | 2.68786e42 | − | 2.05525e43i | 0.272330 | − | 2.08236i | ||||
\(736\) | −2.89352e42 | −0.287249 | ||||||||
\(737\) | − | 6.58909e42i | − | 0.640933i | ||||||
\(738\) | −8.80938e42 | − | 2.34428e42i | −0.839653 | − | 0.223441i | ||||
\(739\) | −2.67662e42 | −0.249988 | −0.124994 | − | 0.992157i | \(-0.539891\pi\) | ||||
−0.124994 | + | 0.992157i | \(0.539891\pi\) | |||||||
\(740\) | − | 1.80426e42i | − | 0.165129i | ||||||
\(741\) | 1.77008e42 | + | 2.31491e41i | 0.158752 | + | 0.0207616i | ||||
\(742\) | 1.25483e42 | 0.110287 | ||||||||
\(743\) | 7.85552e42i | 0.676617i | 0.941035 | + | 0.338309i | \(0.109855\pi\) | ||||
−0.941035 | + | 0.338309i | \(0.890145\pi\) | |||||||
\(744\) | 1.77818e41 | − | 1.35967e42i | 0.0150100 | − | 0.114773i | ||||
\(745\) | 1.52516e43 | 1.26174 | ||||||||
\(746\) | 2.37990e42i | 0.192964i | ||||||||
\(747\) | −2.51018e42 | + | 9.43281e42i | −0.199478 | + | 0.749604i | ||||
\(748\) | −5.94529e42 | −0.463073 | ||||||||
\(749\) | 1.81324e43i | 1.38429i | ||||||||
\(750\) | −5.22704e42 | − | 6.83592e41i | −0.391144 | − | 0.0511538i | ||||
\(751\) | −4.73876e42 | −0.347589 | −0.173794 | − | 0.984782i | \(-0.555603\pi\) | ||||
−0.173794 | + | 0.984782i | \(0.555603\pi\) | |||||||
\(752\) | − | 4.58435e42i | − | 0.329617i | ||||||
\(753\) | 3.07580e42 | − | 2.35189e43i | 0.216787 | − | 1.65765i | ||||
\(754\) | −3.62109e41 | −0.0250190 | ||||||||
\(755\) | 1.42710e43i | 0.966607i | ||||||||
\(756\) | −1.14129e43 | − | 4.69301e42i | −0.757825 | − | 0.311619i | ||||
\(757\) | −1.48938e43 | −0.969544 | −0.484772 | − | 0.874641i | \(-0.661097\pi\) | ||||
−0.484772 | + | 0.874641i | \(0.661097\pi\) | |||||||
\(758\) | 1.16994e43i | 0.746666i | ||||||||
\(759\) | −1.40287e43 | − | 1.83468e42i | −0.877791 | − | 0.114798i | ||||
\(760\) | 5.18259e42 | 0.317938 | ||||||||
\(761\) | − | 2.11532e42i | − | 0.127235i | −0.997974 | − | 0.0636173i | \(-0.979736\pi\) | ||
0.997974 | − | 0.0636173i | \(-0.0202637\pi\) | |||||||
\(762\) | −8.59058e41 | + | 6.56873e42i | −0.0506638 | + | 0.387397i | ||||
\(763\) | 1.22050e43 | 0.705783 | ||||||||
\(764\) | − | 1.03938e43i | − | 0.589350i | ||||||
\(765\) | 3.68114e43 | + | 9.79592e42i | 2.04673 | + | 0.544658i | ||||
\(766\) | 5.85641e42 | 0.319301 | ||||||||
\(767\) | 6.13289e42i | 0.327895i | ||||||||
\(768\) | 1.18200e42 | + | 1.54581e41i | 0.0619723 | + | 0.00810473i | ||||
\(769\) | −2.36246e42 | −0.121470 | −0.0607350 | − | 0.998154i | \(-0.519344\pi\) | ||||
−0.0607350 | + | 0.998154i | \(0.519344\pi\) | |||||||
\(770\) | 1.55986e43i | 0.786547i | ||||||||
\(771\) | −3.34999e42 | + | 2.56155e43i | −0.165664 | + | 1.26674i | ||||
\(772\) | −1.30379e43 | −0.632339 | ||||||||
\(773\) | 3.16955e41i | 0.0150767i | 0.999972 | + | 0.00753834i | \(0.00239955\pi\) | ||||
−0.999972 | + | 0.00753834i | \(0.997600\pi\) | |||||||
\(774\) | −6.47623e42 | + | 2.43365e43i | −0.302140 | + | 1.13539i | ||||
\(775\) | 3.95104e42 | 0.180795 | ||||||||
\(776\) | 2.87460e42i | 0.129019i | ||||||||
\(777\) | −9.78431e42 | − | 1.27959e42i | −0.430740 | − | 0.0563321i | ||||
\(778\) | 2.19270e42 | 0.0946859 | ||||||||
\(779\) | − | 2.09384e43i | − | 0.886915i | ||||||
\(780\) | −4.31238e41 | + | 3.29743e42i | −0.0179184 | + | 0.137011i | ||||
\(781\) | −4.82559e42 | −0.196691 | ||||||||
\(782\) | − | 4.88495e43i | − | 1.95326i | ||||||
\(783\) | 1.54650e42 | − | 3.76093e42i | 0.0606631 | − | 0.147526i | ||||
\(784\) | 1.09507e43 | 0.421405 | ||||||||
\(785\) | − | 1.78742e43i | − | 0.674812i | ||||||
\(786\) | −6.70256e42 | − | 8.76561e41i | −0.248258 | − | 0.0324671i | ||||
\(787\) | 1.83268e43 | 0.665987 | 0.332993 | − | 0.942929i | \(-0.391941\pi\) | ||||
0.332993 | + | 0.942929i | \(0.391941\pi\) | |||||||
\(788\) | 1.81912e43i | 0.648587i | ||||||||
\(789\) | −3.44093e42 | + | 2.63108e43i | −0.120371 | + | 0.920405i | ||||
\(790\) | −1.53030e42 | −0.0525254 | ||||||||
\(791\) | 2.76515e43i | 0.931262i | ||||||||
\(792\) | 5.63268e42 | + | 1.49892e42i | 0.186139 | + | 0.0495337i | ||||
\(793\) | −1.02949e43 | −0.333828 | ||||||||
\(794\) | 5.46686e42i | 0.173953i | ||||||||
\(795\) | 3.76549e42 | + | 4.92450e41i | 0.117575 | + | 0.0153764i | ||||
\(796\) | 2.48014e43 | 0.759941 | ||||||||
\(797\) | − | 4.40895e43i | − | 1.32575i | −0.748732 | − | 0.662873i | \(-0.769337\pi\) | ||
0.748732 | − | 0.662873i | \(-0.230663\pi\) | |||||||
\(798\) | 3.67552e42 | − | 2.81046e43i | 0.108462 | − | 0.829344i | ||||
\(799\) | 7.73947e43 | 2.24135 | ||||||||
\(800\) | 3.43474e42i | 0.0976211i | ||||||||
\(801\) | −1.13917e43 | + | 4.28079e43i | −0.317760 | + | 1.19409i | ||||
\(802\) | 6.75087e42 | 0.184818 | ||||||||
\(803\) | − | 1.24927e43i | − | 0.335679i | ||||||
\(804\) | −2.21157e43 | − | 2.89230e42i | −0.583258 | − | 0.0762785i | ||||
\(805\) | −1.28166e44 | −3.31768 | ||||||||
\(806\) | 2.02102e42i | 0.0513504i | ||||||||
\(807\) | 6.51517e42 | − | 4.98178e43i | 0.162489 | − | 1.24246i | ||||
\(808\) | −6.66965e42 | −0.163280 | ||||||||
\(809\) | − | 3.94451e43i | − | 0.947905i | −0.880550 | − | 0.473953i | \(-0.842827\pi\) | ||
0.880550 | − | 0.473953i | \(-0.157173\pi\) | |||||||
\(810\) | −3.24060e43 | − | 1.85617e43i | −0.764452 | − | 0.437867i | ||||
\(811\) | −3.74911e43 | −0.868192 | −0.434096 | − | 0.900867i | \(-0.642932\pi\) | ||||
−0.434096 | + | 0.900867i | \(0.642932\pi\) | |||||||
\(812\) | 5.74944e42i | 0.130703i | ||||||||
\(813\) | 4.24308e43 | + | 5.54909e42i | 0.946940 | + | 0.123841i | ||||
\(814\) | 4.66086e42 | 0.102117 | ||||||||
\(815\) | − | 2.88314e43i | − | 0.620156i | ||||||
\(816\) | −2.60970e42 | + | 1.99549e43i | −0.0551110 | + | 0.421403i | ||||
\(817\) | −5.78439e43 | −1.19930 | ||||||||
\(818\) | − | 3.00859e42i | − | 0.0612439i | ||||||
\(819\) | 1.75758e43 | + | 4.67712e42i | 0.351283 | + | 0.0934803i | ||||
\(820\) | 3.90057e43 | 0.765455 | ||||||||
\(821\) | − | 3.35570e43i | − | 0.646600i | −0.946296 | − | 0.323300i | \(-0.895208\pi\) | ||
0.946296 | − | 0.323300i | \(-0.104792\pi\) | |||||||
\(822\) | 4.81356e43 | + | 6.29518e42i | 0.910729 | + | 0.119105i | ||||
\(823\) | −1.15500e43 | −0.214578 | −0.107289 | − | 0.994228i | \(-0.534217\pi\) | ||||
−0.107289 | + | 0.994228i | \(0.534217\pi\) | |||||||
\(824\) | − | 2.63230e43i | − | 0.480206i | ||||||
\(825\) | −2.17784e42 | + | 1.66527e43i | −0.0390137 | + | 0.298315i | ||||
\(826\) | 9.73759e43 | 1.71297 | ||||||||
\(827\) | − | 1.92570e43i | − | 0.332664i | −0.986070 | − | 0.166332i | \(-0.946808\pi\) | ||
0.986070 | − | 0.166332i | \(-0.0531923\pi\) | |||||||
\(828\) | −1.23159e43 | + | 4.62809e43i | −0.208935 | + | 0.785140i | ||||
\(829\) | −4.49296e43 | −0.748539 | −0.374270 | − | 0.927320i | \(-0.622107\pi\) | ||||
−0.374270 | + | 0.927320i | \(0.622107\pi\) | |||||||
\(830\) | − | 4.17661e43i | − | 0.683364i | ||||||
\(831\) | 5.26248e43 | + | 6.88227e42i | 0.845619 | + | 0.110590i | ||||
\(832\) | −1.75692e42 | −0.0277269 | ||||||||
\(833\) | 1.84873e44i | 2.86549i | ||||||||
\(834\) | 3.97442e42 | − | 3.03901e43i | 0.0605039 | − | 0.462639i | ||||
\(835\) | −1.28230e43 | −0.191731 | ||||||||
\(836\) | 1.33879e43i | 0.196616i | ||||||||
\(837\) | −2.09907e43 | − | 8.63140e42i | −0.302792 | − | 0.124509i | ||||
\(838\) | −2.30104e43 | −0.326035 | ||||||||
\(839\) | 1.29960e43i | 0.180876i | 0.995902 | + | 0.0904381i | \(0.0288267\pi\) | ||||
−0.995902 | + | 0.0904381i | \(0.971173\pi\) | |||||||
\(840\) | 5.23554e43 | + | 6.84704e42i | 0.715768 | + | 0.0936082i | ||||
\(841\) | 7.25683e43 | 0.974556 | ||||||||
\(842\) | 2.84684e43i | 0.375562i | ||||||||
\(843\) | −5.06761e42 | + | 3.87491e43i | −0.0656734 | + | 0.502167i | ||||
\(844\) | −6.32514e43 | −0.805256 | ||||||||
\(845\) | 9.47146e43i | 1.18458i | ||||||||
\(846\) | −7.33252e43 | − | 1.95127e43i | −0.900943 | − | 0.239751i | ||||
\(847\) | 9.54654e43 | 1.15238 | ||||||||
\(848\) | 2.00630e42i | 0.0237935i | ||||||||
\(849\) | −7.74978e43 | − | 1.01352e43i | −0.902971 | − | 0.118091i | ||||
\(850\) | −5.79866e43 | −0.663810 | ||||||||
\(851\) | 3.82960e43i | 0.430734i | ||||||||
\(852\) | −2.11820e42 | + | 1.61967e43i | −0.0234085 | + | 0.178992i | ||||
\(853\) | 4.50119e43 | 0.488756 | 0.244378 | − | 0.969680i | \(-0.421416\pi\) | ||||
0.244378 | + | 0.969680i | \(0.421416\pi\) | |||||||
\(854\) | 1.63458e44i | 1.74397i | ||||||||
\(855\) | 2.20590e43 | − | 8.28938e43i | 0.231257 | − | 0.869021i | ||||
\(856\) | −2.89912e43 | −0.298648 | ||||||||
\(857\) | − | 1.11384e44i | − | 1.12749i | −0.825949 | − | 0.563744i | \(-0.809360\pi\) | ||
0.825949 | − | 0.563744i | \(-0.190640\pi\) | |||||||
\(858\) | −8.51810e42 | − | 1.11400e42i | −0.0847293 | − | 0.0110809i | ||||
\(859\) | 1.25632e44 | 1.22802 | 0.614008 | − | 0.789300i | \(-0.289556\pi\) | ||||
0.614008 | + | 0.789300i | \(0.289556\pi\) | |||||||
\(860\) | − | 1.07756e44i | − | 1.03506i | ||||||
\(861\) | 2.76631e43 | − | 2.11524e44i | 0.261128 | − | 1.99670i | ||||
\(862\) | −3.60121e43 | −0.334071 | ||||||||
\(863\) | 1.24301e44i | 1.13321i | 0.823988 | + | 0.566607i | \(0.191744\pi\) | ||||
−0.823988 | + | 0.566607i | \(0.808256\pi\) | |||||||
\(864\) | 7.50348e42 | − | 1.82477e43i | 0.0672290 | − | 0.163494i | ||||
\(865\) | −6.47472e43 | −0.570137 | ||||||||
\(866\) | − | 5.71978e43i | − | 0.495007i | ||||||
\(867\) | −2.20312e44 | − | 2.88124e43i | −1.87392 | − | 0.245072i | ||||
\(868\) | 3.20890e43 | 0.268262 | ||||||||
\(869\) | − | 3.95314e42i | − | 0.0324822i | ||||||
\(870\) | −2.25633e42 | + | 1.72529e43i | −0.0182228 | + | 0.139339i | ||||
\(871\) | 3.28728e43 | 0.260954 | ||||||||
\(872\) | 1.95142e43i | 0.152266i | ||||||||
\(873\) | 4.59784e43 | + | 1.22354e43i | 0.352647 | + | 0.0938433i | ||||
\(874\) | −1.10002e44 | −0.829333 | ||||||||
\(875\) | − | 1.23361e44i | − | 0.914232i | ||||||
\(876\) | −4.19308e43 | − | 5.48371e42i | −0.305472 | − | 0.0399497i | ||||
\(877\) | 7.81734e43 | 0.559841 | 0.279921 | − | 0.960023i | \(-0.409692\pi\) | ||||
0.279921 | + | 0.960023i | \(0.409692\pi\) | |||||||
\(878\) | 1.71911e44i | 1.21028i | ||||||||
\(879\) | −1.83372e43 | + | 1.40214e44i | −0.126911 | + | 0.970419i | ||||
\(880\) | −2.49401e43 | −0.169690 | ||||||||
\(881\) | 2.12352e43i | 0.142043i | 0.997475 | + | 0.0710213i | \(0.0226258\pi\) | ||||
−0.997475 | + | 0.0710213i | \(0.977374\pi\) | |||||||
\(882\) | 4.66101e43 | − | 1.75152e44i | 0.306514 | − | 1.15183i | ||||
\(883\) | 1.34653e44 | 0.870571 | 0.435286 | − | 0.900292i | \(-0.356647\pi\) | ||||
0.435286 | + | 0.900292i | \(0.356647\pi\) | |||||||
\(884\) | − | 2.96610e43i | − | 0.188539i | ||||||
\(885\) | 2.92205e44 | + | 3.82146e43i | 1.82616 | + | 0.238825i | ||||
\(886\) | −3.91016e42 | −0.0240264 | ||||||||
\(887\) | − | 4.81971e43i | − | 0.291183i | −0.989345 | − | 0.145592i | \(-0.953491\pi\) | ||
0.989345 | − | 0.145592i | \(-0.0465086\pi\) | |||||||
\(888\) | 2.04590e42 | − | 1.56438e43i | 0.0121532 | − | 0.0929282i | ||||
\(889\) | −1.55025e44 | −0.905475 | ||||||||
\(890\) | − | 1.89542e44i | − | 1.08857i | ||||||
\(891\) | 4.79495e43 | − | 8.37129e43i | 0.270781 | − | 0.472745i | ||||
\(892\) | −2.10697e43 | −0.117000 | ||||||||
\(893\) | − | 1.74282e44i | − | 0.951655i | ||||||
\(894\) | 1.32238e44 | + | 1.72941e43i | 0.710059 | + | 0.0928615i | ||||
\(895\) | −1.11677e44 | −0.589683 | ||||||||
\(896\) | 2.78957e43i | 0.144850i | ||||||||
\(897\) | 9.15316e42 | − | 6.99890e43i | 0.0467395 | − | 0.357391i | ||||
\(898\) | 1.34244e44 | 0.674140 | ||||||||
\(899\) | 1.05744e43i | 0.0522228i | ||||||||
\(900\) | 5.49375e43 | + | 1.46195e43i | 0.266828 | + | 0.0710060i | ||||
\(901\) | −3.38712e43 | −0.161793 | ||||||||
\(902\) | 1.00762e44i | 0.473365i | ||||||||
\(903\) | −5.84350e44 | − | 7.64212e43i | −2.69995 | − | 0.353100i | ||||
\(904\) | −4.42111e43 | −0.200911 | ||||||||
\(905\) | 1.96370e44i | 0.877701i | ||||||||
\(906\) | −1.61822e43 | + | 1.23736e44i | −0.0711403 | + | 0.543969i | ||||
\(907\) | −2.08693e43 | −0.0902397 | −0.0451199 | − | 0.998982i | \(-0.514367\pi\) | ||||
−0.0451199 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(908\) | − | 3.41692e43i | − | 0.145327i | ||||||
\(909\) | −2.83885e43 | + | 1.06679e44i | −0.118764 | + | 0.446293i | ||||
\(910\) | −7.78211e43 | −0.320241 | ||||||||
\(911\) | 1.23452e44i | 0.499717i | 0.968282 | + | 0.249858i | \(0.0803840\pi\) | ||||
−0.968282 | + | 0.249858i | \(0.919616\pi\) | |||||||
\(912\) | 4.49355e43 | + | 5.87667e42i | 0.178924 | + | 0.0233996i | ||||
\(913\) | 1.07892e44 | 0.422599 | ||||||||
\(914\) | 1.27202e44i | 0.490120i | ||||||||
\(915\) | −6.41482e43 | + | 4.90505e44i | −0.243147 | + | 1.85920i | ||||
\(916\) | 6.35245e43 | 0.236870 | ||||||||
\(917\) | − | 1.58184e44i | − | 0.580260i | ||||||
\(918\) | 3.08064e44 | + | 1.26677e44i | 1.11174 | + | 0.457148i | ||||
\(919\) | 5.23347e43 | 0.185805 | 0.0929024 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0929024 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(920\) | − | 2.04920e44i | − | 0.715759i | ||||||
\(921\) | 5.06358e44 | + | 6.62215e43i | 1.74006 | + | 0.227565i | ||||
\(922\) | −4.16642e44 | −1.40864 | ||||||||
\(923\) | − | 2.40748e43i | − | 0.0800823i | ||||||
\(924\) | −1.76876e43 | + | 1.35247e44i | −0.0578883 | + | 0.442639i | ||||
\(925\) | 4.54590e43 | 0.146384 | ||||||||
\(926\) | 2.32012e44i | 0.735099i | ||||||||
\(927\) | −4.21028e44 | − | 1.12040e44i | −1.31255 | − | 0.349284i | ||||
\(928\) | −9.19258e42 | −0.0281980 | ||||||||
\(929\) | 2.89626e44i | 0.874181i | 0.899418 | + | 0.437091i | \(0.143991\pi\) | ||||
−0.899418 | + | 0.437091i | \(0.856009\pi\) | |||||||
\(930\) | 9.62924e43 | + | 1.25931e43i | 0.285988 | + | 0.0374015i | ||||
\(931\) | 4.16308e44 | 1.21666 | ||||||||
\(932\) | − | 3.10952e44i | − | 0.894243i | ||||||
\(933\) | −6.37684e43 | + | 4.87600e44i | −0.180460 | + | 1.37987i | ||||
\(934\) | 2.57495e44 | 0.717078 | ||||||||
\(935\) | − | 4.21048e44i | − | 1.15387i | ||||||
\(936\) | −7.47809e42 | + | 2.81013e43i | −0.0201675 | + | 0.0757860i | ||||
\(937\) | −2.91104e44 | −0.772599 | −0.386300 | − | 0.922373i | \(-0.626247\pi\) | ||||
−0.386300 | + | 0.922373i | \(0.626247\pi\) | |||||||
\(938\) | − | 5.21943e44i | − | 1.36327i | ||||||
\(939\) | −1.50955e44 | − | 1.97419e43i | −0.388028 | − | 0.0507463i | ||||
\(940\) | 3.24665e44 | 0.821330 | ||||||||
\(941\) | 4.64351e44i | 1.15612i | 0.815995 | + | 0.578059i | \(0.196190\pi\) | ||||
−0.815995 | + | 0.578059i | \(0.803810\pi\) | |||||||
\(942\) | 2.02681e43 | − | 1.54978e44i | 0.0496648 | − | 0.379758i | ||||
\(943\) | −8.27907e44 | −1.99667 | ||||||||
\(944\) | 1.55691e44i | 0.369559i | ||||||||
\(945\) | 3.32360e44 | − | 8.08265e44i | 0.776483 | − | 1.88832i | ||||
\(946\) | 2.78361e44 | 0.640090 | ||||||||
\(947\) | − | 8.24458e44i | − | 1.86603i | −0.359835 | − | 0.933016i | \(-0.617167\pi\) | ||
0.359835 | − | 0.933016i | \(-0.382833\pi\) | |||||||
\(948\) | −1.32684e43 | − | 1.73524e42i | −0.0295593 | − | 0.00386576i | ||||
\(949\) | 6.23260e43 | 0.136671 | ||||||||
\(950\) | 1.30577e44i | 0.281847i | ||||||||
\(951\) | 1.24096e43 | − | 9.48891e43i | 0.0263663 | − | 0.201608i | ||||
\(952\) | −4.70946e44 | −0.984957 | ||||||||
\(953\) | − | 8.05488e44i | − | 1.65831i | −0.559020 | − | 0.829154i | \(-0.688822\pi\) | ||
0.559020 | − | 0.829154i | \(-0.311178\pi\) | |||||||
\(954\) | 3.20902e43 | + | 8.53956e42i | 0.0650349 | + | 0.0173065i | ||||
\(955\) | 7.36092e44 | 1.46853 | ||||||||
\(956\) | 2.15490e44i | 0.423213i | ||||||||
\(957\) | −4.45686e43 | − | 5.82868e42i | −0.0861687 | − | 0.0112691i | ||||
\(958\) | 1.12989e44 | 0.215056 | ||||||||
\(959\) | 1.13603e45i | 2.12867i | ||||||||
\(960\) | −1.09475e43 | + | 8.37093e43i | −0.0201951 | + | 0.154421i | ||||
\(961\) | −4.91600e44 | −0.892815 | ||||||||
\(962\) | 2.32529e43i | 0.0415769i | ||||||||
\(963\) | −1.23397e44 | + | 4.63705e44i | −0.217226 | + | 0.816296i | ||||
\(964\) | 2.28108e44 | 0.395353 | ||||||||
\(965\) | − | 9.23352e44i | − | 1.57564i | ||||||
\(966\) | −1.11126e45 | − | 1.45331e44i | −1.86706 | − | 0.244174i | ||||
\(967\) | 3.14393e44 | 0.520086 | 0.260043 | − | 0.965597i | \(-0.416263\pi\) | ||||
0.260043 | + | 0.965597i | \(0.416263\pi\) | |||||||
\(968\) | 1.52636e44i | 0.248615i | ||||||||
\(969\) | −9.92122e43 | + | 7.58619e44i | −0.159114 | + | 1.21665i | ||||
\(970\) | −2.03580e44 | −0.321484 | ||||||||
\(971\) | − | 1.87489e43i | − | 0.0291532i | −0.999894 | − | 0.0145766i | \(-0.995360\pi\) | ||
0.999894 | − | 0.0145766i | \(-0.00464004\pi\) | |||||||
\(972\) | −2.59928e44 | − | 1.97685e44i | −0.397978 | − | 0.302677i | ||||
\(973\) | 7.17223e44 | 1.08134 | ||||||||
\(974\) | − | 4.59965e44i | − | 0.682873i | ||||||
\(975\) | −8.30801e43 | − | 1.08652e43i | −0.121458 | − | 0.0158843i | ||||
\(976\) | −2.61348e44 | −0.376246 | ||||||||
\(977\) | − | 8.73809e44i | − | 1.23879i | −0.785079 | − | 0.619396i | \(-0.787378\pi\) | ||
0.785079 | − | 0.619396i | \(-0.212622\pi\) | |||||||
\(978\) | 3.26926e43 | − | 2.49982e44i | 0.0456422 | − | 0.349000i | ||||
\(979\) | 4.89636e44 | 0.673183 | ||||||||
\(980\) | 7.75530e44i | 1.05004i | ||||||||
\(981\) | 3.12124e44 | + | 8.30597e43i | 0.416190 | + | 0.110753i | ||||
\(982\) | −1.59368e44 | −0.209280 | ||||||||
\(983\) | 3.87923e44i | 0.501698i | 0.968026 | + | 0.250849i | \(0.0807098\pi\) | ||||
−0.968026 | + | 0.250849i | \(0.919290\pi\) | |||||||
\(984\) | 3.38198e44 | + | 4.42295e43i | 0.430769 | + | 0.0563360i | ||||
\(985\) | −1.28831e45 | −1.61613 | ||||||||
\(986\) | − | 1.55193e44i | − | 0.191742i | ||||||
\(987\) | 2.30254e44 | − | 1.76062e45i | 0.280189 | − | 2.14244i | ||||
\(988\) | −6.67922e43 | −0.0800519 | ||||||||
\(989\) | 2.28715e45i | 2.69992i | ||||||||
\(990\) | −1.06154e44 | + | 3.98908e44i | −0.123427 | + | 0.463815i | ||||
\(991\) | 7.70247e44 | 0.882115 | 0.441058 | − | 0.897479i | \(-0.354603\pi\) | ||||
0.441058 | + | 0.897479i | \(0.354603\pi\) | |||||||
\(992\) | 5.13059e43i | 0.0578752i | ||||||||
\(993\) | 1.67953e45 | + | 2.19649e44i | 1.86616 | + | 0.244056i | ||||
\(994\) | −3.82251e44 | −0.418362 | ||||||||
\(995\) | 1.75644e45i | 1.89360i | ||||||||
\(996\) | 4.73596e43 | − | 3.62132e44i | 0.0502942 | − | 0.384571i | ||||
\(997\) | 1.59872e45 | 1.67242 | 0.836209 | − | 0.548411i | \(-0.184767\pi\) | ||||
0.836209 | + | 0.548411i | \(0.184767\pi\) | |||||||
\(998\) | 3.30035e44i | 0.340096i | ||||||||
\(999\) | −2.41509e44 | − | 9.93092e43i | −0.245161 | − | 0.100811i |
(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 | 6.31.b.a.5.5 | ✓ | 10 | |
3.2 | odd | 2 | inner | 6.31.b.a.5.10 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.31.b.a.5.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6.31.b.a.5.10 | yes | 10 | 3.2 | odd | 2 | inner |