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 | 3.2 | ||
Root | \(1.10776e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.37.b.b.3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −227674. | + | 129939.i | −0.868506 | + | 0.495679i | ||||
\(3\) | 1.77242e8i | 0.457492i | 0.973486 | + | 0.228746i | \(0.0734625\pi\) | ||||
−0.973486 | + | 0.228746i | \(0.926537\pi\) | |||||||
\(4\) | 3.49511e10 | − | 5.91675e10i | 0.508605 | − | 0.861000i | ||||
\(5\) | 5.55508e12 | 1.45623 | 0.728116 | − | 0.685454i | \(-0.240396\pi\) | ||||
0.728116 | + | 0.685454i | \(0.240396\pi\) | |||||||
\(6\) | −2.30307e13 | − | 4.03533e13i | −0.226769 | − | 0.397334i | ||||
\(7\) | 2.49971e15i | 1.53506i | 0.641015 | + | 0.767528i | \(0.278514\pi\) | ||||
−0.641015 | + | 0.767528i | \(0.721486\pi\) | |||||||
\(8\) | −2.69262e14 | + | 1.80124e16i | −0.0149471 | + | 0.999888i | ||||
\(9\) | 1.18680e17 | 0.790701 | ||||||||
\(10\) | −1.26475e18 | + | 7.21823e17i | −1.26475 | + | 0.721823i | ||||
\(11\) | − | 5.40459e18i | − | 0.972063i | −0.873941 | − | 0.486032i | \(-0.838444\pi\) | ||
0.873941 | − | 0.486032i | \(-0.161556\pi\) | |||||||
\(12\) | 1.04869e19 | + | 6.19479e18i | 0.393901 | + | 0.232683i | ||||
\(13\) | 1.72435e20 | 1.53336 | 0.766681 | − | 0.642028i | \(-0.221907\pi\) | ||||
0.766681 | + | 0.642028i | \(0.221907\pi\) | |||||||
\(14\) | −3.24810e20 | − | 5.69117e20i | −0.760895 | − | 1.33321i | ||||
\(15\) | 9.84593e20i | 0.666214i | ||||||||
\(16\) | −2.27921e21 | − | 4.13593e21i | −0.482642 | − | 0.875818i | ||||
\(17\) | 8.60485e21 | 0.611875 | 0.305937 | − | 0.952052i | \(-0.401030\pi\) | ||||
0.305937 | + | 0.952052i | \(0.401030\pi\) | |||||||
\(18\) | −2.70203e22 | + | 1.54212e22i | −0.686729 | + | 0.391934i | ||||
\(19\) | − | 1.88804e23i | − | 1.81320i | −0.421989 | − | 0.906601i | \(-0.638668\pi\) | ||
0.421989 | − | 0.906601i | \(-0.361332\pi\) | |||||||
\(20\) | 1.94156e23 | − | 3.28680e23i | 0.740647 | − | 1.25382i | ||||
\(21\) | −4.43052e23 | −0.702276 | ||||||||
\(22\) | 7.02268e23 | + | 1.23048e24i | 0.481831 | + | 0.844243i | ||||
\(23\) | − | 9.41760e23i | − | 0.290295i | −0.989410 | − | 0.145147i | \(-0.953634\pi\) | ||
0.989410 | − | 0.145147i | \(-0.0463656\pi\) | |||||||
\(24\) | −3.19255e24 | − | 4.77245e22i | −0.457441 | − | 0.00683816i | ||||
\(25\) | 1.63070e25 | 1.12061 | ||||||||
\(26\) | −3.92589e25 | + | 2.24060e25i | −1.33173 | + | 0.760055i | ||||
\(27\) | 4.76381e25i | 0.819231i | ||||||||
\(28\) | 1.47901e26 | + | 8.73674e25i | 1.32168 | + | 0.780738i | ||||
\(29\) | −4.55607e25 | −0.216484 | −0.108242 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108242 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(30\) | −1.27937e26 | − | 2.24166e26i | −0.330228 | − | 0.578611i | ||||
\(31\) | − | 5.01332e26i | − | 0.717158i | −0.933499 | − | 0.358579i | \(-0.883261\pi\) | ||
0.933499 | − | 0.358579i | \(-0.116739\pi\) | |||||||
\(32\) | 1.05634e27 | + | 6.45484e26i | 0.853302 | + | 0.521418i | ||||
\(33\) | 9.57919e26 | 0.444711 | ||||||||
\(34\) | −1.95910e27 | + | 1.11811e27i | −0.531417 | + | 0.303293i | ||||
\(35\) | 1.38861e28i | 2.23540i | ||||||||
\(36\) | 4.14799e27 | − | 7.02199e27i | 0.402155 | − | 0.680794i | ||||
\(37\) | 1.31828e28 | 0.780504 | 0.390252 | − | 0.920708i | \(-0.372388\pi\) | ||||
0.390252 | + | 0.920708i | \(0.372388\pi\) | |||||||
\(38\) | 2.45330e28 | + | 4.29857e28i | 0.898766 | + | 1.57478i | ||||
\(39\) | 3.05627e28i | 0.701501i | ||||||||
\(40\) | −1.49578e27 | + | 1.00060e29i | −0.0217664 | + | 1.45607i | ||||
\(41\) | 2.91126e27 | 0.0271626 | 0.0135813 | − | 0.999908i | \(-0.495677\pi\) | ||||
0.0135813 | + | 0.999908i | \(0.495677\pi\) | |||||||
\(42\) | 1.00871e29 | − | 5.75699e28i | 0.609931 | − | 0.348103i | ||||
\(43\) | 6.20563e28i | 0.245671i | 0.992427 | + | 0.122835i | \(0.0391987\pi\) | ||||
−0.992427 | + | 0.122835i | \(0.960801\pi\) | |||||||
\(44\) | −3.19776e29 | − | 1.88896e29i | −0.836946 | − | 0.494396i | ||||
\(45\) | 6.59277e29 | 1.15144 | ||||||||
\(46\) | 1.22372e29 | + | 2.14414e29i | 0.143893 | + | 0.252123i | ||||
\(47\) | − | 4.91358e29i | − | 0.392316i | −0.980572 | − | 0.196158i | \(-0.937153\pi\) | ||
0.980572 | − | 0.196158i | \(-0.0628466\pi\) | |||||||
\(48\) | 7.33060e29 | − | 4.03971e29i | 0.400680 | − | 0.220805i | ||||
\(49\) | −3.59680e30 | −1.35640 | ||||||||
\(50\) | −3.71268e30 | + | 2.11893e30i | −0.973258 | + | 0.555464i | ||||
\(51\) | 1.52514e30i | 0.279928i | ||||||||
\(52\) | 6.02678e30 | − | 1.02025e31i | 0.779876 | − | 1.32022i | ||||
\(53\) | 4.35112e29 | 0.0399609 | 0.0199805 | − | 0.999800i | \(-0.493640\pi\) | ||||
0.0199805 | + | 0.999800i | \(0.493640\pi\) | |||||||
\(54\) | −6.19006e30 | − | 1.08459e31i | −0.406076 | − | 0.711507i | ||||
\(55\) | − | 3.00230e31i | − | 1.41555i | ||||||
\(56\) | −4.50257e31 | − | 6.73077e29i | −1.53489 | − | 0.0229446i | ||||
\(57\) | 3.34639e31 | 0.829525 | ||||||||
\(58\) | 1.03730e31 | − | 5.92012e30i | 0.188018 | − | 0.107307i | ||||
\(59\) | 5.43569e31i | 0.724300i | 0.932120 | + | 0.362150i | \(0.117957\pi\) | ||||
−0.932120 | + | 0.362150i | \(0.882043\pi\) | |||||||
\(60\) | 5.82559e31 | + | 3.44126e31i | 0.573611 | + | 0.338840i | ||||
\(61\) | −3.68830e31 | −0.269705 | −0.134853 | − | 0.990866i | \(-0.543056\pi\) | ||||
−0.134853 | + | 0.990866i | \(0.543056\pi\) | |||||||
\(62\) | 6.51427e31 | + | 1.14140e32i | 0.355480 | + | 0.622856i | ||||
\(63\) | 2.96665e32i | 1.21377i | ||||||||
\(64\) | −3.24374e32 | − | 9.70012e30i | −0.999553 | − | 0.0298908i | ||||
\(65\) | 9.57890e32 | 2.23293 | ||||||||
\(66\) | −2.18093e32 | + | 1.24471e32i | −0.386234 | + | 0.220434i | ||||
\(67\) | 9.33023e32i | 1.26051i | 0.776389 | + | 0.630254i | \(0.217049\pi\) | ||||
−0.776389 | + | 0.630254i | \(0.782951\pi\) | |||||||
\(68\) | 3.00749e32 | − | 5.09127e32i | 0.311203 | − | 0.526824i | ||||
\(69\) | 1.66919e32 | 0.132807 | ||||||||
\(70\) | −1.80435e33 | − | 3.16149e33i | −1.10804 | − | 1.94146i | ||||
\(71\) | − | 1.44228e33i | − | 0.686118i | −0.939314 | − | 0.343059i | \(-0.888537\pi\) | ||
0.939314 | − | 0.343059i | \(-0.111463\pi\) | |||||||
\(72\) | −3.19561e31 | + | 2.13771e33i | −0.0118187 | + | 0.790613i | ||||
\(73\) | 2.43678e33 | 0.703079 | 0.351540 | − | 0.936173i | \(-0.385658\pi\) | ||||
0.351540 | + | 0.936173i | \(0.385658\pi\) | |||||||
\(74\) | −3.00137e33 | + | 1.71296e33i | −0.677873 | + | 0.386879i | ||||
\(75\) | 2.89029e33i | 0.512671i | ||||||||
\(76\) | −1.11711e34 | − | 6.59890e33i | −1.56117 | − | 0.922204i | ||||
\(77\) | 1.35099e34 | 1.49217 | ||||||||
\(78\) | −3.97129e33 | − | 6.95831e33i | −0.347719 | − | 0.609258i | ||||
\(79\) | 4.92391e33i | 0.342786i | 0.985203 | + | 0.171393i | \(0.0548267\pi\) | ||||
−0.985203 | + | 0.171393i | \(0.945173\pi\) | |||||||
\(80\) | −1.26612e34 | − | 2.29755e34i | −0.702838 | − | 1.27539i | ||||
\(81\) | 9.36977e33 | 0.415909 | ||||||||
\(82\) | −6.62818e32 | + | 3.78287e32i | −0.0235909 | + | 0.0134639i | ||||
\(83\) | 3.24535e34i | 0.928659i | 0.885663 | + | 0.464329i | \(0.153705\pi\) | ||||
−0.885663 | + | 0.464329i | \(0.846295\pi\) | |||||||
\(84\) | −1.54852e34 | + | 2.62143e34i | −0.357181 | + | 0.604660i | ||||
\(85\) | 4.78007e34 | 0.891032 | ||||||||
\(86\) | −8.06354e33 | − | 1.41286e34i | −0.121774 | − | 0.213367i | ||||
\(87\) | − | 8.07526e33i | − | 0.0990398i | ||||||
\(88\) | 9.73496e34 | + | 1.45525e33i | 0.971955 | + | 0.0145295i | ||||
\(89\) | 9.08737e34 | 0.740317 | 0.370159 | − | 0.928969i | \(-0.379303\pi\) | ||||
0.370159 | + | 0.928969i | \(0.379303\pi\) | |||||||
\(90\) | −1.50100e35 | + | 8.56660e34i | −1.00004 | + | 0.570747i | ||||
\(91\) | 4.31037e35i | 2.35380i | ||||||||
\(92\) | −5.57215e34 | − | 3.29155e34i | −0.249944 | − | 0.147645i | ||||
\(93\) | 8.88570e34 | 0.328094 | ||||||||
\(94\) | 6.38466e34 | + | 1.11869e35i | 0.194463 | + | 0.340729i | ||||
\(95\) | − | 1.04882e36i | − | 2.64044i | ||||||
\(96\) | −1.14407e35 | + | 1.87227e35i | −0.238544 | + | 0.390379i | ||||
\(97\) | −1.10168e36 | −1.90618 | −0.953089 | − | 0.302692i | \(-0.902115\pi\) | ||||
−0.953089 | + | 0.302692i | \(0.902115\pi\) | |||||||
\(98\) | 8.18897e35 | − | 4.67366e35i | 1.17804 | − | 0.672338i | ||||
\(99\) | − | 6.41417e35i | − | 0.768612i | ||||||
\(100\) | 5.69949e35 | − | 9.64847e35i | 0.569949 | − | 0.964847i | ||||
\(101\) | −6.22174e35 | −0.520148 | −0.260074 | − | 0.965589i | \(-0.583747\pi\) | ||||
−0.260074 | + | 0.965589i | \(0.583747\pi\) | |||||||
\(102\) | −1.98175e35 | − | 3.47234e35i | −0.138754 | − | 0.243119i | ||||
\(103\) | 9.69079e35i | 0.569232i | 0.958642 | + | 0.284616i | \(0.0918661\pi\) | ||||
−0.958642 | + | 0.284616i | \(0.908134\pi\) | |||||||
\(104\) | −4.64302e34 | + | 3.10596e36i | −0.0229193 | + | 1.53319i | ||||
\(105\) | −2.46119e36 | −1.02268 | ||||||||
\(106\) | −9.90636e34 | + | 5.65382e34i | −0.0347063 | + | 0.0198078i | ||||
\(107\) | − | 2.89529e36i | − | 0.856612i | −0.903634 | − | 0.428306i | \(-0.859110\pi\) | ||
0.903634 | − | 0.428306i | \(-0.140890\pi\) | |||||||
\(108\) | 2.81862e36 | + | 1.66500e36i | 0.705358 | + | 0.416665i | ||||
\(109\) | 1.76879e36 | 0.374972 | 0.187486 | − | 0.982267i | \(-0.439966\pi\) | ||||
0.187486 | + | 0.982267i | \(0.439966\pi\) | |||||||
\(110\) | 3.90116e36 | + | 6.83544e36i | 0.701658 | + | 1.22941i | ||||
\(111\) | 2.33654e36i | 0.357074i | ||||||||
\(112\) | 1.03386e37 | − | 5.69736e36i | 1.34443 | − | 0.740883i | ||||
\(113\) | −9.72750e36 | −1.07793 | −0.538963 | − | 0.842329i | \(-0.681184\pi\) | ||||
−0.538963 | + | 0.842329i | \(0.681184\pi\) | |||||||
\(114\) | −7.61886e36 | + | 4.34828e36i | −0.720448 | + | 0.411178i | ||||
\(115\) | − | 5.23155e36i | − | 0.422736i | ||||||
\(116\) | −1.59240e36 | + | 2.69571e36i | −0.110105 | + | 0.186393i | ||||
\(117\) | 2.04646e37 | 1.21243 | ||||||||
\(118\) | −7.06309e36 | − | 1.23756e37i | −0.359020 | − | 0.629059i | ||||
\(119\) | 2.15096e37i | 0.939262i | ||||||||
\(120\) | −1.77349e37 | − | 2.65114e35i | −0.666140 | − | 0.00995795i | ||||
\(121\) | 1.70307e36 | 0.0550930 | ||||||||
\(122\) | 8.39728e36 | − | 4.79255e36i | 0.234240 | − | 0.133687i | ||||
\(123\) | 5.15997e35i | 0.0124267i | ||||||||
\(124\) | −2.96625e37 | − | 1.75221e37i | −0.617473 | − | 0.364750i | ||||
\(125\) | 9.74991e36 | 0.175639 | ||||||||
\(126\) | −3.85484e37 | − | 6.75428e37i | −0.601641 | − | 1.05417i | ||||
\(127\) | − | 1.66370e37i | − | 0.225220i | −0.993639 | − | 0.112610i | \(-0.964079\pi\) | ||
0.993639 | − | 0.112610i | \(-0.0359211\pi\) | |||||||
\(128\) | 7.51117e37 | − | 3.99404e37i | 0.882934 | − | 0.469497i | ||||
\(129\) | −1.09990e37 | −0.112392 | ||||||||
\(130\) | −2.18086e38 | + | 1.24467e38i | −1.93931 | + | 1.10682i | ||||
\(131\) | − | 6.71691e37i | − | 0.520339i | −0.965563 | − | 0.260169i | \(-0.916222\pi\) | ||
0.965563 | − | 0.260169i | \(-0.0837784\pi\) | |||||||
\(132\) | 3.34803e37 | − | 5.66777e37i | 0.226182 | − | 0.382896i | ||||
\(133\) | 4.71955e38 | 2.78337 | ||||||||
\(134\) | −1.21236e38 | − | 2.12425e38i | −0.624807 | − | 1.09476i | ||||
\(135\) | 2.64634e38i | 1.19299i | ||||||||
\(136\) | −2.31696e36 | + | 1.54994e38i | −0.00914573 | + | 0.611806i | ||||
\(137\) | −3.97555e38 | −1.37539 | −0.687696 | − | 0.725998i | \(-0.741378\pi\) | ||||
−0.687696 | + | 0.725998i | \(0.741378\pi\) | |||||||
\(138\) | −3.80031e37 | + | 2.16893e37i | −0.115344 | + | 0.0658298i | ||||
\(139\) | 6.21549e38i | 1.65657i | 0.560310 | + | 0.828283i | \(0.310682\pi\) | ||||
−0.560310 | + | 0.828283i | \(0.689318\pi\) | |||||||
\(140\) | 8.21604e38 | + | 4.85334e38i | 1.92468 | + | 1.13694i | ||||
\(141\) | 8.70891e37 | 0.179482 | ||||||||
\(142\) | 1.87409e38 | + | 3.28369e38i | 0.340094 | + | 0.595898i | ||||
\(143\) | − | 9.31940e38i | − | 1.49052i | ||||||
\(144\) | −2.70497e38 | − | 4.90852e38i | −0.381625 | − | 0.692510i | ||||
\(145\) | −2.53094e38 | −0.315251 | ||||||||
\(146\) | −5.54790e38 | + | 3.16633e38i | −0.610629 | + | 0.348502i | ||||
\(147\) | − | 6.37504e38i | − | 0.620542i | ||||||
\(148\) | 4.60752e38 | − | 7.79990e38i | 0.396968 | − | 0.672014i | ||||
\(149\) | −2.03376e39 | −1.55220 | −0.776099 | − | 0.630612i | \(-0.782804\pi\) | ||||
−0.776099 | + | 0.630612i | \(0.782804\pi\) | |||||||
\(150\) | −3.75562e38 | − | 6.58043e38i | −0.254120 | − | 0.445258i | ||||
\(151\) | − | 8.29777e38i | − | 0.498169i | −0.968482 | − | 0.249084i | \(-0.919870\pi\) | ||
0.968482 | − | 0.249084i | \(-0.0801297\pi\) | |||||||
\(152\) | 3.40081e39 | + | 5.08378e37i | 1.81300 | + | 0.0271021i | ||||
\(153\) | 1.02122e39 | 0.483810 | ||||||||
\(154\) | −3.07585e39 | + | 1.75547e39i | −1.29596 | + | 0.739638i | ||||
\(155\) | − | 2.78494e39i | − | 1.04435i | ||||||
\(156\) | 1.80831e39 | + | 1.06820e39i | 0.603992 | + | 0.356787i | ||||
\(157\) | −5.73764e39 | −1.70820 | −0.854102 | − | 0.520106i | \(-0.825893\pi\) | ||||
−0.854102 | + | 0.520106i | \(0.825893\pi\) | |||||||
\(158\) | −6.39809e38 | − | 1.12105e39i | −0.169912 | − | 0.297711i | ||||
\(159\) | 7.71201e37i | 0.0182818i | ||||||||
\(160\) | 5.86804e39 | + | 3.58572e39i | 1.24261 | + | 0.759305i | ||||
\(161\) | 2.35412e39 | 0.445619 | ||||||||
\(162\) | −2.13325e39 | + | 1.21750e39i | −0.361220 | + | 0.206157i | ||||
\(163\) | 1.05702e40i | 1.60217i | 0.598553 | + | 0.801083i | \(0.295743\pi\) | ||||
−0.598553 | + | 0.801083i | \(0.704257\pi\) | |||||||
\(164\) | 1.01752e38 | − | 1.72252e38i | 0.0138151 | − | 0.0233870i | ||||
\(165\) | 5.32132e39 | 0.647603 | ||||||||
\(166\) | −4.21699e39 | − | 7.38881e39i | −0.460317 | − | 0.806546i | ||||
\(167\) | 5.72510e39i | 0.560902i | 0.959868 | + | 0.280451i | \(0.0904839\pi\) | ||||
−0.959868 | + | 0.280451i | \(0.909516\pi\) | |||||||
\(168\) | 1.19297e38 | − | 7.98043e39i | 0.0104970 | − | 0.702198i | ||||
\(169\) | 1.70876e40 | 1.35120 | ||||||||
\(170\) | −1.08829e40 | + | 6.21118e39i | −0.773866 | + | 0.441666i | ||||
\(171\) | − | 2.24073e40i | − | 1.43370i | ||||||
\(172\) | 3.67171e39 | + | 2.16893e39i | 0.211523 | + | 0.124949i | ||||
\(173\) | 3.94413e39 | 0.204701 | 0.102351 | − | 0.994748i | \(-0.467364\pi\) | ||||
0.102351 | + | 0.994748i | \(0.467364\pi\) | |||||||
\(174\) | 1.04929e39 | + | 1.83852e39i | 0.0490919 | + | 0.0860167i | ||||
\(175\) | 4.07628e40i | 1.72020i | ||||||||
\(176\) | −2.23530e40 | + | 1.23182e40i | −0.851350 | + | 0.469158i | ||||
\(177\) | −9.63431e39 | −0.331361 | ||||||||
\(178\) | −2.06895e40 | + | 1.18081e40i | −0.642970 | + | 0.366960i | ||||
\(179\) | − | 1.65711e40i | − | 0.465584i | −0.972527 | − | 0.232792i | \(-0.925214\pi\) | ||
0.972527 | − | 0.232792i | \(-0.0747861\pi\) | |||||||
\(180\) | 2.30425e40 | − | 3.90078e40i | 0.585630 | − | 0.991394i | ||||
\(181\) | 1.17619e40 | 0.270560 | 0.135280 | − | 0.990807i | \(-0.456807\pi\) | ||||
0.135280 | + | 0.990807i | \(0.456807\pi\) | |||||||
\(182\) | −5.60086e40 | − | 9.81357e40i | −1.16673 | − | 2.04429i | ||||
\(183\) | − | 6.53721e39i | − | 0.123388i | ||||||
\(184\) | 1.69633e40 | + | 2.53581e38i | 0.290262 | + | 0.00433905i | ||||
\(185\) | 7.32313e40 | 1.13660 | ||||||||
\(186\) | −2.02304e40 | + | 1.15460e40i | −0.284952 | + | 0.162629i | ||||
\(187\) | − | 4.65057e40i | − | 0.594781i | ||||||
\(188\) | −2.90724e40 | − | 1.71735e40i | −0.337784 | − | 0.199534i | ||||
\(189\) | −1.19081e41 | −1.25757 | ||||||||
\(190\) | 1.36283e41 | + | 2.38789e41i | 1.30881 | + | 2.29324i | ||||
\(191\) | 3.43456e39i | 0.0300103i | 0.999887 | + | 0.0150052i | \(0.00477647\pi\) | ||||
−0.999887 | + | 0.0150052i | \(0.995224\pi\) | |||||||
\(192\) | 1.71927e39 | − | 5.74925e40i | 0.0136748 | − | 0.457288i | ||||
\(193\) | −1.70230e41 | −1.23312 | −0.616560 | − | 0.787308i | \(-0.711474\pi\) | ||||
−0.616560 | + | 0.787308i | \(0.711474\pi\) | |||||||
\(194\) | 2.50823e41 | − | 1.43151e41i | 1.65553 | − | 0.944852i | ||||
\(195\) | 1.69778e41i | 1.02155i | ||||||||
\(196\) | −1.25712e41 | + | 2.12814e41i | −0.689871 | + | 1.16786i | ||||
\(197\) | 2.06546e41 | 1.03425 | 0.517124 | − | 0.855911i | \(-0.327003\pi\) | ||||
0.517124 | + | 0.855911i | \(0.327003\pi\) | |||||||
\(198\) | 8.33452e40 | + | 1.46034e41i | 0.380984 | + | 0.667544i | ||||
\(199\) | − | 1.76694e41i | − | 0.737677i | −0.929493 | − | 0.368839i | \(-0.879755\pi\) | ||
0.929493 | − | 0.368839i | \(-0.120245\pi\) | |||||||
\(200\) | −4.39088e39 | + | 2.93729e41i | −0.0167499 | + | 1.12049i | ||||
\(201\) | −1.65371e41 | −0.576672 | ||||||||
\(202\) | 1.41653e41 | − | 8.08448e40i | 0.451752 | − | 0.257826i | ||||
\(203\) | − | 1.13888e41i | − | 0.332316i | ||||||
\(204\) | 9.02386e40 | + | 5.33052e40i | 0.241018 | + | 0.142373i | ||||
\(205\) | 1.61723e40 | 0.0395551 | ||||||||
\(206\) | −1.25921e41 | − | 2.20634e41i | −0.282156 | − | 0.494381i | ||||
\(207\) | − | 1.11768e41i | − | 0.229536i | ||||||
\(208\) | −3.93015e41 | − | 7.13179e41i | −0.740065 | − | 1.34295i | ||||
\(209\) | −1.02041e42 | −1.76255 | ||||||||
\(210\) | 5.60349e41 | − | 3.19806e41i | 0.888201 | − | 0.506919i | ||||
\(211\) | − | 5.79120e41i | − | 0.842721i | −0.906893 | − | 0.421361i | \(-0.861553\pi\) | ||
0.906893 | − | 0.421361i | \(-0.138447\pi\) | |||||||
\(212\) | 1.52076e40 | − | 2.57445e40i | 0.0203243 | − | 0.0344064i | ||||
\(213\) | 2.55632e41 | 0.313893 | ||||||||
\(214\) | 3.76212e41 | + | 6.59181e41i | 0.424605 | + | 0.743973i | ||||
\(215\) | 3.44728e41i | 0.357754i | ||||||||
\(216\) | −8.58076e41 | − | 1.28271e40i | −0.819140 | − | 0.0122451i | ||||
\(217\) | 1.25318e42 | 1.10088 | ||||||||
\(218\) | −4.02706e41 | + | 2.29835e41i | −0.325665 | + | 0.185866i | ||||
\(219\) | 4.31899e41i | 0.321653i | ||||||||
\(220\) | −1.77638e42 | − | 1.04933e42i | −1.21879 | − | 0.719956i | ||||
\(221\) | 1.48378e42 | 0.938226 | ||||||||
\(222\) | −3.03608e41 | − | 5.31967e41i | −0.176994 | − | 0.310121i | ||||
\(223\) | 3.33880e42i | 1.79516i | 0.440854 | + | 0.897579i | \(0.354676\pi\) | ||||
−0.440854 | + | 0.897579i | \(0.645324\pi\) | |||||||
\(224\) | −1.61352e42 | + | 2.64053e42i | −0.800406 | + | 1.30987i | ||||
\(225\) | 1.93532e42 | 0.886069 | ||||||||
\(226\) | 2.21470e42 | − | 1.26398e42i | 0.936186 | − | 0.534306i | ||||
\(227\) | − | 2.18249e42i | − | 0.852094i | −0.904701 | − | 0.426047i | \(-0.859906\pi\) | ||
0.904701 | − | 0.426047i | \(-0.140094\pi\) | |||||||
\(228\) | 1.16960e42 | − | 1.97998e42i | 0.421901 | − | 0.714221i | ||||
\(229\) | −4.96346e41 | −0.165480 | −0.0827401 | − | 0.996571i | \(-0.526367\pi\) | ||||
−0.0827401 | + | 0.996571i | \(0.526367\pi\) | |||||||
\(230\) | 6.79784e41 | + | 1.19109e42i | 0.209541 | + | 0.367149i | ||||
\(231\) | 2.39452e42i | 0.682657i | ||||||||
\(232\) | 1.22678e40 | − | 8.20657e41i | 0.00323581 | − | 0.216460i | ||||
\(233\) | 9.17240e40 | 0.0223912 | 0.0111956 | − | 0.999937i | \(-0.496436\pi\) | ||||
0.0111956 | + | 0.999937i | \(0.496436\pi\) | |||||||
\(234\) | −4.65924e42 | + | 2.65915e42i | −1.05300 | + | 0.600976i | ||||
\(235\) | − | 2.72953e42i | − | 0.571304i | ||||||
\(236\) | 3.21616e42 | + | 1.89983e42i | 0.623622 | + | 0.368383i | ||||
\(237\) | −8.72723e41 | −0.156822 | ||||||||
\(238\) | −2.79494e42 | − | 4.89717e42i | −0.465572 | − | 0.815755i | ||||
\(239\) | 1.35213e42i | 0.208861i | 0.994532 | + | 0.104431i | \(0.0333020\pi\) | ||||
−0.994532 | + | 0.104431i | \(0.966698\pi\) | |||||||
\(240\) | 4.07221e42 | − | 2.24410e42i | 0.583482 | − | 0.321543i | ||||
\(241\) | 2.74106e42 | 0.364428 | 0.182214 | − | 0.983259i | \(-0.441674\pi\) | ||||
0.182214 | + | 0.983259i | \(0.441674\pi\) | |||||||
\(242\) | −3.87744e41 | + | 2.21296e41i | −0.0478486 | + | 0.0273084i | ||||
\(243\) | 8.81094e42i | 1.00951i | ||||||||
\(244\) | −1.28910e42 | + | 2.18227e42i | −0.137173 | + | 0.232216i | ||||
\(245\) | −1.99806e43 | −1.97523 | ||||||||
\(246\) | −6.70483e40 | − | 1.17479e41i | −0.00615965 | − | 0.0107927i | ||||
\(247\) | − | 3.25564e43i | − | 2.78030i | ||||||
\(248\) | 9.03019e42 | + | 1.34990e41i | 0.717078 | + | 0.0107194i | ||||
\(249\) | −5.75212e42 | −0.424854 | ||||||||
\(250\) | −2.21980e42 | + | 1.26690e42i | −0.152543 | + | 0.0870604i | ||||
\(251\) | − | 1.24102e43i | − | 0.793690i | −0.917886 | − | 0.396845i | \(-0.870105\pi\) | ||
0.917886 | − | 0.396845i | \(-0.129895\pi\) | |||||||
\(252\) | 1.75529e43 | + | 1.03688e43i | 1.04506 | + | 0.617330i | ||||
\(253\) | −5.08983e42 | −0.282185 | ||||||||
\(254\) | 2.16179e42 | + | 3.78780e42i | 0.111637 | + | 0.195605i | ||||
\(255\) | 8.47227e42i | 0.407640i | ||||||||
\(256\) | −1.19111e43 | + | 1.88533e43i | −0.534114 | + | 0.845413i | ||||
\(257\) | 1.46390e43 | 0.611950 | 0.305975 | − | 0.952039i | \(-0.401018\pi\) | ||||
0.305975 | + | 0.952039i | \(0.401018\pi\) | |||||||
\(258\) | 2.50417e42 | − | 1.42920e42i | 0.0976135 | − | 0.0557105i | ||||
\(259\) | 3.29530e43i | 1.19812i | ||||||||
\(260\) | 3.34793e43 | − | 5.66759e43i | 1.13568 | − | 1.92255i | ||||
\(261\) | −5.40714e42 | −0.171174 | ||||||||
\(262\) | 8.72790e42 | + | 1.52926e43i | 0.257921 | + | 0.451917i | ||||
\(263\) | 3.20359e43i | 0.883961i | 0.897025 | + | 0.441981i | \(0.145724\pi\) | ||||
−0.897025 | + | 0.441981i | \(0.854276\pi\) | |||||||
\(264\) | −2.57932e41 | + | 1.72544e43i | −0.00664713 | + | 0.444661i | ||||
\(265\) | 2.41709e42 | 0.0581924 | ||||||||
\(266\) | −1.07452e44 | + | 6.13254e43i | −2.41737 | + | 1.37966i | ||||
\(267\) | 1.61066e43i | 0.338689i | ||||||||
\(268\) | 5.52046e43 | + | 3.26101e43i | 1.08530 | + | 0.641101i | ||||
\(269\) | 8.67222e43 | 1.59437 | 0.797186 | − | 0.603734i | \(-0.206321\pi\) | ||||
0.797186 | + | 0.603734i | \(0.206321\pi\) | |||||||
\(270\) | −3.43863e43 | − | 6.02501e43i | −0.591340 | − | 1.03612i | ||||
\(271\) | − | 2.10087e43i | − | 0.338028i | −0.985614 | − | 0.169014i | \(-0.945942\pi\) | ||
0.985614 | − | 0.169014i | \(-0.0540582\pi\) | |||||||
\(272\) | −1.96123e43 | − | 3.55891e43i | −0.295316 | − | 0.535891i | ||||
\(273\) | −7.63977e43 | −1.07684 | ||||||||
\(274\) | 9.05127e43 | − | 5.16580e43i | 1.19454 | − | 0.681753i | ||||
\(275\) | − | 8.81329e43i | − | 1.08931i | ||||||
\(276\) | 5.83400e42 | − | 9.87618e42i | 0.0675465 | − | 0.114347i | ||||
\(277\) | 6.95926e43 | 0.754965 | 0.377483 | − | 0.926017i | \(-0.376790\pi\) | ||||
0.377483 | + | 0.926017i | \(0.376790\pi\) | |||||||
\(278\) | −8.07636e43 | − | 1.41510e44i | −0.821125 | − | 1.43874i | ||||
\(279\) | − | 5.94981e43i | − | 0.567058i | ||||||
\(280\) | −2.50122e44 | − | 3.73900e42i | −2.23515 | − | 0.0334127i | ||||
\(281\) | 1.66599e43 | 0.139623 | 0.0698116 | − | 0.997560i | \(-0.477760\pi\) | ||||
0.0698116 | + | 0.997560i | \(0.477760\pi\) | |||||||
\(282\) | −1.98279e43 | + | 1.13163e43i | −0.155881 | + | 0.0889652i | ||||
\(283\) | 2.44437e44i | 1.80306i | 0.432716 | + | 0.901530i | \(0.357555\pi\) | ||||
−0.432716 | + | 0.901530i | \(0.642445\pi\) | |||||||
\(284\) | −8.53360e43 | − | 5.04092e43i | −0.590748 | − | 0.348963i | ||||
\(285\) | 1.85895e44 | 1.20798 | ||||||||
\(286\) | 1.21096e44 | + | 2.12178e44i | 0.738822 | + | 1.29453i | ||||
\(287\) | 7.27731e42i | 0.0416962i | ||||||||
\(288\) | 1.25366e44 | + | 7.66060e43i | 0.674707 | + | 0.412286i | ||||
\(289\) | −1.23727e44 | −0.625609 | ||||||||
\(290\) | 5.76227e43 | − | 3.28868e43i | 0.273798 | − | 0.156263i | ||||
\(291\) | − | 1.95263e44i | − | 0.872061i | ||||||
\(292\) | 8.51680e43 | − | 1.44178e44i | 0.357590 | − | 0.605351i | ||||
\(293\) | −3.79928e44 | −1.49998 | −0.749989 | − | 0.661451i | \(-0.769941\pi\) | ||||
−0.749989 | + | 0.661451i | \(0.769941\pi\) | |||||||
\(294\) | 8.28368e43 | + | 1.45143e44i | 0.307589 | + | 0.538944i | ||||
\(295\) | 3.01957e44i | 1.05475i | ||||||||
\(296\) | −3.54962e42 | + | 2.37453e44i | −0.0116663 | + | 0.780417i | ||||
\(297\) | 2.57464e44 | 0.796345 | ||||||||
\(298\) | 4.63033e44 | − | 2.64265e44i | 1.34809 | − | 0.769391i | ||||
\(299\) | − | 1.62392e44i | − | 0.445127i | ||||||
\(300\) | 1.71011e44 | + | 1.01019e44i | 0.441410 | + | 0.260747i | ||||
\(301\) | −1.55123e44 | −0.377119 | ||||||||
\(302\) | 1.07821e44 | + | 1.88918e44i | 0.246932 | + | 0.432663i | ||||
\(303\) | − | 1.10275e44i | − | 0.237964i | ||||||
\(304\) | −7.80880e44 | + | 4.30324e44i | −1.58803 | + | 0.875127i | ||||
\(305\) | −2.04888e44 | −0.392753 | ||||||||
\(306\) | −2.32506e44 | + | 1.32697e44i | −0.420192 | + | 0.239814i | ||||
\(307\) | − | 2.56547e44i | − | 0.437196i | −0.975815 | − | 0.218598i | \(-0.929852\pi\) | ||
0.975815 | − | 0.218598i | \(-0.0701483\pi\) | |||||||
\(308\) | 4.72185e44 | − | 7.99346e44i | 0.758926 | − | 1.28476i | ||||
\(309\) | −1.71761e44 | −0.260419 | ||||||||
\(310\) | 3.61873e44 | + | 6.34058e44i | 0.517662 | + | 0.907023i | ||||
\(311\) | − | 1.36571e45i | − | 1.84363i | −0.387634 | − | 0.921813i | \(-0.626708\pi\) | ||
0.387634 | − | 0.921813i | \(-0.373292\pi\) | |||||||
\(312\) | −5.50506e44 | − | 8.22937e42i | −0.701422 | − | 0.0104854i | ||||
\(313\) | 1.27288e43 | 0.0153105 | 0.00765526 | − | 0.999971i | \(-0.497563\pi\) | ||||
0.00765526 | + | 0.999971i | \(0.497563\pi\) | |||||||
\(314\) | 1.30631e45 | − | 7.45545e44i | 1.48359 | − | 0.846720i | ||||
\(315\) | 1.64800e45i | 1.76753i | ||||||||
\(316\) | 2.91335e44 | + | 1.72096e44i | 0.295139 | + | 0.174343i | ||||
\(317\) | −1.70217e45 | −1.62906 | −0.814530 | − | 0.580122i | \(-0.803005\pi\) | ||||
−0.814530 | + | 0.580122i | \(0.803005\pi\) | |||||||
\(318\) | −1.00209e43 | − | 1.75582e43i | −0.00906191 | − | 0.0158779i | ||||
\(319\) | 2.46237e44i | 0.210436i | ||||||||
\(320\) | −1.80192e45 | − | 5.38850e43i | −1.45558 | − | 0.0435279i | ||||
\(321\) | 5.13167e44 | 0.391893 | ||||||||
\(322\) | −5.35972e44 | + | 3.05893e44i | −0.387023 | + | 0.220884i | ||||
\(323\) | − | 1.62463e45i | − | 1.10945i | ||||||
\(324\) | 3.27484e44 | − | 5.54386e44i | 0.211534 | − | 0.358098i | ||||
\(325\) | 2.81190e45 | 1.71830 | ||||||||
\(326\) | −1.37349e45 | − | 2.40656e45i | −0.794160 | − | 1.39149i | ||||
\(327\) | 3.13503e44i | 0.171547i | ||||||||
\(328\) | −7.83894e41 | + | 5.24388e43i | −0.000406002 | + | 0.0271596i | ||||
\(329\) | 1.22825e45 | 0.602228 | ||||||||
\(330\) | −1.21152e45 | + | 6.91448e44i | −0.562447 | + | 0.321003i | ||||
\(331\) | 2.28914e45i | 1.00640i | 0.864171 | + | 0.503198i | \(0.167843\pi\) | ||||
−0.864171 | + | 0.503198i | \(0.832157\pi\) | |||||||
\(332\) | 1.92019e45 | + | 1.13429e45i | 0.799575 | + | 0.472321i | ||||
\(333\) | 1.56453e45 | 0.617146 | ||||||||
\(334\) | −7.43915e44 | − | 1.30345e45i | −0.278027 | − | 0.487146i | ||||
\(335\) | 5.18302e45i | 1.83559i | ||||||||
\(336\) | 1.00981e45 | + | 1.83244e45i | 0.338948 | + | 0.615066i | ||||
\(337\) | 1.62264e45 | 0.516277 | 0.258139 | − | 0.966108i | \(-0.416891\pi\) | ||||
0.258139 | + | 0.966108i | \(0.416891\pi\) | |||||||
\(338\) | −3.89039e45 | + | 2.22034e45i | −1.17352 | + | 0.669761i | ||||
\(339\) | − | 1.72412e45i | − | 0.493143i | ||||||
\(340\) | 1.67068e45 | − | 2.82824e45i | 0.453183 | − | 0.767178i | ||||
\(341\) | −2.70949e45 | −0.697123 | ||||||||
\(342\) | 2.91158e45 | + | 5.10154e45i | 0.710655 | + | 1.24518i | ||||
\(343\) | − | 2.36241e45i | − | 0.547092i | ||||||
\(344\) | −1.11778e45 | − | 1.67094e43i | −0.245643 | − | 0.00367206i | ||||
\(345\) | 9.27250e44 | 0.193398 | ||||||||
\(346\) | −8.97973e44 | + | 5.12497e44i | −0.177784 | + | 0.101466i | ||||
\(347\) | − | 4.94592e45i | − | 0.929643i | −0.885404 | − | 0.464821i | \(-0.846119\pi\) | ||
0.885404 | − | 0.464821i | \(-0.153881\pi\) | |||||||
\(348\) | −4.77793e44 | − | 2.82239e44i | −0.0852733 | − | 0.0503722i | ||||
\(349\) | −1.07278e45 | −0.181824 | −0.0909120 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909120 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(350\) | −5.29669e45 | − | 9.28062e45i | −0.852668 | − | 1.49401i | ||||
\(351\) | 8.21447e45i | 1.25618i | ||||||||
\(352\) | 3.48858e45 | − | 5.70907e45i | 0.506851 | − | 0.829463i | ||||
\(353\) | −2.96408e45 | −0.409209 | −0.204605 | − | 0.978845i | \(-0.565591\pi\) | ||||
−0.204605 | + | 0.978845i | \(0.565591\pi\) | |||||||
\(354\) | 2.19348e45 | − | 1.25188e45i | 0.287789 | − | 0.164249i | ||||
\(355\) | − | 8.01198e45i | − | 0.999147i | ||||||
\(356\) | 3.17613e45 | − | 5.37677e45i | 0.376529 | − | 0.637413i | ||||
\(357\) | −3.81240e45 | −0.429705 | ||||||||
\(358\) | 2.15324e45 | + | 3.77281e45i | 0.230780 | + | 0.404362i | ||||
\(359\) | − | 1.60495e46i | − | 1.63592i | −0.575277 | − | 0.817959i | \(-0.695106\pi\) | ||
0.575277 | − | 0.817959i | \(-0.304894\pi\) | |||||||
\(360\) | −1.77519e44 | + | 1.18752e46i | −0.0172107 | + | 1.15132i | ||||
\(361\) | −2.48044e46 | −2.28770 | ||||||||
\(362\) | −2.67788e45 | + | 1.52833e45i | −0.234983 | + | 0.134111i | ||||
\(363\) | 3.01855e44i | 0.0252046i | ||||||||
\(364\) | 2.55033e46 | + | 1.50652e46i | 2.02662 | + | 1.19715i | ||||
\(365\) | 1.35365e46 | 1.02385 | ||||||||
\(366\) | 8.49440e44 | + | 1.48835e45i | 0.0611608 | + | 0.107163i | ||||
\(367\) | 1.32063e46i | 0.905296i | 0.891689 | + | 0.452648i | \(0.149521\pi\) | ||||
−0.891689 | + | 0.452648i | \(0.850479\pi\) | |||||||
\(368\) | −3.89505e45 | + | 2.14647e45i | −0.254245 | + | 0.140108i | ||||
\(369\) | 3.45509e44 | 0.0214775 | ||||||||
\(370\) | −1.66728e46 | + | 9.51562e45i | −0.987140 | + | 0.563386i | ||||
\(371\) | 1.08765e45i | 0.0613423i | ||||||||
\(372\) | 3.10565e45 | − | 5.25744e45i | 0.166870 | − | 0.282489i | ||||
\(373\) | 1.36447e46 | 0.698561 | 0.349281 | − | 0.937018i | \(-0.386426\pi\) | ||||
0.349281 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(374\) | 6.04291e45 | + | 1.05881e46i | 0.294820 | + | 0.516571i | ||||
\(375\) | 1.72809e45i | 0.0803533i | ||||||||
\(376\) | 8.85053e45 | + | 1.32304e44i | 0.392272 | + | 0.00586398i | ||||
\(377\) | −7.85625e45 | −0.331949 | ||||||||
\(378\) | 2.71117e46 | − | 1.54733e46i | 1.09220 | − | 0.623349i | ||||
\(379\) | 4.54211e46i | 1.74483i | 0.488769 | + | 0.872413i | \(0.337446\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(380\) | −6.20561e46 | − | 3.66574e46i | −2.27342 | − | 1.34294i | ||||
\(381\) | 2.94876e45 | 0.103036 | ||||||||
\(382\) | −4.46284e44 | − | 7.81959e44i | −0.0148755 | − | 0.0260642i | ||||
\(383\) | − | 5.17389e46i | − | 1.64528i | −0.568564 | − | 0.822639i | \(-0.692501\pi\) | ||
0.568564 | − | 0.822639i | \(-0.307499\pi\) | |||||||
\(384\) | 7.07910e45 | + | 1.33129e46i | 0.214791 | + | 0.403935i | ||||
\(385\) | 7.50486e46 | 2.17295 | ||||||||
\(386\) | 3.87569e46 | − | 2.21196e46i | 1.07097 | − | 0.611231i | ||||
\(387\) | 7.36484e45i | 0.194252i | ||||||||
\(388\) | −3.85048e46 | + | 6.51835e46i | −0.969491 | + | 1.64122i | ||||
\(389\) | −7.75327e46 | −1.86377 | −0.931884 | − | 0.362755i | \(-0.881836\pi\) | ||||
−0.931884 | + | 0.362755i | \(0.881836\pi\) | |||||||
\(390\) | −2.20608e46 | − | 3.86540e46i | −0.506360 | − | 0.887220i | ||||
\(391\) | − | 8.10370e45i | − | 0.177624i | ||||||
\(392\) | 9.68484e44 | − | 6.47870e46i | 0.0202742 | − | 1.35625i | ||||
\(393\) | 1.19052e46 | 0.238051 | ||||||||
\(394\) | −4.70251e46 | + | 2.68384e46i | −0.898250 | + | 0.512655i | ||||
\(395\) | 2.73528e46i | 0.499176i | ||||||||
\(396\) | −3.79510e46 | − | 2.24182e46i | −0.661774 | − | 0.390920i | ||||
\(397\) | 1.56490e46 | 0.260770 | 0.130385 | − | 0.991463i | \(-0.458379\pi\) | ||||
0.130385 | + | 0.991463i | \(0.458379\pi\) | |||||||
\(398\) | 2.29595e46 | + | 4.02286e46i | 0.365651 | + | 0.640677i | ||||
\(399\) | 8.36500e46i | 1.27337i | ||||||||
\(400\) | −3.71672e46 | − | 6.74449e46i | −0.540854 | − | 0.981452i | ||||
\(401\) | 7.79235e46 | 1.08410 | 0.542051 | − | 0.840346i | \(-0.317648\pi\) | ||||
0.542051 | + | 0.840346i | \(0.317648\pi\) | |||||||
\(402\) | 3.76505e46 | − | 2.14881e46i | 0.500843 | − | 0.285844i | ||||
\(403\) | − | 8.64471e46i | − | 1.09966i | ||||||
\(404\) | −2.17456e46 | + | 3.68124e46i | −0.264550 | + | 0.447847i | ||||
\(405\) | 5.20499e46 | 0.605661 | ||||||||
\(406\) | 1.47986e46 | + | 2.59294e46i | 0.164722 | + | 0.288618i | ||||
\(407\) | − | 7.12474e46i | − | 0.758700i | ||||||
\(408\) | −2.74714e46 | − | 4.10662e44i | −0.279897 | − | 0.00418410i | ||||
\(409\) | −4.70283e46 | −0.458501 | −0.229250 | − | 0.973367i | \(-0.573627\pi\) | ||||
−0.229250 | + | 0.973367i | \(0.573627\pi\) | |||||||
\(410\) | −3.68201e45 | + | 2.10142e45i | −0.0343539 | + | 0.0196066i | ||||
\(411\) | − | 7.04633e46i | − | 0.629231i | ||||||
\(412\) | 5.73380e46 | + | 3.38704e46i | 0.490109 | + | 0.289514i | ||||
\(413\) | −1.35876e47 | −1.11184 | ||||||||
\(414\) | 1.45231e46 | + | 2.54466e46i | 0.113776 | + | 0.199354i | ||||
\(415\) | 1.80282e47i | 1.35234i | ||||||||
\(416\) | 1.82149e47 | + | 1.11304e47i | 1.30842 | + | 0.799522i | ||||
\(417\) | −1.10164e47 | −0.757866 | ||||||||
\(418\) | 2.32320e47 | − | 1.32591e47i | 1.53078 | − | 0.873657i | ||||
\(419\) | 1.28693e47i | 0.812271i | 0.913813 | + | 0.406136i | \(0.133124\pi\) | ||||
−0.913813 | + | 0.406136i | \(0.866876\pi\) | |||||||
\(420\) | −8.60214e46 | + | 1.45623e47i | −0.520139 | + | 0.880525i | ||||
\(421\) | −9.75674e46 | −0.565232 | −0.282616 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282616 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(422\) | 7.52503e46 | + | 1.31850e47i | 0.417719 | + | 0.731908i | ||||
\(423\) | − | 5.83143e46i | − | 0.310205i | ||||||
\(424\) | −1.17159e44 | + | 7.83741e45i | −0.000597299 | + | 0.0399565i | ||||
\(425\) | 1.40320e47 | 0.685674 | ||||||||
\(426\) | −5.82007e46 | + | 3.32166e46i | −0.272618 | + | 0.155590i | ||||
\(427\) | − | 9.21967e46i | − | 0.414013i | ||||||
\(428\) | −1.71307e47 | − | 1.01194e47i | −0.737543 | − | 0.435677i | ||||
\(429\) | 1.65179e47 | 0.681903 | ||||||||
\(430\) | −4.47937e46 | − | 7.84854e46i | −0.177331 | − | 0.310711i | ||||
\(431\) | − | 3.43872e47i | − | 1.30559i | −0.757535 | − | 0.652794i | \(-0.773597\pi\) | ||
0.757535 | − | 0.652794i | \(-0.226403\pi\) | |||||||
\(432\) | 1.97028e47 | − | 1.08577e47i | 0.717497 | − | 0.395395i | ||||
\(433\) | −3.22358e47 | −1.12605 | −0.563023 | − | 0.826441i | \(-0.690362\pi\) | ||||
−0.563023 | + | 0.826441i | \(0.690362\pi\) | |||||||
\(434\) | −2.85317e47 | + | 1.62838e47i | −0.956119 | + | 0.545682i | ||||
\(435\) | − | 4.48587e46i | − | 0.144225i | ||||||
\(436\) | 6.18210e46 | − | 1.04655e47i | 0.190713 | − | 0.322851i | ||||
\(437\) | −1.77808e47 | −0.526363 | ||||||||
\(438\) | −5.61206e46 | − | 9.83319e46i | −0.159437 | − | 0.279358i | ||||
\(439\) | − | 1.85153e47i | − | 0.504857i | −0.967616 | − | 0.252428i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252428i | \(-0.0812292\pi\) | |||||||
\(440\) | 5.40785e47 | + | 8.08406e45i | 1.41539 | + | 0.0211583i | ||||
\(441\) | −4.26869e47 | −1.07251 | ||||||||
\(442\) | −3.37817e47 | + | 1.92801e47i | −0.814854 | + | 0.465058i | ||||
\(443\) | 3.20119e47i | 0.741386i | 0.928756 | + | 0.370693i | \(0.120880\pi\) | ||||
−0.928756 | + | 0.370693i | \(0.879120\pi\) | |||||||
\(444\) | 1.38247e47 | + | 8.16644e46i | 0.307441 | + | 0.181610i | ||||
\(445\) | 5.04811e47 | 1.07807 | ||||||||
\(446\) | −4.33841e47 | − | 7.60156e47i | −0.889822 | − | 1.55911i | ||||
\(447\) | − | 3.60467e47i | − | 0.710118i | ||||||
\(448\) | 2.42475e46 | − | 8.10839e47i | 0.0458841 | − | 1.53437i | ||||
\(449\) | 1.01672e48 | 1.84827 | 0.924136 | − | 0.382065i | \(-0.124787\pi\) | ||||
0.924136 | + | 0.382065i | \(0.124787\pi\) | |||||||
\(450\) | −4.40621e47 | + | 2.51474e47i | −0.769556 | + | 0.439206i | ||||
\(451\) | − | 1.57342e46i | − | 0.0264038i | ||||||
\(452\) | −3.39987e47 | + | 5.75552e47i | −0.548239 | + | 0.928095i | ||||
\(453\) | 1.47071e47 | 0.227908 | ||||||||
\(454\) | 2.83591e47 | + | 4.96896e47i | 0.422365 | + | 0.740048i | ||||
\(455\) | 2.39444e48i | 3.42768i | ||||||||
\(456\) | −9.01058e45 | + | 6.02765e47i | −0.0123990 | + | 0.829433i | ||||
\(457\) | −1.12133e47 | −0.148335 | −0.0741675 | − | 0.997246i | \(-0.523630\pi\) | ||||
−0.0741675 | + | 0.997246i | \(0.523630\pi\) | |||||||
\(458\) | 1.13005e47 | − | 6.44948e46i | 0.143720 | − | 0.0820250i | ||||
\(459\) | 4.09918e47i | 0.501267i | ||||||||
\(460\) | −3.09538e47 | − | 1.82848e47i | −0.363976 | − | 0.215006i | ||||
\(461\) | 1.02919e48 | 1.16380 | 0.581900 | − | 0.813260i | \(-0.302309\pi\) | ||||
0.581900 | + | 0.813260i | \(0.302309\pi\) | |||||||
\(462\) | −3.11142e47 | − | 5.45168e47i | −0.338378 | − | 0.592891i | ||||
\(463\) | − | 1.07221e48i | − | 1.12156i | −0.827966 | − | 0.560778i | \(-0.810502\pi\) | ||
0.827966 | − | 0.560778i | \(-0.189498\pi\) | |||||||
\(464\) | 1.03842e47 | + | 1.88436e47i | 0.104484 | + | 0.189601i | ||||
\(465\) | 4.93608e47 | 0.477781 | ||||||||
\(466\) | −2.08831e46 | + | 1.19185e46i | −0.0194469 | + | 0.0110988i | ||||
\(467\) | 2.64750e47i | 0.237210i | 0.992942 | + | 0.118605i | \(0.0378422\pi\) | ||||
−0.992942 | + | 0.118605i | \(0.962158\pi\) | |||||||
\(468\) | 7.15259e47 | − | 1.21084e48i | 0.616649 | − | 1.04390i | ||||
\(469\) | −2.33228e48 | −1.93495 | ||||||||
\(470\) | 3.54673e47 | + | 6.21443e47i | 0.283183 | + | 0.496181i | ||||
\(471\) | − | 1.01695e48i | − | 0.781489i | ||||||
\(472\) | −9.79098e47 | − | 1.46363e46i | −0.724219 | − | 0.0108262i | ||||
\(473\) | 3.35389e47 | 0.238808 | ||||||||
\(474\) | 1.98696e47 | − | 1.13401e47i | 0.136201 | − | 0.0777332i | ||||
\(475\) | − | 3.07883e48i | − | 2.03190i | ||||||
\(476\) | 1.27267e48 | + | 7.51783e47i | 0.808705 | + | 0.477714i | ||||
\(477\) | 5.16391e46 | 0.0315972 | ||||||||
\(478\) | −1.75695e47 | − | 3.07845e47i | −0.103528 | − | 0.181397i | ||||
\(479\) | 1.15049e48i | 0.652897i | 0.945215 | + | 0.326449i | \(0.105852\pi\) | ||||
−0.945215 | + | 0.326449i | \(0.894148\pi\) | |||||||
\(480\) | −6.35539e47 | + | 1.04006e48i | −0.347376 | + | 0.568482i | ||||
\(481\) | 2.27317e48 | 1.19680 | ||||||||
\(482\) | −6.24067e47 | + | 3.56171e47i | −0.316508 | + | 0.180639i | ||||
\(483\) | 4.17249e47i | 0.203867i | ||||||||
\(484\) | 5.95242e46 | − | 1.00766e47i | 0.0280206 | − | 0.0474351i | ||||
\(485\) | −6.11991e48 | −2.77584 | ||||||||
\(486\) | −1.14489e48 | − | 2.00602e48i | −0.500391 | − | 0.876762i | ||||
\(487\) | 2.97014e48i | 1.25099i | 0.780226 | + | 0.625497i | \(0.215104\pi\) | ||||
−0.780226 | + | 0.625497i | \(0.784896\pi\) | |||||||
\(488\) | 9.93121e45 | − | 6.64351e47i | 0.00403130 | − | 0.269675i | ||||
\(489\) | −1.87349e48 | −0.732978 | ||||||||
\(490\) | 4.54904e48 | − | 2.59626e48i | 1.71550 | − | 0.979080i | ||||
\(491\) | − | 3.36774e48i | − | 1.22425i | −0.790759 | − | 0.612127i | \(-0.790314\pi\) | ||
0.790759 | − | 0.612127i | \(-0.209686\pi\) | |||||||
\(492\) | 3.05303e46 | + | 1.80347e46i | 0.0106994 | + | 0.00632028i | ||||
\(493\) | −3.92043e47 | −0.132461 | ||||||||
\(494\) | 4.23035e48 | + | 7.41223e48i | 1.37813 | + | 2.41470i | ||||
\(495\) | − | 3.56313e48i | − | 1.11928i | ||||||
\(496\) | −2.07348e48 | + | 1.14264e48i | −0.628100 | + | 0.346131i | ||||
\(497\) | 3.60527e48 | 1.05323 | ||||||||
\(498\) | 1.30961e48 | − | 7.47426e47i | 0.368988 | − | 0.210591i | ||||
\(499\) | 4.09580e48i | 1.11309i | 0.830818 | + | 0.556544i | \(0.187873\pi\) | ||||
−0.830818 | + | 0.556544i | \(0.812127\pi\) | |||||||
\(500\) | 3.40770e47 | − | 5.76877e47i | 0.0893308 | − | 0.151225i | ||||
\(501\) | −1.01473e48 | −0.256608 | ||||||||
\(502\) | 1.61257e48 | + | 2.82547e48i | 0.393415 | + | 0.689325i | ||||
\(503\) | − | 4.07583e48i | − | 0.959383i | −0.877437 | − | 0.479692i | \(-0.840749\pi\) | ||
0.877437 | − | 0.479692i | \(-0.159251\pi\) | |||||||
\(504\) | −5.34365e48 | − | 7.98808e46i | −1.21364 | − | 0.0181423i | ||||
\(505\) | −3.45623e48 | −0.757456 | ||||||||
\(506\) | 1.15882e48 | − | 6.61368e47i | 0.245079 | − | 0.139873i | ||||
\(507\) | 3.02863e48i | 0.618163i | ||||||||
\(508\) | −9.84367e47 | − | 5.81480e47i | −0.193914 | − | 0.114548i | ||||
\(509\) | 8.39304e48 | 1.59588 | 0.797938 | − | 0.602740i | \(-0.205924\pi\) | ||||
0.797938 | + | 0.602740i | \(0.205924\pi\) | |||||||
\(510\) | −1.10088e48 | − | 1.92891e48i | −0.202058 | − | 0.354038i | ||||
\(511\) | 6.09123e48i | 1.07927i | ||||||||
\(512\) | 2.62064e47 | − | 5.84013e48i | 0.0448278 | − | 0.998995i | ||||
\(513\) | 8.99426e48 | 1.48543 | ||||||||
\(514\) | −3.33292e48 | + | 1.90218e48i | −0.531483 | + | 0.303331i | ||||
\(515\) | 5.38332e48i | 0.828934i | ||||||||
\(516\) | −3.84426e47 | + | 6.50781e47i | −0.0571633 | + | 0.0967699i | ||||
\(517\) | −2.65559e48 | −0.381356 | ||||||||
\(518\) | −4.28189e48 | − | 7.50254e48i | −0.593882 | − | 1.04057i | ||||
\(519\) | 6.99064e47i | 0.0936493i | ||||||||
\(520\) | −2.57924e47 | + | 1.72539e49i | −0.0333758 | + | 2.23268i | ||||
\(521\) | −2.34160e48 | −0.292708 | −0.146354 | − | 0.989232i | \(-0.546754\pi\) | ||||
−0.146354 | + | 0.989232i | \(0.546754\pi\) | |||||||
\(522\) | 1.23106e48 | − | 7.02600e47i | 0.148666 | − | 0.0848475i | ||||
\(523\) | − | 8.19584e48i | − | 0.956232i | −0.878297 | − | 0.478116i | \(-0.841320\pi\) | ||
0.878297 | − | 0.478116i | \(-0.158680\pi\) | |||||||
\(524\) | −3.97423e48 | − | 2.34763e48i | −0.448012 | − | 0.264647i | ||||
\(525\) | −7.22488e48 | −0.786979 | ||||||||
\(526\) | −4.16272e48 | − | 7.29372e48i | −0.438161 | − | 0.767725i | ||||
\(527\) | − | 4.31389e48i | − | 0.438811i | ||||||
\(528\) | −2.18330e48 | − | 3.96189e48i | −0.214636 | − | 0.389486i | ||||
\(529\) | 9.63760e48 | 0.915729 | ||||||||
\(530\) | −5.50307e47 | + | 3.14074e47i | −0.0505405 | + | 0.0288447i | ||||
\(531\) | 6.45108e48i | 0.572705i | ||||||||
\(532\) | 1.64953e49 | − | 2.79244e49i | 1.41564 | − | 2.39648i | ||||
\(533\) | 5.02003e47 | 0.0416502 | ||||||||
\(534\) | −2.09288e48 | − | 3.66705e48i | −0.167881 | − | 0.294154i | ||||
\(535\) | − | 1.60836e49i | − | 1.24743i | ||||||
\(536\) | −1.68060e49 | − | 2.51228e47i | −1.26037 | − | 0.0188409i | ||||
\(537\) | 2.93710e48 | 0.213001 | ||||||||
\(538\) | −1.97444e49 | + | 1.12686e49i | −1.38472 | + | 0.790296i | ||||
\(539\) | 1.94393e49i | 1.31851i | ||||||||
\(540\) | 1.56577e49 | + | 9.24923e48i | 1.02717 | + | 0.606761i | ||||
\(541\) | −8.30545e48 | −0.527002 | −0.263501 | − | 0.964659i | \(-0.584877\pi\) | ||||
−0.263501 | + | 0.964659i | \(0.584877\pi\) | |||||||
\(542\) | 2.72986e48 | + | 4.78313e48i | 0.167553 | + | 0.293579i | ||||
\(543\) | 2.08470e48i | 0.123779i | ||||||||
\(544\) | 9.08961e48 | + | 5.55429e48i | 0.522114 | + | 0.319042i | ||||
\(545\) | 9.82576e48 | 0.546046 | ||||||||
\(546\) | 1.73937e49 | − | 9.92705e48i | 0.935245 | − | 0.533768i | ||||
\(547\) | − | 1.87034e49i | − | 0.973080i | −0.873658 | − | 0.486540i | \(-0.838259\pi\) | ||
0.873658 | − | 0.486540i | \(-0.161741\pi\) | |||||||
\(548\) | −1.38950e49 | + | 2.35223e49i | −0.699532 | + | 1.18421i | ||||
\(549\) | −4.37727e48 | −0.213256 | ||||||||
\(550\) | 1.14519e49 | + | 2.00655e49i | 0.539946 | + | 0.946068i | ||||
\(551\) | 8.60204e48i | 0.392530i | ||||||||
\(552\) | −4.49451e46 | + | 3.00661e48i | −0.00198508 | + | 0.132793i | ||||
\(553\) | −1.23083e49 | −0.526196 | ||||||||
\(554\) | −1.58444e49 | + | 9.04280e48i | −0.655692 | + | 0.374220i | ||||
\(555\) | 1.29797e49i | 0.519983i | ||||||||
\(556\) | 3.67755e49 | + | 2.17238e49i | 1.42630 | + | 0.842538i | ||||
\(557\) | −2.22627e49 | −0.835957 | −0.417979 | − | 0.908457i | \(-0.637261\pi\) | ||||
−0.417979 | + | 0.908457i | \(0.637261\pi\) | |||||||
\(558\) | 7.73113e48 | + | 1.35461e49i | 0.281079 | + | 0.492493i | ||||
\(559\) | 1.07007e49i | 0.376702i | ||||||||
\(560\) | 5.74319e49 | − | 3.16493e49i | 1.95780 | − | 1.07890i | ||||
\(561\) | 8.24275e48 | 0.272108 | ||||||||
\(562\) | −3.79301e48 | + | 2.16477e48i | −0.121264 | + | 0.0692082i | ||||
\(563\) | − | 5.58851e49i | − | 1.73039i | −0.501433 | − | 0.865197i | \(-0.667194\pi\) | ||
0.501433 | − | 0.865197i | \(-0.332806\pi\) | |||||||
\(564\) | 3.04386e48 | − | 5.15284e48i | 0.0912852 | − | 0.154534i | ||||
\(565\) | −5.40371e49 | −1.56971 | ||||||||
\(566\) | −3.17619e49 | − | 5.56518e49i | −0.893739 | − | 1.56597i | ||||
\(567\) | 2.34217e49i | 0.638444i | ||||||||
\(568\) | 2.59789e49 | + | 3.88351e47i | 0.686041 | + | 0.0102555i | ||||
\(569\) | 2.83847e49 | 0.726213 | 0.363106 | − | 0.931748i | \(-0.381716\pi\) | ||||
0.363106 | + | 0.931748i | \(0.381716\pi\) | |||||||
\(570\) | −4.23234e49 | + | 2.41551e49i | −1.04914 | + | 0.598771i | ||||
\(571\) | − | 1.22959e49i | − | 0.295333i | −0.989037 | − | 0.147666i | \(-0.952824\pi\) | ||
0.989037 | − | 0.147666i | \(-0.0471762\pi\) | |||||||
\(572\) | −5.51405e49 | − | 3.25723e49i | −1.28334 | − | 0.758088i | ||||
\(573\) | −6.08748e47 | −0.0137295 | ||||||||
\(574\) | −9.45608e47 | − | 1.65685e48i | −0.0206679 | − | 0.0362134i | ||||
\(575\) | − | 1.53573e49i | − | 0.325308i | ||||||
\(576\) | −3.84967e49 | − | 1.15121e48i | −0.790348 | − | 0.0236347i | ||||
\(577\) | 5.25738e49 | 1.04618 | 0.523088 | − | 0.852279i | \(-0.324780\pi\) | ||||
0.523088 | + | 0.852279i | \(0.324780\pi\) | |||||||
\(578\) | 2.81694e49 | − | 1.60770e49i | 0.543345 | − | 0.310101i | ||||
\(579\) | − | 3.01719e49i | − | 0.564142i | ||||||
\(580\) | −8.84589e48 | + | 1.49749e49i | −0.160338 | + | 0.271431i | ||||
\(581\) | −8.11243e49 | −1.42554 | ||||||||
\(582\) | 2.53724e49 | + | 4.44563e49i | 0.432262 | + | 0.757390i | ||||
\(583\) | − | 2.35160e48i | − | 0.0388446i | ||||||
\(584\) | −6.56133e47 | + | 4.38922e49i | −0.0105090 | + | 0.703001i | ||||
\(585\) | 1.13682e50 | 1.76558 | ||||||||
\(586\) | 8.64997e49 | − | 4.93676e49i | 1.30274 | − | 0.743507i | ||||
\(587\) | 5.78785e49i | 0.845340i | 0.906284 | + | 0.422670i | \(0.138907\pi\) | ||||
−0.906284 | + | 0.422670i | \(0.861093\pi\) | |||||||
\(588\) | −3.77195e49 | − | 2.22814e49i | −0.534286 | − | 0.315611i | ||||
\(589\) | −9.46535e49 | −1.30035 | ||||||||
\(590\) | −3.92361e49 | − | 6.87477e49i | −0.522817 | − | 0.916056i | ||||
\(591\) | 3.66086e49i | 0.473160i | ||||||||
\(592\) | −3.00463e49 | − | 5.45230e49i | −0.376704 | − | 0.683580i | ||||
\(593\) | 1.05326e50 | 1.28100 | 0.640502 | − | 0.767956i | \(-0.278726\pi\) | ||||
0.640502 | + | 0.767956i | \(0.278726\pi\) | |||||||
\(594\) | −5.86178e49 | + | 3.34547e49i | −0.691630 | + | 0.394731i | ||||
\(595\) | 1.19488e50i | 1.36778i | ||||||||
\(596\) | −7.10821e49 | + | 1.20332e50i | −0.789455 | + | 1.33644i | ||||
\(597\) | 3.13176e49 | 0.337481 | ||||||||
\(598\) | 2.11011e49 | + | 3.69724e49i | 0.220640 | + | 0.386595i | ||||
\(599\) | − | 1.30983e50i | − | 1.32902i | −0.747278 | − | 0.664511i | \(-0.768640\pi\) | ||
0.747278 | − | 0.664511i | \(-0.231360\pi\) | |||||||
\(600\) | −5.20610e49 | − | 7.78246e47i | −0.512614 | − | 0.00766293i | ||||
\(601\) | 1.73160e50 | 1.65466 | 0.827329 | − | 0.561718i | \(-0.189859\pi\) | ||||
0.827329 | + | 0.561718i | \(0.189859\pi\) | |||||||
\(602\) | 3.53173e49 | − | 2.01565e49i | 0.327530 | − | 0.186930i | ||||
\(603\) | 1.10731e50i | 0.996685i | ||||||||
\(604\) | −4.90958e49 | − | 2.90016e49i | −0.428923 | − | 0.253371i | ||||
\(605\) | 9.46071e48 | 0.0802282 | ||||||||
\(606\) | 1.43291e49 | + | 2.51067e49i | 0.117953 | + | 0.206673i | ||||
\(607\) | 9.98769e49i | 0.798121i | 0.916925 | + | 0.399060i | \(0.130664\pi\) | ||||
−0.916925 | + | 0.399060i | \(0.869336\pi\) | |||||||
\(608\) | 1.21870e50 | − | 1.99440e50i | 0.945436 | − | 1.54721i | ||||
\(609\) | 2.01858e49 | 0.152032 | ||||||||
\(610\) | 4.66476e49 | − | 2.66230e49i | 0.341108 | − | 0.194679i | ||||
\(611\) | − | 8.47272e49i | − | 0.601563i | ||||||
\(612\) | 3.56928e49 | − | 6.04232e49i | 0.246068 | − | 0.416560i | ||||
\(613\) | −2.26002e50 | −1.51294 | −0.756472 | − | 0.654026i | \(-0.773079\pi\) | ||||
−0.756472 | + | 0.654026i | \(0.773079\pi\) | |||||||
\(614\) | 3.33355e49 | + | 5.84089e49i | 0.216709 | + | 0.379707i | ||||
\(615\) | 2.86641e48i | 0.0180961i | ||||||||
\(616\) | −3.63771e48 | + | 2.43345e50i | −0.0223036 | + | 1.49201i | ||||
\(617\) | −1.84910e50 | −1.10110 | −0.550552 | − | 0.834801i | \(-0.685583\pi\) | ||||
−0.550552 | + | 0.834801i | \(0.685583\pi\) | |||||||
\(618\) | 3.91055e49 | − | 2.23185e49i | 0.226175 | − | 0.129084i | ||||
\(619\) | − | 2.69650e50i | − | 1.51485i | −0.652924 | − | 0.757424i | \(-0.726458\pi\) | ||
0.652924 | − | 0.757424i | \(-0.273542\pi\) | |||||||
\(620\) | −1.64778e50 | − | 9.73367e49i | −0.899184 | − | 0.531161i | ||||
\(621\) | 4.48636e49 | 0.237818 | ||||||||
\(622\) | 1.77460e50 | + | 3.10937e50i | 0.913847 | + | 1.60120i | ||||
\(623\) | 2.27158e50i | 1.13643i | ||||||||
\(624\) | 1.26405e50 | − | 6.96587e49i | 0.614387 | − | 0.338574i | ||||
\(625\) | −1.83137e50 | −0.864841 | ||||||||
\(626\) | −2.89801e48 | + | 1.65397e48i | −0.0132973 | + | 0.00758910i | ||||
\(627\) | − | 1.80859e50i | − | 0.806351i | ||||||
\(628\) | −2.00537e50 | + | 3.39482e50i | −0.868801 | + | 1.47076i | ||||
\(629\) | 1.13436e50 | 0.477571 | ||||||||
\(630\) | −2.14140e50 | − | 3.75206e50i | −0.876128 | − | 1.53511i | ||||
\(631\) | − | 3.25280e50i | − | 1.29339i | −0.762749 | − | 0.646694i | \(-0.776151\pi\) | ||
0.762749 | − | 0.646694i | \(-0.223849\pi\) | |||||||
\(632\) | −8.86914e49 | − | 1.32583e48i | −0.342747 | − | 0.00512364i | ||||
\(633\) | 1.02644e50 | 0.385538 | ||||||||
\(634\) | 3.87540e50 | − | 2.21179e50i | 1.41485 | − | 0.807490i | ||||
\(635\) | − | 9.24197e49i | − | 0.327973i | ||||||
\(636\) | 4.56300e48 | + | 2.69543e48i | 0.0157406 | + | 0.00929822i | ||||
\(637\) | −6.20214e50 | −2.07985 | ||||||||
\(638\) | −3.19958e49 | − | 5.60617e49i | −0.104309 | − | 0.182765i | ||||
\(639\) | − | 1.71170e50i | − | 0.542514i | ||||||
\(640\) | 4.17252e50 | − | 2.21872e50i | 1.28576 | − | 0.683697i | ||||
\(641\) | 2.58731e50 | 0.775183 | 0.387591 | − | 0.921831i | \(-0.373307\pi\) | ||||
0.387591 | + | 0.921831i | \(0.373307\pi\) | |||||||
\(642\) | −1.16834e50 | + | 6.66805e49i | −0.340362 | + | 0.194253i | ||||
\(643\) | 1.55303e50i | 0.439928i | 0.975508 | + | 0.219964i | \(0.0705940\pi\) | ||||
−0.975508 | + | 0.219964i | \(0.929406\pi\) | |||||||
\(644\) | 8.22791e49 | − | 1.39288e50i | 0.226644 | − | 0.383678i | ||||
\(645\) | −6.11002e49 | −0.163669 | ||||||||
\(646\) | 2.11103e50 | + | 3.69885e50i | 0.549932 | + | 0.963566i | ||||
\(647\) | 6.88086e50i | 1.74327i | 0.490152 | + | 0.871637i | \(0.336941\pi\) | ||||
−0.490152 | + | 0.871637i | \(0.663059\pi\) | |||||||
\(648\) | −2.52293e48 | + | 1.68772e50i | −0.00621663 | + | 0.415863i | ||||
\(649\) | 2.93777e50 | 0.704066 | ||||||||
\(650\) | −6.40196e50 | + | 3.65377e50i | −1.49236 | + | 0.851727i | ||||
\(651\) | 2.22116e50i | 0.503643i | ||||||||
\(652\) | 6.25414e50 | + | 3.69441e50i | 1.37947 | + | 0.814870i | ||||
\(653\) | −1.99284e50 | −0.427596 | −0.213798 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213798 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(654\) | −4.07363e49 | − | 7.13763e49i | −0.0850320 | − | 0.148989i | ||||
\(655\) | − | 3.73130e50i | − | 0.757734i | ||||||
\(656\) | −6.63539e48 | − | 1.20408e49i | −0.0131098 | − | 0.0237895i | ||||
\(657\) | 2.89197e50 | 0.555926 | ||||||||
\(658\) | −2.79640e50 | + | 1.59598e50i | −0.523038 | + | 0.298512i | ||||
\(659\) | 3.60744e50i | 0.656541i | 0.944584 | + | 0.328270i | \(0.106466\pi\) | ||||
−0.944584 | + | 0.328270i | \(0.893534\pi\) | |||||||
\(660\) | 1.85986e50 | − | 3.14849e50i | 0.329374 | − | 0.557586i | ||||
\(661\) | −4.59971e50 | −0.792691 | −0.396346 | − | 0.918101i | \(-0.629722\pi\) | ||||
−0.396346 | + | 0.918101i | \(0.629722\pi\) | |||||||
\(662\) | −2.97449e50 | − | 5.21177e50i | −0.498849 | − | 0.874060i | ||||
\(663\) | 2.62987e50i | 0.429231i | ||||||||
\(664\) | −5.84565e50 | − | 8.73852e48i | −0.928555 | − | 0.0138807i | ||||
\(665\) | 2.62175e51 | 4.05323 | ||||||||
\(666\) | −3.56202e50 | + | 2.03294e50i | −0.535995 | + | 0.305906i | ||||
\(667\) | 4.29072e49i | 0.0628442i | ||||||||
\(668\) | 3.38740e50 | + | 2.00098e50i | 0.482936 | + | 0.285277i | ||||
\(669\) | −5.91774e50 | −0.821270 | ||||||||
\(670\) | −6.73478e50 | − | 1.18004e51i | −0.909864 | − | 1.59422i | ||||
\(671\) | 1.99338e50i | 0.262170i | ||||||||
\(672\) | −4.68012e50 | − | 2.85983e50i | −0.599253 | − | 0.366179i | ||||
\(673\) | −8.21833e50 | −1.02450 | −0.512251 | − | 0.858836i | \(-0.671188\pi\) | ||||
−0.512251 | + | 0.858836i | \(0.671188\pi\) | |||||||
\(674\) | −3.69432e50 | + | 2.10844e50i | −0.448390 | + | 0.255908i | ||||
\(675\) | 7.76837e50i | 0.918040i | ||||||||
\(676\) | 5.97228e50 | − | 1.01103e51i | 0.687227 | − | 1.16338i | ||||
\(677\) | 3.47381e50 | 0.389234 | 0.194617 | − | 0.980879i | \(-0.437654\pi\) | ||||
0.194617 | + | 0.980879i | \(0.437654\pi\) | |||||||
\(678\) | 2.24031e50 | + | 3.92536e50i | 0.244440 | + | 0.428297i | ||||
\(679\) | − | 2.75387e51i | − | 2.92609i | ||||||
\(680\) | −1.28709e49 | + | 8.61004e50i | −0.0133183 | + | 0.890932i | ||||
\(681\) | 3.86829e50 | 0.389826 | ||||||||
\(682\) | 6.16880e50 | − | 3.52070e50i | 0.605456 | − | 0.345549i | ||||
\(683\) | − | 8.87361e50i | − | 0.848257i | −0.905602 | − | 0.424129i | \(-0.860580\pi\) | ||
0.905602 | − | 0.424129i | \(-0.139420\pi\) | |||||||
\(684\) | −1.32578e51 | − | 7.83157e50i | −1.23442 | − | 0.729188i | ||||
\(685\) | −2.20845e51 | −2.00289 | ||||||||
\(686\) | 3.06969e50 | + | 5.37858e50i | 0.271182 | + | 0.475153i | ||||
\(687\) | − | 8.79732e49i | − | 0.0757058i | ||||||
\(688\) | 2.56661e50 | − | 1.41439e50i | 0.215163 | − | 0.118571i | ||||
\(689\) | 7.50285e49 | 0.0612746 | ||||||||
\(690\) | −2.11110e50 | + | 1.20486e50i | −0.167968 | + | 0.0958635i | ||||
\(691\) | 1.71672e51i | 1.33074i | 0.746512 | + | 0.665372i | \(0.231727\pi\) | ||||
−0.746512 | + | 0.665372i | \(0.768273\pi\) | |||||||
\(692\) | 1.37851e50 | − | 2.33364e50i | 0.104112 | − | 0.176248i | ||||
\(693\) | 1.60335e51 | 1.17986 | ||||||||
\(694\) | 6.42668e50 | + | 1.12605e51i | 0.460804 | + | 0.807400i | ||||
\(695\) | 3.45276e51i | 2.41234i | ||||||||
\(696\) | 1.45455e50 | + | 2.17436e48i | 0.0990288 | + | 0.00148035i | ||||
\(697\) | 2.50510e49 | 0.0166201 | ||||||||
\(698\) | 2.44243e50 | − | 1.39396e50i | 0.157915 | − | 0.0901263i | ||||
\(699\) | 1.62573e49i | 0.0102438i | ||||||||
\(700\) | 2.41183e51 | + | 1.42471e51i | 1.48109 | + | 0.874904i | ||||
\(701\) | −2.04153e51 | −1.22189 | −0.610944 | − | 0.791674i | \(-0.709210\pi\) | ||||
−0.610944 | + | 0.791674i | \(0.709210\pi\) | |||||||
\(702\) | −1.06738e51 | − | 1.87022e51i | −0.622661 | − | 1.09100i | ||||
\(703\) | − | 2.48896e51i | − | 1.41521i | ||||||
\(704\) | −5.24252e49 | + | 1.75311e51i | −0.0290557 | + | 0.971629i | ||||
\(705\) | 4.83787e50 | 0.261367 | ||||||||
\(706\) | 6.74843e50 | − | 3.85151e50i | 0.355401 | − | 0.202836i | ||||
\(707\) | − | 1.55525e51i | − | 0.798457i | ||||||
\(708\) | −3.36730e50 | + | 5.70038e50i | −0.168532 | + | 0.285302i | ||||
\(709\) | −1.72817e50 | −0.0843245 | −0.0421622 | − | 0.999111i | \(-0.513425\pi\) | ||||
−0.0421622 | + | 0.999111i | \(0.513425\pi\) | |||||||
\(710\) | 1.04107e51 | + | 1.82412e51i | 0.495256 | + | 0.867765i | ||||
\(711\) | 5.84370e50i | 0.271041i | ||||||||
\(712\) | −2.44689e49 | + | 1.63685e51i | −0.0110656 | + | 0.740235i | ||||
\(713\) | −4.72134e50 | −0.208187 | ||||||||
\(714\) | 8.67983e50 | − | 4.95380e50i | 0.373201 | − | 0.212996i | ||||
\(715\) | − | 5.17700e51i | − | 2.17055i | ||||||
\(716\) | −9.80472e50 | − | 5.79179e50i | −0.400867 | − | 0.236798i | ||||
\(717\) | −2.39655e50 | −0.0955523 | ||||||||
\(718\) | 2.08546e51 | + | 3.65405e51i | 0.810889 | + | 1.42080i | ||||
\(719\) | 3.23849e51i | 1.22807i | 0.789279 | + | 0.614034i | \(0.210454\pi\) | ||||
−0.789279 | + | 0.614034i | \(0.789546\pi\) | |||||||
\(720\) | −1.50263e51 | − | 2.72673e51i | −0.555735 | − | 1.00846i | ||||
\(721\) | −2.42241e51 | −0.873803 | ||||||||
\(722\) | 5.64731e51 | − | 3.22307e51i | 1.98688 | − | 1.13397i | ||||
\(723\) | 4.85830e50i | 0.166723i | ||||||||
\(724\) | 4.11091e50 | − | 6.95922e50i | 0.137608 | − | 0.232952i | ||||
\(725\) | −7.42960e50 | −0.242595 | ||||||||
\(726\) | −3.92229e49 | − | 6.87245e49i | −0.0124934 | − | 0.0218903i | ||||
\(727\) | 2.42075e51i | 0.752196i | 0.926580 | + | 0.376098i | \(0.122734\pi\) | ||||
−0.926580 | + | 0.376098i | \(0.877266\pi\) | |||||||
\(728\) | −7.76400e51 | − | 1.16062e50i | −2.35353 | − | 0.0351824i | ||||
\(729\) | −1.55313e50 | −0.0459317 | ||||||||
\(730\) | −3.08190e51 | + | 1.75892e51i | −0.889217 | + | 0.507499i | ||||
\(731\) | 5.33985e50i | 0.150320i | ||||||||
\(732\) | −3.86790e50 | − | 2.28482e50i | −0.106237 | − | 0.0627557i | ||||
\(733\) | 2.02046e51 | 0.541475 | 0.270738 | − | 0.962653i | \(-0.412732\pi\) | ||||
0.270738 | + | 0.962653i | \(0.412732\pi\) | |||||||
\(734\) | −1.71601e51 | − | 3.00672e51i | −0.448736 | − | 0.786255i | ||||
\(735\) | − | 3.54139e51i | − | 0.903652i | ||||||
\(736\) | 6.07891e50 | − | 9.94815e50i | 0.151365 | − | 0.247709i | ||||
\(737\) | 5.04261e51 | 1.22529 | ||||||||
\(738\) | −7.86632e49 | + | 4.48951e49i | −0.0186534 | + | 0.0106460i | ||||
\(739\) | 2.96849e51i | 0.686966i | 0.939159 | + | 0.343483i | \(0.111607\pi\) | ||||
−0.939159 | + | 0.343483i | \(0.888393\pi\) | |||||||
\(740\) | 2.55951e51 | − | 4.33291e51i | 0.578078 | − | 0.978608i | ||||
\(741\) | 5.77035e51 | 1.27196 | ||||||||
\(742\) | −1.41329e50 | − | 2.47630e50i | −0.0304061 | − | 0.0532762i | ||||
\(743\) | − | 3.73279e51i | − | 0.783854i | −0.919996 | − | 0.391927i | \(-0.871809\pi\) | ||
0.919996 | − | 0.391927i | \(-0.128191\pi\) | |||||||
\(744\) | −2.39258e49 | + | 1.60053e51i | −0.00490404 | + | 0.328057i | ||||
\(745\) | −1.12977e52 | −2.26036 | ||||||||
\(746\) | −3.10653e51 | + | 1.77298e51i | −0.606704 | + | 0.346262i | ||||
\(747\) | 3.85158e51i | 0.734292i | ||||||||
\(748\) | −2.75162e51 | − | 1.62542e51i | −0.512106 | − | 0.302509i | ||||
\(749\) | 7.23738e51 | 1.31495 | ||||||||
\(750\) | −2.24547e50 | − | 3.93441e50i | −0.0398294 | − | 0.0697873i | ||||
\(751\) | 4.60658e51i | 0.797737i | 0.917008 | + | 0.398868i | \(0.130597\pi\) | ||||
−0.917008 | + | 0.398868i | \(0.869403\pi\) | |||||||
\(752\) | −2.03222e51 | + | 1.11991e51i | −0.343598 | + | 0.189348i | ||||
\(753\) | 2.19960e51 | 0.363107 | ||||||||
\(754\) | 1.78866e51 | − | 1.02084e51i | 0.288299 | − | 0.164540i | ||||
\(755\) | − | 4.60948e51i | − | 0.725449i | ||||||
\(756\) | −4.16202e51 | + | 7.04574e51i | −0.639605 | + | 1.08276i | ||||
\(757\) | −7.44791e51 | −1.11766 | −0.558829 | − | 0.829283i | \(-0.688749\pi\) | ||||
−0.558829 | + | 0.829283i | \(0.688749\pi\) | |||||||
\(758\) | −5.90199e51 | − | 1.03412e52i | −0.864873 | − | 1.51539i | ||||
\(759\) | − | 9.02130e50i | − | 0.129097i | ||||||
\(760\) | 1.88918e52 | + | 2.82408e50i | 2.64015 | + | 0.0394669i | ||||
\(761\) | 1.23442e52 | 1.68476 | 0.842380 | − | 0.538884i | \(-0.181154\pi\) | ||||
0.842380 | + | 0.538884i | \(0.181154\pi\) | |||||||
\(762\) | −6.71356e50 | + | 3.83160e50i | −0.0894877 | + | 0.0510729i | ||||
\(763\) | 4.42145e51i | 0.575603i | ||||||||
\(764\) | 2.03214e50 | + | 1.20042e50i | 0.0258389 | + | 0.0152634i | ||||
\(765\) | 5.67298e51 | 0.704540 | ||||||||
\(766\) | 6.72291e51 | + | 1.17796e52i | 0.815529 | + | 1.42893i | ||||
\(767\) | 9.37302e51i | 1.11061i | ||||||||
\(768\) | −3.34160e51 | − | 2.11115e51i | −0.386769 | − | 0.244353i | ||||
\(769\) | 6.04399e51 | 0.683360 | 0.341680 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341680 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(770\) | −1.70866e52 | + | 9.75176e51i | −1.88722 | + | 1.07708i | ||||
\(771\) | 2.59465e51i | 0.279962i | ||||||||
\(772\) | −5.94973e51 | + | 1.00721e52i | −0.627171 | + | 1.06172i | ||||
\(773\) | −8.79086e51 | −0.905316 | −0.452658 | − | 0.891684i | \(-0.649524\pi\) | ||||
−0.452658 | + | 0.891684i | \(0.649524\pi\) | |||||||
\(774\) | −9.56981e50 | − | 1.67678e51i | −0.0962867 | − | 0.168709i | ||||
\(775\) | − | 8.17525e51i | − | 0.803656i | ||||||
\(776\) | 2.96640e50 | − | 1.98438e52i | 0.0284918 | − | 1.90596i | ||||
\(777\) | −5.84065e51 | −0.548129 | ||||||||
\(778\) | 1.76521e52 | − | 1.00745e52i | 1.61869 | − | 0.923831i | ||||
\(779\) | − | 5.49658e50i | − | 0.0492514i | ||||||
\(780\) | 1.00453e52 | + | 5.93393e51i | 0.879553 | + | 0.519564i | ||||
\(781\) | −7.79493e51 | −0.666950 | ||||||||
\(782\) | 1.05299e51 | + | 1.84500e51i | 0.0880444 | + | 0.154267i | ||||
\(783\) | − | 2.17042e51i | − | 0.177351i | ||||||
\(784\) | 8.19788e51 | + | 1.48761e52i | 0.654655 | + | 1.18796i | ||||
\(785\) | −3.18731e52 | −2.48754 | ||||||||
\(786\) | −2.71049e51 | + | 1.54695e51i | −0.206749 | + | 0.117997i | ||||
\(787\) | − | 1.01676e52i | − | 0.758005i | −0.925396 | − | 0.379003i | \(-0.876267\pi\) | ||
0.925396 | − | 0.379003i | \(-0.123733\pi\) | |||||||
\(788\) | 7.21900e51 | − | 1.22208e52i | 0.526024 | − | 0.890487i | ||||
\(789\) | −5.67809e51 | −0.404405 | ||||||||
\(790\) | −3.55420e51 | − | 6.22750e51i | −0.247431 | − | 0.433537i | ||||
\(791\) | − | 2.43159e52i | − | 1.65468i | ||||||
\(792\) | 1.15534e52 | + | 1.72709e50i | 0.768526 | + | 0.0114885i | ||||
\(793\) | −6.35991e51 | −0.413556 | ||||||||
\(794\) | −3.56286e51 | + | 2.03342e51i | −0.226480 | + | 0.129258i | ||||
\(795\) | 4.28409e50i | 0.0266226i | ||||||||
\(796\) | −1.04545e52 | − | 6.17564e51i | −0.635140 | − | 0.375186i | ||||
\(797\) | 2.59769e52 | 1.54290 | 0.771450 | − | 0.636290i | \(-0.219532\pi\) | ||||
0.771450 | + | 0.636290i | \(0.219532\pi\) | |||||||
\(798\) | −1.08694e52 | − | 1.90449e52i | −0.631182 | − | 1.10593i | ||||
\(799\) | − | 4.22806e51i | − | 0.240048i | ||||||
\(800\) | 1.72257e52 | + | 1.05259e52i | 0.956220 | + | 0.584307i | ||||
\(801\) | 1.07849e52 | 0.585370 | ||||||||
\(802\) | −1.77411e52 | + | 1.01253e52i | −0.941549 | + | 0.537366i | ||||
\(803\) | − | 1.31698e52i | − | 0.683438i | ||||||
\(804\) | −5.77988e51 | + | 9.78456e51i | −0.293299 | + | 0.496515i | ||||
\(805\) | 1.30774e52 | 0.648924 | ||||||||
\(806\) | 1.12329e52 | + | 1.96817e52i | 0.545080 | + | 0.955064i | ||||
\(807\) | 1.53708e52i | 0.729412i | ||||||||
\(808\) | 1.67528e50 | − | 1.12068e52i | 0.00777469 | − | 0.520090i | ||||
\(809\) | −3.56777e52 | −1.61929 | −0.809643 | − | 0.586923i | \(-0.800339\pi\) | ||||
−0.809643 | + | 0.586923i | \(0.800339\pi\) | |||||||
\(810\) | −1.18504e52 | + | 6.76332e51i | −0.526020 | + | 0.300213i | ||||
\(811\) | 1.06999e52i | 0.464518i | 0.972654 | + | 0.232259i | \(0.0746117\pi\) | ||||
−0.972654 | + | 0.232259i | \(0.925388\pi\) | |||||||
\(812\) | −6.73849e51 | − | 3.98052e51i | −0.286124 | − | 0.169017i | ||||
\(813\) | 3.72362e51 | 0.154645 | ||||||||
\(814\) | 9.25784e51 | + | 1.62212e52i | 0.376071 | + | 0.658935i | ||||
\(815\) | 5.87185e52i | 2.33313i | ||||||||
\(816\) | 6.30787e51 | − | 3.47611e51i | 0.245166 | − | 0.135105i | ||||
\(817\) | 1.17165e52 | 0.445451 | ||||||||
\(818\) | 1.07071e52 | − | 6.11083e51i | 0.398211 | − | 0.227269i | ||||
\(819\) | 5.11554e52i | 1.86115i | ||||||||
\(820\) | 5.65240e50 | − | 9.56875e50i | 0.0201179 | − | 0.0340570i | ||||
\(821\) | 2.44699e52 | 0.852032 | 0.426016 | − | 0.904716i | \(-0.359917\pi\) | ||||
0.426016 | + | 0.904716i | \(0.359917\pi\) | |||||||
\(822\) | 9.15595e51 | + | 1.60426e52i | 0.311897 | + | 0.546491i | ||||
\(823\) | − | 5.26840e52i | − | 1.75583i | −0.478819 | − | 0.877914i | \(-0.658935\pi\) | ||
0.478819 | − | 0.877914i | \(-0.341065\pi\) | |||||||
\(824\) | −1.74554e52 | − | 2.60937e50i | −0.569168 | − | 0.00850835i | ||||
\(825\) | 1.56208e52 | 0.498349 | ||||||||
\(826\) | 3.09355e52 | − | 1.76557e52i | 0.965641 | − | 0.551116i | ||||
\(827\) | − | 5.95412e52i | − | 1.81852i | −0.416227 | − | 0.909261i | \(-0.636648\pi\) | ||
0.416227 | − | 0.909261i | \(-0.363352\pi\) | |||||||
\(828\) | −6.61303e51 | − | 3.90641e51i | −0.197631 | − | 0.116743i | ||||
\(829\) | 3.96449e52 | 1.15933 | 0.579663 | − | 0.814856i | \(-0.303184\pi\) | ||||
0.579663 | + | 0.814856i | \(0.303184\pi\) | |||||||
\(830\) | −2.34257e52 | − | 4.10455e52i | −0.670328 | − | 1.17452i | ||||
\(831\) | 1.23347e52i | 0.345390i | ||||||||
\(832\) | −5.59333e52 | − | 1.67264e51i | −1.53268 | − | 0.0458334i | ||||
\(833\) | −3.09500e52 | −0.829946 | ||||||||
\(834\) | 2.50815e52 | − | 1.43147e52i | 0.658211 | − | 0.375658i | ||||
\(835\) | 3.18034e52i | 0.816803i | ||||||||
\(836\) | −3.56644e52 | + | 6.03750e52i | −0.896440 | + | 1.51755i | ||||
\(837\) | 2.38825e52 | 0.587518 | ||||||||
\(838\) | −1.67222e52 | − | 2.92999e52i | −0.402626 | − | 0.705462i | ||||
\(839\) | 3.09117e52i | 0.728464i | 0.931308 | + | 0.364232i | \(0.118668\pi\) | ||||
−0.931308 | + | 0.364232i | \(0.881332\pi\) | |||||||
\(840\) | 6.62707e50 | − | 4.43320e52i | 0.0152860 | − | 1.02256i | ||||
\(841\) | −4.22165e52 | −0.953135 | ||||||||
\(842\) | 2.22135e52 | − | 1.26778e52i | 0.490907 | − | 0.280174i | ||||
\(843\) | 2.95282e51i | 0.0638765i | ||||||||
\(844\) | −3.42650e52 | − | 2.02408e52i | −0.725583 | − | 0.428612i | ||||
\(845\) | 9.49228e52 | 1.96766 | ||||||||
\(846\) | 7.57732e51 | + | 1.32766e52i | 0.153762 | + | 0.269415i | ||||
\(847\) | 4.25718e51i | 0.0845708i | ||||||||
\(848\) | −9.91713e50 | − | 1.79960e51i | −0.0192868 | − | 0.0349985i | ||||
\(849\) | −4.33244e52 | −0.824886 | ||||||||
\(850\) | −3.19471e52 | + | 1.82330e52i | −0.595512 | + | 0.339874i | ||||
\(851\) | − | 1.24150e52i | − | 0.226576i | ||||||
\(852\) | 8.93461e51 | − | 1.51251e52i | 0.159648 | − | 0.270262i | ||||
\(853\) | −2.17155e52 | −0.379916 | −0.189958 | − | 0.981792i | \(-0.560835\pi\) | ||||
−0.189958 | + | 0.981792i | \(0.560835\pi\) | |||||||
\(854\) | 1.19800e52 | + | 2.09908e52i | 0.205217 | + | 0.359572i | ||||
\(855\) | − | 1.24474e53i | − | 2.08780i | ||||||
\(856\) | 5.21511e52 | + | 7.79593e50i | 0.856517 | + | 0.0128038i | ||||
\(857\) | −9.70662e52 | −1.56104 | −0.780518 | − | 0.625133i | \(-0.785045\pi\) | ||||
−0.780518 | + | 0.625133i | \(0.785045\pi\) | |||||||
\(858\) | −3.76068e52 | + | 2.14632e52i | −0.592237 | + | 0.338005i | ||||
\(859\) | 3.82443e52i | 0.589780i | 0.955531 | + | 0.294890i | \(0.0952831\pi\) | ||||
−0.955531 | + | 0.294890i | \(0.904717\pi\) | |||||||
\(860\) | 2.03967e52 | + | 1.20486e52i | 0.308026 | + | 0.181955i | ||||
\(861\) | −1.28984e51 | −0.0190757 | ||||||||
\(862\) | 4.46825e52 | + | 7.82906e52i | 0.647152 | + | 1.13391i | ||||
\(863\) | − | 6.79896e52i | − | 0.964380i | −0.876067 | − | 0.482190i | \(-0.839841\pi\) | ||
0.876067 | − | 0.482190i | \(-0.160159\pi\) | |||||||
\(864\) | −3.07496e52 | + | 5.03218e52i | −0.427162 | + | 0.699051i | ||||
\(865\) | 2.19100e52 | 0.298093 | ||||||||
\(866\) | 7.33924e52 | − | 4.18870e52i | 0.977978 | − | 0.558158i | ||||
\(867\) | − | 2.19296e52i | − | 0.286211i | ||||||
\(868\) | 4.38001e52 | − | 7.41477e52i | 0.559912 | − | 0.947856i | ||||
\(869\) | 2.66117e52 | 0.333209 | ||||||||
\(870\) | 5.82891e51 | + | 1.02132e52i | 0.0714893 | + | 0.125260i | ||||
\(871\) | 1.60886e53i | 1.93282i | ||||||||
\(872\) | −4.76268e50 | + | 3.18601e52i | −0.00560473 | + | 0.374930i | ||||
\(873\) | −1.30747e53 | −1.50722 | ||||||||
\(874\) | 4.04822e52 | − | 2.31042e52i | 0.457149 | − | 0.260907i | ||||
\(875\) | 2.43719e52i | 0.269615i | ||||||||
\(876\) | 2.55543e52 | + | 1.50953e52i | 0.276943 | + | 0.163594i | ||||
\(877\) | 1.62144e52 | 0.172151 | 0.0860753 | − | 0.996289i | \(-0.472567\pi\) | ||||
0.0860753 | + | 0.996289i | \(0.472567\pi\) | |||||||
\(878\) | 2.40586e52 | + | 4.21543e52i | 0.250247 | + | 0.438471i | ||||
\(879\) | − | 6.73392e52i | − | 0.686227i | ||||||
\(880\) | −1.24173e53 | + | 6.84287e52i | −1.23976 | + | 0.683203i | ||||
\(881\) | 8.46178e52 | 0.827743 | 0.413871 | − | 0.910335i | \(-0.364176\pi\) | ||||
0.413871 | + | 0.910335i | \(0.364176\pi\) | |||||||
\(882\) | 9.71868e52 | − | 5.54670e52i | 0.931478 | − | 0.531619i | ||||
\(883\) | − | 7.26326e52i | − | 0.682086i | −0.940048 | − | 0.341043i | \(-0.889220\pi\) | ||
0.940048 | − | 0.341043i | \(-0.110780\pi\) | |||||||
\(884\) | 5.18595e52 | − | 8.77912e52i | 0.477186 | − | 0.807812i | ||||
\(885\) | −5.35194e52 | −0.482539 | ||||||||
\(886\) | −4.15960e52 | − | 7.28826e52i | −0.367489 | − | 0.643898i | ||||
\(887\) | 1.74737e53i | 1.51272i | 0.654154 | + | 0.756361i | \(0.273025\pi\) | ||||
−0.654154 | + | 0.756361i | \(0.726975\pi\) | |||||||
\(888\) | −4.20866e52 | − | 6.29141e50i | −0.357035 | − | 0.00533722i | ||||
\(889\) | 4.15875e52 | 0.345725 | ||||||||
\(890\) | −1.14932e53 | + | 6.55947e52i | −0.936314 | + | 0.534378i | ||||
\(891\) | − | 5.06398e52i | − | 0.404290i | ||||||
\(892\) | 1.97548e53 | + | 1.16695e53i | 1.54563 | + | 0.913026i | ||||
\(893\) | −9.27703e52 | −0.711349 | ||||||||
\(894\) | 4.68388e52 | + | 8.20689e52i | 0.351990 | + | 0.616741i | ||||
\(895\) | − | 9.20540e52i | − | 0.677998i | ||||||
\(896\) | 9.98393e52 | + | 1.87757e53i | 0.720704 | + | 1.35535i | ||||
\(897\) | 2.87827e52 | 0.203642 | ||||||||
\(898\) | −2.31479e53 | + | 1.32111e53i | −1.60523 | + | 0.916149i | ||||
\(899\) | 2.28410e52i | 0.155253i | ||||||||
\(900\) | 6.76415e52 | − | 1.14508e53i | 0.450659 | − | 0.762905i | ||||
\(901\) | 3.74408e51 | 0.0244511 | ||||||||
\(902\) | 2.04449e51 | + | 3.58226e51i | 0.0130878 | + | 0.0229319i | ||||
\(903\) | − | 2.74942e52i | − | 0.172529i | ||||||
\(904\) | 2.61925e51 | − | 1.75216e53i | 0.0161118 | − | 1.07781i | ||||
\(905\) | 6.53384e52 | 0.393998 | ||||||||
\(906\) | −3.34842e52 | + | 1.91103e52i | −0.197940 | + | 0.112969i | ||||
\(907\) | − | 1.65404e53i | − | 0.958548i | −0.877665 | − | 0.479274i | \(-0.840900\pi\) | ||
0.877665 | − | 0.479274i | \(-0.159100\pi\) | |||||||
\(908\) | −1.29133e53 | − | 7.62805e52i | −0.733653 | − | 0.433379i | ||||
\(909\) | −7.38396e52 | −0.411282 | ||||||||
\(910\) | −3.11132e53 | − | 5.45152e53i | −1.69903 | − | 2.97696i | ||||
\(911\) | 2.53956e53i | 1.35965i | 0.733373 | + | 0.679826i | \(0.237945\pi\) | ||||
−0.733373 | + | 0.679826i | \(0.762055\pi\) | |||||||
\(912\) | −7.62714e52 | − | 1.38405e53i | −0.400364 | − | 0.726513i | ||||
\(913\) | 1.75398e53 | 0.902715 | ||||||||
\(914\) | 2.55298e52 | − | 1.45705e52i | 0.128830 | − | 0.0735265i | ||||
\(915\) | − | 3.63147e52i | − | 0.179681i | ||||||
\(916\) | −1.73478e52 | + | 2.93675e52i | −0.0841640 | + | 0.142478i | ||||
\(917\) | 1.67903e53 | 0.798750 | ||||||||
\(918\) | −5.32645e52 | − | 9.33276e52i | −0.248467 | − | 0.435353i | ||||
\(919\) | 2.43607e52i | 0.111432i | 0.998447 | + | 0.0557160i | \(0.0177442\pi\) | ||||
−0.998447 | + | 0.0557160i | \(0.982256\pi\) | |||||||
\(920\) | 9.42328e52 | + | 1.40866e51i | 0.422689 | + | 0.00631867i | ||||
\(921\) | 4.54708e52 | 0.200013 | ||||||||
\(922\) | −2.34319e53 | + | 1.33732e53i | −1.01077 | + | 0.576871i | ||||
\(923\) | − | 2.48699e53i | − | 1.05207i | ||||||
\(924\) | 1.41678e53 | + | 8.36910e52i | 0.587767 | + | 0.347203i | ||||
\(925\) | 2.14972e53 | 0.874642 | ||||||||
\(926\) | 1.39322e53 | + | 2.44113e53i | 0.555931 | + | 0.974078i | ||||
\(927\) | 1.15010e53i | 0.450092i | ||||||||
\(928\) | −4.81274e52 | − | 2.94087e52i | −0.184726 | − | 0.112879i | ||||
\(929\) | −4.58586e53 | −1.72639 | −0.863194 | − | 0.504873i | \(-0.831539\pi\) | ||||
−0.863194 | + | 0.504873i | \(0.831539\pi\) | |||||||
\(930\) | −1.12382e53 | + | 6.41390e52i | −0.414956 | + | 0.236826i | ||||
\(931\) | 6.79091e53i | 2.45943i | ||||||||
\(932\) | 3.20585e51 | − | 5.42708e51i | 0.0113883 | − | 0.0192788i | ||||
\(933\) | 2.42062e53 | 0.843444 | ||||||||
\(934\) | −3.44015e52 | − | 6.02767e52i | −0.117580 | − | 0.206018i | ||||
\(935\) | − | 2.58343e53i | − | 0.866139i | ||||||
\(936\) | −5.51034e51 | + | 3.68616e53i | −0.0181223 | + | 1.21230i | ||||
\(937\) | 2.90053e53 | 0.935759 | 0.467880 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467880 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(938\) | 5.30999e53 | − | 3.03055e53i | 1.68052 | − | 0.959115i | ||||
\(939\) | 2.25608e51i | 0.00700444i | ||||||||
\(940\) | −1.61500e53 | − | 9.54001e52i | −0.491892 | − | 0.290568i | ||||
\(941\) | −1.25452e53 | −0.374855 | −0.187427 | − | 0.982278i | \(-0.560015\pi\) | ||||
−0.187427 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(942\) | 1.32142e53 | + | 2.31533e53i | 0.387368 | + | 0.678728i | ||||
\(943\) | − | 2.74171e51i | − | 0.00788517i | ||||||
\(944\) | 2.24817e53 | − | 1.23891e53i | 0.634355 | − | 0.349578i | ||||
\(945\) | −6.61506e53 | −1.83131 | ||||||||
\(946\) | −7.63592e52 | + | 4.35802e52i | −0.207406 | + | 0.118372i | ||||
\(947\) | 4.45622e53i | 1.18759i | 0.804616 | + | 0.593796i | \(0.202371\pi\) | ||||
−0.804616 | + | 0.593796i | \(0.797629\pi\) | |||||||
\(948\) | −3.05026e52 | + | 5.16368e52i | −0.0797603 | + | 0.135023i | ||||
\(949\) | 4.20185e53 | 1.07808 | ||||||||
\(950\) | 4.00061e53 | + | 7.00969e53i | 1.00717 | + | 1.76471i | ||||
\(951\) | − | 3.01696e53i | − | 0.745281i | ||||||
\(952\) | −3.87439e53 | − | 5.79173e51i | −0.939158 | − | 0.0140392i | ||||
\(953\) | −2.89388e52 | −0.0688348 | −0.0344174 | − | 0.999408i | \(-0.510958\pi\) | ||||
−0.0344174 | + | 0.999408i | \(0.510958\pi\) | |||||||
\(954\) | −1.17569e52 | + | 6.70995e51i | −0.0274423 | + | 0.0156620i | ||||
\(955\) | 1.90793e52i | 0.0437020i | ||||||||
\(956\) | 8.00024e52 | + | 4.72585e52i | 0.179829 | + | 0.106228i | ||||
\(957\) | −4.36435e52 | −0.0962730 | ||||||||
\(958\) | −1.49494e53 | − | 2.61937e53i | −0.323627 | − | 0.567045i | ||||
\(959\) | − | 9.93770e53i | − | 2.11131i | ||||||
\(960\) | 9.55067e51 | − | 3.19376e53i | 0.0199137 | − | 0.665917i | ||||
\(961\) | 2.37342e53 | 0.485684 | ||||||||
\(962\) | −5.17540e53 | + | 2.95374e53i | −1.03942 | + | 0.593226i | ||||
\(963\) | − | 3.43613e53i | − | 0.677324i | ||||||
\(964\) | 9.58029e52 | − | 1.62181e53i | 0.185350 | − | 0.313772i | ||||
\(965\) | −9.45643e53 | −1.79571 | ||||||||
\(966\) | −5.42170e52 | − | 9.49966e52i | −0.101053 | − | 0.177060i | ||||
\(967\) | − | 1.29472e53i | − | 0.236864i | −0.992962 | − | 0.118432i | \(-0.962213\pi\) | ||
0.992962 | − | 0.118432i | \(-0.0377868\pi\) | |||||||
\(968\) | −4.58573e50 | + | 3.06764e52i | −0.000823479 | + | 0.0550868i | ||||
\(969\) | 2.87952e53 | 0.507566 | ||||||||
\(970\) | 1.39334e54 | − | 7.95217e53i | 2.41083 | − | 1.37592i | ||||
\(971\) | − | 2.93305e52i | − | 0.0498165i | −0.999690 | − | 0.0249083i | \(-0.992071\pi\) | ||
0.999690 | − | 0.0249083i | \(-0.00792937\pi\) | |||||||
\(972\) | 5.21321e53 | + | 3.07952e53i | 0.869185 | + | 0.513440i | ||||
\(973\) | −1.55369e54 | −2.54292 | ||||||||
\(974\) | −3.85938e53 | − | 6.76222e53i | −0.620092 | − | 1.08650i | ||||
\(975\) | 4.98387e53i | 0.786110i | ||||||||
\(976\) | 8.40641e52 | + | 1.52546e53i | 0.130171 | + | 0.236213i | ||||
\(977\) | −1.42303e53 | −0.216328 | −0.108164 | − | 0.994133i | \(-0.534497\pi\) | ||||
−0.108164 | + | 0.994133i | \(0.534497\pi\) | |||||||
\(978\) | 4.26543e53 | − | 2.43439e53i | 0.636596 | − | 0.363322i | ||||
\(979\) | − | 4.91135e53i | − | 0.719635i | ||||||
\(980\) | −6.98342e53 | + | 1.18220e54i | −1.00461 | + | 1.70067i | ||||
\(981\) | 2.09920e53 | 0.296491 | ||||||||
\(982\) | 4.37602e53 | + | 7.66746e53i | 0.606837 | + | 1.06327i | ||||
\(983\) | 3.48459e53i | 0.474447i | 0.971455 | + | 0.237224i | \(0.0762374\pi\) | ||||
−0.971455 | + | 0.237224i | \(0.923763\pi\) | |||||||
\(984\) | −9.29435e51 | − | 1.38939e50i | −0.0124253 | − | 0.000185743i | ||||
\(985\) | 1.14738e54 | 1.50610 | ||||||||
\(986\) | 8.92578e52 | − | 5.09417e52i | 0.115043 | − | 0.0656583i | ||||
\(987\) | 2.17697e53i | 0.275514i | ||||||||
\(988\) | −1.92628e54 | − | 1.13788e54i | −2.39383 | − | 1.41407i | ||||
\(989\) | 5.84421e52 | 0.0713169 | ||||||||
\(990\) | 4.62990e53 | + | 8.11230e53i | 0.554802 | + | 0.972098i | ||||
\(991\) | 1.15645e54i | 1.36082i | 0.732831 | + | 0.680411i | \(0.238199\pi\) | ||||
−0.732831 | + | 0.680411i | \(0.761801\pi\) | |||||||
\(992\) | 3.23602e53 | − | 5.29575e53i | 0.373939 | − | 0.611952i | ||||
\(993\) | −4.05731e53 | −0.460418 | ||||||||
\(994\) | −8.20826e53 | + | 4.68467e53i | −0.914737 | + | 0.522064i | ||||
\(995\) | − | 9.81550e53i | − | 1.07423i | ||||||
\(996\) | −2.01043e53 | + | 3.40338e53i | −0.216083 | + | 0.365799i | ||||
\(997\) | 8.94257e53 | 0.943951 | 0.471976 | − | 0.881612i | \(-0.343541\pi\) | ||||
0.471976 | + | 0.881612i | \(0.343541\pi\) | |||||||
\(998\) | −5.32205e53 | − | 9.32506e53i | −0.551734 | − | 0.966723i | ||||
\(999\) | 6.28001e53i | 0.639414i |
(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.3.2 | yes | 16 | |
4.3 | odd | 2 | inner | 4.37.b.b.3.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.37.b.b.3.1 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4.37.b.b.3.2 | yes | 16 | 1.1 | even | 1 | trivial |