Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,14,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not 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: | \(105.086310373\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + \cdots + 75\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(114.279 + 197.937i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.14.c.o.67.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | − | 55.4256i | 0.353553 | − | 0.612372i | ||||
\(3\) | −888.214 | − | 1538.43i | −0.703444 | − | 1.21840i | −0.967250 | − | 0.253825i | \(-0.918311\pi\) |
0.263807 | − | 0.964576i | \(-0.415022\pi\) | |||||||
\(4\) | −2048.00 | − | 3547.24i | −0.250000 | − | 0.433013i | ||||
\(5\) | 13071.0 | − | 22639.6i | 0.374113 | − | 0.647983i | −0.616081 | − | 0.787683i | \(-0.711280\pi\) |
0.990194 | + | 0.139700i | \(0.0446138\pi\) | |||||||
\(6\) | −113691. | −0.994820 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | −780686. | + | 1.35219e6i | −0.489666 | + | 0.848126i | ||||
\(10\) | −836543. | − | 1.44893e6i | −0.264538 | − | 0.458193i | ||||
\(11\) | −5.60522e6 | − | 9.70852e6i | −0.953982 | − | 1.65235i | −0.736681 | − | 0.676241i | \(-0.763608\pi\) |
−0.217301 | − | 0.976105i | \(-0.569725\pi\) | |||||||
\(12\) | −3.63812e6 | + | 6.30141e6i | −0.351722 | + | 0.609200i | ||||
\(13\) | 1.74220e7 | 1.00107 | 0.500537 | − | 0.865715i | \(-0.333136\pi\) | ||||
0.500537 | + | 0.865715i | \(0.333136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.64393e7 | −1.05267 | ||||||||
\(16\) | −8.38861e6 | + | 1.45295e7i | −0.125000 | + | 0.216506i | ||||
\(17\) | −8.48313e7 | − | 1.46932e8i | −0.852390 | − | 1.47638i | −0.879046 | − | 0.476737i | \(-0.841819\pi\) |
0.0266563 | − | 0.999645i | \(-0.491514\pi\) | |||||||
\(18\) | 4.99639e7 | + | 8.65400e7i | 0.346246 | + | 0.599716i | ||||
\(19\) | 8.89700e7 | − | 1.54101e8i | 0.433856 | − | 0.751460i | −0.563346 | − | 0.826221i | \(-0.690486\pi\) |
0.997201 | + | 0.0747610i | \(0.0238194\pi\) | |||||||
\(20\) | −1.07077e8 | −0.374113 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.17468e8 | −1.34913 | ||||||||
\(23\) | 2.23644e7 | − | 3.87364e7i | 0.0315012 | − | 0.0545617i | −0.849845 | − | 0.527033i | \(-0.823305\pi\) |
0.881346 | + | 0.472471i | \(0.156638\pi\) | |||||||
\(24\) | 2.32840e8 | + | 4.03291e8i | 0.248705 | + | 0.430770i | ||||
\(25\) | 2.68651e8 | + | 4.65316e8i | 0.220079 | + | 0.381187i | ||||
\(26\) | 5.57504e8 | − | 9.65626e8i | 0.353933 | − | 0.613031i | ||||
\(27\) | −5.85356e7 | −0.0290774 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.14386e9 | −0.981468 | −0.490734 | − | 0.871310i | \(-0.663271\pi\) | ||||
−0.490734 | + | 0.871310i | \(0.663271\pi\) | |||||||
\(30\) | −1.48606e9 | + | 2.57393e9i | −0.372175 | + | 0.644626i | ||||
\(31\) | −1.48731e9 | − | 2.57609e9i | −0.300988 | − | 0.521327i | 0.675372 | − | 0.737477i | \(-0.263983\pi\) |
−0.976360 | + | 0.216151i | \(0.930650\pi\) | |||||||
\(32\) | 5.36871e8 | + | 9.29888e8i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −9.95727e9 | + | 1.72465e10i | −1.34215 | + | 2.32466i | ||||
\(34\) | −1.08584e10 | −1.20546 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.39538e9 | 0.489666 | ||||||||
\(37\) | −2.86014e9 | + | 4.95391e9i | −0.183264 | + | 0.317422i | −0.942990 | − | 0.332821i | \(-0.892000\pi\) |
0.759726 | + | 0.650243i | \(0.225333\pi\) | |||||||
\(38\) | −5.69408e9 | − | 9.86244e9i | −0.306782 | − | 0.531363i | ||||
\(39\) | −1.54745e10 | − | 2.68026e10i | −0.704200 | − | 1.21971i | ||||
\(40\) | −3.42648e9 | + | 5.93484e9i | −0.132269 | + | 0.229097i | ||||
\(41\) | −2.70618e10 | −0.889738 | −0.444869 | − | 0.895596i | \(-0.646750\pi\) | ||||
−0.444869 | + | 0.895596i | \(0.646750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.32764e10 | 0.561527 | 0.280764 | − | 0.959777i | \(-0.409412\pi\) | ||||
0.280764 | + | 0.959777i | \(0.409412\pi\) | |||||||
\(44\) | −2.29590e10 | + | 3.97661e10i | −0.476991 | + | 0.826173i | ||||
\(45\) | 2.04087e10 | + | 3.53488e10i | 0.366381 | + | 0.634591i | ||||
\(46\) | −1.43132e9 | − | 2.47913e9i | −0.0222747 | − | 0.0385809i | ||||
\(47\) | 1.66537e10 | − | 2.88451e10i | 0.225359 | − | 0.390334i | −0.731068 | − | 0.682305i | \(-0.760978\pi\) |
0.956427 | + | 0.291971i | \(0.0943111\pi\) | |||||||
\(48\) | 2.98035e10 | 0.351722 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.43873e10 | 0.311238 | ||||||||
\(51\) | −1.50697e11 | + | 2.61014e11i | −1.19922 | + | 2.07710i | ||||
\(52\) | −3.56803e10 | − | 6.18001e10i | −0.250269 | − | 0.433478i | ||||
\(53\) | −1.01723e11 | − | 1.76189e11i | −0.630411 | − | 1.09190i | −0.987468 | − | 0.157822i | \(-0.949553\pi\) |
0.357056 | − | 0.934083i | \(-0.383780\pi\) | |||||||
\(54\) | −1.87314e9 | + | 3.24437e9i | −0.0102804 | + | 0.0178062i | ||||
\(55\) | −2.93063e11 | −1.42759 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.16098e11 | −1.22077 | ||||||||
\(58\) | −1.00603e11 | + | 1.74250e11i | −0.347001 | + | 0.601024i | ||||
\(59\) | −1.44370e11 | − | 2.50056e11i | −0.445593 | − | 0.771790i | 0.552500 | − | 0.833513i | \(-0.313674\pi\) |
−0.998093 | + | 0.0617228i | \(0.980341\pi\) | |||||||
\(60\) | 9.51077e10 | + | 1.64731e11i | 0.263168 | + | 0.455820i | ||||
\(61\) | 1.05582e11 | − | 1.82874e11i | 0.262390 | − | 0.454472i | −0.704487 | − | 0.709717i | \(-0.748823\pi\) |
0.966876 | + | 0.255245i | \(0.0821561\pi\) | |||||||
\(62\) | −1.90375e11 | −0.425661 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | 2.27723e11 | − | 3.94427e11i | 0.374515 | − | 0.648680i | ||||
\(66\) | 6.37265e11 | + | 1.10378e12i | 0.949040 | + | 1.64379i | ||||
\(67\) | 2.96224e11 | + | 5.13074e11i | 0.400068 | + | 0.692937i | 0.993734 | − | 0.111774i | \(-0.0356533\pi\) |
−0.593666 | + | 0.804712i | \(0.702320\pi\) | |||||||
\(68\) | −3.47469e11 | + | 6.01834e11i | −0.426195 | + | 0.738191i | ||||
\(69\) | −7.94576e10 | −0.0886373 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.43181e12 | 1.32649 | 0.663247 | − | 0.748401i | \(-0.269178\pi\) | ||||
0.663247 | + | 0.748401i | \(0.269178\pi\) | |||||||
\(72\) | 2.04652e11 | − | 3.54468e11i | 0.173123 | − | 0.299858i | ||||
\(73\) | 3.23132e11 | + | 5.59681e11i | 0.249909 | + | 0.432854i | 0.963500 | − | 0.267708i | \(-0.0862661\pi\) |
−0.713592 | + | 0.700562i | \(0.752933\pi\) | |||||||
\(74\) | 1.83049e11 | + | 3.17050e11i | 0.129587 | + | 0.224451i | ||||
\(75\) | 4.77238e11 | − | 8.26601e11i | 0.309626 | − | 0.536287i | ||||
\(76\) | −7.28843e11 | −0.433856 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.98073e12 | −0.995889 | ||||||||
\(79\) | −9.00359e11 | + | 1.55947e12i | −0.416716 | + | 0.721773i | −0.995607 | − | 0.0936322i | \(-0.970152\pi\) |
0.578891 | + | 0.815405i | \(0.303486\pi\) | |||||||
\(80\) | 2.19295e11 | + | 3.79829e11i | 0.0935283 | + | 0.161996i | ||||
\(81\) | 1.29666e12 | + | 2.24588e12i | 0.510120 | + | 0.883554i | ||||
\(82\) | −8.65979e11 | + | 1.49992e12i | −0.314570 | + | 0.544851i | ||||
\(83\) | 4.71815e12 | 1.58403 | 0.792017 | − | 0.610499i | \(-0.209031\pi\) | ||||
0.792017 | + | 0.610499i | \(0.209031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.43531e12 | −1.27556 | ||||||||
\(86\) | 7.44845e11 | − | 1.29011e12i | 0.198530 | − | 0.343864i | ||||
\(87\) | 2.79242e12 | + | 4.83661e12i | 0.690407 | + | 1.19582i | ||||
\(88\) | 1.46937e12 | + | 2.54503e12i | 0.337284 | + | 0.584192i | ||||
\(89\) | 1.31611e12 | − | 2.27956e12i | 0.280709 | − | 0.486202i | −0.690851 | − | 0.722998i | \(-0.742764\pi\) |
0.971560 | + | 0.236795i | \(0.0760971\pi\) | |||||||
\(90\) | 2.61231e12 | 0.518141 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.83210e11 | −0.0315012 | ||||||||
\(93\) | −2.64209e12 | + | 4.57624e12i | −0.423456 | + | 0.733448i | ||||
\(94\) | −1.06584e12 | − | 1.84609e12i | −0.159353 | − | 0.276008i | ||||
\(95\) | −2.32585e12 | − | 4.02849e12i | −0.324622 | − | 0.562263i | ||||
\(96\) | 9.53712e11 | − | 1.65188e12i | 0.124352 | − | 0.215385i | ||||
\(97\) | 7.42070e12 | 0.904542 | 0.452271 | − | 0.891881i | \(-0.350614\pi\) | ||||
0.452271 | + | 0.891881i | \(0.350614\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.75037e13 | 1.86853 | ||||||||
\(100\) | 1.10039e12 | − | 1.90594e12i | 0.110039 | − | 0.190594i | ||||
\(101\) | −7.57462e12 | − | 1.31196e13i | −0.710022 | − | 1.22979i | −0.964848 | − | 0.262807i | \(-0.915352\pi\) |
0.254827 | − | 0.966987i | \(-0.417982\pi\) | |||||||
\(102\) | 9.64459e12 | + | 1.67049e13i | 0.847974 | + | 1.46873i | ||||
\(103\) | −2.23826e12 | + | 3.87678e12i | −0.184701 | + | 0.319911i | −0.943476 | − | 0.331442i | \(-0.892465\pi\) |
0.758775 | + | 0.651353i | \(0.225798\pi\) | |||||||
\(104\) | −4.56708e12 | −0.353933 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.30205e13 | −0.891536 | ||||||||
\(107\) | 1.22649e13 | − | 2.12434e13i | 0.790075 | − | 1.36845i | −0.135845 | − | 0.990730i | \(-0.543375\pi\) |
0.925920 | − | 0.377720i | \(-0.123292\pi\) | |||||||
\(108\) | 1.19881e11 | + | 2.07640e11i | 0.00726935 | + | 0.0125909i | ||||
\(109\) | −1.31592e13 | − | 2.27923e13i | −0.751547 | − | 1.30172i | −0.947073 | − | 0.321019i | \(-0.895975\pi\) |
0.195526 | − | 0.980698i | \(-0.437359\pi\) | |||||||
\(110\) | −9.37801e12 | + | 1.62432e13i | −0.504729 | + | 0.874216i | ||||
\(111\) | 1.01617e13 | 0.515663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.80988e12 | 0.262517 | 0.131258 | − | 0.991348i | \(-0.458098\pi\) | ||||
0.131258 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(114\) | −1.01151e13 | + | 1.75199e13i | −0.431608 | + | 0.747567i | ||||
\(115\) | −5.84650e11 | − | 1.01264e12i | −0.0235700 | − | 0.0408245i | ||||
\(116\) | 6.43862e12 | + | 1.11520e13i | 0.245367 | + | 0.424988i | ||||
\(117\) | −1.36011e13 | + | 2.35578e13i | −0.490192 | + | 0.849038i | ||||
\(118\) | −1.84793e13 | −0.630164 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.21738e13 | 0.372175 | ||||||||
\(121\) | −4.55756e13 | + | 7.89393e13i | −1.32016 | + | 2.28659i | ||||
\(122\) | −6.75726e12 | − | 1.17039e13i | −0.185538 | − | 0.321360i | ||||
\(123\) | 2.40367e13 | + | 4.16328e13i | 0.625881 | + | 1.08406i | ||||
\(124\) | −6.09200e12 | + | 1.05517e13i | −0.150494 | + | 0.260663i | ||||
\(125\) | 4.59577e13 | 1.07756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00151e13 | 1.48070 | 0.740350 | − | 0.672221i | \(-0.234660\pi\) | ||||
0.740350 | + | 0.672221i | \(0.234660\pi\) | |||||||
\(128\) | 2.19902e12 | − | 3.80882e12i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −2.06744e13 | − | 3.58091e13i | −0.395003 | − | 0.684165i | ||||
\(130\) | −1.45743e13 | − | 2.52434e13i | −0.264822 | − | 0.458686i | ||||
\(131\) | −5.84582e12 | + | 1.01253e13i | −0.101061 | + | 0.175042i | −0.912122 | − | 0.409919i | \(-0.865557\pi\) |
0.811061 | + | 0.584961i | \(0.198890\pi\) | |||||||
\(132\) | 8.15699e13 | 1.34215 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.79166e13 | 0.565781 | ||||||||
\(135\) | −7.65118e11 | + | 1.32522e12i | −0.0108782 | + | 0.0188417i | ||||
\(136\) | 2.22380e13 | + | 3.85174e13i | 0.301365 | + | 0.521980i | ||||
\(137\) | 4.59295e13 | + | 7.95522e13i | 0.593482 | + | 1.02794i | 0.993759 | + | 0.111547i | \(0.0355806\pi\) |
−0.400277 | + | 0.916394i | \(0.631086\pi\) | |||||||
\(138\) | −2.54264e12 | + | 4.40399e12i | −0.0313380 | + | 0.0542790i | ||||
\(139\) | 7.33962e13 | 0.863132 | 0.431566 | − | 0.902081i | \(-0.357961\pi\) | ||||
0.431566 | + | 0.902081i | \(0.357961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.91683e13 | −0.634110 | ||||||||
\(142\) | 4.58178e13 | − | 7.93588e13i | 0.468986 | − | 0.812308i | ||||
\(143\) | −9.76542e13 | − | 1.69142e14i | −0.955007 | − | 1.65412i | ||||
\(144\) | −1.30977e13 | − | 2.26859e13i | −0.122417 | − | 0.212032i | ||||
\(145\) | −4.10933e13 | + | 7.11757e13i | −0.367180 | + | 0.635975i | ||||
\(146\) | 4.13609e13 | 0.353424 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.34303e13 | 0.183264 | ||||||||
\(149\) | −4.61464e12 | + | 7.99279e12i | −0.0345483 | + | 0.0598394i | −0.882783 | − | 0.469782i | \(-0.844333\pi\) |
0.848234 | + | 0.529621i | \(0.177666\pi\) | |||||||
\(150\) | −3.05432e13 | − | 5.29025e13i | −0.218938 | − | 0.379212i | ||||
\(151\) | 2.95582e13 | + | 5.11963e13i | 0.202922 | + | 0.351470i | 0.949469 | − | 0.313862i | \(-0.101623\pi\) |
−0.746547 | + | 0.665333i | \(0.768290\pi\) | |||||||
\(152\) | −2.33230e13 | + | 4.03966e13i | −0.153391 | + | 0.265681i | ||||
\(153\) | 2.64906e14 | 1.66954 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.77622e13 | −0.450414 | ||||||||
\(156\) | −6.33834e13 | + | 1.09783e14i | −0.352100 | + | 0.609855i | ||||
\(157\) | 1.05245e14 | + | 1.82289e14i | 0.560857 | + | 0.971433i | 0.997422 | + | 0.0717600i | \(0.0228616\pi\) |
−0.436565 | + | 0.899673i | \(0.643805\pi\) | |||||||
\(158\) | 5.76230e13 | + | 9.98060e13i | 0.294662 | + | 0.510370i | ||||
\(159\) | −1.80703e14 | + | 3.12986e14i | −0.886918 | + | 1.53619i | ||||
\(160\) | 2.80697e13 | 0.132269 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.65972e14 | 0.721419 | ||||||||
\(163\) | 1.90304e14 | − | 3.29617e14i | 0.794748 | − | 1.37654i | −0.128251 | − | 0.991742i | \(-0.540936\pi\) |
0.922999 | − | 0.384802i | \(-0.125730\pi\) | |||||||
\(164\) | 5.54226e13 | + | 9.59948e13i | 0.222435 | + | 0.385268i | ||||
\(165\) | 2.60302e14 | + | 4.50857e14i | 1.00423 | + | 1.73937i | ||||
\(166\) | 1.50981e14 | − | 2.61507e14i | 0.560041 | − | 0.970019i | ||||
\(167\) | −4.07830e12 | −0.0145486 | −0.00727431 | − | 0.999974i | \(-0.502316\pi\) | ||||
−0.00727431 | + | 0.999974i | \(0.502316\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.51455e11 | 0.00215090 | ||||||||
\(170\) | −1.41930e14 | + | 2.45830e14i | −0.450979 | + | 0.781118i | ||||
\(171\) | 1.38915e14 | + | 2.40608e14i | 0.424889 | + | 0.735929i | ||||
\(172\) | −4.76700e13 | − | 8.25669e13i | −0.140382 | − | 0.243148i | ||||
\(173\) | 1.89881e14 | − | 3.28883e14i | 0.538494 | − | 0.932699i | −0.460491 | − | 0.887664i | \(-0.652327\pi\) |
0.998985 | − | 0.0450349i | \(-0.0143399\pi\) | |||||||
\(174\) | 3.57430e14 | 0.976383 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.88080e14 | 0.476991 | ||||||||
\(177\) | −2.56463e14 | + | 4.44206e14i | −0.626899 | + | 1.08582i | ||||
\(178\) | −8.42309e13 | − | 1.45892e14i | −0.198491 | − | 0.343797i | ||||
\(179\) | 1.77670e14 | + | 3.07733e14i | 0.403710 | + | 0.699245i | 0.994170 | − | 0.107821i | \(-0.0343873\pi\) |
−0.590461 | + | 0.807066i | \(0.701054\pi\) | |||||||
\(180\) | 8.35939e13 | − | 1.44789e14i | 0.183191 | − | 0.317295i | ||||
\(181\) | 4.78841e14 | 1.01223 | 0.506117 | − | 0.862465i | \(-0.331081\pi\) | ||||
0.506117 | + | 0.862465i | \(0.331081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.75118e14 | −0.738305 | ||||||||
\(184\) | −5.86270e12 | + | 1.01545e13i | −0.0111374 | + | 0.0192905i | ||||
\(185\) | 7.47697e13 | + | 1.29505e14i | 0.137123 | + | 0.237504i | ||||
\(186\) | 1.69094e14 | + | 2.92879e14i | 0.299429 | + | 0.518626i | ||||
\(187\) | −9.50996e14 | + | 1.64717e15i | −1.62633 | + | 2.81688i | ||||
\(188\) | −1.36427e14 | −0.225359 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.97709e14 | −0.459085 | ||||||||
\(191\) | −5.26670e14 | + | 9.12220e14i | −0.784914 | + | 1.35951i | 0.144136 | + | 0.989558i | \(0.453960\pi\) |
−0.929050 | + | 0.369953i | \(0.879374\pi\) | |||||||
\(192\) | −6.10376e13 | − | 1.05720e14i | −0.0879305 | − | 0.152300i | ||||
\(193\) | −2.76447e14 | − | 4.78821e14i | −0.385026 | − | 0.666884i | 0.606747 | − | 0.794895i | \(-0.292474\pi\) |
−0.991773 | + | 0.128011i | \(0.959141\pi\) | |||||||
\(194\) | 2.37462e14 | − | 4.11297e14i | 0.319804 | − | 0.553916i | ||||
\(195\) | −8.09066e14 | −1.05380 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.54122e14 | 0.309750 | 0.154875 | − | 0.987934i | \(-0.450502\pi\) | ||||
0.154875 | + | 0.987934i | \(0.450502\pi\) | |||||||
\(198\) | 5.60117e14 | − | 9.70151e14i | 0.660625 | − | 1.14424i | ||||
\(199\) | 2.34714e14 | + | 4.06536e14i | 0.267913 | + | 0.464039i | 0.968323 | − | 0.249702i | \(-0.0803328\pi\) |
−0.700410 | + | 0.713741i | \(0.746999\pi\) | |||||||
\(200\) | −7.04251e13 | − | 1.21980e14i | −0.0778095 | − | 0.134770i | ||||
\(201\) | 5.26220e14 | − | 9.11439e14i | 0.562850 | − | 0.974885i | ||||
\(202\) | −9.69551e14 | −1.00412 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.23451e15 | 1.19922 | ||||||||
\(205\) | −3.53725e14 | + | 6.12669e14i | −0.332863 | + | 0.576535i | ||||
\(206\) | 1.43249e14 | + | 2.48114e14i | 0.130603 | + | 0.226211i | ||||
\(207\) | 3.49192e13 | + | 6.04818e13i | 0.0308501 | + | 0.0534340i | ||||
\(208\) | −1.46146e14 | + | 2.53133e14i | −0.125134 | + | 0.216739i | ||||
\(209\) | −1.99479e15 | −1.65556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.12280e14 | 0.165605 | 0.0828026 | − | 0.996566i | \(-0.473613\pi\) | ||||
0.0828026 | + | 0.996566i | \(0.473613\pi\) | |||||||
\(212\) | −4.16656e14 | + | 7.21669e14i | −0.315206 | + | 0.545952i | ||||
\(213\) | −1.27175e15 | − | 2.20274e15i | −0.933114 | − | 1.61620i | ||||
\(214\) | −7.84951e14 | − | 1.35958e15i | −0.558667 | − | 0.967640i | ||||
\(215\) | 3.04245e14 | − | 5.26968e14i | 0.210075 | − | 0.363860i | ||||
\(216\) | 1.53448e13 | 0.0102804 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.68437e15 | −1.06285 | ||||||||
\(219\) | 5.74020e14 | − | 9.94232e14i | 0.351593 | − | 0.608977i | ||||
\(220\) | 6.00193e14 | + | 1.03956e15i | 0.356897 | + | 0.618164i | ||||
\(221\) | −1.47793e15 | − | 2.55985e15i | −0.853306 | − | 1.47797i | ||||
\(222\) | 3.25174e14 | − | 5.63217e14i | 0.182314 | − | 0.315778i | ||||
\(223\) | 2.01582e15 | 1.09766 | 0.548832 | − | 0.835933i | \(-0.315073\pi\) | ||||
0.548832 | + | 0.835933i | \(0.315073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.38927e14 | −0.431060 | ||||||||
\(226\) | 1.85916e14 | − | 3.22016e14i | 0.0928138 | − | 0.160758i | ||||
\(227\) | −1.03207e15 | − | 1.78760e15i | −0.500658 | − | 0.867165i | −1.00000 | 0.000759878i | \(-0.999758\pi\) | |
0.499342 | − | 0.866405i | \(-0.333575\pi\) | |||||||
\(228\) | 6.47368e14 | + | 1.12127e15i | 0.305193 | + | 0.528610i | ||||
\(229\) | −6.95631e14 | + | 1.20487e15i | −0.318749 | + | 0.552089i | −0.980227 | − | 0.197875i | \(-0.936596\pi\) |
0.661478 | + | 0.749964i | \(0.269929\pi\) | |||||||
\(230\) | −7.48352e13 | −0.0333331 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.24144e14 | 0.347001 | ||||||||
\(233\) | 5.49511e14 | − | 9.51781e14i | 0.224990 | − | 0.389694i | −0.731327 | − | 0.682027i | \(-0.761098\pi\) |
0.956316 | + | 0.292334i | \(0.0944318\pi\) | |||||||
\(234\) | 8.70472e14 | + | 1.50770e15i | 0.346618 | + | 0.600361i | ||||
\(235\) | −4.35361e14 | − | 7.54068e14i | −0.168620 | − | 0.292058i | ||||
\(236\) | −5.91339e14 | + | 1.02423e15i | −0.222797 | + | 0.385895i | ||||
\(237\) | 3.19885e15 | 1.17254 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.56720e15 | −0.890991 | −0.445496 | − | 0.895284i | \(-0.646972\pi\) | ||||
−0.445496 | + | 0.895284i | \(0.646972\pi\) | |||||||
\(240\) | 3.89561e14 | − | 6.74740e14i | 0.131584 | − | 0.227910i | ||||
\(241\) | −9.42088e14 | − | 1.63174e15i | −0.309728 | − | 0.536465i | 0.668575 | − | 0.743645i | \(-0.266905\pi\) |
−0.978303 | + | 0.207180i | \(0.933571\pi\) | |||||||
\(242\) | 2.91684e15 | + | 5.05211e15i | 0.933496 | + | 1.61686i | ||||
\(243\) | 2.25676e15 | − | 3.90882e15i | 0.703143 | − | 1.21788i | ||||
\(244\) | −8.64929e14 | −0.262390 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.07670e15 | 0.885129 | ||||||||
\(247\) | 1.55004e15 | − | 2.68474e15i | 0.434322 | − | 0.752268i | ||||
\(248\) | 3.89888e14 | + | 6.75306e14i | 0.106415 | + | 0.184317i | ||||
\(249\) | −4.19073e15 | − | 7.25856e15i | −1.11428 | − | 1.92999i | ||||
\(250\) | 1.47065e15 | − | 2.54723e15i | 0.380976 | − | 0.659870i | ||||
\(251\) | −5.62418e15 | −1.41965 | −0.709823 | − | 0.704380i | \(-0.751225\pi\) | ||||
−0.709823 | + | 0.704380i | \(0.751225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.01430e14 | −0.120206 | ||||||||
\(254\) | 2.24048e15 | − | 3.88063e15i | 0.523507 | − | 0.906740i | ||||
\(255\) | 3.93951e15 | + | 6.82342e15i | 0.897285 | + | 1.55414i | ||||
\(256\) | −1.40737e14 | − | 2.43764e14i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.18486e15 | + | 2.05224e15i | −0.256509 | + | 0.444286i | −0.965304 | − | 0.261128i | \(-0.915906\pi\) |
0.708795 | + | 0.705414i | \(0.249239\pi\) | |||||||
\(258\) | −2.64632e15 | −0.558618 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.86551e15 | −0.374515 | ||||||||
\(261\) | 2.45437e15 | − | 4.25109e15i | 0.480591 | − | 0.832409i | ||||
\(262\) | 3.74133e14 | + | 6.48017e14i | 0.0714607 | + | 0.123774i | ||||
\(263\) | 9.63982e14 | + | 1.66967e15i | 0.179621 | + | 0.311112i | 0.941751 | − | 0.336312i | \(-0.109180\pi\) |
−0.762130 | + | 0.647424i | \(0.775846\pi\) | |||||||
\(264\) | 2.61024e15 | − | 4.52106e15i | 0.474520 | − | 0.821893i | ||||
\(265\) | −5.31845e15 | −0.943381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.67594e15 | −0.789852 | ||||||||
\(268\) | 1.21333e15 | − | 2.10155e15i | 0.200034 | − | 0.346469i | ||||
\(269\) | −2.46115e15 | − | 4.26284e15i | −0.396049 | − | 0.685976i | 0.597186 | − | 0.802103i | \(-0.296285\pi\) |
−0.993234 | + | 0.116127i | \(0.962952\pi\) | |||||||
\(270\) | 4.89676e13 | + | 8.48143e13i | 0.00769208 | + | 0.0133231i | ||||
\(271\) | 1.09879e15 | − | 1.90315e15i | 0.168505 | − | 0.291859i | −0.769389 | − | 0.638780i | \(-0.779439\pi\) |
0.937894 | + | 0.346921i | \(0.112773\pi\) | |||||||
\(272\) | 2.84647e15 | 0.426195 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.87897e15 | 0.839311 | ||||||||
\(275\) | 3.01169e15 | − | 5.21640e15i | 0.419902 | − | 0.727291i | ||||
\(276\) | 1.62729e14 | + | 2.81855e14i | 0.0221593 | + | 0.0383811i | ||||
\(277\) | −5.28042e14 | − | 9.14596e14i | −0.0702345 | − | 0.121650i | 0.828770 | − | 0.559590i | \(-0.189041\pi\) |
−0.899004 | + | 0.437940i | \(0.855708\pi\) | |||||||
\(278\) | 2.34868e15 | − | 4.06803e15i | 0.305163 | − | 0.528559i | ||||
\(279\) | 4.64447e15 | 0.589534 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.64590e15 | −0.320614 | −0.160307 | − | 0.987067i | \(-0.551248\pi\) | ||||
−0.160307 | + | 0.987067i | \(0.551248\pi\) | |||||||
\(282\) | −1.89339e15 | + | 3.27944e15i | −0.224192 | + | 0.388312i | ||||
\(283\) | −3.50100e15 | − | 6.06390e15i | −0.405116 | − | 0.701682i | 0.589219 | − | 0.807974i | \(-0.299436\pi\) |
−0.994335 | + | 0.106291i | \(0.966102\pi\) | |||||||
\(284\) | −2.93234e15 | − | 5.07896e15i | −0.331623 | − | 0.574389i | ||||
\(285\) | −4.13171e15 | + | 7.15632e15i | −0.456707 | + | 0.791040i | ||||
\(286\) | −1.24997e16 | −1.35058 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.67651e15 | −0.173123 | ||||||||
\(289\) | −9.44041e15 | + | 1.63513e16i | −0.953136 | + | 1.65088i | ||||
\(290\) | 2.62997e15 | + | 4.55524e15i | 0.259636 | + | 0.449702i | ||||
\(291\) | −6.59117e15 | − | 1.14162e16i | −0.636294 | − | 1.10209i | ||||
\(292\) | 1.32355e15 | − | 2.29245e15i | 0.124954 | − | 0.216427i | ||||
\(293\) | −8.77788e15 | −0.810495 | −0.405247 | − | 0.914207i | \(-0.632815\pi\) | ||||
−0.405247 | + | 0.914207i | \(0.632815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.54822e15 | −0.666809 | ||||||||
\(296\) | 7.49769e14 | − | 1.29864e15i | 0.0647935 | − | 0.112226i | ||||
\(297\) | 3.28105e14 | + | 5.68295e14i | 0.0277393 | + | 0.0480459i | ||||
\(298\) | 2.95337e14 | + | 5.11538e14i | 0.0244294 | + | 0.0423129i | ||||
\(299\) | 3.89634e14 | − | 6.74865e14i | 0.0315351 | − | 0.0546203i | ||||
\(300\) | −3.90954e15 | −0.309626 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.78345e15 | 0.286974 | ||||||||
\(303\) | −1.34558e16 | + | 2.33061e16i | −0.998921 | + | 1.73018i | ||||
\(304\) | 1.49267e15 | + | 2.58538e15i | 0.108464 | + | 0.187865i | ||||
\(305\) | −2.76013e15 | − | 4.78068e15i | −0.196327 | − | 0.340048i | ||||
\(306\) | 8.47700e15 | − | 1.46826e16i | 0.590273 | − | 1.02238i | ||||
\(307\) | 9.75008e15 | 0.664674 | 0.332337 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332337 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.95222e15 | 0.519706 | ||||||||
\(310\) | −2.48839e15 | + | 4.31002e15i | −0.159246 | + | 0.275821i | ||||
\(311\) | −1.93994e15 | − | 3.36007e15i | −0.121575 | − | 0.210574i | 0.798814 | − | 0.601578i | \(-0.205461\pi\) |
−0.920389 | + | 0.391004i | \(0.872128\pi\) | |||||||
\(312\) | 4.05654e15 | + | 7.02613e15i | 0.248972 | + | 0.431233i | ||||
\(313\) | −8.38718e15 | + | 1.45270e16i | −0.504171 | + | 0.873250i | 0.495817 | + | 0.868427i | \(0.334869\pi\) |
−0.999988 | + | 0.00482294i | \(0.998465\pi\) | |||||||
\(314\) | 1.34713e16 | 0.793171 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.37574e15 | 0.416716 | ||||||||
\(317\) | −7.59188e15 | + | 1.31495e16i | −0.420208 | + | 0.727821i | −0.995960 | − | 0.0898033i | \(-0.971376\pi\) |
0.575752 | + | 0.817625i | \(0.304710\pi\) | |||||||
\(318\) | 1.15650e16 | + | 2.00311e16i | 0.627146 | + | 1.08625i | ||||
\(319\) | 1.76220e16 | + | 3.05222e16i | 0.936302 | + | 1.62172i | ||||
\(320\) | 8.98231e14 | − | 1.55578e15i | 0.0467642 | − | 0.0809979i | ||||
\(321\) | −4.35753e16 | −2.22309 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.01898e16 | −1.47926 | ||||||||
\(324\) | 5.31111e15 | − | 9.19911e15i | 0.255060 | − | 0.441777i | ||||
\(325\) | 4.68043e15 | + | 8.10675e15i | 0.220315 | + | 0.381597i | ||||
\(326\) | −1.21795e16 | − | 2.10955e16i | −0.561972 | − | 0.973363i | ||||
\(327\) | −2.33763e16 | + | 4.04889e16i | −1.05734 | + | 1.83137i | ||||
\(328\) | 7.09410e15 | 0.314570 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.33187e16 | 1.42019 | ||||||||
\(331\) | 1.56486e16 | − | 2.71041e16i | 0.654022 | − | 1.13280i | −0.328116 | − | 0.944637i | \(-0.606414\pi\) |
0.982138 | − | 0.188162i | \(-0.0602529\pi\) | |||||||
\(332\) | −9.66278e15 | − | 1.67364e16i | −0.396008 | − | 0.685907i | ||||
\(333\) | −4.46575e15 | − | 7.73490e15i | −0.179476 | − | 0.310862i | ||||
\(334\) | −1.30506e14 | + | 2.26042e14i | −0.00514372 | + | 0.00890918i | ||||
\(335\) | 1.54877e16 | 0.598682 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.55957e16 | −0.579978 | −0.289989 | − | 0.957030i | \(-0.593652\pi\) | ||||
−0.289989 | + | 0.957030i | \(0.593652\pi\) | |||||||
\(338\) | 2.08466e13 | − | 3.61073e13i | 0.000760459 | − | 0.00131715i | ||||
\(339\) | −5.16042e15 | − | 8.93810e15i | −0.184666 | − | 0.319851i | ||||
\(340\) | 9.08352e15 | + | 1.57331e16i | 0.318890 | + | 0.552334i | ||||
\(341\) | −1.66733e16 | + | 2.88791e16i | −0.574274 | + | 0.994672i | ||||
\(342\) | 1.77812e16 | 0.600884 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.10177e15 | −0.198530 | ||||||||
\(345\) | −1.03859e15 | + | 1.79889e15i | −0.0331604 | + | 0.0574355i | ||||
\(346\) | −1.21524e16 | − | 2.10485e16i | −0.380773 | − | 0.659518i | ||||
\(347\) | 3.14836e16 | + | 5.45312e16i | 0.968150 | + | 1.67688i | 0.700903 | + | 0.713257i | \(0.252781\pi\) |
0.267247 | + | 0.963628i | \(0.413886\pi\) | |||||||
\(348\) | 1.14377e16 | − | 1.98108e16i | 0.345204 | − | 0.597910i | ||||
\(349\) | 6.18328e16 | 1.83170 | 0.915848 | − | 0.401524i | \(-0.131519\pi\) | ||||
0.915848 | + | 0.401524i | \(0.131519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.01981e15 | −0.0291087 | ||||||||
\(352\) | 6.01856e15 | − | 1.04244e16i | 0.168642 | − | 0.292096i | ||||
\(353\) | 5.56148e15 | + | 9.63276e15i | 0.152987 | + | 0.264981i | 0.932324 | − | 0.361623i | \(-0.117777\pi\) |
−0.779337 | + | 0.626605i | \(0.784444\pi\) | |||||||
\(354\) | 1.64136e16 | + | 2.84292e16i | 0.443285 | + | 0.767792i | ||||
\(355\) | 1.87151e16 | − | 3.24155e16i | 0.496259 | − | 0.859546i | ||||
\(356\) | −1.07815e16 | −0.280709 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.27417e16 | 0.570932 | ||||||||
\(359\) | 3.10479e16 | − | 5.37765e16i | 0.765453 | − | 1.32580i | −0.174554 | − | 0.984648i | \(-0.555848\pi\) |
0.940007 | − | 0.341155i | \(-0.110818\pi\) | |||||||
\(360\) | −5.35001e15 | − | 9.26648e15i | −0.129535 | − | 0.224362i | ||||
\(361\) | 5.19515e15 | + | 8.99827e15i | 0.123538 | + | 0.213975i | ||||
\(362\) | 1.53229e16 | − | 2.65401e16i | 0.357879 | − | 0.619864i | ||||
\(363\) | 1.61924e17 | 3.71464 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.68946e16 | 0.373976 | ||||||||
\(366\) | −1.20038e16 | + | 2.07912e16i | −0.261030 | + | 0.452118i | ||||
\(367\) | −1.01257e16 | − | 1.75383e16i | −0.216320 | − | 0.374678i | 0.737360 | − | 0.675500i | \(-0.236072\pi\) |
−0.953680 | + | 0.300822i | \(0.902739\pi\) | |||||||
\(368\) | 3.75213e14 | + | 6.49888e14i | 0.00787530 | + | 0.0136404i | ||||
\(369\) | 2.11268e16 | − | 3.65927e16i | 0.435675 | − | 0.754610i | ||||
\(370\) | 9.57053e15 | 0.193921 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.16440e16 | 0.423456 | ||||||||
\(373\) | −1.91899e16 | + | 3.32379e16i | −0.368949 | + | 0.639038i | −0.989401 | − | 0.145206i | \(-0.953616\pi\) |
0.620453 | + | 0.784244i | \(0.286949\pi\) | |||||||
\(374\) | 6.08637e16 | + | 1.05419e17i | 1.14999 | + | 1.99184i | ||||
\(375\) | −4.08202e16 | − | 7.07027e16i | −0.758005 | − | 1.31290i | ||||
\(376\) | −4.36568e15 | + | 7.56157e15i | −0.0796766 | + | 0.138004i | ||||
\(377\) | −5.47723e16 | −0.982523 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.21687e16 | 0.904180 | 0.452090 | − | 0.891972i | \(-0.350679\pi\) | ||||
0.452090 | + | 0.891972i | \(0.350679\pi\) | |||||||
\(380\) | −9.52669e15 | + | 1.65007e16i | −0.162311 | + | 0.281131i | ||||
\(381\) | −6.21883e16 | − | 1.07713e17i | −1.04159 | − | 1.80409i | ||||
\(382\) | 3.37069e16 | + | 5.83821e16i | 0.555018 | + | 0.961319i | ||||
\(383\) | −4.92433e16 | + | 8.52919e16i | −0.797178 | + | 1.38075i | 0.124269 | + | 0.992249i | \(0.460341\pi\) |
−0.921447 | + | 0.388504i | \(0.872992\pi\) | |||||||
\(384\) | −7.81281e15 | −0.124352 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.53852e16 | −0.544509 | ||||||||
\(387\) | −1.81715e16 | + | 3.14740e16i | −0.274961 | + | 0.476246i | ||||
\(388\) | −1.51976e16 | − | 2.63230e16i | −0.226135 | − | 0.391678i | ||||
\(389\) | 3.52381e16 | + | 6.10343e16i | 0.515633 | + | 0.893102i | 0.999835 | + | 0.0181464i | \(0.00577650\pi\) |
−0.484202 | + | 0.874956i | \(0.660890\pi\) | |||||||
\(390\) | −2.58901e16 | + | 4.48430e16i | −0.372575 | + | 0.645319i | ||||
\(391\) | −7.58882e15 | −0.107405 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.07694e16 | 0.284362 | ||||||||
\(394\) | 8.13190e15 | − | 1.40849e16i | 0.109513 | − | 0.189683i | ||||
\(395\) | 2.35372e16 | + | 4.07675e16i | 0.311798 | + | 0.540049i | ||||
\(396\) | −3.58475e16 | − | 6.20897e16i | −0.467133 | − | 0.809097i | ||||
\(397\) | −6.16634e16 | + | 1.06804e17i | −0.790477 | + | 1.36915i | 0.135195 | + | 0.990819i | \(0.456834\pi\) |
−0.925672 | + | 0.378327i | \(0.876499\pi\) | |||||||
\(398\) | 3.00434e16 | 0.378886 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.01442e15 | −0.110039 | ||||||||
\(401\) | −3.63043e16 | + | 6.28809e16i | −0.436033 | + | 0.755232i | −0.997379 | − | 0.0723493i | \(-0.976950\pi\) |
0.561346 | + | 0.827581i | \(0.310284\pi\) | |||||||
\(402\) | −3.36781e16 | − | 5.83321e16i | −0.397995 | − | 0.689348i | ||||
\(403\) | −2.59119e16 | − | 4.48807e16i | −0.301312 | − | 0.521887i | ||||
\(404\) | −3.10256e16 | + | 5.37380e16i | −0.355011 | + | 0.614897i | ||||
\(405\) | 6.77943e16 | 0.763371 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.41269e16 | 0.699321 | ||||||||
\(408\) | 3.95042e16 | − | 6.84233e16i | 0.423987 | − | 0.734367i | ||||
\(409\) | −3.12800e16 | − | 5.41785e16i | −0.330419 | − | 0.572302i | 0.652175 | − | 0.758068i | \(-0.273857\pi\) |
−0.982594 | + | 0.185766i | \(0.940523\pi\) | |||||||
\(410\) | 2.26384e16 | + | 3.92108e16i | 0.235370 | + | 0.407672i | ||||
\(411\) | 8.15904e16 | − | 1.41319e17i | 0.834963 | − | 1.44620i | ||||
\(412\) | 1.83358e16 | 0.184701 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.46966e15 | 0.0436287 | ||||||||
\(415\) | 6.16709e16 | − | 1.06817e17i | 0.592608 | − | 1.02643i | ||||
\(416\) | 9.35337e15 | + | 1.62005e16i | 0.0884834 | + | 0.153258i | ||||
\(417\) | −6.51915e16 | − | 1.12915e17i | −0.607165 | − | 1.05164i | ||||
\(418\) | −6.38332e16 | + | 1.10562e17i | −0.585330 | + | 1.01382i | ||||
\(419\) | −1.88865e17 | −1.70514 | −0.852569 | − | 0.522615i | \(-0.824956\pi\) | ||||
−0.852569 | + | 0.522615i | \(0.824956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.13170e17 | −0.990597 | −0.495299 | − | 0.868723i | \(-0.664941\pi\) | ||||
−0.495299 | + | 0.868723i | \(0.664941\pi\) | |||||||
\(422\) | 6.79297e15 | − | 1.17658e16i | 0.0585502 | − | 0.101412i | ||||
\(423\) | 2.60027e16 | + | 4.50379e16i | 0.220702 | + | 0.382266i | ||||
\(424\) | 2.66660e16 | + | 4.61868e16i | 0.222884 | + | 0.386047i | ||||
\(425\) | 4.55799e16 | − | 7.89468e16i | 0.375185 | − | 0.649840i | ||||
\(426\) | −1.62784e17 | −1.31962 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.00474e17 | −0.790075 | ||||||||
\(429\) | −1.73476e17 | + | 3.00469e17i | −1.34359 | + | 2.32716i | ||||
\(430\) | −1.94717e16 | − | 3.37260e16i | −0.148545 | − | 0.257288i | ||||
\(431\) | 5.90084e16 | + | 1.02205e17i | 0.443416 | + | 0.768019i | 0.997940 | − | 0.0641485i | \(-0.0204331\pi\) |
−0.554524 | + | 0.832167i | \(0.687100\pi\) | |||||||
\(432\) | 4.91032e14 | − | 8.50493e14i | 0.00363468 | − | 0.00629545i | ||||
\(433\) | −1.18291e17 | −0.862540 | −0.431270 | − | 0.902223i | \(-0.641934\pi\) | ||||
−0.431270 | + | 0.902223i | \(0.641934\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.45999e17 | 1.03316 | ||||||||
\(436\) | −5.38999e16 | + | 9.33574e16i | −0.375773 | + | 0.650859i | ||||
\(437\) | −3.97953e15 | − | 6.89275e15i | −0.0273340 | − | 0.0473438i | ||||
\(438\) | −3.67373e16 | − | 6.36309e16i | −0.248614 | − | 0.430612i | ||||
\(439\) | 3.45621e16 | − | 5.98633e16i | 0.230452 | − | 0.399155i | −0.727489 | − | 0.686119i | \(-0.759313\pi\) |
0.957941 | + | 0.286965i | \(0.0926462\pi\) | |||||||
\(440\) | 7.68247e16 | 0.504729 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.89175e17 | −1.20676 | ||||||||
\(443\) | −2.99317e15 | + | 5.18432e15i | −0.0188151 | + | 0.0325888i | −0.875280 | − | 0.483617i | \(-0.839323\pi\) |
0.856465 | + | 0.516206i | \(0.172656\pi\) | |||||||
\(444\) | −2.08111e16 | − | 3.60459e16i | −0.128916 | − | 0.223289i | ||||
\(445\) | −3.44056e16 | − | 5.95923e16i | −0.210034 | − | 0.363789i | ||||
\(446\) | 6.45061e16 | − | 1.11728e17i | 0.388083 | − | 0.672179i | ||||
\(447\) | 1.63951e16 | 0.0972112 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.34988e16 | −0.0777491 | −0.0388745 | − | 0.999244i | \(-0.512377\pi\) | ||||
−0.0388745 | + | 0.999244i | \(0.512377\pi\) | |||||||
\(450\) | −2.68457e16 | + | 4.64980e16i | −0.152403 | + | 0.263969i | ||||
\(451\) | 1.51688e17 | + | 2.62730e17i | 0.848794 | + | 1.47015i | ||||
\(452\) | −1.18986e16 | − | 2.06090e16i | −0.0656292 | − | 0.113673i | ||||
\(453\) | 5.25080e16 | − | 9.09466e16i | 0.285488 | − | 0.494479i | ||||
\(454\) | −1.32105e17 | −0.708037 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.28631e16 | 0.431608 | ||||||||
\(457\) | 1.48650e17 | − | 2.57470e17i | 0.763327 | − | 1.32212i | −0.177800 | − | 0.984067i | \(-0.556898\pi\) |
0.941127 | − | 0.338054i | \(-0.109769\pi\) | |||||||
\(458\) | 4.45204e16 | + | 7.71116e16i | 0.225389 | + | 0.390386i | ||||
\(459\) | 4.96565e15 | + | 8.60076e15i | 0.0247853 | + | 0.0429294i | ||||
\(460\) | −2.39473e15 | + | 4.14779e15i | −0.0117850 | + | 0.0204123i | ||||
\(461\) | 4.11410e16 | 0.199627 | 0.0998135 | − | 0.995006i | \(-0.468175\pi\) | ||||
0.0998135 | + | 0.995006i | \(0.468175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.23516e17 | −1.52623 | −0.763114 | − | 0.646264i | \(-0.776331\pi\) | ||||
−0.763114 | + | 0.646264i | \(0.776331\pi\) | |||||||
\(464\) | 2.63726e16 | − | 4.56787e16i | 0.122683 | − | 0.212494i | ||||
\(465\) | 6.90694e16 | + | 1.19632e17i | 0.316841 | + | 0.548785i | ||||
\(466\) | −3.51687e16 | − | 6.09140e16i | −0.159092 | − | 0.275555i | ||||
\(467\) | 8.99909e16 | − | 1.55869e17i | 0.401457 | − | 0.695344i | −0.592445 | − | 0.805611i | \(-0.701837\pi\) |
0.993902 | + | 0.110267i | \(0.0351706\pi\) | |||||||
\(468\) | 1.11420e17 | 0.490192 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.57262e16 | −0.238464 | ||||||||
\(471\) | 1.86959e17 | − | 3.23823e17i | 0.789063 | − | 1.36670i | ||||
\(472\) | 3.78457e16 | + | 6.55507e16i | 0.157541 | + | 0.272869i | ||||
\(473\) | −1.30469e17 | − | 2.25979e17i | −0.535687 | − | 0.927837i | ||||
\(474\) | 1.02363e17 | − | 1.77298e17i | 0.414557 | − | 0.718033i | ||||
\(475\) | 9.56074e16 | 0.381929 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.17653e17 | 1.23476 | ||||||||
\(478\) | −8.21504e16 | + | 1.42289e17i | −0.315013 | + | 0.545618i | ||||
\(479\) | 9.02899e15 | + | 1.56387e16i | 0.0341553 | + | 0.0591588i | 0.882598 | − | 0.470129i | \(-0.155793\pi\) |
−0.848442 | + | 0.529288i | \(0.822459\pi\) | |||||||
\(480\) | −2.49319e16 | − | 4.31833e16i | −0.0930438 | − | 0.161157i | ||||
\(481\) | −4.98295e16 | + | 8.63071e16i | −0.183461 | + | 0.317763i | ||||
\(482\) | −1.20587e17 | −0.438022 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.73355e17 | 1.32016 | ||||||||
\(485\) | 9.69958e16 | − | 1.68002e17i | 0.338401 | − | 0.586128i | ||||
\(486\) | −1.44432e17 | − | 2.50164e17i | −0.497197 | − | 0.861171i | ||||
\(487\) | 2.06142e17 | + | 3.57048e17i | 0.700209 | + | 1.21280i | 0.968393 | + | 0.249430i | \(0.0802432\pi\) |
−0.268184 | + | 0.963368i | \(0.586423\pi\) | |||||||
\(488\) | −2.76777e16 | + | 4.79393e16i | −0.0927688 | + | 0.160680i | ||||
\(489\) | −6.76124e17 | −2.23624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.06256e17 | 0.986405 | 0.493203 | − | 0.869915i | \(-0.335826\pi\) | ||||
0.493203 | + | 0.869915i | \(0.335826\pi\) | |||||||
\(492\) | 9.84543e16 | − | 1.70528e17i | 0.312940 | − | 0.542029i | ||||
\(493\) | 2.66698e17 | + | 4.61934e17i | 0.836593 | + | 1.44902i | ||||
\(494\) | −9.92024e16 | − | 1.71824e17i | −0.307112 | − | 0.531934i | ||||
\(495\) | 2.28790e17 | − | 3.96276e17i | 0.699042 | − | 1.21078i | ||||
\(496\) | 4.99057e16 | 0.150494 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.36413e17 | −1.57583 | ||||||||
\(499\) | 1.78606e17 | − | 3.09354e17i | 0.517895 | − | 0.897021i | −0.481889 | − | 0.876232i | \(-0.660049\pi\) |
0.999784 | − | 0.0207882i | \(-0.00661756\pi\) | |||||||
\(500\) | −9.41213e16 | − | 1.63023e17i | −0.269391 | − | 0.466599i | ||||
\(501\) | 3.62240e15 | + | 6.27418e15i | 0.0102341 | + | 0.0177261i | ||||
\(502\) | −1.79974e17 | + | 3.11724e17i | −0.501921 | + | 0.869352i | ||||
\(503\) | −1.26023e17 | −0.346944 | −0.173472 | − | 0.984839i | \(-0.555499\pi\) | ||||
−0.173472 | + | 0.984839i | \(0.555499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.96031e17 | −1.06251 | ||||||||
\(506\) | −1.60458e16 | + | 2.77921e16i | −0.0424994 | + | 0.0736110i | ||||
\(507\) | −5.78631e14 | − | 1.00222e15i | −0.00151304 | − | 0.00262066i | ||||
\(508\) | −1.43391e17 | − | 2.48360e17i | −0.370175 | − | 0.641162i | ||||
\(509\) | 2.09517e16 | − | 3.62895e16i | 0.0534016 | − | 0.0924943i | −0.838089 | − | 0.545534i | \(-0.816327\pi\) |
0.891490 | + | 0.453039i | \(0.149660\pi\) | |||||||
\(510\) | 5.04257e17 | 1.26895 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | −5.20792e15 | + | 9.02038e15i | −0.0126154 | + | 0.0218505i | ||||
\(514\) | 7.58311e16 | + | 1.31343e17i | 0.181379 | + | 0.314158i | ||||
\(515\) | 5.85125e16 | + | 1.01347e17i | 0.138198 | + | 0.239366i | ||||
\(516\) | −8.46824e16 | + | 1.46674e17i | −0.197501 | + | 0.342082i | ||||
\(517\) | −3.73391e17 | −0.859955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.74618e17 | −1.51520 | ||||||||
\(520\) | −5.96962e16 | + | 1.03397e17i | −0.132411 | + | 0.229343i | ||||
\(521\) | −3.14279e17 | − | 5.44347e17i | −0.688446 | − | 1.19242i | −0.972340 | − | 0.233568i | \(-0.924960\pi\) |
0.283894 | − | 0.958856i | \(-0.408374\pi\) | |||||||
\(522\) | −1.57079e17 | − | 2.72070e17i | −0.339829 | − | 0.588602i | ||||
\(523\) | −5.09947e16 | + | 8.83254e16i | −0.108959 | + | 0.188723i | −0.915349 | − | 0.402662i | \(-0.868085\pi\) |
0.806390 | + | 0.591385i | \(0.201418\pi\) | |||||||
\(524\) | 4.78890e16 | 0.101061 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.23390e17 | 0.254022 | ||||||||
\(527\) | −2.52340e17 | + | 4.37066e17i | −0.513118 | + | 0.888747i | ||||
\(528\) | −1.67055e17 | − | 2.89348e17i | −0.335536 | − | 0.581166i | ||||
\(529\) | 2.51018e17 | + | 4.34776e17i | 0.498015 | + | 0.862588i | ||||
\(530\) | −1.70191e17 | + | 2.94779e17i | −0.333536 | + | 0.577701i | ||||
\(531\) | 4.50830e17 | 0.872767 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.71472e17 | −0.890694 | ||||||||
\(534\) | −1.49630e17 | + | 2.59167e17i | −0.279255 | + | 0.483683i | ||||
\(535\) | −3.20628e17 | − | 5.55343e17i | −0.591155 | − | 1.02391i | ||||
\(536\) | −7.76532e16 | − | 1.34499e17i | −0.141445 | − | 0.244990i | ||||
\(537\) | 3.15618e17 | − | 5.46666e17i | 0.567974 | − | 0.983760i | ||||
\(538\) | −3.15027e17 | −0.560097 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.26785e15 | 0.0108782 | ||||||||
\(541\) | −1.79876e17 | + | 3.11555e17i | −0.308455 | + | 0.534259i | −0.978025 | − | 0.208490i | \(-0.933145\pi\) |
0.669570 | + | 0.742749i | \(0.266478\pi\) | |||||||
\(542\) | −7.03224e16 | − | 1.21802e17i | −0.119151 | − | 0.206376i | ||||
\(543\) | −4.25313e17 | − | 7.36664e17i | −0.712049 | − | 1.23331i | ||||
\(544\) | 9.10869e16 | − | 1.57767e17i | 0.150683 | − | 0.260990i | ||||
\(545\) | −6.88013e17 | −1.12465 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.34678e17 | 1.17268 | 0.586340 | − | 0.810065i | \(-0.300568\pi\) | ||||
0.586340 | + | 0.810065i | \(0.300568\pi\) | |||||||
\(548\) | 1.88127e17 | − | 3.25846e17i | 0.296741 | − | 0.513971i | ||||
\(549\) | 1.64853e17 | + | 2.85534e17i | 0.256967 | + | 0.445079i | ||||
\(550\) | −1.92748e17 | − | 3.33850e17i | −0.296915 | − | 0.514273i | ||||
\(551\) | −2.79709e17 | + | 4.84471e17i | −0.425815 | + | 0.737534i | ||||
\(552\) | 2.08293e16 | 0.0313380 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.75894e16 | −0.0993265 | ||||||||
\(555\) | 1.32823e17 | − | 2.30056e17i | 0.192916 | − | 0.334141i | ||||
\(556\) | −1.50315e17 | − | 2.60354e17i | −0.215783 | − | 0.373747i | ||||
\(557\) | −2.47501e17 | − | 4.28683e17i | −0.351170 | − | 0.608244i | 0.635285 | − | 0.772278i | \(-0.280883\pi\) |
−0.986455 | + | 0.164034i | \(0.947549\pi\) | |||||||
\(558\) | 1.48623e17 | − | 2.57423e17i | 0.208432 | − | 0.361015i | ||||
\(559\) | 4.05522e17 | 0.562131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.37875e18 | 4.57612 | ||||||||
\(562\) | −8.46688e16 | + | 1.46651e17i | −0.113354 | + | 0.196335i | ||||
\(563\) | 2.63438e17 | + | 4.56288e17i | 0.348637 | + | 0.603857i | 0.986008 | − | 0.166700i | \(-0.0533112\pi\) |
−0.637371 | + | 0.770557i | \(0.719978\pi\) | |||||||
\(564\) | 1.21177e17 | + | 2.09884e17i | 0.158528 | + | 0.274578i | ||||
\(565\) | 7.59408e16 | − | 1.31533e17i | 0.0982111 | − | 0.170107i | ||||
\(566\) | −4.48128e17 | −0.572921 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.75340e17 | −0.468986 | ||||||||
\(569\) | 4.42870e17 | − | 7.67074e17i | 0.547075 | − | 0.947562i | −0.451398 | − | 0.892323i | \(-0.649075\pi\) |
0.998473 | − | 0.0552391i | \(-0.0175921\pi\) | |||||||
\(570\) | 2.64429e17 | + | 4.58005e17i | 0.322941 | + | 0.559350i | ||||
\(571\) | 2.52094e17 | + | 4.36639e17i | 0.304388 | + | 0.527215i | 0.977125 | − | 0.212666i | \(-0.0682147\pi\) |
−0.672737 | + | 0.739882i | \(0.734881\pi\) | |||||||
\(572\) | −3.99992e17 | + | 6.92806e17i | −0.477504 | + | 0.827061i | ||||
\(573\) | 1.87118e18 | 2.20857 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.40329e16 | 0.0277310 | ||||||||
\(576\) | −5.36483e16 | + | 9.29216e16i | −0.0612083 | + | 0.106016i | ||||
\(577\) | −1.73113e17 | − | 2.99840e17i | −0.195293 | − | 0.338257i | 0.751704 | − | 0.659501i | \(-0.229232\pi\) |
−0.946996 | + | 0.321244i | \(0.895899\pi\) | |||||||
\(578\) | 6.04186e17 | + | 1.04648e18i | 0.673969 | + | 1.16735i | ||||
\(579\) | −4.91088e17 | + | 8.50590e17i | −0.541688 | + | 0.938231i | ||||
\(580\) | 3.36636e17 | 0.367180 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.43670e17 | −0.899856 | ||||||||
\(583\) | −1.14035e18 | + | 1.97515e18i | −1.20280 | + | 2.08331i | ||||
\(584\) | −8.47071e16 | − | 1.46717e17i | −0.0883560 | − | 0.153037i | ||||
\(585\) | 3.55560e17 | + | 6.15848e17i | 0.366775 | + | 0.635273i | ||||
\(586\) | −2.80892e17 | + | 4.86520e17i | −0.286553 | + | 0.496325i | ||||
\(587\) | −9.20829e17 | −0.929033 | −0.464517 | − | 0.885564i | \(-0.653772\pi\) | ||||
−0.464517 | + | 0.885564i | \(0.653772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.29303e17 | −0.522342 | ||||||||
\(590\) | −2.41543e17 | + | 4.18365e17i | −0.235753 | + | 0.408336i | ||||
\(591\) | −2.25715e17 | − | 3.90949e17i | −0.217892 | − | 0.377400i | ||||
\(592\) | −4.79852e16 | − | 8.31129e16i | −0.0458159 | − | 0.0793555i | ||||
\(593\) | 2.62681e17 | − | 4.54977e17i | 0.248069 | − | 0.429669i | −0.714921 | − | 0.699205i | \(-0.753537\pi\) |
0.962990 | + | 0.269537i | \(0.0868706\pi\) | |||||||
\(594\) | 4.19974e16 | 0.0392293 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.78031e16 | 0.0345483 | ||||||||
\(597\) | 4.16952e17 | − | 7.22182e17i | 0.376923 | − | 0.652850i | ||||
\(598\) | −2.49366e16 | − | 4.31914e16i | −0.0222987 | − | 0.0386224i | ||||
\(599\) | −4.11615e17 | − | 7.12937e17i | −0.364096 | − | 0.630634i | 0.624534 | − | 0.780997i | \(-0.285289\pi\) |
−0.988631 | + | 0.150364i | \(0.951955\pi\) | |||||||
\(600\) | −1.25105e17 | + | 2.16688e17i | −0.109469 | + | 0.189606i | ||||
\(601\) | 1.43103e18 | 1.23869 | 0.619347 | − | 0.785118i | \(-0.287398\pi\) | ||||
0.619347 | + | 0.785118i | \(0.287398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.25030e17 | −0.783598 | ||||||||
\(604\) | 1.21070e17 | − | 2.09700e17i | 0.101461 | − | 0.175735i | ||||
\(605\) | 1.19144e18 | + | 2.06363e18i | 0.987781 | + | 1.71089i | ||||
\(606\) | 8.61168e17 | + | 1.49159e18i | 0.706344 | + | 1.22342i | ||||
\(607\) | 3.30113e17 | − | 5.71773e17i | 0.267878 | − | 0.463978i | −0.700436 | − | 0.713715i | \(-0.747011\pi\) |
0.968314 | + | 0.249738i | \(0.0803444\pi\) | |||||||
\(608\) | 1.91062e17 | 0.153391 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.53296e17 | −0.277648 | ||||||||
\(611\) | 2.90142e17 | − | 5.02540e17i | 0.225602 | − | 0.390753i | ||||
\(612\) | −5.42528e17 | − | 9.39686e17i | −0.417386 | − | 0.722934i | ||||
\(613\) | 4.67096e17 | + | 8.09034e17i | 0.355560 | + | 0.615848i | 0.987214 | − | 0.159403i | \(-0.0509568\pi\) |
−0.631654 | + | 0.775251i | \(0.717624\pi\) | |||||||
\(614\) | 3.12003e17 | − | 5.40404e17i | 0.234998 | − | 0.407028i | ||||
\(615\) | 1.25673e18 | 0.936601 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.39791e18 | −1.74977 | −0.874883 | − | 0.484334i | \(-0.839062\pi\) | ||||
−0.874883 | + | 0.484334i | \(0.839062\pi\) | |||||||
\(618\) | 2.54471e17 | − | 4.40757e17i | 0.183744 | − | 0.318254i | ||||
\(619\) | 5.77253e16 | + | 9.99832e16i | 0.0412456 | + | 0.0714394i | 0.885911 | − | 0.463855i | \(-0.153534\pi\) |
−0.844666 | + | 0.535294i | \(0.820201\pi\) | |||||||
\(620\) | 1.59257e17 | + | 2.75841e17i | 0.112604 | + | 0.195035i | ||||
\(621\) | −1.30912e15 | + | 2.26746e15i | −0.000915974 | + | 0.00158651i | ||||
\(622\) | −2.48312e17 | −0.171933 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.19237e17 | 0.352100 | ||||||||
\(625\) | 2.72769e17 | − | 4.72450e17i | 0.183052 | − | 0.317056i | ||||
\(626\) | 5.36780e17 | + | 9.29730e17i | 0.356503 | + | 0.617481i | ||||
\(627\) | 1.77180e18 | + | 3.06884e18i | 1.16459 | + | 2.01714i | ||||
\(628\) | 4.31082e17 | − | 7.46656e17i | 0.280428 | − | 0.485716i | ||||
\(629\) | 9.70519e17 | 0.624848 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.98112e18 | 1.24945 | 0.624726 | − | 0.780844i | \(-0.285211\pi\) | ||||
0.624726 | + | 0.780844i | \(0.285211\pi\) | |||||||
\(632\) | 2.36024e17 | − | 4.08805e17i | 0.147331 | − | 0.255185i | ||||
\(633\) | −1.88550e17 | − | 3.26579e17i | −0.116494 | − | 0.201773i | ||||
\(634\) | 4.85880e17 | + | 8.41569e17i | 0.297132 | + | 0.514647i | ||||
\(635\) | 9.15165e17 | − | 1.58511e18i | 0.553950 | − | 0.959469i | ||||
\(636\) | 1.48032e18 | 0.886918 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.25562e18 | 1.32413 | ||||||||
\(639\) | −1.11779e18 | + | 1.93607e18i | −0.649539 | + | 1.12503i | ||||
\(640\) | −5.74868e16 | − | 9.95700e16i | −0.0330673 | − | 0.0572742i | ||||
\(641\) | −4.73875e17 | − | 8.20775e17i | −0.269828 | − | 0.467355i | 0.698990 | − | 0.715132i | \(-0.253633\pi\) |
−0.968817 | + | 0.247777i | \(0.920300\pi\) | |||||||
\(642\) | −1.39441e18 | + | 2.41519e18i | −0.785982 | + | 1.36136i | ||||
\(643\) | 2.02473e16 | 0.0112978 | 0.00564891 | − | 0.999984i | \(-0.498202\pi\) | ||||
0.00564891 | + | 0.999984i | \(0.498202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.08094e18 | −0.591103 | ||||||||
\(646\) | −9.66073e17 | + | 1.67329e18i | −0.522996 | + | 0.905856i | ||||
\(647\) | −4.30875e17 | − | 7.46297e17i | −0.230926 | − | 0.399976i | 0.727155 | − | 0.686474i | \(-0.240842\pi\) |
−0.958081 | + | 0.286498i | \(0.907509\pi\) | |||||||
\(648\) | −3.39911e17 | − | 5.88743e17i | −0.180355 | − | 0.312384i | ||||
\(649\) | −1.61845e18 | + | 2.80324e18i | −0.850176 | + | 1.47255i | ||||
\(650\) | 5.99095e17 | 0.311573 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.55897e18 | −0.794748 | ||||||||
\(653\) | 1.73045e16 | − | 2.99723e16i | 0.00873422 | − | 0.0151281i | −0.861625 | − | 0.507545i | \(-0.830553\pi\) |
0.870359 | + | 0.492417i | \(0.163886\pi\) | |||||||
\(654\) | 1.49608e18 | + | 2.59129e18i | 0.747653 | + | 1.29497i | ||||
\(655\) | 1.52821e17 | + | 2.64694e17i | 0.0756163 | + | 0.130971i | ||||
\(656\) | 2.27011e17 | − | 3.93195e17i | 0.111217 | − | 0.192634i | ||||
\(657\) | −1.00906e18 | −0.489487 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.84217e17 | −0.230295 | −0.115148 | − | 0.993348i | \(-0.536734\pi\) | ||||
−0.115148 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(660\) | 1.06620e18 | − | 1.84671e18i | 0.502114 | − | 0.869687i | ||||
\(661\) | −1.47958e18 | − | 2.56271e18i | −0.689970 | − | 1.19506i | −0.971847 | − | 0.235612i | \(-0.924291\pi\) |
0.281878 | − | 0.959450i | \(-0.409043\pi\) | |||||||
\(662\) | −1.00151e18 | − | 1.73466e18i | −0.462463 | − | 0.801010i | ||||
\(663\) | −2.62544e18 | + | 4.54739e18i | −1.20051 | + | 2.07934i | ||||
\(664\) | −1.23684e18 | −0.560041 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.71616e17 | −0.253817 | ||||||||
\(667\) | −7.03106e16 | + | 1.21782e17i | −0.0309174 | + | 0.0535505i | ||||
\(668\) | 8.35236e15 | + | 1.44667e16i | 0.00363716 | + | 0.00629974i | ||||
\(669\) | −1.79048e18 | − | 3.10119e18i | −0.772144 | − | 1.33739i | ||||
\(670\) | 4.95607e17 | − | 8.58417e17i | 0.211666 | − | 0.366617i | ||||
\(671\) | −2.36725e18 | −1.00126 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.37383e18 | 0.984807 | 0.492404 | − | 0.870367i | \(-0.336118\pi\) | ||||
0.492404 | + | 0.870367i | \(0.336118\pi\) | |||||||
\(674\) | −4.99063e17 | + | 8.64403e17i | −0.205053 | + | 0.355162i | ||||
\(675\) | −1.57256e16 | − | 2.72376e16i | −0.00639932 | − | 0.0110839i | ||||
\(676\) | −1.33418e15 | − | 2.31087e15i | −0.000537726 | − | 0.000931368i | ||||
\(677\) | 1.88783e18 | − | 3.26982e18i | 0.753594 | − | 1.30526i | −0.192476 | − | 0.981302i | \(-0.561652\pi\) |
0.946070 | − | 0.323962i | \(-0.105015\pi\) | |||||||
\(678\) | −6.60533e17 | −0.261157 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.16269e18 | 0.450979 | ||||||||
\(681\) | −1.83340e18 | + | 3.17554e18i | −0.704369 | + | 1.22000i | ||||
\(682\) | 1.06709e18 | + | 1.84826e18i | 0.406073 | + | 0.703339i | ||||
\(683\) | −1.00170e18 | − | 1.73500e18i | −0.377576 | − | 0.653981i | 0.613133 | − | 0.789980i | \(-0.289909\pi\) |
−0.990709 | + | 0.135999i | \(0.956576\pi\) | |||||||
\(684\) | 5.68997e17 | − | 9.85532e17i | 0.212444 | − | 0.367965i | ||||
\(685\) | 2.40137e18 | 0.888118 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.47148e18 | 0.896887 | ||||||||
\(688\) | −1.95257e17 | + | 3.38194e17i | −0.0701909 | + | 0.121574i | ||||
\(689\) | −1.77221e18 | − | 3.06956e18i | −0.631089 | − | 1.09308i | ||||
\(690\) | 6.64697e16 | + | 1.15129e17i | 0.0234479 | + | 0.0406130i | ||||
\(691\) | 1.63537e16 | − | 2.83255e16i | 0.00571491 | − | 0.00989852i | −0.863154 | − | 0.504941i | \(-0.831514\pi\) |
0.868869 | + | 0.495043i | \(0.164848\pi\) | |||||||
\(692\) | −1.55550e18 | −0.538494 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.02990e18 | 1.36917 | ||||||||
\(695\) | 9.59360e17 | − | 1.66166e18i | 0.322909 | − | 0.559295i | ||||
\(696\) | −7.32016e17 | − | 1.26789e18i | −0.244096 | − | 0.422786i | ||||
\(697\) | 2.29569e18 | + | 3.97625e18i | 0.758403 | + | 1.31359i | ||||
\(698\) | 1.97865e18 | − | 3.42712e18i | 0.647603 | − | 1.12168i | ||||
\(699\) | −1.95233e18 | −0.633071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.10250e18 | −1.62411 | −0.812057 | − | 0.583579i | \(-0.801652\pi\) | ||||
−0.812057 | + | 0.583579i | \(0.801652\pi\) | |||||||
\(702\) | −3.26339e16 | + | 5.65235e16i | −0.0102915 | + | 0.0178253i | ||||
\(703\) | 5.08934e17 | + | 8.81500e17i | 0.159020 | + | 0.275431i | ||||
\(704\) | −3.85188e17 | − | 6.67165e17i | −0.119248 | − | 0.206543i | ||||
\(705\) | −7.73388e17 | + | 1.33955e18i | −0.237229 | + | 0.410893i | ||||
\(706\) | 7.11869e17 | 0.216356 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.10094e18 | 0.626899 | ||||||||
\(709\) | 1.12804e18 | − | 1.95383e18i | 0.333522 | − | 0.577678i | −0.649677 | − | 0.760210i | \(-0.725096\pi\) |
0.983200 | + | 0.182532i | \(0.0584294\pi\) | |||||||
\(710\) | −1.19777e18 | − | 2.07459e18i | −0.350908 | − | 0.607791i | ||||
\(711\) | −1.40580e18 | − | 2.43491e18i | −0.408103 | − | 0.706855i | ||||
\(712\) | −3.45010e17 | + | 5.97574e17i | −0.0992456 | + | 0.171898i | ||||
\(713\) | −1.33051e17 | −0.0379259 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.10574e18 | −1.42912 | ||||||||
\(716\) | 7.27736e17 | − | 1.26048e18i | 0.201855 | − | 0.349623i | ||||
\(717\) | 2.28022e18 | + | 3.94946e18i | 0.626762 | + | 1.08558i | ||||
\(718\) | −1.98707e18 | − | 3.44170e18i | −0.541257 | − | 0.937484i | ||||
\(719\) | −1.13496e18 | + | 1.96581e18i | −0.306368 | + | 0.530645i | −0.977565 | − | 0.210634i | \(-0.932447\pi\) |
0.671197 | + | 0.741279i | \(0.265781\pi\) | |||||||
\(720\) | −6.84801e17 | −0.183191 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.64980e17 | 0.174710 | ||||||||
\(723\) | −1.67355e18 | + | 2.89868e18i | −0.435753 | + | 0.754746i | ||||
\(724\) | −9.80666e17 | − | 1.69856e18i | −0.253058 | − | 0.438310i | ||||
\(725\) | −8.44599e17 | − | 1.46289e18i | −0.216000 | − | 0.374123i | ||||
\(726\) | 5.18155e18 | − | 8.97471e18i | 1.31332 | − | 2.27474i | ||||
\(727\) | −3.34385e18 | −0.839988 | −0.419994 | − | 0.907527i | \(-0.637968\pi\) | ||||
−0.419994 | + | 0.907527i | \(0.637968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.88334e18 | −0.958246 | ||||||||
\(730\) | 5.40627e17 | − | 9.36393e17i | 0.132221 | − | 0.229013i | ||||
\(731\) | −1.97457e18 | − | 3.42005e18i | −0.478640 | − | 0.829028i | ||||
\(732\) | 7.68242e17 | + | 1.33063e18i | 0.184576 | + | 0.319696i | ||||
\(733\) | 3.50530e17 | − | 6.07135e17i | 0.0834736 | − | 0.144580i | −0.821266 | − | 0.570545i | \(-0.806732\pi\) |
0.904740 | + | 0.425965i | \(0.140065\pi\) | |||||||
\(734\) | −1.29609e18 | −0.305923 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.80273e16 | 0.0111374 | ||||||||
\(737\) | 3.32080e18 | − | 5.75179e18i | 0.763314 | − | 1.32210i | ||||
\(738\) | −1.35211e18 | − | 2.34193e18i | −0.308068 | − | 0.533590i | ||||
\(739\) | −3.88505e18 | − | 6.72910e18i | −0.877420 | − | 1.51974i | −0.854162 | − | 0.520006i | \(-0.825930\pi\) |
−0.0232577 | − | 0.999730i | \(-0.507404\pi\) | |||||||
\(740\) | 3.06257e17 | − | 5.30452e17i | 0.0685614 | − | 0.118752i | ||||
\(741\) | −5.50706e18 | −1.22208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.35319e18 | 0.513132 | 0.256566 | − | 0.966527i | \(-0.417409\pi\) | ||||
0.256566 | + | 0.966527i | \(0.417409\pi\) | |||||||
\(744\) | 6.92608e17 | − | 1.19963e18i | 0.149714 | − | 0.259313i | ||||
\(745\) | 1.20636e17 | + | 2.08947e17i | 0.0258500 | + | 0.0447735i | ||||
\(746\) | 1.22816e18 | + | 2.12723e18i | 0.260886 | + | 0.451868i | ||||
\(747\) | −3.68340e18 | + | 6.37983e18i | −0.775648 | + | 1.34346i | ||||
\(748\) | 7.79056e18 | 1.62633 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.22499e18 | −1.07198 | ||||||||
\(751\) | 9.97951e17 | − | 1.72850e18i | 0.202978 | − | 0.351569i | −0.746508 | − | 0.665376i | \(-0.768271\pi\) |
0.949487 | + | 0.313807i | \(0.101605\pi\) | |||||||
\(752\) | 2.79403e17 | + | 4.83941e17i | 0.0563398 | + | 0.0975835i | ||||
\(753\) | 4.99547e18 | + | 8.65241e18i | 0.998641 | + | 1.72970i | ||||
\(754\) | −1.75271e18 | + | 3.03579e18i | −0.347374 | + | 0.601670i | ||||
\(755\) | 1.54542e18 | 0.303663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.58530e18 | −1.07876 | −0.539378 | − | 0.842064i | \(-0.681340\pi\) | ||||
−0.539378 | + | 0.842064i | \(0.681340\pi\) | |||||||
\(758\) | 1.66940e18 | − | 2.89148e18i | 0.319676 | − | 0.553695i | ||||
\(759\) | 4.45377e17 | + | 7.71416e17i | 0.0845584 | + | 0.146459i | ||||
\(760\) | 6.09708e17 | + | 1.05605e18i | 0.114771 | + | 0.198790i | ||||
\(761\) | 1.92256e18 | − | 3.32997e18i | 0.358823 | − | 0.621499i | −0.628942 | − | 0.777452i | \(-0.716512\pi\) |
0.987764 | + | 0.155953i | \(0.0498449\pi\) | |||||||
\(762\) | −7.96011e18 | −1.47303 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.31448e18 | 0.784914 | ||||||||
\(765\) | 3.46259e18 | − | 5.99737e18i | 0.624599 | − | 1.08184i | ||||
\(766\) | 3.15157e18 | + | 5.45868e18i | 0.563690 | + | 0.976340i | ||||
\(767\) | −2.51521e18 | − | 4.35648e18i | −0.446072 | − | 0.772620i | ||||
\(768\) | −2.50010e17 | + | 4.33030e17i | −0.0439652 | + | 0.0761500i | ||||
\(769\) | 1.59052e18 | 0.277343 | 0.138671 | − | 0.990338i | \(-0.455717\pi\) | ||||
0.138671 | + | 0.990338i | \(0.455717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.20964e18 | 0.721758 | ||||||||
\(772\) | −1.13233e18 | + | 1.96125e18i | −0.192513 | + | 0.333442i | ||||
\(773\) | 4.24436e18 | + | 7.35145e18i | 0.715559 | + | 1.23939i | 0.962743 | + | 0.270417i | \(0.0871614\pi\) |
−0.247184 | + | 0.968969i | \(0.579505\pi\) | |||||||
\(774\) | 1.16298e18 | + | 2.01434e18i | 0.194427 | + | 0.336757i | ||||
\(775\) | 7.99131e17 | − | 1.38414e18i | 0.132482 | − | 0.229466i | ||||
\(776\) | −1.94529e18 | −0.319804 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.51048e18 | 0.729215 | ||||||||
\(779\) | −2.40769e18 | + | 4.17025e18i | −0.386018 | + | 0.668603i | ||||
\(780\) | 1.65697e18 | + | 2.86995e18i | 0.263450 | + | 0.456310i | ||||
\(781\) | −8.02559e18 | − | 1.39007e19i | −1.26545 | − | 2.19183i | ||||
\(782\) | −2.42842e17 | + | 4.20615e17i | −0.0379735 | + | 0.0657720i | ||||
\(783\) | 1.84028e17 | 0.0285385 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.50260e18 | 0.839296 | ||||||||
\(786\) | 6.64620e17 | − | 1.15115e18i | 0.100537 | − | 0.174135i | ||||
\(787\) | −3.38035e18 | − | 5.85494e18i | −0.507138 | − | 0.878389i | −0.999966 | − | 0.00826189i | \(-0.997370\pi\) |
0.492828 | − | 0.870127i | \(-0.335963\pi\) | |||||||
\(788\) | −5.20442e17 | − | 9.01432e17i | −0.0774376 | − | 0.134126i | ||||
\(789\) | 1.71244e18 | − | 2.96604e18i | 0.252706 | − | 0.437700i | ||||
\(790\) | 3.01276e18 | 0.440948 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.58848e18 | −0.660625 | ||||||||
\(793\) | 1.83945e18 | − | 3.18603e18i | 0.262672 | − | 0.454961i | ||||
\(794\) | 3.94646e18 | + | 6.83547e18i | 0.558952 | + | 0.968133i | ||||
\(795\) | 4.72392e18 | + | 8.18208e18i | 0.663616 | + | 1.14942i | ||||
\(796\) | 9.61387e17 | − | 1.66517e18i | 0.133956 | − | 0.232019i | ||||
\(797\) | 8.33383e17 | 0.115177 | 0.0575885 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575885 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.65103e18 | −0.768376 | ||||||||
\(800\) | −2.88461e17 | + | 4.99630e17i | −0.0389048 | + | 0.0673850i | ||||
\(801\) | 2.05493e18 | + | 3.55925e18i | 0.274907 | + | 0.476153i | ||||
\(802\) | 2.32348e18 | + | 4.02438e18i | 0.308322 | + | 0.534030i | ||||
\(803\) | 3.62245e18 | − | 6.27427e18i | 0.476816 | − | 0.825870i | ||||
\(804\) | −4.31079e18 | −0.562850 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.31672e18 | −0.426119 | ||||||||
\(807\) | −4.37206e18 | + | 7.57262e18i | −0.557196 | + | 0.965091i | ||||
\(808\) | 1.98564e18 | + | 3.43923e18i | 0.251031 | + | 0.434798i | ||||
\(809\) | 1.30255e18 | + | 2.25608e18i | 0.163354 | + | 0.282937i | 0.936069 | − | 0.351815i | \(-0.114435\pi\) |
−0.772716 | + | 0.634752i | \(0.781102\pi\) | |||||||
\(810\) | 2.16942e18 | − | 3.75754e18i | 0.269892 | − | 0.467467i | ||||
\(811\) | 8.39030e18 | 1.03548 | 0.517740 | − | 0.855538i | \(-0.326773\pi\) | ||||
0.517740 | + | 0.855538i | \(0.326773\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.90383e18 | −0.474135 | ||||||||
\(814\) | 2.05206e18 | − | 3.55427e18i | 0.247247 | − | 0.428245i | ||||
\(815\) | −4.97493e18 | − | 8.61683e18i | −0.594651 | − | 1.02997i | ||||
\(816\) | −2.52827e18 | − | 4.37909e18i | −0.299804 | − | 0.519276i | ||||
\(817\) | 2.07090e18 | − | 3.58691e18i | 0.243622 | − | 0.421965i | ||||
\(818\) | −4.00384e18 | −0.467283 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.89771e18 | 0.332863 | ||||||||
\(821\) | −3.01483e18 | + | 5.22184e18i | −0.343583 | + | 0.595104i | −0.985095 | − | 0.172009i | \(-0.944974\pi\) |
0.641512 | + | 0.767113i | \(0.278307\pi\) | |||||||
\(822\) | −5.22178e18 | − | 9.04439e18i | −0.590408 | − | 1.02262i | ||||
\(823\) | −2.95985e16 | − | 5.12662e16i | −0.00332025 | − | 0.00575085i | 0.864361 | − | 0.502873i | \(-0.167724\pi\) |
−0.867681 | + | 0.497122i | \(0.834390\pi\) | |||||||
\(824\) | 5.86747e17 | − | 1.01627e18i | 0.0653016 | − | 0.113106i | ||||
\(825\) | −1.07001e19 | −1.18151 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.98297e18 | −0.650326 | −0.325163 | − | 0.945658i | \(-0.605419\pi\) | ||||
−0.325163 | + | 0.945658i | \(0.605419\pi\) | |||||||
\(828\) | 1.43029e17 | − | 2.47734e17i | 0.0154251 | − | 0.0267170i | ||||
\(829\) | −5.18792e18 | − | 8.98574e18i | −0.555122 | − | 0.961500i | −0.997894 | − | 0.0648656i | \(-0.979338\pi\) |
0.442772 | − | 0.896634i | \(-0.353995\pi\) | |||||||
\(830\) | −3.94694e18 | − | 6.83630e18i | −0.419037 | − | 0.725794i | ||||
\(831\) | −9.38029e17 | + | 1.62471e18i | −0.0988120 | + | 0.171147i | ||||
\(832\) | 1.19723e18 | 0.125134 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.34451e18 | −0.858661 | ||||||||
\(835\) | −5.33074e16 | + | 9.23311e16i | −0.00544284 | + | 0.00942727i | ||||
\(836\) | 4.08532e18 | + | 7.07599e18i | 0.413891 | + | 0.716880i | ||||
\(837\) | 8.70604e16 | + | 1.50793e17i | 0.00875195 | + | 0.0151588i | ||||
\(838\) | −6.04367e18 | + | 1.04679e19i | −0.602857 | + | 1.04418i | ||||
\(839\) | −1.62942e18 | −0.161280 | −0.0806400 | − | 0.996743i | \(-0.525696\pi\) | ||||
−0.0806400 | + | 0.996743i | \(0.525696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.76784e17 | −0.0367213 | ||||||||
\(842\) | −3.62144e18 | + | 6.27251e18i | −0.350229 | + | 0.606614i | ||||
\(843\) | 2.35012e18 | + | 4.07054e18i | 0.225534 | + | 0.390636i | ||||
\(844\) | −4.34750e17 | − | 7.53009e17i | −0.0414013 | − | 0.0717091i | ||||
\(845\) | 8.51515e15 | − | 1.47487e16i | 0.000804681 | − | 0.00139375i | ||||
\(846\) | 3.32834e18 | 0.312119 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.41324e18 | 0.315206 | ||||||||
\(849\) | −6.21927e18 | + | 1.07721e19i | −0.569953 | + | 0.987188i | ||||
\(850\) | −2.91712e18 | − | 5.05259e18i | −0.265296 | − | 0.459506i | ||||
\(851\) | 1.27931e17 | + | 2.21583e17i | 0.0115461 | + | 0.0199984i | ||||
\(852\) | −5.20909e18 | + | 9.02241e18i | −0.466557 | + | 0.808100i | ||||
\(853\) | −1.81502e19 | −1.61329 | −0.806644 | − | 0.591038i | \(-0.798718\pi\) | ||||
−0.806644 | + | 0.591038i | \(0.798718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.26304e18 | 0.635826 | ||||||||
\(856\) | −3.21516e18 | + | 5.56882e18i | −0.279334 | + | 0.483820i | ||||
\(857\) | 2.68334e18 | + | 4.64769e18i | 0.231367 | + | 0.400739i | 0.958211 | − | 0.286064i | \(-0.0923469\pi\) |
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(858\) | 1.11024e19 | + | 1.92300e19i | 0.950060 | + | 1.64555i | ||||
\(859\) | 1.72767e17 | − | 2.99242e17i | 0.0146726 | − | 0.0254136i | −0.858596 | − | 0.512653i | \(-0.828663\pi\) |
0.873268 | + | 0.487239i | \(0.161996\pi\) | |||||||
\(860\) | −2.49238e18 | −0.210075 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.55307e18 | 0.627085 | ||||||||
\(863\) | −3.68850e18 | + | 6.38867e18i | −0.303934 | + | 0.526430i | −0.977023 | − | 0.213132i | \(-0.931634\pi\) |
0.673089 | + | 0.739561i | \(0.264967\pi\) | |||||||
\(864\) | −3.14261e16 | − | 5.44316e16i | −0.00257010 | − | 0.00445155i | ||||
\(865\) | −4.96385e18 | − | 8.59764e18i | −0.402916 | − | 0.697870i | ||||
\(866\) | −3.78530e18 | + | 6.55634e18i | −0.304954 | + | 0.528196i | ||||
\(867\) | 3.35404e19 | 2.68191 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.01868e19 | 1.59016 | ||||||||
\(870\) | 4.67195e18 | − | 8.09206e18i | 0.365278 | − | 0.632680i | ||||
\(871\) | 5.16081e18 | + | 8.93879e18i | 0.400498 | + | 0.693682i | ||||
\(872\) | 3.44960e18 | + | 5.97487e18i | 0.265712 | + | 0.460226i | ||||
\(873\) | −5.79324e18 | + | 1.00342e19i | −0.442923 | + | 0.767166i | ||||
\(874\) | −5.09380e17 | −0.0386561 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.70237e18 | −0.351593 | ||||||||
\(877\) | −2.63293e18 | + | 4.56036e18i | −0.195408 | + | 0.338456i | −0.947034 | − | 0.321133i | \(-0.895936\pi\) |
0.751626 | + | 0.659589i | \(0.229270\pi\) | |||||||
\(878\) | −2.21197e18 | − | 3.83125e18i | −0.162954 | − | 0.282245i | ||||
\(879\) | 7.79663e18 | + | 1.35042e19i | 0.570137 | + | 0.987507i | ||||
\(880\) | 2.45839e18 | − | 4.25805e18i | 0.178449 | − | 0.309082i | ||||
\(881\) | −2.11091e19 | −1.52099 | −0.760494 | − | 0.649344i | \(-0.775043\pi\) | ||||
−0.760494 | + | 0.649344i | \(0.775043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.58202e18 | 0.680319 | 0.340159 | − | 0.940368i | \(-0.389519\pi\) | ||||
0.340159 | + | 0.940368i | \(0.389519\pi\) | |||||||
\(884\) | −6.05361e18 | + | 1.04852e19i | −0.426653 | + | 0.738984i | ||||
\(885\) | 6.70444e18 | + | 1.16124e19i | 0.469063 | + | 0.812441i | ||||
\(886\) | 1.91563e17 | + | 3.31797e17i | 0.0133043 | + | 0.0230437i | ||||
\(887\) | 6.92733e18 | − | 1.19985e19i | 0.477598 | − | 0.827223i | −0.522073 | − | 0.852901i | \(-0.674841\pi\) |
0.999670 | + | 0.0256778i | \(0.00817439\pi\) | |||||||
\(888\) | −2.66382e18 | −0.182314 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.40392e18 | −0.297033 | ||||||||
\(891\) | 1.45361e19 | − | 2.51773e19i | 0.973291 | − | 1.68579i | ||||
\(892\) | −4.12839e18 | − | 7.15058e18i | −0.274416 | − | 0.475302i | ||||
\(893\) | −2.96337e18 | − | 5.13270e18i | −0.195547 | − | 0.338697i | ||||
\(894\) | 5.24645e17 | − | 9.08711e17i | 0.0343693 | − | 0.0595295i | ||||
\(895\) | 9.28928e18 | 0.604132 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.38431e18 | −0.0887326 | ||||||||
\(898\) | −4.31963e17 | + | 7.48182e17i | −0.0274885 | + | 0.0476114i | ||||
\(899\) | 4.67588e18 | + | 8.09886e18i | 0.295410 | + | 0.511665i | ||||
\(900\) | 1.71812e18 | + | 2.97587e18i | 0.107765 | + | 0.186654i | ||||
\(901\) | −1.72585e19 | + | 2.98926e19i | −1.07471 | + | 1.86146i | ||||
\(902\) | 1.94160e19 | 1.20038 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.52303e18 | −0.0928138 | ||||||||
\(905\) | 6.25892e18 | − | 1.08408e19i | 0.378690 | − | 0.655910i | ||||
\(906\) | −3.36051e18 | − | 5.82058e18i | −0.201870 | − | 0.349650i | ||||
\(907\) | 6.77394e18 | + | 1.17328e19i | 0.404012 | + | 0.699769i | 0.994206 | − | 0.107492i | \(-0.0342821\pi\) |
−0.590194 | + | 0.807262i | \(0.700949\pi\) | |||||||
\(908\) | −4.22736e18 | + | 7.32200e18i | −0.250329 | + | 0.433582i | ||||
\(909\) | 2.36536e19 | 1.39069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.29525e18 | 0.190994 | 0.0954969 | − | 0.995430i | \(-0.469556\pi\) | ||||
0.0954969 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(912\) | 2.65162e18 | − | 4.59274e18i | 0.152597 | − | 0.264305i | ||||
\(913\) | −2.64463e19 | − | 4.58063e19i | −1.51114 | − | 2.61737i | ||||
\(914\) | −9.51362e18 | − | 1.64781e19i | −0.539753 | − | 0.934880i | ||||
\(915\) | −4.90316e18 | + | 8.49253e18i | −0.276210 | + | 0.478410i | ||||
\(916\) | 5.69861e18 | 0.318749 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.35604e17 | 0.0350517 | ||||||||
\(919\) | −8.57441e18 | + | 1.48513e19i | −0.469519 | + | 0.813231i | −0.999393 | − | 0.0348456i | \(-0.988906\pi\) |
0.529874 | + | 0.848077i | \(0.322239\pi\) | |||||||
\(920\) | 1.53263e17 | + | 2.65459e17i | 0.00833327 | + | 0.0144336i | ||||
\(921\) | −8.66016e18 | − | 1.49998e19i | −0.467561 | − | 0.809839i | ||||
\(922\) | 1.31651e18 | − | 2.28027e18i | 0.0705788 | − | 0.122246i | ||||
\(923\) | 2.49450e19 | 1.32792 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.07352e18 | −0.161330 | ||||||||
\(926\) | −1.03525e19 | + | 1.79311e19i | −0.539603 | + | 0.934620i | ||||
\(927\) | −3.49476e18 | − | 6.05310e18i | −0.180883 | − | 0.313299i | ||||
\(928\) | −1.68785e18 | − | 2.92344e18i | −0.0867503 | − | 0.150256i | ||||
\(929\) | 5.00038e18 | − | 8.66092e18i | 0.255212 | − | 0.442040i | −0.709741 | − | 0.704463i | \(-0.751188\pi\) |
0.964953 | + | 0.262422i | \(0.0845214\pi\) | |||||||
\(930\) | 8.84089e18 | 0.448081 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.50159e18 | −0.224990 | ||||||||
\(933\) | −3.44616e18 | + | 5.96892e18i | −0.171043 | + | 0.296254i | ||||
\(934\) | −5.75942e18 | − | 9.97561e18i | −0.283873 | − | 0.491682i | ||||
\(935\) | 2.48609e19 | + | 4.30603e19i | 1.21686 | + | 2.10767i | ||||
\(936\) | 3.56545e18 | − | 6.17554e18i | 0.173309 | − | 0.300180i | ||||
\(937\) | 2.08207e19 | 1.00505 | 0.502525 | − | 0.864562i | \(-0.332404\pi\) | ||||
0.502525 | + | 0.864562i | \(0.332404\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.97984e19 | 1.41862 | ||||||||
\(940\) | −1.78324e18 | + | 3.08866e18i | −0.0843099 | + | 0.146029i | ||||
\(941\) | 4.13796e18 | + | 7.16716e18i | 0.194291 | + | 0.336523i | 0.946668 | − | 0.322211i | \(-0.104426\pi\) |
−0.752377 | + | 0.658733i | \(0.771093\pi\) | |||||||
\(942\) | −1.19654e19 | − | 2.07247e19i | −0.557951 | − | 0.966400i | ||||
\(943\) | −6.05223e17 | + | 1.04828e18i | −0.0280278 | + | 0.0485456i | ||||
\(944\) | 4.84425e18 | 0.222797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.67001e19 | −0.757575 | ||||||||
\(947\) | 1.08265e19 | − | 1.87520e19i | 0.487767 | − | 0.844837i | −0.512134 | − | 0.858905i | \(-0.671145\pi\) |
0.999901 | + | 0.0140688i | \(0.00447837\pi\) | |||||||
\(948\) | −6.55124e18 | − | 1.13471e19i | −0.293136 | − | 0.507726i | ||||
\(949\) | 5.62961e18 | + | 9.75076e18i | 0.250177 | + | 0.433320i | ||||
\(950\) | 3.05944e18 | − | 5.29910e18i | 0.135032 | − | 0.233883i | ||||
\(951\) | 2.69729e19 | 1.18237 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.75657e18 | −0.421884 | −0.210942 | − | 0.977499i | \(-0.567653\pi\) | ||||
−0.210942 | + | 0.977499i | \(0.567653\pi\) | |||||||
\(954\) | 1.01649e19 | − | 1.76061e19i | 0.436555 | − | 0.756136i | ||||
\(955\) | 1.37682e19 | + | 2.38472e19i | 0.587293 | + | 1.01722i | ||||
\(956\) | 5.25763e18 | + | 9.10647e18i | 0.222748 | + | 0.385810i | ||||
\(957\) | 3.13042e19 | − | 5.42205e19i | 1.31727 | − | 2.28158i | ||||
\(958\) | 1.15571e18 | 0.0483029 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.19128e18 | −0.131584 | ||||||||
\(961\) | 7.78462e18 | − | 1.34834e19i | 0.318812 | − | 0.552199i | ||||
\(962\) | 3.18909e18 | + | 5.52366e18i | 0.129726 | + | 0.224693i | ||||
\(963\) | 1.91500e19 | + | 3.31688e19i | 0.773746 | + | 1.34017i | ||||
\(964\) | −3.85879e18 | + | 6.68362e18i | −0.154864 | + | 0.268232i | ||||
\(965\) | −1.44537e19 | −0.576173 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.86140e19 | −1.91201 | −0.956003 | − | 0.293358i | \(-0.905227\pi\) | ||||
−0.956003 | + | 0.293358i | \(0.905227\pi\) | |||||||
\(968\) | 1.19474e19 | − | 2.06935e19i | 0.466748 | − | 0.808431i | ||||
\(969\) | 2.68150e19 | + | 4.64449e19i | 1.04057 | + | 1.80233i | ||||
\(970\) | −6.20773e18 | − | 1.07521e19i | −0.239286 | − | 0.414455i | ||||
\(971\) | −9.82587e18 | + | 1.70189e19i | −0.376224 | + | 0.651639i | −0.990509 | − | 0.137445i | \(-0.956111\pi\) |
0.614286 | + | 0.789084i | \(0.289444\pi\) | |||||||
\(972\) | −1.84873e19 | −0.703143 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.63861e19 | 0.990245 | ||||||||
\(975\) | 8.31445e18 | − | 1.44011e19i | 0.309959 | − | 0.536864i | ||||
\(976\) | 1.77138e18 | + | 3.06811e18i | 0.0655974 | + | 0.113618i | ||||
\(977\) | −4.37285e18 | − | 7.57400e18i | −0.160861 | − | 0.278619i | 0.774317 | − | 0.632798i | \(-0.218094\pi\) |
−0.935178 | + | 0.354179i | \(0.884760\pi\) | |||||||
\(978\) | −2.16360e19 | + | 3.74746e19i | −0.790631 | + | 1.36941i | ||||
\(979\) | −2.95083e19 | −1.07116 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.10927e19 | 1.47203 | ||||||||
\(982\) | 9.80020e18 | − | 1.69744e19i | 0.348747 | − | 0.604047i | ||||
\(983\) | −5.27981e18 | − | 9.14490e18i | −0.186647 | − | 0.323282i | 0.757483 | − | 0.652854i | \(-0.226429\pi\) |
−0.944130 | + | 0.329573i | \(0.893095\pi\) | |||||||
\(984\) | −6.30108e18 | − | 1.09138e19i | −0.221282 | − | 0.383272i | ||||
\(985\) | 3.32162e18 | − | 5.75322e18i | 0.115882 | − | 0.200713i | ||||
\(986\) | 3.41373e19 | 1.18312 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.26979e19 | −0.434322 | ||||||||
\(989\) | 5.20564e17 | − | 9.01642e17i | 0.0176888 | − | 0.0306379i | ||||
\(990\) | −1.46426e19 | − | 2.53617e19i | −0.494297 | − | 0.856148i | ||||
\(991\) | 2.40484e19 | + | 4.16530e19i | 0.806505 | + | 1.39691i | 0.915270 | + | 0.402841i | \(0.131977\pi\) |
−0.108765 | + | 0.994068i | \(0.534690\pi\) | |||||||
\(992\) | 1.59698e18 | − | 2.76605e18i | 0.0532077 | − | 0.0921584i | ||||
\(993\) | −5.55970e19 | −1.84027 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.22718e19 | 0.400919 | ||||||||
\(996\) | −1.71652e19 | + | 2.97310e19i | −0.557139 | + | 0.964994i | ||||
\(997\) | −2.09456e19 | − | 3.62788e19i | −0.675421 | − | 1.16986i | −0.976346 | − | 0.216215i | \(-0.930629\pi\) |
0.300925 | − | 0.953648i | \(-0.402705\pi\) | |||||||
\(998\) | −1.14308e19 | − | 1.97987e19i | −0.366207 | − | 0.634289i | ||||
\(999\) | 1.67420e17 | − | 2.89980e17i | 0.00532884 | − | 0.00922982i |
(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 | 98.14.c.o.79.1 | 8 | ||
7.2 | even | 3 | 98.14.a.j.1.4 | 4 | |||
7.3 | odd | 6 | 14.14.c.b.11.4 | yes | 8 | ||
7.4 | even | 3 | inner | 98.14.c.o.67.1 | 8 | ||
7.5 | odd | 6 | 98.14.a.h.1.1 | 4 | |||
7.6 | odd | 2 | 14.14.c.b.9.4 | ✓ | 8 | ||
21.17 | even | 6 | 126.14.g.b.109.4 | 8 | |||
21.20 | even | 2 | 126.14.g.b.37.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.14.c.b.9.4 | ✓ | 8 | 7.6 | odd | 2 | ||
14.14.c.b.11.4 | yes | 8 | 7.3 | odd | 6 | ||
98.14.a.h.1.1 | 4 | 7.5 | odd | 6 | |||
98.14.a.j.1.4 | 4 | 7.2 | even | 3 | |||
98.14.c.o.67.1 | 8 | 7.4 | even | 3 | inner | ||
98.14.c.o.79.1 | 8 | 1.1 | even | 1 | trivial | ||
126.14.g.b.37.4 | 8 | 21.20 | even | 2 | |||
126.14.g.b.109.4 | 8 | 21.17 | even | 6 |