Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(11,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.11");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.c (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: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{20}\cdot 5^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.10 | ||
Root | \(29.7613i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.11 |
Dual form | 15.11.c.a.11.5 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 27.5253i | 0.860164i | 0.902790 | + | 0.430082i | \(0.141515\pi\) | ||||
−0.902790 | + | 0.430082i | \(0.858485\pi\) | |||||||
\(3\) | −80.1400 | − | 229.405i | −0.329794 | − | 0.944053i | ||||
\(4\) | 266.360 | 0.260117 | ||||||||
\(5\) | 1397.54i | 0.447214i | ||||||||
\(6\) | 6314.43 | − | 2205.87i | 0.812041 | − | 0.283677i | ||||
\(7\) | −24115.7 | −1.43486 | −0.717432 | − | 0.696629i | \(-0.754682\pi\) | ||||
−0.717432 | + | 0.696629i | \(0.754682\pi\) | |||||||
\(8\) | 35517.5i | 1.08391i | ||||||||
\(9\) | −46204.2 | + | 36769.0i | −0.782472 | + | 0.622686i | ||||
\(10\) | −38467.7 | −0.384677 | ||||||||
\(11\) | − | 218929.i | − | 1.35938i | −0.733500 | − | 0.679689i | \(-0.762115\pi\) | ||
0.733500 | − | 0.679689i | \(-0.237885\pi\) | |||||||
\(12\) | −21346.1 | − | 61104.3i | −0.0857851 | − | 0.245564i | ||||
\(13\) | −435784. | −1.17369 | −0.586847 | − | 0.809698i | \(-0.699631\pi\) | ||||
−0.586847 | + | 0.809698i | \(0.699631\pi\) | |||||||
\(14\) | − | 663792.i | − | 1.23422i | ||||||
\(15\) | 320603. | − | 111999.i | 0.422193 | − | 0.147488i | ||||
\(16\) | −704876. | −0.672222 | ||||||||
\(17\) | 1.40198e6i | 0.987412i | 0.869629 | + | 0.493706i | \(0.164358\pi\) | ||||
−0.869629 | + | 0.493706i | \(0.835642\pi\) | |||||||
\(18\) | −1.01208e6 | − | 1.27178e6i | −0.535613 | − | 0.673054i | ||||
\(19\) | −3.96480e6 | −1.60123 | −0.800615 | − | 0.599180i | \(-0.795494\pi\) | ||||
−0.800615 | + | 0.599180i | \(0.795494\pi\) | |||||||
\(20\) | 372249.i | 0.116328i | ||||||||
\(21\) | 1.93264e6 | + | 5.53227e6i | 0.473210 | + | 1.35459i | ||||
\(22\) | 6.02608e6 | 1.16929 | ||||||||
\(23\) | − | 1.21648e6i | − | 0.189002i | −0.995525 | − | 0.0945009i | \(-0.969874\pi\) | ||
0.995525 | − | 0.0945009i | \(-0.0301255\pi\) | |||||||
\(24\) | 8.14789e6 | − | 2.84637e6i | 1.02327 | − | 0.357467i | ||||
\(25\) | −1.95312e6 | −0.200000 | ||||||||
\(26\) | − | 1.19951e7i | − | 1.00957i | ||||||
\(27\) | 1.21378e7 | + | 7.65279e6i | 0.845903 | + | 0.533336i | ||||
\(28\) | −6.42347e6 | −0.373233 | ||||||||
\(29\) | − | 1.00025e6i | − | 0.0487663i | −0.999703 | − | 0.0243831i | \(-0.992238\pi\) | ||
0.999703 | − | 0.0243831i | \(-0.00776216\pi\) | |||||||
\(30\) | 3.08280e6 | + | 8.82468e6i | 0.126864 | + | 0.363156i | ||||
\(31\) | 5.09524e7 | 1.77974 | 0.889870 | − | 0.456215i | \(-0.150795\pi\) | ||||
0.889870 | + | 0.456215i | \(0.150795\pi\) | |||||||
\(32\) | 1.69680e7i | 0.505687i | ||||||||
\(33\) | −5.02234e7 | + | 1.75450e7i | −1.28333 | + | 0.448315i | ||||
\(34\) | −3.85900e7 | −0.849336 | ||||||||
\(35\) | − | 3.37028e7i | − | 0.641690i | ||||||
\(36\) | −1.23069e7 | + | 9.79379e6i | −0.203534 | + | 0.161971i | ||||
\(37\) | 9.23155e6 | 0.133127 | 0.0665635 | − | 0.997782i | \(-0.478797\pi\) | ||||
0.0665635 | + | 0.997782i | \(0.478797\pi\) | |||||||
\(38\) | − | 1.09132e8i | − | 1.37732i | ||||||
\(39\) | 3.49238e7 | + | 9.99710e7i | 0.387077 | + | 1.10803i | ||||
\(40\) | −4.96372e7 | −0.484738 | ||||||||
\(41\) | − | 4.72120e7i | − | 0.407505i | −0.979022 | − | 0.203753i | \(-0.934686\pi\) | ||
0.979022 | − | 0.203753i | \(-0.0653138\pi\) | |||||||
\(42\) | −1.52277e8 | + | 5.31963e7i | −1.16517 | + | 0.407038i | ||||
\(43\) | −7.55356e7 | −0.513818 | −0.256909 | − | 0.966436i | \(-0.582704\pi\) | ||||
−0.256909 | + | 0.966436i | \(0.582704\pi\) | |||||||
\(44\) | − | 5.83140e7i | − | 0.353598i | ||||||
\(45\) | −5.13862e7 | − | 6.45723e7i | −0.278474 | − | 0.349932i | ||||
\(46\) | 3.34839e7 | 0.162573 | ||||||||
\(47\) | − | 1.53639e8i | − | 0.669905i | −0.942235 | − | 0.334953i | \(-0.891280\pi\) | ||
0.942235 | − | 0.334953i | \(-0.108720\pi\) | |||||||
\(48\) | 5.64887e7 | + | 1.61702e8i | 0.221695 | + | 0.634613i | ||||
\(49\) | 2.99094e8 | 1.05883 | ||||||||
\(50\) | − | 5.37603e7i | − | 0.172033i | ||||||
\(51\) | 3.21622e8 | − | 1.12355e8i | 0.932169 | − | 0.325643i | ||||
\(52\) | −1.16076e8 | −0.305298 | ||||||||
\(53\) | 3.89040e8i | 0.930283i | 0.885236 | + | 0.465141i | \(0.153997\pi\) | ||||
−0.885236 | + | 0.465141i | \(0.846003\pi\) | |||||||
\(54\) | −2.10645e8 | + | 3.34096e8i | −0.458757 | + | 0.727616i | ||||
\(55\) | 3.05963e8 | 0.607933 | ||||||||
\(56\) | − | 8.56531e8i | − | 1.55526i | ||||||
\(57\) | 3.17739e8 | + | 9.09545e8i | 0.528076 | + | 1.51165i | ||||
\(58\) | 2.75322e7 | 0.0419470 | ||||||||
\(59\) | 1.11064e8i | 0.155350i | 0.996979 | + | 0.0776751i | \(0.0247497\pi\) | ||||
−0.996979 | + | 0.0776751i | \(0.975250\pi\) | |||||||
\(60\) | 8.53958e7 | − | 2.98321e7i | 0.109820 | − | 0.0383643i | ||||
\(61\) | −6.20166e7 | −0.0734275 | −0.0367138 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367138 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(62\) | 1.40248e9i | 1.53087i | ||||||||
\(63\) | 1.11425e9 | − | 8.86712e8i | 1.12274 | − | 0.893470i | ||||
\(64\) | −1.18884e9 | −1.10720 | ||||||||
\(65\) | − | 6.09027e8i | − | 0.524892i | ||||||
\(66\) | −4.82930e8 | − | 1.38241e9i | −0.385625 | − | 1.10387i | ||||
\(67\) | −8.74334e8 | −0.647595 | −0.323798 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323798 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(68\) | 3.73432e8i | 0.256843i | ||||||||
\(69\) | −2.79066e8 | + | 9.74887e7i | −0.178428 | + | 0.0623317i | ||||
\(70\) | 9.27678e8 | 0.551959 | ||||||||
\(71\) | − | 1.83375e9i | − | 1.01636i | −0.861251 | − | 0.508180i | \(-0.830319\pi\) | ||
0.861251 | − | 0.508180i | \(-0.169681\pi\) | |||||||
\(72\) | −1.30594e9 | − | 1.64106e9i | −0.674935 | − | 0.848127i | ||||
\(73\) | 7.05499e7 | 0.0340316 | 0.0170158 | − | 0.999855i | \(-0.494583\pi\) | ||||
0.0170158 | + | 0.999855i | \(0.494583\pi\) | |||||||
\(74\) | 2.54101e8i | 0.114511i | ||||||||
\(75\) | 1.56523e8 | + | 4.48056e8i | 0.0659588 | + | 0.188811i | ||||
\(76\) | −1.05606e9 | −0.416507 | ||||||||
\(77\) | 5.27964e9i | 1.95052i | ||||||||
\(78\) | −2.75173e9 | + | 9.61285e8i | −0.953087 | + | 0.332950i | ||||
\(79\) | −6.40192e8 | −0.208053 | −0.104027 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104027 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(80\) | − | 9.85094e8i | − | 0.300627i | ||||||
\(81\) | 7.82866e8 | − | 3.39776e9i | 0.224524 | − | 0.974469i | ||||
\(82\) | 1.29952e9 | 0.350521 | ||||||||
\(83\) | 3.98887e9i | 1.01265i | 0.862343 | + | 0.506325i | \(0.168996\pi\) | ||||
−0.862343 | + | 0.506325i | \(0.831004\pi\) | |||||||
\(84\) | 5.14777e8 | + | 1.47358e9i | 0.123090 | + | 0.352351i | ||||
\(85\) | −1.95933e9 | −0.441584 | ||||||||
\(86\) | − | 2.07914e9i | − | 0.441968i | ||||||
\(87\) | −2.29463e8 | + | 8.01602e7i | −0.0460379 | + | 0.0160828i | ||||
\(88\) | 7.77582e9 | 1.47344 | ||||||||
\(89\) | 3.01940e9i | 0.540718i | 0.962760 | + | 0.270359i | \(0.0871424\pi\) | ||||
−0.962760 | + | 0.270359i | \(0.912858\pi\) | |||||||
\(90\) | 1.77737e9 | − | 1.41442e9i | 0.300999 | − | 0.239533i | ||||
\(91\) | 1.05093e10 | 1.68409 | ||||||||
\(92\) | − | 3.24022e8i | − | 0.0491626i | ||||||
\(93\) | −4.08333e9 | − | 1.16887e10i | −0.586948 | − | 1.68017i | ||||
\(94\) | 4.22896e9 | 0.576229 | ||||||||
\(95\) | − | 5.54098e9i | − | 0.716091i | ||||||
\(96\) | 3.89255e9 | − | 1.35982e9i | 0.477395 | − | 0.166773i | ||||
\(97\) | −1.02491e10 | −1.19351 | −0.596754 | − | 0.802424i | \(-0.703543\pi\) | ||||
−0.596754 | + | 0.802424i | \(0.703543\pi\) | |||||||
\(98\) | 8.23264e9i | 0.910770i | ||||||||
\(99\) | 8.04981e9 | + | 1.01154e10i | 0.846466 | + | 1.06368i | ||||
\(100\) | −5.20234e8 | −0.0520234 | ||||||||
\(101\) | 1.14343e10i | 1.08793i | 0.839106 | + | 0.543967i | \(0.183079\pi\) | ||||
−0.839106 | + | 0.543967i | \(0.816921\pi\) | |||||||
\(102\) | 3.09260e9 | + | 8.85272e9i | 0.280106 | + | 0.801818i | ||||
\(103\) | −1.84678e10 | −1.59305 | −0.796525 | − | 0.604606i | \(-0.793331\pi\) | ||||
−0.796525 | + | 0.604606i | \(0.793331\pi\) | |||||||
\(104\) | − | 1.54780e10i | − | 1.27218i | ||||||
\(105\) | −7.73158e9 | + | 2.70094e9i | −0.605790 | + | 0.211626i | ||||
\(106\) | −1.07084e10 | −0.800196 | ||||||||
\(107\) | − | 1.27274e10i | − | 0.907449i | −0.891142 | − | 0.453724i | \(-0.850095\pi\) | ||
0.891142 | − | 0.453724i | \(-0.149905\pi\) | |||||||
\(108\) | 3.23302e9 | + | 2.03840e9i | 0.220034 | + | 0.138730i | ||||
\(109\) | −7.89967e9 | −0.513425 | −0.256712 | − | 0.966488i | \(-0.582639\pi\) | ||||
−0.256712 | + | 0.966488i | \(0.582639\pi\) | |||||||
\(110\) | 8.42171e9i | 0.522922i | ||||||||
\(111\) | −7.39816e8 | − | 2.11776e9i | −0.0439045 | − | 0.125679i | ||||
\(112\) | 1.69986e10 | 0.964546 | ||||||||
\(113\) | − | 1.24747e10i | − | 0.677074i | −0.940953 | − | 0.338537i | \(-0.890068\pi\) | ||
0.940953 | − | 0.338537i | \(-0.109932\pi\) | |||||||
\(114\) | −2.50355e10 | + | 8.74585e9i | −1.30026 | + | 0.454232i | ||||
\(115\) | 1.70008e9 | 0.0845242 | ||||||||
\(116\) | − | 2.66427e8i | − | 0.0126849i | ||||||
\(117\) | 2.01351e10 | − | 1.60234e10i | 0.918382 | − | 0.730843i | ||||
\(118\) | −3.05706e9 | −0.133627 | ||||||||
\(119\) | − | 3.38099e10i | − | 1.41680i | ||||||
\(120\) | 3.97793e9 | + | 1.13870e10i | 0.159864 | + | 0.457619i | ||||
\(121\) | −2.19926e10 | −0.847910 | ||||||||
\(122\) | − | 1.70702e9i | − | 0.0631597i | ||||||
\(123\) | −1.08307e10 | + | 3.78357e9i | −0.384706 | + | 0.134393i | ||||
\(124\) | 1.35717e10 | 0.462941 | ||||||||
\(125\) | − | 2.72958e9i | − | 0.0894427i | ||||||
\(126\) | 2.44070e10 | + | 3.06700e10i | 0.768531 | + | 0.965741i | ||||
\(127\) | −1.29905e10 | −0.393194 | −0.196597 | − | 0.980484i | \(-0.562989\pi\) | ||||
−0.196597 | + | 0.980484i | \(0.562989\pi\) | |||||||
\(128\) | − | 1.53479e10i | − | 0.446683i | ||||||
\(129\) | 6.05342e9 | + | 1.73282e10i | 0.169454 | + | 0.485072i | ||||
\(130\) | 1.67636e10 | 0.451493 | ||||||||
\(131\) | 4.93423e10i | 1.27898i | 0.768801 | + | 0.639488i | \(0.220854\pi\) | ||||
−0.768801 | + | 0.639488i | \(0.779146\pi\) | |||||||
\(132\) | −1.33775e10 | + | 4.67328e9i | −0.333815 | + | 0.116614i | ||||
\(133\) | 9.56142e10 | 2.29755 | ||||||||
\(134\) | − | 2.40663e10i | − | 0.557038i | ||||||
\(135\) | −1.06951e10 | + | 1.69631e10i | −0.238515 | + | 0.378299i | ||||
\(136\) | −4.97949e10 | −1.07026 | ||||||||
\(137\) | − | 2.13856e10i | − | 0.443117i | −0.975147 | − | 0.221559i | \(-0.928886\pi\) | ||
0.975147 | − | 0.221559i | \(-0.0711144\pi\) | |||||||
\(138\) | −2.68340e9 | − | 7.68138e9i | −0.0536155 | − | 0.153477i | ||||
\(139\) | 3.80392e10 | 0.733090 | 0.366545 | − | 0.930400i | \(-0.380541\pi\) | ||||
0.366545 | + | 0.930400i | \(0.380541\pi\) | |||||||
\(140\) | − | 8.97707e9i | − | 0.166915i | ||||||
\(141\) | −3.52456e10 | + | 1.23127e10i | −0.632426 | + | 0.220931i | ||||
\(142\) | 5.04743e10 | 0.874236 | ||||||||
\(143\) | 9.54059e10i | 1.59549i | ||||||||
\(144\) | 3.25682e10 | − | 2.59176e10i | 0.525994 | − | 0.418583i | ||||
\(145\) | 1.39789e9 | 0.0218089 | ||||||||
\(146\) | 1.94190e9i | 0.0292727i | ||||||||
\(147\) | −2.39694e10 | − | 6.86136e10i | −0.349197 | − | 0.999594i | ||||
\(148\) | 2.45892e9 | 0.0346286 | ||||||||
\(149\) | 3.55299e10i | 0.483797i | 0.970302 | + | 0.241898i | \(0.0777701\pi\) | ||||
−0.970302 | + | 0.241898i | \(0.922230\pi\) | |||||||
\(150\) | −1.23329e10 | + | 4.30835e9i | −0.162408 | + | 0.0567354i | ||||
\(151\) | −6.10213e9 | −0.0777315 | −0.0388657 | − | 0.999244i | \(-0.512374\pi\) | ||||
−0.0388657 | + | 0.999244i | \(0.512374\pi\) | |||||||
\(152\) | − | 1.40820e11i | − | 1.73559i | ||||||
\(153\) | −5.15495e10 | − | 6.47775e10i | −0.614848 | − | 0.772622i | ||||
\(154\) | −1.45324e11 | −1.67777 | ||||||||
\(155\) | 7.12082e10i | 0.795924i | ||||||||
\(156\) | 9.30229e9 | + | 2.66283e10i | 0.100686 | + | 0.288217i | ||||
\(157\) | −1.48553e11 | −1.55734 | −0.778668 | − | 0.627436i | \(-0.784104\pi\) | ||||
−0.778668 | + | 0.627436i | \(0.784104\pi\) | |||||||
\(158\) | − | 1.76214e10i | − | 0.178960i | ||||||
\(159\) | 8.92477e10 | − | 3.11777e10i | 0.878236 | − | 0.306802i | ||||
\(160\) | −2.37135e10 | −0.226150 | ||||||||
\(161\) | 2.93363e10i | 0.271192i | ||||||||
\(162\) | 9.35243e10 | + | 2.15486e10i | 0.838203 | + | 0.193127i | ||||
\(163\) | 1.30154e11 | 1.13115 | 0.565573 | − | 0.824698i | \(-0.308655\pi\) | ||||
0.565573 | + | 0.824698i | \(0.308655\pi\) | |||||||
\(164\) | − | 1.25754e10i | − | 0.105999i | ||||||
\(165\) | −2.45199e10 | − | 7.01894e10i | −0.200493 | − | 0.573920i | ||||
\(166\) | −1.09795e11 | −0.871045 | ||||||||
\(167\) | 1.61088e11i | 1.24017i | 0.784536 | + | 0.620083i | \(0.212901\pi\) | ||||
−0.784536 | + | 0.620083i | \(0.787099\pi\) | |||||||
\(168\) | −1.96492e11 | + | 6.86424e10i | −1.46825 | + | 0.512916i | ||||
\(169\) | 5.20495e10 | 0.377558 | ||||||||
\(170\) | − | 5.39311e10i | − | 0.379835i | ||||||
\(171\) | 1.83190e11 | − | 1.45782e11i | 1.25292 | − | 0.997063i | ||||
\(172\) | −2.01197e10 | −0.133653 | ||||||||
\(173\) | − | 1.51842e11i | − | 0.979854i | −0.871763 | − | 0.489927i | \(-0.837023\pi\) | ||
0.871763 | − | 0.489927i | \(-0.162977\pi\) | |||||||
\(174\) | −2.20643e9 | − | 6.31602e9i | −0.0138339 | − | 0.0396002i | ||||
\(175\) | 4.71011e10 | 0.286973 | ||||||||
\(176\) | 1.54318e11i | 0.913804i | ||||||||
\(177\) | 2.54785e10 | − | 8.90064e9i | 0.146659 | − | 0.0512336i | ||||
\(178\) | −8.31098e10 | −0.465106 | ||||||||
\(179\) | 2.98641e11i | 1.62512i | 0.582880 | + | 0.812558i | \(0.301926\pi\) | ||||
−0.582880 | + | 0.812558i | \(0.698074\pi\) | |||||||
\(180\) | −1.36872e10 | − | 1.71995e10i | −0.0724358 | − | 0.0910233i | ||||
\(181\) | 5.00350e10 | 0.257561 | 0.128781 | − | 0.991673i | \(-0.458894\pi\) | ||||
0.128781 | + | 0.991673i | \(0.458894\pi\) | |||||||
\(182\) | 2.89270e11i | 1.44859i | ||||||||
\(183\) | 4.97001e9 | + | 1.42269e10i | 0.0242160 | + | 0.0693194i | ||||
\(184\) | 4.32063e10 | 0.204861 | ||||||||
\(185\) | 1.29015e10i | 0.0595362i | ||||||||
\(186\) | 3.21735e11 | − | 1.12395e11i | 1.44522 | − | 0.504871i | ||||
\(187\) | 3.06935e11 | 1.34227 | ||||||||
\(188\) | − | 4.09234e10i | − | 0.174254i | ||||||
\(189\) | −2.92712e11 | − | 1.84553e11i | −1.21376 | − | 0.765265i | ||||
\(190\) | 1.52517e11 | 0.615956 | ||||||||
\(191\) | − | 4.67558e11i | − | 1.83937i | −0.392660 | − | 0.919684i | \(-0.628445\pi\) | ||
0.392660 | − | 0.919684i | \(-0.371555\pi\) | |||||||
\(192\) | 9.52738e10 | + | 2.72726e11i | 0.365147 | + | 1.04525i | ||||
\(193\) | 4.65772e10 | 0.173935 | 0.0869675 | − | 0.996211i | \(-0.472282\pi\) | ||||
0.0869675 | + | 0.996211i | \(0.472282\pi\) | |||||||
\(194\) | − | 2.82108e11i | − | 1.02661i | ||||||
\(195\) | −1.39714e11 | + | 4.88074e10i | −0.495526 | + | 0.173106i | ||||
\(196\) | 7.96667e10 | 0.275421 | ||||||||
\(197\) | − | 1.04345e11i | − | 0.351675i | −0.984419 | − | 0.175837i | \(-0.943737\pi\) | ||
0.984419 | − | 0.175837i | \(-0.0562633\pi\) | |||||||
\(198\) | −2.78430e11 | + | 2.21573e11i | −0.914935 | + | 0.728100i | ||||
\(199\) | −5.99954e10 | −0.192244 | −0.0961219 | − | 0.995370i | \(-0.530644\pi\) | ||||
−0.0961219 | + | 0.995370i | \(0.530644\pi\) | |||||||
\(200\) | − | 6.93701e10i | − | 0.216782i | ||||||
\(201\) | 7.00691e10 | + | 2.00577e11i | 0.213573 | + | 0.611364i | ||||
\(202\) | −3.14732e11 | −0.935803 | ||||||||
\(203\) | 2.41218e10i | 0.0699729i | ||||||||
\(204\) | 8.56672e10 | − | 2.99269e10i | 0.242473 | − | 0.0847053i | ||||
\(205\) | 6.59808e10 | 0.182242 | ||||||||
\(206\) | − | 5.08331e11i | − | 1.37028i | ||||||
\(207\) | 4.47288e10 | + | 5.62065e10i | 0.117689 | + | 0.147889i | ||||
\(208\) | 3.07174e11 | 0.788983 | ||||||||
\(209\) | 8.68011e11i | 2.17668i | ||||||||
\(210\) | −7.43441e10 | − | 2.12814e11i | −0.182033 | − | 0.521079i | ||||
\(211\) | −7.49985e11 | −1.79325 | −0.896624 | − | 0.442792i | \(-0.853988\pi\) | ||||
−0.896624 | + | 0.442792i | \(0.853988\pi\) | |||||||
\(212\) | 1.03625e11i | 0.241983i | ||||||||
\(213\) | −4.20670e11 | + | 1.46956e11i | −0.959497 | + | 0.335189i | ||||
\(214\) | 3.50326e11 | 0.780555 | ||||||||
\(215\) | − | 1.05564e11i | − | 0.229787i | ||||||
\(216\) | −2.71808e11 | + | 4.31104e11i | −0.578087 | + | 0.916881i | ||||
\(217\) | −1.22876e12 | −2.55368 | ||||||||
\(218\) | − | 2.17441e11i | − | 0.441630i | ||||||
\(219\) | −5.65387e9 | − | 1.61845e10i | −0.0112234 | − | 0.0321276i | ||||
\(220\) | 8.14963e10 | 0.158134 | ||||||||
\(221\) | − | 6.10962e11i | − | 1.15892i | ||||||
\(222\) | 5.82920e10 | − | 2.03636e10i | 0.108104 | − | 0.0377651i | ||||
\(223\) | 1.06490e12 | 1.93101 | 0.965503 | − | 0.260394i | \(-0.0838523\pi\) | ||||
0.965503 | + | 0.260394i | \(0.0838523\pi\) | |||||||
\(224\) | − | 4.09197e11i | − | 0.725591i | ||||||
\(225\) | 9.02425e10 | − | 7.18145e10i | 0.156494 | − | 0.124537i | ||||
\(226\) | 3.43368e11 | 0.582395 | ||||||||
\(227\) | 3.01663e10i | 0.0500487i | 0.999687 | + | 0.0250244i | \(0.00796633\pi\) | ||||
−0.999687 | + | 0.0250244i | \(0.992034\pi\) | |||||||
\(228\) | 8.46330e10 | + | 2.42266e11i | 0.137362 | + | 0.393205i | ||||
\(229\) | −8.11842e11 | −1.28912 | −0.644561 | − | 0.764553i | \(-0.722960\pi\) | ||||
−0.644561 | + | 0.764553i | \(0.722960\pi\) | |||||||
\(230\) | 4.67952e10i | 0.0727047i | ||||||||
\(231\) | 1.21118e12 | − | 4.23110e11i | 1.84140 | − | 0.643271i | ||||
\(232\) | 3.55265e10 | 0.0528581 | ||||||||
\(233\) | − | 5.24222e11i | − | 0.763371i | −0.924292 | − | 0.381685i | \(-0.875344\pi\) | ||
0.924292 | − | 0.381685i | \(-0.124656\pi\) | |||||||
\(234\) | 4.41047e11 | + | 5.54223e11i | 0.628645 | + | 0.789960i | ||||
\(235\) | 2.14718e11 | 0.299591 | ||||||||
\(236\) | 2.95829e10i | 0.0404093i | ||||||||
\(237\) | 5.13049e10 | + | 1.46863e11i | 0.0686147 | + | 0.196413i | ||||
\(238\) | 9.30626e11 | 1.21868 | ||||||||
\(239\) | 1.66440e11i | 0.213437i | 0.994289 | + | 0.106718i | \(0.0340343\pi\) | ||||
−0.994289 | + | 0.106718i | \(0.965966\pi\) | |||||||
\(240\) | −2.25985e11 | + | 7.89454e10i | −0.283808 | + | 0.0991449i | ||||
\(241\) | −1.21763e12 | −1.49772 | −0.748862 | − | 0.662726i | \(-0.769399\pi\) | ||||
−0.748862 | + | 0.662726i | \(0.769399\pi\) | |||||||
\(242\) | − | 6.05352e11i | − | 0.729342i | ||||||
\(243\) | −8.42202e11 | + | 9.27034e10i | −0.993997 | + | 0.109412i | ||||
\(244\) | −1.65187e10 | −0.0190998 | ||||||||
\(245\) | 4.17997e11i | 0.473524i | ||||||||
\(246\) | −1.04144e11 | − | 2.98117e11i | −0.115600 | − | 0.330911i | ||||
\(247\) | 1.72780e12 | 1.87935 | ||||||||
\(248\) | 1.80970e12i | 1.92907i | ||||||||
\(249\) | 9.15065e11 | − | 3.19668e11i | 0.955995 | − | 0.333966i | ||||
\(250\) | 7.51323e10 | 0.0769354 | ||||||||
\(251\) | 1.64602e12i | 1.65222i | 0.563512 | + | 0.826108i | \(0.309450\pi\) | ||||
−0.563512 | + | 0.826108i | \(0.690550\pi\) | |||||||
\(252\) | 2.96791e11 | − | 2.36185e11i | 0.292044 | − | 0.232407i | ||||
\(253\) | −2.66323e11 | −0.256925 | ||||||||
\(254\) | − | 3.57567e11i | − | 0.338212i | ||||||
\(255\) | 1.57021e11 | + | 4.49480e11i | 0.145632 | + | 0.416879i | ||||
\(256\) | −7.94919e11 | −0.722974 | ||||||||
\(257\) | 1.27887e11i | 0.114067i | 0.998372 | + | 0.0570336i | \(0.0181642\pi\) | ||||
−0.998372 | + | 0.0570336i | \(0.981836\pi\) | |||||||
\(258\) | −4.76964e11 | + | 1.66622e11i | −0.417241 | + | 0.145759i | ||||
\(259\) | −2.22626e11 | −0.191019 | ||||||||
\(260\) | − | 1.62220e11i | − | 0.136533i | ||||||
\(261\) | 3.67783e10 | + | 4.62158e10i | 0.0303661 | + | 0.0381582i | ||||
\(262\) | −1.35816e12 | −1.10013 | ||||||||
\(263\) | − | 2.48857e12i | − | 1.97775i | −0.148741 | − | 0.988876i | \(-0.547522\pi\) | ||
0.148741 | − | 0.988876i | \(-0.452478\pi\) | |||||||
\(264\) | −6.23154e11 | − | 1.78381e12i | −0.485932 | − | 1.39101i | ||||
\(265\) | −5.43700e11 | −0.416035 | ||||||||
\(266\) | 2.63180e12i | 1.97627i | ||||||||
\(267\) | 6.92666e11 | − | 2.41975e11i | 0.510467 | − | 0.178326i | ||||
\(268\) | −2.32888e11 | −0.168451 | ||||||||
\(269\) | − | 1.03039e12i | − | 0.731547i | −0.930704 | − | 0.365773i | \(-0.880804\pi\) | ||
0.930704 | − | 0.365773i | \(-0.119196\pi\) | |||||||
\(270\) | −4.66913e11 | − | 2.94385e11i | −0.325400 | − | 0.205162i | ||||
\(271\) | 1.62656e12 | 1.11282 | 0.556409 | − | 0.830909i | \(-0.312179\pi\) | ||||
0.556409 | + | 0.830909i | \(0.312179\pi\) | |||||||
\(272\) | − | 9.88224e11i | − | 0.663760i | ||||||
\(273\) | −8.42212e11 | − | 2.41088e12i | −0.555403 | − | 1.58987i | ||||
\(274\) | 5.88644e11 | 0.381154 | ||||||||
\(275\) | 4.27596e11i | 0.271876i | ||||||||
\(276\) | −7.43322e10 | + | 2.59671e10i | −0.0464121 | + | 0.0162135i | ||||
\(277\) | 1.37251e12 | 0.841624 | 0.420812 | − | 0.907148i | \(-0.361745\pi\) | ||||
0.420812 | + | 0.907148i | \(0.361745\pi\) | |||||||
\(278\) | 1.04704e12i | 0.630578i | ||||||||
\(279\) | −2.35421e12 | + | 1.87347e12i | −1.39260 | + | 1.10822i | ||||
\(280\) | 1.19704e12 | 0.695533 | ||||||||
\(281\) | − | 6.12902e11i | − | 0.349832i | −0.984583 | − | 0.174916i | \(-0.944035\pi\) | ||
0.984583 | − | 0.174916i | \(-0.0559654\pi\) | |||||||
\(282\) | −3.38909e11 | − | 9.70145e11i | −0.190037 | − | 0.543990i | ||||
\(283\) | −9.61960e11 | −0.529938 | −0.264969 | − | 0.964257i | \(-0.585362\pi\) | ||||
−0.264969 | + | 0.964257i | \(0.585362\pi\) | |||||||
\(284\) | − | 4.88437e11i | − | 0.264373i | ||||||
\(285\) | −1.27113e12 | + | 4.44054e11i | −0.676028 | + | 0.236163i | ||||
\(286\) | −2.62607e12 | −1.37239 | ||||||||
\(287\) | 1.13855e12i | 0.584714i | ||||||||
\(288\) | −6.23897e11 | − | 7.83994e11i | −0.314884 | − | 0.395685i | ||||
\(289\) | 5.04362e10 | 0.0250180 | ||||||||
\(290\) | 3.84774e10i | 0.0187593i | ||||||||
\(291\) | 8.21359e11 | + | 2.35118e12i | 0.393612 | + | 1.12673i | ||||
\(292\) | 1.87917e10 | 0.00885220 | ||||||||
\(293\) | 3.28624e12i | 1.52181i | 0.648862 | + | 0.760906i | \(0.275245\pi\) | ||||
−0.648862 | + | 0.760906i | \(0.724755\pi\) | |||||||
\(294\) | 1.88861e12 | − | 6.59764e11i | 0.859815 | − | 0.300367i | ||||
\(295\) | −1.55216e11 | −0.0694748 | ||||||||
\(296\) | 3.27882e11i | 0.144297i | ||||||||
\(297\) | 1.67542e12 | − | 2.65732e12i | 0.725006 | − | 1.14990i | ||||
\(298\) | −9.77971e11 | −0.416145 | ||||||||
\(299\) | 5.30123e11i | 0.221830i | ||||||||
\(300\) | 4.16916e10 | + | 1.19344e11i | 0.0171570 | + | 0.0491129i | ||||
\(301\) | 1.82160e12 | 0.737259 | ||||||||
\(302\) | − | 1.67963e11i | − | 0.0668618i | ||||||
\(303\) | 2.62309e12 | − | 9.16345e11i | 1.02707 | − | 0.358795i | ||||
\(304\) | 2.79469e12 | 1.07638 | ||||||||
\(305\) | − | 8.66708e10i | − | 0.0328378i | ||||||
\(306\) | 1.78302e12 | − | 1.41891e12i | 0.664582 | − | 0.528870i | ||||
\(307\) | −4.36270e11 | −0.159979 | −0.0799896 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799896 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(308\) | 1.40629e12i | 0.507364i | ||||||||
\(309\) | 1.48001e12 | + | 4.23661e12i | 0.525379 | + | 1.50392i | ||||
\(310\) | −1.96002e12 | −0.684625 | ||||||||
\(311\) | − | 1.17043e11i | − | 0.0402295i | −0.999798 | − | 0.0201148i | \(-0.993597\pi\) | ||
0.999798 | − | 0.0201148i | \(-0.00640316\pi\) | |||||||
\(312\) | −3.55072e12 | + | 1.24040e12i | −1.20100 | + | 0.419556i | ||||
\(313\) | 2.82819e12 | 0.941428 | 0.470714 | − | 0.882286i | \(-0.343996\pi\) | ||||
0.470714 | + | 0.882286i | \(0.343996\pi\) | |||||||
\(314\) | − | 4.08895e12i | − | 1.33957i | ||||||
\(315\) | 1.23922e12 | + | 1.55721e12i | 0.399572 | + | 0.502104i | ||||
\(316\) | −1.70521e11 | −0.0541182 | ||||||||
\(317\) | − | 4.21635e12i | − | 1.31717i | −0.752508 | − | 0.658583i | \(-0.771156\pi\) | ||
0.752508 | − | 0.658583i | \(-0.228844\pi\) | |||||||
\(318\) | 8.58173e11 | + | 2.45657e12i | 0.263900 | + | 0.755428i | ||||
\(319\) | −2.18984e11 | −0.0662918 | ||||||||
\(320\) | − | 1.66146e12i | − | 0.495153i | ||||||
\(321\) | −2.91974e12 | + | 1.01998e12i | −0.856680 | + | 0.299271i | ||||
\(322\) | −8.07490e11 | −0.233269 | ||||||||
\(323\) | − | 5.55859e12i | − | 1.58107i | ||||||
\(324\) | 2.08524e11 | − | 9.05028e11i | 0.0584025 | − | 0.253476i | ||||
\(325\) | 8.51141e11 | 0.234739 | ||||||||
\(326\) | 3.58251e12i | 0.972971i | ||||||||
\(327\) | 6.33080e11 | + | 1.81222e12i | 0.169324 | + | 0.484700i | ||||
\(328\) | 1.67685e12 | 0.441698 | ||||||||
\(329\) | 3.70513e12i | 0.961222i | ||||||||
\(330\) | 1.93198e12 | − | 6.74916e11i | 0.493666 | − | 0.172457i | ||||
\(331\) | −3.65692e12 | −0.920398 | −0.460199 | − | 0.887816i | \(-0.652222\pi\) | ||||
−0.460199 | + | 0.887816i | \(0.652222\pi\) | |||||||
\(332\) | 1.06247e12i | 0.263408i | ||||||||
\(333\) | −4.26536e11 | + | 3.39435e11i | −0.104168 | + | 0.0828963i | ||||
\(334\) | −4.43398e12 | −1.06675 | ||||||||
\(335\) | − | 1.22192e12i | − | 0.289613i | ||||||
\(336\) | −1.36227e12 | − | 3.89956e12i | −0.318102 | − | 0.910583i | ||||
\(337\) | −3.50041e12 | −0.805322 | −0.402661 | − | 0.915349i | \(-0.631915\pi\) | ||||
−0.402661 | + | 0.915349i | \(0.631915\pi\) | |||||||
\(338\) | 1.43268e12i | 0.324762i | ||||||||
\(339\) | −2.86175e12 | + | 9.99718e11i | −0.639194 | + | 0.223295i | ||||
\(340\) | −5.21888e11 | −0.114864 | ||||||||
\(341\) | − | 1.11550e13i | − | 2.41934i | ||||||
\(342\) | 4.01268e12 | + | 5.04236e12i | 0.857638 | + | 1.07771i | ||||
\(343\) | −4.00774e11 | −0.0844167 | ||||||||
\(344\) | − | 2.68284e12i | − | 0.556932i | ||||||
\(345\) | −1.36245e11 | − | 3.90007e11i | −0.0278756 | − | 0.0797953i | ||||
\(346\) | 4.17949e12 | 0.842836 | ||||||||
\(347\) | 6.85033e12i | 1.36165i | 0.732448 | + | 0.680823i | \(0.238378\pi\) | ||||
−0.732448 | + | 0.680823i | \(0.761622\pi\) | |||||||
\(348\) | −6.11197e10 | + | 2.13515e10i | −0.0119753 | + | 0.00418342i | ||||
\(349\) | −5.11040e12 | −0.987024 | −0.493512 | − | 0.869739i | \(-0.664287\pi\) | ||||
−0.493512 | + | 0.869739i | \(0.664287\pi\) | |||||||
\(350\) | 1.29647e12i | 0.246844i | ||||||||
\(351\) | −5.28946e12 | − | 3.33497e12i | −0.992832 | − | 0.625974i | ||||
\(352\) | 3.71480e12 | 0.687420 | ||||||||
\(353\) | 2.89458e12i | 0.528095i | 0.964510 | + | 0.264047i | \(0.0850575\pi\) | ||||
−0.964510 | + | 0.264047i | \(0.914942\pi\) | |||||||
\(354\) | 2.44992e11 | + | 7.01304e11i | 0.0440693 | + | 0.126151i | ||||
\(355\) | 2.56274e12 | 0.454530 | ||||||||
\(356\) | 8.04248e11i | 0.140650i | ||||||||
\(357\) | −7.75615e12 | + | 2.70952e12i | −1.33753 | + | 0.467253i | ||||
\(358\) | −8.22017e12 | −1.39787 | ||||||||
\(359\) | − | 5.87330e12i | − | 0.984940i | −0.870329 | − | 0.492470i | \(-0.836094\pi\) | ||
0.870329 | − | 0.492470i | \(-0.163906\pi\) | |||||||
\(360\) | 2.29345e12 | − | 1.82511e12i | 0.379294 | − | 0.301840i | ||||
\(361\) | 9.58859e12 | 1.56394 | ||||||||
\(362\) | 1.37723e12i | 0.221545i | ||||||||
\(363\) | 1.76249e12 | + | 5.04521e12i | 0.279636 | + | 0.800472i | ||||
\(364\) | 2.79925e12 | 0.438061 | ||||||||
\(365\) | 9.85964e10i | 0.0152194i | ||||||||
\(366\) | −3.91599e11 | + | 1.36801e11i | −0.0596261 | + | 0.0208297i | ||||
\(367\) | −1.26759e12 | −0.190392 | −0.0951960 | − | 0.995459i | \(-0.530348\pi\) | ||||
−0.0951960 | + | 0.995459i | \(0.530348\pi\) | |||||||
\(368\) | 8.57467e11i | 0.127051i | ||||||||
\(369\) | 1.73594e12 | + | 2.18139e12i | 0.253748 | + | 0.318861i | ||||
\(370\) | −3.55117e11 | −0.0512109 | ||||||||
\(371\) | − | 9.38199e12i | − | 1.33483i | ||||||
\(372\) | −1.08764e12 | − | 3.11341e12i | −0.152675 | − | 0.437041i | ||||
\(373\) | 6.12110e10 | 0.00847785 | 0.00423892 | − | 0.999991i | \(-0.498651\pi\) | ||||
0.00423892 | + | 0.999991i | \(0.498651\pi\) | |||||||
\(374\) | 8.44847e12i | 1.15457i | ||||||||
\(375\) | −6.26178e11 | + | 2.18748e11i | −0.0844387 | + | 0.0294977i | ||||
\(376\) | 5.45689e12 | 0.726116 | ||||||||
\(377\) | 4.35894e11i | 0.0572367i | ||||||||
\(378\) | 5.07986e12 | − | 8.05697e12i | 0.658253 | − | 1.04403i | ||||
\(379\) | 8.02388e12 | 1.02610 | 0.513049 | − | 0.858360i | \(-0.328516\pi\) | ||||
0.513049 | + | 0.858360i | \(0.328516\pi\) | |||||||
\(380\) | − | 1.47590e12i | − | 0.186268i | ||||||
\(381\) | 1.04106e12 | + | 2.98008e12i | 0.129673 | + | 0.371196i | ||||
\(382\) | 1.28696e13 | 1.58216 | ||||||||
\(383\) | − | 3.43547e12i | − | 0.416862i | −0.978037 | − | 0.208431i | \(-0.933164\pi\) | ||
0.978037 | − | 0.208431i | \(-0.0668357\pi\) | |||||||
\(384\) | −3.52089e12 | + | 1.22998e12i | −0.421693 | + | 0.147314i | ||||
\(385\) | −7.37852e12 | −0.872300 | ||||||||
\(386\) | 1.28205e12i | 0.149613i | ||||||||
\(387\) | 3.49006e12 | − | 2.77737e12i | 0.402048 | − | 0.319948i | ||||
\(388\) | −2.72994e12 | −0.310452 | ||||||||
\(389\) | 1.43402e13i | 1.60993i | 0.593322 | + | 0.804965i | \(0.297816\pi\) | ||||
−0.593322 | + | 0.804965i | \(0.702184\pi\) | |||||||
\(390\) | −1.34344e12 | − | 3.84566e12i | −0.148900 | − | 0.426234i | ||||
\(391\) | 1.70549e12 | 0.186623 | ||||||||
\(392\) | 1.06231e13i | 1.14768i | ||||||||
\(393\) | 1.13194e13 | − | 3.95429e12i | 1.20742 | − | 0.421799i | ||||
\(394\) | 2.87213e12 | 0.302498 | ||||||||
\(395\) | − | 8.94695e11i | − | 0.0930442i | ||||||
\(396\) | 2.14415e12 | + | 2.69435e12i | 0.220180 | + | 0.276680i | ||||
\(397\) | −7.76634e12 | −0.787524 | −0.393762 | − | 0.919212i | \(-0.628827\pi\) | ||||
−0.393762 | + | 0.919212i | \(0.628827\pi\) | |||||||
\(398\) | − | 1.65139e12i | − | 0.165361i | ||||||
\(399\) | −7.66252e12 | − | 2.19344e13i | −0.757717 | − | 2.16900i | ||||
\(400\) | 1.37671e12 | 0.134444 | ||||||||
\(401\) | 1.13589e13i | 1.09551i | 0.836640 | + | 0.547754i | \(0.184517\pi\) | ||||
−0.836640 | + | 0.547754i | \(0.815483\pi\) | |||||||
\(402\) | −5.52092e12 | + | 1.92867e12i | −0.525873 | + | 0.183708i | ||||
\(403\) | −2.22043e13 | −2.08887 | ||||||||
\(404\) | 3.04564e12i | 0.282991i | ||||||||
\(405\) | 4.74852e12 | + | 1.09409e12i | 0.435796 | + | 0.100410i | ||||
\(406\) | −6.63960e11 | −0.0601882 | ||||||||
\(407\) | − | 2.02106e12i | − | 0.180970i | ||||||
\(408\) | 3.99057e12 | + | 1.14232e13i | 0.352967 | + | 1.01039i | ||||
\(409\) | 9.79320e12 | 0.855673 | 0.427837 | − | 0.903856i | \(-0.359276\pi\) | ||||
0.427837 | + | 0.903856i | \(0.359276\pi\) | |||||||
\(410\) | 1.81614e12i | 0.156758i | ||||||||
\(411\) | −4.90596e12 | + | 1.71384e12i | −0.418326 | + | 0.146138i | ||||
\(412\) | −4.91909e12 | −0.414380 | ||||||||
\(413\) | − | 2.67838e12i | − | 0.222906i | ||||||
\(414\) | −1.54710e12 | + | 1.23117e12i | −0.127208 | + | 0.101232i | ||||
\(415\) | −5.57461e12 | −0.452871 | ||||||||
\(416\) | − | 7.39440e12i | − | 0.593521i | ||||||
\(417\) | −3.04846e12 | − | 8.72637e12i | −0.241769 | − | 0.692076i | ||||
\(418\) | −2.38922e13 | −1.87230 | ||||||||
\(419\) | 1.97848e13i | 1.53201i | 0.642833 | + | 0.766006i | \(0.277759\pi\) | ||||
−0.642833 | + | 0.766006i | \(0.722241\pi\) | |||||||
\(420\) | −2.05938e12 | + | 7.19423e11i | −0.157576 | + | 0.0550475i | ||||
\(421\) | 9.74675e12 | 0.736970 | 0.368485 | − | 0.929634i | \(-0.379877\pi\) | ||||
0.368485 | + | 0.929634i | \(0.379877\pi\) | |||||||
\(422\) | − | 2.06435e13i | − | 1.54249i | ||||||
\(423\) | 5.64917e12 | + | 7.09878e12i | 0.417141 | + | 0.524182i | ||||
\(424\) | −1.38177e13 | −1.00834 | ||||||||
\(425\) | − | 2.73825e12i | − | 0.197482i | ||||||
\(426\) | −4.04501e12 | − | 1.15791e13i | −0.288318 | − | 0.825325i | ||||
\(427\) | 1.49558e12 | 0.105358 | ||||||||
\(428\) | − | 3.39008e12i | − | 0.236043i | ||||||
\(429\) | 2.18866e13 | − | 7.64583e12i | 1.50623 | − | 0.526185i | ||||
\(430\) | 2.90568e12 | 0.197654 | ||||||||
\(431\) | 1.81943e12i | 0.122334i | 0.998128 | + | 0.0611671i | \(0.0194823\pi\) | ||||
−0.998128 | + | 0.0611671i | \(0.980518\pi\) | |||||||
\(432\) | −8.55563e12 | − | 5.39427e12i | −0.568635 | − | 0.358520i | ||||
\(433\) | 1.88176e13 | 1.23631 | 0.618153 | − | 0.786058i | \(-0.287881\pi\) | ||||
0.618153 | + | 0.786058i | \(0.287881\pi\) | |||||||
\(434\) | − | 3.38218e13i | − | 2.19659i | ||||||
\(435\) | −1.12027e11 | − | 3.20684e11i | −0.00719246 | − | 0.0205888i | ||||
\(436\) | −2.10416e12 | −0.133551 | ||||||||
\(437\) | 4.82310e12i | 0.302635i | ||||||||
\(438\) | 4.45482e11 | − | 1.55624e11i | 0.0276350 | − | 0.00965398i | ||||
\(439\) | −1.31625e13 | −0.807266 | −0.403633 | − | 0.914921i | \(-0.632253\pi\) | ||||
−0.403633 | + | 0.914921i | \(0.632253\pi\) | |||||||
\(440\) | 1.08670e13i | 0.658943i | ||||||||
\(441\) | −1.38194e13 | + | 1.09974e13i | −0.828506 | + | 0.659320i | ||||
\(442\) | 1.68169e13 | 0.996861 | ||||||||
\(443\) | 1.22492e12i | 0.0717943i | 0.999355 | + | 0.0358972i | \(0.0114289\pi\) | ||||
−0.999355 | + | 0.0358972i | \(0.988571\pi\) | |||||||
\(444\) | −1.97057e11 | − | 5.64087e11i | −0.0114203 | − | 0.0326912i | ||||
\(445\) | −4.21974e12 | −0.241817 | ||||||||
\(446\) | 2.93116e13i | 1.66098i | ||||||||
\(447\) | 8.15074e12 | − | 2.84737e12i | 0.456730 | − | 0.159553i | ||||
\(448\) | 2.86698e13 | 1.58867 | ||||||||
\(449\) | − | 2.63416e12i | − | 0.144348i | −0.997392 | − | 0.0721741i | \(-0.977006\pi\) | ||
0.997392 | − | 0.0721741i | \(-0.0229937\pi\) | |||||||
\(450\) | 1.97671e12 | + | 2.48395e12i | 0.107123 | + | 0.134611i | ||||
\(451\) | −1.03361e13 | −0.553954 | ||||||||
\(452\) | − | 3.32275e12i | − | 0.176119i | ||||||
\(453\) | 4.89025e11 | + | 1.39986e12i | 0.0256354 | + | 0.0733826i | ||||
\(454\) | −8.30336e11 | −0.0430501 | ||||||||
\(455\) | 1.46871e13i | 0.753148i | ||||||||
\(456\) | −3.23048e13 | + | 1.12853e13i | −1.63848 | + | 0.572386i | ||||
\(457\) | 2.23624e13 | 1.12186 | 0.560928 | − | 0.827864i | \(-0.310444\pi\) | ||||
0.560928 | + | 0.827864i | \(0.310444\pi\) | |||||||
\(458\) | − | 2.23462e13i | − | 1.10886i | ||||||
\(459\) | −1.07291e13 | + | 1.70170e13i | −0.526623 | + | 0.835255i | ||||
\(460\) | 4.52834e11 | 0.0219862 | ||||||||
\(461\) | 9.31576e12i | 0.447418i | 0.974656 | + | 0.223709i | \(0.0718165\pi\) | ||||
−0.974656 | + | 0.223709i | \(0.928183\pi\) | |||||||
\(462\) | 1.16462e13 | + | 3.33379e13i | 0.553319 | + | 1.58390i | ||||
\(463\) | −7.64194e12 | −0.359169 | −0.179584 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179584 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(464\) | 7.05053e11i | 0.0327817i | ||||||||
\(465\) | 1.63355e13 | − | 5.70662e12i | 0.751394 | − | 0.262491i | ||||
\(466\) | 1.44293e13 | 0.656624 | ||||||||
\(467\) | − | 2.60999e13i | − | 1.17504i | −0.809209 | − | 0.587521i | \(-0.800104\pi\) | ||
0.809209 | − | 0.587521i | \(-0.199896\pi\) | |||||||
\(468\) | 5.36317e12 | − | 4.26798e12i | 0.238887 | − | 0.190105i | ||||
\(469\) | 2.10852e13 | 0.929210 | ||||||||
\(470\) | 5.91016e12i | 0.257697i | ||||||||
\(471\) | 1.19050e13 | + | 3.40787e13i | 0.513600 | + | 1.47021i | ||||
\(472\) | −3.94470e12 | −0.168385 | ||||||||
\(473\) | 1.65370e13i | 0.698474i | ||||||||
\(474\) | −4.04244e12 | + | 1.41218e12i | −0.168948 | + | 0.0590200i | ||||
\(475\) | 7.74375e12 | 0.320246 | ||||||||
\(476\) | − | 9.00560e12i | − | 0.368534i | ||||||
\(477\) | −1.43046e13 | − | 1.79753e13i | −0.579274 | − | 0.727920i | ||||
\(478\) | −4.58131e12 | −0.183591 | ||||||||
\(479\) | − | 4.08677e13i | − | 1.62070i | −0.585946 | − | 0.810350i | \(-0.699277\pi\) | ||
0.585946 | − | 0.810350i | \(-0.300723\pi\) | |||||||
\(480\) | 1.90040e12 | + | 5.44000e12i | 0.0745829 | + | 0.213498i | ||||
\(481\) | −4.02296e12 | −0.156250 | ||||||||
\(482\) | − | 3.35157e13i | − | 1.28829i | ||||||
\(483\) | 6.72990e12 | − | 2.35101e12i | 0.256019 | − | 0.0894374i | ||||
\(484\) | −5.85795e12 | −0.220556 | ||||||||
\(485\) | − | 1.43235e13i | − | 0.533753i | ||||||
\(486\) | −2.55169e12 | − | 2.31818e13i | −0.0941122 | − | 0.855000i | ||||
\(487\) | 5.24504e12 | 0.191471 | 0.0957357 | − | 0.995407i | \(-0.469480\pi\) | ||||
0.0957357 | + | 0.995407i | \(0.469480\pi\) | |||||||
\(488\) | − | 2.20267e12i | − | 0.0795887i | ||||||
\(489\) | −1.04305e13 | − | 2.98579e13i | −0.373045 | − | 1.06786i | ||||
\(490\) | −1.15055e13 | −0.407309 | ||||||||
\(491\) | − | 3.09503e13i | − | 1.08457i | −0.840194 | − | 0.542285i | \(-0.817559\pi\) | ||
0.840194 | − | 0.542285i | \(-0.182441\pi\) | |||||||
\(492\) | −2.88486e12 | + | 1.00779e12i | −0.100069 | + | 0.0349579i | ||||
\(493\) | 1.40234e12 | 0.0481524 | ||||||||
\(494\) | 4.75581e13i | 1.61655i | ||||||||
\(495\) | −1.41368e13 | + | 1.12500e13i | −0.475690 | + | 0.378551i | ||||
\(496\) | −3.59151e13 | −1.19638 | ||||||||
\(497\) | 4.42221e13i | 1.45834i | ||||||||
\(498\) | 8.79894e12 | + | 2.51874e13i | 0.287266 | + | 0.822313i | ||||
\(499\) | 2.83274e12 | 0.0915595 | 0.0457798 | − | 0.998952i | \(-0.485423\pi\) | ||||
0.0457798 | + | 0.998952i | \(0.485423\pi\) | |||||||
\(500\) | − | 7.27050e11i | − | 0.0232656i | ||||||
\(501\) | 3.69543e13 | − | 1.29096e13i | 1.17078 | − | 0.409000i | ||||
\(502\) | −4.53071e13 | −1.42118 | ||||||||
\(503\) | 1.23847e13i | 0.384634i | 0.981333 | + | 0.192317i | \(0.0616001\pi\) | ||||
−0.981333 | + | 0.192317i | \(0.938400\pi\) | |||||||
\(504\) | 3.14938e13 | + | 3.95753e13i | 0.968439 | + | 1.21695i | ||||
\(505\) | −1.59799e13 | −0.486539 | ||||||||
\(506\) | − | 7.33061e12i | − | 0.220998i | ||||||
\(507\) | −4.17125e12 | − | 1.19404e13i | −0.124516 | − | 0.356434i | ||||
\(508\) | −3.46015e12 | −0.102277 | ||||||||
\(509\) | − | 1.15213e13i | − | 0.337220i | −0.985683 | − | 0.168610i | \(-0.946072\pi\) | ||
0.985683 | − | 0.168610i | \(-0.0539279\pi\) | |||||||
\(510\) | −1.23721e13 | + | 4.32204e12i | −0.358584 | + | 0.125267i | ||||
\(511\) | −1.70136e12 | −0.0488306 | ||||||||
\(512\) | − | 3.75966e13i | − | 1.06856i | ||||||
\(513\) | −4.81239e13 | − | 3.03418e13i | −1.35449 | − | 0.853994i | ||||
\(514\) | −3.52012e12 | −0.0981165 | ||||||||
\(515\) | − | 2.58096e13i | − | 0.712434i | ||||||
\(516\) | 1.61239e12 | + | 4.61555e12i | 0.0440780 | + | 0.126175i | ||||
\(517\) | −3.36362e13 | −0.910655 | ||||||||
\(518\) | − | 6.12783e12i | − | 0.164308i | ||||||
\(519\) | −3.48333e13 | + | 1.21686e13i | −0.925034 | + | 0.323150i | ||||
\(520\) | 2.16311e13 | 0.568935 | ||||||||
\(521\) | 5.60633e13i | 1.46046i | 0.683200 | + | 0.730231i | \(0.260588\pi\) | ||||
−0.683200 | + | 0.730231i | \(0.739412\pi\) | |||||||
\(522\) | −1.27210e12 | + | 1.01233e12i | −0.0328223 | + | 0.0261198i | ||||
\(523\) | −5.51546e13 | −1.40953 | −0.704763 | − | 0.709442i | \(-0.748947\pi\) | ||||
−0.704763 | + | 0.709442i | \(0.748947\pi\) | |||||||
\(524\) | 1.31428e13i | 0.332684i | ||||||||
\(525\) | −3.77468e12 | − | 1.08052e13i | −0.0946419 | − | 0.270917i | ||||
\(526\) | 6.84987e13 | 1.70119 | ||||||||
\(527\) | 7.14345e13i | 1.75734i | ||||||||
\(528\) | 3.54013e13 | − | 1.23670e13i | 0.862679 | − | 0.301367i | ||||
\(529\) | 3.99467e13 | 0.964278 | ||||||||
\(530\) | − | 1.49655e13i | − | 0.357859i | ||||||
\(531\) | −4.08370e12 | − | 5.13160e12i | −0.0967345 | − | 0.121557i | ||||
\(532\) | 2.54678e13 | 0.597631 | ||||||||
\(533\) | 2.05743e13i | 0.478286i | ||||||||
\(534\) | 6.66042e12 | + | 1.90658e13i | 0.153389 | + | 0.439085i | ||||
\(535\) | 1.77871e13 | 0.405823 | ||||||||
\(536\) | − | 3.10542e13i | − | 0.701933i | ||||||
\(537\) | 6.85097e13 | − | 2.39331e13i | 1.53420 | − | 0.535954i | ||||
\(538\) | 2.83619e13 | 0.629251 | ||||||||
\(539\) | − | 6.54804e13i | − | 1.43935i | ||||||
\(540\) | −2.84875e12 | + | 4.51829e12i | −0.0620419 | + | 0.0984022i | ||||
\(541\) | −4.10912e13 | −0.886671 | −0.443336 | − | 0.896356i | \(-0.646205\pi\) | ||||
−0.443336 | + | 0.896356i | \(0.646205\pi\) | |||||||
\(542\) | 4.47715e13i | 0.957206i | ||||||||
\(543\) | −4.00980e12 | − | 1.14783e13i | −0.0849423 | − | 0.243152i | ||||
\(544\) | −2.37889e13 | −0.499321 | ||||||||
\(545\) | − | 1.10401e13i | − | 0.229610i | ||||||
\(546\) | 6.63600e13 | − | 2.31821e13i | 1.36755 | − | 0.477738i | ||||
\(547\) | −8.84674e11 | −0.0180654 | −0.00903268 | − | 0.999959i | \(-0.502875\pi\) | ||||
−0.00903268 | + | 0.999959i | \(0.502875\pi\) | |||||||
\(548\) | − | 5.69627e12i | − | 0.115262i | ||||||
\(549\) | 2.86543e12 | − | 2.28029e12i | 0.0574549 | − | 0.0457223i | ||||
\(550\) | −1.17697e13 | −0.233858 | ||||||||
\(551\) | 3.96580e12i | 0.0780860i | ||||||||
\(552\) | −3.46255e12 | − | 9.91174e12i | −0.0675618 | − | 0.193399i | ||||
\(553\) | 1.54387e13 | 0.298528 | ||||||||
\(554\) | 3.77788e13i | 0.723935i | ||||||||
\(555\) | 2.95966e12 | − | 1.03392e12i | 0.0562053 | − | 0.0196347i | ||||
\(556\) | 1.01321e13 | 0.190689 | ||||||||
\(557\) | 4.89810e13i | 0.913591i | 0.889572 | + | 0.456795i | \(0.151003\pi\) | ||||
−0.889572 | + | 0.456795i | \(0.848997\pi\) | |||||||
\(558\) | −5.15677e13 | − | 6.48004e13i | −0.953251 | − | 1.19786i | ||||
\(559\) | 3.29172e13 | 0.603065 | ||||||||
\(560\) | 2.37563e13i | 0.431358i | ||||||||
\(561\) | −2.45978e13 | − | 7.04124e13i | −0.442672 | − | 1.26717i | ||||
\(562\) | 1.68703e13 | 0.300913 | ||||||||
\(563\) | 8.08485e13i | 1.42932i | 0.699471 | + | 0.714661i | \(0.253419\pi\) | ||||
−0.699471 | + | 0.714661i | \(0.746581\pi\) | |||||||
\(564\) | −9.38803e12 | + | 3.27960e12i | −0.164505 | + | 0.0574679i | ||||
\(565\) | 1.74339e13 | 0.302797 | ||||||||
\(566\) | − | 2.64782e13i | − | 0.455834i | ||||||
\(567\) | −1.88794e13 | + | 8.19396e13i | −0.322161 | + | 1.39823i | ||||
\(568\) | 6.51300e13 | 1.10164 | ||||||||
\(569\) | 4.70230e13i | 0.788405i | 0.919024 | + | 0.394203i | \(0.128979\pi\) | ||||
−0.919024 | + | 0.394203i | \(0.871021\pi\) | |||||||
\(570\) | −1.22227e13 | − | 3.49881e13i | −0.203139 | − | 0.581495i | ||||
\(571\) | 3.94741e13 | 0.650327 | 0.325164 | − | 0.945658i | \(-0.394581\pi\) | ||||
0.325164 | + | 0.945658i | \(0.394581\pi\) | |||||||
\(572\) | 2.54123e13i | 0.415016i | ||||||||
\(573\) | −1.07260e14 | + | 3.74701e13i | −1.73646 | + | 0.606613i | ||||
\(574\) | −3.13390e13 | −0.502950 | ||||||||
\(575\) | 2.37594e12i | 0.0378004i | ||||||||
\(576\) | 5.49295e13 | − | 4.37125e13i | 0.866349 | − | 0.689435i | ||||
\(577\) | 2.72198e12 | 0.0425605 | 0.0212802 | − | 0.999774i | \(-0.493226\pi\) | ||||
0.0212802 | + | 0.999774i | \(0.493226\pi\) | |||||||
\(578\) | 1.38827e12i | 0.0215196i | ||||||||
\(579\) | −3.73270e12 | − | 1.06850e13i | −0.0573628 | − | 0.164204i | ||||
\(580\) | 3.72343e11 | 0.00567288 | ||||||||
\(581\) | − | 9.61945e13i | − | 1.45301i | ||||||
\(582\) | −6.47169e13 | + | 2.26081e13i | −0.969177 | + | 0.338571i | ||||
\(583\) | 8.51723e13 | 1.26461 | ||||||||
\(584\) | 2.50575e12i | 0.0368871i | ||||||||
\(585\) | 2.23933e13 | + | 2.81396e13i | 0.326843 | + | 0.410713i | ||||
\(586\) | −9.04546e13 | −1.30901 | ||||||||
\(587\) | − | 1.01511e14i | − | 1.45654i | −0.685293 | − | 0.728268i | \(-0.740326\pi\) | ||
0.685293 | − | 0.728268i | \(-0.259674\pi\) | |||||||
\(588\) | −6.38449e12 | − | 1.82759e13i | −0.0908321 | − | 0.260012i | ||||
\(589\) | −2.02016e14 | −2.84977 | ||||||||
\(590\) | − | 4.27237e12i | − | 0.0597597i | ||||||
\(591\) | −2.39373e13 | + | 8.36222e12i | −0.331999 | + | 0.115980i | ||||
\(592\) | −6.50709e12 | −0.0894908 | ||||||||
\(593\) | 3.33265e13i | 0.454481i | 0.973839 | + | 0.227241i | \(0.0729704\pi\) | ||||
−0.973839 | + | 0.227241i | \(0.927030\pi\) | |||||||
\(594\) | 7.31433e13 | + | 4.61164e13i | 0.989105 | + | 0.623624i | ||||
\(595\) | 4.72507e13 | 0.633613 | ||||||||
\(596\) | 9.46375e12i | 0.125844i | ||||||||
\(597\) | 4.80803e12 | + | 1.37632e13i | 0.0634009 | + | 0.181488i | ||||
\(598\) | −1.45918e13 | −0.190810 | ||||||||
\(599\) | − | 8.32579e13i | − | 1.07967i | −0.841771 | − | 0.539835i | \(-0.818487\pi\) | ||
0.841771 | − | 0.539835i | \(-0.181513\pi\) | |||||||
\(600\) | −1.59138e13 | + | 5.55932e12i | −0.204653 | + | 0.0714933i | ||||
\(601\) | −2.42358e13 | −0.309091 | −0.154545 | − | 0.987986i | \(-0.549391\pi\) | ||||
−0.154545 | + | 0.987986i | \(0.549391\pi\) | |||||||
\(602\) | 5.01400e13i | 0.634164i | ||||||||
\(603\) | 4.03979e13 | − | 3.21484e13i | 0.506725 | − | 0.403249i | ||||
\(604\) | −1.62536e12 | −0.0202193 | ||||||||
\(605\) | − | 3.07356e13i | − | 0.379197i | ||||||
\(606\) | 2.52226e13 | + | 7.22011e13i | 0.308622 | + | 0.883447i | ||||
\(607\) | −7.69672e13 | −0.934033 | −0.467016 | − | 0.884249i | \(-0.654671\pi\) | ||||
−0.467016 | + | 0.884249i | \(0.654671\pi\) | |||||||
\(608\) | − | 6.72749e13i | − | 0.809720i | ||||||
\(609\) | 5.53366e12 | − | 1.93312e12i | 0.0660581 | − | 0.0230767i | ||||
\(610\) | 2.38564e12 | 0.0282459 | ||||||||
\(611\) | 6.69536e13i | 0.786264i | ||||||||
\(612\) | −1.37307e13 | − | 1.72541e13i | −0.159932 | − | 0.200972i | ||||
\(613\) | 1.31289e14 | 1.51679 | 0.758396 | − | 0.651794i | \(-0.225983\pi\) | ||||
0.758396 | + | 0.651794i | \(0.225983\pi\) | |||||||
\(614\) | − | 1.20084e13i | − | 0.137608i | ||||||
\(615\) | −5.28770e12 | − | 1.51363e13i | −0.0601023 | − | 0.172046i | ||||
\(616\) | −1.87520e14 | −2.11419 | ||||||||
\(617\) | − | 4.12100e13i | − | 0.460869i | −0.973088 | − | 0.230434i | \(-0.925985\pi\) | ||
0.973088 | − | 0.230434i | \(-0.0740147\pi\) | |||||||
\(618\) | −1.16614e14 | + | 4.07377e13i | −1.29362 | + | 0.451912i | ||||
\(619\) | 1.33201e14 | 1.46574 | 0.732868 | − | 0.680371i | \(-0.238181\pi\) | ||||
0.732868 | + | 0.680371i | \(0.238181\pi\) | |||||||
\(620\) | 1.89670e13i | 0.207033i | ||||||||
\(621\) | 9.30947e12 | − | 1.47654e13i | 0.100802 | − | 0.159877i | ||||
\(622\) | 3.22165e12 | 0.0346040 | ||||||||
\(623\) | − | 7.28151e13i | − | 0.775857i | ||||||
\(624\) | −2.46169e13 | − | 7.04672e13i | −0.260202 | − | 0.744841i | ||||
\(625\) | 3.81470e12 | 0.0400000 | ||||||||
\(626\) | 7.78467e13i | 0.809783i | ||||||||
\(627\) | 1.99126e14 | − | 6.95624e13i | 2.05490 | − | 0.717855i | ||||
\(628\) | −3.95685e13 | −0.405090 | ||||||||
\(629\) | 1.29425e13i | 0.131451i | ||||||||
\(630\) | −4.28626e13 | + | 3.41098e13i | −0.431892 | + | 0.343697i | ||||
\(631\) | −3.77275e13 | −0.377148 | −0.188574 | − | 0.982059i | \(-0.560386\pi\) | ||||
−0.188574 | + | 0.982059i | \(0.560386\pi\) | |||||||
\(632\) | − | 2.27380e13i | − | 0.225511i | ||||||
\(633\) | 6.01038e13 | + | 1.72050e14i | 0.591403 | + | 1.69292i | ||||
\(634\) | 1.16056e14 | 1.13298 | ||||||||
\(635\) | − | 1.81548e13i | − | 0.175842i | ||||||
\(636\) | 2.37720e13 | − | 8.30448e12i | 0.228444 | − | 0.0798045i | ||||
\(637\) | −1.30340e14 | −1.24275 | ||||||||
\(638\) | − | 6.02760e12i | − | 0.0570219i | ||||||
\(639\) | 6.74250e13 | + | 8.47267e13i | 0.632873 | + | 0.795272i | ||||
\(640\) | 2.14494e13 | 0.199763 | ||||||||
\(641\) | − | 9.57378e13i | − | 0.884695i | −0.896844 | − | 0.442347i | \(-0.854146\pi\) | ||
0.896844 | − | 0.442347i | \(-0.145854\pi\) | |||||||
\(642\) | −2.80751e13 | − | 8.03665e13i | −0.257423 | − | 0.736885i | ||||
\(643\) | 1.53187e14 | 1.39370 | 0.696849 | − | 0.717218i | \(-0.254585\pi\) | ||||
0.696849 | + | 0.717218i | \(0.254585\pi\) | |||||||
\(644\) | 7.81403e12i | 0.0705416i | ||||||||
\(645\) | −2.42170e13 | + | 8.45992e12i | −0.216931 | + | 0.0757823i | ||||
\(646\) | 1.53002e14 | 1.35998 | ||||||||
\(647\) | − | 1.03278e14i | − | 0.910935i | −0.890252 | − | 0.455468i | \(-0.849472\pi\) | ||
0.890252 | − | 0.455468i | \(-0.150528\pi\) | |||||||
\(648\) | 1.20680e14 | + | 2.78054e13i | 1.05623 | + | 0.243363i | ||||
\(649\) | 2.43151e13 | 0.211180 | ||||||||
\(650\) | 2.34279e13i | 0.201914i | ||||||||
\(651\) | 9.84725e13 | + | 2.81883e14i | 0.842190 | + | 2.41081i | ||||
\(652\) | 3.46677e13 | 0.294230 | ||||||||
\(653\) | − | 4.61490e13i | − | 0.388684i | −0.980934 | − | 0.194342i | \(-0.937743\pi\) | ||
0.980934 | − | 0.194342i | \(-0.0622572\pi\) | |||||||
\(654\) | −4.98819e13 | + | 1.74257e13i | −0.416922 | + | 0.145647i | ||||
\(655\) | −6.89579e13 | −0.571976 | ||||||||
\(656\) | 3.32786e13i | 0.273934i | ||||||||
\(657\) | −3.25970e12 | + | 2.59405e12i | −0.0266287 | + | 0.0211910i | ||||
\(658\) | −1.01985e14 | −0.826809 | ||||||||
\(659\) | 1.66936e14i | 1.34315i | 0.740939 | + | 0.671573i | \(0.234381\pi\) | ||||
−0.740939 | + | 0.671573i | \(0.765619\pi\) | |||||||
\(660\) | −6.53111e12 | − | 1.86956e13i | −0.0521516 | − | 0.149287i | ||||
\(661\) | −9.89499e9 | −7.84166e−5 | −3.92083e−5 | − | 1.00000i | \(-0.500012\pi\) | ||||
−3.92083e−5 | 1.00000i | \(0.500012\pi\) | ||||||||
\(662\) | − | 1.00658e14i | − | 0.791693i | ||||||
\(663\) | −1.40158e14 | + | 4.89625e13i | −1.09408 | + | 0.382205i | ||||
\(664\) | −1.41675e14 | −1.09762 | ||||||||
\(665\) | 1.33625e14i | 1.02749i | ||||||||
\(666\) | −9.34303e12 | − | 1.17405e13i | −0.0713045 | − | 0.0896017i | ||||
\(667\) | −1.21679e12 | −0.00921691 | ||||||||
\(668\) | 4.29073e13i | 0.322589i | ||||||||
\(669\) | −8.53409e13 | − | 2.44293e14i | −0.636834 | − | 1.82297i | ||||
\(670\) | 3.36336e13 | 0.249115 | ||||||||
\(671\) | 1.35772e13i | 0.0998158i | ||||||||
\(672\) | −9.38717e13 | + | 3.27930e13i | −0.684997 | + | 0.239296i | ||||
\(673\) | −1.95710e14 | −1.41755 | −0.708773 | − | 0.705436i | \(-0.750751\pi\) | ||||
−0.708773 | + | 0.705436i | \(0.750751\pi\) | |||||||
\(674\) | − | 9.63497e13i | − | 0.692709i | ||||||
\(675\) | −2.37066e13 | − | 1.49469e13i | −0.169181 | − | 0.106667i | ||||
\(676\) | 1.38639e13 | 0.0982092 | ||||||||
\(677\) | 8.39435e13i | 0.590261i | 0.955457 | + | 0.295130i | \(0.0953631\pi\) | ||||
−0.955457 | + | 0.295130i | \(0.904637\pi\) | |||||||
\(678\) | −2.75175e13 | − | 7.87703e13i | −0.192070 | − | 0.549812i | ||||
\(679\) | 2.47164e14 | 1.71252 | ||||||||
\(680\) | − | 6.95905e13i | − | 0.478636i | ||||||
\(681\) | 6.92030e12 | − | 2.41753e12i | 0.0472486 | − | 0.0165058i | ||||
\(682\) | 3.07044e14 | 2.08103 | ||||||||
\(683\) | − | 1.05484e14i | − | 0.709717i | −0.934920 | − | 0.354858i | \(-0.884529\pi\) | ||
0.934920 | − | 0.354858i | \(-0.115471\pi\) | |||||||
\(684\) | 4.87946e13 | − | 3.88304e13i | 0.325905 | − | 0.259353i | ||||
\(685\) | 2.98873e13 | 0.198168 | ||||||||
\(686\) | − | 1.10314e13i | − | 0.0726122i | ||||||
\(687\) | 6.50610e13 | + | 1.86240e14i | 0.425145 | + | 1.21700i | ||||
\(688\) | 5.32432e13 | 0.345400 | ||||||||
\(689\) | − | 1.69538e14i | − | 1.09187i | ||||||
\(690\) | 1.07351e13 | − | 3.75017e12i | 0.0686371 | − | 0.0239776i | ||||
\(691\) | −2.96033e14 | −1.87910 | −0.939551 | − | 0.342409i | \(-0.888757\pi\) | ||||
−0.939551 | + | 0.342409i | \(0.888757\pi\) | |||||||
\(692\) | − | 4.04447e13i | − | 0.254877i | ||||||
\(693\) | −1.94127e14 | − | 2.43941e14i | −1.21456 | − | 1.52623i | ||||
\(694\) | −1.88557e14 | −1.17124 | ||||||||
\(695\) | 5.31614e13i | 0.327848i | ||||||||
\(696\) | −2.84709e12 | − | 8.14994e12i | −0.0174323 | − | 0.0499009i | ||||
\(697\) | 6.61905e13 | 0.402375 | ||||||||
\(698\) | − | 1.40665e14i | − | 0.849003i | ||||||
\(699\) | −1.20259e14 | + | 4.20111e13i | −0.720662 | + | 0.251755i | ||||
\(700\) | 1.25458e13 | 0.0746465 | ||||||||
\(701\) | 3.27773e14i | 1.93635i | 0.250276 | + | 0.968175i | \(0.419479\pi\) | ||||
−0.250276 | + | 0.968175i | \(0.580521\pi\) | |||||||
\(702\) | 9.17958e13 | − | 1.45594e14i | 0.538440 | − | 0.853998i | ||||
\(703\) | −3.66013e13 | −0.213167 | ||||||||
\(704\) | 2.60272e14i | 1.50510i | ||||||||
\(705\) | −1.72075e13 | − | 4.92573e13i | −0.0988033 | − | 0.282829i | ||||
\(706\) | −7.96740e13 | −0.454248 | ||||||||
\(707\) | − | 2.75747e14i | − | 1.56104i | ||||||
\(708\) | 6.78647e12 | − | 2.37078e12i | 0.0381485 | − | 0.0133267i | ||||
\(709\) | −4.95628e13 | −0.276646 | −0.138323 | − | 0.990387i | \(-0.544171\pi\) | ||||
−0.138323 | + | 0.990387i | \(0.544171\pi\) | |||||||
\(710\) | 7.05400e13i | 0.390970i | ||||||||
\(711\) | 2.95795e13 | − | 2.35392e13i | 0.162796 | − | 0.129552i | ||||
\(712\) | −1.07242e14 | −0.586089 | ||||||||
\(713\) | − | 6.19826e13i | − | 0.336374i | ||||||
\(714\) | −7.45803e13 | − | 2.13490e14i | −0.401914 | − | 1.15050i | ||||
\(715\) | −1.33334e14 | −0.713527 | ||||||||
\(716\) | 7.95460e13i | 0.422721i | ||||||||
\(717\) | 3.81822e13 | − | 1.33385e13i | 0.201495 | − | 0.0703902i | ||||
\(718\) | 1.61664e14 | 0.847211 | ||||||||
\(719\) | − | 5.69586e13i | − | 0.296425i | −0.988956 | − | 0.148213i | \(-0.952648\pi\) | ||
0.988956 | − | 0.148213i | \(-0.0473520\pi\) | |||||||
\(720\) | 3.62209e13 | + | 4.55154e13i | 0.187196 | + | 0.235232i | ||||
\(721\) | 4.45365e14 | 2.28581 | ||||||||
\(722\) | 2.63928e14i | 1.34524i | ||||||||
\(723\) | 9.75812e13 | + | 2.79331e14i | 0.493940 | + | 1.41393i | ||||
\(724\) | 1.33273e13 | 0.0669962 | ||||||||
\(725\) | 1.95362e12i | 0.00975325i | ||||||||
\(726\) | −1.38871e14 | + | 4.85129e13i | −0.688537 | + | 0.240533i | ||||
\(727\) | −2.81767e14 | −1.38745 | −0.693726 | − | 0.720239i | \(-0.744032\pi\) | ||||
−0.693726 | + | 0.720239i | \(0.744032\pi\) | |||||||
\(728\) | 3.73263e14i | 1.82540i | ||||||||
\(729\) | 8.87607e13 | + | 1.85776e14i | 0.431105 | + | 0.902302i | ||||
\(730\) | −2.71389e12 | −0.0130912 | ||||||||
\(731\) | − | 1.05900e14i | − | 0.507350i | ||||||
\(732\) | 1.32381e12 | + | 3.78948e12i | 0.00629899 | + | 0.0180312i | ||||
\(733\) | −1.04493e14 | −0.493819 | −0.246909 | − | 0.969039i | \(-0.579415\pi\) | ||||
−0.246909 | + | 0.969039i | \(0.579415\pi\) | |||||||
\(734\) | − | 3.48908e13i | − | 0.163768i | ||||||
\(735\) | 9.58904e13 | − | 3.34982e13i | 0.447032 | − | 0.156166i | ||||
\(736\) | 2.06413e13 | 0.0955757 | ||||||||
\(737\) | 1.91417e14i | 0.880327i | ||||||||
\(738\) | −6.00434e13 | + | 4.77822e13i | −0.274273 | + | 0.218265i | ||||
\(739\) | −2.65253e13 | −0.120348 | −0.0601740 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601740 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(740\) | 3.43644e12i | 0.0154864i | ||||||||
\(741\) | −1.38466e14 | − | 3.96365e14i | −0.619800 | − | 1.77421i | ||||
\(742\) | 2.58242e14 | 1.14817 | ||||||||
\(743\) | − | 1.68581e14i | − | 0.744499i | −0.928133 | − | 0.372249i | \(-0.878587\pi\) | ||
0.928133 | − | 0.372249i | \(-0.121413\pi\) | |||||||
\(744\) | 4.15155e14 | − | 1.45030e14i | 1.82115 | − | 0.636197i | ||||
\(745\) | −4.96546e13 | −0.216361 | ||||||||
\(746\) | 1.68485e12i | 0.00729234i | ||||||||
\(747\) | −1.46667e14 | − | 1.84302e14i | −0.630563 | − | 0.792369i | ||||
\(748\) | 8.17553e13 | 0.349147 | ||||||||
\(749\) | 3.06932e14i | 1.30206i | ||||||||
\(750\) | −6.02110e12 | − | 1.72357e13i | −0.0253729 | − | 0.0726311i | ||||
\(751\) | 1.56240e14 | 0.654021 | 0.327011 | − | 0.945021i | \(-0.393959\pi\) | ||||
0.327011 | + | 0.945021i | \(0.393959\pi\) | |||||||
\(752\) | 1.08297e14i | 0.450325i | ||||||||
\(753\) | 3.77605e14 | − | 1.31912e14i | 1.55978 | − | 0.544891i | ||||
\(754\) | −1.19981e13 | −0.0492329 | ||||||||
\(755\) | − | 8.52799e12i | − | 0.0347626i | ||||||
\(756\) | −7.79667e13 | − | 4.91575e13i | −0.315719 | − | 0.199059i | ||||
\(757\) | −1.61527e14 | −0.649779 | −0.324890 | − | 0.945752i | \(-0.605327\pi\) | ||||
−0.324890 | + | 0.945752i | \(0.605327\pi\) | |||||||
\(758\) | 2.20859e14i | 0.882612i | ||||||||
\(759\) | 2.13431e13 | + | 6.10958e13i | 0.0847323 | + | 0.242551i | ||||
\(760\) | 1.96802e14 | 0.776177 | ||||||||
\(761\) | − | 3.55804e14i | − | 1.39408i | −0.717033 | − | 0.697039i | \(-0.754500\pi\) | ||
0.717033 | − | 0.697039i | \(-0.245500\pi\) | |||||||
\(762\) | −8.20276e13 | + | 2.86554e13i | −0.319290 | + | 0.111540i | ||||
\(763\) | 1.90507e14 | 0.736694 | ||||||||
\(764\) | − | 1.24539e14i | − | 0.478451i | ||||||
\(765\) | 9.05293e13 | − | 7.20427e13i | 0.345527 | − | 0.274968i | ||||
\(766\) | 9.45622e13 | 0.358570 | ||||||||
\(767\) | − | 4.83998e13i | − | 0.182334i | ||||||
\(768\) | 6.37048e13 | + | 1.82358e14i | 0.238433 | + | 0.682526i | ||||
\(769\) | 1.37014e13 | 0.0509489 | 0.0254744 | − | 0.999675i | \(-0.491890\pi\) | ||||
0.0254744 | + | 0.999675i | \(0.491890\pi\) | |||||||
\(770\) | − | 2.03096e14i | − | 0.750321i | ||||||
\(771\) | 2.93379e13 | − | 1.02489e13i | 0.107685 | − | 0.0376187i | ||||
\(772\) | 1.24063e13 | 0.0452435 | ||||||||
\(773\) | − | 6.08347e13i | − | 0.220421i | −0.993908 | − | 0.110211i | \(-0.964847\pi\) | ||
0.993908 | − | 0.110211i | \(-0.0351526\pi\) | |||||||
\(774\) | 7.64478e13 | + | 9.60648e13i | 0.275208 | + | 0.345828i | ||||
\(775\) | −9.95165e13 | −0.355948 | ||||||||
\(776\) | − | 3.64021e14i | − | 1.29365i | ||||||
\(777\) | 1.78412e13 | + | 5.10714e13i | 0.0629969 | + | 0.180332i | ||||
\(778\) | −3.94718e14 | −1.38481 | ||||||||
\(779\) | 1.87186e14i | 0.652509i | ||||||||
\(780\) | −3.72142e13 | + | 1.30003e13i | −0.128895 | + | 0.0450279i | ||||
\(781\) | −4.01461e14 | −1.38162 | ||||||||
\(782\) | 4.69439e13i | 0.160526i | ||||||||
\(783\) | 7.65472e12 | − | 1.21408e13i | 0.0260088 | − | 0.0412515i | ||||
\(784\) | −2.10824e14 | −0.711770 | ||||||||
\(785\) | − | 2.07609e14i | − | 0.696462i | ||||||
\(786\) | 1.08843e14 | + | 3.11568e14i | 0.362817 | + | 1.03858i | ||||
\(787\) | −8.80368e13 | −0.291602 | −0.145801 | − | 0.989314i | \(-0.546576\pi\) | ||||
−0.145801 | + | 0.989314i | \(0.546576\pi\) | |||||||
\(788\) | − | 2.77934e13i | − | 0.0914766i | ||||||
\(789\) | −5.70891e14 | + | 1.99434e14i | −1.86710 | + | 0.652251i | ||||
\(790\) | 2.46267e13 | 0.0800333 | ||||||||
\(791\) | 3.00836e14i | 0.971509i | ||||||||
\(792\) | −3.59275e14 | + | 2.85909e14i | −1.15293 | + | 0.917492i | ||||
\(793\) | 2.70259e13 | 0.0861814 | ||||||||
\(794\) | − | 2.13770e14i | − | 0.677400i | ||||||
\(795\) | 4.35721e13 | + | 1.24727e14i | 0.137206 | + | 0.392759i | ||||
\(796\) | −1.59804e13 | −0.0500059 | ||||||||
\(797\) | 2.80333e14i | 0.871731i | 0.900012 | + | 0.435865i | \(0.143558\pi\) | ||||
−0.900012 | + | 0.435865i | \(0.856442\pi\) | |||||||
\(798\) | 6.03749e14 | − | 2.10913e14i | 1.86570 | − | 0.651761i | ||||
\(799\) | 2.15400e14 | 0.661472 | ||||||||
\(800\) | − | 3.31407e13i | − | 0.101137i | ||||||
\(801\) | −1.11020e14 | − | 1.39509e14i | −0.336698 | − | 0.423097i | ||||
\(802\) | −3.12657e14 | −0.942317 | ||||||||
\(803\) | − | 1.54454e13i | − | 0.0462618i | ||||||
\(804\) | 1.86636e13 | + | 5.34256e13i | 0.0555540 | + | 0.159026i | ||||
\(805\) | −4.09988e13 | −0.121281 | ||||||||
\(806\) | − | 6.11178e14i | − | 1.79677i | ||||||
\(807\) | −2.36378e14 | + | 8.25758e13i | −0.690619 | + | 0.241260i | ||||
\(808\) | −4.06118e14 | −1.17922 | ||||||||
\(809\) | 3.04518e14i | 0.878759i | 0.898302 | + | 0.439379i | \(0.144802\pi\) | ||||
−0.898302 | + | 0.439379i | \(0.855198\pi\) | |||||||
\(810\) | −3.01151e13 | + | 1.30704e14i | −0.0863691 | + | 0.374856i | ||||
\(811\) | 4.61813e14 | 1.31632 | 0.658161 | − | 0.752877i | \(-0.271335\pi\) | ||||
0.658161 | + | 0.752877i | \(0.271335\pi\) | |||||||
\(812\) | 6.42509e12i | 0.0182012i | ||||||||
\(813\) | −1.30353e14 | − | 3.73141e14i | −0.367001 | − | 1.05056i | ||||
\(814\) | 5.56301e13 | 0.155664 | ||||||||
\(815\) | 1.81895e14i | 0.505864i | ||||||||
\(816\) | −2.26703e14 | + | 7.91963e13i | −0.626624 | + | 0.218904i | ||||
\(817\) | 2.99484e14 | 0.822741 | ||||||||
\(818\) | 2.69560e14i | 0.736020i | ||||||||
\(819\) | −4.85572e14 | + | 3.86415e14i | −1.31775 | + | 1.04866i | ||||
\(820\) | 1.75746e13 | 0.0474043 | ||||||||
\(821\) | − | 2.35728e14i | − | 0.631968i | −0.948764 | − | 0.315984i | \(-0.897665\pi\) | ||
0.948764 | − | 0.315984i | \(-0.102335\pi\) | |||||||
\(822\) | −4.71740e13 | − | 1.35038e14i | −0.125702 | − | 0.359829i | ||||
\(823\) | −6.77056e13 | −0.179319 | −0.0896593 | − | 0.995972i | \(-0.528578\pi\) | ||||
−0.0896593 | + | 0.995972i | \(0.528578\pi\) | |||||||
\(824\) | − | 6.55931e14i | − | 1.72672i | ||||||
\(825\) | 9.80926e13 | − | 3.42676e13i | 0.256665 | − | 0.0896630i | ||||
\(826\) | 7.37232e13 | 0.191736 | ||||||||
\(827\) | − | 5.95756e14i | − | 1.54007i | −0.638001 | − | 0.770036i | \(-0.720238\pi\) | ||
0.638001 | − | 0.770036i | \(-0.279762\pi\) | |||||||
\(828\) | 1.19140e13 | + | 1.49712e13i | 0.0306129 | + | 0.0384684i | ||||
\(829\) | 5.82336e14 | 1.48731 | 0.743654 | − | 0.668565i | \(-0.233091\pi\) | ||||
0.743654 | + | 0.668565i | \(0.233091\pi\) | |||||||
\(830\) | − | 1.53443e14i | − | 0.389543i | ||||||
\(831\) | −1.09993e14 | − | 3.14861e14i | −0.277563 | − | 0.794537i | ||||
\(832\) | 5.18079e14 | 1.29951 | ||||||||
\(833\) | 4.19325e14i | 1.04550i | ||||||||
\(834\) | 2.40196e14 | − | 8.39097e13i | 0.595299 | − | 0.207961i | ||||
\(835\) | −2.25127e14 | −0.554619 | ||||||||
\(836\) | 2.31203e14i | 0.566191i | ||||||||
\(837\) | 6.18450e14 | + | 3.89928e14i | 1.50549 | + | 0.949200i | ||||
\(838\) | −5.44583e14 | −1.31778 | ||||||||
\(839\) | − | 5.35480e14i | − | 1.28805i | −0.765003 | − | 0.644026i | \(-0.777263\pi\) | ||
0.765003 | − | 0.644026i | \(-0.222737\pi\) | |||||||
\(840\) | −9.59306e13 | − | 2.74606e14i | −0.229383 | − | 0.656620i | ||||
\(841\) | 4.19707e14 | 0.997622 | ||||||||
\(842\) | 2.68282e14i | 0.633915i | ||||||||
\(843\) | −1.40603e14 | + | 4.91180e13i | −0.330260 | + | 0.115373i | ||||
\(844\) | −1.99766e14 | −0.466455 | ||||||||
\(845\) | 7.27414e13i | 0.168849i | ||||||||
\(846\) | −1.95396e14 | + | 1.55495e14i | −0.450882 | + | 0.358810i | ||||
\(847\) | 5.30368e14 | 1.21663 | ||||||||
\(848\) | − | 2.74225e14i | − | 0.625356i | ||||||
\(849\) | 7.70915e13 | + | 2.20678e14i | 0.174770 | + | 0.500289i | ||||
\(850\) | 7.53710e13 | 0.169867 | ||||||||
\(851\) | − | 1.12300e13i | − | 0.0251612i | ||||||
\(852\) | −1.12050e14 | + | 3.91433e13i | −0.249582 | + | 0.0871885i | ||||
\(853\) | −1.47772e14 | −0.327225 | −0.163612 | − | 0.986525i | \(-0.552315\pi\) | ||||
−0.163612 | + | 0.986525i | \(0.552315\pi\) | |||||||
\(854\) | 4.11661e13i | 0.0906256i | ||||||||
\(855\) | 2.03736e14 | + | 2.56016e14i | 0.445900 | + | 0.560321i | ||||
\(856\) | 4.52047e14 | 0.983591 | ||||||||
\(857\) | 8.21818e14i | 1.77775i | 0.458146 | + | 0.888877i | \(0.348514\pi\) | ||||
−0.458146 | + | 0.888877i | \(0.651486\pi\) | |||||||
\(858\) | 2.10453e14 | + | 6.02434e14i | 0.452605 | + | 1.29561i | ||||
\(859\) | −6.19313e14 | −1.32417 | −0.662086 | − | 0.749428i | \(-0.730328\pi\) | ||||
−0.662086 | + | 0.749428i | \(0.730328\pi\) | |||||||
\(860\) | − | 2.81181e13i | − | 0.0597714i | ||||||
\(861\) | 2.61190e14 | − | 9.12436e13i | 0.552001 | − | 0.192835i | ||||
\(862\) | −5.00801e13 | −0.105228 | ||||||||
\(863\) | − | 6.20768e14i | − | 1.29681i | −0.761297 | − | 0.648403i | \(-0.775437\pi\) | ||
0.761297 | − | 0.648403i | \(-0.224563\pi\) | |||||||
\(864\) | −1.29853e14 | + | 2.05954e14i | −0.269701 | + | 0.427762i | ||||
\(865\) | 2.12206e14 | 0.438204 | ||||||||
\(866\) | 5.17960e14i | 1.06343i | ||||||||
\(867\) | −4.04196e12 | − | 1.15703e13i | −0.00825080 | − | 0.0236183i | ||||
\(868\) | −3.27291e14 | −0.664257 | ||||||||
\(869\) | 1.40157e14i | 0.282823i | ||||||||
\(870\) | 8.82691e12 | − | 3.08358e12i | 0.0177097 | − | 0.00618670i | ||||
\(871\) | 3.81021e14 | 0.760078 | ||||||||
\(872\) | − | 2.80577e14i | − | 0.556505i | ||||||
\(873\) | 4.73549e14 | − | 3.76848e14i | 0.933886 | − | 0.743181i | ||||
\(874\) | −1.32757e14 | −0.260316 | ||||||||
\(875\) | 6.58257e13i | 0.128338i | ||||||||
\(876\) | −1.50596e12 | − | 4.31090e12i | −0.00291940 | − | 0.00835694i | ||||
\(877\) | −4.15719e14 | −0.801313 | −0.400656 | − | 0.916228i | \(-0.631218\pi\) | ||||
−0.400656 | + | 0.916228i | \(0.631218\pi\) | |||||||
\(878\) | − | 3.62302e14i | − | 0.694381i | ||||||
\(879\) | 7.53879e14 | − | 2.63359e14i | 1.43667 | − | 0.501885i | ||||
\(880\) | −2.15666e14 | −0.408665 | ||||||||
\(881\) | 9.63563e14i | 1.81552i | 0.419491 | + | 0.907759i | \(0.362208\pi\) | ||||
−0.419491 | + | 0.907759i | \(0.637792\pi\) | |||||||
\(882\) | −3.02706e14 | − | 3.80382e14i | −0.567124 | − | 0.712652i | ||||
\(883\) | −1.56289e14 | −0.291156 | −0.145578 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145578 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(884\) | − | 1.62736e14i | − | 0.301455i | ||||||
\(885\) | 1.24390e13 | + | 3.56074e13i | 0.0229124 | + | 0.0655878i | ||||
\(886\) | −3.37163e13 | −0.0617549 | ||||||||
\(887\) | − | 4.22682e14i | − | 0.769831i | −0.922952 | − | 0.384916i | \(-0.874231\pi\) | ||
0.922952 | − | 0.384916i | \(-0.125769\pi\) | |||||||
\(888\) | 7.52176e13 | − | 2.62764e13i | 0.136224 | − | 0.0475884i | ||||
\(889\) | 3.13276e14 | 0.564180 | ||||||||
\(890\) | − | 1.16150e14i | − | 0.208002i | ||||||
\(891\) | −7.43870e14 | − | 1.71392e14i | −1.32467 | − | 0.305213i | ||||
\(892\) | 2.83646e14 | 0.502288 | ||||||||
\(893\) | 6.09150e14i | 1.07267i | ||||||||
\(894\) | 7.83746e13 | + | 2.24351e14i | 0.137242 | + | 0.392863i | ||||
\(895\) | −4.17364e14 | −0.726774 | ||||||||
\(896\) | 3.70127e14i | 0.640930i | ||||||||
\(897\) | 1.21613e14 | − | 4.24841e13i | 0.209419 | − | 0.0731583i | ||||
\(898\) | 7.25061e13 | 0.124163 | ||||||||
\(899\) | − | 5.09653e13i | − | 0.0867912i | ||||||
\(900\) | 2.40370e13 | − | 1.91285e13i | 0.0407069 | − | 0.0323943i | ||||
\(901\) | −5.45428e14 | −0.918572 | ||||||||
\(902\) | − | 2.84504e14i | − | 0.476491i | ||||||
\(903\) | −1.45983e14 | − | 4.17883e14i | −0.243144 | − | 0.696011i | ||||
\(904\) | 4.43068e14 | 0.733886 | ||||||||
\(905\) | 6.99260e13i | 0.115185i | ||||||||
\(906\) | −3.85315e13 | + | 1.34605e13i | −0.0631211 | + | 0.0220506i | ||||
\(907\) | −4.69868e14 | −0.765490 | −0.382745 | − | 0.923854i | \(-0.625021\pi\) | ||||
−0.382745 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(908\) | 8.03510e12i | 0.0130185i | ||||||||
\(909\) | −4.20428e14 | − | 5.28313e14i | −0.677442 | − | 0.851278i | ||||
\(910\) | −4.04267e14 | −0.647831 | ||||||||
\(911\) | 4.83462e14i | 0.770496i | 0.922813 | + | 0.385248i | \(0.125884\pi\) | ||||
−0.922813 | + | 0.385248i | \(0.874116\pi\) | |||||||
\(912\) | −2.23967e14 | − | 6.41116e14i | −0.354984 | − | 1.01616i | ||||
\(913\) | 8.73280e14 | 1.37657 | ||||||||
\(914\) | 6.15531e14i | 0.964981i | ||||||||
\(915\) | −1.98827e13 | + | 6.94580e12i | −0.0310006 | + | 0.0108297i | ||||
\(916\) | −2.16242e14 | −0.335323 | ||||||||
\(917\) | − | 1.18993e15i | − | 1.83516i | ||||||
\(918\) | −4.68397e14 | − | 2.95321e14i | −0.718457 | − | 0.452982i | ||||
\(919\) | −6.42475e14 | −0.980118 | −0.490059 | − | 0.871689i | \(-0.663025\pi\) | ||||
−0.490059 | + | 0.871689i | \(0.663025\pi\) | |||||||
\(920\) | 6.03827e13i | 0.0916164i | ||||||||
\(921\) | 3.49627e13 | + | 1.00082e14i | 0.0527602 | + | 0.151029i | ||||
\(922\) | −2.56419e14 | −0.384853 | ||||||||
\(923\) | 7.99118e14i | 1.19289i | ||||||||
\(924\) | 3.22609e14 | − | 1.12700e14i | 0.478979 | − | 0.167326i | ||||
\(925\) | −1.80304e13 | −0.0266254 | ||||||||
\(926\) | − | 2.10346e14i | − | 0.308944i | ||||||
\(927\) | 8.53290e14 | − | 6.79043e14i | 1.24652 | − | 0.991970i | ||||
\(928\) | 1.69723e13 | 0.0246605 | ||||||||
\(929\) | − | 1.29783e14i | − | 0.187559i | −0.995593 | − | 0.0937796i | \(-0.970105\pi\) | ||
0.995593 | − | 0.0937796i | \(-0.0298949\pi\) | |||||||
\(930\) | 1.57076e14 | + | 4.49639e14i | 0.225785 | + | 0.646322i | ||||
\(931\) | −1.18585e15 | −1.69543 | ||||||||
\(932\) | − | 1.39632e14i | − | 0.198566i | ||||||
\(933\) | −2.68503e13 | + | 9.37985e12i | −0.0379788 | + | 0.0132675i | ||||
\(934\) | 7.18405e14 | 1.01073 | ||||||||
\(935\) | 4.28955e14i | 0.600280i | ||||||||
\(936\) | 5.69109e14 | + | 7.15147e14i | 0.792167 | + | 0.995442i | ||||
\(937\) | −4.95593e14 | −0.686163 | −0.343081 | − | 0.939306i | \(-0.611471\pi\) | ||||
−0.343081 | + | 0.939306i | \(0.611471\pi\) | |||||||
\(938\) | 5.80376e14i | 0.799274i | ||||||||
\(939\) | −2.26651e14 | − | 6.48801e14i | −0.310477 | − | 0.888758i | ||||
\(940\) | 5.71922e13 | 0.0779287 | ||||||||
\(941\) | − | 1.14019e15i | − | 1.54536i | −0.634794 | − | 0.772682i | \(-0.718915\pi\) | ||
0.634794 | − | 0.772682i | \(-0.281085\pi\) | |||||||
\(942\) | −9.38026e14 | + | 3.27689e14i | −1.26462 | + | 0.441781i | ||||
\(943\) | −5.74325e13 | −0.0770192 | ||||||||
\(944\) | − | 7.82861e13i | − | 0.104430i | ||||||
\(945\) | 2.57920e14 | − | 4.09077e14i | 0.342237 | − | 0.542808i | ||||
\(946\) | −4.55184e14 | −0.600802 | ||||||||
\(947\) | 5.62820e14i | 0.738958i | 0.929239 | + | 0.369479i | \(0.120464\pi\) | ||||
−0.929239 | + | 0.369479i | \(0.879536\pi\) | |||||||
\(948\) | 1.36656e13 | + | 3.91184e13i | 0.0178479 | + | 0.0510905i | ||||
\(949\) | −3.07445e13 | −0.0399426 | ||||||||
\(950\) | 2.13149e14i | 0.275464i | ||||||||
\(951\) | −9.67251e14 | + | 3.37898e14i | −1.24347 | + | 0.434394i | ||||
\(952\) | 1.20084e15 | 1.53568 | ||||||||
\(953\) | − | 3.36550e14i | − | 0.428140i | −0.976818 | − | 0.214070i | \(-0.931328\pi\) | ||
0.976818 | − | 0.214070i | \(-0.0686720\pi\) | |||||||
\(954\) | 4.94774e14 | − | 3.93738e14i | 0.626131 | − | 0.498271i | ||||
\(955\) | 6.53432e14 | 0.822590 | ||||||||
\(956\) | 4.43330e13i | 0.0555185i | ||||||||
\(957\) | 1.75494e13 | + | 5.02361e13i | 0.0218627 | + | 0.0625830i | ||||
\(958\) | 1.12489e15 | 1.39407 | ||||||||
\(959\) | 5.15730e14i | 0.635813i | ||||||||
\(960\) | −3.81146e14 | + | 1.33149e14i | −0.467450 | + | 0.163299i | ||||
\(961\) | 1.77652e15 | 2.16747 | ||||||||
\(962\) | − | 1.10733e14i | − | 0.134401i | ||||||
\(963\) | 4.67975e14 | + | 5.88061e14i | 0.565056 | + | 0.710053i | ||||
\(964\) | −3.24329e14 | −0.389584 | ||||||||
\(965\) | 6.50936e13i | 0.0777861i | ||||||||
\(966\) | 6.47122e13 | + | 1.85242e14i | 0.0769309 | + | 0.220219i | ||||
\(967\) | 1.61188e14 | 0.190634 | 0.0953172 | − | 0.995447i | \(-0.469613\pi\) | ||||
0.0953172 | + | 0.995447i | \(0.469613\pi\) | |||||||
\(968\) | − | 7.81122e14i | − | 0.919056i | ||||||
\(969\) | −1.27517e15 | + | 4.45465e14i | −1.49262 | + | 0.521429i | ||||
\(970\) | 3.94258e14 | 0.459115 | ||||||||
\(971\) | 1.34616e15i | 1.55955i | 0.626060 | + | 0.779775i | \(0.284666\pi\) | ||||
−0.626060 | + | 0.779775i | \(0.715334\pi\) | |||||||
\(972\) | −2.24329e14 | + | 2.46925e13i | −0.258556 | + | 0.0284599i | ||||
\(973\) | −9.17343e14 | −1.05188 | ||||||||
\(974\) | 1.44371e14i | 0.164697i | ||||||||
\(975\) | −6.82104e13 | − | 1.95256e14i | −0.0774155 | − | 0.221606i | ||||
\(976\) | 4.37140e13 | 0.0493596 | ||||||||
\(977\) | 1.10154e15i | 1.23745i | 0.785609 | + | 0.618724i | \(0.212350\pi\) | ||||
−0.785609 | + | 0.618724i | \(0.787650\pi\) | |||||||
\(978\) | 8.21846e14 | − | 2.87103e14i | 0.918536 | − | 0.320880i | ||||
\(979\) | 6.61035e14 | 0.735041 | ||||||||
\(980\) | 1.11338e14i | 0.123172i | ||||||||
\(981\) | 3.64998e14 | − | 2.90463e14i | 0.401740 | − | 0.319702i | ||||
\(982\) | 8.51916e14 | 0.932909 | ||||||||
\(983\) | − | 9.85641e14i | − | 1.07387i | −0.843624 | − | 0.536934i | \(-0.819582\pi\) | ||
0.843624 | − | 0.536934i | \(-0.180418\pi\) | |||||||
\(984\) | −1.34383e14 | − | 3.84678e14i | −0.145669 | − | 0.416986i | ||||
\(985\) | 1.45827e14 | 0.157274 | ||||||||
\(986\) | 3.85997e13i | 0.0414190i | ||||||||
\(987\) | 8.49975e14 | − | 2.96929e14i | 0.907445 | − | 0.317006i | ||||
\(988\) | 4.60217e14 | 0.488852 | ||||||||
\(989\) | 9.18876e13i | 0.0971126i | ||||||||
\(990\) | −3.09658e14 | − | 3.89118e14i | −0.325616 | − | 0.409172i | ||||
\(991\) | −1.20714e15 | −1.26296 | −0.631481 | − | 0.775392i | \(-0.717552\pi\) | ||||
−0.631481 | + | 0.775392i | \(0.717552\pi\) | |||||||
\(992\) | 8.64562e14i | 0.899991i | ||||||||
\(993\) | 2.93066e14 | + | 8.38915e14i | 0.303542 | + | 0.868904i | ||||
\(994\) | −1.21723e15 | −1.25441 | ||||||||
\(995\) | − | 8.38461e13i | − | 0.0859740i | ||||||
\(996\) | 2.43737e14 | − | 8.51467e13i | 0.248671 | − | 0.0868703i | ||||
\(997\) | −1.43111e15 | −1.45277 | −0.726387 | − | 0.687286i | \(-0.758802\pi\) | ||||
−0.726387 | + | 0.687286i | \(0.758802\pi\) | |||||||
\(998\) | 7.79718e13i | 0.0787563i | ||||||||
\(999\) | 1.12051e14 | + | 7.06471e13i | 0.112613 | + | 0.0710014i |
(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 | 15.11.c.a.11.10 | yes | 14 | |
3.2 | odd | 2 | inner | 15.11.c.a.11.5 | ✓ | 14 | |
4.3 | odd | 2 | 240.11.l.b.161.10 | 14 | |||
5.2 | odd | 4 | 75.11.d.d.74.10 | 28 | |||
5.3 | odd | 4 | 75.11.d.d.74.19 | 28 | |||
5.4 | even | 2 | 75.11.c.g.26.5 | 14 | |||
12.11 | even | 2 | 240.11.l.b.161.9 | 14 | |||
15.2 | even | 4 | 75.11.d.d.74.20 | 28 | |||
15.8 | even | 4 | 75.11.d.d.74.9 | 28 | |||
15.14 | odd | 2 | 75.11.c.g.26.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.c.a.11.5 | ✓ | 14 | 3.2 | odd | 2 | inner | |
15.11.c.a.11.10 | yes | 14 | 1.1 | even | 1 | trivial | |
75.11.c.g.26.5 | 14 | 5.4 | even | 2 | |||
75.11.c.g.26.10 | 14 | 15.14 | odd | 2 | |||
75.11.d.d.74.9 | 28 | 15.8 | even | 4 | |||
75.11.d.d.74.10 | 28 | 5.2 | odd | 4 | |||
75.11.d.d.74.19 | 28 | 5.3 | odd | 4 | |||
75.11.d.d.74.20 | 28 | 15.2 | even | 4 | |||
240.11.l.b.161.9 | 14 | 12.11 | even | 2 | |||
240.11.l.b.161.10 | 14 | 4.3 | odd | 2 |