Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,33,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.4599965427\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 954745942 x^{8} + \cdots + 31\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{61}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.9 | ||
Root | \(17303.1i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.33.b.a.2.2 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 103819.i | 1.58415i | 0.610423 | + | 0.792075i | \(0.290999\pi\) | ||||
−0.610423 | + | 0.792075i | \(0.709001\pi\) | |||||||
\(3\) | −2.32547e7 | − | 3.62248e7i | −0.540220 | − | 0.841524i | ||||
\(4\) | −6.48340e9 | −1.50953 | ||||||||
\(5\) | − | 2.49832e11i | − | 1.63730i | −0.574295 | − | 0.818648i | \(-0.694724\pi\) | ||
0.574295 | − | 0.818648i | \(-0.305276\pi\) | |||||||
\(6\) | 3.76082e12 | − | 2.41428e12i | 1.33310 | − | 0.855790i | ||||
\(7\) | −3.04380e13 | −0.915897 | −0.457949 | − | 0.888979i | \(-0.651416\pi\) | ||||
−0.457949 | + | 0.888979i | \(0.651416\pi\) | |||||||
\(8\) | − | 2.27200e14i | − | 0.807177i | ||||||
\(9\) | −7.71458e14 | + | 1.68480e15i | −0.416324 | + | 0.909216i | ||||
\(10\) | 2.59372e16 | 2.59372 | ||||||||
\(11\) | 4.78234e16i | 1.04078i | 0.853930 | + | 0.520388i | \(0.174213\pi\) | ||||
−0.853930 | + | 0.520388i | \(0.825787\pi\) | |||||||
\(12\) | 1.50769e17 | + | 2.34860e17i | 0.815480 | + | 1.27031i | ||||
\(13\) | 5.67246e17 | 0.852468 | 0.426234 | − | 0.904613i | \(-0.359840\pi\) | ||||
0.426234 | + | 0.904613i | \(0.359840\pi\) | |||||||
\(14\) | − | 3.16003e18i | − | 1.45092i | ||||||
\(15\) | −9.05011e18 | + | 5.80976e18i | −1.37782 | + | 0.884501i | ||||
\(16\) | −4.25830e18 | −0.230843 | ||||||||
\(17\) | 9.91887e18i | 0.203835i | 0.994793 | + | 0.101918i | \(0.0324978\pi\) | ||||
−0.994793 | + | 0.101918i | \(0.967502\pi\) | |||||||
\(18\) | −1.74914e20 | − | 8.00919e19i | −1.44034 | − | 0.659521i | ||||
\(19\) | 3.55318e20 | 1.23185 | 0.615927 | − | 0.787803i | \(-0.288782\pi\) | ||||
0.615927 | + | 0.787803i | \(0.288782\pi\) | |||||||
\(20\) | 1.61976e21i | 2.47155i | ||||||||
\(21\) | 7.07826e20 | + | 1.10261e21i | 0.494786 | + | 0.770749i | ||||
\(22\) | −4.96497e21 | −1.64875 | ||||||||
\(23\) | 3.07553e20i | 0.0501504i | 0.999686 | + | 0.0250752i | \(0.00798252\pi\) | ||||
−0.999686 | + | 0.0250752i | \(0.992017\pi\) | |||||||
\(24\) | −8.23029e21 | + | 5.28347e21i | −0.679259 | + | 0.436053i | ||||
\(25\) | −3.91328e22 | −1.68074 | ||||||||
\(26\) | 5.88909e22i | 1.35044i | ||||||||
\(27\) | 7.89715e22 | − | 1.12335e22i | 0.990034 | − | 0.140830i | ||||
\(28\) | 1.97341e23 | 1.38258 | ||||||||
\(29\) | 3.31674e23i | 1.32539i | 0.748890 | + | 0.662694i | \(0.230587\pi\) | ||||
−0.748890 | + | 0.662694i | \(0.769413\pi\) | |||||||
\(30\) | −6.03163e23 | − | 9.39573e23i | −1.40118 | − | 2.18268i | ||||
\(31\) | 3.59216e23 | 0.493820 | 0.246910 | − | 0.969038i | \(-0.420585\pi\) | ||||
0.246910 | + | 0.969038i | \(0.420585\pi\) | |||||||
\(32\) | − | 1.41791e24i | − | 1.17287i | ||||||
\(33\) | 1.73239e24 | − | 1.11212e24i | 0.875838 | − | 0.562248i | ||||
\(34\) | −1.02977e24 | −0.322906 | ||||||||
\(35\) | 7.60436e24i | 1.49960i | ||||||||
\(36\) | 5.00167e24 | − | 1.09232e25i | 0.628456 | − | 1.37249i | ||||
\(37\) | 3.31930e24 | 0.269041 | 0.134520 | − | 0.990911i | \(-0.457051\pi\) | ||||
0.134520 | + | 0.990911i | \(0.457051\pi\) | |||||||
\(38\) | 3.68887e25i | 1.95144i | ||||||||
\(39\) | −1.31911e25 | − | 2.05484e25i | −0.460520 | − | 0.717372i | ||||
\(40\) | −5.67618e25 | −1.32159 | ||||||||
\(41\) | 3.35484e25i | 0.526175i | 0.964772 | + | 0.263087i | \(0.0847408\pi\) | ||||
−0.964772 | + | 0.263087i | \(0.915259\pi\) | |||||||
\(42\) | −1.14472e26 | + | 7.34857e25i | −1.22098 | + | 0.783816i | ||||
\(43\) | 1.34260e26 | 0.982767 | 0.491384 | − | 0.870943i | \(-0.336491\pi\) | ||||
0.491384 | + | 0.870943i | \(0.336491\pi\) | |||||||
\(44\) | − | 3.10058e26i | − | 1.57109i | ||||||
\(45\) | 4.20915e26 | + | 1.92735e26i | 1.48866 | + | 0.681647i | ||||
\(46\) | −3.19298e25 | −0.0794457 | ||||||||
\(47\) | − | 9.71468e23i | − | 0.00171342i | −1.00000 | 0.000856708i | \(-0.999727\pi\) | |||
1.00000 | 0.000856708i | \(-0.000272699\pi\) | ||||||||
\(48\) | 9.90254e25 | + | 1.54256e26i | 0.124706 | + | 0.194260i | ||||
\(49\) | −1.77959e26 | −0.161132 | ||||||||
\(50\) | − | 4.06272e27i | − | 2.66255i | ||||||
\(51\) | 3.59310e26 | − | 2.30660e26i | 0.171532 | − | 0.110116i | ||||
\(52\) | −3.67768e27 | −1.28683 | ||||||||
\(53\) | 5.82182e27i | 1.50191i | 0.660351 | + | 0.750957i | \(0.270408\pi\) | ||||
−0.660351 | + | 0.750957i | \(0.729592\pi\) | |||||||
\(54\) | 1.16625e27 | + | 8.19873e27i | 0.223096 | + | 1.56836i | ||||
\(55\) | 1.19478e28 | 1.70406 | ||||||||
\(56\) | 6.91551e27i | 0.739292i | ||||||||
\(57\) | −8.26280e27 | − | 1.28713e28i | −0.665472 | − | 1.03663i | ||||
\(58\) | −3.44340e28 | −2.09961 | ||||||||
\(59\) | 1.32634e28i | 0.615208i | 0.951514 | + | 0.307604i | \(0.0995272\pi\) | ||||
−0.951514 | + | 0.307604i | \(0.900473\pi\) | |||||||
\(60\) | 5.86755e28 | − | 3.76670e28i | 2.07987 | − | 1.33518i | ||||
\(61\) | −6.55279e28 | −1.78299 | −0.891494 | − | 0.453032i | \(-0.850342\pi\) | ||||
−0.891494 | + | 0.453032i | \(0.850342\pi\) | |||||||
\(62\) | 3.72934e28i | 0.782285i | ||||||||
\(63\) | 2.34816e28 | − | 5.12817e28i | 0.381310 | − | 0.832749i | ||||
\(64\) | 1.28917e29 | 1.62716 | ||||||||
\(65\) | − | 1.41716e29i | − | 1.39574i | ||||||
\(66\) | 1.15459e29 | + | 1.79855e29i | 0.890686 | + | 1.38746i | ||||
\(67\) | −8.95668e28 | −0.543188 | −0.271594 | − | 0.962412i | \(-0.587551\pi\) | ||||
−0.271594 | + | 0.962412i | \(0.587551\pi\) | |||||||
\(68\) | − | 6.43080e28i | − | 0.307696i | ||||||
\(69\) | 1.11410e28 | − | 7.15205e27i | 0.0422027 | − | 0.0270922i | ||||
\(70\) | −7.89477e29 | −2.37559 | ||||||||
\(71\) | 4.59368e28i | 0.110161i | 0.998482 | + | 0.0550805i | \(0.0175415\pi\) | ||||
−0.998482 | + | 0.0550805i | \(0.982458\pi\) | |||||||
\(72\) | 3.82786e29 | + | 1.75275e29i | 0.733899 | + | 0.336048i | ||||
\(73\) | 2.56589e28 | 0.0394524 | 0.0197262 | − | 0.999805i | \(-0.493721\pi\) | ||||
0.0197262 | + | 0.999805i | \(0.493721\pi\) | |||||||
\(74\) | 3.44606e29i | 0.426201i | ||||||||
\(75\) | 9.10022e29 | + | 1.41758e30i | 0.907970 | + | 1.41438i | ||||
\(76\) | −2.30366e30 | −1.85952 | ||||||||
\(77\) | − | 1.45565e30i | − | 0.953244i | ||||||
\(78\) | 2.13331e30 | − | 1.36949e30i | 1.13642 | − | 0.729533i | ||||
\(79\) | 3.75026e30 | 1.62940 | 0.814700 | − | 0.579883i | \(-0.196902\pi\) | ||||
0.814700 | + | 0.579883i | \(0.196902\pi\) | |||||||
\(80\) | 1.06386e30i | 0.377958i | ||||||||
\(81\) | −2.24339e30 | − | 2.59950e30i | −0.653348 | − | 0.757058i | ||||
\(82\) | −3.48296e30 | −0.833540 | ||||||||
\(83\) | − | 1.44084e30i | − | 0.284032i | −0.989864 | − | 0.142016i | \(-0.954642\pi\) | ||
0.989864 | − | 0.142016i | \(-0.0453585\pi\) | |||||||
\(84\) | −4.58911e30 | − | 7.14866e30i | −0.746896 | − | 1.16347i | ||||
\(85\) | 2.47805e30 | 0.333739 | ||||||||
\(86\) | 1.39387e31i | 1.55685i | ||||||||
\(87\) | 1.20148e31 | − | 7.71297e30i | 1.11535 | − | 0.716001i | ||||
\(88\) | 1.08655e31 | 0.840091 | ||||||||
\(89\) | 4.42071e30i | 0.285268i | 0.989776 | + | 0.142634i | \(0.0455571\pi\) | ||||
−0.989776 | + | 0.142634i | \(0.954443\pi\) | |||||||
\(90\) | −2.00095e31 | + | 4.36990e31i | −1.07983 | + | 2.35826i | ||||
\(91\) | −1.72658e31 | −0.780773 | ||||||||
\(92\) | − | 1.99399e30i | − | 0.0757036i | ||||||
\(93\) | −8.35346e30 | − | 1.30125e31i | −0.266771 | − | 0.415561i | ||||
\(94\) | 1.00857e29 | 0.00271431 | ||||||||
\(95\) | − | 8.87696e31i | − | 2.01691i | ||||||
\(96\) | −5.13635e31 | + | 3.29731e31i | −0.986995 | + | 0.633606i | ||||
\(97\) | 7.67762e31 | 1.24991 | 0.624955 | − | 0.780661i | \(-0.285117\pi\) | ||||
0.624955 | + | 0.780661i | \(0.285117\pi\) | |||||||
\(98\) | − | 1.84755e31i | − | 0.255257i | ||||||
\(99\) | −8.05726e31 | − | 3.68937e31i | −0.946291 | − | 0.433301i | ||||
\(100\) | 2.53713e32 | 2.53713 | ||||||||
\(101\) | 1.25779e32i | 1.07267i | 0.844006 | + | 0.536334i | \(0.180191\pi\) | ||||
−0.844006 | + | 0.536334i | \(0.819809\pi\) | |||||||
\(102\) | 2.39469e31 | + | 3.73031e31i | 0.174440 | + | 0.271733i | ||||
\(103\) | −5.21843e31 | −0.325195 | −0.162598 | − | 0.986692i | \(-0.551987\pi\) | ||||
−0.162598 | + | 0.986692i | \(0.551987\pi\) | |||||||
\(104\) | − | 1.28878e32i | − | 0.688093i | ||||||
\(105\) | 2.75467e32 | − | 1.76837e32i | 1.26195 | − | 0.810112i | ||||
\(106\) | −6.04415e32 | −2.37926 | ||||||||
\(107\) | − | 1.50915e32i | − | 0.511200i | −0.966783 | − | 0.255600i | \(-0.917727\pi\) | ||
0.966783 | − | 0.255600i | \(-0.0822731\pi\) | |||||||
\(108\) | −5.12003e32 | + | 7.28312e31i | −1.49449 | + | 0.212587i | ||||
\(109\) | 2.44952e32 | 0.616961 | 0.308481 | − | 0.951231i | \(-0.400180\pi\) | ||||
0.308481 | + | 0.951231i | \(0.400180\pi\) | |||||||
\(110\) | 1.24041e33i | 2.69949i | ||||||||
\(111\) | −7.71893e31 | − | 1.20241e32i | −0.145341 | − | 0.226404i | ||||
\(112\) | 1.29614e32 | 0.211428 | ||||||||
\(113\) | 7.51269e32i | 1.06302i | 0.847053 | + | 0.531509i | \(0.178375\pi\) | ||||
−0.847053 | + | 0.531509i | \(0.821625\pi\) | |||||||
\(114\) | 1.33629e33 | − | 8.57835e32i | 1.64218 | − | 1.05421i | ||||
\(115\) | 7.68364e31 | 0.0821110 | ||||||||
\(116\) | − | 2.15037e33i | − | 2.00072i | ||||||
\(117\) | −4.37606e32 | + | 9.55694e32i | −0.354903 | + | 0.775077i | ||||
\(118\) | −1.37699e33 | −0.974582 | ||||||||
\(119\) | − | 3.01910e32i | − | 0.186692i | ||||||
\(120\) | 1.31998e33 | + | 2.05619e33i | 0.713949 | + | 1.11215i | ||||
\(121\) | −1.75699e32 | −0.0832153 | ||||||||
\(122\) | − | 6.80303e33i | − | 2.82452i | ||||||
\(123\) | 1.21529e33 | − | 7.80158e32i | 0.442789 | − | 0.284250i | ||||
\(124\) | −2.32894e33 | −0.745437 | ||||||||
\(125\) | 3.95977e33i | 1.11458i | ||||||||
\(126\) | 5.32401e33 | + | 2.43783e33i | 1.31920 | + | 0.604053i | ||||
\(127\) | −5.93082e33 | −1.29496 | −0.647479 | − | 0.762084i | \(-0.724176\pi\) | ||||
−0.647479 | + | 0.762084i | \(0.724176\pi\) | |||||||
\(128\) | 7.29410e33i | 1.40479i | ||||||||
\(129\) | −3.12217e33 | − | 4.86354e33i | −0.530911 | − | 0.827022i | ||||
\(130\) | 1.47128e34 | 2.21107 | ||||||||
\(131\) | 6.98819e33i | 0.929018i | 0.885568 | + | 0.464509i | \(0.153769\pi\) | ||||
−0.885568 | + | 0.464509i | \(0.846231\pi\) | |||||||
\(132\) | −1.12318e34 | + | 7.21031e33i | −1.32211 | + | 0.848732i | ||||
\(133\) | −1.08151e34 | −1.12825 | ||||||||
\(134\) | − | 9.29872e33i | − | 0.860491i | ||||||
\(135\) | −2.80648e33 | − | 1.97296e34i | −0.230580 | − | 1.62098i | ||||
\(136\) | 2.25357e33 | 0.164531 | ||||||||
\(137\) | 2.45169e34i | 1.59198i | 0.605312 | + | 0.795989i | \(0.293048\pi\) | ||||
−0.605312 | + | 0.795989i | \(0.706952\pi\) | |||||||
\(138\) | 7.42518e32 | + | 1.15665e33i | 0.0429182 | + | 0.0668555i | ||||
\(139\) | 1.85811e34 | 0.956828 | 0.478414 | − | 0.878134i | \(-0.341212\pi\) | ||||
0.478414 | + | 0.878134i | \(0.341212\pi\) | |||||||
\(140\) | − | 4.93021e34i | − | 2.26369i | ||||||
\(141\) | −3.51913e31 | + | 2.25912e31i | −0.00144188 | + | 0.000925622i | ||||
\(142\) | −4.76911e33 | −0.174512 | ||||||||
\(143\) | 2.71276e34i | 0.887228i | ||||||||
\(144\) | 3.28509e33 | − | 7.17436e33i | 0.0961054 | − | 0.209886i | ||||
\(145\) | 8.28626e34 | 2.17005 | ||||||||
\(146\) | 2.66388e33i | 0.0624985i | ||||||||
\(147\) | 4.13838e33 | + | 6.44653e33i | 0.0870468 | + | 0.135596i | ||||
\(148\) | −2.15203e34 | −0.406126 | ||||||||
\(149\) | − | 1.74564e34i | − | 0.295784i | −0.989004 | − | 0.147892i | \(-0.952751\pi\) | ||
0.989004 | − | 0.147892i | \(-0.0472488\pi\) | |||||||
\(150\) | −1.47172e35 | + | 9.44775e34i | −2.24060 | + | 1.43836i | ||||
\(151\) | −1.31115e35 | −1.79482 | −0.897410 | − | 0.441197i | \(-0.854554\pi\) | ||||
−0.897410 | + | 0.441197i | \(0.854554\pi\) | |||||||
\(152\) | − | 8.07282e34i | − | 0.994324i | ||||||
\(153\) | −1.67113e34 | − | 7.65199e33i | −0.185330 | − | 0.0848617i | ||||
\(154\) | 1.51124e35 | 1.51008 | ||||||||
\(155\) | − | 8.97435e34i | − | 0.808530i | ||||||
\(156\) | 8.55234e34 | + | 1.33223e35i | 0.695170 | + | 1.08290i | ||||
\(157\) | 5.79275e34 | 0.425099 | 0.212549 | − | 0.977150i | \(-0.431823\pi\) | ||||
0.212549 | + | 0.977150i | \(0.431823\pi\) | |||||||
\(158\) | 3.89348e35i | 2.58121i | ||||||||
\(159\) | 2.10895e35 | − | 1.35385e35i | 1.26390 | − | 0.811364i | ||||
\(160\) | −3.54239e35 | −1.92033 | ||||||||
\(161\) | − | 9.36127e33i | − | 0.0459326i | ||||||
\(162\) | 2.69877e35 | − | 2.32906e35i | 1.19929 | − | 1.03500i | ||||
\(163\) | −3.16517e34 | −0.127466 | −0.0637332 | − | 0.997967i | \(-0.520301\pi\) | ||||
−0.0637332 | + | 0.997967i | \(0.520301\pi\) | |||||||
\(164\) | − | 2.17508e35i | − | 0.794278i | ||||||
\(165\) | −2.77843e35 | − | 4.32807e35i | −0.920567 | − | 1.43401i | ||||
\(166\) | 1.49587e35 | 0.449950 | ||||||||
\(167\) | − | 5.63562e34i | − | 0.153985i | −0.997032 | − | 0.0769925i | \(-0.975468\pi\) | ||
0.997032 | − | 0.0769925i | \(-0.0245317\pi\) | |||||||
\(168\) | 2.50513e35 | − | 1.60818e35i | 0.622131 | − | 0.399380i | ||||
\(169\) | −1.21011e35 | −0.273299 | ||||||||
\(170\) | 2.57268e35i | 0.528693i | ||||||||
\(171\) | −2.74112e35 | + | 5.98638e35i | −0.512851 | + | 1.12002i | ||||
\(172\) | −8.70459e35 | −1.48352 | ||||||||
\(173\) | 1.61709e34i | 0.0251186i | 0.999921 | + | 0.0125593i | \(0.00399786\pi\) | ||||
−0.999921 | + | 0.0125593i | \(0.996002\pi\) | |||||||
\(174\) | 8.00752e35 | + | 1.24737e36i | 1.13425 | + | 1.76687i | ||||
\(175\) | 1.19112e36 | 1.53939 | ||||||||
\(176\) | − | 2.03646e35i | − | 0.240256i | ||||||
\(177\) | 4.80464e35 | − | 3.08436e35i | 0.517712 | − | 0.332348i | ||||
\(178\) | −4.58954e35 | −0.451907 | ||||||||
\(179\) | 8.90367e35i | 0.801532i | 0.916180 | + | 0.400766i | \(0.131256\pi\) | ||||
−0.916180 | + | 0.400766i | \(0.868744\pi\) | |||||||
\(180\) | −2.72896e36 | − | 1.24957e36i | −2.24718 | − | 1.02897i | ||||
\(181\) | −1.19270e36 | −0.898826 | −0.449413 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449413 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(182\) | − | 1.79252e36i | − | 1.23686i | ||||||
\(183\) | 1.52383e36 | + | 2.37374e36i | 0.963206 | + | 1.50043i | ||||
\(184\) | 6.98760e34 | 0.0404802 | ||||||||
\(185\) | − | 8.29265e35i | − | 0.440500i | ||||||
\(186\) | 1.35095e36 | − | 8.67247e35i | 0.658311 | − | 0.422606i | ||||
\(187\) | −4.74354e35 | −0.212147 | ||||||||
\(188\) | 6.29841e33i | 0.00258646i | ||||||||
\(189\) | −2.40373e36 | + | 3.41925e35i | −0.906769 | + | 0.128986i | ||||
\(190\) | 9.21596e36 | 3.19509 | ||||||||
\(191\) | − | 3.89653e36i | − | 1.24207i | −0.783784 | − | 0.621033i | \(-0.786713\pi\) | ||
0.783784 | − | 0.621033i | \(-0.213287\pi\) | |||||||
\(192\) | −2.99792e36 | − | 4.66998e36i | −0.879022 | − | 1.36929i | ||||
\(193\) | 1.90013e36 | 0.512703 | 0.256351 | − | 0.966584i | \(-0.417480\pi\) | ||||
0.256351 | + | 0.966584i | \(0.417480\pi\) | |||||||
\(194\) | 7.97082e36i | 1.98005i | ||||||||
\(195\) | −5.13364e36 | + | 3.29556e36i | −1.17455 | + | 0.754008i | ||||
\(196\) | 1.15378e36 | 0.243234 | ||||||||
\(197\) | 3.35666e36i | 0.652300i | 0.945318 | + | 0.326150i | \(0.105752\pi\) | ||||
−0.945318 | + | 0.326150i | \(0.894248\pi\) | |||||||
\(198\) | 3.83027e36 | − | 8.36496e36i | 0.686413 | − | 1.49907i | ||||
\(199\) | −7.69959e36 | −1.27297 | −0.636485 | − | 0.771289i | \(-0.719612\pi\) | ||||
−0.636485 | + | 0.771289i | \(0.719612\pi\) | |||||||
\(200\) | 8.89098e36i | 1.35666i | ||||||||
\(201\) | 2.08285e36 | + | 3.24454e36i | 0.293441 | + | 0.457105i | ||||
\(202\) | −1.30582e37 | −1.69927 | ||||||||
\(203\) | − | 1.00955e37i | − | 1.21392i | ||||||
\(204\) | −2.32955e36 | + | 1.49546e36i | −0.258934 | + | 0.166224i | ||||
\(205\) | 8.38145e36 | 0.861504 | ||||||||
\(206\) | − | 5.41772e36i | − | 0.515158i | ||||||
\(207\) | −5.18163e35 | − | 2.37264e35i | −0.0455975 | − | 0.0208788i | ||||
\(208\) | −2.41550e36 | −0.196786 | ||||||||
\(209\) | 1.69925e37i | 1.28208i | ||||||||
\(210\) | 1.83590e37 | + | 2.85987e37i | 1.28334 | + | 1.99911i | ||||
\(211\) | 6.84634e36 | 0.443546 | 0.221773 | − | 0.975098i | \(-0.428816\pi\) | ||||
0.221773 | + | 0.975098i | \(0.428816\pi\) | |||||||
\(212\) | − | 3.77452e37i | − | 2.26719i | ||||||
\(213\) | 1.66405e36 | − | 1.06825e36i | 0.0927030 | − | 0.0595111i | ||||
\(214\) | 1.56678e37 | 0.809818 | ||||||||
\(215\) | − | 3.35424e37i | − | 1.60908i | ||||||
\(216\) | −2.55225e36 | − | 1.79423e37i | −0.113675 | − | 0.799133i | ||||
\(217\) | −1.09338e37 | −0.452288 | ||||||||
\(218\) | 2.54307e37i | 0.977359i | ||||||||
\(219\) | −5.96691e35 | − | 9.29491e35i | −0.0213130 | − | 0.0332001i | ||||
\(220\) | −7.74623e37 | −2.57233 | ||||||||
\(221\) | 5.62644e36i | 0.173763i | ||||||||
\(222\) | 1.24833e37 | − | 8.01370e36i | 0.358659 | − | 0.230243i | ||||
\(223\) | 5.43018e37 | 1.45190 | 0.725950 | − | 0.687748i | \(-0.241401\pi\) | ||||
0.725950 | + | 0.687748i | \(0.241401\pi\) | |||||||
\(224\) | 4.31583e37i | 1.07423i | ||||||||
\(225\) | 3.01893e37 | − | 6.59308e37i | 0.699734 | − | 1.52816i | ||||
\(226\) | −7.79960e37 | −1.68398 | ||||||||
\(227\) | 4.49436e37i | 0.904178i | 0.891973 | + | 0.452089i | \(0.149321\pi\) | ||||
−0.891973 | + | 0.452089i | \(0.850679\pi\) | |||||||
\(228\) | 5.35710e37 | + | 8.34499e37i | 1.00455 | + | 1.56483i | ||||
\(229\) | 2.48444e37 | 0.434372 | 0.217186 | − | 0.976130i | \(-0.430312\pi\) | ||||
0.217186 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(230\) | 7.97707e36i | 0.130076i | ||||||||
\(231\) | −5.27305e37 | + | 3.38506e37i | −0.802178 | + | 0.514962i | ||||
\(232\) | 7.53563e37 | 1.06982 | ||||||||
\(233\) | 8.15150e37i | 1.08030i | 0.841570 | + | 0.540148i | \(0.181632\pi\) | ||||
−0.841570 | + | 0.540148i | \(0.818368\pi\) | |||||||
\(234\) | −9.92191e37 | − | 4.54318e37i | −1.22784 | − | 0.562220i | ||||
\(235\) | −2.42704e35 | −0.00280537 | ||||||||
\(236\) | − | 8.59917e37i | − | 0.928677i | ||||||
\(237\) | −8.72111e37 | − | 1.35852e38i | −0.880234 | − | 1.37118i | ||||
\(238\) | 3.13440e37 | 0.295749 | ||||||||
\(239\) | − | 1.65146e38i | − | 1.45714i | −0.684971 | − | 0.728570i | \(-0.740185\pi\) | ||
0.684971 | − | 0.728570i | \(-0.259815\pi\) | |||||||
\(240\) | 3.85381e37 | − | 2.47397e37i | 0.318061 | − | 0.204180i | ||||
\(241\) | −1.04519e38 | −0.807092 | −0.403546 | − | 0.914959i | \(-0.632222\pi\) | ||||
−0.403546 | + | 0.914959i | \(0.632222\pi\) | |||||||
\(242\) | − | 1.82409e37i | − | 0.131826i | ||||||
\(243\) | −4.19970e37 | + | 1.41717e38i | −0.284130 | + | 0.958786i | ||||
\(244\) | 4.24843e38 | 2.69148 | ||||||||
\(245\) | 4.44597e37i | 0.263821i | ||||||||
\(246\) | 8.09951e37 | + | 1.26170e38i | 0.450295 | + | 0.701444i | ||||
\(247\) | 2.01552e38 | 1.05012 | ||||||||
\(248\) | − | 8.16139e37i | − | 0.398600i | ||||||
\(249\) | −5.21943e37 | + | 3.35064e37i | −0.239020 | + | 0.153440i | ||||
\(250\) | −4.11099e38 | −1.76566 | ||||||||
\(251\) | 5.56329e37i | 0.224157i | 0.993699 | + | 0.112079i | \(0.0357508\pi\) | ||||
−0.993699 | + | 0.112079i | \(0.964249\pi\) | |||||||
\(252\) | −1.52240e38 | + | 3.32480e38i | −0.575601 | + | 1.25706i | ||||
\(253\) | −1.47082e37 | −0.0521953 | ||||||||
\(254\) | − | 6.15731e38i | − | 2.05141i | ||||||
\(255\) | −5.76263e37 | − | 8.97669e37i | −0.180293 | − | 0.280849i | ||||
\(256\) | −2.03573e38 | −0.598247 | ||||||||
\(257\) | 4.70854e38i | 1.30004i | 0.759917 | + | 0.650020i | \(0.225239\pi\) | ||||
−0.759917 | + | 0.650020i | \(0.774761\pi\) | |||||||
\(258\) | 5.04927e38 | − | 3.24140e38i | 1.31013 | − | 0.841043i | ||||
\(259\) | −1.01033e38 | −0.246414 | ||||||||
\(260\) | 9.18801e38i | 2.10692i | ||||||||
\(261\) | −5.58802e38 | − | 2.55872e38i | −1.20506 | − | 0.551791i | ||||
\(262\) | −7.25506e38 | −1.47170 | ||||||||
\(263\) | 8.36358e38i | 1.59625i | 0.602494 | + | 0.798124i | \(0.294174\pi\) | ||||
−0.602494 | + | 0.798124i | \(0.705826\pi\) | |||||||
\(264\) | −2.52674e38 | − | 3.93600e38i | −0.453834 | − | 0.706957i | ||||
\(265\) | 1.45448e39 | 2.45908 | ||||||||
\(266\) | − | 1.12282e39i | − | 1.78732i | ||||||
\(267\) | 1.60140e38 | − | 1.02802e38i | 0.240059 | − | 0.154107i | ||||
\(268\) | 5.80697e38 | 0.819960 | ||||||||
\(269\) | − | 1.11243e38i | − | 0.147992i | −0.997259 | − | 0.0739960i | \(-0.976425\pi\) | ||
0.997259 | − | 0.0739960i | \(-0.0235752\pi\) | |||||||
\(270\) | 2.04830e39 | − | 2.91366e38i | 2.56788 | − | 0.365274i | ||||
\(271\) | −6.87434e38 | −0.812311 | −0.406156 | − | 0.913804i | \(-0.633131\pi\) | ||||
−0.406156 | + | 0.913804i | \(0.633131\pi\) | |||||||
\(272\) | − | 4.22375e37i | − | 0.0470539i | ||||||
\(273\) | 4.01511e38 | + | 6.25451e38i | 0.421789 | + | 0.657039i | ||||
\(274\) | −2.54532e39 | −2.52193 | ||||||||
\(275\) | − | 1.87146e39i | − | 1.74928i | ||||||
\(276\) | −7.22318e37 | + | 4.63695e37i | −0.0637064 | + | 0.0408966i | ||||
\(277\) | −1.52657e39 | −1.27070 | −0.635348 | − | 0.772226i | \(-0.719143\pi\) | ||||
−0.635348 | + | 0.772226i | \(0.719143\pi\) | |||||||
\(278\) | 1.92907e39i | 1.51576i | ||||||||
\(279\) | −2.77120e38 | + | 6.05206e38i | −0.205589 | + | 0.448989i | ||||
\(280\) | 1.72771e39 | 1.21044 | ||||||||
\(281\) | − | 1.62418e39i | − | 1.07481i | −0.843324 | − | 0.537405i | \(-0.819405\pi\) | ||
0.843324 | − | 0.537405i | \(-0.180595\pi\) | |||||||
\(282\) | −2.34539e36 | − | 3.65352e36i | −0.00146632 | − | 0.00228416i | ||||
\(283\) | 2.63488e39 | 1.55661 | 0.778303 | − | 0.627889i | \(-0.216081\pi\) | ||||
0.778303 | + | 0.627889i | \(0.216081\pi\) | |||||||
\(284\) | − | 2.97827e38i | − | 0.166292i | ||||||
\(285\) | −3.21566e39 | + | 2.06431e39i | −1.69728 | + | 1.08958i | ||||
\(286\) | −2.81636e39 | −1.40550 | ||||||||
\(287\) | − | 1.02114e39i | − | 0.481922i | ||||||
\(288\) | 2.38889e39 | + | 1.09386e39i | 1.06639 | + | 0.488293i | ||||
\(289\) | 2.26953e39 | 0.958451 | ||||||||
\(290\) | 8.60270e39i | 3.43769i | ||||||||
\(291\) | −1.78541e39 | − | 2.78121e39i | −0.675227 | − | 1.05183i | ||||
\(292\) | −1.66357e38 | −0.0595547 | ||||||||
\(293\) | − | 5.48987e39i | − | 1.86072i | −0.366651 | − | 0.930359i | \(-0.619496\pi\) | ||
0.366651 | − | 0.930359i | \(-0.380504\pi\) | |||||||
\(294\) | −6.69271e38 | + | 4.29642e38i | −0.214805 | + | 0.137895i | ||||
\(295\) | 3.31361e39 | 1.00728 | ||||||||
\(296\) | − | 7.54145e38i | − | 0.217164i | ||||||
\(297\) | 5.37224e38 | + | 3.77668e39i | 0.146572 | + | 1.03040i | ||||
\(298\) | 1.81231e39 | 0.468567 | ||||||||
\(299\) | 1.74458e38i | 0.0427516i | ||||||||
\(300\) | −5.90003e39 | − | 9.19073e39i | −1.37061 | − | 2.13506i | ||||
\(301\) | −4.08659e39 | −0.900114 | ||||||||
\(302\) | − | 1.36122e40i | − | 2.84327i | ||||||
\(303\) | 4.55631e39 | − | 2.92495e39i | 0.902675 | − | 0.579476i | ||||
\(304\) | −1.51305e39 | −0.284364 | ||||||||
\(305\) | 1.63709e40i | 2.91928i | ||||||||
\(306\) | 7.94421e38 | − | 1.73495e39i | 0.134434 | − | 0.293591i | ||||
\(307\) | 4.15729e39 | 0.667724 | 0.333862 | − | 0.942622i | \(-0.391648\pi\) | ||||
0.333862 | + | 0.942622i | \(0.391648\pi\) | |||||||
\(308\) | 9.43753e39i | 1.43895i | ||||||||
\(309\) | 1.21353e39 | + | 1.89037e39i | 0.175677 | + | 0.273660i | ||||
\(310\) | 9.31707e39 | 1.28083 | ||||||||
\(311\) | − | 4.12881e39i | − | 0.539087i | −0.962988 | − | 0.269543i | \(-0.913127\pi\) | ||
0.962988 | − | 0.269543i | \(-0.0868728\pi\) | |||||||
\(312\) | −4.66860e39 | + | 2.99703e39i | −0.579046 | + | 0.371721i | ||||
\(313\) | 1.51328e40 | 1.78324 | 0.891618 | − | 0.452788i | \(-0.149570\pi\) | ||||
0.891618 | + | 0.452788i | \(0.149570\pi\) | |||||||
\(314\) | 6.01397e39i | 0.673421i | ||||||||
\(315\) | −1.28118e40 | − | 5.86645e39i | −1.36346 | − | 0.624318i | ||||
\(316\) | −2.43144e40 | −2.45963 | ||||||||
\(317\) | − | 1.30044e39i | − | 0.125067i | −0.998043 | − | 0.0625336i | \(-0.980082\pi\) | ||
0.998043 | − | 0.0625336i | \(-0.0199181\pi\) | |||||||
\(318\) | 1.40555e40 | + | 2.18948e40i | 1.28532 | + | 2.00220i | ||||
\(319\) | −1.58618e40 | −1.37943 | ||||||||
\(320\) | − | 3.22074e40i | − | 2.66414i | ||||||
\(321\) | −5.46686e39 | + | 3.50948e39i | −0.430187 | + | 0.276161i | ||||
\(322\) | 9.71877e38 | 0.0727641 | ||||||||
\(323\) | 3.52435e39i | 0.251095i | ||||||||
\(324\) | 1.45448e40 | + | 1.68536e40i | 0.986250 | + | 1.14280i | ||||
\(325\) | −2.21979e40 | −1.43278 | ||||||||
\(326\) | − | 3.28605e39i | − | 0.201926i | ||||||
\(327\) | −5.69630e39 | − | 8.87336e39i | −0.333295 | − | 0.519187i | ||||
\(328\) | 7.62220e39 | 0.424716 | ||||||||
\(329\) | 2.95695e37i | 0.00156931i | ||||||||
\(330\) | 4.49335e40 | − | 2.88453e40i | 2.27168 | − | 1.45832i | ||||
\(331\) | 3.01231e40 | 1.45095 | 0.725475 | − | 0.688249i | \(-0.241620\pi\) | ||||
0.725475 | + | 0.688249i | \(0.241620\pi\) | |||||||
\(332\) | 9.34156e39i | 0.428756i | ||||||||
\(333\) | −2.56070e39 | + | 5.59234e39i | −0.112008 | + | 0.244616i | ||||
\(334\) | 5.85084e39 | 0.243935 | ||||||||
\(335\) | 2.23766e40i | 0.889360i | ||||||||
\(336\) | −3.01413e39 | − | 4.69524e39i | −0.114218 | − | 0.177922i | ||||
\(337\) | −4.23569e40 | −1.53054 | −0.765272 | − | 0.643707i | \(-0.777396\pi\) | ||||
−0.765272 | + | 0.643707i | \(0.777396\pi\) | |||||||
\(338\) | − | 1.25632e40i | − | 0.432947i | ||||||
\(339\) | 2.72146e40 | − | 1.74705e40i | 0.894555 | − | 0.574264i | ||||
\(340\) | −1.60662e40 | −0.503790 | ||||||||
\(341\) | 1.71789e40i | 0.513956i | ||||||||
\(342\) | −6.21499e40 | − | 2.84580e40i | −1.77428 | − | 0.812433i | ||||
\(343\) | 3.90332e40 | 1.06348 | ||||||||
\(344\) | − | 3.05039e40i | − | 0.793268i | ||||||
\(345\) | −1.78681e39 | − | 2.78339e39i | −0.0443580 | − | 0.0690984i | ||||
\(346\) | −1.67884e39 | −0.0397917 | ||||||||
\(347\) | − | 1.86252e40i | − | 0.421530i | −0.977537 | − | 0.210765i | \(-0.932405\pi\) | ||
0.977537 | − | 0.210765i | \(-0.0675954\pi\) | |||||||
\(348\) | −7.78969e40 | + | 5.00063e40i | −1.68365 | + | 1.08083i | ||||
\(349\) | −2.35818e40 | −0.486822 | −0.243411 | − | 0.969923i | \(-0.578266\pi\) | ||||
−0.243411 | + | 0.969923i | \(0.578266\pi\) | |||||||
\(350\) | 1.23661e41i | 2.43862i | ||||||||
\(351\) | 4.47963e40 | − | 6.37216e39i | 0.843972 | − | 0.120053i | ||||
\(352\) | 6.78092e40 | 1.22069 | ||||||||
\(353\) | 4.50171e40i | 0.774430i | 0.921989 | + | 0.387215i | \(0.126563\pi\) | ||||
−0.921989 | + | 0.387215i | \(0.873437\pi\) | |||||||
\(354\) | 3.20215e40 | + | 4.98812e40i | 0.526489 | + | 0.820134i | ||||
\(355\) | 1.14765e40 | 0.180366 | ||||||||
\(356\) | − | 2.86612e40i | − | 0.430621i | ||||||
\(357\) | −1.09366e40 | + | 7.02083e39i | −0.157106 | + | 0.100855i | ||||
\(358\) | −9.24370e40 | −1.26975 | ||||||||
\(359\) | − | 9.66820e40i | − | 1.27009i | −0.772475 | − | 0.635045i | \(-0.780981\pi\) | ||
0.772475 | − | 0.635045i | \(-0.219019\pi\) | |||||||
\(360\) | 4.37893e40 | − | 9.56321e40i | 0.550210 | − | 1.20161i | ||||
\(361\) | 4.30521e40 | 0.517463 | ||||||||
\(362\) | − | 1.23825e41i | − | 1.42388i | ||||||
\(363\) | 4.08583e39 | + | 6.36467e39i | 0.0449546 | + | 0.0700277i | ||||
\(364\) | 1.11941e41 | 1.17860 | ||||||||
\(365\) | − | 6.41042e39i | − | 0.0645952i | ||||||
\(366\) | −2.46439e41 | + | 1.58202e41i | −2.37690 | + | 1.52586i | ||||
\(367\) | 7.40639e40 | 0.683832 | 0.341916 | − | 0.939730i | \(-0.388924\pi\) | ||||
0.341916 | + | 0.939730i | \(0.388924\pi\) | |||||||
\(368\) | − | 1.30965e39i | − | 0.0115768i | ||||||
\(369\) | −5.65222e40 | − | 2.58812e40i | −0.478407 | − | 0.219059i | ||||
\(370\) | 8.60934e40 | 0.697818 | ||||||||
\(371\) | − | 1.77204e41i | − | 1.37560i | ||||||
\(372\) | 5.41588e40 | + | 8.43654e40i | 0.402700 | + | 0.627303i | ||||
\(373\) | −8.48695e40 | −0.604519 | −0.302260 | − | 0.953226i | \(-0.597741\pi\) | ||||
−0.302260 | + | 0.953226i | \(0.597741\pi\) | |||||||
\(374\) | − | 4.92469e40i | − | 0.336073i | ||||||
\(375\) | 1.43442e41 | − | 9.20832e40i | 0.937942 | − | 0.602116i | ||||
\(376\) | −2.20718e38 | −0.00138303 | ||||||||
\(377\) | 1.88141e41i | 1.12985i | ||||||||
\(378\) | −3.54983e40 | − | 2.49553e41i | −0.204333 | − | 1.43646i | ||||
\(379\) | −2.86987e41 | −1.58356 | −0.791781 | − | 0.610805i | \(-0.790846\pi\) | ||||
−0.791781 | + | 0.610805i | \(0.790846\pi\) | |||||||
\(380\) | 5.75528e41i | 3.04459i | ||||||||
\(381\) | 1.37920e41 | + | 2.14843e41i | 0.699562 | + | 1.08974i | ||||
\(382\) | 4.04534e41 | 1.96762 | ||||||||
\(383\) | − | 2.93471e41i | − | 1.36894i | −0.729041 | − | 0.684470i | \(-0.760034\pi\) | ||
0.729041 | − | 0.684470i | \(-0.239966\pi\) | |||||||
\(384\) | 2.64228e41 | − | 1.69622e41i | 1.18217 | − | 0.758897i | ||||
\(385\) | −3.63666e41 | −1.56074 | ||||||||
\(386\) | 1.97269e41i | 0.812199i | ||||||||
\(387\) | −1.03576e41 | + | 2.26200e41i | −0.409150 | + | 0.893548i | ||||
\(388\) | −4.97770e41 | −1.88678 | ||||||||
\(389\) | 5.36936e41i | 1.95312i | 0.215245 | + | 0.976560i | \(0.430945\pi\) | ||||
−0.215245 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(390\) | −3.42142e41 | − | 5.32969e41i | −1.19446 | − | 1.86066i | ||||
\(391\) | −3.05058e39 | −0.0102224 | ||||||||
\(392\) | 4.04323e40i | 0.130062i | ||||||||
\(393\) | 2.53146e41 | − | 1.62508e41i | 0.781790 | − | 0.501874i | ||||
\(394\) | −3.48485e41 | −1.03334 | ||||||||
\(395\) | − | 9.36933e41i | − | 2.66781i | ||||||
\(396\) | 5.22384e41 | + | 2.39197e41i | 1.42846 | + | 0.654082i | ||||
\(397\) | 4.82964e41 | 1.26843 | 0.634216 | − | 0.773156i | \(-0.281323\pi\) | ||||
0.634216 | + | 0.773156i | \(0.281323\pi\) | |||||||
\(398\) | − | 7.99363e41i | − | 2.01658i | ||||||
\(399\) | 2.51503e41 | + | 3.91777e41i | 0.609504 | + | 0.949450i | ||||
\(400\) | 1.66639e41 | 0.387987 | ||||||||
\(401\) | 6.81584e41i | 1.52479i | 0.647114 | + | 0.762394i | \(0.275976\pi\) | ||||
−0.647114 | + | 0.762394i | \(0.724024\pi\) | |||||||
\(402\) | −3.36845e41 | + | 2.16239e41i | −0.724124 | + | 0.464855i | ||||
\(403\) | 2.03764e41 | 0.420965 | ||||||||
\(404\) | − | 8.15473e41i | − | 1.61923i | ||||||
\(405\) | −6.49437e41 | + | 5.60470e41i | −1.23953 | + | 1.06972i | ||||
\(406\) | 1.04810e42 | 1.92303 | ||||||||
\(407\) | 1.58740e41i | 0.280011i | ||||||||
\(408\) | −5.24061e40 | − | 8.16352e40i | −0.0888831 | − | 0.138457i | ||||
\(409\) | −9.34417e41 | −1.52394 | −0.761970 | − | 0.647613i | \(-0.775767\pi\) | ||||
−0.761970 | + | 0.647613i | \(0.775767\pi\) | |||||||
\(410\) | 8.70153e41i | 1.36475i | ||||||||
\(411\) | 8.88121e41 | − | 5.70134e41i | 1.33969 | − | 0.860018i | ||||
\(412\) | 3.38331e41 | 0.490893 | ||||||||
\(413\) | − | 4.03710e41i | − | 0.563467i | ||||||
\(414\) | 2.46325e40 | − | 5.37952e40i | 0.0330752 | − | 0.0722333i | ||||
\(415\) | −3.59968e41 | −0.465045 | ||||||||
\(416\) | − | 8.04303e41i | − | 0.999831i | ||||||
\(417\) | −4.32097e41 | − | 6.73096e41i | −0.516898 | − | 0.805194i | ||||
\(418\) | −1.76414e42 | −2.03101 | ||||||||
\(419\) | 1.19503e42i | 1.32421i | 0.749412 | + | 0.662104i | \(0.230336\pi\) | ||||
−0.749412 | + | 0.662104i | \(0.769664\pi\) | |||||||
\(420\) | −1.78596e42 | + | 1.14651e42i | −1.90495 | + | 1.22289i | ||||
\(421\) | −1.01400e41 | −0.104118 | −0.0520590 | − | 0.998644i | \(-0.516578\pi\) | ||||
−0.0520590 | + | 0.998644i | \(0.516578\pi\) | |||||||
\(422\) | 7.10779e41i | 0.702644i | ||||||||
\(423\) | 1.63673e39 | + | 7.49447e38i | 0.00155787 | + | 0.000713337i | ||||
\(424\) | 1.32272e42 | 1.21231 | ||||||||
\(425\) | − | 3.88153e41i | − | 0.342595i | ||||||
\(426\) | 1.10904e41 | + | 1.72760e41i | 0.0942746 | + | 0.146856i | ||||
\(427\) | 1.99453e42 | 1.63303 | ||||||||
\(428\) | 9.78440e41i | 0.771674i | ||||||||
\(429\) | 9.82694e41 | − | 6.30845e41i | 0.746624 | − | 0.479298i | ||||
\(430\) | 3.48233e42 | 2.54903 | ||||||||
\(431\) | 1.23004e42i | 0.867524i | 0.901028 | + | 0.433762i | \(0.142814\pi\) | ||||
−0.901028 | + | 0.433762i | \(0.857186\pi\) | |||||||
\(432\) | −3.36284e41 | + | 4.78356e40i | −0.228542 | + | 0.0325096i | ||||
\(433\) | −1.88664e42 | −1.23561 | −0.617806 | − | 0.786330i | \(-0.711978\pi\) | ||||
−0.617806 | + | 0.786330i | \(0.711978\pi\) | |||||||
\(434\) | − | 1.13513e42i | − | 0.716493i | ||||||
\(435\) | −1.92694e42 | − | 3.00168e42i | −1.17231 | − | 1.82615i | ||||
\(436\) | −1.58812e42 | −0.931323 | ||||||||
\(437\) | 1.09279e41i | 0.0617779i | ||||||||
\(438\) | 9.64987e40 | − | 6.19478e40i | 0.0525940 | − | 0.0337629i | ||||
\(439\) | 8.54191e41 | 0.448872 | 0.224436 | − | 0.974489i | \(-0.427946\pi\) | ||||
0.224436 | + | 0.974489i | \(0.427946\pi\) | |||||||
\(440\) | − | 2.71454e42i | − | 1.37548i | ||||||
\(441\) | 1.37288e41 | − | 2.99824e41i | 0.0670832 | − | 0.146504i | ||||
\(442\) | −5.84131e41 | −0.275267 | ||||||||
\(443\) | − | 2.00522e42i | − | 0.911384i | −0.890137 | − | 0.455692i | \(-0.849392\pi\) | ||
0.890137 | − | 0.455692i | \(-0.150608\pi\) | |||||||
\(444\) | 5.00449e41 | + | 7.79570e41i | 0.219398 | + | 0.341765i | ||||
\(445\) | 1.10443e42 | 0.467068 | ||||||||
\(446\) | 5.63755e42i | 2.30003i | ||||||||
\(447\) | −6.32356e41 | + | 4.05944e41i | −0.248909 | + | 0.159789i | ||||
\(448\) | −3.92395e42 | −1.49031 | ||||||||
\(449\) | − | 3.93631e42i | − | 1.44261i | −0.692619 | − | 0.721304i | \(-0.743543\pi\) | ||
0.692619 | − | 0.721304i | \(-0.256457\pi\) | |||||||
\(450\) | 6.84486e42 | + | 3.13422e42i | 2.42083 | + | 1.10848i | ||||
\(451\) | −1.60440e42 | −0.547630 | ||||||||
\(452\) | − | 4.87078e42i | − | 1.60466i | ||||||
\(453\) | 3.04904e42 | + | 4.74962e42i | 0.969598 | + | 1.51038i | ||||
\(454\) | −4.66599e42 | −1.43235 | ||||||||
\(455\) | 4.31355e42i | 1.27836i | ||||||||
\(456\) | −2.92437e42 | + | 1.87731e42i | −0.836747 | + | 0.537154i | ||||
\(457\) | 4.01009e42 | 1.10789 | 0.553943 | − | 0.832554i | \(-0.313122\pi\) | ||||
0.553943 | + | 0.832554i | \(0.313122\pi\) | |||||||
\(458\) | 2.57932e42i | 0.688110i | ||||||||
\(459\) | 1.11424e41 | + | 7.83308e41i | 0.0287061 | + | 0.201804i | ||||
\(460\) | −4.98161e41 | −0.123949 | ||||||||
\(461\) | 1.44532e42i | 0.347335i | 0.984804 | + | 0.173668i | \(0.0555619\pi\) | ||||
−0.984804 | + | 0.173668i | \(0.944438\pi\) | |||||||
\(462\) | −3.51433e42 | − | 5.47443e42i | −0.815777 | − | 1.27077i | ||||
\(463\) | 4.37917e42 | 0.981964 | 0.490982 | − | 0.871170i | \(-0.336638\pi\) | ||||
0.490982 | + | 0.871170i | \(0.336638\pi\) | |||||||
\(464\) | − | 1.41236e42i | − | 0.305956i | ||||||
\(465\) | −3.25094e42 | + | 2.08696e42i | −0.680397 | + | 0.436784i | ||||
\(466\) | −8.46280e42 | −1.71135 | ||||||||
\(467\) | − | 4.22719e42i | − | 0.826002i | −0.910731 | − | 0.413001i | \(-0.864481\pi\) | ||
0.910731 | − | 0.413001i | \(-0.135519\pi\) | |||||||
\(468\) | 2.83718e42 | − | 6.19614e42i | 0.535738 | − | 1.17000i | ||||
\(469\) | 2.72623e42 | 0.497504 | ||||||||
\(470\) | − | 2.51972e40i | − | 0.00444413i | ||||||
\(471\) | −1.34709e42 | − | 2.09841e42i | −0.229647 | − | 0.357731i | ||||
\(472\) | 3.01344e42 | 0.496582 | ||||||||
\(473\) | 6.42076e42i | 1.02284i | ||||||||
\(474\) | 1.41041e43 | − | 9.05416e42i | 2.17215 | − | 1.39442i | ||||
\(475\) | −1.39046e43 | −2.07043 | ||||||||
\(476\) | 1.95740e42i | 0.281818i | ||||||||
\(477\) | −9.80859e42 | − | 4.49129e42i | −1.36556 | − | 0.625284i | ||||
\(478\) | 1.71453e43 | 2.30833 | ||||||||
\(479\) | 1.09686e43i | 1.42818i | 0.700054 | + | 0.714090i | \(0.253159\pi\) | ||||
−0.700054 | + | 0.714090i | \(0.746841\pi\) | |||||||
\(480\) | 8.23771e42 | + | 1.28322e43i | 1.03740 | + | 1.61600i | ||||
\(481\) | 1.88286e42 | 0.229349 | ||||||||
\(482\) | − | 1.08511e43i | − | 1.27856i | ||||||
\(483\) | −3.39111e41 | + | 2.17694e41i | −0.0386534 | + | 0.0248137i | ||||
\(484\) | 1.13913e42 | 0.125616 | ||||||||
\(485\) | − | 1.91811e43i | − | 2.04647i | ||||||
\(486\) | −1.47129e43 | − | 4.36008e42i | −1.51886 | − | 0.450105i | ||||
\(487\) | 9.98519e42 | 0.997454 | 0.498727 | − | 0.866759i | \(-0.333801\pi\) | ||||
0.498727 | + | 0.866759i | \(0.333801\pi\) | |||||||
\(488\) | 1.48879e43i | 1.43919i | ||||||||
\(489\) | 7.36052e41 | + | 1.14658e42i | 0.0688599 | + | 0.107266i | ||||
\(490\) | −4.61576e42 | −0.417932 | ||||||||
\(491\) | − | 4.39197e42i | − | 0.384907i | −0.981306 | − | 0.192453i | \(-0.938356\pi\) | ||
0.981306 | − | 0.192453i | \(-0.0616444\pi\) | |||||||
\(492\) | −7.87918e42 | + | 5.05807e42i | −0.668404 | + | 0.429085i | ||||
\(493\) | −3.28983e42 | −0.270161 | ||||||||
\(494\) | 2.09250e43i | 1.66354i | ||||||||
\(495\) | −9.21722e42 | + | 2.01296e43i | −0.709442 | + | 1.54936i | ||||
\(496\) | −1.52965e42 | −0.113995 | ||||||||
\(497\) | − | 1.39822e42i | − | 0.100896i | ||||||
\(498\) | −3.47860e42 | − | 5.41876e42i | −0.243072 | − | 0.378643i | ||||
\(499\) | −9.63135e42 | −0.651746 | −0.325873 | − | 0.945414i | \(-0.605658\pi\) | ||||
−0.325873 | + | 0.945414i | \(0.605658\pi\) | |||||||
\(500\) | − | 2.56727e43i | − | 1.68249i | ||||||
\(501\) | −2.04150e42 | + | 1.31055e42i | −0.129582 | + | 0.0831858i | ||||
\(502\) | −5.77575e42 | −0.355099 | ||||||||
\(503\) | 2.08881e42i | 0.124397i | 0.998064 | + | 0.0621986i | \(0.0198112\pi\) | ||||
−0.998064 | + | 0.0621986i | \(0.980189\pi\) | |||||||
\(504\) | −1.16512e43 | − | 5.33502e42i | −0.672176 | − | 0.307785i | ||||
\(505\) | 3.14235e43 | 1.75627 | ||||||||
\(506\) | − | 1.52699e42i | − | 0.0826852i | ||||||
\(507\) | 2.81408e42 | + | 4.38361e42i | 0.147642 | + | 0.229988i | ||||
\(508\) | 3.84519e43 | 1.95478 | ||||||||
\(509\) | − | 1.42164e43i | − | 0.700335i | −0.936687 | − | 0.350167i | \(-0.886125\pi\) | ||
0.936687 | − | 0.350167i | \(-0.113875\pi\) | |||||||
\(510\) | 9.31950e42 | − | 5.98270e42i | 0.444908 | − | 0.285611i | ||||
\(511\) | −7.81006e41 | −0.0361343 | ||||||||
\(512\) | 1.01932e43i | 0.457079i | ||||||||
\(513\) | 2.80600e43 | − | 3.99146e42i | 1.21958 | − | 0.173482i | ||||
\(514\) | −4.88836e43 | −2.05946 | ||||||||
\(515\) | 1.30373e43i | 0.532441i | ||||||||
\(516\) | 2.02423e43 | + | 3.15323e43i | 0.801427 | + | 1.24842i | ||||
\(517\) | 4.64589e40 | 0.00178328 | ||||||||
\(518\) | − | 1.04891e43i | − | 0.390357i | ||||||
\(519\) | 5.85788e41 | − | 3.76049e41i | 0.0211379 | − | 0.0135696i | ||||
\(520\) | −3.21979e43 | −1.12661 | ||||||||
\(521\) | − | 4.58192e42i | − | 0.155469i | −0.996974 | − | 0.0777345i | \(-0.975231\pi\) | ||
0.996974 | − | 0.0777345i | \(-0.0247686\pi\) | |||||||
\(522\) | 2.65644e43 | − | 5.80142e43i | 0.874121 | − | 1.90900i | ||||
\(523\) | 1.51005e43 | 0.481907 | 0.240953 | − | 0.970537i | \(-0.422540\pi\) | ||||
0.240953 | + | 0.970537i | \(0.422540\pi\) | |||||||
\(524\) | − | 4.53072e43i | − | 1.40238i | ||||||
\(525\) | −2.76992e43 | − | 4.31482e43i | −0.831607 | − | 1.29543i | ||||
\(526\) | −8.68297e43 | −2.52870 | ||||||||
\(527\) | 3.56302e42i | 0.100658i | ||||||||
\(528\) | −7.37705e42 | + | 4.73573e42i | −0.202181 | + | 0.129791i | ||||
\(529\) | 3.75143e43 | 0.997485 | ||||||||
\(530\) | 1.51002e44i | 3.89555i | ||||||||
\(531\) | −2.23461e43 | − | 1.02321e43i | −0.559357 | − | 0.256126i | ||||
\(532\) | 7.01188e43 | 1.70313 | ||||||||
\(533\) | 1.90302e43i | 0.448547i | ||||||||
\(534\) | 1.06728e43 | + | 1.66255e43i | 0.244129 | + | 0.380290i | ||||
\(535\) | −3.77033e43 | −0.836987 | ||||||||
\(536\) | 2.03496e43i | 0.438449i | ||||||||
\(537\) | 3.22534e43 | − | 2.07052e43i | 0.674508 | − | 0.433004i | ||||
\(538\) | 1.15492e43 | 0.234442 | ||||||||
\(539\) | − | 8.51059e42i | − | 0.167702i | ||||||
\(540\) | 1.81955e43 | + | 1.27915e44i | 0.348069 | + | 2.44692i | ||||
\(541\) | −5.59972e43 | −1.03994 | −0.519972 | − | 0.854183i | \(-0.674058\pi\) | ||||
−0.519972 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(542\) | − | 7.13687e43i | − | 1.28682i | ||||||
\(543\) | 2.77360e43 | + | 4.32055e43i | 0.485564 | + | 0.756383i | ||||
\(544\) | 1.40641e43 | 0.239072 | ||||||||
\(545\) | − | 6.11969e43i | − | 1.01015i | ||||||
\(546\) | −6.49337e43 | + | 4.16845e43i | −1.04085 | + | 0.668178i | ||||
\(547\) | −8.07963e43 | −1.25775 | −0.628875 | − | 0.777506i | \(-0.716484\pi\) | ||||
−0.628875 | + | 0.777506i | \(0.716484\pi\) | |||||||
\(548\) | − | 1.58953e44i | − | 2.40314i | ||||||
\(549\) | 5.05520e43 | − | 1.10401e44i | 0.742302 | − | 1.62112i | ||||
\(550\) | 1.94293e44 | 2.77112 | ||||||||
\(551\) | 1.17849e44i | 1.63268i | ||||||||
\(552\) | −1.62495e42 | − | 2.53125e42i | −0.0218682 | − | 0.0340651i | ||||
\(553\) | −1.14150e44 | −1.49236 | ||||||||
\(554\) | − | 1.58487e44i | − | 2.01297i | ||||||
\(555\) | −3.00400e43 | + | 1.92843e43i | −0.370691 | + | 0.237967i | ||||
\(556\) | −1.20468e44 | −1.44436 | ||||||||
\(557\) | 6.48513e43i | 0.755501i | 0.925907 | + | 0.377751i | \(0.123302\pi\) | ||||
−0.925907 | + | 0.377751i | \(0.876698\pi\) | |||||||
\(558\) | −6.28318e43 | − | 2.87703e43i | −0.711266 | − | 0.325684i | ||||
\(559\) | 7.61584e43 | 0.837777 | ||||||||
\(560\) | − | 3.23816e43i | − | 0.346171i | ||||||
\(561\) | 1.10310e43 | + | 1.71834e43i | 0.114606 | + | 0.178527i | ||||
\(562\) | 1.68620e44 | 1.70266 | ||||||||
\(563\) | 1.87769e41i | 0.00184285i | 1.00000 | 0.000921424i | \(0.000293298\pi\) | |||||
−1.00000 | 0.000921424i | \(0.999707\pi\) | ||||||||
\(564\) | 2.28159e41 | − | 1.46468e41i | 0.00217657 | − | 0.00139726i | ||||
\(565\) | 1.87691e44 | 1.74048 | ||||||||
\(566\) | 2.73551e44i | 2.46590i | ||||||||
\(567\) | 6.82842e43 | + | 7.91234e43i | 0.598400 | + | 0.693387i | ||||
\(568\) | 1.04369e43 | 0.0889194 | ||||||||
\(569\) | 1.01006e44i | 0.836661i | 0.908295 | + | 0.418330i | \(0.137385\pi\) | ||||
−0.908295 | + | 0.418330i | \(0.862615\pi\) | |||||||
\(570\) | −2.14314e44 | − | 3.33847e44i | −1.72605 | − | 2.68874i | ||||
\(571\) | 1.16891e44 | 0.915385 | 0.457692 | − | 0.889111i | \(-0.348676\pi\) | ||||
0.457692 | + | 0.889111i | \(0.348676\pi\) | |||||||
\(572\) | − | 1.75879e44i | − | 1.33930i | ||||||
\(573\) | −1.41151e44 | + | 9.06128e43i | −1.04523 | + | 0.670989i | ||||
\(574\) | 1.06014e44 | 0.763437 | ||||||||
\(575\) | − | 1.20354e43i | − | 0.0842898i | ||||||
\(576\) | −9.94536e43 | + | 2.17198e44i | −0.677425 | + | 1.47944i | ||||
\(577\) | −2.29862e44 | −1.52284 | −0.761421 | − | 0.648258i | \(-0.775498\pi\) | ||||
−0.761421 | + | 0.648258i | \(0.775498\pi\) | |||||||
\(578\) | 2.35620e44i | 1.51833i | ||||||||
\(579\) | −4.41869e43 | − | 6.88318e43i | −0.276972 | − | 0.431452i | ||||
\(580\) | −5.37231e44 | −3.27577 | ||||||||
\(581\) | 4.38563e43i | 0.260144i | ||||||||
\(582\) | 2.88742e44 | − | 1.85359e44i | 1.66626 | − | 1.06966i | ||||
\(583\) | −2.78419e44 | −1.56316 | ||||||||
\(584\) | − | 5.82972e42i | − | 0.0318451i | ||||||
\(585\) | 2.38763e44 | + | 1.09328e44i | 1.26903 | + | 0.581082i | ||||
\(586\) | 5.69953e44 | 2.94766 | ||||||||
\(587\) | − | 3.36020e44i | − | 1.69105i | −0.533937 | − | 0.845524i | \(-0.679288\pi\) | ||
0.533937 | − | 0.845524i | \(-0.320712\pi\) | |||||||
\(588\) | −2.68307e43 | − | 4.17954e43i | −0.131400 | − | 0.204687i | ||||
\(589\) | 1.27636e44 | 0.608314 | ||||||||
\(590\) | 3.44016e44i | 1.59568i | ||||||||
\(591\) | 1.21594e44 | − | 7.80581e43i | 0.548926 | − | 0.352386i | ||||
\(592\) | −1.41345e43 | −0.0621061 | ||||||||
\(593\) | − | 2.81908e44i | − | 1.20568i | −0.797862 | − | 0.602840i | \(-0.794036\pi\) | ||
0.797862 | − | 0.602840i | \(-0.205964\pi\) | |||||||
\(594\) | −3.92091e44 | + | 5.57740e43i | −1.63231 | + | 0.232193i | ||||
\(595\) | −7.54267e43 | −0.305671 | ||||||||
\(596\) | 1.13177e44i | 0.446496i | ||||||||
\(597\) | 1.79052e44 | + | 2.78916e44i | 0.687684 | + | 1.07123i | ||||
\(598\) | −1.81120e43 | −0.0677249 | ||||||||
\(599\) | − | 1.15173e44i | − | 0.419296i | −0.977777 | − | 0.209648i | \(-0.932768\pi\) | ||
0.977777 | − | 0.209648i | \(-0.0672318\pi\) | |||||||
\(600\) | 3.22074e44 | − | 2.06757e44i | 1.14166 | − | 0.732893i | ||||
\(601\) | −3.44390e44 | −1.18866 | −0.594332 | − | 0.804220i | \(-0.702583\pi\) | ||||
−0.594332 | + | 0.804220i | \(0.702583\pi\) | |||||||
\(602\) | − | 4.24266e44i | − | 1.42592i | ||||||
\(603\) | 6.90970e43 | − | 1.50902e44i | 0.226142 | − | 0.493875i | ||||
\(604\) | 8.50070e44 | 2.70934 | ||||||||
\(605\) | 4.38952e43i | 0.136248i | ||||||||
\(606\) | 3.03665e44 | + | 4.73031e44i | 0.917978 | + | 1.42997i | ||||
\(607\) | 9.80874e43 | 0.288798 | 0.144399 | − | 0.989520i | \(-0.453875\pi\) | ||||
0.144399 | + | 0.989520i | \(0.453875\pi\) | |||||||
\(608\) | − | 5.03808e44i | − | 1.44480i | ||||||
\(609\) | −3.65707e44 | + | 2.34767e44i | −1.02154 | + | 0.655784i | ||||
\(610\) | −1.69961e45 | −4.62458 | ||||||||
\(611\) | − | 5.51062e41i | − | 0.00146063i | ||||||
\(612\) | 1.08346e44 | + | 4.96109e43i | 0.279762 | + | 0.128101i | ||||
\(613\) | 4.37991e44 | 1.10179 | 0.550893 | − | 0.834576i | \(-0.314287\pi\) | ||||
0.550893 | + | 0.834576i | \(0.314287\pi\) | |||||||
\(614\) | 4.31606e44i | 1.05777i | ||||||||
\(615\) | −1.94908e44 | − | 3.03617e44i | −0.465402 | − | 0.724976i | ||||
\(616\) | −3.30723e44 | −0.769437 | ||||||||
\(617\) | − | 5.00298e43i | − | 0.113414i | −0.998391 | − | 0.0567069i | \(-0.981940\pi\) | ||
0.998391 | − | 0.0567069i | \(-0.0180601\pi\) | |||||||
\(618\) | −1.96256e44 | + | 1.25987e44i | −0.433518 | + | 0.278299i | ||||
\(619\) | 1.56567e44 | 0.337015 | 0.168508 | − | 0.985700i | \(-0.446105\pi\) | ||||
0.168508 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(620\) | 5.81843e44i | 1.22050i | ||||||||
\(621\) | 3.45489e42 | + | 2.42879e43i | 0.00706267 | + | 0.0496506i | ||||
\(622\) | 4.28649e44 | 0.853995 | ||||||||
\(623\) | − | 1.34558e44i | − | 0.261276i | ||||||
\(624\) | 5.61718e43 | + | 8.75012e43i | 0.106308 | + | 0.165600i | ||||
\(625\) | 7.81436e43 | 0.144149 | ||||||||
\(626\) | 1.57107e45i | 2.82492i | ||||||||
\(627\) | 6.15550e44 | − | 3.95155e44i | 1.07890 | − | 0.692607i | ||||
\(628\) | −3.75567e44 | −0.641701 | ||||||||
\(629\) | 3.29237e43i | 0.0548401i | ||||||||
\(630\) | 6.09048e44 | − | 1.33011e45i | 0.989014 | − | 2.15992i | ||||
\(631\) | 7.55460e43 | 0.119603 | 0.0598015 | − | 0.998210i | \(-0.480953\pi\) | ||||
0.0598015 | + | 0.998210i | \(0.480953\pi\) | |||||||
\(632\) | − | 8.52059e44i | − | 1.31521i | ||||||
\(633\) | −1.59210e44 | − | 2.48007e44i | −0.239613 | − | 0.373255i | ||||
\(634\) | 1.35011e44 | 0.198125 | ||||||||
\(635\) | 1.48171e45i | 2.12023i | ||||||||
\(636\) | −1.36731e45 | + | 8.77753e44i | −1.90789 | + | 1.22478i | ||||
\(637\) | −1.00946e44 | −0.137360 | ||||||||
\(638\) | − | 1.64675e45i | − | 2.18523i | ||||||
\(639\) | −7.73942e43 | − | 3.54383e43i | −0.100160 | − | 0.0458627i | ||||
\(640\) | 1.82230e45 | 2.30006 | ||||||||
\(641\) | − | 5.20543e44i | − | 0.640808i | −0.947281 | − | 0.320404i | \(-0.896181\pi\) | ||
0.947281 | − | 0.320404i | \(-0.103819\pi\) | |||||||
\(642\) | −3.64350e44 | − | 5.67563e44i | −0.437480 | − | 0.681481i | ||||
\(643\) | 7.31934e44 | 0.857229 | 0.428614 | − | 0.903488i | \(-0.359002\pi\) | ||||
0.428614 | + | 0.903488i | \(0.359002\pi\) | |||||||
\(644\) | 6.06928e43i | 0.0693368i | ||||||||
\(645\) | −1.21507e45 | + | 7.80017e44i | −1.35408 | + | 0.869258i | ||||
\(646\) | −3.65894e44 | −0.397773 | ||||||||
\(647\) | − | 9.70518e44i | − | 1.02928i | −0.857405 | − | 0.514642i | \(-0.827925\pi\) | ||
0.857405 | − | 0.514642i | \(-0.172075\pi\) | |||||||
\(648\) | −5.90606e44 | + | 5.09699e44i | −0.611080 | + | 0.527368i | ||||
\(649\) | −6.34300e44 | −0.640294 | ||||||||
\(650\) | − | 2.30456e45i | − | 2.26974i | ||||||
\(651\) | 2.54262e44 | + | 3.96075e44i | 0.244335 | + | 0.380611i | ||||
\(652\) | 2.05211e44 | 0.192415 | ||||||||
\(653\) | 1.23878e45i | 1.13340i | 0.823923 | + | 0.566702i | \(0.191781\pi\) | ||||
−0.823923 | + | 0.566702i | \(0.808219\pi\) | |||||||
\(654\) | 9.21223e44 | − | 5.91383e44i | 0.822471 | − | 0.527989i | ||||
\(655\) | 1.74587e45 | 1.52108 | ||||||||
\(656\) | − | 1.42859e44i | − | 0.121464i | ||||||
\(657\) | −1.97948e43 | + | 4.32301e43i | −0.0164250 | + | 0.0358707i | ||||
\(658\) | −3.06987e42 | −0.00248603 | ||||||||
\(659\) | 2.31547e43i | 0.0183009i | 0.999958 | + | 0.00915045i | \(0.00291272\pi\) | ||||
−0.999958 | + | 0.00915045i | \(0.997087\pi\) | |||||||
\(660\) | 1.80136e45 | + | 2.80606e45i | 1.38963 | + | 2.16468i | ||||
\(661\) | −2.39852e45 | −1.80601 | −0.903004 | − | 0.429632i | \(-0.858643\pi\) | ||||
−0.903004 | + | 0.429632i | \(0.858643\pi\) | |||||||
\(662\) | 3.12735e45i | 2.29852i | ||||||||
\(663\) | 2.03817e44 | − | 1.30841e44i | 0.146226 | − | 0.0938703i | ||||
\(664\) | −3.27360e44 | −0.229264 | ||||||||
\(665\) | 2.70196e45i | 1.84728i | ||||||||
\(666\) | −5.80590e44 | − | 2.65849e44i | −0.387509 | − | 0.177438i | ||||
\(667\) | −1.02007e44 | −0.0664687 | ||||||||
\(668\) | 3.65380e44i | 0.232445i | ||||||||
\(669\) | −1.26277e45 | − | 1.96707e45i | −0.784345 | − | 1.22181i | ||||
\(670\) | −2.32312e45 | −1.40888 | ||||||||
\(671\) | − | 3.13376e45i | − | 1.85569i | ||||||
\(672\) | 1.56340e45 | − | 1.00363e45i | 0.903986 | − | 0.580318i | ||||
\(673\) | 7.52414e44 | 0.424831 | 0.212415 | − | 0.977179i | \(-0.431867\pi\) | ||||
0.212415 | + | 0.977179i | \(0.431867\pi\) | |||||||
\(674\) | − | 4.39745e45i | − | 2.42461i | ||||||
\(675\) | −3.09038e45 | + | 4.39598e44i | −1.66399 | + | 0.236699i | ||||
\(676\) | 7.84563e44 | 0.412554 | ||||||||
\(677\) | 1.36007e44i | 0.0698464i | 0.999390 | + | 0.0349232i | \(0.0111187\pi\) | ||||
−0.999390 | + | 0.0349232i | \(0.988881\pi\) | |||||||
\(678\) | 1.81377e45 | + | 2.82539e45i | 0.909720 | + | 1.41711i | ||||
\(679\) | −2.33691e45 | −1.14479 | ||||||||
\(680\) | − | 5.63013e44i | − | 0.269387i | ||||||
\(681\) | 1.62807e45 | − | 1.04515e45i | 0.760887 | − | 0.488455i | ||||
\(682\) | −1.78350e45 | −0.814184 | ||||||||
\(683\) | 2.47049e45i | 1.10167i | 0.834614 | + | 0.550835i | \(0.185691\pi\) | ||||
−0.834614 | + | 0.550835i | \(0.814309\pi\) | |||||||
\(684\) | 1.77718e45 | − | 3.88120e45i | 0.774165 | − | 1.69071i | ||||
\(685\) | 6.12510e45 | 2.60654 | ||||||||
\(686\) | 4.05239e45i | 1.68471i | ||||||||
\(687\) | −5.77750e44 | − | 8.99986e44i | −0.234656 | − | 0.365534i | ||||
\(688\) | −5.71718e44 | −0.226865 | ||||||||
\(689\) | 3.30241e45i | 1.28033i | ||||||||
\(690\) | 2.88968e44 | − | 1.85504e44i | 0.109462 | − | 0.0702698i | ||||
\(691\) | −2.79704e43 | −0.0103526 | −0.00517631 | − | 0.999987i | \(-0.501648\pi\) | ||||
−0.00517631 | + | 0.999987i | \(0.501648\pi\) | |||||||
\(692\) | − | 1.04842e44i | − | 0.0379174i | ||||||
\(693\) | 2.45247e45 | + | 1.12297e45i | 0.866705 | + | 0.396859i | ||||
\(694\) | 1.93364e45 | 0.667767 | ||||||||
\(695\) | − | 4.64214e45i | − | 1.56661i | ||||||
\(696\) | −1.75239e45 | − | 2.72977e45i | −0.577940 | − | 0.900282i | ||||
\(697\) | −3.32762e44 | −0.107253 | ||||||||
\(698\) | − | 2.44824e45i | − | 0.771199i | ||||||
\(699\) | 2.95287e45 | − | 1.89561e45i | 0.909095 | − | 0.583598i | ||||
\(700\) | −7.72252e45 | −2.32375 | ||||||||
\(701\) | − | 1.62599e45i | − | 0.478224i | −0.970992 | − | 0.239112i | \(-0.923144\pi\) | ||
0.970992 | − | 0.239112i | \(-0.0768562\pi\) | |||||||
\(702\) | 6.61551e44 | + | 4.65070e45i | 0.190182 | + | 1.33698i | ||||
\(703\) | 1.17940e45 | 0.331419 | ||||||||
\(704\) | 6.16522e45i | 1.69350i | ||||||||
\(705\) | 5.64400e42 | + | 8.79190e42i | 0.00151552 | + | 0.00236079i | ||||
\(706\) | −4.67362e45 | −1.22681 | ||||||||
\(707\) | − | 3.82844e45i | − | 0.982453i | ||||||
\(708\) | −3.11504e45 | + | 1.99971e45i | −0.781504 | + | 0.501690i | ||||
\(709\) | −3.85475e45 | −0.945488 | −0.472744 | − | 0.881200i | \(-0.656736\pi\) | ||||
−0.472744 | + | 0.881200i | \(0.656736\pi\) | |||||||
\(710\) | 1.19148e45i | 0.285727i | ||||||||
\(711\) | −2.89316e45 | + | 6.31842e45i | −0.678359 | + | 1.48148i | ||||
\(712\) | 1.00439e45 | 0.230262 | ||||||||
\(713\) | 1.10478e44i | 0.0247652i | ||||||||
\(714\) | −7.28895e44 | − | 1.13543e45i | −0.159769 | − | 0.248880i | ||||
\(715\) | 6.77734e45 | 1.45266 | ||||||||
\(716\) | − | 5.77260e45i | − | 1.20994i | ||||||
\(717\) | −5.98239e45 | + | 3.84042e45i | −1.22622 | + | 0.787177i | ||||
\(718\) | 1.00374e46 | 2.01201 | ||||||||
\(719\) | 2.74164e45i | 0.537462i | 0.963215 | + | 0.268731i | \(0.0866043\pi\) | ||||
−0.963215 | + | 0.268731i | \(0.913396\pi\) | |||||||
\(720\) | −1.79238e45 | − | 8.20721e44i | −0.343645 | − | 0.157353i | ||||
\(721\) | 1.58838e45 | 0.297845 | ||||||||
\(722\) | 4.46962e45i | 0.819739i | ||||||||
\(723\) | 2.43056e45 | + | 3.78619e45i | 0.436007 | + | 0.679187i | ||||
\(724\) | 7.73277e45 | 1.35681 | ||||||||
\(725\) | − | 1.29793e46i | − | 2.22763i | ||||||
\(726\) | −6.60773e44 | + | 4.24186e44i | −0.110934 | + | 0.0712148i | ||||
\(727\) | −2.80128e45 | −0.460050 | −0.230025 | − | 0.973185i | \(-0.573881\pi\) | ||||
−0.230025 | + | 0.973185i | \(0.573881\pi\) | |||||||
\(728\) | 3.92280e45i | 0.630222i | ||||||||
\(729\) | 6.11030e45 | − | 1.77425e45i | 0.960334 | − | 0.278853i | ||||
\(730\) | 6.65522e44 | 0.102329 | ||||||||
\(731\) | 1.33171e45i | 0.200323i | ||||||||
\(732\) | −9.87960e45 | − | 1.53899e46i | −1.45399 | − | 2.26495i | ||||
\(733\) | −1.89755e45 | −0.273231 | −0.136616 | − | 0.990624i | \(-0.543622\pi\) | ||||
−0.136616 | + | 0.990624i | \(0.543622\pi\) | |||||||
\(734\) | 7.68923e45i | 1.08329i | ||||||||
\(735\) | 1.61055e45 | − | 1.03390e45i | 0.222012 | − | 0.142521i | ||||
\(736\) | 4.36082e44 | 0.0588197 | ||||||||
\(737\) | − | 4.28339e45i | − | 0.565337i | ||||||
\(738\) | 2.68695e45 | − | 5.86807e45i | 0.347023 | − | 0.757868i | ||||
\(739\) | −1.43939e46 | −1.81915 | −0.909573 | − | 0.415544i | \(-0.863591\pi\) | ||||
−0.909573 | + | 0.415544i | \(0.863591\pi\) | |||||||
\(740\) | 5.37646e45i | 0.664949i | ||||||||
\(741\) | −4.68704e45 | − | 7.30121e45i | −0.567293 | − | 0.883697i | ||||
\(742\) | 1.83972e46 | 2.17916 | ||||||||
\(743\) | 2.04644e45i | 0.237234i | 0.992940 | + | 0.118617i | \(0.0378461\pi\) | ||||
−0.992940 | + | 0.118617i | \(0.962154\pi\) | |||||||
\(744\) | −2.95645e45 | + | 1.89791e45i | −0.335432 | + | 0.215332i | ||||
\(745\) | −4.36117e45 | −0.484286 | ||||||||
\(746\) | − | 8.81105e45i | − | 0.957650i | ||||||
\(747\) | 2.42753e45 | + | 1.11155e45i | 0.258247 | + | 0.118250i | ||||
\(748\) | 3.07543e45 | 0.320243 | ||||||||
\(749\) | 4.59353e45i | 0.468207i | ||||||||
\(750\) | 9.55998e45 | + | 1.48920e46i | 0.953842 | + | 1.48584i | ||||
\(751\) | −5.69616e45 | −0.556344 | −0.278172 | − | 0.960531i | \(-0.589729\pi\) | ||||
−0.278172 | + | 0.960531i | \(0.589729\pi\) | |||||||
\(752\) | 4.13680e42i | 0.000395530i | ||||||||
\(753\) | 2.01529e45 | − | 1.29373e45i | 0.188633 | − | 0.121094i | ||||
\(754\) | −1.95325e46 | −1.78985 | ||||||||
\(755\) | 3.27567e46i | 2.93865i | ||||||||
\(756\) | 1.55843e46 | − | 2.21683e45i | 1.36880 | − | 0.194708i | ||||
\(757\) | 1.09110e46 | 0.938272 | 0.469136 | − | 0.883126i | \(-0.344565\pi\) | ||||
0.469136 | + | 0.883126i | \(0.344565\pi\) | |||||||
\(758\) | − | 2.97947e46i | − | 2.50860i | ||||||
\(759\) | 3.42035e44 | + | 5.32803e44i | 0.0281970 | + | 0.0439236i | ||||
\(760\) | −2.01685e46 | −1.62800 | ||||||||
\(761\) | − | 5.51472e45i | − | 0.435882i | −0.975962 | − | 0.217941i | \(-0.930066\pi\) | ||
0.975962 | − | 0.217941i | \(-0.0699341\pi\) | |||||||
\(762\) | −2.23048e46 | + | 1.43187e46i | −1.72631 | + | 1.10821i | ||||
\(763\) | −7.45585e45 | −0.565073 | ||||||||
\(764\) | 2.52628e46i | 1.87494i | ||||||||
\(765\) | −1.91171e45 | + | 4.17501e45i | −0.138944 | + | 0.303441i | ||||
\(766\) | 3.04678e46 | 2.16861 | ||||||||
\(767\) | 7.52360e45i | 0.524445i | ||||||||
\(768\) | 4.73403e45 | + | 7.37440e45i | 0.323185 | + | 0.503439i | ||||
\(769\) | 2.37357e46 | 1.58702 | 0.793508 | − | 0.608560i | \(-0.208253\pi\) | ||||
0.793508 | + | 0.608560i | \(0.208253\pi\) | |||||||
\(770\) | − | 3.77555e46i | − | 2.47245i | ||||||
\(771\) | 1.70566e46 | − | 1.09496e46i | 1.09401 | − | 0.702308i | ||||
\(772\) | −1.23193e46 | −0.773942 | ||||||||
\(773\) | − | 4.02656e45i | − | 0.247778i | −0.992296 | − | 0.123889i | \(-0.960463\pi\) | ||
0.992296 | − | 0.123889i | \(-0.0395366\pi\) | |||||||
\(774\) | −2.34839e46 | − | 1.07531e46i | −1.41551 | − | 0.648155i | ||||
\(775\) | −1.40571e46 | −0.829983 | ||||||||
\(776\) | − | 1.74436e46i | − | 1.00890i | ||||||
\(777\) | 2.34948e45 | + | 3.65989e45i | 0.133118 | + | 0.207363i | ||||
\(778\) | −5.57441e46 | −3.09404 | ||||||||
\(779\) | 1.19203e46i | 0.648170i | ||||||||
\(780\) | 3.32834e46 | − | 2.13665e46i | 1.77302 | − | 1.13820i | ||||
\(781\) | −2.19686e45 | −0.114653 | ||||||||
\(782\) | − | 3.16707e44i | − | 0.0161939i | ||||||
\(783\) | 3.72586e45 | + | 2.61928e46i | 0.186654 | + | 1.31218i | ||||
\(784\) | 7.57801e44 | 0.0371962 | ||||||||
\(785\) | − | 1.44721e46i | − | 0.696013i | ||||||
\(786\) | 1.68714e46 | + | 2.62813e46i | 0.795044 | + | 1.23847i | ||||
\(787\) | −5.78760e45 | −0.267241 | −0.133620 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133620 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(788\) | − | 2.17626e46i | − | 0.984669i | ||||||
\(789\) | 3.02969e46 | − | 1.94493e46i | 1.34328 | − | 0.862325i | ||||
\(790\) | 9.72714e46 | 4.22621 | ||||||||
\(791\) | − | 2.28671e46i | − | 0.973615i | ||||||
\(792\) | −8.38226e45 | + | 1.83061e46i | −0.349750 | + | 0.763824i | ||||
\(793\) | −3.71704e46 | −1.51994 | ||||||||
\(794\) | 5.01408e46i | 2.00939i | ||||||||
\(795\) | −3.38234e46 | − | 5.26882e46i | −1.32844 | − | 2.06937i | ||||
\(796\) | 4.99195e46 | 1.92159 | ||||||||
\(797\) | 1.60304e46i | 0.604797i | 0.953182 | + | 0.302399i | \(0.0977874\pi\) | ||||
−0.953182 | + | 0.302399i | \(0.902213\pi\) | |||||||
\(798\) | −4.06738e46 | + | 2.61107e46i | −1.50407 | + | 0.965546i | ||||
\(799\) | 9.63587e42 | 0.000349255 | ||||||||
\(800\) | 5.54868e46i | 1.97129i | ||||||||
\(801\) | −7.44800e45 | − | 3.41039e45i | −0.259370 | − | 0.118764i | ||||
\(802\) | −7.07613e46 | −2.41549 | ||||||||
\(803\) | 1.22710e45i | 0.0410611i | ||||||||
\(804\) | −1.35039e46 | − | 2.10356e46i | −0.442959 | − | 0.690016i | ||||
\(805\) | −2.33874e45 | −0.0752053 | ||||||||
\(806\) | 2.11545e46i | 0.666873i | ||||||||
\(807\) | −4.02978e45 | + | 2.58693e45i | −0.124539 | + | 0.0799482i | ||||
\(808\) | 2.85769e46 | 0.865833 | ||||||||
\(809\) | − | 3.31969e46i | − | 0.986102i | −0.870000 | − | 0.493051i | \(-0.835882\pi\) | ||
0.870000 | − | 0.493051i | \(-0.164118\pi\) | |||||||
\(810\) | −5.81874e46 | − | 6.74238e46i | −1.69460 | − | 1.96360i | ||||
\(811\) | 1.78101e46 | 0.508549 | 0.254275 | − | 0.967132i | \(-0.418163\pi\) | ||||
0.254275 | + | 0.967132i | \(0.418163\pi\) | |||||||
\(812\) | 6.54529e46i | 1.83245i | ||||||||
\(813\) | 1.59861e46 | + | 2.49022e46i | 0.438827 | + | 0.683579i | ||||
\(814\) | −1.64802e46 | −0.443580 | ||||||||
\(815\) | 7.90761e45i | 0.208700i | ||||||||
\(816\) | −1.53005e45 | + | 9.82220e44i | −0.0395970 | + | 0.0254195i | ||||
\(817\) | 4.77049e46 | 1.21063 | ||||||||
\(818\) | − | 9.70101e46i | − | 2.41415i | ||||||
\(819\) | 1.33198e46 | − | 2.90894e46i | 0.325055 | − | 0.709891i | ||||
\(820\) | −5.43403e46 | −1.30047 | ||||||||
\(821\) | − | 1.00347e46i | − | 0.235514i | −0.993042 | − | 0.117757i | \(-0.962430\pi\) | ||
0.993042 | − | 0.117757i | \(-0.0375703\pi\) | |||||||
\(822\) | 5.91906e46 | + | 9.22038e46i | 1.36240 | + | 2.12227i | ||||
\(823\) | 2.83736e46 | 0.640497 | 0.320249 | − | 0.947334i | \(-0.396234\pi\) | ||||
0.320249 | + | 0.947334i | \(0.396234\pi\) | |||||||
\(824\) | 1.18563e46i | 0.262490i | ||||||||
\(825\) | −6.77935e46 | + | 4.35203e46i | −1.47206 | + | 0.944994i | ||||
\(826\) | 4.19127e46 | 0.892617 | ||||||||
\(827\) | 3.50954e45i | 0.0733098i | 0.999328 | + | 0.0366549i | \(0.0116702\pi\) | ||||
−0.999328 | + | 0.0366549i | \(0.988330\pi\) | |||||||
\(828\) | 3.35946e45 | + | 1.53828e45i | 0.0688310 | + | 0.0315173i | ||||
\(829\) | 1.92501e46 | 0.386866 | 0.193433 | − | 0.981113i | \(-0.438038\pi\) | ||||
0.193433 | + | 0.981113i | \(0.438038\pi\) | |||||||
\(830\) | − | 3.73715e46i | − | 0.736701i | ||||||
\(831\) | 3.55000e46 | + | 5.52999e46i | 0.686455 | + | 1.06932i | ||||
\(832\) | 7.31274e46 | 1.38710 | ||||||||
\(833\) | − | 1.76515e45i | − | 0.0328444i | ||||||
\(834\) | 6.98801e46 | − | 4.48599e46i | 1.27555 | − | 0.818844i | ||||
\(835\) | −1.40796e46 | −0.252119 | ||||||||
\(836\) | − | 1.10169e47i | − | 1.93535i | ||||||
\(837\) | 2.83678e46 | − | 4.03525e45i | 0.488898 | − | 0.0695446i | ||||
\(838\) | −1.24067e47 | −2.09775 | ||||||||
\(839\) | − | 2.15724e46i | − | 0.357855i | −0.983862 | − | 0.178928i | \(-0.942737\pi\) | ||
0.983862 | − | 0.178928i | \(-0.0572628\pi\) | |||||||
\(840\) | −4.01775e46 | − | 6.25861e46i | −0.653904 | − | 1.01861i | ||||
\(841\) | −4.73841e46 | −0.756653 | ||||||||
\(842\) | − | 1.05273e46i | − | 0.164939i | ||||||
\(843\) | −5.88355e46 | + | 3.77697e46i | −0.904478 | + | 0.580634i | ||||
\(844\) | −4.43875e46 | −0.669548 | ||||||||
\(845\) | 3.02324e46i | 0.447472i | ||||||||
\(846\) | −7.78067e43 | + | 1.69923e44i | −0.00113003 | + | 0.00246789i | ||||
\(847\) | 5.34792e45 | 0.0762167 | ||||||||
\(848\) | − | 2.47910e46i | − | 0.346706i | ||||||
\(849\) | −6.12735e46 | − | 9.54483e46i | −0.840910 | − | 1.30992i | ||||
\(850\) | 4.02976e46 | 0.542721 | ||||||||
\(851\) | 1.02086e45i | 0.0134925i | ||||||||
\(852\) | −1.07887e46 | + | 6.92587e45i | −0.139938 | + | 0.0898341i | ||||
\(853\) | 8.01950e46 | 1.02085 | 0.510426 | − | 0.859922i | \(-0.329488\pi\) | ||||
0.510426 | + | 0.859922i | \(0.329488\pi\) | |||||||
\(854\) | 2.07070e47i | 2.58697i | ||||||||
\(855\) | 1.49559e47 | + | 6.84820e46i | 1.83381 | + | 0.839689i | ||||
\(856\) | −3.42879e46 | −0.412629 | ||||||||
\(857\) | 1.07502e47i | 1.26976i | 0.772610 | + | 0.634880i | \(0.218951\pi\) | ||||
−0.772610 | + | 0.634880i | \(0.781049\pi\) | |||||||
\(858\) | 6.54936e46 | + | 1.02022e47i | 0.759281 | + | 1.18276i | ||||
\(859\) | −6.14759e46 | −0.699543 | −0.349772 | − | 0.936835i | \(-0.613741\pi\) | ||||
−0.349772 | + | 0.936835i | \(0.613741\pi\) | |||||||
\(860\) | 2.17468e47i | 2.42896i | ||||||||
\(861\) | −3.69908e46 | + | 2.37464e46i | −0.405549 | + | 0.260344i | ||||
\(862\) | −1.27701e47 | −1.37429 | ||||||||
\(863\) | − | 1.62772e47i | − | 1.71952i | −0.510698 | − | 0.859760i | \(-0.670613\pi\) | ||
0.510698 | − | 0.859760i | \(-0.329387\pi\) | |||||||
\(864\) | −1.59281e46 | − | 1.11974e47i | −0.165175 | − | 1.16118i | ||||
\(865\) | 4.04000e45 | 0.0411267 | ||||||||
\(866\) | − | 1.95869e47i | − | 1.95740i | ||||||
\(867\) | −5.27772e46 | − | 8.22133e46i | −0.517775 | − | 0.806559i | ||||
\(868\) | 7.08881e46 | 0.682744 | ||||||||
\(869\) | 1.79350e47i | 1.69584i | ||||||||
\(870\) | 3.11631e47 | − | 2.00053e47i | 2.89290 | − | 1.85711i | ||||
\(871\) | −5.08064e46 | −0.463050 | ||||||||
\(872\) | − | 5.56533e46i | − | 0.497997i | ||||||
\(873\) | −5.92296e46 | + | 1.29352e47i | −0.520368 | + | 1.13644i | ||||
\(874\) | −1.13452e46 | −0.0978655 | ||||||||
\(875\) | − | 1.20527e47i | − | 1.02084i | ||||||
\(876\) | 3.86859e45 | + | 6.02626e45i | 0.0321726 | + | 0.0501167i | ||||
\(877\) | −1.21911e47 | −0.995520 | −0.497760 | − | 0.867315i | \(-0.665844\pi\) | ||||
−0.497760 | + | 0.867315i | \(0.665844\pi\) | |||||||
\(878\) | 8.86812e46i | 0.711081i | ||||||||
\(879\) | −1.98870e47 | + | 1.27665e47i | −1.56584 | + | 1.00520i | ||||
\(880\) | −5.08773e46 | −0.393370 | ||||||||
\(881\) | − | 1.52849e47i | − | 1.16051i | −0.814435 | − | 0.580254i | \(-0.802953\pi\) | ||
0.814435 | − | 0.580254i | \(-0.197047\pi\) | |||||||
\(882\) | 3.11274e46 | + | 1.42530e46i | 0.232084 | + | 0.106270i | ||||
\(883\) | 1.12145e47 | 0.821121 | 0.410561 | − | 0.911833i | \(-0.365333\pi\) | ||||
0.410561 | + | 0.911833i | \(0.365333\pi\) | |||||||
\(884\) | − | 3.64785e46i | − | 0.262301i | ||||||
\(885\) | −7.70571e46 | − | 1.20035e47i | −0.544152 | − | 0.847649i | ||||
\(886\) | 2.08179e47 | 1.44377 | ||||||||
\(887\) | − | 4.57609e46i | − | 0.311685i | −0.987782 | − | 0.155843i | \(-0.950191\pi\) | ||
0.987782 | − | 0.155843i | \(-0.0498093\pi\) | |||||||
\(888\) | −2.73188e46 | + | 1.75374e46i | −0.182749 | + | 0.117316i | ||||
\(889\) | 1.80522e47 | 1.18605 | ||||||||
\(890\) | 1.14661e47i | 0.739906i | ||||||||
\(891\) | 1.24317e47 | − | 1.07287e47i | 0.787928 | − | 0.679989i | ||||
\(892\) | −3.52060e47 | −2.19169 | ||||||||
\(893\) | − | 3.45180e44i | − | 0.00211068i | ||||||
\(894\) | −4.21446e46 | − | 6.56505e46i | −0.253129 | − | 0.394310i | ||||
\(895\) | 2.22442e47 | 1.31235 | ||||||||
\(896\) | − | 2.22017e47i | − | 1.28665i | ||||||
\(897\) | 6.31971e45 | − | 4.05697e45i | 0.0359765 | − | 0.0230953i | ||||
\(898\) | 4.08664e47 | 2.28531 | ||||||||
\(899\) | 1.19142e47i | 0.654503i | ||||||||
\(900\) | −1.95729e47 | + | 4.27455e47i | −1.05627 | + | 2.30680i | ||||
\(901\) | −5.77459e46 | −0.306143 | ||||||||
\(902\) | − | 1.66567e47i | − | 0.867529i | ||||||
\(903\) | 9.50325e46 | + | 1.48036e47i | 0.486260 | + | 0.757467i | ||||
\(904\) | 1.70689e47 | 0.858044 | ||||||||
\(905\) | 2.97975e47i | 1.47164i | ||||||||
\(906\) | −4.93100e47 | + | 3.16548e47i | −2.39268 | + | 1.53599i | ||||
\(907\) | 1.96956e46 | 0.0938970 | 0.0469485 | − | 0.998897i | \(-0.485050\pi\) | ||||
0.0469485 | + | 0.998897i | \(0.485050\pi\) | |||||||
\(908\) | − | 2.91387e47i | − | 1.36489i | ||||||
\(909\) | −2.11911e47 | − | 9.70329e46i | −0.975286 | − | 0.446578i | ||||
\(910\) | −4.47828e47 | −2.02511 | ||||||||
\(911\) | − | 2.69386e46i | − | 0.119696i | −0.998207 | − | 0.0598481i | \(-0.980938\pi\) | ||
0.998207 | − | 0.0598481i | \(-0.0190616\pi\) | |||||||
\(912\) | 3.51855e46 | + | 5.48099e46i | 0.153619 | + | 0.239299i | ||||
\(913\) | 6.89060e46 | 0.295614 | ||||||||
\(914\) | 4.16324e47i | 1.75506i | ||||||||
\(915\) | 5.93034e47 | − | 3.80701e47i | 2.45665 | − | 1.57705i | ||||
\(916\) | −1.61076e47 | −0.655698 | ||||||||
\(917\) | − | 2.12706e47i | − | 0.850885i | ||||||
\(918\) | −8.13222e46 | + | 1.15679e46i | −0.319688 | + | 0.0454748i | ||||
\(919\) | −2.40970e47 | −0.930924 | −0.465462 | − | 0.885068i | \(-0.654112\pi\) | ||||
−0.465462 | + | 0.885068i | \(0.654112\pi\) | |||||||
\(920\) | − | 1.74572e46i | − | 0.0662782i | ||||||
\(921\) | −9.66767e46 | − | 1.50597e47i | −0.360718 | − | 0.561905i | ||||
\(922\) | −1.50052e47 | −0.550232 | ||||||||
\(923\) | 2.60575e46i | 0.0939086i | ||||||||
\(924\) | 3.41873e47 | − | 2.19467e47i | 1.21091 | − | 0.777352i | ||||
\(925\) | −1.29893e47 | −0.452188 | ||||||||
\(926\) | 4.54640e47i | 1.55558i | ||||||||
\(927\) | 4.02580e46 | − | 8.79199e46i | 0.135387 | − | 0.295673i | ||||
\(928\) | 4.70283e47 | 1.55450 | ||||||||
\(929\) | 3.65634e47i | 1.18794i | 0.804486 | + | 0.593971i | \(0.202441\pi\) | ||||
−0.804486 | + | 0.593971i | \(0.797559\pi\) | |||||||
\(930\) | −2.16666e47 | − | 3.37509e47i | −0.691932 | − | 1.07785i | ||||
\(931\) | −6.32319e46 | −0.198491 | ||||||||
\(932\) | − | 5.28494e47i | − | 1.63074i | ||||||
\(933\) | −1.49566e47 | + | 9.60143e46i | −0.453654 | + | 0.291226i | ||||
\(934\) | 4.38862e47 | 1.30851 | ||||||||
\(935\) | 1.18509e47i | 0.347348i | ||||||||
\(936\) | 2.17134e47 | + | 9.94243e46i | 0.625625 | + | 0.286470i | ||||
\(937\) | 5.54359e47 | 1.57021 | 0.785104 | − | 0.619364i | \(-0.212609\pi\) | ||||
0.785104 | + | 0.619364i | \(0.212609\pi\) | |||||||
\(938\) | 2.83034e47i | 0.788122i | ||||||||
\(939\) | −3.51908e47 | − | 5.48182e47i | −0.963340 | − | 1.50064i | ||||
\(940\) | 1.57354e45 | 0.00423480 | ||||||||
\(941\) | − | 2.48801e47i | − | 0.658291i | −0.944279 | − | 0.329146i | \(-0.893239\pi\) | ||
0.944279 | − | 0.329146i | \(-0.106761\pi\) | |||||||
\(942\) | 2.17855e47 | − | 1.39853e47i | 0.566700 | − | 0.363795i | ||||
\(943\) | −1.03179e46 | −0.0263879 | ||||||||
\(944\) | − | 5.64794e46i | − | 0.142016i | ||||||
\(945\) | 8.54236e46 | + | 6.00528e47i | 0.211188 | + | 1.48465i | ||||
\(946\) | −6.66596e47 | −1.62033 | ||||||||
\(947\) | 1.57355e47i | 0.376080i | 0.982161 | + | 0.188040i | \(0.0602134\pi\) | ||||
−0.982161 | + | 0.188040i | \(0.939787\pi\) | |||||||
\(948\) | 5.65424e47 | + | 8.80785e47i | 1.32874 | + | 2.06984i | ||||
\(949\) | 1.45549e46 | 0.0336319 | ||||||||
\(950\) | − | 1.44356e48i | − | 3.27987i | ||||||
\(951\) | −4.71084e46 | + | 3.02414e46i | −0.105247 | + | 0.0675638i | ||||
\(952\) | −6.85941e46 | −0.150694 | ||||||||
\(953\) | 9.60355e46i | 0.207465i | 0.994605 | + | 0.103733i | \(0.0330786\pi\) | ||||
−0.994605 | + | 0.103733i | \(0.966921\pi\) | |||||||
\(954\) | 4.66281e47 | − | 1.01832e48i | 0.990544 | − | 2.16326i | ||||
\(955\) | −9.73478e47 | −2.03363 | ||||||||
\(956\) | 1.07071e48i | 2.19960i | ||||||||
\(957\) | 3.68860e47 | + | 5.74590e47i | 0.745197 | + | 1.16082i | ||||
\(958\) | −1.13875e48 | −2.26245 | ||||||||
\(959\) | − | 7.46245e47i | − | 1.45809i | ||||||
\(960\) | −1.16671e48 | + | 7.48974e47i | −2.24193 | + | 1.43922i | ||||
\(961\) | −4.00108e47 | −0.756142 | ||||||||
\(962\) | 1.95476e47i | 0.363323i | ||||||||
\(963\) | 2.54260e47 | + | 1.16424e47i | 0.464792 | + | 0.212825i | ||||
\(964\) | 6.77639e47 | 1.21833 | ||||||||
\(965\) | − | 4.74712e47i | − | 0.839447i | ||||||
\(966\) | −2.26007e46 | − | 3.52061e46i | −0.0393086 | − | 0.0612327i | ||||
\(967\) | −2.92514e47 | −0.500407 | −0.250203 | − | 0.968193i | \(-0.580498\pi\) | ||||
−0.250203 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(968\) | 3.99188e46i | 0.0671695i | ||||||||
\(969\) | 1.27669e47 | − | 8.19577e46i | 0.211303 | − | 0.135647i | ||||
\(970\) | 1.99136e48 | 3.24192 | ||||||||
\(971\) | 1.19954e48i | 1.92092i | 0.278423 | + | 0.960459i | \(0.410188\pi\) | ||||
−0.278423 | + | 0.960459i | \(0.589812\pi\) | |||||||
\(972\) | 2.72283e47 | − | 9.18807e47i | 0.428904 | − | 1.44732i | ||||
\(973\) | −5.65570e47 | −0.876356 | ||||||||
\(974\) | 1.03665e48i | 1.58012i | ||||||||
\(975\) | 5.16206e47 | + | 8.04116e47i | 0.774015 | + | 1.20572i | ||||
\(976\) | 2.79037e47 | 0.411590 | ||||||||
\(977\) | − | 3.06016e47i | − | 0.444049i | −0.975041 | − | 0.222024i | \(-0.928734\pi\) | ||
0.975041 | − | 0.222024i | \(-0.0712664\pi\) | |||||||
\(978\) | −1.19037e47 | + | 7.64161e46i | −0.169926 | + | 0.109084i | ||||
\(979\) | −2.11414e47 | −0.296900 | ||||||||
\(980\) | − | 2.88250e47i | − | 0.398247i | ||||||
\(981\) | −1.88970e47 | + | 4.12695e47i | −0.256856 | + | 0.560951i | ||||
\(982\) | 4.55970e47 | 0.609751 | ||||||||
\(983\) | − | 1.51512e48i | − | 1.99338i | −0.0813053 | − | 0.996689i | \(-0.525909\pi\) | ||
0.0813053 | − | 0.996689i | \(-0.474091\pi\) | |||||||
\(984\) | −1.77252e47 | − | 2.76113e47i | −0.229440 | − | 0.357409i | ||||
\(985\) | 8.38600e47 | 1.06801 | ||||||||
\(986\) | − | 3.41546e47i | − | 0.427976i | ||||||
\(987\) | 1.07115e45 | − | 6.87630e44i | 0.00132061 | − | 0.000847775i | ||||
\(988\) | −1.30674e48 | −1.58518 | ||||||||
\(989\) | 4.12920e46i | 0.0492861i | ||||||||
\(990\) | −2.08983e48 | − | 9.56922e47i | −2.45442 | − | 1.12386i | ||||
\(991\) | 3.37053e47 | 0.389511 | 0.194756 | − | 0.980852i | \(-0.437609\pi\) | ||||
0.194756 | + | 0.980852i | \(0.437609\pi\) | |||||||
\(992\) | − | 5.09336e47i | − | 0.579185i | ||||||
\(993\) | −7.00504e47 | − | 1.09121e48i | −0.783832 | − | 1.22101i | ||||
\(994\) | 1.45162e47 | 0.159835 | ||||||||
\(995\) | 1.92360e48i | 2.08423i | ||||||||
\(996\) | 3.38397e47 | − | 2.17235e47i | 0.360808 | − | 0.231623i | ||||
\(997\) | 1.52934e48 | 1.60466 | 0.802329 | − | 0.596882i | \(-0.203594\pi\) | ||||
0.802329 | + | 0.596882i | \(0.203594\pi\) | |||||||
\(998\) | − | 9.99916e47i | − | 1.03246i | ||||||
\(999\) | 2.62130e47 | − | 3.72873e46i | 0.266360 | − | 0.0378890i |
(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 | 3.33.b.a.2.9 | yes | 10 | |
3.2 | odd | 2 | inner | 3.33.b.a.2.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.33.b.a.2.2 | ✓ | 10 | 3.2 | odd | 2 | inner | |
3.33.b.a.2.9 | yes | 10 | 1.1 | even | 1 | trivial |