Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,43,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, 43, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 43);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 43 \) |
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: | \(33.5183121516\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(-103520. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.43.b.b.2.11 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.72673e6i | − | 1.77704i | −0.458836 | − | 0.888521i | \(-0.651734\pi\) | ||
0.458836 | − | 0.888521i | \(-0.348266\pi\) | |||||||
\(3\) | −8.44421e9 | − | 6.17368e9i | −0.807258 | − | 0.590198i | ||||
\(4\) | −9.49045e12 | −2.15788 | ||||||||
\(5\) | − | 9.25532e14i | − | 1.94098i | −0.241140 | − | 0.970490i | \(-0.577521\pi\) | ||
0.241140 | − | 0.970490i | \(-0.422479\pi\) | |||||||
\(6\) | −2.30076e16 | + | 3.14693e16i | −1.04881 | + | 1.43453i | ||||
\(7\) | 7.62151e16 | 0.136453 | 0.0682263 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682263 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(8\) | 1.89780e19i | 2.05760i | ||||||||
\(9\) | 3.31903e19 | + | 1.04264e20i | 0.303332 | + | 0.952885i | ||||
\(10\) | −3.44920e21 | −3.44920 | ||||||||
\(11\) | 2.76672e21i | 0.373868i | 0.982372 | + | 0.186934i | \(0.0598551\pi\) | ||||
−0.982372 | + | 0.186934i | \(0.940145\pi\) | |||||||
\(12\) | 8.01393e22 | + | 5.85910e22i | 1.74196 | + | 1.27358i | ||||
\(13\) | −4.84047e22 | −0.195919 | −0.0979596 | − | 0.995190i | \(-0.531232\pi\) | ||||
−0.0979596 | + | 0.995190i | \(0.531232\pi\) | |||||||
\(14\) | − | 2.84033e23i | − | 0.242482i | ||||||
\(15\) | −5.71394e24 | + | 7.81538e24i | −1.14556 | + | 1.56687i | ||||
\(16\) | 2.89863e25 | 1.49856 | ||||||||
\(17\) | 6.14895e25i | 0.889967i | 0.895539 | + | 0.444984i | \(0.146790\pi\) | ||||
−0.895539 | + | 0.444984i | \(0.853210\pi\) | |||||||
\(18\) | 3.88562e26 | − | 1.23691e26i | 1.69332 | − | 0.539034i | ||||
\(19\) | 4.90280e26 | 0.686465 | 0.343233 | − | 0.939250i | \(-0.388478\pi\) | ||||
0.343233 | + | 0.939250i | \(0.388478\pi\) | |||||||
\(20\) | 8.78371e27i | 4.18840i | ||||||||
\(21\) | −6.43576e26 | − | 4.70528e26i | −0.110153 | − | 0.0805341i | ||||
\(22\) | 1.03108e28 | 0.664379 | ||||||||
\(23\) | − | 2.38969e28i | − | 0.605420i | −0.953083 | − | 0.302710i | \(-0.902109\pi\) | ||
0.953083 | − | 0.302710i | \(-0.0978914\pi\) | |||||||
\(24\) | 1.17164e29 | − | 1.60254e29i | 1.21439 | − | 1.66101i | ||||
\(25\) | −6.29235e29 | −2.76741 | ||||||||
\(26\) | 1.80391e29i | 0.348157i | ||||||||
\(27\) | 3.63425e29 | − | 1.08533e30i | 0.317523 | − | 0.948250i | ||||
\(28\) | −7.23315e29 | −0.294448 | ||||||||
\(29\) | − | 3.61235e30i | − | 0.703773i | −0.936043 | − | 0.351886i | \(-0.885540\pi\) | ||
0.936043 | − | 0.351886i | \(-0.114460\pi\) | |||||||
\(30\) | 2.91258e31 | + | 2.12943e31i | 2.78440 | + | 2.03571i | ||||
\(31\) | −1.89712e31 | −0.910960 | −0.455480 | − | 0.890246i | \(-0.650532\pi\) | ||||
−0.455480 | + | 0.890246i | \(0.650532\pi\) | |||||||
\(32\) | − | 2.45581e31i | − | 0.605403i | ||||||
\(33\) | 1.70808e31 | − | 2.33627e31i | 0.220656 | − | 0.301808i | ||||
\(34\) | 2.29155e32 | 1.58151 | ||||||||
\(35\) | − | 7.05395e31i | − | 0.264852i | ||||||
\(36\) | −3.14991e32 | − | 9.89509e32i | −0.654554 | − | 2.05621i | ||||
\(37\) | 2.49339e32 | 0.291443 | 0.145721 | − | 0.989326i | \(-0.453450\pi\) | ||||
0.145721 | + | 0.989326i | \(0.453450\pi\) | |||||||
\(38\) | − | 1.82714e33i | − | 1.21988i | ||||||
\(39\) | 4.08739e32 | + | 2.98835e32i | 0.158157 | + | 0.115631i | ||||
\(40\) | 1.75647e34 | 3.99376 | ||||||||
\(41\) | 5.17484e33i | 0.700545i | 0.936648 | + | 0.350273i | \(0.113911\pi\) | ||||
−0.936648 | + | 0.350273i | \(0.886089\pi\) | |||||||
\(42\) | −1.75353e33 | + | 2.39843e33i | −0.143112 | + | 0.195746i | ||||
\(43\) | −2.37160e34 | −1.18087 | −0.590437 | − | 0.807084i | \(-0.701045\pi\) | ||||
−0.590437 | + | 0.807084i | \(0.701045\pi\) | |||||||
\(44\) | − | 2.62574e34i | − | 0.806762i | ||||||
\(45\) | 9.64994e34 | − | 3.07187e34i | 1.84953 | − | 0.588762i | ||||
\(46\) | −8.90572e34 | −1.07586 | ||||||||
\(47\) | − | 9.55888e34i | − | 0.735109i | −0.930002 | − | 0.367555i | \(-0.880195\pi\) | ||
0.930002 | − | 0.367555i | \(-0.119805\pi\) | |||||||
\(48\) | −2.44767e35 | − | 1.78952e35i | −1.20972 | − | 0.884446i | ||||
\(49\) | −3.06165e35 | −0.981381 | ||||||||
\(50\) | 2.34499e36i | 4.91780i | ||||||||
\(51\) | 3.79617e35 | − | 5.19231e35i | 0.525257 | − | 0.718433i | ||||
\(52\) | 4.59382e35 | 0.422770 | ||||||||
\(53\) | − | 4.75877e35i | − | 0.293563i | −0.989169 | − | 0.146781i | \(-0.953109\pi\) | ||
0.989169 | − | 0.146781i | \(-0.0468914\pi\) | |||||||
\(54\) | −4.04473e36 | − | 1.35438e36i | −1.68508 | − | 0.564252i | ||||
\(55\) | 2.56068e36 | 0.725671 | ||||||||
\(56\) | 1.44641e36i | 0.280765i | ||||||||
\(57\) | −4.14003e36 | − | 3.02683e36i | −0.554155 | − | 0.405151i | ||||
\(58\) | −1.34623e37 | −1.25063 | ||||||||
\(59\) | 1.88111e37i | 1.22045i | 0.792227 | + | 0.610227i | \(0.208922\pi\) | ||||
−0.792227 | + | 0.610227i | \(0.791078\pi\) | |||||||
\(60\) | 5.42278e37 | − | 7.41715e37i | 2.47198 | − | 3.38112i | ||||
\(61\) | 3.45997e37 | 1.11467 | 0.557335 | − | 0.830288i | \(-0.311824\pi\) | ||||
0.557335 | + | 0.830288i | \(0.311824\pi\) | |||||||
\(62\) | 7.07005e37i | 1.61881i | ||||||||
\(63\) | 2.52960e36 | + | 7.94646e36i | 0.0413905 | + | 0.130024i | ||||
\(64\) | 3.59620e37 | 0.422731 | ||||||||
\(65\) | 4.48001e37i | 0.380275i | ||||||||
\(66\) | −8.70666e37 | − | 6.36556e37i | −0.536326 | − | 0.392115i | ||||
\(67\) | −6.89699e37 | −0.309805 | −0.154903 | − | 0.987930i | \(-0.549506\pi\) | ||||
−0.154903 | + | 0.987930i | \(0.549506\pi\) | |||||||
\(68\) | − | 5.83563e38i | − | 1.92044i | ||||||
\(69\) | −1.47532e38 | + | 2.01790e38i | −0.357318 | + | 0.488731i | ||||
\(70\) | −2.62881e38 | −0.470653 | ||||||||
\(71\) | 1.00119e39i | 1.33074i | 0.746514 | + | 0.665370i | \(0.231726\pi\) | ||||
−0.746514 | + | 0.665370i | \(0.768274\pi\) | |||||||
\(72\) | −1.97871e39 | + | 6.29885e38i | −1.96065 | + | 0.624136i | ||||
\(73\) | 1.07589e39 | 0.797971 | 0.398986 | − | 0.916957i | \(-0.369362\pi\) | ||||
0.398986 | + | 0.916957i | \(0.369362\pi\) | |||||||
\(74\) | − | 9.29217e38i | − | 0.517906i | ||||||
\(75\) | 5.31339e39 | + | 3.88470e39i | 2.23401 | + | 1.63332i | ||||
\(76\) | −4.65298e39 | −1.48131 | ||||||||
\(77\) | 2.10866e38i | 0.0510153i | ||||||||
\(78\) | 1.11368e39 | − | 1.52326e39i | 0.205481 | − | 0.281052i | ||||
\(79\) | −8.81067e38 | −0.124406 | −0.0622028 | − | 0.998064i | \(-0.519813\pi\) | ||||
−0.0622028 | + | 0.998064i | \(0.519813\pi\) | |||||||
\(80\) | − | 2.68278e40i | − | 2.90867i | ||||||
\(81\) | −9.76932e39 | + | 6.92109e39i | −0.815979 | + | 0.578082i | ||||
\(82\) | 1.92852e40 | 1.24490 | ||||||||
\(83\) | − | 2.06470e40i | − | 1.03328i | −0.856204 | − | 0.516638i | \(-0.827183\pi\) | ||
0.856204 | − | 0.516638i | \(-0.172817\pi\) | |||||||
\(84\) | 6.10782e39 | + | 4.46552e39i | 0.237696 | + | 0.173783i | ||||
\(85\) | 5.69105e40 | 1.72741 | ||||||||
\(86\) | 8.83830e40i | 2.09846i | ||||||||
\(87\) | −2.23015e40 | + | 3.05035e40i | −0.415365 | + | 0.568127i | ||||
\(88\) | −5.25067e40 | −0.769270 | ||||||||
\(89\) | 9.55931e40i | 1.10468i | 0.833619 | + | 0.552340i | \(0.186265\pi\) | ||||
−0.833619 | + | 0.552340i | \(0.813735\pi\) | |||||||
\(90\) | −1.14480e41 | − | 3.59627e41i | −1.04625 | − | 3.28669i | ||||
\(91\) | −3.68917e39 | −0.0267337 | ||||||||
\(92\) | 2.26792e41i | 1.30642i | ||||||||
\(93\) | 1.60197e41 | + | 1.17122e41i | 0.735380 | + | 0.537647i | ||||
\(94\) | −3.56233e41 | −1.30632 | ||||||||
\(95\) | − | 4.53770e41i | − | 1.33242i | ||||||
\(96\) | −1.51614e41 | + | 2.07373e41i | −0.357308 | + | 0.488717i | ||||
\(97\) | −8.45265e41 | −1.60246 | −0.801229 | − | 0.598358i | \(-0.795820\pi\) | ||||
−0.801229 | + | 0.598358i | \(0.795820\pi\) | |||||||
\(98\) | 1.14099e42i | 1.74395i | ||||||||
\(99\) | −2.88468e41 | + | 9.18282e40i | −0.356253 | + | 0.113406i | ||||
\(100\) | 5.97172e42 | 5.97172 | ||||||||
\(101\) | − | 1.25810e42i | − | 1.02086i | −0.859920 | − | 0.510429i | \(-0.829487\pi\) | ||
0.859920 | − | 0.510429i | \(-0.170513\pi\) | |||||||
\(102\) | −1.93503e42 | − | 1.41473e42i | −1.27669 | − | 0.933403i | ||||
\(103\) | −1.49136e42 | −0.801679 | −0.400840 | − | 0.916148i | \(-0.631282\pi\) | ||||
−0.400840 | + | 0.916148i | \(0.631282\pi\) | |||||||
\(104\) | − | 9.18623e41i | − | 0.403123i | ||||||
\(105\) | −4.35488e41 | + | 5.95650e41i | −0.156315 | + | 0.213804i | ||||
\(106\) | −1.77346e42 | −0.521673 | ||||||||
\(107\) | − | 5.91303e42i | − | 1.42807i | −0.700108 | − | 0.714037i | \(-0.746865\pi\) | ||
0.700108 | − | 0.714037i | \(-0.253135\pi\) | |||||||
\(108\) | −3.44906e42 | + | 1.03003e43i | −0.685176 | + | 2.04621i | ||||
\(109\) | 8.08579e42 | 1.32363 | 0.661814 | − | 0.749668i | \(-0.269787\pi\) | ||||
0.661814 | + | 0.749668i | \(0.269787\pi\) | |||||||
\(110\) | − | 9.54297e42i | − | 1.28955i | ||||||
\(111\) | −2.10547e42 | − | 1.53934e42i | −0.235270 | − | 0.172009i | ||||
\(112\) | 2.20919e42 | 0.204482 | ||||||||
\(113\) | 1.58175e43i | 1.21476i | 0.794411 | + | 0.607381i | \(0.207780\pi\) | ||||
−0.794411 | + | 0.607381i | \(0.792220\pi\) | |||||||
\(114\) | −1.12802e43 | + | 1.54287e43i | −0.719969 | + | 0.984756i | ||||
\(115\) | −2.21173e43 | −1.17511 | ||||||||
\(116\) | 3.42829e43i | 1.51866i | ||||||||
\(117\) | −1.60657e42 | − | 5.04685e42i | −0.0594286 | − | 0.186688i | ||||
\(118\) | 7.01037e43 | 2.16880 | ||||||||
\(119\) | 4.68643e42i | 0.121438i | ||||||||
\(120\) | −1.48320e44 | − | 1.08439e44i | −3.22399 | − | 2.35711i | ||||
\(121\) | 4.71090e43 | 0.860223 | ||||||||
\(122\) | − | 1.28944e44i | − | 1.98081i | ||||||
\(123\) | 3.19478e43 | − | 4.36975e43i | 0.413461 | − | 0.565521i | ||||
\(124\) | 1.80045e44 | 1.96574 | ||||||||
\(125\) | 3.71936e44i | 3.43050i | ||||||||
\(126\) | 2.96143e43 | − | 9.42714e42i | 0.231057 | − | 0.0735527i | ||||
\(127\) | −1.40045e44 | −0.925531 | −0.462765 | − | 0.886481i | \(-0.653143\pi\) | ||||
−0.462765 | + | 0.886481i | \(0.653143\pi\) | |||||||
\(128\) | − | 2.42028e44i | − | 1.35661i | ||||||
\(129\) | 2.00263e44 | + | 1.46415e44i | 0.953270 | + | 0.696950i | ||||
\(130\) | 1.66958e44 | 0.675765 | ||||||||
\(131\) | − | 1.97668e44i | − | 0.681146i | −0.940218 | − | 0.340573i | \(-0.889379\pi\) | ||
0.940218 | − | 0.340573i | \(-0.110621\pi\) | |||||||
\(132\) | −1.62105e44 | + | 2.21723e44i | −0.476149 | + | 0.651265i | ||||
\(133\) | 3.73667e43 | 0.0936700 | ||||||||
\(134\) | 2.57032e44i | 0.550537i | ||||||||
\(135\) | −1.00451e45 | − | 3.36361e44i | −1.84054 | − | 0.616306i | ||||
\(136\) | −1.16695e45 | −1.83119 | ||||||||
\(137\) | − | 8.24366e44i | − | 1.10914i | −0.832136 | − | 0.554572i | \(-0.812882\pi\) | ||
0.832136 | − | 0.554572i | \(-0.187118\pi\) | |||||||
\(138\) | 7.52018e44 | + | 5.49811e44i | 0.868495 | + | 0.634969i | ||||
\(139\) | −6.92426e43 | −0.0687168 | −0.0343584 | − | 0.999410i | \(-0.510939\pi\) | ||||
−0.0343584 | + | 0.999410i | \(0.510939\pi\) | |||||||
\(140\) | 6.69451e44i | 0.571518i | ||||||||
\(141\) | −5.90135e44 | + | 8.07171e44i | −0.433860 | + | 0.593423i | ||||
\(142\) | 3.73118e45 | 2.36478 | ||||||||
\(143\) | − | 1.33922e44i | − | 0.0732480i | ||||||
\(144\) | 9.62065e44 | + | 3.02222e45i | 0.454561 | + | 1.42795i | ||||
\(145\) | −3.34335e45 | −1.36601 | ||||||||
\(146\) | − | 4.00954e45i | − | 1.41803i | ||||||
\(147\) | 2.58532e45 | + | 1.89016e45i | 0.792228 | + | 0.579209i | ||||
\(148\) | −2.36633e45 | −0.628898 | ||||||||
\(149\) | − | 1.73231e45i | − | 0.399681i | −0.979828 | − | 0.199841i | \(-0.935958\pi\) | ||
0.979828 | − | 0.199841i | \(-0.0640425\pi\) | |||||||
\(150\) | 1.44772e46 | − | 1.98016e46i | 2.90247 | − | 3.96993i | ||||
\(151\) | −9.40484e45 | −1.63997 | −0.819985 | − | 0.572386i | \(-0.806018\pi\) | ||||
−0.819985 | + | 0.572386i | \(0.806018\pi\) | |||||||
\(152\) | 9.30453e45i | 1.41247i | ||||||||
\(153\) | −6.41113e45 | + | 2.04086e45i | −0.848036 | + | 0.269956i | ||||
\(154\) | 7.85838e44 | 0.0906563 | ||||||||
\(155\) | 1.75584e46i | 1.76816i | ||||||||
\(156\) | −3.87912e45 | − | 2.83608e45i | −0.341284 | − | 0.249518i | ||||
\(157\) | 5.32848e45 | 0.409931 | 0.204966 | − | 0.978769i | \(-0.434292\pi\) | ||||
0.204966 | + | 0.978769i | \(0.434292\pi\) | |||||||
\(158\) | 3.28350e45i | 0.221074i | ||||||||
\(159\) | −2.93791e45 | + | 4.01840e45i | −0.173260 | + | 0.236981i | ||||
\(160\) | −2.27293e46 | −1.17508 | ||||||||
\(161\) | − | 1.82130e45i | − | 0.0826112i | ||||||
\(162\) | 2.57930e46 | + | 3.64076e46i | 1.02728 | + | 1.45003i | ||||
\(163\) | 2.85126e46 | 0.997922 | 0.498961 | − | 0.866624i | \(-0.333715\pi\) | ||||
0.498961 | + | 0.866624i | \(0.333715\pi\) | |||||||
\(164\) | − | 4.91116e46i | − | 1.51169i | ||||||
\(165\) | −2.16230e46 | − | 1.58089e46i | −0.585804 | − | 0.428290i | ||||
\(166\) | −7.69457e46 | −1.83618 | ||||||||
\(167\) | 7.75663e46i | 1.63165i | 0.578298 | + | 0.815826i | \(0.303717\pi\) | ||||
−0.578298 | + | 0.815826i | \(0.696283\pi\) | |||||||
\(168\) | 8.92966e45 | − | 1.22138e46i | 0.165707 | − | 0.226650i | ||||
\(169\) | −5.86979e46 | −0.961616 | ||||||||
\(170\) | − | 2.12090e47i | − | 3.06968i | ||||||
\(171\) | 1.62726e46 | + | 5.11184e46i | 0.208227 | + | 0.654122i | ||||
\(172\) | 2.25075e47 | 2.54818 | ||||||||
\(173\) | − | 5.71829e45i | − | 0.0573189i | −0.999589 | − | 0.0286595i | \(-0.990876\pi\) | ||
0.999589 | − | 0.0286595i | \(-0.00912384\pi\) | |||||||
\(174\) | 1.13678e47 | + | 8.31117e46i | 1.00958 | + | 0.738122i | ||||
\(175\) | −4.79572e46 | −0.377620 | ||||||||
\(176\) | 8.01970e46i | 0.560263i | ||||||||
\(177\) | 1.16134e47 | − | 1.58845e47i | 0.720310 | − | 0.985222i | ||||
\(178\) | 3.56249e47 | 1.96306 | ||||||||
\(179\) | 1.13886e47i | 0.557900i | 0.960306 | + | 0.278950i | \(0.0899864\pi\) | ||||
−0.960306 | + | 0.278950i | \(0.910014\pi\) | |||||||
\(180\) | −9.15822e47 | + | 2.91534e47i | −3.99106 | + | 1.27048i | ||||
\(181\) | −1.93929e47 | −0.752302 | −0.376151 | − | 0.926558i | \(-0.622753\pi\) | ||||
−0.376151 | + | 0.926558i | \(0.622753\pi\) | |||||||
\(182\) | 1.37485e46i | 0.0475069i | ||||||||
\(183\) | −2.92167e47 | − | 2.13608e47i | −0.899826 | − | 0.657876i | ||||
\(184\) | 4.53515e47 | 1.24571 | ||||||||
\(185\) | − | 2.30771e47i | − | 0.565685i | ||||||
\(186\) | 4.36482e47 | − | 5.97010e47i | 0.955421 | − | 1.30680i | ||||
\(187\) | −1.70124e47 | −0.332730 | ||||||||
\(188\) | 9.07180e47i | 1.58628i | ||||||||
\(189\) | 2.76984e46 | − | 8.27186e46i | 0.0433269 | − | 0.129391i | ||||
\(190\) | −1.69108e48 | −2.36776 | ||||||||
\(191\) | − | 1.43772e46i | − | 0.0180291i | −0.999959 | − | 0.00901455i | \(-0.997131\pi\) | ||
0.999959 | − | 0.00901455i | \(-0.00286946\pi\) | |||||||
\(192\) | −3.03671e47 | − | 2.22018e47i | −0.341253 | − | 0.249495i | ||||
\(193\) | 1.62529e48 | 1.63767 | 0.818836 | − | 0.574027i | \(-0.194620\pi\) | ||||
0.818836 | + | 0.574027i | \(0.194620\pi\) | |||||||
\(194\) | 3.15007e48i | 2.84763i | ||||||||
\(195\) | 2.76581e47 | − | 3.78301e47i | 0.224438 | − | 0.306981i | ||||
\(196\) | 2.90564e48 | 2.11770 | ||||||||
\(197\) | − | 4.19882e47i | − | 0.275003i | −0.990502 | − | 0.137501i | \(-0.956093\pi\) | ||
0.990502 | − | 0.137501i | \(-0.0439071\pi\) | |||||||
\(198\) | 3.42219e47 | + | 1.07504e48i | 0.201528 | + | 0.633077i | ||||
\(199\) | −2.81109e47 | −0.148923 | −0.0744613 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744613 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(200\) | − | 1.19416e49i | − | 5.69420i | ||||||
\(201\) | 5.82397e47 | + | 4.25798e47i | 0.250093 | + | 0.182847i | ||||
\(202\) | −4.68859e48 | −1.81411 | ||||||||
\(203\) | − | 2.75316e47i | − | 0.0960317i | ||||||
\(204\) | −3.60273e48 | + | 4.92773e48i | −1.13344 | + | 1.55029i | ||||
\(205\) | 4.78948e48 | 1.35975 | ||||||||
\(206\) | 5.55789e48i | 1.42462i | ||||||||
\(207\) | 2.49158e48 | − | 7.93146e47i | 0.576896 | − | 0.183644i | ||||
\(208\) | −1.40307e48 | −0.293596 | ||||||||
\(209\) | 1.35647e48i | 0.256648i | ||||||||
\(210\) | 2.21982e48 | + | 1.62295e48i | 0.379939 | + | 0.277779i | ||||
\(211\) | −3.62991e48 | −0.562295 | −0.281147 | − | 0.959665i | \(-0.590715\pi\) | ||||
−0.281147 | + | 0.959665i | \(0.590715\pi\) | |||||||
\(212\) | 4.51628e48i | 0.633473i | ||||||||
\(213\) | 6.18106e48 | − | 8.45430e48i | 0.785400 | − | 1.07425i | ||||
\(214\) | −2.20362e49 | −2.53775 | ||||||||
\(215\) | 2.19499e49i | 2.29205i | ||||||||
\(216\) | 2.05974e49 | + | 6.89707e48i | 1.95112 | + | 0.653335i | ||||
\(217\) | −1.44589e48 | −0.124303 | ||||||||
\(218\) | − | 3.01335e49i | − | 2.35214i | ||||||
\(219\) | −9.08503e48 | − | 6.64219e48i | −0.644169 | − | 0.470961i | ||||
\(220\) | −2.43020e49 | −1.56591 | ||||||||
\(221\) | − | 2.97638e48i | − | 0.174362i | ||||||
\(222\) | −5.73669e48 | + | 7.84650e48i | −0.305667 | + | 0.418084i | ||||
\(223\) | 3.36955e49 | 1.63369 | 0.816845 | − | 0.576857i | \(-0.195721\pi\) | ||||
0.816845 | + | 0.576857i | \(0.195721\pi\) | |||||||
\(224\) | − | 1.87169e48i | − | 0.0826088i | ||||||
\(225\) | −2.08845e49 | − | 6.56064e49i | −0.839444 | − | 2.63702i | ||||
\(226\) | 5.89476e49 | 2.15868 | ||||||||
\(227\) | 2.59547e49i | 0.866309i | 0.901320 | + | 0.433154i | \(0.142599\pi\) | ||||
−0.901320 | + | 0.433154i | \(0.857401\pi\) | |||||||
\(228\) | 3.92907e49 | + | 2.87260e49i | 1.19580 | + | 0.874265i | ||||
\(229\) | −4.49974e49 | −1.24923 | −0.624615 | − | 0.780933i | \(-0.714744\pi\) | ||||
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(230\) | 8.24253e49i | 2.08822i | ||||||||
\(231\) | 1.30182e48 | − | 1.78059e48i | 0.0301091 | − | 0.0411825i | ||||
\(232\) | 6.85552e49 | 1.44808 | ||||||||
\(233\) | − | 3.61477e49i | − | 0.697601i | −0.937197 | − | 0.348800i | \(-0.886589\pi\) | ||
0.937197 | − | 0.348800i | \(-0.113411\pi\) | |||||||
\(234\) | −1.88082e49 | + | 5.98724e48i | −0.331753 | + | 0.105607i | ||||
\(235\) | −8.84704e49 | −1.42683 | ||||||||
\(236\) | − | 1.78525e50i | − | 2.63359i | ||||||
\(237\) | 7.43991e48 | + | 5.43943e48i | 0.100428 | + | 0.0734240i | ||||
\(238\) | 1.74650e49 | 0.215801 | ||||||||
\(239\) | 7.67891e49i | 0.868848i | 0.900709 | + | 0.434424i | \(0.143048\pi\) | ||||
−0.900709 | + | 0.434424i | \(0.856952\pi\) | |||||||
\(240\) | −1.65626e50 | + | 2.26539e50i | −1.71669 | + | 2.34805i | ||||
\(241\) | 4.55318e49 | 0.432471 | 0.216236 | − | 0.976341i | \(-0.430622\pi\) | ||||
0.216236 | + | 0.976341i | \(0.430622\pi\) | |||||||
\(242\) | − | 1.75562e50i | − | 1.52865i | ||||||
\(243\) | 1.25223e50 | + | 1.86954e48i | 0.999889 | + | 0.0149281i | ||||
\(244\) | −3.28367e50 | −2.40532 | ||||||||
\(245\) | 2.83365e50i | 1.90484i | ||||||||
\(246\) | −1.62849e50 | − | 1.19061e50i | −1.00495 | − | 0.734737i | ||||
\(247\) | −2.37319e49 | −0.134492 | ||||||||
\(248\) | − | 3.60035e50i | − | 1.87439i | ||||||
\(249\) | −1.27468e50 | + | 1.74347e50i | −0.609838 | + | 0.834121i | ||||
\(250\) | 1.38610e51 | 6.09614 | ||||||||
\(251\) | 1.16717e50i | 0.472048i | 0.971747 | + | 0.236024i | \(0.0758444\pi\) | ||||
−0.971747 | + | 0.236024i | \(0.924156\pi\) | |||||||
\(252\) | −2.40071e49 | − | 7.54155e49i | −0.0893156 | − | 0.280575i | ||||
\(253\) | 6.61160e49 | 0.226347 | ||||||||
\(254\) | 5.21911e50i | 1.64471i | ||||||||
\(255\) | −4.80564e50 | − | 3.51347e50i | −1.39447 | − | 1.01951i | ||||
\(256\) | −7.43810e50 | −1.98803 | ||||||||
\(257\) | 2.35428e50i | 0.579778i | 0.957060 | + | 0.289889i | \(0.0936184\pi\) | ||||
−0.957060 | + | 0.289889i | \(0.906382\pi\) | |||||||
\(258\) | 5.45648e50 | − | 7.46324e50i | 1.23851 | − | 1.69400i | ||||
\(259\) | 1.90034e49 | 0.0397681 | ||||||||
\(260\) | − | 4.25173e50i | − | 0.820588i | ||||||
\(261\) | 3.76637e50 | − | 1.19895e50i | 0.670614 | − | 0.213477i | ||||
\(262\) | −7.36656e50 | −1.21043 | ||||||||
\(263\) | − | 2.93238e50i | − | 0.444784i | −0.974957 | − | 0.222392i | \(-0.928614\pi\) | ||
0.974957 | − | 0.222392i | \(-0.0713864\pi\) | |||||||
\(264\) | 4.43378e50 | + | 3.24160e50i | 0.621000 | + | 0.454022i | ||||
\(265\) | −4.40439e50 | −0.569800 | ||||||||
\(266\) | − | 1.39256e50i | − | 0.166456i | ||||||
\(267\) | 5.90161e50 | − | 8.07208e50i | 0.651980 | − | 0.891762i | ||||
\(268\) | 6.54555e50 | 0.668522 | ||||||||
\(269\) | 9.44885e50i | 0.892444i | 0.894922 | + | 0.446222i | \(0.147231\pi\) | ||||
−0.894922 | + | 0.446222i | \(0.852769\pi\) | |||||||
\(270\) | −1.25353e51 | + | 3.74353e51i | −1.09520 | + | 3.27071i | ||||
\(271\) | −1.90890e50 | −0.154322 | −0.0771611 | − | 0.997019i | \(-0.524586\pi\) | ||||
−0.0771611 | + | 0.997019i | \(0.524586\pi\) | |||||||
\(272\) | 1.78236e51i | 1.33367i | ||||||||
\(273\) | 3.11521e49 | + | 2.27757e49i | 0.0215810 | + | 0.0157782i | ||||
\(274\) | −3.07219e51 | −1.97100 | ||||||||
\(275\) | − | 1.74092e51i | − | 1.03464i | ||||||
\(276\) | 1.40014e51 | − | 1.91508e51i | 0.771048 | − | 1.05462i | ||||
\(277\) | 8.93871e50 | 0.456247 | 0.228123 | − | 0.973632i | \(-0.426741\pi\) | ||||
0.228123 | + | 0.973632i | \(0.426741\pi\) | |||||||
\(278\) | 2.58048e50i | 0.122113i | ||||||||
\(279\) | −6.29660e50 | − | 1.97801e51i | −0.276324 | − | 0.868040i | ||||
\(280\) | 1.33870e51 | 0.544959 | ||||||||
\(281\) | − | 2.69788e51i | − | 1.01904i | −0.860460 | − | 0.509519i | \(-0.829823\pi\) | ||
0.860460 | − | 0.509519i | \(-0.170177\pi\) | |||||||
\(282\) | 3.00811e51 | + | 2.19927e51i | 1.05454 | + | 0.770987i | ||||
\(283\) | −6.26675e50 | −0.203952 | −0.101976 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101976 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(284\) | − | 9.50179e51i | − | 2.87157i | ||||||
\(285\) | −2.80143e51 | + | 3.83173e51i | −0.786389 | + | 1.07560i | ||||
\(286\) | −4.99091e50 | −0.130165 | ||||||||
\(287\) | 3.94401e50i | 0.0955913i | ||||||||
\(288\) | 2.56051e51 | − | 8.15090e50i | 0.576879 | − | 0.183638i | ||||
\(289\) | 9.92731e50 | 0.207959 | ||||||||
\(290\) | 1.24597e52i | 2.42746i | ||||||||
\(291\) | 7.13759e51 | + | 5.21840e51i | 1.29360 | + | 0.945767i | ||||
\(292\) | −1.02107e52 | −1.72192 | ||||||||
\(293\) | − | 8.06847e50i | − | 0.126640i | −0.997993 | − | 0.0633200i | \(-0.979831\pi\) | ||
0.997993 | − | 0.0633200i | \(-0.0201689\pi\) | |||||||
\(294\) | 7.04412e51 | − | 9.63478e51i | 1.02928 | − | 1.40782i | ||||
\(295\) | 1.74102e52 | 2.36888 | ||||||||
\(296\) | 4.73194e51i | 0.599671i | ||||||||
\(297\) | 3.00280e51 | + | 1.00549e51i | 0.354521 | + | 0.118712i | ||||
\(298\) | −6.45585e51 | −0.710251 | ||||||||
\(299\) | 1.15672e51i | 0.118613i | ||||||||
\(300\) | −5.04265e52 | − | 3.68675e52i | −4.82072 | − | 3.52450i | ||||
\(301\) | −1.80752e51 | −0.161133 | ||||||||
\(302\) | 3.50493e52i | 2.91429i | ||||||||
\(303\) | −7.76709e51 | + | 1.06236e52i | −0.602509 | + | 0.824096i | ||||
\(304\) | 1.42114e52 | 1.02871 | ||||||||
\(305\) | − | 3.20231e52i | − | 2.16355i | ||||||
\(306\) | 7.60572e51 | + | 2.38925e52i | 0.479723 | + | 1.50700i | ||||
\(307\) | −2.81133e52 | −1.65579 | −0.827896 | − | 0.560881i | \(-0.810462\pi\) | ||||
−0.827896 | + | 0.560881i | \(0.810462\pi\) | |||||||
\(308\) | − | 2.00121e51i | − | 0.110085i | ||||||
\(309\) | 1.25934e52 | + | 9.20718e51i | 0.647162 | + | 0.473150i | ||||
\(310\) | 6.54355e52 | 3.14209 | ||||||||
\(311\) | 1.39156e49i | 0.000624500i | 1.00000 | 0.000312250i | \(9.93923e-5\pi\) | |||||
−1.00000 | 0.000312250i | \(0.999901\pi\) | ||||||||
\(312\) | −5.67129e51 | + | 7.75705e51i | −0.237922 | + | 0.325424i | ||||
\(313\) | −1.83072e52 | −0.718110 | −0.359055 | − | 0.933316i | \(-0.616901\pi\) | ||||
−0.359055 | + | 0.933316i | \(0.616901\pi\) | |||||||
\(314\) | − | 1.98578e52i | − | 0.728465i | ||||||
\(315\) | 7.35470e51 | − | 2.34123e51i | 0.252373 | − | 0.0803382i | ||||
\(316\) | 8.36172e51 | 0.268452 | ||||||||
\(317\) | − | 1.45252e52i | − | 0.436394i | −0.975905 | − | 0.218197i | \(-0.929983\pi\) | ||
0.975905 | − | 0.218197i | \(-0.0700175\pi\) | |||||||
\(318\) | 1.49755e52 | + | 1.09488e52i | 0.421125 | + | 0.307891i | ||||
\(319\) | 9.99437e51 | 0.263118 | ||||||||
\(320\) | − | 3.32840e52i | − | 0.820513i | ||||||
\(321\) | −3.65052e52 | + | 4.99309e52i | −0.842847 | + | 1.15282i | ||||
\(322\) | −6.78750e51 | −0.146804 | ||||||||
\(323\) | 3.01471e52i | 0.610932i | ||||||||
\(324\) | 9.27152e52 | − | 6.56842e52i | 1.76078 | − | 1.24743i | ||||
\(325\) | 3.04579e52 | 0.542188 | ||||||||
\(326\) | − | 1.06259e53i | − | 1.77335i | ||||||
\(327\) | −6.82781e52 | − | 4.99191e52i | −1.06851 | − | 0.781203i | ||||
\(328\) | −9.82081e52 | −1.44144 | ||||||||
\(329\) | − | 7.28530e51i | − | 0.100308i | ||||||
\(330\) | −5.89153e52 | + | 8.05829e52i | −0.761088 | + | 1.04100i | ||||
\(331\) | −1.47798e53 | −1.79176 | −0.895881 | − | 0.444294i | \(-0.853455\pi\) | ||||
−0.895881 | + | 0.444294i | \(0.853455\pi\) | |||||||
\(332\) | 1.95949e53i | 2.22968i | ||||||||
\(333\) | 8.27562e51 | + | 2.59970e52i | 0.0884040 | + | 0.277711i | ||||
\(334\) | 2.89069e53 | 2.89951 | ||||||||
\(335\) | 6.38339e52i | 0.601326i | ||||||||
\(336\) | −1.86549e52 | − | 1.36389e52i | −0.165070 | − | 0.120685i | ||||
\(337\) | 1.02469e53 | 0.851851 | 0.425926 | − | 0.904758i | \(-0.359949\pi\) | ||||
0.425926 | + | 0.904758i | \(0.359949\pi\) | |||||||
\(338\) | 2.18751e53i | 1.70883i | ||||||||
\(339\) | 9.76524e52 | − | 1.33567e53i | 0.716950 | − | 0.980627i | ||||
\(340\) | −5.40106e53 | −3.72754 | ||||||||
\(341\) | − | 5.24880e52i | − | 0.340579i | ||||||
\(342\) | 1.90504e53 | − | 6.06434e52i | 1.16240 | − | 0.370028i | ||||
\(343\) | −4.71114e52 | −0.270365 | ||||||||
\(344\) | − | 4.50081e53i | − | 2.42976i | ||||||
\(345\) | 1.86763e53 | + | 1.36545e53i | 0.948617 | + | 0.693547i | ||||
\(346\) | −2.13105e52 | −0.101858 | ||||||||
\(347\) | 3.43095e53i | 1.54346i | 0.635949 | + | 0.771731i | \(0.280609\pi\) | ||||
−0.635949 | + | 0.771731i | \(0.719391\pi\) | |||||||
\(348\) | 2.11651e53 | − | 2.89492e53i | 0.896308 | − | 1.22595i | ||||
\(349\) | −2.94558e53 | −1.17446 | −0.587228 | − | 0.809421i | \(-0.699781\pi\) | ||||
−0.587228 | + | 0.809421i | \(0.699781\pi\) | |||||||
\(350\) | 1.78723e53i | 0.671046i | ||||||||
\(351\) | −1.75915e52 | + | 5.25351e52i | −0.0622089 | + | 0.185780i | ||||
\(352\) | 6.79452e52 | 0.226341 | ||||||||
\(353\) | − | 2.46186e53i | − | 0.772671i | −0.922358 | − | 0.386335i | \(-0.873741\pi\) | ||
0.922358 | − | 0.386335i | \(-0.126259\pi\) | |||||||
\(354\) | −5.91971e53 | − | 4.32798e53i | −1.75078 | − | 1.28002i | ||||
\(355\) | 9.26638e53 | 2.58294 | ||||||||
\(356\) | − | 9.07221e53i | − | 2.38376i | ||||||
\(357\) | 2.89325e52 | − | 3.95732e52i | 0.0716727 | − | 0.0980322i | ||||
\(358\) | 4.24422e53 | 0.991412 | ||||||||
\(359\) | 4.66209e53i | 1.02706i | 0.858071 | + | 0.513531i | \(0.171663\pi\) | ||||
−0.858071 | + | 0.513531i | \(0.828337\pi\) | |||||||
\(360\) | 5.82979e53 | + | 1.83136e54i | 1.21144 | + | 3.80559i | ||||
\(361\) | −2.69721e53 | −0.528765 | ||||||||
\(362\) | 7.22720e53i | 1.33687i | ||||||||
\(363\) | −3.97798e53 | − | 2.90836e53i | −0.694422 | − | 0.507702i | ||||
\(364\) | 3.50118e52 | 0.0576880 | ||||||||
\(365\) | − | 9.95769e53i | − | 1.54885i | ||||||
\(366\) | −7.96057e53 | + | 1.08883e54i | −1.16907 | + | 1.59903i | ||||
\(367\) | −5.40062e53 | −0.748955 | −0.374478 | − | 0.927236i | \(-0.622178\pi\) | ||||
−0.374478 | + | 0.927236i | \(0.622178\pi\) | |||||||
\(368\) | − | 6.92683e53i | − | 0.907257i | ||||||
\(369\) | −5.39548e53 | + | 1.71755e53i | −0.667539 | + | 0.212498i | ||||
\(370\) | −8.60019e53 | −1.00525 | ||||||||
\(371\) | − | 3.62690e52i | − | 0.0400574i | ||||||
\(372\) | −1.52034e54 | − | 1.11154e54i | −1.58686 | − | 1.16018i | ||||
\(373\) | 5.62332e53 | 0.554763 | 0.277381 | − | 0.960760i | \(-0.410533\pi\) | ||||
0.277381 | + | 0.960760i | \(0.410533\pi\) | |||||||
\(374\) | 6.34006e53i | 0.591276i | ||||||||
\(375\) | 2.29621e54 | − | 3.14070e54i | 2.02467 | − | 2.76930i | ||||
\(376\) | 1.81408e54 | 1.51256 | ||||||||
\(377\) | 1.74855e53i | 0.137883i | ||||||||
\(378\) | −3.08269e53 | − | 1.03225e53i | −0.229934 | − | 0.0769937i | ||||
\(379\) | −1.60530e54 | −1.13274 | −0.566372 | − | 0.824150i | \(-0.691653\pi\) | ||||
−0.566372 | + | 0.824150i | \(0.691653\pi\) | |||||||
\(380\) | 4.30648e54i | 2.87519i | ||||||||
\(381\) | 1.18257e54 | + | 8.64596e53i | 0.747142 | + | 0.546246i | ||||
\(382\) | −5.35799e52 | −0.0320384 | ||||||||
\(383\) | 2.05660e54i | 1.16406i | 0.813168 | + | 0.582029i | \(0.197741\pi\) | ||||
−0.813168 | + | 0.582029i | \(0.802259\pi\) | |||||||
\(384\) | −1.49420e54 | + | 2.04374e54i | −0.800671 | + | 1.09514i | ||||
\(385\) | 1.95163e53 | 0.0990197 | ||||||||
\(386\) | − | 6.05701e54i | − | 2.91021i | ||||||
\(387\) | −7.87141e53 | − | 2.47272e54i | −0.358197 | − | 1.12524i | ||||
\(388\) | 8.02194e54 | 3.45791 | ||||||||
\(389\) | 2.66324e54i | 1.08760i | 0.839215 | + | 0.543800i | \(0.183015\pi\) | ||||
−0.839215 | + | 0.543800i | \(0.816985\pi\) | |||||||
\(390\) | −1.40982e54 | − | 1.03074e54i | −0.545517 | − | 0.398835i | ||||
\(391\) | 1.46941e54 | 0.538804 | ||||||||
\(392\) | − | 5.81039e54i | − | 2.01929i | ||||||
\(393\) | −1.22034e54 | + | 1.66915e54i | −0.402011 | + | 0.549861i | ||||
\(394\) | −1.56479e54 | −0.488691 | ||||||||
\(395\) | 8.15456e53i | 0.241469i | ||||||||
\(396\) | 2.73769e54 | − | 8.71491e53i | 0.768751 | − | 0.244717i | ||||
\(397\) | −2.65478e54 | −0.707013 | −0.353507 | − | 0.935432i | \(-0.615011\pi\) | ||||
−0.353507 | + | 0.935432i | \(0.615011\pi\) | |||||||
\(398\) | 1.04762e54i | 0.264642i | ||||||||
\(399\) | −3.15532e53 | − | 2.30690e53i | −0.0756159 | − | 0.0552839i | ||||
\(400\) | −1.82392e55 | −4.14712 | ||||||||
\(401\) | − | 2.41130e54i | − | 0.520260i | −0.965574 | − | 0.260130i | \(-0.916235\pi\) | ||
0.965574 | − | 0.260130i | \(-0.0837654\pi\) | |||||||
\(402\) | 1.58683e54 | − | 2.17043e54i | 0.324926 | − | 0.444426i | ||||
\(403\) | 9.18295e53 | 0.178475 | ||||||||
\(404\) | 1.19399e55i | 2.20289i | ||||||||
\(405\) | 6.40569e54 | + | 9.04182e54i | 1.12205 | + | 1.58380i | ||||
\(406\) | −1.02603e54 | −0.170652 | ||||||||
\(407\) | 6.89849e53i | 0.108961i | ||||||||
\(408\) | 9.85395e54 | + | 7.20436e54i | 1.47825 | + | 1.08077i | ||||
\(409\) | 8.57205e53 | 0.122150 | 0.0610752 | − | 0.998133i | \(-0.480547\pi\) | ||||
0.0610752 | + | 0.998133i | \(0.480547\pi\) | |||||||
\(410\) | − | 1.78491e55i | − | 2.41632i | ||||||
\(411\) | −5.08937e54 | + | 6.96112e54i | −0.654615 | + | 0.895366i | ||||
\(412\) | 1.41537e55 | 1.72993 | ||||||||
\(413\) | 1.43369e54i | 0.166534i | ||||||||
\(414\) | −2.95584e54 | − | 9.28543e54i | −0.326342 | − | 1.02517i | ||||
\(415\) | −1.91094e55 | −2.00557 | ||||||||
\(416\) | 1.18873e54i | 0.118610i | ||||||||
\(417\) | 5.84699e53 | + | 4.27482e53i | 0.0554722 | + | 0.0405565i | ||||
\(418\) | 5.05518e54 | 0.456073 | ||||||||
\(419\) | − | 8.87392e54i | − | 0.761414i | −0.924696 | − | 0.380707i | \(-0.875681\pi\) | ||
0.924696 | − | 0.380707i | \(-0.124319\pi\) | |||||||
\(420\) | 4.13298e54 | − | 5.65298e54i | 0.337309 | − | 0.461363i | ||||
\(421\) | −6.71691e54 | −0.521489 | −0.260745 | − | 0.965408i | \(-0.583968\pi\) | ||||
−0.260745 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(422\) | 1.35277e55i | 0.999222i | ||||||||
\(423\) | 9.96644e54 | − | 3.17262e54i | 0.700474 | − | 0.222982i | ||||
\(424\) | 9.03117e54 | 0.604034 | ||||||||
\(425\) | − | 3.86914e55i | − | 2.46290i | ||||||
\(426\) | −3.15069e55 | − | 2.30351e55i | −1.90899 | − | 1.39569i | ||||
\(427\) | 2.63702e54 | 0.152100 | ||||||||
\(428\) | 5.61173e55i | 3.08161i | ||||||||
\(429\) | −8.26792e53 | + | 1.13087e54i | −0.0432308 | + | 0.0591300i | ||||
\(430\) | 8.18012e55 | 4.07307 | ||||||||
\(431\) | 1.57059e55i | 0.744799i | 0.928072 | + | 0.372400i | \(0.121465\pi\) | ||||
−0.928072 | + | 0.372400i | \(0.878535\pi\) | |||||||
\(432\) | 1.05343e55 | − | 3.14597e55i | 0.475827 | − | 1.42101i | ||||
\(433\) | −3.31327e55 | −1.42564 | −0.712822 | − | 0.701345i | \(-0.752583\pi\) | ||||
−0.712822 | + | 0.701345i | \(0.752583\pi\) | |||||||
\(434\) | 5.38844e54i | 0.220891i | ||||||||
\(435\) | 2.82319e55 | + | 2.06408e55i | 1.10272 | + | 0.806216i | ||||
\(436\) | −7.67378e55 | −2.85623 | ||||||||
\(437\) | − | 1.17162e55i | − | 0.415600i | ||||||
\(438\) | −2.47536e55 | + | 3.38574e55i | −0.836918 | + | 1.14472i | ||||
\(439\) | −9.41508e54 | −0.303437 | −0.151719 | − | 0.988424i | \(-0.548481\pi\) | ||||
−0.151719 | + | 0.988424i | \(0.548481\pi\) | |||||||
\(440\) | 4.85966e55i | 1.49314i | ||||||||
\(441\) | −1.01617e55 | − | 3.19219e55i | −0.297684 | − | 0.935143i | ||||
\(442\) | −1.10922e55 | −0.309848 | ||||||||
\(443\) | 4.31274e55i | 1.14888i | 0.818546 | + | 0.574440i | \(0.194780\pi\) | ||||
−0.818546 | + | 0.574440i | \(0.805220\pi\) | |||||||
\(444\) | 1.99818e55 | + | 1.46090e55i | 0.507683 | + | 0.371174i | ||||
\(445\) | 8.84745e55 | 2.14416 | ||||||||
\(446\) | − | 1.25574e56i | − | 2.90313i | ||||||
\(447\) | −1.06947e55 | + | 1.46280e55i | −0.235891 | + | 0.322646i | ||||
\(448\) | 2.74085e54 | 0.0576828 | ||||||||
\(449\) | − | 4.04251e55i | − | 0.811853i | −0.913906 | − | 0.405927i | \(-0.866949\pi\) | ||
0.913906 | − | 0.405927i | \(-0.133051\pi\) | |||||||
\(450\) | −2.44497e56 | + | 7.78309e55i | −4.68609 | + | 1.49173i | ||||
\(451\) | −1.43173e55 | −0.261912 | ||||||||
\(452\) | − | 1.50115e56i | − | 2.62131i | ||||||
\(453\) | 7.94165e55 | + | 5.80625e55i | 1.32388 | + | 0.967907i | ||||
\(454\) | 9.67260e55 | 1.53947 | ||||||||
\(455\) | 3.41444e54i | 0.0518896i | ||||||||
\(456\) | 5.74432e55 | − | 7.85693e55i | 0.833636 | − | 1.14023i | ||||
\(457\) | −9.40516e55 | −1.30355 | −0.651773 | − | 0.758414i | \(-0.725974\pi\) | ||||
−0.651773 | + | 0.758414i | \(0.725974\pi\) | |||||||
\(458\) | 1.67693e56i | 2.21993i | ||||||||
\(459\) | 6.67365e55 | + | 2.23468e55i | 0.843912 | + | 0.282585i | ||||
\(460\) | 2.09903e56 | 2.53574 | ||||||||
\(461\) | 1.25903e56i | 1.45317i | 0.687078 | + | 0.726584i | \(0.258893\pi\) | ||||
−0.687078 | + | 0.726584i | \(0.741107\pi\) | |||||||
\(462\) | −6.63578e54 | − | 4.85152e54i | −0.0731831 | − | 0.0535052i | ||||
\(463\) | 5.75276e55 | 0.606283 | 0.303142 | − | 0.952946i | \(-0.401964\pi\) | ||||
0.303142 | + | 0.952946i | \(0.401964\pi\) | |||||||
\(464\) | − | 1.04709e56i | − | 1.05464i | ||||||
\(465\) | 1.08400e56 | − | 1.48267e56i | 1.04356 | − | 1.42736i | ||||
\(466\) | −1.34713e56 | −1.23967 | ||||||||
\(467\) | − | 1.88059e56i | − | 1.65440i | −0.561911 | − | 0.827198i | \(-0.689934\pi\) | ||
0.561911 | − | 0.827198i | \(-0.310066\pi\) | |||||||
\(468\) | 1.52470e55 | + | 4.78969e55i | 0.128240 | + | 0.402851i | ||||
\(469\) | −5.25655e54 | −0.0422738 | ||||||||
\(470\) | 3.29705e56i | 2.53554i | ||||||||
\(471\) | −4.49948e55 | − | 3.28964e55i | −0.330920 | − | 0.241941i | ||||
\(472\) | −3.56996e56 | −2.51120 | ||||||||
\(473\) | − | 6.56154e55i | − | 0.441491i | ||||||
\(474\) | 2.02713e55 | − | 2.77265e55i | 0.130477 | − | 0.178464i | ||||
\(475\) | −3.08501e56 | −1.89973 | ||||||||
\(476\) | − | 4.44763e55i | − | 0.262049i | ||||||
\(477\) | 4.96166e55 | − | 1.57945e55i | 0.279732 | − | 0.0890471i | ||||
\(478\) | 2.86172e56 | 1.54398 | ||||||||
\(479\) | − | 1.69047e56i | − | 0.872896i | −0.899729 | − | 0.436448i | \(-0.856236\pi\) | ||
0.899729 | − | 0.436448i | \(-0.143764\pi\) | |||||||
\(480\) | 1.91931e56 | + | 1.40323e56i | 0.948590 | + | 0.693527i | ||||
\(481\) | −1.20692e55 | −0.0570992 | ||||||||
\(482\) | − | 1.69685e56i | − | 0.768519i | ||||||
\(483\) | −1.12441e55 | + | 1.53795e55i | −0.0487570 | + | 0.0666886i | ||||
\(484\) | −4.47085e56 | −1.85625 | ||||||||
\(485\) | 7.82320e56i | 3.11034i | ||||||||
\(486\) | 6.96727e54 | − | 4.66671e56i | 0.0265278 | − | 1.77684i | ||||
\(487\) | −5.61969e55 | −0.204929 | −0.102465 | − | 0.994737i | \(-0.532673\pi\) | ||||
−0.102465 | + | 0.994737i | \(0.532673\pi\) | |||||||
\(488\) | 6.56633e56i | 2.29354i | ||||||||
\(489\) | −2.40766e56 | − | 1.76027e56i | −0.805581 | − | 0.588972i | ||||
\(490\) | 1.05602e57 | 3.38498 | ||||||||
\(491\) | − | 3.11506e56i | − | 0.956655i | −0.878182 | − | 0.478327i | \(-0.841243\pi\) | ||
0.878182 | − | 0.478327i | \(-0.158757\pi\) | |||||||
\(492\) | −3.03199e56 | + | 4.14708e56i | −0.892197 | + | 1.22033i | ||||
\(493\) | 2.22122e56 | 0.626335 | ||||||||
\(494\) | 8.84421e55i | 0.238997i | ||||||||
\(495\) | 8.49899e55 | + | 2.66986e56i | 0.220119 | + | 0.691481i | ||||
\(496\) | −5.49905e56 | −1.36513 | ||||||||
\(497\) | 7.63061e55i | 0.181583i | ||||||||
\(498\) | 6.49745e56 | + | 4.75038e56i | 1.48227 | + | 1.08371i | ||||
\(499\) | −5.54023e56 | −1.21176 | −0.605879 | − | 0.795557i | \(-0.707179\pi\) | ||||
−0.605879 | + | 0.795557i | \(0.707179\pi\) | |||||||
\(500\) | − | 3.52983e57i | − | 7.40260i | ||||||
\(501\) | 4.78870e56 | − | 6.54986e56i | 0.962998 | − | 1.31716i | ||||
\(502\) | 4.34973e56 | 0.838849 | ||||||||
\(503\) | 6.48555e56i | 1.19955i | 0.800168 | + | 0.599776i | \(0.204744\pi\) | ||||
−0.800168 | + | 0.599776i | \(0.795256\pi\) | |||||||
\(504\) | −1.50808e56 | + | 4.80067e55i | −0.267536 | + | 0.0851650i | ||||
\(505\) | −1.16441e57 | −1.98147 | ||||||||
\(506\) | − | 2.46396e56i | − | 0.402229i | ||||||
\(507\) | 4.95657e56 | + | 3.62382e56i | 0.776272 | + | 0.567544i | ||||
\(508\) | 1.32909e57 | 1.99718 | ||||||||
\(509\) | 3.07619e56i | 0.443548i | 0.975098 | + | 0.221774i | \(0.0711847\pi\) | ||||
−0.975098 | + | 0.221774i | \(0.928815\pi\) | |||||||
\(510\) | −1.30938e57 | + | 1.79093e57i | −1.81172 | + | 2.47802i | ||||
\(511\) | 8.19989e55 | 0.108885 | ||||||||
\(512\) | 1.70753e57i | 2.17620i | ||||||||
\(513\) | 1.78180e56 | − | 5.32116e56i | 0.217969 | − | 0.650941i | ||||
\(514\) | 8.77374e56 | 1.03029 | ||||||||
\(515\) | 1.38030e57i | 1.55604i | ||||||||
\(516\) | −1.90058e57 | − | 1.38954e57i | −2.05704 | − | 1.50393i | ||||
\(517\) | 2.64467e56 | 0.274834 | ||||||||
\(518\) | − | 7.08203e55i | − | 0.0706696i | ||||||
\(519\) | −3.53029e55 | + | 4.82864e55i | −0.0338295 | + | 0.0462712i | ||||
\(520\) | −8.50215e56 | −0.782453 | ||||||||
\(521\) | − | 8.69046e56i | − | 0.768158i | −0.923300 | − | 0.384079i | \(-0.874519\pi\) | ||
0.923300 | − | 0.384079i | \(-0.125481\pi\) | |||||||
\(522\) | −4.46817e56 | − | 1.40362e57i | −0.379358 | − | 1.19171i | ||||
\(523\) | 2.09639e57 | 1.70977 | 0.854884 | − | 0.518820i | \(-0.173628\pi\) | ||||
0.854884 | + | 0.518820i | \(0.173628\pi\) | |||||||
\(524\) | 1.87596e57i | 1.46983i | ||||||||
\(525\) | 4.04961e56 | + | 2.96072e56i | 0.304837 | + | 0.222871i | ||||
\(526\) | −1.09282e57 | −0.790399 | ||||||||
\(527\) | − | 1.16653e57i | − | 0.810724i | ||||||
\(528\) | 4.95111e56 | − | 6.77200e56i | 0.330666 | − | 0.452277i | ||||
\(529\) | 9.86944e56 | 0.633466 | ||||||||
\(530\) | 1.64139e57i | 1.01256i | ||||||||
\(531\) | −1.96131e57 | + | 6.24346e56i | −1.16295 | + | 0.370203i | ||||
\(532\) | −3.54627e56 | −0.202128 | ||||||||
\(533\) | − | 2.50487e56i | − | 0.137250i | ||||||
\(534\) | −3.00824e57 | − | 2.19937e57i | −1.58470 | − | 1.15860i | ||||
\(535\) | −5.47270e57 | −2.77186 | ||||||||
\(536\) | − | 1.30891e57i | − | 0.637455i | ||||||
\(537\) | 7.03095e56 | − | 9.61676e56i | 0.329272 | − | 0.450370i | ||||
\(538\) | 3.52133e57 | 1.58591 | ||||||||
\(539\) | − | 8.47071e56i | − | 0.366907i | ||||||
\(540\) | 9.53323e57 | + | 3.19222e57i | 3.97165 | + | 1.32991i | ||||
\(541\) | 3.23852e57 | 1.29779 | 0.648895 | − | 0.760878i | \(-0.275232\pi\) | ||||
0.648895 | + | 0.760878i | \(0.275232\pi\) | |||||||
\(542\) | 7.11395e56i | 0.274237i | ||||||||
\(543\) | 1.63758e57 | + | 1.19726e57i | 0.607302 | + | 0.444007i | ||||
\(544\) | 1.51006e57 | 0.538789 | ||||||||
\(545\) | − | 7.48366e57i | − | 2.56914i | ||||||
\(546\) | 8.48790e55 | − | 1.16095e56i | 0.0280385 | − | 0.0383503i | ||||
\(547\) | −1.51432e57 | −0.481376 | −0.240688 | − | 0.970602i | \(-0.577373\pi\) | ||||
−0.240688 | + | 0.970602i | \(0.577373\pi\) | |||||||
\(548\) | 7.82360e57i | 2.39340i | ||||||||
\(549\) | 1.14838e57 | + | 3.60750e57i | 0.338115 | + | 1.06215i | ||||
\(550\) | −6.48792e57 | −1.83861 | ||||||||
\(551\) | − | 1.77107e57i | − | 0.483116i | ||||||
\(552\) | −3.82957e57 | − | 2.79986e57i | −1.00561 | − | 0.735216i | ||||
\(553\) | −6.71506e55 | −0.0169755 | ||||||||
\(554\) | − | 3.33121e57i | − | 0.810769i | ||||||
\(555\) | −1.42470e57 | + | 1.94868e57i | −0.333866 | + | 0.456654i | ||||
\(556\) | 6.57144e56 | 0.148282 | ||||||||
\(557\) | − | 2.75915e56i | − | 0.0599536i | −0.999551 | − | 0.0299768i | \(-0.990457\pi\) | ||
0.999551 | − | 0.0299768i | \(-0.00954335\pi\) | |||||||
\(558\) | −7.37149e57 | + | 2.34657e57i | −1.54254 | + | 0.491039i | ||||
\(559\) | 1.14796e57 | 0.231356 | ||||||||
\(560\) | − | 2.04468e57i | − | 0.396896i | ||||||
\(561\) | 1.43656e57 | + | 1.05029e57i | 0.268599 | + | 0.196377i | ||||
\(562\) | −1.00543e58 | −1.81087 | ||||||||
\(563\) | 3.66567e57i | 0.636030i | 0.948086 | + | 0.318015i | \(0.103016\pi\) | ||||
−0.948086 | + | 0.318015i | \(0.896984\pi\) | |||||||
\(564\) | 5.60064e57 | − | 7.66042e57i | 0.936217 | − | 1.28053i | ||||
\(565\) | 1.46396e58 | 2.35783 | ||||||||
\(566\) | 2.33544e57i | 0.362430i | ||||||||
\(567\) | −7.44569e56 | + | 5.27491e56i | −0.111343 | + | 0.0788808i | ||||
\(568\) | −1.90007e58 | −2.73813 | ||||||||
\(569\) | − | 6.88329e57i | − | 0.955957i | −0.878372 | − | 0.477979i | \(-0.841370\pi\) | ||
0.878372 | − | 0.477979i | \(-0.158630\pi\) | |||||||
\(570\) | 1.42798e58 | + | 1.04402e58i | 1.91139 | + | 1.39745i | ||||
\(571\) | −6.60942e57 | −0.852717 | −0.426359 | − | 0.904554i | \(-0.640204\pi\) | ||||
−0.426359 | + | 0.904554i | \(0.640204\pi\) | |||||||
\(572\) | 1.27098e57i | 0.158060i | ||||||||
\(573\) | −8.87603e55 | + | 1.21404e56i | −0.0106407 | + | 0.0145541i | ||||
\(574\) | 1.46983e57 | 0.169870 | ||||||||
\(575\) | 1.50368e58i | 1.67544i | ||||||||
\(576\) | 1.19359e57 | + | 3.74953e57i | 0.128228 | + | 0.402814i | ||||
\(577\) | 1.34069e57 | 0.138879 | 0.0694393 | − | 0.997586i | \(-0.477879\pi\) | ||||
0.0694393 | + | 0.997586i | \(0.477879\pi\) | |||||||
\(578\) | − | 3.69964e57i | − | 0.369551i | ||||||
\(579\) | −1.37243e58 | − | 1.00340e58i | −1.32202 | − | 0.966551i | ||||
\(580\) | 3.17299e58 | 2.94768 | ||||||||
\(581\) | − | 1.57361e57i | − | 0.140993i | ||||||
\(582\) | 1.94475e58 | − | 2.65999e58i | 1.68067 | − | 2.29878i | ||||
\(583\) | 1.31662e57 | 0.109754 | ||||||||
\(584\) | 2.04182e58i | 1.64190i | ||||||||
\(585\) | −4.67102e57 | + | 1.48693e57i | −0.362359 | + | 0.115350i | ||||
\(586\) | −3.00690e57 | −0.225045 | ||||||||
\(587\) | 2.55179e58i | 1.84266i | 0.388783 | + | 0.921329i | \(0.372896\pi\) | ||||
−0.388783 | + | 0.921329i | \(0.627104\pi\) | |||||||
\(588\) | −2.45358e58 | − | 1.79385e58i | −1.70953 | − | 1.24986i | ||||
\(589\) | −9.30120e57 | −0.625342 | ||||||||
\(590\) | − | 6.48832e58i | − | 4.20959i | ||||||
\(591\) | −2.59222e57 | + | 3.54557e57i | −0.162306 | + | 0.221998i | ||||
\(592\) | 7.22741e57 | 0.436744 | ||||||||
\(593\) | − | 1.87124e57i | − | 0.109139i | −0.998510 | − | 0.0545697i | \(-0.982621\pi\) | ||
0.998510 | − | 0.0545697i | \(-0.0173787\pi\) | |||||||
\(594\) | 3.74720e57 | − | 1.11906e58i | 0.210956 | − | 0.629998i | ||||
\(595\) | 4.33744e57 | 0.235710 | ||||||||
\(596\) | 1.64404e58i | 0.862464i | ||||||||
\(597\) | 2.37374e57 | + | 1.73548e57i | 0.120219 | + | 0.0878938i | ||||
\(598\) | 4.31079e57 | 0.210781 | ||||||||
\(599\) | 3.92182e57i | 0.185150i | 0.995706 | + | 0.0925752i | \(0.0295099\pi\) | ||||
−0.995706 | + | 0.0925752i | \(0.970490\pi\) | |||||||
\(600\) | −7.37237e58 | + | 1.00837e59i | −3.36071 | + | 4.59669i | ||||
\(601\) | 7.48410e57 | 0.329440 | 0.164720 | − | 0.986340i | \(-0.447328\pi\) | ||||
0.164720 | + | 0.986340i | \(0.447328\pi\) | |||||||
\(602\) | 6.73611e57i | 0.286341i | ||||||||
\(603\) | −2.28913e57 | − | 7.19106e57i | −0.0939740 | − | 0.295209i | ||||
\(604\) | 8.92562e58 | 3.53885 | ||||||||
\(605\) | − | 4.36008e58i | − | 1.66968i | ||||||
\(606\) | 3.95914e58 | + | 2.89458e58i | 1.46445 | + | 1.07068i | ||||
\(607\) | −2.11459e58 | −0.755552 | −0.377776 | − | 0.925897i | \(-0.623311\pi\) | ||||
−0.377776 | + | 0.925897i | \(0.623311\pi\) | |||||||
\(608\) | − | 1.20403e58i | − | 0.415588i | ||||||
\(609\) | −1.69971e57 | + | 2.32482e57i | −0.0566777 | + | 0.0775224i | ||||
\(610\) | −1.19342e59 | −3.84472 | ||||||||
\(611\) | 4.62694e57i | 0.144022i | ||||||||
\(612\) | 6.08445e58 | − | 1.93686e58i | 1.82996 | − | 0.582532i | ||||
\(613\) | −7.77952e57 | −0.226091 | −0.113045 | − | 0.993590i | \(-0.536061\pi\) | ||||
−0.113045 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(614\) | 1.04771e59i | 2.94241i | ||||||||
\(615\) | −4.04434e58 | − | 2.95687e58i | −1.09767 | − | 0.802519i | ||||
\(616\) | −4.00180e57 | −0.104969 | ||||||||
\(617\) | − | 4.12643e57i | − | 0.104613i | −0.998631 | − | 0.0523065i | \(-0.983343\pi\) | ||
0.998631 | − | 0.0523065i | \(-0.0166573\pi\) | |||||||
\(618\) | 3.43126e58 | − | 4.69320e58i | 0.840807 | − | 1.15003i | ||||
\(619\) | −5.35791e58 | −1.26909 | −0.634544 | − | 0.772887i | \(-0.718812\pi\) | ||||
−0.634544 | + | 0.772887i | \(0.718812\pi\) | |||||||
\(620\) | − | 1.66637e59i | − | 3.81546i | ||||||
\(621\) | −2.59360e58 | − | 8.68472e57i | −0.574090 | − | 0.192235i | ||||
\(622\) | 5.18595e55 | 0.00110976 | ||||||||
\(623\) | 7.28564e57i | 0.150737i | ||||||||
\(624\) | 1.18478e58 | + | 8.66213e57i | 0.237008 | + | 0.173280i | ||||
\(625\) | 2.01167e59 | 3.89113 | ||||||||
\(626\) | 6.82260e58i | 1.27611i | ||||||||
\(627\) | 8.37439e57 | − | 1.14543e58i | 0.151473 | − | 0.207181i | ||||
\(628\) | −5.05697e58 | −0.884581 | ||||||||
\(629\) | 1.53317e58i | 0.259374i | ||||||||
\(630\) | −8.72511e57 | − | 2.74090e58i | −0.142764 | − | 0.448478i | ||||
\(631\) | 7.12248e58 | 1.12724 | 0.563618 | − | 0.826036i | \(-0.309409\pi\) | ||||
0.563618 | + | 0.826036i | \(0.309409\pi\) | |||||||
\(632\) | − | 1.67209e58i | − | 0.255977i | ||||||
\(633\) | 3.06517e58 | + | 2.24099e58i | 0.453917 | + | 0.331865i | ||||
\(634\) | −5.41316e58 | −0.775490 | ||||||||
\(635\) | 1.29616e59i | 1.79644i | ||||||||
\(636\) | 2.78821e58 | − | 3.81364e58i | 0.373874 | − | 0.511376i | ||||
\(637\) | 1.48198e58 | 0.192271 | ||||||||
\(638\) | − | 3.72463e58i | − | 0.467572i | ||||||
\(639\) | −1.04388e59 | + | 3.32300e58i | −1.26804 | + | 0.403657i | ||||
\(640\) | −2.24005e59 | −2.63316 | ||||||||
\(641\) | 1.15105e59i | 1.30941i | 0.755883 | + | 0.654707i | \(0.227208\pi\) | ||||
−0.755883 | + | 0.654707i | \(0.772792\pi\) | |||||||
\(642\) | 1.86079e59 | + | 1.36045e59i | 2.04862 | + | 1.49777i | ||||
\(643\) | −8.15086e57 | −0.0868506 | −0.0434253 | − | 0.999057i | \(-0.513827\pi\) | ||||
−0.0434253 | + | 0.999057i | \(0.513827\pi\) | |||||||
\(644\) | 1.72850e58i | 0.178265i | ||||||||
\(645\) | 1.35512e59 | − | 1.85349e59i | 1.35277 | − | 1.85028i | ||||
\(646\) | 1.12350e59 | 1.08565 | ||||||||
\(647\) | − | 3.63923e58i | − | 0.340424i | −0.985407 | − | 0.170212i | \(-0.945555\pi\) | ||
0.985407 | − | 0.170212i | \(-0.0544452\pi\) | |||||||
\(648\) | −1.31348e59 | − | 1.85402e59i | −1.18946 | − | 1.67896i | ||||
\(649\) | −5.20449e58 | −0.456289 | ||||||||
\(650\) | − | 1.13508e59i | − | 0.963491i | ||||||
\(651\) | 1.22094e58 | + | 8.92647e57i | 0.100345 | + | 0.0733633i | ||||
\(652\) | −2.70597e59 | −2.15339 | ||||||||
\(653\) | − | 2.30345e59i | − | 1.77501i | −0.460796 | − | 0.887506i | \(-0.652436\pi\) | ||
0.460796 | − | 0.887506i | \(-0.347564\pi\) | |||||||
\(654\) | −1.86035e59 | + | 2.54454e59i | −1.38823 | + | 1.89879i | ||||
\(655\) | −1.82948e59 | −1.32209 | ||||||||
\(656\) | 1.50000e59i | 1.04981i | ||||||||
\(657\) | 3.57091e58 | + | 1.12176e59i | 0.242050 | + | 0.760375i | ||||
\(658\) | −2.71503e58 | −0.178251 | ||||||||
\(659\) | − | 1.39143e59i | − | 0.884848i | −0.896806 | − | 0.442424i | \(-0.854119\pi\) | ||
0.896806 | − | 0.442424i | \(-0.145881\pi\) | |||||||
\(660\) | 2.05211e59 | + | 1.50033e59i | 1.26409 | + | 0.924196i | ||||
\(661\) | 1.94176e59 | 1.15868 | 0.579341 | − | 0.815085i | \(-0.303310\pi\) | ||||
0.579341 | + | 0.815085i | \(0.303310\pi\) | |||||||
\(662\) | 5.50802e59i | 3.18404i | ||||||||
\(663\) | −1.83752e58 | + | 2.51332e58i | −0.102908 | + | 0.140755i | ||||
\(664\) | 3.91838e59 | 2.12607 | ||||||||
\(665\) | − | 3.45841e58i | − | 0.181812i | ||||||
\(666\) | 9.68835e58 | − | 3.08410e58i | 0.493505 | − | 0.157098i | ||||
\(667\) | −8.63241e58 | −0.426078 | ||||||||
\(668\) | − | 7.36139e59i | − | 3.52090i | ||||||
\(669\) | −2.84532e59 | − | 2.08025e59i | −1.31881 | − | 0.964201i | ||||
\(670\) | 2.37891e59 | 1.06858 | ||||||||
\(671\) | 9.57277e58i | 0.416739i | ||||||||
\(672\) | −1.15552e58 | + | 1.58050e58i | −0.0487556 | + | 0.0666867i | ||||
\(673\) | 4.25186e59 | 1.73885 | 0.869426 | − | 0.494064i | \(-0.164489\pi\) | ||||
0.869426 | + | 0.494064i | \(0.164489\pi\) | |||||||
\(674\) | − | 3.81873e59i | − | 1.51378i | ||||||
\(675\) | −2.28680e59 | + | 6.82928e59i | −0.878716 | + | 2.62419i | ||||
\(676\) | 5.57069e59 | 2.07505 | ||||||||
\(677\) | − | 5.18811e59i | − | 1.87347i | −0.350039 | − | 0.936735i | \(-0.613832\pi\) | ||
0.350039 | − | 0.936735i | \(-0.386168\pi\) | |||||||
\(678\) | −4.97766e59 | − | 3.63924e59i | −1.74262 | − | 1.27405i | ||||
\(679\) | −6.44219e58 | −0.218660 | ||||||||
\(680\) | 1.08005e60i | 3.55431i | ||||||||
\(681\) | 1.60236e59 | − | 2.19167e59i | 0.511294 | − | 0.699335i | ||||
\(682\) | −1.95608e59 | −0.605223 | ||||||||
\(683\) | 1.31944e59i | 0.395872i | 0.980215 | + | 0.197936i | \(0.0634237\pi\) | ||||
−0.980215 | + | 0.197936i | \(0.936576\pi\) | |||||||
\(684\) | −1.54434e59 | − | 4.85137e59i | −0.449329 | − | 1.41152i | ||||
\(685\) | −7.62977e59 | −2.15283 | ||||||||
\(686\) | 1.75571e59i | 0.480449i | ||||||||
\(687\) | 3.79967e59 | + | 2.77800e59i | 1.00845 | + | 0.737293i | ||||
\(688\) | −6.87439e59 | −1.76961 | ||||||||
\(689\) | 2.30347e58i | 0.0575146i | ||||||||
\(690\) | 5.08867e59 | − | 6.96016e59i | 1.23246 | − | 1.68573i | ||||
\(691\) | −2.84007e59 | −0.667252 | −0.333626 | − | 0.942705i | \(-0.608272\pi\) | ||||
−0.333626 | + | 0.942705i | \(0.608272\pi\) | |||||||
\(692\) | 5.42691e58i | 0.123687i | ||||||||
\(693\) | −2.19856e58 | + | 6.99870e57i | −0.0486117 | + | 0.0154746i | ||||
\(694\) | 1.27862e60 | 2.74280 | ||||||||
\(695\) | 6.40863e58i | 0.133378i | ||||||||
\(696\) | −5.78894e59 | − | 4.23238e59i | −1.16898 | − | 0.854654i | ||||
\(697\) | −3.18199e59 | −0.623462 | ||||||||
\(698\) | 1.09774e60i | 2.08706i | ||||||||
\(699\) | −2.23165e59 | + | 3.05239e59i | −0.411723 | + | 0.563144i | ||||
\(700\) | 4.55135e59 | 0.814857 | ||||||||
\(701\) | 6.37124e59i | 1.10700i | 0.832851 | + | 0.553498i | \(0.186707\pi\) | ||||
−0.832851 | + | 0.553498i | \(0.813293\pi\) | |||||||
\(702\) | 1.95784e59 | + | 6.55586e58i | 0.330140 | + | 0.110548i | ||||
\(703\) | 1.22246e59 | 0.200065 | ||||||||
\(704\) | 9.94967e58i | 0.158046i | ||||||||
\(705\) | 7.47063e59 | + | 5.46188e59i | 1.15182 | + | 0.842114i | ||||
\(706\) | −9.17468e59 | −1.37307 | ||||||||
\(707\) | − | 9.58860e58i | − | 0.139299i | ||||||
\(708\) | −1.10216e60 | + | 1.50751e60i | −1.55434 | + | 2.12599i | ||||
\(709\) | 9.34454e59 | 1.27934 | 0.639672 | − | 0.768648i | \(-0.279070\pi\) | ||||
0.639672 | + | 0.768648i | \(0.279070\pi\) | |||||||
\(710\) | − | 3.45332e60i | − | 4.58999i | ||||||
\(711\) | −2.92429e58 | − | 9.18633e58i | −0.0377363 | − | 0.118544i | ||||
\(712\) | −1.81416e60 | −2.27299 | ||||||||
\(713\) | 4.53353e59i | 0.551513i | ||||||||
\(714\) | −1.47478e59 | − | 1.07824e59i | −0.174207 | − | 0.127365i | ||||
\(715\) | −1.23949e59 | −0.142173 | ||||||||
\(716\) | − | 1.08083e60i | − | 1.20388i | ||||||
\(717\) | 4.74071e59 | − | 6.48423e59i | 0.512792 | − | 0.701385i | ||||
\(718\) | 1.73743e60 | 1.82513 | ||||||||
\(719\) | − | 1.54952e60i | − | 1.58085i | −0.612560 | − | 0.790424i | \(-0.709860\pi\) | ||
0.612560 | − | 0.790424i | \(-0.290140\pi\) | |||||||
\(720\) | 2.79716e60 | − | 8.90422e59i | 2.77163 | − | 0.882294i | ||||
\(721\) | −1.13664e59 | −0.109391 | ||||||||
\(722\) | 1.00518e60i | 0.939638i | ||||||||
\(723\) | −3.84480e59 | − | 2.81099e59i | −0.349116 | − | 0.255244i | ||||
\(724\) | 1.84047e60 | 1.62338 | ||||||||
\(725\) | 2.27302e60i | 1.94762i | ||||||||
\(726\) | −1.08387e60 | + | 1.48248e60i | −0.902207 | + | 1.23402i | ||||
\(727\) | −1.51238e60 | −1.22304 | −0.611518 | − | 0.791230i | \(-0.709441\pi\) | ||||
−0.611518 | + | 0.791230i | \(0.709441\pi\) | |||||||
\(728\) | − | 7.00129e58i | − | 0.0550072i | ||||||
\(729\) | −1.04587e60 | − | 7.88872e59i | −0.798358 | − | 0.602183i | ||||
\(730\) | −3.71096e60 | −2.75236 | ||||||||
\(731\) | − | 1.45828e60i | − | 1.05094i | ||||||
\(732\) | 2.77280e60 | + | 2.02723e60i | 1.94172 | + | 1.41962i | ||||
\(733\) | 2.51815e59 | 0.171355 | 0.0856776 | − | 0.996323i | \(-0.472694\pi\) | ||||
0.0856776 | + | 0.996323i | \(0.472694\pi\) | |||||||
\(734\) | 2.01266e60i | 1.33093i | ||||||||
\(735\) | 1.74941e60 | − | 2.39279e60i | 1.12423 | − | 1.53770i | ||||
\(736\) | −5.86861e59 | −0.366523 | ||||||||
\(737\) | − | 1.90820e59i | − | 0.115826i | ||||||
\(738\) | 6.40083e59 | + | 2.01075e60i | 0.377618 | + | 1.18624i | ||||
\(739\) | 6.64821e59 | 0.381217 | 0.190608 | − | 0.981666i | \(-0.438954\pi\) | ||||
0.190608 | + | 0.981666i | \(0.438954\pi\) | |||||||
\(740\) | 2.19012e60i | 1.22068i | ||||||||
\(741\) | 2.00397e59 | + | 1.46513e59i | 0.108570 | + | 0.0793768i | ||||
\(742\) | −1.35165e59 | −0.0711837 | ||||||||
\(743\) | − | 9.10560e59i | − | 0.466169i | −0.972456 | − | 0.233085i | \(-0.925118\pi\) | ||
0.972456 | − | 0.233085i | \(-0.0748819\pi\) | |||||||
\(744\) | −2.22274e60 | + | 3.04021e60i | −1.10626 | + | 1.51312i | ||||
\(745\) | −1.60331e60 | −0.775774 | ||||||||
\(746\) | − | 2.09566e60i | − | 0.985836i | ||||||
\(747\) | 2.15273e60 | − | 6.85280e59i | 0.984594 | − | 0.313426i | ||||
\(748\) | 1.61455e60 | 0.717991 | ||||||||
\(749\) | − | 4.50662e59i | − | 0.194865i | ||||||
\(750\) | −1.17045e61 | − | 8.55735e60i | −4.92116 | − | 3.59793i | ||||
\(751\) | −2.23704e59 | −0.0914607 | −0.0457303 | − | 0.998954i | \(-0.514561\pi\) | ||||
−0.0457303 | + | 0.998954i | \(0.514561\pi\) | |||||||
\(752\) | − | 2.77077e60i | − | 1.10160i | ||||||
\(753\) | 7.20574e59 | − | 9.85583e59i | 0.278602 | − | 0.381065i | ||||
\(754\) | 6.51636e59 | 0.245023 | ||||||||
\(755\) | 8.70448e60i | 3.18315i | ||||||||
\(756\) | −2.62871e59 | + | 7.85036e59i | −0.0934941 | + | 0.279211i | ||||
\(757\) | 4.53142e58 | 0.0156755 | 0.00783774 | − | 0.999969i | \(-0.497505\pi\) | ||||
0.00783774 | + | 0.999969i | \(0.497505\pi\) | |||||||
\(758\) | 5.98250e60i | 2.01293i | ||||||||
\(759\) | −5.58297e59 | − | 4.08179e59i | −0.182721 | − | 0.133590i | ||||
\(760\) | 8.61163e60 | 2.74157 | ||||||||
\(761\) | − | 5.57015e60i | − | 1.72500i | −0.506057 | − | 0.862500i | \(-0.668898\pi\) | ||
0.506057 | − | 0.862500i | \(-0.331102\pi\) | |||||||
\(762\) | 3.22211e60 | − | 4.40713e60i | 0.970703 | − | 1.32770i | ||||
\(763\) | 6.16259e59 | 0.180613 | ||||||||
\(764\) | 1.36446e59i | 0.0389046i | ||||||||
\(765\) | 1.88888e60 | + | 5.93370e60i | 0.523979 | + | 1.64602i | ||||
\(766\) | 7.66437e60 | 2.06858 | ||||||||
\(767\) | − | 9.10544e59i | − | 0.239110i | ||||||
\(768\) | 6.28089e60 | + | 4.59204e60i | 1.60485 | + | 1.17333i | ||||
\(769\) | −5.85974e60 | −1.45688 | −0.728442 | − | 0.685107i | \(-0.759755\pi\) | ||||
−0.728442 | + | 0.685107i | \(0.759755\pi\) | |||||||
\(770\) | − | 7.27318e59i | − | 0.175962i | ||||||
\(771\) | 1.45346e60 | − | 1.98800e60i | 0.342184 | − | 0.468031i | ||||
\(772\) | −1.54247e61 | −3.53390 | ||||||||
\(773\) | 1.90869e60i | 0.425565i | 0.977100 | + | 0.212782i | \(0.0682526\pi\) | ||||
−0.977100 | + | 0.212782i | \(0.931747\pi\) | |||||||
\(774\) | −9.21514e60 | + | 2.93346e60i | −1.99959 | + | 0.636531i | ||||
\(775\) | 1.19373e61 | 2.52100 | ||||||||
\(776\) | − | 1.60414e61i | − | 3.29721i | ||||||
\(777\) | −1.60468e59 | − | 1.17321e59i | −0.0321032 | − | 0.0234711i | ||||
\(778\) | 9.92517e60 | 1.93271 | ||||||||
\(779\) | 2.53712e60i | 0.480900i | ||||||||
\(780\) | −2.62488e60 | + | 3.59025e60i | −0.484309 | + | 0.662426i | ||||
\(781\) | −2.77002e60 | −0.497521 | ||||||||
\(782\) | − | 5.47609e60i | − | 0.957477i | ||||||
\(783\) | −3.92060e60 | − | 1.31282e60i | −0.667353 | − | 0.223464i | ||||
\(784\) | −8.87459e60 | −1.47066 | ||||||||
\(785\) | − | 4.93168e60i | − | 0.795668i | ||||||
\(786\) | 6.22048e60 | + | 4.54788e60i | 0.977126 | + | 0.714391i | ||||
\(787\) | −8.42104e60 | −1.28794 | −0.643971 | − | 0.765050i | \(-0.722714\pi\) | ||||
−0.643971 | + | 0.765050i | \(0.722714\pi\) | |||||||
\(788\) | 3.98487e60i | 0.593422i | ||||||||
\(789\) | −1.81036e60 | + | 2.47616e60i | −0.262511 | + | 0.359055i | ||||
\(790\) | 3.03898e60 | 0.429100 | ||||||||
\(791\) | 1.20553e60i | 0.165758i | ||||||||
\(792\) | −1.74271e60 | − | 5.47454e60i | −0.233344 | − | 0.733026i | ||||
\(793\) | −1.67479e60 | −0.218385 | ||||||||
\(794\) | 9.89363e60i | 1.25639i | ||||||||
\(795\) | 3.71916e60 | + | 2.71913e60i | 0.459976 | + | 0.336295i | ||||
\(796\) | 2.66785e60 | 0.321357 | ||||||||
\(797\) | 1.46593e60i | 0.171984i | 0.996296 | + | 0.0859920i | \(0.0274059\pi\) | ||||
−0.996296 | + | 0.0859920i | \(0.972594\pi\) | |||||||
\(798\) | −8.59720e59 | + | 1.17590e60i | −0.0982418 | + | 0.134373i | ||||
\(799\) | 5.87771e60 | 0.654223 | ||||||||
\(800\) | 1.54528e61i | 1.67540i | ||||||||
\(801\) | −9.96689e60 | + | 3.17277e60i | −1.05263 | + | 0.335085i | ||||
\(802\) | −8.98627e60 | −0.924523 | ||||||||
\(803\) | 2.97668e60i | 0.298336i | ||||||||
\(804\) | −5.52720e60 | − | 4.04102e60i | −0.539670 | − | 0.394561i | ||||
\(805\) | −1.68567e60 | −0.160347 | ||||||||
\(806\) | − | 3.42223e60i | − | 0.317157i | ||||||
\(807\) | 5.83342e60 | − | 7.97881e60i | 0.526719 | − | 0.720433i | ||||
\(808\) | 2.38761e61 | 2.10051 | ||||||||
\(809\) | 1.47552e61i | 1.26481i | 0.774638 | + | 0.632405i | \(0.217932\pi\) | ||||
−0.774638 | + | 0.632405i | \(0.782068\pi\) | |||||||
\(810\) | 3.36964e61 | − | 2.38722e61i | 2.81448 | − | 1.99392i | ||||
\(811\) | −2.01099e61 | −1.63671 | −0.818355 | − | 0.574713i | \(-0.805114\pi\) | ||||
−0.818355 | + | 0.574713i | \(0.805114\pi\) | |||||||
\(812\) | 2.61287e60i | 0.207225i | ||||||||
\(813\) | 1.61192e60 | + | 1.17849e60i | 0.124578 | + | 0.0910807i | ||||
\(814\) | 2.57088e60 | 0.193629 | ||||||||
\(815\) | − | 2.63893e61i | − | 1.93695i | ||||||
\(816\) | 1.10037e61 | − | 1.50506e61i | 0.787128 | − | 1.07661i | ||||
\(817\) | −1.16275e61 | −0.810629 | ||||||||
\(818\) | − | 3.19457e60i | − | 0.217067i | ||||||
\(819\) | −1.22445e59 | − | 3.84646e59i | −0.00810920 | − | 0.0254741i | ||||
\(820\) | −4.54543e61 | −2.93416 | ||||||||
\(821\) | − | 7.93309e60i | − | 0.499156i | −0.968355 | − | 0.249578i | \(-0.919708\pi\) | ||
0.968355 | − | 0.249578i | \(-0.0802919\pi\) | |||||||
\(822\) | 2.59422e61 | + | 1.89667e61i | 1.59110 | + | 1.16328i | ||||
\(823\) | 5.15535e60 | 0.308221 | 0.154110 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154110 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(824\) | − | 2.83030e61i | − | 1.64953i | ||||||
\(825\) | −1.07479e61 | + | 1.47007e61i | −0.610645 | + | 0.835226i | ||||
\(826\) | 5.34296e60 | 0.295938 | ||||||||
\(827\) | 2.66521e60i | 0.143918i | 0.997408 | + | 0.0719590i | \(0.0229251\pi\) | ||||
−0.997408 | + | 0.0719590i | \(0.977075\pi\) | |||||||
\(828\) | −2.36462e61 | + | 7.52730e60i | −1.24487 | + | 0.396280i | ||||
\(829\) | 1.95335e61 | 1.00262 | 0.501309 | − | 0.865268i | \(-0.332852\pi\) | ||||
0.501309 | + | 0.865268i | \(0.332852\pi\) | |||||||
\(830\) | 7.12157e61i | 3.56398i | ||||||||
\(831\) | −7.54803e60 | − | 5.51847e60i | −0.368309 | − | 0.269276i | ||||
\(832\) | −1.74073e60 | −0.0828212 | ||||||||
\(833\) | − | 1.88259e61i | − | 0.873396i | ||||||
\(834\) | 1.59311e60 | − | 2.17901e60i | 0.0720706 | − | 0.0985764i | ||||
\(835\) | 7.17901e61 | 3.16700 | ||||||||
\(836\) | − | 1.28735e61i | − | 0.553814i | ||||||
\(837\) | −6.89460e60 | + | 2.05900e61i | −0.289251 | + | 0.863818i | ||||
\(838\) | −3.30707e61 | −1.35307 | ||||||||
\(839\) | − | 4.52741e61i | − | 1.80655i | −0.429067 | − | 0.903273i | \(-0.641157\pi\) | ||
0.429067 | − | 0.903273i | \(-0.358843\pi\) | |||||||
\(840\) | −1.13042e61 | − | 8.26468e60i | −0.439922 | − | 0.321633i | ||||
\(841\) | 1.32970e61 | 0.504704 | ||||||||
\(842\) | 2.50321e61i | 0.926708i | ||||||||
\(843\) | −1.66559e61 | + | 2.27815e61i | −0.601434 | + | 0.822627i | ||||
\(844\) | 3.44495e61 | 1.21336 | ||||||||
\(845\) | 5.43267e61i | 1.86648i | ||||||||
\(846\) | −1.18235e61 | − | 3.71422e61i | −0.396249 | − | 1.24477i | ||||
\(847\) | 3.59041e60 | 0.117380 | ||||||||
\(848\) | − | 1.37939e61i | − | 0.439921i | ||||||
\(849\) | 5.29177e60 | + | 3.86889e60i | 0.164642 | + | 0.120372i | ||||
\(850\) | −1.44192e62 | −4.37668 | ||||||||
\(851\) | − | 5.95842e60i | − | 0.176445i | ||||||
\(852\) | −5.86610e61 | + | 8.02351e61i | −1.69480 | + | 2.31810i | ||||
\(853\) | −5.96149e61 | −1.68045 | −0.840224 | − | 0.542240i | \(-0.817576\pi\) | ||||
−0.840224 | + | 0.542240i | \(0.817576\pi\) | |||||||
\(854\) | − | 9.82746e60i | − | 0.270287i | ||||||
\(855\) | 4.73117e61 | − | 1.50608e61i | 1.26964 | − | 0.404165i | ||||
\(856\) | 1.12217e62 | 2.93840 | ||||||||
\(857\) | 6.42053e59i | 0.0164049i | 0.999966 | + | 0.00820245i | \(0.00261095\pi\) | ||||
−0.999966 | + | 0.00820245i | \(0.997389\pi\) | |||||||
\(858\) | 4.21443e60 | + | 3.08123e60i | 0.105077 | + | 0.0768229i | ||||
\(859\) | 5.24704e61 | 1.27661 | 0.638304 | − | 0.769784i | \(-0.279636\pi\) | ||||
0.638304 | + | 0.769784i | \(0.279636\pi\) | |||||||
\(860\) | − | 2.08314e62i | − | 4.94597i | ||||||
\(861\) | 2.43491e60 | − | 3.33041e60i | 0.0564178 | − | 0.0771669i | ||||
\(862\) | 5.85315e61 | 1.32354 | ||||||||
\(863\) | − | 4.07881e60i | − | 0.0900132i | −0.998987 | − | 0.0450066i | \(-0.985669\pi\) | ||
0.998987 | − | 0.0450066i | \(-0.0143309\pi\) | |||||||
\(864\) | −2.66536e61 | − | 8.92501e60i | −0.574074 | − | 0.192230i | ||||
\(865\) | −5.29246e60 | −0.111255 | ||||||||
\(866\) | 1.23477e62i | 2.53343i | ||||||||
\(867\) | −8.38283e60 | − | 6.12880e60i | −0.167876 | − | 0.122737i | ||||
\(868\) | 1.37222e61 | 0.268230 | ||||||||
\(869\) | − | 2.43766e60i | − | 0.0465113i | ||||||
\(870\) | 7.69225e61 | − | 1.05213e62i | 1.43268 | − | 1.95958i | ||||
\(871\) | 3.33847e60 | 0.0606968 | ||||||||
\(872\) | 1.53452e62i | 2.72349i | ||||||||
\(873\) | −2.80546e61 | − | 8.81305e61i | −0.486077 | − | 1.52696i | ||||
\(874\) | −4.36630e61 | −0.738539 | ||||||||
\(875\) | 2.83471e61i | 0.468101i | ||||||||
\(876\) | 8.62209e61 | + | 6.30374e61i | 1.39004 | + | 1.01628i | ||||
\(877\) | 3.47453e61 | 0.546895 | 0.273448 | − | 0.961887i | \(-0.411836\pi\) | ||||
0.273448 | + | 0.961887i | \(0.411836\pi\) | |||||||
\(878\) | 3.50874e61i | 0.539221i | ||||||||
\(879\) | −4.98121e60 | + | 6.81318e60i | −0.0747427 | + | 0.102231i | ||||
\(880\) | 7.42248e61 | 1.08746 | ||||||||
\(881\) | 1.23936e62i | 1.77298i | 0.462745 | + | 0.886491i | \(0.346864\pi\) | ||||
−0.462745 | + | 0.886491i | \(0.653136\pi\) | |||||||
\(882\) | −1.18964e62 | + | 3.78699e61i | −1.66179 | + | 0.528998i | ||||
\(883\) | −8.10245e61 | −1.10520 | −0.552601 | − | 0.833446i | \(-0.686365\pi\) | ||||
−0.552601 | + | 0.833446i | \(0.686365\pi\) | |||||||
\(884\) | 2.82472e61i | 0.376251i | ||||||||
\(885\) | −1.47016e62 | − | 1.07485e62i | −1.91230 | − | 1.39811i | ||||
\(886\) | 1.60724e62 | 2.04161 | ||||||||
\(887\) | − | 5.84393e61i | − | 0.724952i | −0.931993 | − | 0.362476i | \(-0.881932\pi\) | ||
0.931993 | − | 0.362476i | \(-0.118068\pi\) | |||||||
\(888\) | 2.92135e61 | − | 3.99575e61i | 0.353925 | − | 0.484090i | ||||
\(889\) | −1.06736e61 | −0.126291 | ||||||||
\(890\) | − | 3.29720e62i | − | 3.81027i | ||||||
\(891\) | −1.91487e61 | − | 2.70290e61i | −0.216126 | − | 0.305069i | ||||
\(892\) | −3.19785e62 | −3.52530 | ||||||||
\(893\) | − | 4.68653e61i | − | 0.504627i | ||||||
\(894\) | 5.45145e61 | + | 3.98563e61i | 0.573356 | + | 0.419189i | ||||
\(895\) | 1.05405e62 | 1.08287 | ||||||||
\(896\) | − | 1.84462e61i | − | 0.185114i | ||||||
\(897\) | 7.14123e60 | − | 9.76760e60i | 0.0700054 | − | 0.0957517i | ||||
\(898\) | −1.50653e62 | −1.44270 | ||||||||
\(899\) | 6.85307e61i | 0.641109i | ||||||||
\(900\) | 1.98203e62 | + | 6.22634e62i | 1.81142 | + | 5.69036i | ||||
\(901\) | 2.92614e61 | 0.261261 | ||||||||
\(902\) | 5.33568e61i | 0.465428i | ||||||||
\(903\) | 1.52630e61 | + | 1.11590e61i | 0.130076 | + | 0.0951006i | ||||
\(904\) | −3.00185e62 | −2.49949 | ||||||||
\(905\) | 1.79487e62i | 1.46020i | ||||||||
\(906\) | 2.16383e62 | − | 2.95963e62i | 1.72001 | − | 2.35259i | ||||
\(907\) | −6.42901e61 | −0.499334 | −0.249667 | − | 0.968332i | \(-0.580321\pi\) | ||||
−0.249667 | + | 0.968332i | \(0.580321\pi\) | |||||||
\(908\) | − | 2.46321e62i | − | 1.86939i | ||||||
\(909\) | 1.31174e62 | − | 4.17567e61i | 0.972760 | − | 0.309659i | ||||
\(910\) | 1.27247e61 | 0.0922100 | ||||||||
\(911\) | − | 5.51019e61i | − | 0.390194i | −0.980784 | − | 0.195097i | \(-0.937498\pi\) | ||
0.980784 | − | 0.195097i | \(-0.0625021\pi\) | |||||||
\(912\) | −1.20004e62 | − | 8.77367e61i | −0.830433 | − | 0.607141i | ||||
\(913\) | 5.71244e61 | 0.386309 | ||||||||
\(914\) | 3.50505e62i | 2.31645i | ||||||||
\(915\) | −1.97701e62 | + | 2.70410e62i | −1.27692 | + | 1.74655i | ||||
\(916\) | 4.27045e62 | 2.69568 | ||||||||
\(917\) | − | 1.50653e61i | − | 0.0929442i | ||||||
\(918\) | 8.32805e61 | − | 2.48709e62i | 0.502166 | − | 1.49967i | ||||
\(919\) | −1.73999e62 | −1.02546 | −0.512732 | − | 0.858549i | \(-0.671366\pi\) | ||||
−0.512732 | + | 0.858549i | \(0.671366\pi\) | |||||||
\(920\) | − | 4.19742e62i | − | 2.41790i | ||||||
\(921\) | 2.37395e62 | + | 1.73563e62i | 1.33665 | + | 0.977246i | ||||
\(922\) | 4.69205e62 | 2.58234 | ||||||||
\(923\) | − | 4.84625e61i | − | 0.260718i | ||||||
\(924\) | −1.23548e61 | + | 1.68986e61i | −0.0649718 | + | 0.0888669i | ||||
\(925\) | −1.56893e62 | −0.806540 | ||||||||
\(926\) | − | 2.14390e62i | − | 1.07739i | ||||||
\(927\) | −4.94987e61 | − | 1.55495e62i | −0.243175 | − | 0.763908i | ||||
\(928\) | −8.87124e61 | −0.426066 | ||||||||
\(929\) | 1.95586e60i | 0.00918351i | 0.999989 | + | 0.00459175i | \(0.00146161\pi\) | ||||
−0.999989 | + | 0.00459175i | \(0.998538\pi\) | |||||||
\(930\) | −5.52551e62 | − | 4.03978e62i | −2.53648 | − | 1.85445i | ||||
\(931\) | −1.50106e62 | −0.673684 | ||||||||
\(932\) | 3.43058e62i | 1.50534i | ||||||||
\(933\) | 8.59102e58 | − | 1.17506e59i | 0.000368579 | − | 0.000504133i | ||||
\(934\) | −7.00844e62 | −2.93993 | ||||||||
\(935\) | 1.57455e62i | 0.645823i | ||||||||
\(936\) | 9.57790e61 | − | 3.04894e61i | 0.384130 | − | 0.122280i | ||||
\(937\) | 4.26896e62 | 1.67414 | 0.837069 | − | 0.547098i | \(-0.184268\pi\) | ||||
0.837069 | + | 0.547098i | \(0.184268\pi\) | |||||||
\(938\) | 1.95897e61i | 0.0751223i | ||||||||
\(939\) | 1.54590e62 | + | 1.13023e62i | 0.579701 | + | 0.423827i | ||||
\(940\) | 8.39624e62 | 3.07893 | ||||||||
\(941\) | − | 2.64347e62i | − | 0.947965i | −0.880534 | − | 0.473983i | \(-0.842816\pi\) | ||
0.880534 | − | 0.473983i | \(-0.157184\pi\) | |||||||
\(942\) | −1.22596e62 | + | 1.67683e62i | −0.429939 | + | 0.588059i | ||||
\(943\) | 1.23663e62 | 0.424124 | ||||||||
\(944\) | 5.45264e62i | 1.82892i | ||||||||
\(945\) | −7.65586e61 | − | 2.56358e61i | −0.251146 | − | 0.0840967i | ||||
\(946\) | −2.44531e62 | −0.784548 | ||||||||
\(947\) | 2.63301e62i | 0.826235i | 0.910678 | + | 0.413117i | \(0.135560\pi\) | ||||
−0.910678 | + | 0.413117i | \(0.864440\pi\) | |||||||
\(948\) | −7.06081e61 | − | 5.16226e61i | −0.216710 | − | 0.158440i | ||||
\(949\) | −5.20780e61 | −0.156338 | ||||||||
\(950\) | 1.14970e63i | 3.37590i | ||||||||
\(951\) | −8.96741e61 | + | 1.22654e62i | −0.257559 | + | 0.352282i | ||||
\(952\) | −8.89390e61 | −0.249871 | ||||||||
\(953\) | − | 4.85271e62i | − | 1.33362i | −0.745227 | − | 0.666811i | \(-0.767659\pi\) | ||
0.745227 | − | 0.666811i | \(-0.232341\pi\) | |||||||
\(954\) | −5.88618e61 | − | 1.84908e62i | −0.158240 | − | 0.497095i | ||||
\(955\) | −1.33066e61 | −0.0349941 | ||||||||
\(956\) | − | 7.28763e62i | − | 1.87487i | ||||||
\(957\) | −8.43945e61 | − | 6.17020e61i | −0.212404 | − | 0.155292i | ||||
\(958\) | −6.29993e62 | −1.55117 | ||||||||
\(959\) | − | 6.28291e61i | − | 0.151346i | ||||||
\(960\) | −2.05485e62 | + | 2.81057e62i | −0.484265 | + | 0.662366i | ||||
\(961\) | −7.37953e61 | −0.170152 | ||||||||
\(962\) | 4.49784e61i | 0.101468i | ||||||||
\(963\) | 6.16514e62 | − | 1.96255e62i | 1.36079 | − | 0.433181i | ||||
\(964\) | −4.32117e62 | −0.933220 | ||||||||
\(965\) | − | 1.50426e63i | − | 3.17869i | ||||||
\(966\) | 5.73151e61 | + | 4.19039e61i | 0.118508 | + | 0.0866432i | ||||
\(967\) | −4.76466e62 | −0.963998 | −0.481999 | − | 0.876172i | \(-0.660089\pi\) | ||||
−0.481999 | + | 0.876172i | \(0.660089\pi\) | |||||||
\(968\) | 8.94033e62i | 1.76999i | ||||||||
\(969\) | 1.86119e62 | − | 2.54568e62i | 0.360571 | − | 0.493180i | ||||
\(970\) | 2.91549e63 | 5.52720 | ||||||||
\(971\) | − | 6.87992e61i | − | 0.127638i | −0.997961 | − | 0.0638189i | \(-0.979672\pi\) | ||
0.997961 | − | 0.0638189i | \(-0.0203280\pi\) | |||||||
\(972\) | −1.18842e63 | − | 1.77428e61i | −2.15764 | − | 0.0322129i | ||||
\(973\) | −5.27733e60 | −0.00937659 | ||||||||
\(974\) | 2.09430e62i | 0.364168i | ||||||||
\(975\) | −2.57193e62 | − | 1.88038e62i | −0.437686 | − | 0.319998i | ||||
\(976\) | 1.00292e63 | 1.67040 | ||||||||
\(977\) | 3.25635e62i | 0.530818i | 0.964136 | + | 0.265409i | \(0.0855070\pi\) | ||||
−0.964136 | + | 0.265409i | \(0.914493\pi\) | |||||||
\(978\) | −6.56006e62 | + | 8.97269e62i | −1.04663 | + | 1.43155i | ||||
\(979\) | −2.64479e62 | −0.413005 | ||||||||
\(980\) | − | 2.68926e63i | − | 4.11041i | ||||||
\(981\) | 2.68370e62 | + | 8.43055e62i | 0.401499 | + | 1.26127i | ||||
\(982\) | −1.16090e63 | −1.70002 | ||||||||
\(983\) | 8.96354e62i | 1.28486i | 0.766344 | + | 0.642430i | \(0.222074\pi\) | ||||
−0.766344 | + | 0.642430i | \(0.777926\pi\) | |||||||
\(984\) | 8.29290e62 | + | 6.06305e62i | 1.16361 | + | 0.850735i | ||||
\(985\) | −3.88614e62 | −0.533775 | ||||||||
\(986\) | − | 8.27788e62i | − | 1.11302i | ||||||
\(987\) | −4.49771e61 | + | 6.15186e61i | −0.0592014 | + | 0.0809742i | ||||
\(988\) | 2.25226e62 | 0.290217 | ||||||||
\(989\) | 5.66738e62i | 0.714925i | ||||||||
\(990\) | 9.94986e62 | − | 3.16734e62i | 1.22879 | − | 0.391161i | ||||
\(991\) | 1.51607e62 | 0.183304 | 0.0916522 | − | 0.995791i | \(-0.470785\pi\) | ||||
0.0916522 | + | 0.995791i | \(0.470785\pi\) | |||||||
\(992\) | 4.65896e62i | 0.551498i | ||||||||
\(993\) | 1.24804e63 | + | 9.12457e62i | 1.44642 | + | 1.05749i | ||||
\(994\) | 2.84372e62 | 0.322681 | ||||||||
\(995\) | 2.60175e62i | 0.289056i | ||||||||
\(996\) | 1.20973e63 | − | 1.65463e63i | 1.31596 | − | 1.79993i | ||||
\(997\) | 1.51339e63 | 1.61195 | 0.805975 | − | 0.591949i | \(-0.201641\pi\) | ||||
0.805975 | + | 0.591949i | \(0.201641\pi\) | |||||||
\(998\) | 2.06469e63i | 2.15335i | ||||||||
\(999\) | 9.06158e61 | − | 2.70615e62i | 0.0925398 | − | 0.276361i |
(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 | 3.43.b.b.2.2 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.43.b.b.2.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.43.b.b.2.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.43.b.b.2.11 | yes | 12 | 3.2 | odd | 2 | inner |