Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,15,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.97315872608\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 88x^{4} - 1824x^{3} + 325632x^{2} + 21572352x + 982333440 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.3 | ||
Root | \(-4.07037 - 30.9656i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.15.b.a.3.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32.2815 | − | 123.862i | −0.252199 | − | 0.967675i | ||||
\(3\) | 2369.41i | 1.08341i | 0.840570 | + | 0.541703i | \(0.182220\pi\) | ||||
−0.840570 | + | 0.541703i | \(0.817780\pi\) | |||||||
\(4\) | −14299.8 | + | 7996.93i | −0.872791 | + | 0.488094i | ||||
\(5\) | 113343. | 1.45080 | 0.725398 | − | 0.688329i | \(-0.241656\pi\) | ||||
0.725398 | + | 0.688329i | \(0.241656\pi\) | |||||||
\(6\) | 293481. | − | 76488.1i | 1.04839 | − | 0.273234i | ||||
\(7\) | 697667.i | 0.847153i | 0.905860 | + | 0.423577i | \(0.139226\pi\) | ||||
−0.905860 | + | 0.423577i | \(0.860774\pi\) | |||||||
\(8\) | 1.45214e6 | + | 1.51306e6i | 0.692433 | + | 0.721482i | ||||
\(9\) | −831139. | −0.173771 | ||||||||
\(10\) | −3.65890e6 | − | 1.40390e7i | −0.365890 | − | 1.40390i | ||||
\(11\) | 2.00895e7i | 1.03091i | 0.856917 | + | 0.515454i | \(0.172377\pi\) | ||||
−0.856917 | + | 0.515454i | \(0.827623\pi\) | |||||||
\(12\) | −1.89480e7 | − | 3.38821e7i | −0.528804 | − | 0.945588i | ||||
\(13\) | −6.13899e7 | −0.978348 | −0.489174 | − | 0.872186i | \(-0.662702\pi\) | ||||
−0.489174 | + | 0.872186i | \(0.662702\pi\) | |||||||
\(14\) | 8.64148e7 | − | 2.25217e7i | 0.819769 | − | 0.213651i | ||||
\(15\) | 2.68557e8i | 1.57180i | ||||||||
\(16\) | 1.40534e8 | − | 2.28709e8i | 0.523529 | − | 0.852008i | ||||
\(17\) | 3.44542e8 | 0.839653 | 0.419827 | − | 0.907604i | \(-0.362091\pi\) | ||||
0.419827 | + | 0.907604i | \(0.362091\pi\) | |||||||
\(18\) | 2.68304e7 | + | 1.02947e8i | 0.0438248 | + | 0.168154i | ||||
\(19\) | − | 3.17454e8i | − | 0.355145i | −0.984108 | − | 0.177573i | \(-0.943176\pi\) | ||
0.984108 | − | 0.177573i | \(-0.0568245\pi\) | |||||||
\(20\) | −1.62079e9 | + | 9.06399e8i | −1.26624 | + | 0.708125i | ||||
\(21\) | −1.65306e9 | −0.917812 | ||||||||
\(22\) | 2.48833e9 | − | 6.48519e8i | 0.997585 | − | 0.259994i | ||||
\(23\) | − | 5.79264e9i | − | 1.70130i | −0.525731 | − | 0.850651i | \(-0.676208\pi\) | ||
0.525731 | − | 0.850651i | \(-0.323792\pi\) | |||||||
\(24\) | −3.58505e9 | + | 3.44071e9i | −0.781659 | + | 0.750187i | ||||
\(25\) | 6.74323e9 | 1.10481 | ||||||||
\(26\) | 1.98176e9 | + | 7.60390e9i | 0.246738 | + | 0.946723i | ||||
\(27\) | 9.36351e9i | 0.895143i | ||||||||
\(28\) | −5.57919e9 | − | 9.97651e9i | −0.413490 | − | 0.739388i | ||||
\(29\) | −3.72362e9 | −0.215864 | −0.107932 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107932 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(30\) | 3.32642e10 | − | 8.66943e9i | 1.52100 | − | 0.396407i | ||||
\(31\) | 8.57575e8i | 0.0311702i | 0.999879 | + | 0.0155851i | \(0.00496110\pi\) | ||||
−0.999879 | + | 0.0155851i | \(0.995039\pi\) | |||||||
\(32\) | −3.28651e10 | − | 1.00238e10i | −0.956500 | − | 0.291731i | ||||
\(33\) | −4.76003e10 | −1.11689 | ||||||||
\(34\) | −1.11223e10 | − | 4.26758e10i | −0.211760 | − | 0.812512i | ||||
\(35\) | 7.90760e10i | 1.22905i | ||||||||
\(36\) | 1.18851e10 | − | 6.64656e9i | 0.151665 | − | 0.0848163i | ||||
\(37\) | 9.83497e10 | 1.03600 | 0.518002 | − | 0.855380i | \(-0.326676\pi\) | ||||
0.518002 | + | 0.855380i | \(0.326676\pi\) | |||||||
\(38\) | −3.93207e10 | + | 1.02479e10i | −0.343665 | + | 0.0895673i | ||||
\(39\) | − | 1.45458e11i | − | 1.05995i | ||||||
\(40\) | 1.64590e11 | + | 1.71495e11i | 1.00458 | + | 1.04672i | ||||
\(41\) | −8.26198e9 | −0.0424226 | −0.0212113 | − | 0.999775i | \(-0.506752\pi\) | ||||
−0.0212113 | + | 0.999775i | \(0.506752\pi\) | |||||||
\(42\) | 5.33632e10 | + | 2.04752e11i | 0.231471 | + | 0.888144i | ||||
\(43\) | − | 1.16363e11i | − | 0.428089i | −0.976824 | − | 0.214045i | \(-0.931336\pi\) | ||
0.976824 | − | 0.214045i | \(-0.0686638\pi\) | |||||||
\(44\) | −1.60654e11 | − | 2.87276e11i | −0.503180 | − | 0.899768i | ||||
\(45\) | −9.42042e10 | −0.252106 | ||||||||
\(46\) | −7.17490e11 | + | 1.86995e11i | −1.64631 | + | 0.429067i | ||||
\(47\) | − | 3.17697e11i | − | 0.627087i | −0.949574 | − | 0.313543i | \(-0.898484\pi\) | ||
0.949574 | − | 0.313543i | \(-0.101516\pi\) | |||||||
\(48\) | 5.41906e11 | + | 3.32982e11i | 0.923071 | + | 0.567195i | ||||
\(49\) | 1.91484e11 | 0.282332 | ||||||||
\(50\) | −2.17681e11 | − | 8.35233e11i | −0.278632 | − | 1.06910i | ||||
\(51\) | 8.16362e11i | 0.909686i | ||||||||
\(52\) | 8.77864e11 | − | 4.90930e11i | 0.853894 | − | 0.477525i | ||||
\(53\) | −6.36538e11 | −0.541867 | −0.270934 | − | 0.962598i | \(-0.587332\pi\) | ||||
−0.270934 | + | 0.962598i | \(0.587332\pi\) | |||||||
\(54\) | 1.15979e12 | − | 3.02268e11i | 0.866208 | − | 0.225754i | ||||
\(55\) | 2.27701e12i | 1.49564i | ||||||||
\(56\) | −1.05561e12 | + | 1.01311e12i | −0.611206 | + | 0.586597i | ||||
\(57\) | 7.52180e11 | 0.384767 | ||||||||
\(58\) | 1.20204e11 | + | 4.61217e11i | 0.0544406 | + | 0.208886i | ||||
\(59\) | − | 2.87412e12i | − | 1.15489i | −0.816429 | − | 0.577445i | \(-0.804050\pi\) | ||
0.816429 | − | 0.577445i | \(-0.195950\pi\) | |||||||
\(60\) | −2.14763e12 | − | 3.84032e12i | −0.767187 | − | 1.37186i | ||||
\(61\) | 8.45647e11 | 0.269079 | 0.134540 | − | 0.990908i | \(-0.457044\pi\) | ||||
0.134540 | + | 0.990908i | \(0.457044\pi\) | |||||||
\(62\) | 1.06221e11 | − | 2.76838e10i | 0.0301627 | − | 0.00786110i | ||||
\(63\) | − | 5.79859e11i | − | 0.147210i | ||||||
\(64\) | −1.80638e11 | + | 4.39434e12i | −0.0410723 | + | 0.999156i | ||||
\(65\) | −6.95814e12 | −1.41938 | ||||||||
\(66\) | 1.53661e12 | + | 5.89589e12i | 0.281680 | + | 1.08079i | ||||
\(67\) | − | 6.82161e12i | − | 1.12555i | −0.826611 | − | 0.562773i | \(-0.809734\pi\) | ||
0.826611 | − | 0.562773i | \(-0.190266\pi\) | |||||||
\(68\) | −4.92689e12 | + | 2.75528e12i | −0.732842 | + | 0.409829i | ||||
\(69\) | 1.37251e13 | 1.84320 | ||||||||
\(70\) | 9.79455e12 | − | 2.55269e12i | 1.18932 | − | 0.309964i | ||||
\(71\) | 3.28972e12i | 0.361702i | 0.983511 | + | 0.180851i | \(0.0578851\pi\) | ||||
−0.983511 | + | 0.180851i | \(0.942115\pi\) | |||||||
\(72\) | −1.20693e12 | − | 1.25756e12i | −0.120325 | − | 0.125372i | ||||
\(73\) | 6.25122e10 | 0.00565854 | 0.00282927 | − | 0.999996i | \(-0.499099\pi\) | ||||
0.00282927 | + | 0.999996i | \(0.499099\pi\) | |||||||
\(74\) | −3.17487e12 | − | 1.21818e13i | −0.261279 | − | 1.00251i | ||||
\(75\) | 1.59775e13i | 1.19696i | ||||||||
\(76\) | 2.53866e12 | + | 4.53954e12i | 0.173344 | + | 0.309968i | ||||
\(77\) | −1.40158e13 | −0.873338 | ||||||||
\(78\) | −1.80168e13 | + | 4.69560e12i | −1.02569 | + | 0.267318i | ||||
\(79\) | − | 1.05071e13i | − | 0.547135i | −0.961853 | − | 0.273568i | \(-0.911796\pi\) | ||
0.961853 | − | 0.273568i | \(-0.0882037\pi\) | |||||||
\(80\) | 1.59286e13 | − | 2.59227e13i | 0.759535 | − | 1.23609i | ||||
\(81\) | −2.61613e13 | −1.14357 | ||||||||
\(82\) | 2.66709e11 | + | 1.02335e12i | 0.0106989 | + | 0.0410513i | ||||
\(83\) | 2.38301e13i | 0.878171i | 0.898445 | + | 0.439086i | \(0.144698\pi\) | ||||
−0.898445 | + | 0.439086i | \(0.855302\pi\) | |||||||
\(84\) | 2.36384e13 | − | 1.32194e13i | 0.801058 | − | 0.447978i | ||||
\(85\) | 3.90516e13 | 1.21817 | ||||||||
\(86\) | −1.44130e13 | + | 3.75636e12i | −0.414251 | + | 0.107964i | ||||
\(87\) | − | 8.82279e12i | − | 0.233868i | ||||||
\(88\) | −3.03966e13 | + | 2.91727e13i | −0.743782 | + | 0.713836i | ||||
\(89\) | 3.23837e13 | 0.732143 | 0.366071 | − | 0.930587i | \(-0.380703\pi\) | ||||
0.366071 | + | 0.930587i | \(0.380703\pi\) | |||||||
\(90\) | 3.04105e12 | + | 1.16684e13i | 0.0635808 | + | 0.243957i | ||||
\(91\) | − | 4.28297e13i | − | 0.828811i | ||||||
\(92\) | 4.63233e13 | + | 8.28336e13i | 0.830395 | + | 1.48488i | ||||
\(93\) | −2.03195e12 | −0.0337701 | ||||||||
\(94\) | −3.93507e13 | + | 1.02557e13i | −0.606816 | + | 0.158151i | ||||
\(95\) | − | 3.59814e13i | − | 0.515243i | ||||||
\(96\) | 2.37505e13 | − | 7.78709e13i | 0.316063 | − | 1.03628i | ||||
\(97\) | −1.34788e14 | −1.66820 | −0.834101 | − | 0.551612i | \(-0.814013\pi\) | ||||
−0.834101 | + | 0.551612i | \(0.814013\pi\) | |||||||
\(98\) | −6.18138e12 | − | 2.37176e13i | −0.0712037 | − | 0.273205i | ||||
\(99\) | − | 1.66972e13i | − | 0.179142i | ||||||
\(100\) | −9.64269e13 | + | 5.39251e13i | −0.964269 | + | 0.539251i | ||||
\(101\) | 1.79994e14 | 1.67884 | 0.839419 | − | 0.543485i | \(-0.182896\pi\) | ||||
0.839419 | + | 0.543485i | \(0.182896\pi\) | |||||||
\(102\) | 1.01117e14 | − | 2.63534e13i | 0.880281 | − | 0.229422i | ||||
\(103\) | 5.09045e12i | 0.0413900i | 0.999786 | + | 0.0206950i | \(0.00658790\pi\) | ||||
−0.999786 | + | 0.0206950i | \(0.993412\pi\) | |||||||
\(104\) | −8.91466e13 | − | 9.28864e13i | −0.677441 | − | 0.705860i | ||||
\(105\) | −1.87364e14 | −1.33156 | ||||||||
\(106\) | 2.05484e13 | + | 7.88431e13i | 0.136658 | + | 0.524352i | ||||
\(107\) | 2.79523e14i | 1.74073i | 0.492407 | + | 0.870365i | \(0.336117\pi\) | ||||
−0.492407 | + | 0.870365i | \(0.663883\pi\) | |||||||
\(108\) | −7.48793e13 | − | 1.33896e14i | −0.436913 | − | 0.781273i | ||||
\(109\) | 2.45434e14 | 1.34261 | 0.671305 | − | 0.741182i | \(-0.265734\pi\) | ||||
0.671305 | + | 0.741182i | \(0.265734\pi\) | |||||||
\(110\) | 2.82036e14 | − | 7.35054e13i | 1.44729 | − | 0.377199i | ||||
\(111\) | 2.33031e14i | 1.12241i | ||||||||
\(112\) | 1.59563e14 | + | 9.80458e13i | 0.721781 | + | 0.443509i | ||||
\(113\) | −2.38170e14 | −1.01237 | −0.506184 | − | 0.862426i | \(-0.668944\pi\) | ||||
−0.506184 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(114\) | −2.42815e13 | − | 9.31668e13i | −0.0970378 | − | 0.372329i | ||||
\(115\) | − | 6.56558e14i | − | 2.46824i | ||||||
\(116\) | 5.32471e13 | − | 2.97775e13i | 0.188404 | − | 0.105362i | ||||
\(117\) | 5.10236e13 | 0.170008 | ||||||||
\(118\) | −3.55995e14 | + | 9.27808e13i | −1.11756 | + | 0.291262i | ||||
\(119\) | 2.40376e14i | 0.711315i | ||||||||
\(120\) | −4.06343e14 | + | 3.89982e14i | −1.13403 | + | 1.08837i | ||||
\(121\) | −2.38380e13 | −0.0627730 | ||||||||
\(122\) | −2.72987e13 | − | 1.04744e14i | −0.0678616 | − | 0.260381i | ||||
\(123\) | − | 1.95760e13i | − | 0.0459609i | ||||||
\(124\) | −6.85796e12 | − | 1.22632e13i | −0.0152140 | − | 0.0272051i | ||||
\(125\) | 7.25076e13 | 0.152060 | ||||||||
\(126\) | −7.18227e13 | + | 1.87187e13i | −0.142452 | + | 0.0371263i | ||||
\(127\) | − | 9.50007e14i | − | 1.78279i | −0.453225 | − | 0.891396i | \(-0.649727\pi\) | ||
0.453225 | − | 0.891396i | \(-0.350273\pi\) | |||||||
\(128\) | 5.50124e14 | − | 1.19481e14i | 0.977217 | − | 0.212242i | ||||
\(129\) | 2.75711e14 | 0.463795 | ||||||||
\(130\) | 2.24619e14 | + | 8.61853e14i | 0.357967 | + | 1.37350i | ||||
\(131\) | 3.13334e14i | 0.473270i | 0.971599 | + | 0.236635i | \(0.0760445\pi\) | ||||
−0.971599 | + | 0.236635i | \(0.923955\pi\) | |||||||
\(132\) | 6.80675e14 | − | 3.80656e14i | 0.974815 | − | 0.545149i | ||||
\(133\) | 2.21477e14 | 0.300862 | ||||||||
\(134\) | −8.44942e14 | + | 2.20212e14i | −1.08916 | + | 0.283862i | ||||
\(135\) | 1.06129e15i | 1.29867i | ||||||||
\(136\) | 5.00323e14 | + | 5.21312e14i | 0.581404 | + | 0.605794i | ||||
\(137\) | −1.05928e15 | −1.16941 | −0.584704 | − | 0.811247i | \(-0.698789\pi\) | ||||
−0.584704 | + | 0.811247i | \(0.698789\pi\) | |||||||
\(138\) | −4.43068e14 | − | 1.70003e15i | −0.464854 | − | 1.78362i | ||||
\(139\) | 1.02367e15i | 1.02108i | 0.859855 | + | 0.510538i | \(0.170554\pi\) | ||||
−0.859855 | + | 0.510538i | \(0.829446\pi\) | |||||||
\(140\) | −6.32365e14 | − | 1.13077e15i | −0.599890 | − | 1.07270i | ||||
\(141\) | 7.52754e14 | 0.679390 | ||||||||
\(142\) | 4.07473e14 | − | 1.06197e14i | 0.350010 | − | 0.0912208i | ||||
\(143\) | − | 1.23329e15i | − | 1.00859i | ||||||
\(144\) | −1.16803e14 | + | 1.90089e14i | −0.0909740 | + | 0.148054i | ||||
\(145\) | −4.22048e14 | −0.313174 | ||||||||
\(146\) | −2.01799e12 | − | 7.74291e12i | −0.00142708 | − | 0.00547563i | ||||
\(147\) | 4.53704e14i | 0.305880i | ||||||||
\(148\) | −1.40638e15 | + | 7.86495e14i | −0.904215 | + | 0.505667i | ||||
\(149\) | −9.53793e14 | −0.584993 | −0.292496 | − | 0.956267i | \(-0.594486\pi\) | ||||
−0.292496 | + | 0.956267i | \(0.594486\pi\) | |||||||
\(150\) | 1.97901e15 | − | 5.15777e14i | 1.15827 | − | 0.301872i | ||||
\(151\) | − | 2.50228e14i | − | 0.139797i | −0.997554 | − | 0.0698984i | \(-0.977732\pi\) | ||
0.997554 | − | 0.0698984i | \(-0.0222675\pi\) | |||||||
\(152\) | 4.80326e14 | − | 4.60987e14i | 0.256231 | − | 0.245914i | ||||
\(153\) | −2.86363e14 | −0.145907 | ||||||||
\(154\) | 4.52450e14 | + | 1.73603e15i | 0.220255 | + | 0.845107i | ||||
\(155\) | 9.72005e13i | 0.0452217i | ||||||||
\(156\) | 1.16322e15 | + | 2.08002e15i | 0.517354 | + | 0.925114i | ||||
\(157\) | 2.72276e15 | 1.15801 | 0.579005 | − | 0.815324i | \(-0.303441\pi\) | ||||
0.579005 | + | 0.815324i | \(0.303441\pi\) | |||||||
\(158\) | −1.30144e15 | + | 3.39186e14i | −0.529449 | + | 0.137987i | ||||
\(159\) | − | 1.50822e15i | − | 0.587063i | ||||||
\(160\) | −3.72505e15 | − | 1.13613e15i | −1.38769 | − | 0.423242i | ||||
\(161\) | 4.04133e15 | 1.44126 | ||||||||
\(162\) | 8.44526e14 | + | 3.24040e15i | 0.288408 | + | 1.10661i | ||||
\(163\) | − | 4.12649e15i | − | 1.34979i | −0.737912 | − | 0.674897i | \(-0.764188\pi\) | ||
0.737912 | − | 0.674897i | \(-0.235812\pi\) | |||||||
\(164\) | 1.18145e14 | − | 6.60705e13i | 0.0370261 | − | 0.0207062i | ||||
\(165\) | −5.39518e15 | −1.62039 | ||||||||
\(166\) | 2.95166e15 | − | 7.69271e14i | 0.849785 | − | 0.221474i | ||||
\(167\) | 3.19518e15i | 0.882024i | 0.897501 | + | 0.441012i | \(0.145380\pi\) | ||||
−0.897501 | + | 0.441012i | \(0.854620\pi\) | |||||||
\(168\) | −2.40047e15 | − | 2.50117e15i | −0.635523 | − | 0.662184i | ||||
\(169\) | −1.68658e14 | −0.0428351 | ||||||||
\(170\) | −1.26064e15 | − | 4.83703e15i | −0.307220 | − | 1.17879i | ||||
\(171\) | 2.63849e14i | 0.0617138i | ||||||||
\(172\) | 9.30543e14 | + | 1.66396e15i | 0.208948 | + | 0.373632i | ||||
\(173\) | −7.49126e15 | −1.61522 | −0.807611 | − | 0.589716i | \(-0.799240\pi\) | ||||
−0.807611 | + | 0.589716i | \(0.799240\pi\) | |||||||
\(174\) | −1.09281e15 | + | 2.84813e14i | −0.226309 | + | 0.0589814i | ||||
\(175\) | 4.70453e15i | 0.935944i | ||||||||
\(176\) | 4.59465e15 | + | 2.82325e15i | 0.878342 | + | 0.539711i | ||||
\(177\) | 6.80997e15 | 1.25122 | ||||||||
\(178\) | −1.04539e15 | − | 4.01112e15i | −0.184646 | − | 0.708476i | ||||
\(179\) | 1.06547e15i | 0.180955i | 0.995899 | + | 0.0904773i | \(0.0288393\pi\) | ||||
−0.995899 | + | 0.0904773i | \(0.971161\pi\) | |||||||
\(180\) | 1.34710e15 | − | 7.53344e14i | 0.220036 | − | 0.123051i | ||||
\(181\) | 7.52697e14 | 0.118269 | 0.0591344 | − | 0.998250i | \(-0.481166\pi\) | ||||
0.0591344 | + | 0.998250i | \(0.481166\pi\) | |||||||
\(182\) | −5.30499e15 | + | 1.38261e15i | −0.802020 | + | 0.209025i | ||||
\(183\) | 2.00369e15i | 0.291522i | ||||||||
\(184\) | 8.76459e15 | − | 8.41171e15i | 1.22746 | − | 1.17804i | ||||
\(185\) | 1.11473e16 | 1.50303 | ||||||||
\(186\) | 6.55943e13 | + | 2.51682e14i | 0.00851678 | + | 0.0326785i | ||||
\(187\) | 6.92168e15i | 0.865606i | ||||||||
\(188\) | 2.54060e15 | + | 4.54300e15i | 0.306077 | + | 0.547316i | ||||
\(189\) | −6.53261e15 | −0.758323 | ||||||||
\(190\) | −4.45674e15 | + | 1.16153e15i | −0.498588 | + | 0.129944i | ||||
\(191\) | − | 9.65360e15i | − | 1.04101i | −0.853858 | − | 0.520506i | \(-0.825743\pi\) | ||
0.853858 | − | 0.520506i | \(-0.174257\pi\) | |||||||
\(192\) | −1.04120e16 | − | 4.28005e14i | −1.08249 | − | 0.0444980i | ||||
\(193\) | −1.80058e16 | −1.80515 | −0.902573 | − | 0.430538i | \(-0.858324\pi\) | ||||
−0.902573 | + | 0.430538i | \(0.858324\pi\) | |||||||
\(194\) | 4.35115e15 | + | 1.66951e16i | 0.420719 | + | 1.61428i | ||||
\(195\) | − | 1.64867e16i | − | 1.53777i | ||||||
\(196\) | −2.73818e15 | + | 1.53128e15i | −0.246416 | + | 0.137804i | ||||
\(197\) | 4.30570e15 | 0.373921 | 0.186961 | − | 0.982367i | \(-0.440136\pi\) | ||||
0.186961 | + | 0.982367i | \(0.440136\pi\) | |||||||
\(198\) | −2.06815e15 | + | 5.39009e14i | −0.173351 | + | 0.0451794i | ||||
\(199\) | − | 3.57983e15i | − | 0.289662i | −0.989456 | − | 0.144831i | \(-0.953736\pi\) | ||
0.989456 | − | 0.144831i | \(-0.0462638\pi\) | |||||||
\(200\) | 9.79210e15 | + | 1.02029e16i | 0.765008 | + | 0.797101i | ||||
\(201\) | 1.61632e16 | 1.21942 | ||||||||
\(202\) | −5.81048e15 | − | 2.22945e16i | −0.423401 | − | 1.62457i | ||||
\(203\) | − | 2.59785e15i | − | 0.182870i | ||||||
\(204\) | −6.52839e15 | − | 1.16738e16i | −0.444012 | − | 0.793966i | ||||
\(205\) | −9.36442e14 | −0.0615466 | ||||||||
\(206\) | 6.30516e14 | − | 1.64327e14i | 0.0400521 | − | 0.0104385i | ||||
\(207\) | 4.81449e15i | 0.295636i | ||||||||
\(208\) | −8.62736e15 | + | 1.40404e16i | −0.512194 | + | 0.833560i | ||||
\(209\) | 6.37750e15 | 0.366122 | ||||||||
\(210\) | 6.04837e15 | + | 2.32073e16i | 0.335818 | + | 1.28852i | ||||
\(211\) | 3.54222e16i | 1.90238i | 0.308599 | + | 0.951192i | \(0.400140\pi\) | ||||
−0.308599 | + | 0.951192i | \(0.599860\pi\) | |||||||
\(212\) | 9.10237e15 | − | 5.09034e15i | 0.472937 | − | 0.264482i | ||||
\(213\) | −7.79470e15 | −0.391870 | ||||||||
\(214\) | 3.46224e16 | − | 9.02343e15i | 1.68446 | − | 0.439011i | ||||
\(215\) | − | 1.31889e16i | − | 0.621070i | ||||||
\(216\) | −1.41675e16 | + | 1.35971e16i | −0.645829 | + | 0.619827i | ||||
\(217\) | −5.98302e14 | −0.0264060 | ||||||||
\(218\) | −7.92298e15 | − | 3.04001e16i | −0.338605 | − | 1.29921i | ||||
\(219\) | 1.48117e14i | 0.00613051i | ||||||||
\(220\) | −1.82091e16 | − | 3.25609e16i | −0.730012 | − | 1.30538i | ||||
\(221\) | −2.11514e16 | −0.821473 | ||||||||
\(222\) | 2.88638e16 | − | 7.52258e15i | 1.08613 | − | 0.283071i | ||||
\(223\) | 1.98330e16i | 0.723194i | 0.932335 | + | 0.361597i | \(0.117768\pi\) | ||||
−0.932335 | + | 0.361597i | \(0.882232\pi\) | |||||||
\(224\) | 6.99327e15 | − | 2.29289e16i | 0.247141 | − | 0.810302i | ||||
\(225\) | −5.60457e15 | −0.191984 | ||||||||
\(226\) | 7.68849e15 | + | 2.95003e16i | 0.255318 | + | 0.979643i | ||||
\(227\) | 1.14566e16i | 0.368870i | 0.982845 | + | 0.184435i | \(0.0590455\pi\) | ||||
−0.982845 | + | 0.184435i | \(0.940955\pi\) | |||||||
\(228\) | −1.07560e16 | + | 6.01512e15i | −0.335821 | + | 0.187802i | ||||
\(229\) | 1.23732e16 | 0.374657 | 0.187328 | − | 0.982297i | \(-0.440017\pi\) | ||||
0.187328 | + | 0.982297i | \(0.440017\pi\) | |||||||
\(230\) | −8.13228e16 | + | 2.11947e16i | −2.38846 | + | 0.622489i | ||||
\(231\) | − | 3.32091e16i | − | 0.946180i | ||||||
\(232\) | −5.40721e15 | − | 5.63406e15i | −0.149471 | − | 0.155742i | ||||
\(233\) | 3.86944e15 | 0.103790 | 0.0518951 | − | 0.998653i | \(-0.483474\pi\) | ||||
0.0518951 | + | 0.998653i | \(0.483474\pi\) | |||||||
\(234\) | −1.64712e15 | − | 6.31990e15i | −0.0428759 | − | 0.164513i | ||||
\(235\) | − | 3.60088e16i | − | 0.909775i | ||||||
\(236\) | 2.29841e16 | + | 4.10994e16i | 0.563695 | + | 1.00798i | ||||
\(237\) | 2.48957e16 | 0.592770 | ||||||||
\(238\) | 2.97735e16 | − | 7.75968e15i | 0.688322 | − | 0.179393i | ||||
\(239\) | 1.42837e16i | 0.320668i | 0.987063 | + | 0.160334i | \(0.0512572\pi\) | ||||
−0.987063 | + | 0.160334i | \(0.948743\pi\) | |||||||
\(240\) | 6.14215e16 | + | 3.77414e16i | 1.33919 | + | 0.822885i | ||||
\(241\) | −4.35287e15 | −0.0921841 | −0.0460921 | − | 0.998937i | \(-0.514677\pi\) | ||||
−0.0460921 | + | 0.998937i | \(0.514677\pi\) | |||||||
\(242\) | 7.69527e14 | + | 2.95264e15i | 0.0158313 | + | 0.0607439i | ||||
\(243\) | − | 1.72015e16i | − | 0.343814i | ||||||
\(244\) | −1.20926e16 | + | 6.76258e15i | −0.234850 | + | 0.131336i | ||||
\(245\) | 2.17034e16 | 0.409606 | ||||||||
\(246\) | −2.42474e15 | + | 6.31943e14i | −0.0444753 | + | 0.0115913i | ||||
\(247\) | 1.94885e16i | 0.347456i | ||||||||
\(248\) | −1.29756e15 | + | 1.24532e15i | −0.0224888 | + | 0.0215833i | ||||
\(249\) | −5.64633e16 | −0.951417 | ||||||||
\(250\) | −2.34065e15 | − | 8.98097e15i | −0.0383493 | − | 0.147144i | ||||
\(251\) | − | 1.03484e17i | − | 1.64876i | −0.566040 | − | 0.824378i | \(-0.691525\pi\) | ||
0.566040 | − | 0.824378i | \(-0.308475\pi\) | |||||||
\(252\) | 4.63709e15 | + | 8.29187e15i | 0.0718524 | + | 0.128484i | ||||
\(253\) | 1.16371e17 | 1.75389 | ||||||||
\(254\) | −1.17670e17 | + | 3.06676e16i | −1.72516 | + | 0.449618i | ||||
\(255\) | 9.25293e16i | 1.31977i | ||||||||
\(256\) | −3.25581e16 | − | 6.42827e16i | −0.451834 | − | 0.892102i | ||||
\(257\) | −1.39119e17 | −1.87868 | −0.939342 | − | 0.342981i | \(-0.888563\pi\) | ||||
−0.939342 | + | 0.342981i | \(0.888563\pi\) | |||||||
\(258\) | −8.90035e15 | − | 3.41502e16i | −0.116969 | − | 0.448803i | ||||
\(259\) | 6.86154e16i | 0.877653i | ||||||||
\(260\) | 9.95002e16 | − | 5.56438e16i | 1.23883 | − | 0.692792i | ||||
\(261\) | 3.09485e15 | 0.0375108 | ||||||||
\(262\) | 3.88103e16 | − | 1.01149e16i | 0.457972 | − | 0.119358i | ||||
\(263\) | 2.95629e16i | 0.339669i | 0.985473 | + | 0.169835i | \(0.0543234\pi\) | ||||
−0.985473 | + | 0.169835i | \(0.945677\pi\) | |||||||
\(264\) | −6.91222e16 | − | 7.20219e16i | −0.773374 | − | 0.805819i | ||||
\(265\) | −7.21474e16 | −0.786139 | ||||||||
\(266\) | −7.14962e15 | − | 2.74327e16i | −0.0758772 | − | 0.291137i | ||||
\(267\) | 7.67302e16i | 0.793209i | ||||||||
\(268\) | 5.45519e16 | + | 9.75478e16i | 0.549372 | + | 0.982367i | ||||
\(269\) | 8.72957e16 | 0.856499 | 0.428249 | − | 0.903661i | \(-0.359130\pi\) | ||||
0.428249 | + | 0.903661i | \(0.359130\pi\) | |||||||
\(270\) | 1.31454e17 | − | 3.42601e16i | 1.25669 | − | 0.327523i | ||||
\(271\) | − | 1.77937e17i | − | 1.65760i | −0.559543 | − | 0.828801i | \(-0.689023\pi\) | ||
0.559543 | − | 0.828801i | \(-0.310977\pi\) | |||||||
\(272\) | 4.84198e16 | − | 7.87999e16i | 0.439583 | − | 0.715391i | ||||
\(273\) | 1.01481e17 | 0.897939 | ||||||||
\(274\) | 3.41950e16 | + | 1.31205e17i | 0.294923 | + | 1.13161i | ||||
\(275\) | 1.35468e17i | 1.13896i | ||||||||
\(276\) | −1.96267e17 | + | 1.09759e17i | −1.60873 | + | 0.899655i | ||||
\(277\) | −1.24976e17 | −0.998778 | −0.499389 | − | 0.866378i | \(-0.666442\pi\) | ||||
−0.499389 | + | 0.866378i | \(0.666442\pi\) | |||||||
\(278\) | 1.26795e17 | − | 3.30457e16i | 0.988071 | − | 0.257515i | ||||
\(279\) | − | 7.12764e14i | − | 0.00541647i | ||||||
\(280\) | −1.19647e17 | + | 1.14829e17i | −0.886735 | + | 0.851033i | ||||
\(281\) | 9.16435e16 | 0.662457 | 0.331228 | − | 0.943551i | \(-0.392537\pi\) | ||||
0.331228 | + | 0.943551i | \(0.392537\pi\) | |||||||
\(282\) | −2.43000e16 | − | 9.32379e16i | −0.171342 | − | 0.657429i | ||||
\(283\) | − | 7.61168e16i | − | 0.523571i | −0.965126 | − | 0.261785i | \(-0.915689\pi\) | ||
0.965126 | − | 0.261785i | \(-0.0843112\pi\) | |||||||
\(284\) | −2.63077e16 | − | 4.70424e16i | −0.176544 | − | 0.315690i | ||||
\(285\) | 8.52547e16 | 0.558218 | ||||||||
\(286\) | −1.52759e17 | + | 3.98125e16i | −0.975985 | + | 0.254365i | ||||
\(287\) | − | 5.76411e15i | − | 0.0359384i | ||||||
\(288\) | 2.73155e16 | + | 8.33117e15i | 0.166212 | + | 0.0506942i | ||||
\(289\) | −4.96686e16 | −0.294983 | ||||||||
\(290\) | 1.36243e16 | + | 5.22760e16i | 0.0789823 | + | 0.303051i | ||||
\(291\) | − | 3.19368e17i | − | 1.80734i | ||||||
\(292\) | −8.93913e14 | + | 4.99905e14i | −0.00493873 | + | 0.00276190i | ||||
\(293\) | −8.23784e16 | −0.444365 | −0.222183 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222183 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(294\) | 5.61968e16 | − | 1.46462e16i | 0.295992 | − | 0.0771426i | ||||
\(295\) | − | 3.25763e17i | − | 1.67551i | ||||||
\(296\) | 1.42817e17 | + | 1.48809e17i | 0.717363 | + | 0.747458i | ||||
\(297\) | −1.88108e17 | −0.922810 | ||||||||
\(298\) | 3.07899e16 | + | 1.18139e17i | 0.147535 | + | 0.566083i | ||||
\(299\) | 3.55609e17i | 1.66447i | ||||||||
\(300\) | −1.27771e17 | − | 2.28475e17i | −0.584229 | − | 1.04470i | ||||
\(301\) | 8.11823e16 | 0.362657 | ||||||||
\(302\) | −3.09938e16 | + | 8.07773e15i | −0.135278 | + | 0.0352566i | ||||
\(303\) | 4.26480e17i | 1.81886i | ||||||||
\(304\) | −7.26047e16 | − | 4.46131e16i | −0.302586 | − | 0.185929i | ||||
\(305\) | 9.58486e16 | 0.390379 | ||||||||
\(306\) | 9.24421e15 | + | 3.54696e16i | 0.0367976 | + | 0.141191i | ||||
\(307\) | 1.52343e17i | 0.592726i | 0.955075 | + | 0.296363i | \(0.0957738\pi\) | ||||
−0.955075 | + | 0.296363i | \(0.904226\pi\) | |||||||
\(308\) | 2.00423e17 | − | 1.12083e17i | 0.762242 | − | 0.426271i | ||||
\(309\) | −1.20614e16 | −0.0448422 | ||||||||
\(310\) | 1.20395e16 | − | 3.13778e15i | 0.0437599 | − | 0.0114049i | ||||
\(311\) | 1.11654e16i | 0.0396781i | 0.999803 | + | 0.0198390i | \(0.00631538\pi\) | ||||
−0.999803 | + | 0.0198390i | \(0.993685\pi\) | |||||||
\(312\) | 2.20086e17 | − | 2.11225e17i | 0.764734 | − | 0.733944i | ||||
\(313\) | 4.49996e17 | 1.52897 | 0.764483 | − | 0.644644i | \(-0.222994\pi\) | ||||
0.764483 | + | 0.644644i | \(0.222994\pi\) | |||||||
\(314\) | −8.78948e16 | − | 3.37248e17i | −0.292049 | − | 1.12058i | ||||
\(315\) | − | 6.57232e16i | − | 0.213572i | ||||||
\(316\) | 8.40248e16 | + | 1.50250e17i | 0.267053 | + | 0.477535i | ||||
\(317\) | 2.34027e16 | 0.0727531 | 0.0363766 | − | 0.999338i | \(-0.488418\pi\) | ||||
0.0363766 | + | 0.999338i | \(0.488418\pi\) | |||||||
\(318\) | −1.86812e17 | + | 4.86875e16i | −0.568086 | + | 0.148057i | ||||
\(319\) | − | 7.48057e16i | − | 0.222536i | ||||||
\(320\) | −2.04741e16 | + | 4.98069e17i | −0.0595875 | + | 1.44957i | ||||
\(321\) | −6.62306e17 | −1.88592 | ||||||||
\(322\) | −1.30460e17 | − | 5.00569e17i | −0.363485 | − | 1.39468i | ||||
\(323\) | − | 1.09376e17i | − | 0.298199i | ||||||
\(324\) | 3.74102e17 | − | 2.09210e17i | 0.998102 | − | 0.558171i | ||||
\(325\) | −4.13966e17 | −1.08089 | ||||||||
\(326\) | −5.11117e17 | + | 1.33209e17i | −1.30616 | + | 0.340417i | ||||
\(327\) | 5.81535e17i | 1.45459i | ||||||||
\(328\) | −1.19975e16 | − | 1.25009e16i | −0.0293748 | − | 0.0306071i | ||||
\(329\) | 2.21646e17 | 0.531239 | ||||||||
\(330\) | 1.74164e17 | + | 6.68260e17i | 0.408660 | + | 1.56801i | ||||
\(331\) | − | 4.74292e17i | − | 1.08956i | −0.838580 | − | 0.544778i | \(-0.816614\pi\) | ||
0.838580 | − | 0.544778i | \(-0.183386\pi\) | |||||||
\(332\) | −1.90568e17 | − | 3.40766e17i | −0.428630 | − | 0.766460i | ||||
\(333\) | −8.17423e16 | −0.180027 | ||||||||
\(334\) | 3.95763e17 | − | 1.03145e17i | 0.853513 | − | 0.222446i | ||||
\(335\) | − | 7.73185e17i | − | 1.63294i | ||||||
\(336\) | −2.32311e17 | + | 3.78070e17i | −0.480501 | + | 0.781983i | ||||
\(337\) | 6.48884e17 | 1.31449 | 0.657245 | − | 0.753677i | \(-0.271722\pi\) | ||||
0.657245 | + | 0.753677i | \(0.271722\pi\) | |||||||
\(338\) | 5.44452e15 | + | 2.08904e16i | 0.0108030 | + | 0.0414504i | ||||
\(339\) | − | 5.64323e17i | − | 1.09681i | ||||||
\(340\) | −5.58431e17 | + | 3.12293e17i | −1.06320 | + | 0.594579i | ||||
\(341\) | −1.72282e16 | −0.0321337 | ||||||||
\(342\) | 3.26810e16 | − | 8.51743e15i | 0.0597189 | − | 0.0155642i | ||||
\(343\) | 6.06766e17i | 1.08633i | ||||||||
\(344\) | 1.76063e17 | − | 1.68975e17i | 0.308859 | − | 0.296423i | ||||
\(345\) | 1.55565e18 | 2.67411 | ||||||||
\(346\) | 2.41829e17 | + | 9.27885e17i | 0.407357 | + | 1.56301i | ||||
\(347\) | 7.04504e17i | 1.16299i | 0.813549 | + | 0.581496i | \(0.197532\pi\) | ||||
−0.813549 | + | 0.581496i | \(0.802468\pi\) | |||||||
\(348\) | 7.05552e16 | + | 1.26164e17i | 0.114150 | + | 0.204118i | ||||
\(349\) | −9.26668e17 | −1.46942 | −0.734711 | − | 0.678381i | \(-0.762682\pi\) | ||||
−0.734711 | + | 0.678381i | \(0.762682\pi\) | |||||||
\(350\) | 5.82715e17 | − | 1.51869e17i | 0.905690 | − | 0.236044i | ||||
\(351\) | − | 5.74825e17i | − | 0.875761i | ||||||
\(352\) | 2.01373e17 | − | 6.60243e17i | 0.300748 | − | 0.986065i | ||||
\(353\) | −1.15975e18 | −1.69801 | −0.849005 | − | 0.528385i | \(-0.822798\pi\) | ||||
−0.849005 | + | 0.528385i | \(0.822798\pi\) | |||||||
\(354\) | −2.19836e17 | − | 8.43500e17i | −0.315556 | − | 1.21077i | ||||
\(355\) | 3.72868e17i | 0.524756i | ||||||||
\(356\) | −4.63080e17 | + | 2.58970e17i | −0.639008 | + | 0.357354i | ||||
\(357\) | −5.69549e17 | −0.770643 | ||||||||
\(358\) | 1.31972e17 | − | 3.43949e16i | 0.175105 | − | 0.0456366i | ||||
\(359\) | 8.35881e16i | 0.108764i | 0.998520 | + | 0.0543818i | \(0.0173188\pi\) | ||||
−0.998520 | + | 0.0543818i | \(0.982681\pi\) | |||||||
\(360\) | −1.36798e17 | − | 1.42536e17i | −0.174566 | − | 0.181890i | ||||
\(361\) | 6.98229e17 | 0.873872 | ||||||||
\(362\) | −2.42982e16 | − | 9.32309e16i | −0.0298273 | − | 0.114446i | ||||
\(363\) | − | 5.64821e16i | − | 0.0680087i | ||||||
\(364\) | 3.42506e17 | + | 6.12457e17i | 0.404537 | + | 0.723379i | ||||
\(365\) | 7.08535e15 | 0.00820940 | ||||||||
\(366\) | 2.48181e17 | − | 6.46819e16i | 0.282099 | − | 0.0735217i | ||||
\(367\) | 8.77749e17i | 0.978831i | 0.872051 | + | 0.489416i | \(0.162790\pi\) | ||||
−0.872051 | + | 0.489416i | \(0.837210\pi\) | |||||||
\(368\) | −1.32483e18 | − | 8.14061e17i | −1.44952 | − | 0.890681i | ||||
\(369\) | 6.86686e15 | 0.00737180 | ||||||||
\(370\) | −3.59851e17 | − | 1.38073e18i | −0.379063 | − | 1.45445i | ||||
\(371\) | − | 4.44091e17i | − | 0.459045i | ||||||
\(372\) | 2.90565e16 | − | 1.62493e16i | 0.0294742 | − | 0.0164829i | ||||
\(373\) | −5.51683e17 | −0.549196 | −0.274598 | − | 0.961559i | \(-0.588545\pi\) | ||||
−0.274598 | + | 0.961559i | \(0.588545\pi\) | |||||||
\(374\) | 8.57336e17 | − | 2.23442e17i | 0.837625 | − | 0.218305i | ||||
\(375\) | 1.71800e17i | 0.164742i | ||||||||
\(376\) | 4.80693e17 | − | 4.61339e17i | 0.452432 | − | 0.434216i | ||||
\(377\) | 2.28593e17 | 0.211190 | ||||||||
\(378\) | 2.10882e17 | + | 8.09145e17i | 0.191248 | + | 0.733810i | ||||
\(379\) | 1.91257e18i | 1.70272i | 0.524580 | + | 0.851361i | \(0.324222\pi\) | ||||
−0.524580 | + | 0.851361i | \(0.675778\pi\) | |||||||
\(380\) | 2.87740e17 | + | 5.14527e17i | 0.251487 | + | 0.449700i | ||||
\(381\) | 2.25096e18 | 1.93149 | ||||||||
\(382\) | −1.19572e18 | + | 3.11632e17i | −1.00736 | + | 0.262542i | ||||
\(383\) | − | 1.96195e18i | − | 1.62291i | −0.584412 | − | 0.811457i | \(-0.698675\pi\) | ||
0.584412 | − | 0.811457i | \(-0.301325\pi\) | |||||||
\(384\) | 2.83101e17 | + | 1.30347e18i | 0.229944 | + | 1.05872i | ||||
\(385\) | −1.58860e18 | −1.26704 | ||||||||
\(386\) | 5.81255e17 | + | 2.23025e18i | 0.455256 | + | 1.74679i | ||||
\(387\) | 9.67135e16i | 0.0743893i | ||||||||
\(388\) | 1.92744e18 | − | 1.07789e18i | 1.45599 | − | 0.814239i | ||||
\(389\) | −2.25076e17 | −0.166987 | −0.0834933 | − | 0.996508i | \(-0.526608\pi\) | ||||
−0.0834933 | + | 0.996508i | \(0.526608\pi\) | |||||||
\(390\) | −2.04208e18 | + | 5.32215e17i | −1.48806 | + | 0.387824i | ||||
\(391\) | − | 1.99581e18i | − | 1.42850i | ||||||
\(392\) | 2.78061e17 | + | 2.89726e17i | 0.195496 | + | 0.203697i | ||||
\(393\) | −7.42418e17 | −0.512744 | ||||||||
\(394\) | −1.38994e17 | − | 5.33314e17i | −0.0943026 | − | 0.361834i | ||||
\(395\) | − | 1.19092e18i | − | 0.793782i | ||||||
\(396\) | 1.33526e17 | + | 2.38766e17i | 0.0874379 | + | 0.156353i | ||||
\(397\) | 2.10584e18 | 1.35485 | 0.677427 | − | 0.735590i | \(-0.263095\pi\) | ||||
0.677427 | + | 0.735590i | \(0.263095\pi\) | |||||||
\(398\) | −4.43407e17 | + | 1.15562e17i | −0.280299 | + | 0.0730524i | ||||
\(399\) | 5.24771e17i | 0.325956i | ||||||||
\(400\) | 9.47652e17 | − | 1.54224e18i | 0.578401 | − | 0.941308i | ||||
\(401\) | 1.01874e18 | 0.611014 | 0.305507 | − | 0.952190i | \(-0.401174\pi\) | ||||
0.305507 | + | 0.952190i | \(0.401174\pi\) | |||||||
\(402\) | −5.21772e17 | − | 2.00201e18i | −0.307538 | − | 1.18001i | ||||
\(403\) | − | 5.26464e16i | − | 0.0304953i | ||||||
\(404\) | −2.57388e18 | + | 1.43940e18i | −1.46527 | + | 0.819430i | ||||
\(405\) | −2.96521e18 | −1.65909 | ||||||||
\(406\) | −3.21776e17 | + | 8.38624e16i | −0.176958 | + | 0.0461196i | ||||
\(407\) | 1.97580e18i | 1.06802i | ||||||||
\(408\) | −1.23520e18 | + | 1.18547e18i | −0.656322 | + | 0.629897i | ||||
\(409\) | −5.09887e17 | −0.266324 | −0.133162 | − | 0.991094i | \(-0.542513\pi\) | ||||
−0.133162 | + | 0.991094i | \(0.542513\pi\) | |||||||
\(410\) | 3.02297e16 | + | 1.15990e17i | 0.0155220 | + | 0.0595571i | ||||
\(411\) | − | 2.50986e18i | − | 1.26694i | ||||||
\(412\) | −4.07080e16 | − | 7.27925e16i | −0.0202022 | − | 0.0361249i | ||||
\(413\) | 2.00518e18 | 0.978369 | ||||||||
\(414\) | 5.96334e17 | − | 1.55419e17i | 0.286080 | − | 0.0745592i | ||||
\(415\) | 2.70099e18i | 1.27405i | ||||||||
\(416\) | 2.01759e18 | + | 6.15360e17i | 0.935790 | + | 0.285414i | ||||
\(417\) | −2.42551e18 | −1.10624 | ||||||||
\(418\) | −2.05875e17 | − | 7.89932e17i | −0.0923357 | − | 0.354288i | ||||
\(419\) | 1.48939e18i | 0.656917i | 0.944518 | + | 0.328459i | \(0.106529\pi\) | ||||
−0.944518 | + | 0.328459i | \(0.893471\pi\) | |||||||
\(420\) | 2.67926e18 | − | 1.49833e18i | 1.16217 | − | 0.649925i | ||||
\(421\) | −3.84687e17 | −0.164109 | −0.0820546 | − | 0.996628i | \(-0.526148\pi\) | ||||
−0.0820546 | + | 0.996628i | \(0.526148\pi\) | |||||||
\(422\) | 4.38748e18 | − | 1.14348e18i | 1.84089 | − | 0.479780i | ||||
\(423\) | 2.64050e17i | 0.108969i | ||||||||
\(424\) | −9.24340e17 | − | 9.63118e17i | −0.375207 | − | 0.390948i | ||||
\(425\) | 2.32333e18 | 0.927658 | ||||||||
\(426\) | 2.51624e17 | + | 9.65471e17i | 0.0988293 | + | 0.379203i | ||||
\(427\) | 5.89980e17i | 0.227951i | ||||||||
\(428\) | −2.23533e18 | − | 3.99713e18i | −0.849640 | − | 1.51929i | ||||
\(429\) | 2.92218e18 | 1.09271 | ||||||||
\(430\) | −1.63361e18 | + | 4.25759e17i | −0.600994 | + | 0.156633i | ||||
\(431\) | 3.54760e18i | 1.28408i | 0.766669 | + | 0.642042i | \(0.221913\pi\) | ||||
−0.766669 | + | 0.642042i | \(0.778087\pi\) | |||||||
\(432\) | 2.14152e18 | + | 1.31589e18i | 0.762668 | + | 0.468633i | ||||
\(433\) | −2.75629e18 | −0.965849 | −0.482925 | − | 0.875662i | \(-0.660426\pi\) | ||||
−0.482925 | + | 0.875662i | \(0.660426\pi\) | |||||||
\(434\) | 1.93141e16 | + | 7.41071e16i | 0.00665956 | + | 0.0255524i | ||||
\(435\) | − | 1.00001e18i | − | 0.339295i | ||||||
\(436\) | −3.50966e18 | + | 1.96272e18i | −1.17182 | + | 0.655319i | ||||
\(437\) | −1.83890e18 | −0.604209 | ||||||||
\(438\) | 1.83461e16 | − | 4.78144e15i | 0.00593234 | − | 0.00154611i | ||||
\(439\) | − | 3.70584e18i | − | 1.17933i | −0.807648 | − | 0.589665i | \(-0.799260\pi\) | ||
0.807648 | − | 0.589665i | \(-0.200740\pi\) | |||||||
\(440\) | −3.44525e18 | + | 3.30654e18i | −1.07908 | + | 1.03563i | ||||
\(441\) | −1.59150e17 | −0.0490609 | ||||||||
\(442\) | 6.82799e17 | + | 2.61986e18i | 0.207175 | + | 0.794919i | ||||
\(443\) | − | 1.77582e18i | − | 0.530362i | −0.964199 | − | 0.265181i | \(-0.914568\pi\) | ||
0.964199 | − | 0.265181i | \(-0.0854317\pi\) | |||||||
\(444\) | −1.86353e18 | − | 3.33230e18i | −0.547843 | − | 0.979632i | ||||
\(445\) | 3.67048e18 | 1.06219 | ||||||||
\(446\) | 2.45657e18 | − | 6.40239e17i | 0.699817 | − | 0.182389i | ||||
\(447\) | − | 2.25993e18i | − | 0.633785i | ||||||
\(448\) | −3.06578e18 | − | 1.26025e17i | −0.846438 | − | 0.0347945i | ||||
\(449\) | −3.86648e18 | −1.05097 | −0.525486 | − | 0.850802i | \(-0.676116\pi\) | ||||
−0.525486 | + | 0.850802i | \(0.676116\pi\) | |||||||
\(450\) | 1.80924e17 | + | 6.94195e17i | 0.0484181 | + | 0.185778i | ||||
\(451\) | − | 1.65979e17i | − | 0.0437338i | ||||||
\(452\) | 3.40579e18 | − | 1.90463e18i | 0.883586 | − | 0.494130i | ||||
\(453\) | 5.92893e17 | 0.151457 | ||||||||
\(454\) | 1.41904e18 | − | 3.69835e17i | 0.356946 | − | 0.0930286i | ||||
\(455\) | − | 4.85447e18i | − | 1.20244i | ||||||
\(456\) | 1.09227e18 | + | 1.13809e18i | 0.266425 | + | 0.277602i | ||||
\(457\) | −1.78862e18 | −0.429639 | −0.214820 | − | 0.976654i | \(-0.568916\pi\) | ||||
−0.214820 | + | 0.976654i | \(0.568916\pi\) | |||||||
\(458\) | −3.99425e17 | − | 1.53257e18i | −0.0944881 | − | 0.362546i | ||||
\(459\) | 3.22612e18i | 0.751609i | ||||||||
\(460\) | 5.25044e18 | + | 9.38865e18i | 1.20473 | + | 2.15426i | ||||
\(461\) | 3.38458e18 | 0.764889 | 0.382444 | − | 0.923979i | \(-0.375082\pi\) | ||||
0.382444 | + | 0.923979i | \(0.375082\pi\) | |||||||
\(462\) | −4.11337e18 | + | 1.07204e18i | −0.915595 | + | 0.238626i | ||||
\(463\) | − | 1.27172e18i | − | 0.278821i | −0.990235 | − | 0.139410i | \(-0.955479\pi\) | ||
0.990235 | − | 0.139410i | \(-0.0445207\pi\) | |||||||
\(464\) | −5.23295e17 | + | 8.51626e17i | −0.113011 | + | 0.183918i | ||||
\(465\) | −2.30308e17 | −0.0489935 | ||||||||
\(466\) | −1.24911e17 | − | 4.79278e17i | −0.0261758 | − | 0.100435i | ||||
\(467\) | 1.67912e18i | 0.346628i | 0.984867 | + | 0.173314i | \(0.0554475\pi\) | ||||
−0.984867 | + | 0.173314i | \(0.944553\pi\) | |||||||
\(468\) | −7.29627e17 | + | 4.08032e17i | −0.148382 | + | 0.0829799i | ||||
\(469\) | 4.75921e18 | 0.953510 | ||||||||
\(470\) | −4.46014e18 | + | 1.16242e18i | −0.880367 | + | 0.229444i | ||||
\(471\) | 6.45134e18i | 1.25460i | ||||||||
\(472\) | 4.34871e18 | − | 4.17362e18i | 0.833232 | − | 0.799684i | ||||
\(473\) | 2.33767e18 | 0.441321 | ||||||||
\(474\) | −8.03671e17 | − | 3.08365e18i | −0.149496 | − | 0.573609i | ||||
\(475\) | − | 2.14067e18i | − | 0.392368i | ||||||
\(476\) | −1.92227e18 | − | 3.43733e18i | −0.347188 | − | 0.620829i | ||||
\(477\) | 5.29052e17 | 0.0941606 | ||||||||
\(478\) | 1.76922e18 | − | 4.61100e17i | 0.310303 | − | 0.0808722i | ||||
\(479\) | 2.63877e18i | 0.456092i | 0.973650 | + | 0.228046i | \(0.0732337\pi\) | ||||
−0.973650 | + | 0.228046i | \(0.926766\pi\) | |||||||
\(480\) | 2.69196e18 | − | 8.82616e18i | 0.458543 | − | 1.50343i | ||||
\(481\) | −6.03768e18 | −1.01357 | ||||||||
\(482\) | 1.40517e17 | + | 5.39157e17i | 0.0232488 | + | 0.0892043i | ||||
\(483\) | 9.57558e18i | 1.56147i | ||||||||
\(484\) | 3.40879e17 | − | 1.90631e17i | 0.0547877 | − | 0.0306391i | ||||
\(485\) | −1.52773e19 | −2.42022 | ||||||||
\(486\) | −2.13062e18 | + | 5.55291e17i | −0.332700 | + | 0.0867095i | ||||
\(487\) | − | 6.02454e18i | − | 0.927303i | −0.886018 | − | 0.463651i | \(-0.846539\pi\) | ||
0.886018 | − | 0.463651i | \(-0.153461\pi\) | |||||||
\(488\) | 1.22800e18 | + | 1.27951e18i | 0.186320 | + | 0.194136i | ||||
\(489\) | 9.77735e18 | 1.46238 | ||||||||
\(490\) | −7.00619e17 | − | 2.68824e18i | −0.103302 | − | 0.396365i | ||||
\(491\) | − | 3.04593e18i | − | 0.442741i | −0.975190 | − | 0.221371i | \(-0.928947\pi\) | ||
0.975190 | − | 0.221371i | \(-0.0710531\pi\) | |||||||
\(492\) | 1.56548e17 | + | 2.79934e17i | 0.0224332 | + | 0.0401143i | ||||
\(493\) | −1.28295e18 | −0.181251 | ||||||||
\(494\) | 2.41389e18 | − | 6.29117e17i | 0.336224 | − | 0.0876280i | ||||
\(495\) | − | 1.89252e18i | − | 0.259898i | ||||||
\(496\) | 1.96135e17 | + | 1.20518e17i | 0.0265573 | + | 0.0163185i | ||||
\(497\) | −2.29513e18 | −0.306417 | ||||||||
\(498\) | 1.82272e18 | + | 6.99368e18i | 0.239946 | + | 0.920663i | ||||
\(499\) | − | 4.15397e18i | − | 0.539212i | −0.962971 | − | 0.269606i | \(-0.913106\pi\) | ||
0.962971 | − | 0.269606i | \(-0.0868935\pi\) | |||||||
\(500\) | −1.03685e18 | + | 5.79838e17i | −0.132716 | + | 0.0742193i | ||||
\(501\) | −7.57070e18 | −0.955591 | ||||||||
\(502\) | −1.28178e19 | + | 3.34061e18i | −1.59546 | + | 0.415815i | ||||
\(503\) | 8.28512e18i | 1.01700i | 0.861061 | + | 0.508502i | \(0.169801\pi\) | ||||
−0.861061 | + | 0.508502i | \(0.830199\pi\) | |||||||
\(504\) | 8.77359e17 | − | 8.42035e17i | 0.106210 | − | 0.101933i | ||||
\(505\) | 2.04012e19 | 2.43565 | ||||||||
\(506\) | −3.75663e18 | − | 1.44140e19i | −0.442329 | − | 1.69719i | ||||
\(507\) | − | 3.99620e17i | − | 0.0464078i | ||||||
\(508\) | 7.59713e18 | + | 1.35849e19i | 0.870169 | + | 1.55601i | ||||
\(509\) | −1.06268e17 | −0.0120054 | −0.00600270 | − | 0.999982i | \(-0.501911\pi\) | ||||
−0.00600270 | + | 0.999982i | \(0.501911\pi\) | |||||||
\(510\) | 1.14609e19 | − | 2.98698e18i | 1.27711 | − | 0.332845i | ||||
\(511\) | 4.36127e16i | 0.00479365i | ||||||||
\(512\) | −6.91119e18 | + | 6.10787e18i | −0.749313 | + | 0.662216i | ||||
\(513\) | 2.97249e18 | 0.317906 | ||||||||
\(514\) | 4.49096e18 | + | 1.72316e19i | 0.473803 | + | 1.81796i | ||||
\(515\) | 5.76970e17i | 0.0600485i | ||||||||
\(516\) | −3.94261e18 | + | 2.20484e18i | −0.404796 | + | 0.226375i | ||||
\(517\) | 6.38237e18 | 0.646469 | ||||||||
\(518\) | 8.49887e18 | − | 2.21501e18i | 0.849284 | − | 0.221343i | ||||
\(519\) | − | 1.77499e19i | − | 1.74994i | ||||||
\(520\) | −1.01042e19 | − | 1.05281e19i | −0.982829 | − | 1.02406i | ||||
\(521\) | 5.25175e18 | 0.504011 | 0.252006 | − | 0.967726i | \(-0.418910\pi\) | ||||
0.252006 | + | 0.967726i | \(0.418910\pi\) | |||||||
\(522\) | −9.99063e16 | − | 3.83336e17i | −0.00946018 | − | 0.0362983i | ||||
\(523\) | − | 1.39466e19i | − | 1.30304i | −0.758632 | − | 0.651519i | \(-0.774132\pi\) | ||
0.758632 | − | 0.651519i | \(-0.225868\pi\) | |||||||
\(524\) | −2.50571e18 | − | 4.48062e18i | −0.231000 | − | 0.413066i | ||||
\(525\) | −1.11470e19 | −1.01401 | ||||||||
\(526\) | 3.66173e18 | − | 9.54333e17i | 0.328690 | − | 0.0856643i | ||||
\(527\) | 2.95471e17i | 0.0261722i | ||||||||
\(528\) | −6.68945e18 | + | 1.08866e19i | −0.584727 | + | 0.951602i | ||||
\(529\) | −2.19618e19 | −1.89443 | ||||||||
\(530\) | 2.32902e18 | + | 8.93635e18i | 0.198264 | + | 0.760728i | ||||
\(531\) | 2.38879e18i | 0.200686i | ||||||||
\(532\) | −3.16708e18 | + | 1.77114e18i | −0.262590 | + | 0.146849i | ||||
\(533\) | 5.07202e17 | 0.0415041 | ||||||||
\(534\) | 9.50399e18 | − | 2.47696e18i | 0.767568 | − | 0.200046i | ||||
\(535\) | 3.16821e19i | 2.52545i | ||||||||
\(536\) | 1.03215e19 | − | 9.90592e18i | 0.812061 | − | 0.779366i | ||||
\(537\) | −2.52454e18 | −0.196048 | ||||||||
\(538\) | −2.81803e18 | − | 1.08127e19i | −0.216008 | − | 0.828813i | ||||
\(539\) | 3.84681e18i | 0.291058i | ||||||||
\(540\) | −8.48708e18 | − | 1.51763e19i | −0.633873 | − | 1.13347i | ||||
\(541\) | −7.44833e18 | −0.549134 | −0.274567 | − | 0.961568i | \(-0.588534\pi\) | ||||
−0.274567 | + | 0.961568i | \(0.588534\pi\) | |||||||
\(542\) | −2.20397e19 | + | 5.74406e18i | −1.60402 | + | 0.418046i | ||||
\(543\) | 1.78345e18i | 0.128133i | ||||||||
\(544\) | −1.13234e19 | − | 3.45362e18i | −0.803129 | − | 0.244953i | ||||
\(545\) | 2.78184e19 | 1.94785 | ||||||||
\(546\) | −3.27596e18 | − | 1.25697e19i | −0.226459 | − | 0.868914i | ||||
\(547\) | − | 1.84776e19i | − | 1.26106i | −0.776167 | − | 0.630528i | \(-0.782838\pi\) | ||
0.776167 | − | 0.630528i | \(-0.217162\pi\) | |||||||
\(548\) | 1.51475e19 | − | 8.47096e18i | 1.02065 | − | 0.570780i | ||||
\(549\) | −7.02851e17 | −0.0467581 | ||||||||
\(550\) | 1.67794e19 | − | 4.37311e18i | 1.10214 | − | 0.287244i | ||||
\(551\) | 1.18208e18i | 0.0766630i | ||||||||
\(552\) | 1.99308e19 | + | 2.07669e19i | 1.27629 | + | 1.32984i | ||||
\(553\) | 7.33048e18 | 0.463507 | ||||||||
\(554\) | 4.03442e18 | + | 1.54799e19i | 0.251891 | + | 0.966493i | ||||
\(555\) | 2.64125e19i | 1.62839i | ||||||||
\(556\) | −8.18625e18 | − | 1.46384e19i | −0.498381 | − | 0.891187i | ||||
\(557\) | 1.27693e19 | 0.767683 | 0.383841 | − | 0.923399i | \(-0.374601\pi\) | ||||
0.383841 | + | 0.923399i | \(0.374601\pi\) | |||||||
\(558\) | −8.82847e16 | + | 2.30091e16i | −0.00524139 | + | 0.00136603i | ||||
\(559\) | 7.14349e18i | 0.418820i | ||||||||
\(560\) | 1.80854e19 | + | 1.11129e19i | 1.04716 | + | 0.643442i | ||||
\(561\) | −1.64003e19 | −0.937803 | ||||||||
\(562\) | −2.95839e18 | − | 1.13512e19i | −0.167071 | − | 0.641043i | ||||
\(563\) | − | 1.53198e18i | − | 0.0854467i | −0.999087 | − | 0.0427234i | \(-0.986397\pi\) | ||
0.999087 | − | 0.0427234i | \(-0.0136034\pi\) | |||||||
\(564\) | −1.07642e19 | + | 6.01972e18i | −0.592966 | + | 0.331606i | ||||
\(565\) | −2.69950e19 | −1.46874 | ||||||||
\(566\) | −9.42801e18 | + | 2.45716e18i | −0.506646 | + | 0.132044i | ||||
\(567\) | − | 1.82519e19i | − | 0.968783i | ||||||
\(568\) | −4.97754e18 | + | 4.77713e18i | −0.260961 | + | 0.250454i | ||||
\(569\) | −1.27708e19 | −0.661350 | −0.330675 | − | 0.943745i | \(-0.607276\pi\) | ||||
−0.330675 | + | 0.943745i | \(0.607276\pi\) | |||||||
\(570\) | −2.75215e18 | − | 1.05599e19i | −0.140782 | − | 0.540174i | ||||
\(571\) | 3.30749e19i | 1.67127i | 0.549286 | + | 0.835635i | \(0.314900\pi\) | ||||
−0.549286 | + | 0.835635i | \(0.685100\pi\) | |||||||
\(572\) | 9.86254e18 | + | 1.76358e19i | 0.492285 | + | 0.880287i | ||||
\(573\) | 2.28733e19 | 1.12784 | ||||||||
\(574\) | −7.13957e17 | + | 1.86074e17i | −0.0347767 | + | 0.00906364i | ||||
\(575\) | − | 3.90611e19i | − | 1.87962i | ||||||
\(576\) | 1.50135e17 | − | 3.65231e18i | 0.00713715 | − | 0.173624i | ||||
\(577\) | 2.53825e19 | 1.19207 | 0.596037 | − | 0.802957i | \(-0.296741\pi\) | ||||
0.596037 | + | 0.802957i | \(0.296741\pi\) | |||||||
\(578\) | 1.60337e18 | + | 6.15207e18i | 0.0743944 | + | 0.285448i | ||||
\(579\) | − | 4.26632e19i | − | 1.95571i | ||||||
\(580\) | 6.03521e18 | − | 3.37509e18i | 0.273336 | − | 0.152858i | ||||
\(581\) | −1.66255e19 | −0.743946 | ||||||||
\(582\) | −3.95577e19 | + | 1.03097e19i | −1.74892 | + | 0.455810i | ||||
\(583\) | − | 1.27877e19i | − | 0.558616i | ||||||
\(584\) | 9.07763e16 | + | 9.45845e16i | 0.00391816 | + | 0.00408254i | ||||
\(585\) | 5.78319e18 | 0.246647 | ||||||||
\(586\) | 2.65930e18 | + | 1.02036e19i | 0.112068 | + | 0.430001i | ||||
\(587\) | − | 8.66644e18i | − | 0.360889i | −0.983585 | − | 0.180445i | \(-0.942246\pi\) | ||
0.983585 | − | 0.180445i | \(-0.0577537\pi\) | |||||||
\(588\) | −3.62823e18 | − | 6.48788e18i | −0.149298 | − | 0.266969i | ||||
\(589\) | 2.72241e17 | 0.0110700 | ||||||||
\(590\) | −4.03498e19 | + | 1.05161e19i | −1.62135 | + | 0.422562i | ||||
\(591\) | 1.02020e19i | 0.405109i | ||||||||
\(592\) | 1.38215e19 | − | 2.24935e19i | 0.542378 | − | 0.882683i | ||||
\(593\) | 1.33237e18 | 0.0516704 | 0.0258352 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258352 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(594\) | 6.07241e18 | + | 2.32995e19i | 0.232732 | + | 0.892981i | ||||
\(595\) | 2.72450e19i | 1.03197i | ||||||||
\(596\) | 1.36391e19 | − | 7.62741e18i | 0.510576 | − | 0.285531i | ||||
\(597\) | 8.48210e18 | 0.313822 | ||||||||
\(598\) | 4.40466e19 | − | 1.14796e19i | 1.61066 | − | 0.419777i | ||||
\(599\) | 3.49944e19i | 1.26477i | 0.774656 | + | 0.632383i | \(0.217923\pi\) | ||||
−0.774656 | + | 0.632383i | \(0.782077\pi\) | |||||||
\(600\) | −2.41749e19 | + | 2.32015e19i | −0.863585 | + | 0.828815i | ||||
\(601\) | −2.22716e19 | −0.786376 | −0.393188 | − | 0.919458i | \(-0.628628\pi\) | ||||
−0.393188 | + | 0.919458i | \(0.628628\pi\) | |||||||
\(602\) | −2.62069e18 | − | 1.00554e19i | −0.0914618 | − | 0.350934i | ||||
\(603\) | 5.66971e18i | 0.195587i | ||||||||
\(604\) | 2.00105e18 | + | 3.57821e18i | 0.0682339 | + | 0.122013i | ||||
\(605\) | −2.70189e18 | −0.0910709 | ||||||||
\(606\) | 5.28249e19 | − | 1.37674e19i | 1.76007 | − | 0.458716i | ||||
\(607\) | − | 2.81797e19i | − | 0.928145i | −0.885797 | − | 0.464073i | \(-0.846388\pi\) | ||
0.885797 | − | 0.464073i | \(-0.153612\pi\) | |||||||
\(608\) | −3.18210e18 | + | 1.04332e19i | −0.103607 | + | 0.339697i | ||||
\(609\) | 6.15537e18 | 0.198122 | ||||||||
\(610\) | −3.09413e18 | − | 1.18720e19i | −0.0984533 | − | 0.377761i | ||||
\(611\) | 1.95034e19i | 0.613509i | ||||||||
\(612\) | 4.09493e18 | − | 2.29002e18i | 0.127346 | − | 0.0712163i | ||||
\(613\) | 2.19343e19 | 0.674372 | 0.337186 | − | 0.941438i | \(-0.390525\pi\) | ||||
0.337186 | + | 0.941438i | \(0.390525\pi\) | |||||||
\(614\) | 1.88696e19 | − | 4.91786e18i | 0.573566 | − | 0.149485i | ||||
\(615\) | − | 2.21882e18i | − | 0.0666800i | ||||||
\(616\) | −2.03528e19 | − | 2.12067e19i | −0.604728 | − | 0.630097i | ||||
\(617\) | −4.07723e19 | −1.19776 | −0.598879 | − | 0.800840i | \(-0.704387\pi\) | ||||
−0.598879 | + | 0.800840i | \(0.704387\pi\) | |||||||
\(618\) | 3.89359e17 | + | 1.49395e18i | 0.0113092 | + | 0.0433927i | ||||
\(619\) | 1.07476e19i | 0.308658i | 0.988019 | + | 0.154329i | \(0.0493216\pi\) | ||||
−0.988019 | + | 0.154329i | \(0.950678\pi\) | |||||||
\(620\) | −7.77305e17 | − | 1.38995e18i | −0.0220724 | − | 0.0394691i | ||||
\(621\) | 5.42394e19 | 1.52291 | ||||||||
\(622\) | 1.38297e18 | − | 3.60435e17i | 0.0383955 | − | 0.0100068i | ||||
\(623\) | 2.25930e19i | 0.620237i | ||||||||
\(624\) | −3.32675e19 | − | 2.04418e19i | −0.903085 | − | 0.554914i | ||||
\(625\) | −3.29391e19 | −0.884204 | ||||||||
\(626\) | −1.45265e19 | − | 5.57375e19i | −0.385604 | − | 1.47954i | ||||
\(627\) | 1.51109e19i | 0.396659i | ||||||||
\(628\) | −3.89350e19 | + | 2.17737e19i | −1.01070 | + | 0.565217i | ||||
\(629\) | 3.38856e19 | 0.869883 | ||||||||
\(630\) | −8.14064e18 | + | 2.12164e18i | −0.206669 | + | 0.0538627i | ||||
\(631\) | 6.39901e19i | 1.60660i | 0.595575 | + | 0.803300i | \(0.296924\pi\) | ||||
−0.595575 | + | 0.803300i | \(0.703076\pi\) | |||||||
\(632\) | 1.58979e19 | − | 1.52578e19i | 0.394748 | − | 0.378855i | ||||
\(633\) | −8.39297e19 | −2.06106 | ||||||||
\(634\) | −7.55475e17 | − | 2.89872e18i | −0.0183483 | − | 0.0704014i | ||||
\(635\) | − | 1.07677e20i | − | 2.58647i | ||||||
\(636\) | 1.20611e19 | + | 2.15673e19i | 0.286542 | + | 0.512383i | ||||
\(637\) | −1.17552e19 | −0.276218 | ||||||||
\(638\) | −9.26562e18 | + | 2.41484e18i | −0.215342 | + | 0.0561233i | ||||
\(639\) | − | 2.73422e18i | − | 0.0628531i | ||||||
\(640\) | 6.23530e19 | − | 1.35424e19i | 1.41774 | − | 0.307919i | ||||
\(641\) | 5.57952e18 | 0.125485 | 0.0627423 | − | 0.998030i | \(-0.480015\pi\) | ||||
0.0627423 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(642\) | 2.13802e19 | + | 8.20348e19i | 0.475627 | + | 1.82496i | ||||
\(643\) | − | 3.16664e19i | − | 0.696822i | −0.937342 | − | 0.348411i | \(-0.886721\pi\) | ||
0.937342 | − | 0.348411i | \(-0.113279\pi\) | |||||||
\(644\) | −5.77903e19 | + | 3.23182e19i | −1.25792 | + | 0.703471i | ||||
\(645\) | 3.12500e19 | 0.672872 | ||||||||
\(646\) | −1.35476e19 | + | 3.53083e18i | −0.288560 | + | 0.0752054i | ||||
\(647\) | − | 4.14438e19i | − | 0.873231i | −0.899648 | − | 0.436616i | \(-0.856177\pi\) | ||
0.899648 | − | 0.436616i | \(-0.143823\pi\) | |||||||
\(648\) | −3.79898e19 | − | 3.95836e19i | −0.791849 | − | 0.825068i | ||||
\(649\) | 5.77396e19 | 1.19059 | ||||||||
\(650\) | 1.33634e19 | + | 5.12749e19i | 0.272599 | + | 1.04595i | ||||
\(651\) | − | 1.41762e18i | − | 0.0286084i | ||||||
\(652\) | 3.29992e19 | + | 5.90080e19i | 0.658826 | + | 1.17809i | ||||
\(653\) | −3.03333e19 | −0.599138 | −0.299569 | − | 0.954075i | \(-0.596843\pi\) | ||||
−0.299569 | + | 0.954075i | \(0.596843\pi\) | |||||||
\(654\) | 7.20303e19 | − | 1.87728e19i | 1.40757 | − | 0.366847i | ||||
\(655\) | 3.55144e19i | 0.686618i | ||||||||
\(656\) | −1.16109e18 | + | 1.88959e18i | −0.0222095 | + | 0.0361444i | ||||
\(657\) | −5.19563e16 | −0.000983289 | ||||||||
\(658\) | −7.15508e18 | − | 2.74537e19i | −0.133978 | − | 0.514066i | ||||
\(659\) | 5.74518e18i | 0.106440i | 0.998583 | + | 0.0532201i | \(0.0169485\pi\) | ||||
−0.998583 | + | 0.0532201i | \(0.983051\pi\) | |||||||
\(660\) | 7.71501e19 | − | 4.31449e19i | 1.41426 | − | 0.790900i | ||||
\(661\) | 7.51512e19 | 1.36309 | 0.681547 | − | 0.731775i | \(-0.261308\pi\) | ||||
0.681547 | + | 0.731775i | \(0.261308\pi\) | |||||||
\(662\) | −5.87469e19 | + | 1.53108e19i | −1.05434 | + | 0.274785i | ||||
\(663\) | − | 5.01164e19i | − | 0.889989i | ||||||
\(664\) | −3.60563e19 | + | 3.46046e19i | −0.633585 | + | 0.608075i | ||||
\(665\) | 2.51030e19 | 0.436490 | ||||||||
\(666\) | 2.63876e18 | + | 1.01248e19i | 0.0454026 | + | 0.174208i | ||||
\(667\) | 2.15696e19i | 0.367249i | ||||||||
\(668\) | −2.55516e19 | − | 4.56905e19i | −0.430510 | − | 0.769823i | ||||
\(669\) | −4.69926e19 | −0.783513 | ||||||||
\(670\) | −9.57686e19 | + | 2.49596e19i | −1.58015 | + | 0.411826i | ||||
\(671\) | 1.69886e19i | 0.277396i | ||||||||
\(672\) | 5.43280e19 | + | 1.65699e19i | 0.877887 | + | 0.267754i | ||||
\(673\) | −2.08259e19 | −0.333041 | −0.166521 | − | 0.986038i | \(-0.553253\pi\) | ||||
−0.166521 | + | 0.986038i | \(0.553253\pi\) | |||||||
\(674\) | −2.09469e19 | − | 8.03723e19i | −0.331513 | − | 1.27200i | ||||
\(675\) | 6.31403e19i | 0.988964i | ||||||||
\(676\) | 2.41178e18 | − | 1.34874e18i | 0.0373861 | − | 0.0209075i | ||||
\(677\) | −1.13345e19 | −0.173893 | −0.0869464 | − | 0.996213i | \(-0.527711\pi\) | ||||
−0.0869464 | + | 0.996213i | \(0.527711\pi\) | |||||||
\(678\) | −6.98984e19 | + | 1.82172e19i | −1.06135 | + | 0.276614i | ||||
\(679\) | − | 9.40370e19i | − | 1.41322i | ||||||
\(680\) | 5.67083e19 | + | 5.90873e19i | 0.843499 | + | 0.878885i | ||||
\(681\) | −2.71453e19 | −0.399636 | ||||||||
\(682\) | 5.56153e17 | + | 2.13393e18i | 0.00810408 | + | 0.0310950i | ||||
\(683\) | 7.73552e19i | 1.11569i | 0.829944 | + | 0.557846i | \(0.188372\pi\) | ||||
−0.829944 | + | 0.557846i | \(0.811628\pi\) | |||||||
\(684\) | −2.10998e18 | − | 3.77299e18i | −0.0301221 | − | 0.0538633i | ||||
\(685\) | −1.20062e20 | −1.69657 | ||||||||
\(686\) | 7.51555e19 | − | 1.95873e19i | 1.05122 | − | 0.273972i | ||||
\(687\) | 2.93172e19i | 0.405906i | ||||||||
\(688\) | −2.66132e19 | − | 1.63529e19i | −0.364735 | − | 0.224117i | ||||
\(689\) | 3.90770e19 | 0.530135 | ||||||||
\(690\) | −5.02188e19 | − | 1.92687e20i | −0.674408 | − | 2.58767i | ||||
\(691\) | − | 7.17459e19i | − | 0.953786i | −0.878961 | − | 0.476893i | \(-0.841763\pi\) | ||
0.878961 | − | 0.476893i | \(-0.158237\pi\) | |||||||
\(692\) | 1.07124e20 | − | 5.99070e19i | 1.40975 | − | 0.788379i | ||||
\(693\) | 1.16491e19 | 0.151760 | ||||||||
\(694\) | 8.72615e19 | − | 2.27424e19i | 1.12540 | − | 0.293306i | ||||
\(695\) | 1.16027e20i | 1.48137i | ||||||||
\(696\) | 1.33494e19 | − | 1.28119e19i | 0.168732 | − | 0.161938i | ||||
\(697\) | −2.84660e18 | −0.0356203 | ||||||||
\(698\) | 2.99142e19 | + | 1.14779e20i | 0.370587 | + | 1.42192i | ||||
\(699\) | 9.16829e18i | 0.112447i | ||||||||
\(700\) | −3.76218e19 | − | 6.72739e19i | −0.456828 | − | 0.816884i | ||||
\(701\) | −2.41146e19 | −0.289904 | −0.144952 | − | 0.989439i | \(-0.546303\pi\) | ||||
−0.144952 | + | 0.989439i | \(0.546303\pi\) | |||||||
\(702\) | −7.11992e19 | + | 1.85562e19i | −0.847452 | + | 0.220866i | ||||
\(703\) | − | 3.12215e19i | − | 0.367932i | ||||||
\(704\) | −8.82800e19 | − | 3.62892e18i | −1.03004 | − | 0.0423418i | ||||
\(705\) | 8.53198e19 | 0.985657 | ||||||||
\(706\) | 3.74383e19 | + | 1.43649e20i | 0.428236 | + | 1.64312i | ||||
\(707\) | 1.25576e20i | 1.42223i | ||||||||
\(708\) | −9.73813e19 | + | 5.44588e19i | −1.09205 | + | 0.610711i | ||||
\(709\) | 1.28450e20 | 1.42630 | 0.713151 | − | 0.701011i | \(-0.247268\pi\) | ||||
0.713151 | + | 0.701011i | \(0.247268\pi\) | |||||||
\(710\) | 4.61844e19 | − | 1.20367e19i | 0.507793 | − | 0.132343i | ||||
\(711\) | 8.73289e18i | 0.0950760i | ||||||||
\(712\) | 4.70255e19 | + | 4.89983e19i | 0.506960 | + | 0.528228i | ||||
\(713\) | 4.96762e18 | 0.0530300 | ||||||||
\(714\) | 1.83859e19 | + | 7.05457e19i | 0.194356 | + | 0.745733i | ||||
\(715\) | − | 1.39786e20i | − | 1.46326i | ||||||
\(716\) | −8.52048e18 | − | 1.52360e19i | −0.0883228 | − | 0.157936i | ||||
\(717\) | −3.38440e19 | −0.347414 | ||||||||
\(718\) | 1.03534e19 | − | 2.69835e18i | 0.105248 | − | 0.0274301i | ||||
\(719\) | − | 4.82643e19i | − | 0.485874i | −0.970042 | − | 0.242937i | \(-0.921889\pi\) | ||
0.970042 | − | 0.242937i | \(-0.0781109\pi\) | |||||||
\(720\) | −1.32389e19 | + | 2.15454e19i | −0.131985 | + | 0.214796i | ||||
\(721\) | −3.55144e18 | −0.0350637 | ||||||||
\(722\) | −2.25399e19 | − | 8.64844e19i | −0.220390 | − | 0.845624i | ||||
\(723\) | − | 1.03137e19i | − | 0.0998729i | ||||||
\(724\) | −1.07634e19 | + | 6.01926e18i | −0.103224 | + | 0.0577263i | ||||
\(725\) | −2.51093e19 | −0.238489 | ||||||||
\(726\) | −6.99601e18 | + | 1.82333e18i | −0.0658103 | + | 0.0171517i | ||||
\(727\) | − | 1.76865e20i | − | 1.64779i | −0.566743 | − | 0.823895i | \(-0.691797\pi\) | ||
0.566743 | − | 0.823895i | \(-0.308203\pi\) | |||||||
\(728\) | 6.48038e19 | − | 6.21946e19i | 0.597972 | − | 0.573896i | ||||
\(729\) | −8.43712e19 | −0.771084 | ||||||||
\(730\) | −2.28726e17 | − | 8.77609e17i | −0.00207040 | − | 0.00794403i | ||||
\(731\) | − | 4.00918e19i | − | 0.359446i | ||||||
\(732\) | −1.60233e19 | − | 2.86523e19i | −0.142290 | − | 0.254438i | ||||
\(733\) | −6.10273e19 | −0.536780 | −0.268390 | − | 0.963310i | \(-0.586492\pi\) | ||||
−0.268390 | + | 0.963310i | \(0.586492\pi\) | |||||||
\(734\) | 1.08720e20 | − | 2.83350e19i | 0.947191 | − | 0.246860i | ||||
\(735\) | 5.14244e19i | 0.443770i | ||||||||
\(736\) | −5.80642e19 | + | 1.90376e20i | −0.496322 | + | 1.62730i | ||||
\(737\) | 1.37043e20 | 1.16034 | ||||||||
\(738\) | −2.21672e17 | − | 8.50546e17i | −0.00185916 | − | 0.00713351i | ||||
\(739\) | 8.22272e19i | 0.683131i | 0.939858 | + | 0.341566i | \(0.110957\pi\) | ||||
−0.939858 | + | 0.341566i | \(0.889043\pi\) | |||||||
\(740\) | −1.59404e20 | + | 8.91441e19i | −1.31183 | + | 0.733619i | ||||
\(741\) | −4.61762e19 | −0.376436 | ||||||||
\(742\) | −5.50062e19 | + | 1.43359e19i | −0.444206 | + | 0.115771i | ||||
\(743\) | − | 1.41500e20i | − | 1.13197i | −0.824417 | − | 0.565983i | \(-0.808497\pi\) | ||
0.824417 | − | 0.565983i | \(-0.191503\pi\) | |||||||
\(744\) | −2.95067e18 | − | 3.07445e18i | −0.0233835 | − | 0.0243645i | ||||
\(745\) | −1.08106e20 | −0.848705 | ||||||||
\(746\) | 1.78091e19 | + | 6.83328e19i | 0.138507 | + | 0.531444i | ||||
\(747\) | − | 1.98061e19i | − | 0.152600i | ||||||
\(748\) | −5.53521e19 | − | 9.89787e19i | −0.422497 | − | 0.755493i | ||||
\(749\) | −1.95014e20 | −1.47467 | ||||||||
\(750\) | 2.12796e19 | − | 5.54597e18i | 0.159417 | − | 0.0415479i | ||||
\(751\) | 1.20048e20i | 0.890996i | 0.895283 | + | 0.445498i | \(0.146973\pi\) | ||||
−0.895283 | + | 0.445498i | \(0.853027\pi\) | |||||||
\(752\) | −7.26601e19 | − | 4.46471e19i | −0.534283 | − | 0.328298i | ||||
\(753\) | 2.45196e20 | 1.78627 | ||||||||
\(754\) | −7.37931e18 | − | 2.83141e19i | −0.0532619 | − | 0.204363i | ||||
\(755\) | − | 2.83617e19i | − | 0.202817i | ||||||
\(756\) | 9.34151e19 | − | 5.22408e19i | 0.661858 | − | 0.370133i | ||||
\(757\) | 1.53107e20 | 1.07479 | 0.537395 | − | 0.843331i | \(-0.319408\pi\) | ||||
0.537395 | + | 0.843331i | \(0.319408\pi\) | |||||||
\(758\) | 2.36896e20 | − | 6.17407e19i | 1.64768 | − | 0.429425i | ||||
\(759\) | 2.75731e20i | 1.90017i | ||||||||
\(760\) | 5.44419e19 | − | 5.22499e19i | 0.371739 | − | 0.356772i | ||||
\(761\) | 2.17872e20 | 1.47404 | 0.737018 | − | 0.675873i | \(-0.236233\pi\) | ||||
0.737018 | + | 0.675873i | \(0.236233\pi\) | |||||||
\(762\) | −7.26642e19 | − | 2.78809e20i | −0.487120 | − | 1.86905i | ||||
\(763\) | 1.71231e20i | 1.13740i | ||||||||
\(764\) | 7.71991e19 | + | 1.38045e20i | 0.508111 | + | 0.908586i | ||||
\(765\) | −3.24573e19 | −0.211681 | ||||||||
\(766\) | −2.43011e20 | + | 6.33345e19i | −1.57045 | + | 0.409297i | ||||
\(767\) | 1.76442e20i | 1.12988i | ||||||||
\(768\) | 1.52312e20 | − | 7.71435e19i | 0.966509 | − | 0.489520i | ||||
\(769\) | −7.62132e19 | −0.479232 | −0.239616 | − | 0.970868i | \(-0.577022\pi\) | ||||
−0.239616 | + | 0.970868i | \(0.577022\pi\) | |||||||
\(770\) | 5.12823e19 | + | 1.96768e20i | 0.319545 | + | 1.22608i | ||||
\(771\) | − | 3.29630e20i | − | 2.03538i | ||||||
\(772\) | 2.57480e20 | − | 1.43991e20i | 1.57552 | − | 0.881080i | ||||
\(773\) | −2.83396e20 | −1.71845 | −0.859226 | − | 0.511597i | \(-0.829054\pi\) | ||||
−0.859226 | + | 0.511597i | \(0.829054\pi\) | |||||||
\(774\) | 1.19792e19 | − | 3.12206e18i | 0.0719847 | − | 0.0187609i | ||||
\(775\) | 5.78283e18i | 0.0344372i | ||||||||
\(776\) | −1.95731e20 | − | 2.03942e20i | −1.15512 | − | 1.20358i | ||||
\(777\) | −1.62578e20 | −0.950856 | ||||||||
\(778\) | 7.26578e18 | + | 2.78784e19i | 0.0421139 | + | 0.161589i | ||||
\(779\) | 2.62280e18i | 0.0150662i | ||||||||
\(780\) | 1.31843e20 | + | 2.35757e20i | 0.750576 | + | 1.34215i | ||||
\(781\) | −6.60888e19 | −0.372882 | ||||||||
\(782\) | −2.47206e20 | + | 6.44276e19i | −1.38233 | + | 0.360267i | ||||
\(783\) | − | 3.48662e19i | − | 0.193229i | ||||||
\(784\) | 2.69099e19 | − | 4.37941e19i | 0.147809 | − | 0.240549i | ||||
\(785\) | 3.08607e20 | 1.68004 | ||||||||
\(786\) | 2.39663e19 | + | 9.19577e19i | 0.129313 | + | 0.496170i | ||||
\(787\) | 1.63309e20i | 0.873345i | 0.899621 | + | 0.436672i | \(0.143843\pi\) | ||||
−0.899621 | + | 0.436672i | \(0.856157\pi\) | |||||||
\(788\) | −6.15707e19 | + | 3.44324e19i | −0.326355 | + | 0.182509i | ||||
\(789\) | −7.00466e19 | −0.368000 | ||||||||
\(790\) | −1.47510e20 | + | 3.84445e19i | −0.768123 | + | 0.200191i | ||||
\(791\) | − | 1.66164e20i | − | 0.857631i | ||||||
\(792\) | 2.52638e19 | − | 2.42466e19i | 0.129247 | − | 0.124044i | ||||
\(793\) | −5.19142e19 | −0.263253 | ||||||||
\(794\) | −6.79797e19 | − | 2.60835e20i | −0.341693 | − | 1.31106i | ||||
\(795\) | − | 1.70947e20i | − | 0.851709i | ||||||
\(796\) | 2.86277e19 | + | 5.11909e19i | 0.141382 | + | 0.252814i | ||||
\(797\) | −8.26020e19 | −0.404373 | −0.202187 | − | 0.979347i | \(-0.564805\pi\) | ||||
−0.202187 | + | 0.979347i | \(0.564805\pi\) | |||||||
\(798\) | 6.49994e19 | − | 1.69404e19i | 0.315420 | − | 0.0822059i | ||||
\(799\) | − | 1.09460e20i | − | 0.526535i | ||||||
\(800\) | −2.21617e20 | − | 6.75928e19i | −1.05675 | − | 0.322307i | ||||
\(801\) | −2.69153e19 | −0.127225 | ||||||||
\(802\) | −3.28863e19 | − | 1.26183e20i | −0.154097 | − | 0.591263i | ||||
\(803\) | 1.25584e18i | 0.00583344i | ||||||||
\(804\) | −2.31131e20 | + | 1.29256e20i | −1.06430 | + | 0.595193i | ||||
\(805\) | 4.58059e20 | 2.09098 | ||||||||
\(806\) | −6.52091e18 | + | 1.69950e18i | −0.0295096 | + | 0.00769090i | ||||
\(807\) | 2.06839e20i | 0.927937i | ||||||||
\(808\) | 2.61376e20 | + | 2.72341e20i | 1.16248 | + | 1.21125i | ||||
\(809\) | −2.49148e20 | −1.09854 | −0.549272 | − | 0.835643i | \(-0.685095\pi\) | ||||
−0.549272 | + | 0.835643i | \(0.685095\pi\) | |||||||
\(810\) | 9.57215e19 | + | 3.67279e20i | 0.418422 | + | 1.60546i | ||||
\(811\) | − | 1.92894e20i | − | 0.835937i | −0.908462 | − | 0.417968i | \(-0.862742\pi\) | ||
0.908462 | − | 0.417968i | \(-0.137258\pi\) | |||||||
\(812\) | 2.07748e19 | + | 3.71488e19i | 0.0892575 | + | 0.159607i | ||||
\(813\) | 4.21605e20 | 1.79586 | ||||||||
\(814\) | 2.44727e20 | − | 6.37816e19i | 1.03350 | − | 0.269355i | ||||
\(815\) | − | 4.67711e20i | − | 1.95828i | ||||||
\(816\) | 1.86709e20 | + | 1.14726e20i | 0.775059 | + | 0.476247i | ||||
\(817\) | −3.69398e19 | −0.152034 | ||||||||
\(818\) | 1.64599e19 | + | 6.31559e19i | 0.0671667 | + | 0.257715i | ||||
\(819\) | 3.55975e19i | 0.144023i | ||||||||
\(820\) | 1.33909e19 | − | 7.48866e18i | 0.0537173 | − | 0.0300405i | ||||
\(821\) | −1.20724e20 | −0.480167 | −0.240084 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240084 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(822\) | −3.10878e20 | + | 8.10221e19i | −1.22599 | + | 0.319522i | ||||
\(823\) | 1.98153e20i | 0.774821i | 0.921907 | + | 0.387411i | \(0.126630\pi\) | ||||
−0.921907 | + | 0.387411i | \(0.873370\pi\) | |||||||
\(824\) | −7.70214e18 | + | 7.39204e18i | −0.0298622 | + | 0.0286598i | ||||
\(825\) | −3.20980e20 | −1.23396 | ||||||||
\(826\) | −6.47301e19 | − | 2.48366e20i | −0.246744 | − | 0.946744i | ||||
\(827\) | 4.73938e20i | 1.79136i | 0.444699 | + | 0.895680i | \(0.353311\pi\) | ||||
−0.444699 | + | 0.895680i | \(0.646689\pi\) | |||||||
\(828\) | −3.85011e19 | − | 6.88463e19i | −0.144298 | − | 0.258029i | ||||
\(829\) | 6.87626e19 | 0.255547 | 0.127773 | − | 0.991803i | \(-0.459217\pi\) | ||||
0.127773 | + | 0.991803i | \(0.459217\pi\) | |||||||
\(830\) | 3.34551e20 | − | 8.71919e19i | 1.23287 | − | 0.321314i | ||||
\(831\) | − | 2.96120e20i | − | 1.08208i | ||||||
\(832\) | 1.10893e19 | − | 2.69768e20i | 0.0401830 | − | 0.977523i | ||||
\(833\) | 6.59742e19 | 0.237061 | ||||||||
\(834\) | 7.82989e19 | + | 3.00429e20i | 0.278993 | + | 1.07048i | ||||
\(835\) | 3.62153e20i | 1.27964i | ||||||||
\(836\) | −9.11970e19 | + | 5.10004e19i | −0.319548 | + | 0.178702i | ||||
\(837\) | −8.02991e18 | −0.0279018 | ||||||||
\(838\) | 1.84480e20 | − | 4.80798e19i | 0.635683 | − | 0.165674i | ||||
\(839\) | 9.49839e19i | 0.324576i | 0.986743 | + | 0.162288i | \(0.0518874\pi\) | ||||
−0.986743 | + | 0.162288i | \(0.948113\pi\) | |||||||
\(840\) | −2.72078e20 | − | 2.83492e20i | −0.922015 | − | 0.960695i | ||||
\(841\) | −2.83693e20 | −0.953403 | ||||||||
\(842\) | 1.24183e19 | + | 4.76483e19i | 0.0413882 | + | 0.158804i | ||||
\(843\) | 2.17141e20i | 0.717710i | ||||||||
\(844\) | −2.83269e20 | − | 5.06531e20i | −0.928542 | − | 1.66038i | ||||
\(845\) | −1.91163e19 | −0.0621450 | ||||||||
\(846\) | 3.27059e19 | − | 8.52393e18i | 0.105447 | − | 0.0274819i | ||||
\(847\) | − | 1.66310e19i | − | 0.0531783i | ||||||
\(848\) | −8.94551e19 | + | 1.45582e20i | −0.283683 | + | 0.461675i | ||||
\(849\) | 1.80352e20 | 0.567240 | ||||||||
\(850\) | −7.50004e19 | − | 2.87773e20i | −0.233954 | − | 0.897672i | ||||
\(851\) | − | 5.69704e20i | − | 1.76255i | ||||||
\(852\) | 1.11463e20 | − | 6.23336e19i | 0.342021 | − | 0.191269i | ||||
\(853\) | 2.02272e20 | 0.615593 | 0.307796 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307796 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(854\) | 7.30764e19 | − | 1.90454e19i | 0.220583 | − | 0.0574891i | ||||
\(855\) | 2.99055e19i | 0.0895342i | ||||||||
\(856\) | −4.22935e20 | + | 4.05906e20i | −1.25591 | + | 1.20534i | ||||
\(857\) | 4.20343e19 | 0.123805 | 0.0619025 | − | 0.998082i | \(-0.480283\pi\) | ||||
0.0619025 | + | 0.998082i | \(0.480283\pi\) | |||||||
\(858\) | −9.43321e19 | − | 3.61948e20i | −0.275581 | − | 1.05739i | ||||
\(859\) | 2.14936e20i | 0.622811i | 0.950277 | + | 0.311406i | \(0.100800\pi\) | ||||
−0.950277 | + | 0.311406i | \(0.899200\pi\) | |||||||
\(860\) | 1.05471e20 | + | 1.88599e20i | 0.303140 | + | 0.542065i | ||||
\(861\) | 1.36576e19 | 0.0389360 | ||||||||
\(862\) | 4.39414e20 | − | 1.14522e20i | 1.24258 | − | 0.323845i | ||||
\(863\) | 2.61596e20i | 0.733762i | 0.930268 | + | 0.366881i | \(0.119574\pi\) | ||||
−0.930268 | + | 0.366881i | \(0.880426\pi\) | |||||||
\(864\) | 9.38579e19 | − | 3.07733e20i | 0.261141 | − | 0.856204i | ||||
\(865\) | −8.49085e20 | −2.34336 | ||||||||
\(866\) | 8.89771e19 | + | 3.41401e20i | 0.243586 | + | 0.934629i | ||||
\(867\) | − | 1.17685e20i | − | 0.319586i | ||||||
\(868\) | 8.55560e18 | − | 4.78457e18i | 0.0230469 | − | 0.0128886i | ||||
\(869\) | 2.11083e20 | 0.564047 | ||||||||
\(870\) | −1.23863e20 | + | 3.22817e19i | −0.328328 | + | 0.0855700i | ||||
\(871\) | 4.18778e20i | 1.10118i | ||||||||
\(872\) | 3.56404e20 | + | 3.71356e20i | 0.929667 | + | 0.968668i | ||||
\(873\) | 1.12027e20 | 0.289884 | ||||||||
\(874\) | 5.93623e19 | + | 2.27770e20i | 0.152381 | + | 0.584678i | ||||
\(875\) | 5.05862e19i | 0.128818i | ||||||||
\(876\) | −1.18448e18 | − | 2.11805e18i | −0.00299226 | − | 0.00535065i | ||||
\(877\) | −3.90992e20 | −0.979875 | −0.489938 | − | 0.871758i | \(-0.662980\pi\) | ||||
−0.489938 | + | 0.871758i | \(0.662980\pi\) | |||||||
\(878\) | −4.59014e20 | + | 1.19630e20i | −1.14121 | + | 0.297426i | ||||
\(879\) | − | 1.95188e20i | − | 0.481428i | ||||||
\(880\) | 5.20774e20 | + | 3.19997e20i | 1.27430 | + | 0.783011i | ||||
\(881\) | 5.40581e20 | 1.31229 | 0.656144 | − | 0.754636i | \(-0.272186\pi\) | ||||
0.656144 | + | 0.754636i | \(0.272186\pi\) | |||||||
\(882\) | 5.13759e18 | + | 1.97127e19i | 0.0123731 | + | 0.0474750i | ||||
\(883\) | − | 3.86863e20i | − | 0.924342i | −0.886791 | − | 0.462171i | \(-0.847071\pi\) | ||
0.886791 | − | 0.462171i | \(-0.152929\pi\) | |||||||
\(884\) | 3.02461e20 | − | 1.69146e20i | 0.716974 | − | 0.400956i | ||||
\(885\) | 7.71866e20 | 1.81526 | ||||||||
\(886\) | −2.19957e20 | + | 5.73260e19i | −0.513218 | + | 0.133757i | ||||
\(887\) | − | 6.78127e20i | − | 1.56981i | −0.619619 | − | 0.784903i | \(-0.712713\pi\) | ||
0.619619 | − | 0.784903i | \(-0.287287\pi\) | |||||||
\(888\) | −3.52589e20 | + | 3.38393e20i | −0.809801 | + | 0.777196i | ||||
\(889\) | 6.62788e20 | 1.51030 | ||||||||
\(890\) | −1.18488e20 | − | 4.54634e20i | −0.267883 | − | 1.02786i | ||||
\(891\) | − | 5.25568e20i | − | 1.17892i | ||||||
\(892\) | −1.58603e20 | − | 2.83608e20i | −0.352986 | − | 0.631197i | ||||
\(893\) | −1.00854e20 | −0.222707 | ||||||||
\(894\) | −2.79920e20 | + | 7.29538e19i | −0.613298 | + | 0.159840i | ||||
\(895\) | 1.20764e20i | 0.262528i | ||||||||
\(896\) | 8.33582e19 | + | 3.83804e20i | 0.179801 | + | 0.827853i | ||||
\(897\) | −8.42585e20 | −1.80329 | ||||||||
\(898\) | 1.24816e20 | + | 4.78911e20i | 0.265054 | + | 1.01700i | ||||
\(899\) | − | 3.19329e18i | − | 0.00672853i | ||||||
\(900\) | 8.01442e19 | − | 4.48193e19i | 0.167562 | − | 0.0937060i | ||||
\(901\) | −2.19314e20 | −0.454981 | ||||||||
\(902\) | −2.05586e19 | + | 5.35805e18i | −0.0423202 | + | 0.0110296i | ||||
\(903\) | 1.92354e20i | 0.392905i | ||||||||
\(904\) | −3.45856e20 | − | 3.60365e20i | −0.700997 | − | 0.730405i | ||||
\(905\) | 8.53133e19 | 0.171584 | ||||||||
\(906\) | −1.91395e19 | − | 7.34371e19i | −0.0381973 | − | 0.146561i | ||||
\(907\) | 9.18773e18i | 0.0181952i | 0.999959 | + | 0.00909761i | \(0.00289590\pi\) | ||||
−0.999959 | + | 0.00909761i | \(0.997104\pi\) | |||||||
\(908\) | −9.16173e19 | − | 1.63827e20i | −0.180043 | − | 0.321946i | ||||
\(909\) | −1.49600e20 | −0.291733 | ||||||||
\(910\) | −6.01286e20 | + | 1.56709e20i | −1.16357 | + | 0.303253i | ||||
\(911\) | 1.02841e21i | 1.97486i | 0.158046 | + | 0.987432i | \(0.449481\pi\) | ||||
−0.158046 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(912\) | 1.05707e20 | − | 1.72030e20i | 0.201437 | − | 0.327824i | ||||
\(913\) | −4.78735e20 | −0.905315 | ||||||||
\(914\) | 5.77392e19 | + | 2.21542e20i | 0.108355 | + | 0.415751i | ||||
\(915\) | 2.27105e20i | 0.422940i | ||||||||
\(916\) | −1.76934e20 | + | 9.89476e19i | −0.326997 | + | 0.182868i | ||||
\(917\) | −2.18603e20 | −0.400932 | ||||||||
\(918\) | 3.99595e20 | − | 1.04144e20i | 0.727314 | − | 0.189555i | ||||
\(919\) | − | 8.16694e20i | − | 1.47520i | −0.675238 | − | 0.737600i | \(-0.735959\pi\) | ||
0.675238 | − | 0.737600i | \(-0.264041\pi\) | |||||||
\(920\) | 9.93409e20 | − | 9.53412e20i | 1.78079 | − | 1.70909i | ||||
\(921\) | −3.60963e20 | −0.642163 | ||||||||
\(922\) | −1.09259e20 | − | 4.19222e20i | −0.192904 | − | 0.740164i | ||||
\(923\) | − | 2.01956e20i | − | 0.353870i | ||||||
\(924\) | 2.65571e20 | + | 4.74885e20i | 0.461824 | + | 0.825818i | ||||
\(925\) | 6.63195e20 | 1.14459 | ||||||||
\(926\) | −1.57519e20 | + | 4.10530e19i | −0.269808 | + | 0.0703183i | ||||
\(927\) | − | 4.23088e18i | − | 0.00719237i | ||||||
\(928\) | 1.22377e20 | + | 3.73248e19i | 0.206474 | + | 0.0629741i | ||||
\(929\) | 7.17263e19 | 0.120107 | 0.0600535 | − | 0.998195i | \(-0.480873\pi\) | ||||
0.0600535 | + | 0.998195i | \(0.480873\pi\) | |||||||
\(930\) | 7.43468e18 | + | 2.85265e19i | 0.0123561 | + | 0.0474098i | ||||
\(931\) | − | 6.07873e19i | − | 0.100269i | ||||||
\(932\) | −5.53323e19 | + | 3.09436e19i | −0.0905873 | + | 0.0506594i | ||||
\(933\) | −2.64554e19 | −0.0429875 | ||||||||
\(934\) | 2.07980e20 | − | 5.42044e19i | 0.335423 | − | 0.0874191i | ||||
\(935\) | 7.84527e20i | 1.25582i | ||||||||
\(936\) | 7.40932e19 | + | 7.72016e19i | 0.117719 | + | 0.122658i | ||||
\(937\) | 9.33303e20 | 1.47179 | 0.735894 | − | 0.677096i | \(-0.236762\pi\) | ||||
0.735894 | + | 0.677096i | \(0.236762\pi\) | |||||||
\(938\) | −1.53634e20 | − | 5.89488e20i | −0.240474 | − | 0.922688i | ||||
\(939\) | 1.06622e21i | 1.65649i | ||||||||
\(940\) | 2.87960e20 | + | 5.14920e20i | 0.444056 | + | 0.794044i | ||||
\(941\) | 3.59055e20 | 0.549583 | 0.274791 | − | 0.961504i | \(-0.411391\pi\) | ||||
0.274791 | + | 0.961504i | \(0.411391\pi\) | |||||||
\(942\) | 7.99079e20 | − | 2.08259e20i | 1.21404 | − | 0.316408i | ||||
\(943\) | 4.78587e19i | 0.0721737i | ||||||||
\(944\) | −6.57337e20 | − | 4.03911e20i | −0.983975 | − | 0.604619i | ||||
\(945\) | −7.40429e20 | −1.10017 | ||||||||
\(946\) | −7.54633e19 | − | 2.89549e20i | −0.111301 | − | 0.427055i | ||||
\(947\) | 8.55162e20i | 1.25198i | 0.779830 | + | 0.625991i | \(0.215305\pi\) | ||||
−0.779830 | + | 0.625991i | \(0.784695\pi\) | |||||||
\(948\) | −3.56004e20 | + | 1.99089e20i | −0.517365 | + | 0.289327i | ||||
\(949\) | −3.83762e18 | −0.00553603 | ||||||||
\(950\) | −2.65148e20 | + | 6.91039e19i | −0.379685 | + | 0.0989549i | ||||
\(951\) | 5.54507e19i | 0.0788212i | ||||||||
\(952\) | −3.63702e20 | + | 3.49059e20i | −0.513201 | + | 0.492538i | ||||
\(953\) | −1.03188e20 | −0.144538 | −0.0722688 | − | 0.997385i | \(-0.523024\pi\) | ||||
−0.0722688 | + | 0.997385i | \(0.523024\pi\) | |||||||
\(954\) | −1.70786e19 | − | 6.55296e19i | −0.0237472 | − | 0.0911169i | ||||
\(955\) | − | 1.09417e21i | − | 1.51030i | ||||||
\(956\) | −1.14226e20 | − | 2.04255e20i | −0.156516 | − | 0.279877i | ||||
\(957\) | 1.77246e20 | 0.241097 | ||||||||
\(958\) | 3.26844e20 | − | 8.51834e19i | 0.441349 | − | 0.115026i | ||||
\(959\) | − | 7.39023e20i | − | 0.990667i | ||||||
\(960\) | −1.18013e21 | − | 4.85116e19i | −1.57048 | − | 0.0645575i | ||||
\(961\) | 7.56209e20 | 0.999028 | ||||||||
\(962\) | 1.94905e20 | + | 7.47842e20i | 0.255622 | + | 0.980808i | ||||
\(963\) | − | 2.32323e20i | − | 0.302488i | ||||||
\(964\) | 6.22452e19 | − | 3.48096e19i | 0.0804575 | − | 0.0449945i | ||||
\(965\) | −2.04084e21 | −2.61890 | ||||||||
\(966\) | 1.18605e21 | − | 3.09114e20i | 1.51100 | − | 0.393802i | ||||
\(967\) | − | 8.55095e20i | − | 1.08151i | −0.841181 | − | 0.540753i | \(-0.818139\pi\) | ||
0.841181 | − | 0.540753i | \(-0.181861\pi\) | |||||||
\(968\) | −3.46161e19 | − | 3.60683e19i | −0.0434661 | − | 0.0452896i | ||||
\(969\) | 2.59158e20 | 0.323071 | ||||||||
\(970\) | 4.93175e20 | + | 1.89229e21i | 0.610377 | + | 2.34199i | ||||
\(971\) | − | 4.99804e20i | − | 0.614136i | −0.951688 | − | 0.307068i | \(-0.900652\pi\) | ||
0.951688 | − | 0.307068i | \(-0.0993480\pi\) | |||||||
\(972\) | 1.37559e20 | + | 2.45979e20i | 0.167813 | + | 0.300078i | ||||
\(973\) | −7.14184e20 | −0.865008 | ||||||||
\(974\) | −7.46215e20 | + | 1.94481e20i | −0.897328 | + | 0.233865i | ||||
\(975\) | − | 9.80856e20i | − | 1.17104i | ||||||
\(976\) | 1.18842e20 | − | 1.93407e20i | 0.140871 | − | 0.229258i | ||||
\(977\) | 1.26501e21 | 1.48879 | 0.744395 | − | 0.667739i | \(-0.232738\pi\) | ||||
0.744395 | + | 0.667739i | \(0.232738\pi\) | |||||||
\(978\) | −3.15627e20 | − | 1.21105e21i | −0.368810 | − | 1.41511i | ||||
\(979\) | 6.50571e20i | 0.754772i | ||||||||
\(980\) | −3.10355e20 | + | 1.73561e20i | −0.357500 | + | 0.199926i | ||||
\(981\) | −2.03990e20 | −0.233306 | ||||||||
\(982\) | −3.77277e20 | + | 9.83272e19i | −0.428430 | + | 0.111659i | ||||
\(983\) | − | 4.78813e20i | − | 0.539873i | −0.962878 | − | 0.269936i | \(-0.912997\pi\) | ||
0.962878 | − | 0.269936i | \(-0.0870026\pi\) | |||||||
\(984\) | 2.96197e19 | − | 2.84271e19i | 0.0331600 | − | 0.0318249i | ||||
\(985\) | 4.88023e20 | 0.542484 | ||||||||
\(986\) | 4.14154e19 | + | 1.58909e20i | 0.0457112 | + | 0.175392i | ||||
\(987\) | 5.25172e20i | 0.575548i | ||||||||
\(988\) | −1.55848e20 | − | 2.78682e20i | −0.169591 | − | 0.303256i | ||||
\(989\) | −6.74046e20 | −0.728309 | ||||||||
\(990\) | −2.34412e20 | + | 6.10932e19i | −0.251497 | + | 0.0655461i | ||||
\(991\) | 1.15848e21i | 1.23417i | 0.786897 | + | 0.617085i | \(0.211686\pi\) | ||||
−0.786897 | + | 0.617085i | \(0.788314\pi\) | |||||||
\(992\) | 8.59615e18 | − | 2.81843e19i | 0.00909332 | − | 0.0298143i | ||||
\(993\) | 1.12379e21 | 1.18043 | ||||||||
\(994\) | 7.40902e19 | + | 2.84280e20i | 0.0772780 | + | 0.296512i | ||||
\(995\) | − | 4.05751e20i | − | 0.420240i | ||||||
\(996\) | 8.07415e20 | − | 4.51533e20i | 0.830388 | − | 0.464381i | ||||
\(997\) | −1.22877e20 | −0.125488 | −0.0627442 | − | 0.998030i | \(-0.519985\pi\) | ||||
−0.0627442 | + | 0.998030i | \(0.519985\pi\) | |||||||
\(998\) | −5.14521e20 | + | 1.34096e20i | −0.521783 | + | 0.135989i | ||||
\(999\) | 9.20898e20i | 0.927371i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4.15.b.a.3.3 | ✓ | 6 | |
3.2 | odd | 2 | 36.15.d.c.19.4 | 6 | |||
4.3 | odd | 2 | inner | 4.15.b.a.3.4 | yes | 6 | |
8.3 | odd | 2 | 64.15.c.d.63.5 | 6 | |||
8.5 | even | 2 | 64.15.c.d.63.2 | 6 | |||
12.11 | even | 2 | 36.15.d.c.19.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.15.b.a.3.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4.15.b.a.3.4 | yes | 6 | 4.3 | odd | 2 | inner | |
36.15.d.c.19.3 | 6 | 12.11 | even | 2 | |||
36.15.d.c.19.4 | 6 | 3.2 | odd | 2 | |||
64.15.c.d.63.2 | 6 | 8.5 | even | 2 | |||
64.15.c.d.63.5 | 6 | 8.3 | odd | 2 |