Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,23,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 23, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 23);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 23 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), degree \(2\), 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: | \(64.4085613168\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.2 |
Dual form | 21.23.h.a.11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 88573.5 | + | 153414.i | 0.500000 | + | 0.866025i | ||||
\(4\) | −2.09715e6 | − | 3.63237e6i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.98966e8 | − | 1.70643e9i | 0.505210 | − | 0.862996i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.56905e10 | + | 2.71768e10i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 3.71504e11 | − | 6.43464e11i | 0.500000 | − | 0.866025i | ||||
\(13\) | 2.09432e12 | 1.16860 | 0.584299 | − | 0.811538i | \(-0.301369\pi\) | ||||
0.584299 | + | 0.811538i | \(0.301369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.79609e12 | + | 1.52353e13i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.03370e13 | + | 1.79042e13i | −0.0887368 | + | 0.153697i | −0.906977 | − | 0.421179i | \(-0.861616\pi\) |
0.818241 | + | 0.574876i | \(0.194950\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.50271e14 | + | 2.11109e12i | 0.999982 | + | 0.00602689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.19209e15 | − | 2.06477e15i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.55906e15 | −1.00000 | ||||||||
\(28\) | −8.29336e15 | − | 4.99841e13i | −0.999982 | − | 0.00602689i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.85408e16 | − | 3.21136e16i | −0.729710 | − | 1.26389i | −0.957006 | − | 0.290069i | \(-0.906322\pi\) |
0.227296 | − | 0.973826i | \(-0.427011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.31622e17 | 1.00000 | ||||||||
\(37\) | −4.22284e16 | + | 7.31418e16i | −0.237348 | + | 0.411099i | −0.959953 | − | 0.280163i | \(-0.909612\pi\) |
0.722604 | + | 0.691262i | \(0.242945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.85501e17 | + | 3.21297e17i | 0.584299 | + | 1.01204i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.26850e18 | 1.36502 | 0.682509 | − | 0.730877i | \(-0.260889\pi\) | ||||
0.682509 | + | 0.730877i | \(0.260889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | −3.11640e18 | −1.00000 | ||||||||
\(49\) | −1.91396e18 | − | 3.40932e18i | −0.489525 | − | 0.871989i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.39210e18 | − | 7.60734e18i | −0.584299 | − | 1.01204i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.66233e18 | −0.177474 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.36973e19 | − | 5.83654e19i | 0.774403 | − | 1.34131i | −0.160727 | − | 0.986999i | \(-0.551384\pi\) |
0.935130 | − | 0.354306i | \(-0.115283\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.07009e19 | + | 5.39234e19i | 0.494771 | + | 0.869023i | ||||
\(64\) | 7.37870e19 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.07065e20 | − | 1.85442e20i | −0.876646 | − | 1.51839i | −0.854999 | − | 0.518629i | \(-0.826443\pi\) |
−0.0216461 | − | 0.999766i | \(-0.506891\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.10685e20 | − | 5.38121e20i | −0.990303 | − | 1.71526i | −0.615463 | − | 0.788166i | \(-0.711031\pi\) |
−0.374840 | − | 0.927089i | \(-0.622302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.11176e20 | − | 3.65767e20i | 0.500000 | − | 0.866025i | ||||
\(76\) | 8.67128e19 | 0.177474 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.18791e20 | − | 8.98573e20i | 0.693577 | − | 1.20131i | −0.277081 | − | 0.960847i | \(-0.589367\pi\) |
0.970658 | − | 0.240464i | \(-0.0772997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.92385e20 | − | 8.52837e20i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −7.26904e20 | − | 1.27674e21i | −0.494771 | − | 0.869023i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09215e21 | − | 3.57379e21i | 0.590388 | − | 1.00850i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.28445e21 | − | 5.68883e21i | 0.729710 | − | 1.26389i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.61889e21 | −0.226322 | −0.113161 | − | 0.993577i | \(-0.536098\pi\) | ||||
−0.113161 | + | 0.993577i | \(0.536098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e21 | + | 8.66025e21i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.49051e21 | − | 2.58164e21i | 0.107678 | − | 0.186503i | −0.807151 | − | 0.590344i | \(-0.798992\pi\) |
0.914829 | + | 0.403841i | \(0.132325\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 1.16582e22 | + | 2.01926e22i | 0.500000 | + | 0.866025i | ||||
\(109\) | −1.25416e22 | − | 2.17227e22i | −0.486029 | − | 0.841828i | 0.513842 | − | 0.857885i | \(-0.328222\pi\) |
−0.999871 | + | 0.0160575i | \(0.994889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.49613e22 | −0.474697 | ||||||||
\(112\) | 1.72109e22 | + | 3.02294e22i | 0.494771 | + | 0.869023i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.28609e22 | + | 5.69168e22i | −0.584299 | + | 1.01204i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.07014e22 | + | 7.04968e22i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.77658e22 | + | 1.34694e23i | −0.729710 | + | 1.26389i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.76555e23 | 1.99499 | 0.997496 | − | 0.0707258i | \(-0.0225315\pi\) | ||||
0.997496 | + | 0.0707258i | \(0.0225315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.12356e23 | + | 1.94606e23i | 0.682509 | + | 1.18214i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.02258e22 | + | 3.55249e22i | 0.0878088 | + | 0.154229i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.03681e23 | −1.88024 | −0.940119 | − | 0.340845i | \(-0.889287\pi\) | ||||
−0.940119 | + | 0.340845i | \(0.889287\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.76031e23 | − | 4.78099e23i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.53511e23 | − | 5.95603e23i | 0.510402 | − | 0.859936i | ||||
\(148\) | 3.54238e23 | 0.474697 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.35858e23 | − | 1.44775e24i | −0.898227 | − | 1.55578i | −0.829759 | − | 0.558122i | \(-0.811522\pi\) |
−0.0684684 | − | 0.997653i | \(-0.521811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.78047e23 | − | 1.34762e24i | 0.584299 | − | 1.01204i | ||||
\(157\) | 1.27068e24 | + | 2.20088e24i | 0.889487 | + | 1.54064i | 0.840483 | + | 0.541838i | \(0.182271\pi\) |
0.0490037 | + | 0.998799i | \(0.484395\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.61163e24 | − | 2.79143e24i | 0.746797 | − | 1.29349i | −0.202553 | − | 0.979271i | \(-0.564924\pi\) |
0.949350 | − | 0.314219i | \(-0.101743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17432e24 | 0.365622 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.24385e23 | − | 5.61851e23i | −0.0887368 | − | 0.153697i | ||||
\(172\) | −2.66024e24 | − | 4.60768e24i | −0.682509 | − | 1.18214i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.71423e24 | − | 2.84127e22i | −0.999982 | − | 0.00602689i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.20332e25 | −1.76163 | −0.880817 | − | 0.473458i | \(-0.843006\pi\) | ||||
−0.880817 | + | 0.473458i | \(0.843006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.19388e25 | 1.54881 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.55331e24 | + | 9.48612e24i | −0.505210 | + | 0.862996i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 6.53557e24 | + | 1.13199e25i | 0.500000 | + | 0.866025i | ||||
\(193\) | 1.20825e25 | + | 2.09275e25i | 0.873023 | + | 1.51212i | 0.858854 | + | 0.512220i | \(0.171177\pi\) |
0.0141686 | + | 0.999900i | \(0.495490\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.37008e24 | + | 1.41021e25i | −0.510402 | + | 0.859936i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.75881e25 | + | 3.04635e25i | 0.907476 | + | 1.57180i | 0.817558 | + | 0.575846i | \(0.195327\pi\) |
0.0899181 | + | 0.995949i | \(0.471339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.89662e25 | − | 3.28504e25i | 0.876646 | − | 1.51839i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.84218e25 | + | 3.19075e25i | −0.584299 | + | 1.01204i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.12329e25 | −1.93007 | −0.965037 | − | 0.262115i | \(-0.915580\pi\) | ||||
−0.965037 | + | 0.262115i | \(0.915580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.33212e25 | − | 4.41907e23i | −1.45939 | − | 0.00879577i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50368e25 | − | 9.53266e25i | 0.990303 | − | 1.71526i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.78784e24 | 0.0705970 | 0.0352985 | − | 0.999377i | \(-0.488762\pi\) | ||||
0.0352985 | + | 0.999377i | \(0.488762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.48183e25 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 7.68045e24 | + | 1.33029e25i | 0.0887368 | + | 0.153697i | ||||
\(229\) | 3.72331e25 | − | 6.44896e25i | 0.409958 | − | 0.710067i | −0.584927 | − | 0.811086i | \(-0.698877\pi\) |
0.994885 | + | 0.101019i | \(0.0322102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.83805e26 | 1.38715 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.03143e26 | − | 1.78649e26i | −0.647517 | − | 1.12153i | −0.983714 | − | 0.179741i | \(-0.942474\pi\) |
0.336197 | − | 0.941792i | \(-0.390859\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.72246e25 | − | 1.51077e26i | 0.500000 | − | 0.866025i | ||||
\(244\) | −2.82673e26 | −1.54881 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.16489e25 | + | 3.74970e25i | −0.103698 | + | 0.179610i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 1.31486e26 | − | 2.24603e26i | 0.505210 | − | 0.862996i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.54743e26 | − | 2.68022e26i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.26263e25 | + | 1.45126e26i | 0.234866 | + | 0.412522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.49062e26 | + | 7.77799e26i | −0.876646 | + | 1.51839i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.37914e26 | + | 9.31695e26i | −0.929075 | + | 1.60920i | −0.144202 | + | 0.989548i | \(0.546061\pi\) |
−0.784873 | + | 0.619657i | \(0.787272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.33578e26 | + | 4.42128e24i | 1.16858 | + | 0.00704302i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.51225e26 | + | 4.35135e26i | 0.341025 | + | 0.590672i | 0.984623 | − | 0.174691i | \(-0.0558927\pi\) |
−0.643599 | + | 0.765363i | \(0.722559\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.16366e27 | 1.45942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.45168e25 | − | 1.63708e26i | −0.101358 | − | 0.175557i | 0.810886 | − | 0.585204i | \(-0.198985\pi\) |
−0.912244 | + | 0.409646i | \(0.865652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.87281e26 | + | 1.01720e27i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.43390e26 | − | 2.48360e26i | −0.113161 | − | 0.196001i | ||||
\(292\) | −1.30311e27 | + | 2.25704e27i | −0.990303 | + | 1.71526i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.77147e27 | −1.00000 | ||||||||
\(301\) | 1.26719e27 | − | 2.16461e27i | 0.689621 | − | 1.17801i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.81850e26 | − | 3.14973e26i | −0.0887368 | − | 0.153697i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12057e27 | 0.928816 | 0.464408 | − | 0.885621i | \(-0.346267\pi\) | ||||
0.464408 | + | 0.885621i | \(0.346267\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.28079e26 | 0.215355 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.81044e27 | − | 4.86782e27i | 0.994916 | − | 1.72325i | 0.410245 | − | 0.911976i | \(-0.365443\pi\) |
0.584672 | − | 0.811270i | \(-0.301223\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.35194e27 | −1.38715 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.06521e27 | + | 3.57706e27i | −0.500000 | + | 0.866025i | ||||
\(325\) | −2.49662e27 | − | 4.32427e27i | −0.584299 | − | 1.01204i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.22171e27 | − | 3.84812e27i | 0.486029 | − | 0.841828i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.29871e27 | − | 7.44558e27i | 0.822678 | − | 1.42492i | −0.0810032 | − | 0.996714i | \(-0.525812\pi\) |
0.903681 | − | 0.428206i | \(-0.140854\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.32517e27 | − | 2.29527e27i | −0.237348 | − | 0.411099i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.11318e27 | + | 5.31791e27i | −0.505210 | + | 0.862996i | ||||
\(337\) | 1.26159e28 | 1.98147 | 0.990737 | − | 0.135792i | \(-0.0433579\pi\) | ||||
0.990737 | + | 0.135792i | \(0.0433579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.72973e27 | − | 1.39775e26i | −0.999837 | − | 0.0180798i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.04982e28 | 1.12211 | 0.561057 | − | 0.827777i | \(-0.310395\pi\) | ||||
0.561057 | + | 0.827777i | \(0.310395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.16424e28 | −1.16860 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.57128e27 | + | 1.13818e28i | 0.484252 | + | 0.838748i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.44203e28 | −1.00000 | ||||||||
\(364\) | −1.73689e28 | − | 1.04683e26i | −1.16858 | − | 0.00704302i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.59218e28 | + | 2.75774e28i | 0.978738 | + | 1.69522i | 0.667002 | + | 0.745056i | \(0.267577\pi\) |
0.311736 | + | 0.950169i | \(0.399089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.75520e28 | −1.45942 | ||||||||
\(373\) | 5.78887e27 | − | 1.00266e28i | 0.297712 | − | 0.515653i | −0.677900 | − | 0.735154i | \(-0.737110\pi\) |
0.975612 | + | 0.219501i | \(0.0704430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.59449e28 | 1.55098 | 0.775489 | − | 0.631361i | \(-0.217503\pi\) | ||||
0.775489 | + | 0.631361i | \(0.217503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.44955e28 | + | 4.24274e28i | 0.997496 | + | 1.72771i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.99035e28 | + | 3.44738e28i | −0.682509 | + | 1.18214i | ||||
\(388\) | 3.39505e27 | + | 5.88040e27i | 0.113161 | + | 0.196001i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.10151e27 | − | 1.90788e27i | 0.0285295 | − | 0.0494145i | −0.851408 | − | 0.524504i | \(-0.824251\pi\) |
0.879938 | + | 0.475089i | \(0.157584\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.65854e27 | + | 6.24949e27i | −0.0896615 | + | 0.153159i | ||||
\(400\) | 4.19430e28 | 1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.88303e28 | − | 6.72561e28i | −0.852738 | − | 1.47698i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.14863e28 | − | 7.18563e28i | −0.774369 | − | 1.34125i | −0.935148 | − | 0.354256i | \(-0.884734\pi\) |
0.160779 | − | 0.986990i | \(-0.448599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.25033e28 | −0.215355 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.23275e28 | − | 1.07954e29i | −0.940119 | − | 1.62833i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.80624e28 | 0.788482 | 0.394241 | − | 0.919007i | \(-0.371007\pi\) | ||||
0.394241 | + | 0.919007i | \(0.371007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.59338e28 | − | 1.15807e29i | −0.766305 | − | 1.34595i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 4.88980e28 | − | 8.46938e28i | 0.500000 | − | 0.866025i | ||||
\(433\) | 2.00619e29 | 1.99989 | 0.999945 | − | 0.0104622i | \(-0.00333027\pi\) | ||||
0.999945 | + | 0.0104622i | \(0.00333027\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.26034e28 | + | 9.11118e28i | −0.486029 | + | 0.841828i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.07908e29 | + | 1.86903e29i | −0.924582 | + | 1.60142i | −0.132351 | + | 0.991203i | \(0.542253\pi\) |
−0.792231 | + | 0.610221i | \(0.791081\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.22685e29 | + | 1.47890e27i | 0.999927 | + | 0.0120536i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 3.13761e28 | + | 5.43450e28i | 0.237348 | + | 0.411099i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.37107e28 | − | 1.25912e29i | 0.505210 | − | 0.862996i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.48070e29 | − | 2.56464e29i | 0.898227 | − | 1.55578i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.81422e29 | + | 3.14232e29i | −0.999106 | + | 1.73050i | −0.462934 | + | 0.886393i | \(0.653203\pi\) |
−0.536172 | + | 0.844109i | \(0.680130\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.13744e29 | −1.97397 | −0.986985 | − | 0.160810i | \(-0.948590\pi\) | ||||
−0.986985 | + | 0.160810i | \(0.948590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 2.75657e29 | 1.16860 | ||||||||
\(469\) | −4.23397e29 | − | 2.55181e27i | −1.75326 | − | 0.0105669i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.25097e29 | + | 3.89879e29i | −0.889487 | + | 1.54064i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.92905e28 | 0.177474 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.84397e28 | + | 1.53182e29i | −0.277365 | + | 0.480410i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.41428e29 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.83862e29 | + | 4.91663e29i | 0.776762 | + | 1.34539i | 0.933799 | + | 0.357799i | \(0.116473\pi\) |
−0.157036 | + | 0.987593i | \(0.550194\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.70992e29 | 1.49359 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.52347e29 | 1.45942 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.64295e29 | + | 8.04182e29i | −0.972048 | + | 1.68364i | −0.282698 | + | 0.959209i | \(0.591229\pi\) |
−0.689350 | + | 0.724428i | \(0.742104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.04014e29 | + | 1.80157e29i | 0.182811 | + | 0.316638i | ||||
\(508\) | −5.79979e29 | − | 1.00455e30i | −0.997496 | − | 1.72771i | ||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.22863e30 | − | 7.40494e27i | −1.98057 | − | 0.0119369i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.74638e28 | − | 9.95303e28i | 0.0887368 | − | 0.153697i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.71254e29 | − | 8.16236e29i | 0.682509 | − | 1.18214i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.59905e29 | − | 1.31619e30i | 0.948944 | − | 1.64362i | 0.201290 | − | 0.979532i | \(-0.435487\pi\) |
0.747654 | − | 0.664088i | \(-0.231180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.13197e29 | − | 7.25744e29i | −0.494771 | − | 0.869023i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.53923e29 | − | 7.86218e29i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.66231e28 | − | 1.47969e29i | 0.0896615 | − | 0.153159i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.22232e29 | + | 1.25094e30i | −0.621594 | + | 1.07663i | 0.367595 | + | 0.929986i | \(0.380181\pi\) |
−0.989189 | + | 0.146646i | \(0.953152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.06582e30 | − | 1.84605e30i | −0.880817 | − | 1.52562i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.19905e30 | 1.67639 | 0.838193 | − | 0.545374i | \(-0.183612\pi\) | ||||
0.838193 | + | 0.545374i | \(0.183612\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.05746e30 | + | 1.83157e30i | 0.774403 | + | 1.34131i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.01509e30 | − | 1.78292e30i | −0.686324 | − | 1.20547i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.47573e30 | + | 2.55603e30i | 0.940119 | + | 1.62833i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.65665e30 | 1.59516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.94718e30 | − | 1.17357e28i | −0.999982 | − | 0.00602689i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.06977e30 | − | 3.58494e30i | −0.983840 | − | 1.70406i | −0.646981 | − | 0.762506i | \(-0.723969\pi\) |
−0.336860 | − | 0.941555i | \(-0.609365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.15776e30 | + | 2.00529e30i | −0.500000 | + | 0.866025i | ||||
\(577\) | 1.47889e30 | + | 2.56151e30i | 0.626617 | + | 1.08533i | 0.988226 | + | 0.153002i | \(0.0488941\pi\) |
−0.361609 | + | 0.932330i | \(0.617773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.14037e30 | + | 3.70724e30i | −0.873023 | + | 1.51212i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −2.90482e30 | − | 3.50160e28i | −0.999927 | − | 0.0120536i | ||||
\(589\) | 7.66623e29 | 0.259008 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.42891e29 | − | 1.28672e30i | −0.237348 | − | 0.411099i | ||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.11568e30 | + | 5.39652e30i | −0.907476 | + | 1.57180i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.26756e30 | 1.42557 | 0.712787 | − | 0.701380i | \(-0.247432\pi\) | ||||
0.712787 | + | 0.701380i | \(0.247432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.71962e30 | 1.75329 | ||||||||
\(604\) | −3.50584e30 | + | 6.07230e30i | −0.898227 | + | 1.55578i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.81999e30 | − | 4.88437e30i | 0.684184 | − | 1.18504i | −0.289509 | − | 0.957175i | \(-0.593492\pi\) |
0.973693 | − | 0.227865i | \(-0.0731746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.08617e30 | − | 1.88131e30i | −0.236502 | − | 0.409633i | 0.723206 | − | 0.690632i | \(-0.242668\pi\) |
−0.959708 | + | 0.280999i | \(0.909334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.88698e30 | + | 6.73244e30i | 0.760352 | + | 1.31697i | 0.942669 | + | 0.333729i | \(0.108307\pi\) |
−0.182317 | + | 0.983240i | \(0.558360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.52673e30 | −1.16860 | ||||||||
\(625\) | −2.84217e30 | + | 4.92278e30i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.32961e30 | − | 9.23116e30i | 0.889487 | − | 1.54064i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.08052e30 | 0.171124 | 0.0855620 | − | 0.996333i | \(-0.472731\pi\) | ||||
0.0855620 | + | 0.996333i | \(0.472731\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.30935e30 | − | 1.09281e31i | −0.965037 | − | 1.67149i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00843e30 | − | 7.14020e30i | −0.572058 | − | 1.01901i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.54659e31 | 1.99093 | 0.995464 | − | 0.0951395i | \(-0.0303297\pi\) | ||||
0.995464 | + | 0.0951395i | \(0.0303297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.42652e30 | − | 1.12876e31i | −0.722079 | − | 1.26827i | ||||
\(652\) | −1.35194e31 | −1.49359 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.94992e31 | 1.98061 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.27164e30 | − | 1.60590e31i | −0.880928 | − | 1.52581i | −0.850311 | − | 0.526281i | \(-0.823586\pi\) |
−0.0306177 | − | 0.999531i | \(-0.509747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.24076e29 | + | 7.34521e29i | 0.0352985 | + | 0.0611388i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.79437e30 | −0.373737 | −0.186868 | − | 0.982385i | \(-0.559834\pi\) | ||||
−0.186868 | + | 0.982385i | \(0.559834\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.62692e30 | + | 1.14782e31i | 0.500000 | + | 0.866025i | ||||
\(676\) | −2.46273e30 | − | 4.26557e30i | −0.182811 | − | 0.316638i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.61721e30 | + | 2.76251e30i | −0.114340 | + | 0.195315i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −1.36057e30 | + | 2.35658e30i | −0.0887368 | + | 0.153697i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.31915e31 | 0.819915 | ||||||||
\(688\) | −1.11579e31 | + | 1.93260e31i | −0.682509 | + | 1.18214i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.14109e30 | − | 8.90464e30i | 0.299776 | − | 0.519228i | −0.676308 | − | 0.736619i | \(-0.736421\pi\) |
0.976085 | + | 0.217391i | \(0.0697547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.78325e30 | + | 1.71834e31i | 0.494771 | + | 0.869023i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.73028e29 | − | 1.51213e30i | −0.0421230 | − | 0.0729592i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.27215e31 | + | 3.93547e31i | −0.998453 | + | 1.72937i | −0.451077 | + | 0.892485i | \(0.648960\pi\) |
−0.547376 | + | 0.836887i | \(0.684373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62802e31 | + | 2.81982e31i | 0.693577 | + | 1.20131i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.91641e30 | − | 5.12241e30i | −0.106552 | − | 0.187149i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.82714e31 | − | 3.16470e31i | 0.647517 | − | 1.12153i | ||||
\(724\) | 2.52354e31 | + | 4.37090e31i | 0.880817 | + | 1.52562i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.98866e31 | −1.99734 | −0.998668 | − | 0.0516010i | \(-0.983568\pi\) | ||||
−0.998668 | + | 0.0516010i | \(0.983568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.09032e31 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.50374e31 | − | 4.33660e31i | −0.774403 | − | 1.34131i | ||||
\(733\) | −3.14541e31 | + | 5.44802e31i | −0.958372 | + | 1.65995i | −0.231917 | + | 0.972736i | \(0.574500\pi\) |
−0.726455 | + | 0.687214i | \(0.758834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.36695e30 | − | 1.44920e31i | −0.233066 | − | 0.403682i | 0.725643 | − | 0.688071i | \(-0.241542\pi\) |
−0.958709 | + | 0.284390i | \(0.908209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.67007e30 | −0.207395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.14538e31 | − | 7.18001e31i | 0.967219 | − | 1.67527i | 0.263689 | − | 0.964608i | \(-0.415061\pi\) |
0.703531 | − | 0.710665i | \(-0.251606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.61033e31 | + | 2.77865e29i | 0.999982 | + | 0.00602689i | ||||
\(757\) | 1.57356e31 | 0.336379 | 0.168189 | − | 0.985755i | \(-0.446208\pi\) | ||||
0.168189 | + | 0.985755i | \(0.446208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.95969e31 | − | 2.98921e29i | −0.972041 | − | 0.00585850i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.74122e31 | − | 4.74793e31i | 0.500000 | − | 0.866025i | ||||
\(769\) | −2.96591e31 | −0.533296 | −0.266648 | − | 0.963794i | \(-0.585916\pi\) | ||||
−0.266648 | + | 0.963794i | \(0.585916\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.06776e31 | − | 8.77761e31i | 0.873023 | − | 1.51212i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.42047e31 | + | 7.65649e31i | −0.729710 | + | 1.26389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.49458e31 | + | 2.55303e31i | −0.239822 | + | 0.409661i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.87773e31 | + | 8.29072e29i | 0.999927 | + | 0.0120536i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50680e31 | − | 2.60985e31i | −0.210055 | − | 0.363826i | 0.741677 | − | 0.670758i | \(-0.234031\pi\) |
−0.951731 | + | 0.306932i | \(0.900698\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.05728e31 | − | 1.22236e32i | 0.904966 | − | 1.56745i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.37699e31 | − | 1.27773e32i | 0.907476 | − | 1.57180i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.59100e32 | −1.75329 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.24855e32 | −1.25076 | −0.625381 | − | 0.780319i | \(-0.715057\pi\) | ||||
−0.625381 | + | 0.780319i | \(0.715057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90580e32 | −1.85815 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.31125e31 | + | 2.27115e31i | −0.121127 | + | 0.209799i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.42973e31 | + | 1.12933e32i | 0.578189 | + | 1.01554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15540e32 | + | 2.00120e32i | 0.984765 | + | 1.70566i | 0.642977 | + | 0.765885i | \(0.277699\pi\) |
0.341787 | + | 0.939777i | \(0.388968\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.13840e32 | − | 1.97177e32i | −0.895767 | − | 1.55151i | −0.832852 | − | 0.553496i | \(-0.813293\pi\) |
−0.0629156 | − | 0.998019i | \(-0.520040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.45038e31 | + | 7.70828e31i | −0.341025 | + | 0.590672i | ||||
\(832\) | 1.54533e32 | 1.16860 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.03069e32 | + | 1.78522e32i | 0.729710 | + | 1.26389i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.48852e32 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.49386e32 | + | 2.58745e32i | 0.965037 | + | 1.67149i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.96383e31 | + | 1.39878e32i | 0.494771 | + | 0.869023i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.67434e31 | − | 2.90004e31i | 0.101358 | − | 0.175557i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.51656e29 | −0.00489581 | −0.00244791 | − | 0.999997i | \(-0.500779\pi\) | ||||
−0.00244791 | + | 0.999997i | \(0.500779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.78597e32 | + | 3.09338e32i | −0.950492 | + | 1.64630i | −0.206128 | + | 0.978525i | \(0.566086\pi\) |
−0.744363 | + | 0.667775i | \(0.767247\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.08070e32 | −1.00000 | ||||||||
\(868\) | 1.52160e32 | + | 2.67257e32i | 0.722079 | + | 1.26827i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.24228e32 | − | 3.88374e32i | −1.02445 | − | 1.77439i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.54012e31 | − | 4.39962e31i | 0.113161 | − | 0.196001i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.61682e32 | −1.98061 | ||||||||
\(877\) | 1.49418e32 | − | 2.58800e32i | 0.633007 | − | 1.09640i | −0.353926 | − | 0.935273i | \(-0.615154\pi\) |
0.986934 | − | 0.161128i | \(-0.0515130\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75662e32 | −0.690414 | −0.345207 | − | 0.938527i | \(-0.612191\pi\) | ||||
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.76269e32 | − | 4.71921e32i | 1.00789 | − | 1.72167i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00408e31 | − | 1.73912e31i | −0.0352985 | − | 0.0611388i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.56905e32 | − | 2.71768e32i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.44320e32 | + | 2.67792e30i | 1.36499 | + | 0.00822682i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.57085e31 | + | 1.48451e32i | 0.250809 | + | 0.434414i | 0.963749 | − | 0.266811i | \(-0.0859700\pi\) |
−0.712940 | + | 0.701225i | \(0.752637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 3.22142e31 | − | 5.57966e31i | 0.0887368 | − | 0.153697i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.12334e32 | −0.819915 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69170e32 | − | 6.39422e32i | 0.934881 | − | 1.61926i | 0.160035 | − | 0.987111i | \(-0.448839\pi\) |
0.774846 | − | 0.632150i | \(-0.217827\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.87826e32 | + | 3.25324e32i | 0.464408 | + | 0.804378i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.01361e32 | 0.474697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.67738e31 | + | 8.10145e31i | 0.107678 | + | 0.186503i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.08255e31 | + | 9.74307e29i | 0.177461 | + | 0.00213919i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.65292e32 | −1.36106 | −0.680529 | − | 0.732721i | \(-0.738250\pi\) | ||||
−0.680529 | + | 0.732721i | \(0.738250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.95722e32 | 1.98983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −3.85466e32 | − | 6.67647e32i | −0.693577 | − | 1.20131i | ||||
\(949\) | −6.50671e32 | − | 1.12700e33i | −1.15727 | − | 2.00444i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.64728e32 | + | 6.31728e32i | −0.564952 | + | 0.978526i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.32612e32 | + | 7.49306e32i | −0.647517 | + | 1.12153i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.33247e32 | −0.771324 | −0.385662 | − | 0.922640i | \(-0.626027\pi\) | ||||
−0.385662 | + | 0.922640i | \(0.626027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | −7.31693e32 | −1.00000 | ||||||||
\(973\) | −7.02953e32 | + | 1.20078e33i | −0.949916 | + | 1.62264i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.42269e32 | − | 7.66032e32i | 0.584299 | − | 1.01204i | ||||
\(976\) | 5.92809e32 | + | 1.02678e33i | 0.774403 | + | 1.34131i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.87139e32 | 0.972059 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.81604e32 | 0.207395 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.72952e32 | + | 1.51200e33i | 0.964229 | + | 1.67009i | 0.711673 | + | 0.702511i | \(0.247938\pi\) |
0.252556 | + | 0.967582i | \(0.418729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.52301e33 | 1.64536 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.45970e32 | + | 1.29206e33i | 0.771036 | + | 1.33547i | 0.936995 | + | 0.349342i | \(0.113595\pi\) |
−0.165959 | + | 0.986133i | \(0.553072\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.34750e32 | − | 4.06600e32i | 0.237348 | − | 0.411099i |
(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 | 21.23.h.a.2.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.23.h.a.2.1 | ✓ | 2 | |
7.4 | even | 3 | inner | 21.23.h.a.11.1 | yes | 2 | |
21.11 | odd | 6 | inner | 21.23.h.a.11.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.23.h.a.2.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.23.h.a.2.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.23.h.a.11.1 | yes | 2 | 7.4 | even | 3 | inner | |
21.23.h.a.11.1 | yes | 2 | 21.11 | odd | 6 | inner |