Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(428,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.428");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.e (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 428.4 | ||
Root | \(-0.578737 + 2.15988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.428 |
Dual form | 429.2.e.b.428.6 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.16228 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | 3.46410 | 1.30931 | 0.654654 | − | 0.755929i | \(-0.272814\pi\) | ||||
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | − | 3.16228i | − | 1.00000i | ||||||
\(11\) | −3.16228 | + | 1.00000i | −0.953463 | + | 0.301511i | ||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | 1.73205 | − | 3.16228i | 0.480384 | − | 0.877058i | ||||
\(14\) | − | 3.46410i | − | 0.925820i | ||||||
\(15\) | 5.47723i | 1.41421i | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.47723 | −1.32842 | −0.664211 | − | 0.747545i | \(-0.731232\pi\) | ||||
−0.664211 | + | 0.747545i | \(0.731232\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | −3.46410 | −0.794719 | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 3.16228 | 0.707107 | ||||||||
\(21\) | 6.00000i | 1.30931i | ||||||||
\(22\) | 1.00000 | + | 3.16228i | 0.213201 | + | 0.674200i | ||||
\(23\) | 6.92820i | 1.44463i | 0.691564 | + | 0.722315i | \(0.256922\pi\) | ||||
−0.691564 | + | 0.722315i | \(0.743078\pi\) | |||||||
\(24\) | 5.19615 | 1.06066 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −3.16228 | − | 1.73205i | −0.620174 | − | 0.339683i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 3.46410 | 0.654654 | ||||||||
\(29\) | −5.47723 | −1.01710 | −0.508548 | − | 0.861034i | \(-0.669817\pi\) | ||||
−0.508548 | + | 0.861034i | \(0.669817\pi\) | |||||||
\(30\) | 5.47723 | 1.00000 | ||||||||
\(31\) | − | 5.47723i | − | 0.983739i | −0.870669 | − | 0.491869i | \(-0.836314\pi\) | ||
0.870669 | − | 0.491869i | \(-0.163686\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | −1.73205 | − | 5.47723i | −0.301511 | − | 0.953463i | ||||
\(34\) | 5.47723i | 0.939336i | ||||||||
\(35\) | 10.9545 | 1.85164 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 3.46410i | 0.561951i | ||||||||
\(39\) | 5.47723 | + | 3.00000i | 0.877058 | + | 0.480384i | ||||
\(40\) | − | 9.48683i | − | 1.50000i | ||||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 6.00000 | 0.925820 | ||||||||
\(43\) | 9.48683i | 1.44673i | 0.690467 | + | 0.723364i | \(0.257405\pi\) | ||||
−0.690467 | + | 0.723364i | \(0.742595\pi\) | |||||||
\(44\) | −3.16228 | + | 1.00000i | −0.476731 | + | 0.150756i | ||||
\(45\) | −9.48683 | −1.41421 | ||||||||
\(46\) | 6.92820 | 1.02151 | ||||||||
\(47\) | 6.32456 | 0.922531 | 0.461266 | − | 0.887262i | \(-0.347396\pi\) | ||||
0.461266 | + | 0.887262i | \(0.347396\pi\) | |||||||
\(48\) | − | 1.73205i | − | 0.250000i | ||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | − | 5.00000i | − | 0.707107i | ||||||
\(51\) | − | 9.48683i | − | 1.32842i | ||||||
\(52\) | 1.73205 | − | 3.16228i | 0.240192 | − | 0.438529i | ||||
\(53\) | − | 6.92820i | − | 0.951662i | −0.879537 | − | 0.475831i | \(-0.842147\pi\) | ||
0.879537 | − | 0.475831i | \(-0.157853\pi\) | |||||||
\(54\) | −5.19615 | −0.707107 | ||||||||
\(55\) | −10.0000 | + | 3.16228i | −1.34840 | + | 0.426401i | ||||
\(56\) | − | 10.3923i | − | 1.38873i | ||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 5.47723i | 0.719195i | ||||||||
\(59\) | 6.32456 | 0.823387 | 0.411693 | − | 0.911322i | \(-0.364937\pi\) | ||||
0.411693 | + | 0.911322i | \(0.364937\pi\) | |||||||
\(60\) | 5.47723i | 0.707107i | ||||||||
\(61\) | 12.6491i | 1.61955i | 0.586739 | + | 0.809776i | \(0.300412\pi\) | ||||
−0.586739 | + | 0.809776i | \(0.699588\pi\) | |||||||
\(62\) | −5.47723 | −0.695608 | ||||||||
\(63\) | −10.3923 | −1.30931 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 5.47723 | − | 10.0000i | 0.679366 | − | 1.24035i | ||||
\(66\) | −5.47723 | + | 1.73205i | −0.674200 | + | 0.213201i | ||||
\(67\) | 5.47723i | 0.669150i | 0.942369 | + | 0.334575i | \(0.108593\pi\) | ||||
−0.942369 | + | 0.334575i | \(0.891407\pi\) | |||||||
\(68\) | −5.47723 | −0.664211 | ||||||||
\(69\) | −12.0000 | −1.44463 | ||||||||
\(70\) | − | 10.9545i | − | 1.30931i | ||||||
\(71\) | −6.32456 | −0.750587 | −0.375293 | − | 0.926906i | \(-0.622458\pi\) | ||||
−0.375293 | + | 0.926906i | \(0.622458\pi\) | |||||||
\(72\) | 9.00000i | 1.06066i | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.66025i | 1.00000i | ||||||||
\(76\) | −3.46410 | −0.397360 | ||||||||
\(77\) | −10.9545 | + | 3.46410i | −1.24838 | + | 0.394771i | ||||
\(78\) | 3.00000 | − | 5.47723i | 0.339683 | − | 0.620174i | ||||
\(79\) | 3.16228i | 0.355784i | 0.984050 | + | 0.177892i | \(0.0569278\pi\) | ||||
−0.984050 | + | 0.177892i | \(0.943072\pi\) | |||||||
\(80\) | −3.16228 | −0.353553 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | − | 2.00000i | − | 0.219529i | −0.993958 | − | 0.109764i | \(-0.964990\pi\) | ||
0.993958 | − | 0.109764i | \(-0.0350096\pi\) | |||||||
\(84\) | 6.00000i | 0.654654i | ||||||||
\(85\) | −17.3205 | −1.87867 | ||||||||
\(86\) | 9.48683 | 1.02299 | ||||||||
\(87\) | − | 9.48683i | − | 1.01710i | ||||||
\(88\) | 3.00000 | + | 9.48683i | 0.319801 | + | 1.01130i | ||||
\(89\) | 3.16228 | 0.335201 | 0.167600 | − | 0.985855i | \(-0.446398\pi\) | ||||
0.167600 | + | 0.985855i | \(0.446398\pi\) | |||||||
\(90\) | 9.48683i | 1.00000i | ||||||||
\(91\) | 6.00000 | − | 10.9545i | 0.628971 | − | 1.14834i | ||||
\(92\) | 6.92820i | 0.722315i | ||||||||
\(93\) | 9.48683 | 0.983739 | ||||||||
\(94\) | − | 6.32456i | − | 0.652328i | ||||||
\(95\) | −10.9545 | −1.12390 | ||||||||
\(96\) | 8.66025 | 0.883883 | ||||||||
\(97\) | − | 10.9545i | − | 1.11226i | −0.831097 | − | 0.556128i | \(-0.812286\pi\) | ||
0.831097 | − | 0.556128i | \(-0.187714\pi\) | |||||||
\(98\) | − | 5.00000i | − | 0.505076i | ||||||
\(99\) | 9.48683 | − | 3.00000i | 0.953463 | − | 0.301511i | ||||
\(100\) | 5.00000 | 0.500000 | ||||||||
\(101\) | 5.47723 | 0.545004 | 0.272502 | − | 0.962155i | \(-0.412149\pi\) | ||||
0.272502 | + | 0.962155i | \(0.412149\pi\) | |||||||
\(102\) | −9.48683 | −0.939336 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −9.48683 | − | 5.19615i | −0.930261 | − | 0.509525i | ||||
\(105\) | 18.9737i | 1.85164i | ||||||||
\(106\) | −6.92820 | −0.672927 | ||||||||
\(107\) | 10.9545 | 1.05901 | 0.529503 | − | 0.848308i | \(-0.322378\pi\) | ||||
0.529503 | + | 0.848308i | \(0.322378\pi\) | |||||||
\(108\) | − | 5.19615i | − | 0.500000i | ||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 3.16228 | + | 10.0000i | 0.301511 | + | 0.953463i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | 6.92820i | 0.651751i | 0.945413 | + | 0.325875i | \(0.105659\pi\) | ||||
−0.945413 | + | 0.325875i | \(0.894341\pi\) | |||||||
\(114\) | −6.00000 | −0.561951 | ||||||||
\(115\) | 21.9089i | 2.04302i | ||||||||
\(116\) | −5.47723 | −0.508548 | ||||||||
\(117\) | −5.19615 | + | 9.48683i | −0.480384 | + | 0.877058i | ||||
\(118\) | − | 6.32456i | − | 0.582223i | ||||||
\(119\) | −18.9737 | −1.73931 | ||||||||
\(120\) | 16.4317 | 1.50000 | ||||||||
\(121\) | 9.00000 | − | 6.32456i | 0.818182 | − | 0.574960i | ||||
\(122\) | 12.6491 | 1.14520 | ||||||||
\(123\) | −3.46410 | −0.312348 | ||||||||
\(124\) | − | 5.47723i | − | 0.491869i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.3923i | 0.925820i | ||||||||
\(127\) | − | 3.16228i | − | 0.280607i | −0.990109 | − | 0.140303i | \(-0.955192\pi\) | ||
0.990109 | − | 0.140303i | \(-0.0448078\pi\) | |||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | −16.4317 | −1.44673 | ||||||||
\(130\) | −10.0000 | − | 5.47723i | −0.877058 | − | 0.480384i | ||||
\(131\) | 10.9545 | 0.957095 | 0.478547 | − | 0.878062i | \(-0.341163\pi\) | ||||
0.478547 | + | 0.878062i | \(0.341163\pi\) | |||||||
\(132\) | −1.73205 | − | 5.47723i | −0.150756 | − | 0.476731i | ||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 5.47723 | 0.473160 | ||||||||
\(135\) | − | 16.4317i | − | 1.41421i | ||||||
\(136\) | 16.4317i | 1.40900i | ||||||||
\(137\) | 3.16228 | 0.270172 | 0.135086 | − | 0.990834i | \(-0.456869\pi\) | ||||
0.135086 | + | 0.990834i | \(0.456869\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | − | 9.48683i | − | 0.804663i | −0.915494 | − | 0.402331i | \(-0.868200\pi\) | ||
0.915494 | − | 0.402331i | \(-0.131800\pi\) | |||||||
\(140\) | 10.9545 | 0.925820 | ||||||||
\(141\) | 10.9545i | 0.922531i | ||||||||
\(142\) | 6.32456i | 0.530745i | ||||||||
\(143\) | −2.31495 | + | 11.7321i | −0.193586 | + | 0.981083i | ||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −17.3205 | −1.43839 | ||||||||
\(146\) | 6.92820i | 0.573382i | ||||||||
\(147\) | 8.66025i | 0.714286i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 22.0000i | − | 1.80231i | −0.433497 | − | 0.901155i | \(-0.642720\pi\) | ||
0.433497 | − | 0.901155i | \(-0.357280\pi\) | |||||||
\(150\) | 8.66025 | 0.707107 | ||||||||
\(151\) | 10.3923 | 0.845714 | 0.422857 | − | 0.906196i | \(-0.361027\pi\) | ||||
0.422857 | + | 0.906196i | \(0.361027\pi\) | |||||||
\(152\) | 10.3923i | 0.842927i | ||||||||
\(153\) | 16.4317 | 1.32842 | ||||||||
\(154\) | 3.46410 | + | 10.9545i | 0.279145 | + | 0.882735i | ||||
\(155\) | − | 17.3205i | − | 1.39122i | ||||||
\(156\) | 5.47723 | + | 3.00000i | 0.438529 | + | 0.240192i | ||||
\(157\) | −16.0000 | −1.27694 | −0.638470 | − | 0.769647i | \(-0.720432\pi\) | ||||
−0.638470 | + | 0.769647i | \(0.720432\pi\) | |||||||
\(158\) | 3.16228 | 0.251577 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | − | 15.8114i | − | 1.25000i | ||||||
\(161\) | 24.0000i | 1.89146i | ||||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | − | 5.47723i | − | 0.429009i | −0.976723 | − | 0.214505i | \(-0.931186\pi\) | ||
0.976723 | − | 0.214505i | \(-0.0688137\pi\) | |||||||
\(164\) | 2.00000i | 0.156174i | ||||||||
\(165\) | −5.47723 | − | 17.3205i | −0.426401 | − | 1.34840i | ||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 10.0000i | 0.773823i | 0.922117 | + | 0.386912i | \(0.126458\pi\) | ||||
−0.922117 | + | 0.386912i | \(0.873542\pi\) | |||||||
\(168\) | 18.0000 | 1.38873 | ||||||||
\(169\) | −7.00000 | − | 10.9545i | −0.538462 | − | 0.842650i | ||||
\(170\) | 17.3205i | 1.32842i | ||||||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | 9.48683i | 0.723364i | ||||||||
\(173\) | −16.4317 | −1.24928 | −0.624639 | − | 0.780914i | \(-0.714754\pi\) | ||||
−0.624639 | + | 0.780914i | \(0.714754\pi\) | |||||||
\(174\) | −9.48683 | −0.719195 | ||||||||
\(175\) | 17.3205 | 1.30931 | ||||||||
\(176\) | 3.16228 | − | 1.00000i | 0.238366 | − | 0.0753778i | ||||
\(177\) | 10.9545i | 0.823387i | ||||||||
\(178\) | − | 3.16228i | − | 0.237023i | ||||||
\(179\) | − | 13.8564i | − | 1.03568i | −0.855479 | − | 0.517838i | \(-0.826737\pi\) | ||
0.855479 | − | 0.517838i | \(-0.173263\pi\) | |||||||
\(180\) | −9.48683 | −0.707107 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | −10.9545 | − | 6.00000i | −0.811998 | − | 0.444750i | ||||
\(183\) | −21.9089 | −1.61955 | ||||||||
\(184\) | 20.7846 | 1.53226 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 9.48683i | − | 0.695608i | ||||||
\(187\) | 17.3205 | − | 5.47723i | 1.26660 | − | 0.400534i | ||||
\(188\) | 6.32456 | 0.461266 | ||||||||
\(189\) | − | 18.0000i | − | 1.30931i | ||||||
\(190\) | 10.9545i | 0.794719i | ||||||||
\(191\) | − | 10.3923i | − | 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(192\) | − | 12.1244i | − | 0.875000i | ||||||
\(193\) | −20.7846 | −1.49611 | −0.748054 | − | 0.663637i | \(-0.769012\pi\) | ||||
−0.748054 | + | 0.663637i | \(0.769012\pi\) | |||||||
\(194\) | −10.9545 | −0.786484 | ||||||||
\(195\) | 17.3205 | + | 9.48683i | 1.24035 | + | 0.679366i | ||||
\(196\) | 5.00000 | 0.357143 | ||||||||
\(197\) | − | 14.0000i | − | 0.997459i | −0.866758 | − | 0.498729i | \(-0.833800\pi\) | ||
0.866758 | − | 0.498729i | \(-0.166200\pi\) | |||||||
\(198\) | −3.00000 | − | 9.48683i | −0.213201 | − | 0.674200i | ||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | − | 15.0000i | − | 1.06066i | ||||||
\(201\) | −9.48683 | −0.669150 | ||||||||
\(202\) | − | 5.47723i | − | 0.385376i | ||||||
\(203\) | −18.9737 | −1.33169 | ||||||||
\(204\) | − | 9.48683i | − | 0.664211i | ||||||
\(205\) | 6.32456i | 0.441726i | ||||||||
\(206\) | 8.00000i | 0.557386i | ||||||||
\(207\) | − | 20.7846i | − | 1.44463i | ||||||
\(208\) | −1.73205 | + | 3.16228i | −0.120096 | + | 0.219265i | ||||
\(209\) | 10.9545 | − | 3.46410i | 0.757735 | − | 0.239617i | ||||
\(210\) | 18.9737 | 1.30931 | ||||||||
\(211\) | − | 3.16228i | − | 0.217700i | −0.994058 | − | 0.108850i | \(-0.965283\pi\) | ||
0.994058 | − | 0.108850i | \(-0.0347168\pi\) | |||||||
\(212\) | − | 6.92820i | − | 0.475831i | ||||||
\(213\) | − | 10.9545i | − | 0.750587i | ||||||
\(214\) | − | 10.9545i | − | 0.748831i | ||||||
\(215\) | 30.0000i | 2.04598i | ||||||||
\(216\) | −15.5885 | −1.06066 | ||||||||
\(217\) | − | 18.9737i | − | 1.28802i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 12.0000i | − | 0.810885i | ||||||
\(220\) | −10.0000 | + | 3.16228i | −0.674200 | + | 0.213201i | ||||
\(221\) | −9.48683 | + | 17.3205i | −0.638153 | + | 1.16510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4317i | 1.10035i | 0.835051 | + | 0.550173i | \(0.185438\pi\) | ||||
−0.835051 | + | 0.550173i | \(0.814562\pi\) | |||||||
\(224\) | − | 17.3205i | − | 1.15728i | ||||||
\(225\) | −15.0000 | −1.00000 | ||||||||
\(226\) | 6.92820 | 0.460857 | ||||||||
\(227\) | 4.00000i | 0.265489i | 0.991150 | + | 0.132745i | \(0.0423790\pi\) | ||||
−0.991150 | + | 0.132745i | \(0.957621\pi\) | |||||||
\(228\) | − | 6.00000i | − | 0.397360i | ||||||
\(229\) | 21.9089i | 1.44778i | 0.689915 | + | 0.723891i | \(0.257648\pi\) | ||||
−0.689915 | + | 0.723891i | \(0.742352\pi\) | |||||||
\(230\) | 21.9089 | 1.44463 | ||||||||
\(231\) | −6.00000 | − | 18.9737i | −0.394771 | − | 1.24838i | ||||
\(232\) | 16.4317i | 1.07879i | ||||||||
\(233\) | 27.3861 | 1.79412 | 0.897062 | − | 0.441904i | \(-0.145697\pi\) | ||||
0.897062 | + | 0.441904i | \(0.145697\pi\) | |||||||
\(234\) | 9.48683 | + | 5.19615i | 0.620174 | + | 0.339683i | ||||
\(235\) | 20.0000 | 1.30466 | ||||||||
\(236\) | 6.32456 | 0.411693 | ||||||||
\(237\) | −5.47723 | −0.355784 | ||||||||
\(238\) | 18.9737i | 1.22988i | ||||||||
\(239\) | − | 8.00000i | − | 0.517477i | −0.965947 | − | 0.258738i | \(-0.916693\pi\) | ||
0.965947 | − | 0.258738i | \(-0.0833068\pi\) | |||||||
\(240\) | − | 5.47723i | − | 0.353553i | ||||||
\(241\) | 24.2487 | 1.56200 | 0.780998 | − | 0.624533i | \(-0.214711\pi\) | ||||
0.780998 | + | 0.624533i | \(0.214711\pi\) | |||||||
\(242\) | −6.32456 | − | 9.00000i | −0.406558 | − | 0.578542i | ||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 12.6491i | 0.809776i | ||||||||
\(245\) | 15.8114 | 1.01015 | ||||||||
\(246\) | 3.46410i | 0.220863i | ||||||||
\(247\) | −6.00000 | + | 10.9545i | −0.381771 | + | 0.697015i | ||||
\(248\) | −16.4317 | −1.04341 | ||||||||
\(249\) | 3.46410 | 0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.2487i | 1.53057i | 0.643695 | + | 0.765283i | \(0.277401\pi\) | ||||
−0.643695 | + | 0.765283i | \(0.722599\pi\) | |||||||
\(252\) | −10.3923 | −0.654654 | ||||||||
\(253\) | −6.92820 | − | 21.9089i | −0.435572 | − | 1.37740i | ||||
\(254\) | −3.16228 | −0.198419 | ||||||||
\(255\) | − | 30.0000i | − | 1.87867i | ||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 6.92820i | − | 0.432169i | −0.976375 | − | 0.216085i | \(-0.930671\pi\) | ||
0.976375 | − | 0.216085i | \(-0.0693287\pi\) | |||||||
\(258\) | 16.4317i | 1.02299i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.47723 | − | 10.0000i | 0.339683 | − | 0.620174i | ||||
\(261\) | 16.4317 | 1.01710 | ||||||||
\(262\) | − | 10.9545i | − | 0.676768i | ||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −16.4317 | + | 5.19615i | −1.01130 | + | 0.319801i | ||||
\(265\) | − | 21.9089i | − | 1.34585i | ||||||
\(266\) | 12.0000i | 0.735767i | ||||||||
\(267\) | 5.47723i | 0.335201i | ||||||||
\(268\) | 5.47723i | 0.334575i | ||||||||
\(269\) | − | 13.8564i | − | 0.844840i | −0.906400 | − | 0.422420i | \(-0.861181\pi\) | ||
0.906400 | − | 0.422420i | \(-0.138819\pi\) | |||||||
\(270\) | −16.4317 | −1.00000 | ||||||||
\(271\) | 24.2487 | 1.47300 | 0.736502 | − | 0.676435i | \(-0.236476\pi\) | ||||
0.736502 | + | 0.676435i | \(0.236476\pi\) | |||||||
\(272\) | 5.47723 | 0.332106 | ||||||||
\(273\) | 18.9737 | + | 10.3923i | 1.14834 | + | 0.628971i | ||||
\(274\) | − | 3.16228i | − | 0.191040i | ||||||
\(275\) | −15.8114 | + | 5.00000i | −0.953463 | + | 0.301511i | ||||
\(276\) | −12.0000 | −0.722315 | ||||||||
\(277\) | − | 18.9737i | − | 1.14002i | −0.821639 | − | 0.570009i | \(-0.806940\pi\) | ||
0.821639 | − | 0.570009i | \(-0.193060\pi\) | |||||||
\(278\) | −9.48683 | −0.568982 | ||||||||
\(279\) | 16.4317i | 0.983739i | ||||||||
\(280\) | − | 32.8634i | − | 1.96396i | ||||||
\(281\) | 14.0000i | 0.835170i | 0.908638 | + | 0.417585i | \(0.137123\pi\) | ||||
−0.908638 | + | 0.417585i | \(0.862877\pi\) | |||||||
\(282\) | 10.9545 | 0.652328 | ||||||||
\(283\) | 3.16228i | 0.187978i | 0.995573 | + | 0.0939889i | \(0.0299618\pi\) | ||||
−0.995573 | + | 0.0939889i | \(0.970038\pi\) | |||||||
\(284\) | −6.32456 | −0.375293 | ||||||||
\(285\) | − | 18.9737i | − | 1.12390i | ||||||
\(286\) | 11.7321 | + | 2.31495i | 0.693731 | + | 0.136886i | ||||
\(287\) | 6.92820i | 0.408959i | ||||||||
\(288\) | 15.0000i | 0.883883i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 17.3205i | 1.01710i | ||||||||
\(291\) | 18.9737 | 1.11226 | ||||||||
\(292\) | −6.92820 | −0.405442 | ||||||||
\(293\) | − | 2.00000i | − | 0.116841i | −0.998292 | − | 0.0584206i | \(-0.981394\pi\) | ||
0.998292 | − | 0.0584206i | \(-0.0186065\pi\) | |||||||
\(294\) | 8.66025 | 0.505076 | ||||||||
\(295\) | 20.0000 | 1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.19615 | + | 16.4317i | 0.301511 | + | 0.953463i | ||||
\(298\) | −22.0000 | −1.27443 | ||||||||
\(299\) | 21.9089 | + | 12.0000i | 1.26702 | + | 0.693978i | ||||
\(300\) | 8.66025i | 0.500000i | ||||||||
\(301\) | 32.8634i | 1.89421i | ||||||||
\(302\) | − | 10.3923i | − | 0.598010i | ||||||
\(303\) | 9.48683i | 0.545004i | ||||||||
\(304\) | 3.46410 | 0.198680 | ||||||||
\(305\) | 40.0000i | 2.29039i | ||||||||
\(306\) | − | 16.4317i | − | 0.939336i | ||||||
\(307\) | −3.46410 | −0.197707 | −0.0988534 | − | 0.995102i | \(-0.531517\pi\) | ||||
−0.0988534 | + | 0.995102i | \(0.531517\pi\) | |||||||
\(308\) | −10.9545 | + | 3.46410i | −0.624188 | + | 0.197386i | ||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | −17.3205 | −0.983739 | ||||||||
\(311\) | − | 6.92820i | − | 0.392862i | −0.980518 | − | 0.196431i | \(-0.937065\pi\) | ||
0.980518 | − | 0.196431i | \(-0.0629352\pi\) | |||||||
\(312\) | 9.00000 | − | 16.4317i | 0.509525 | − | 0.930261i | ||||
\(313\) | −12.0000 | −0.678280 | −0.339140 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339140 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(314\) | 16.0000i | 0.902932i | ||||||||
\(315\) | −32.8634 | −1.85164 | ||||||||
\(316\) | 3.16228i | 0.177892i | ||||||||
\(317\) | −3.16228 | −0.177611 | −0.0888056 | − | 0.996049i | \(-0.528305\pi\) | ||||
−0.0888056 | + | 0.996049i | \(0.528305\pi\) | |||||||
\(318\) | − | 12.0000i | − | 0.672927i | ||||||
\(319\) | 17.3205 | − | 5.47723i | 0.969762 | − | 0.306666i | ||||
\(320\) | −22.1359 | −1.23744 | ||||||||
\(321\) | 18.9737i | 1.05901i | ||||||||
\(322\) | 24.0000 | 1.33747 | ||||||||
\(323\) | 18.9737 | 1.05572 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | 8.66025 | − | 15.8114i | 0.480384 | − | 0.877058i | ||||
\(326\) | −5.47723 | −0.303355 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 21.9089 | 1.20788 | ||||||||
\(330\) | −17.3205 | + | 5.47723i | −0.953463 | + | 0.301511i | ||||
\(331\) | − | 5.47723i | − | 0.301056i | −0.988606 | − | 0.150528i | \(-0.951903\pi\) | ||
0.988606 | − | 0.150528i | \(-0.0480973\pi\) | |||||||
\(332\) | − | 2.00000i | − | 0.109764i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0000 | 0.547176 | ||||||||
\(335\) | 17.3205i | 0.946320i | ||||||||
\(336\) | − | 6.00000i | − | 0.327327i | ||||||
\(337\) | 25.2982i | 1.37808i | 0.724722 | + | 0.689041i | \(0.241968\pi\) | ||||
−0.724722 | + | 0.689041i | \(0.758032\pi\) | |||||||
\(338\) | −10.9545 | + | 7.00000i | −0.595844 | + | 0.380750i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | −17.3205 | −0.939336 | ||||||||
\(341\) | 5.47723 | + | 17.3205i | 0.296608 | + | 0.937958i | ||||
\(342\) | − | 10.3923i | − | 0.561951i | ||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 28.4605 | 1.53449 | ||||||||
\(345\) | −37.9473 | −2.04302 | ||||||||
\(346\) | 16.4317i | 0.883372i | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | − | 9.48683i | − | 0.508548i | ||||||
\(349\) | −17.3205 | −0.927146 | −0.463573 | − | 0.886059i | \(-0.653433\pi\) | ||||
−0.463573 | + | 0.886059i | \(0.653433\pi\) | |||||||
\(350\) | − | 17.3205i | − | 0.925820i | ||||||
\(351\) | −16.4317 | − | 9.00000i | −0.877058 | − | 0.480384i | ||||
\(352\) | 5.00000 | + | 15.8114i | 0.266501 | + | 0.842750i | ||||
\(353\) | −15.8114 | −0.841555 | −0.420778 | − | 0.907164i | \(-0.638243\pi\) | ||||
−0.420778 | + | 0.907164i | \(0.638243\pi\) | |||||||
\(354\) | 10.9545 | 0.582223 | ||||||||
\(355\) | −20.0000 | −1.06149 | ||||||||
\(356\) | 3.16228 | 0.167600 | ||||||||
\(357\) | − | 32.8634i | − | 1.73931i | ||||||
\(358\) | −13.8564 | −0.732334 | ||||||||
\(359\) | 32.0000i | 1.68890i | 0.535638 | + | 0.844448i | \(0.320071\pi\) | ||||
−0.535638 | + | 0.844448i | \(0.679929\pi\) | |||||||
\(360\) | 28.4605i | 1.50000i | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | − | 8.00000i | − | 0.420471i | ||||||
\(363\) | 10.9545 | + | 15.5885i | 0.574960 | + | 0.818182i | ||||
\(364\) | 6.00000 | − | 10.9545i | 0.314485 | − | 0.574169i | ||||
\(365\) | −21.9089 | −1.14676 | ||||||||
\(366\) | 21.9089i | 1.14520i | ||||||||
\(367\) | −16.0000 | −0.835193 | −0.417597 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417597 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(368\) | − | 6.92820i | − | 0.361158i | ||||||
\(369\) | − | 6.00000i | − | 0.312348i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 24.0000i | − | 1.24602i | ||||||
\(372\) | 9.48683 | 0.491869 | ||||||||
\(373\) | 31.6228i | 1.63737i | 0.574246 | + | 0.818683i | \(0.305295\pi\) | ||||
−0.574246 | + | 0.818683i | \(0.694705\pi\) | |||||||
\(374\) | −5.47723 | − | 17.3205i | −0.283221 | − | 0.895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 18.9737i | − | 0.978492i | ||||||
\(377\) | −9.48683 | + | 17.3205i | −0.488597 | + | 0.892052i | ||||
\(378\) | −18.0000 | −0.925820 | ||||||||
\(379\) | − | 27.3861i | − | 1.40673i | −0.710828 | − | 0.703365i | \(-0.751680\pi\) | ||
0.710828 | − | 0.703365i | \(-0.248320\pi\) | |||||||
\(380\) | −10.9545 | −0.561951 | ||||||||
\(381\) | 5.47723 | 0.280607 | ||||||||
\(382\) | −10.3923 | −0.531717 | ||||||||
\(383\) | 25.2982 | 1.29268 | 0.646339 | − | 0.763050i | \(-0.276299\pi\) | ||||
0.646339 | + | 0.763050i | \(0.276299\pi\) | |||||||
\(384\) | 5.19615 | 0.265165 | ||||||||
\(385\) | −34.6410 | + | 10.9545i | −1.76547 | + | 0.558291i | ||||
\(386\) | 20.7846i | 1.05791i | ||||||||
\(387\) | − | 28.4605i | − | 1.44673i | ||||||
\(388\) | − | 10.9545i | − | 0.556128i | ||||||
\(389\) | 20.7846i | 1.05382i | 0.849921 | + | 0.526911i | \(0.176650\pi\) | ||||
−0.849921 | + | 0.526911i | \(0.823350\pi\) | |||||||
\(390\) | 9.48683 | − | 17.3205i | 0.480384 | − | 0.877058i | ||||
\(391\) | − | 37.9473i | − | 1.91908i | ||||||
\(392\) | − | 15.0000i | − | 0.757614i | ||||||
\(393\) | 18.9737i | 0.957095i | ||||||||
\(394\) | −14.0000 | −0.705310 | ||||||||
\(395\) | 10.0000i | 0.503155i | ||||||||
\(396\) | 9.48683 | − | 3.00000i | 0.476731 | − | 0.150756i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | − | 24.0000i | − | 1.20301i | ||||||
\(399\) | − | 20.7846i | − | 1.04053i | ||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 22.1359 | 1.10542 | 0.552708 | − | 0.833375i | \(-0.313594\pi\) | ||||
0.552708 | + | 0.833375i | \(0.313594\pi\) | |||||||
\(402\) | 9.48683i | 0.473160i | ||||||||
\(403\) | −17.3205 | − | 9.48683i | −0.862796 | − | 0.472573i | ||||
\(404\) | 5.47723 | 0.272502 | ||||||||
\(405\) | 28.4605 | 1.41421 | ||||||||
\(406\) | 18.9737i | 0.941647i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −28.4605 | −1.40900 | ||||||||
\(409\) | 20.7846 | 1.02773 | 0.513866 | − | 0.857870i | \(-0.328213\pi\) | ||||
0.513866 | + | 0.857870i | \(0.328213\pi\) | |||||||
\(410\) | 6.32456 | 0.312348 | ||||||||
\(411\) | 5.47723i | 0.270172i | ||||||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 21.9089 | 1.07807 | ||||||||
\(414\) | −20.7846 | −1.02151 | ||||||||
\(415\) | − | 6.32456i | − | 0.310460i | ||||||
\(416\) | −15.8114 | − | 8.66025i | −0.775217 | − | 0.424604i | ||||
\(417\) | 16.4317 | 0.804663 | ||||||||
\(418\) | −3.46410 | − | 10.9545i | −0.169435 | − | 0.535800i | ||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 18.9737i | 0.925820i | ||||||||
\(421\) | − | 32.8634i | − | 1.60166i | −0.598891 | − | 0.800831i | \(-0.704392\pi\) | ||
0.598891 | − | 0.800831i | \(-0.295608\pi\) | |||||||
\(422\) | −3.16228 | −0.153937 | ||||||||
\(423\) | −18.9737 | −0.922531 | ||||||||
\(424\) | −20.7846 | −1.00939 | ||||||||
\(425\) | −27.3861 | −1.32842 | ||||||||
\(426\) | −10.9545 | −0.530745 | ||||||||
\(427\) | 43.8178i | 2.12049i | ||||||||
\(428\) | 10.9545 | 0.529503 | ||||||||
\(429\) | −20.3205 | − | 4.00961i | −0.981083 | − | 0.193586i | ||||
\(430\) | 30.0000 | 1.44673 | ||||||||
\(431\) | − | 14.0000i | − | 0.674356i | −0.941441 | − | 0.337178i | \(-0.890528\pi\) | ||
0.941441 | − | 0.337178i | \(-0.109472\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | 18.0000 | 0.865025 | 0.432512 | − | 0.901628i | \(-0.357627\pi\) | ||||
0.432512 | + | 0.901628i | \(0.357627\pi\) | |||||||
\(434\) | −18.9737 | −0.910765 | ||||||||
\(435\) | − | 30.0000i | − | 1.43839i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 24.0000i | − | 1.14808i | ||||||
\(438\) | −12.0000 | −0.573382 | ||||||||
\(439\) | 28.4605i | 1.35835i | 0.733978 | + | 0.679173i | \(0.237661\pi\) | ||||
−0.733978 | + | 0.679173i | \(0.762339\pi\) | |||||||
\(440\) | 9.48683 | + | 30.0000i | 0.452267 | + | 1.43019i | ||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 17.3205 | + | 9.48683i | 0.823853 | + | 0.451243i | ||||
\(443\) | − | 10.3923i | − | 0.493753i | −0.969047 | − | 0.246877i | \(-0.920596\pi\) | ||
0.969047 | − | 0.246877i | \(-0.0794043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 16.4317 | 0.778062 | ||||||||
\(447\) | 38.1051 | 1.80231 | ||||||||
\(448\) | −24.2487 | −1.14564 | ||||||||
\(449\) | −15.8114 | −0.746186 | −0.373093 | − | 0.927794i | \(-0.621703\pi\) | ||||
−0.373093 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(450\) | 15.0000i | 0.707107i | ||||||||
\(451\) | −2.00000 | − | 6.32456i | −0.0941763 | − | 0.297812i | ||||
\(452\) | 6.92820i | 0.325875i | ||||||||
\(453\) | 18.0000i | 0.845714i | ||||||||
\(454\) | 4.00000 | 0.187729 | ||||||||
\(455\) | 18.9737 | − | 34.6410i | 0.889499 | − | 1.62400i | ||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | 3.46410 | 0.162044 | 0.0810219 | − | 0.996712i | \(-0.474182\pi\) | ||||
0.0810219 | + | 0.996712i | \(0.474182\pi\) | |||||||
\(458\) | 21.9089 | 1.02374 | ||||||||
\(459\) | 28.4605i | 1.32842i | ||||||||
\(460\) | 21.9089i | 1.02151i | ||||||||
\(461\) | − | 14.0000i | − | 0.652045i | −0.945362 | − | 0.326023i | \(-0.894291\pi\) | ||
0.945362 | − | 0.326023i | \(-0.105709\pi\) | |||||||
\(462\) | −18.9737 | + | 6.00000i | −0.882735 | + | 0.279145i | ||||
\(463\) | − | 16.4317i | − | 0.763645i | −0.924236 | − | 0.381822i | \(-0.875297\pi\) | ||
0.924236 | − | 0.381822i | \(-0.124703\pi\) | |||||||
\(464\) | 5.47723 | 0.254274 | ||||||||
\(465\) | 30.0000 | 1.39122 | ||||||||
\(466\) | − | 27.3861i | − | 1.26864i | ||||||
\(467\) | 20.7846i | 0.961797i | 0.876776 | + | 0.480899i | \(0.159689\pi\) | ||||
−0.876776 | + | 0.480899i | \(0.840311\pi\) | |||||||
\(468\) | −5.19615 | + | 9.48683i | −0.240192 | + | 0.438529i | ||||
\(469\) | 18.9737i | 0.876122i | ||||||||
\(470\) | − | 20.0000i | − | 0.922531i | ||||||
\(471\) | − | 27.7128i | − | 1.27694i | ||||||
\(472\) | − | 18.9737i | − | 0.873334i | ||||||
\(473\) | −9.48683 | − | 30.0000i | −0.436205 | − | 1.37940i | ||||
\(474\) | 5.47723i | 0.251577i | ||||||||
\(475\) | −17.3205 | −0.794719 | ||||||||
\(476\) | −18.9737 | −0.869657 | ||||||||
\(477\) | 20.7846i | 0.951662i | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | − | 8.00000i | − | 0.365529i | −0.983157 | − | 0.182765i | \(-0.941495\pi\) | ||
0.983157 | − | 0.182765i | \(-0.0585046\pi\) | |||||||
\(480\) | 27.3861 | 1.25000 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 24.2487i | − | 1.10450i | ||||||
\(483\) | −41.5692 | −1.89146 | ||||||||
\(484\) | 9.00000 | − | 6.32456i | 0.409091 | − | 0.287480i | ||||
\(485\) | − | 34.6410i | − | 1.57297i | ||||||
\(486\) | 15.5885 | 0.707107 | ||||||||
\(487\) | 27.3861i | 1.24098i | 0.784213 | + | 0.620492i | \(0.213067\pi\) | ||||
−0.784213 | + | 0.620492i | \(0.786933\pi\) | |||||||
\(488\) | 37.9473 | 1.71780 | ||||||||
\(489\) | 9.48683 | 0.429009 | ||||||||
\(490\) | − | 15.8114i | − | 0.714286i | ||||||
\(491\) | −21.9089 | −0.988735 | −0.494367 | − | 0.869253i | \(-0.664600\pi\) | ||||
−0.494367 | + | 0.869253i | \(0.664600\pi\) | |||||||
\(492\) | −3.46410 | −0.156174 | ||||||||
\(493\) | 30.0000 | 1.35113 | ||||||||
\(494\) | 10.9545 | + | 6.00000i | 0.492864 | + | 0.269953i | ||||
\(495\) | 30.0000 | − | 9.48683i | 1.34840 | − | 0.426401i | ||||
\(496\) | 5.47723i | 0.245935i | ||||||||
\(497\) | −21.9089 | −0.982749 | ||||||||
\(498\) | − | 3.46410i | − | 0.155230i | ||||||
\(499\) | − | 38.3406i | − | 1.71636i | −0.513349 | − | 0.858180i | \(-0.671595\pi\) | ||
0.513349 | − | 0.858180i | \(-0.328405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3205 | −0.773823 | ||||||||
\(502\) | 24.2487 | 1.08227 | ||||||||
\(503\) | −21.9089 | −0.976870 | −0.488435 | − | 0.872600i | \(-0.662432\pi\) | ||||
−0.488435 | + | 0.872600i | \(0.662432\pi\) | |||||||
\(504\) | 31.1769i | 1.38873i | ||||||||
\(505\) | 17.3205 | 0.770752 | ||||||||
\(506\) | −21.9089 | + | 6.92820i | −0.973970 | + | 0.307996i | ||||
\(507\) | 18.9737 | − | 12.1244i | 0.842650 | − | 0.538462i | ||||
\(508\) | − | 3.16228i | − | 0.140303i | ||||||
\(509\) | −15.8114 | −0.700827 | −0.350414 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350414 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(510\) | −30.0000 | −1.32842 | ||||||||
\(511\) | −24.0000 | −1.06170 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 18.0000i | 0.794719i | ||||||||
\(514\) | −6.92820 | −0.305590 | ||||||||
\(515\) | −25.2982 | −1.11477 | ||||||||
\(516\) | −16.4317 | −0.723364 | ||||||||
\(517\) | −20.0000 | + | 6.32456i | −0.879599 | + | 0.278154i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 28.4605i | − | 1.24928i | ||||||
\(520\) | −30.0000 | − | 16.4317i | −1.31559 | − | 0.720577i | ||||
\(521\) | − | 6.92820i | − | 0.303530i | −0.988417 | − | 0.151765i | \(-0.951504\pi\) | ||
0.988417 | − | 0.151765i | \(-0.0484957\pi\) | |||||||
\(522\) | − | 16.4317i | − | 0.719195i | ||||||
\(523\) | 9.48683i | 0.414830i | 0.978253 | + | 0.207415i | \(0.0665051\pi\) | ||||
−0.978253 | + | 0.207415i | \(0.933495\pi\) | |||||||
\(524\) | 10.9545 | 0.478547 | ||||||||
\(525\) | 30.0000i | 1.30931i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0000i | 1.30682i | ||||||||
\(528\) | 1.73205 | + | 5.47723i | 0.0753778 | + | 0.238366i | ||||
\(529\) | −25.0000 | −1.08696 | ||||||||
\(530\) | −21.9089 | −0.951662 | ||||||||
\(531\) | −18.9737 | −0.823387 | ||||||||
\(532\) | −12.0000 | −0.520266 | ||||||||
\(533\) | 6.32456 | + | 3.46410i | 0.273947 | + | 0.150047i | ||||
\(534\) | 5.47723 | 0.237023 | ||||||||
\(535\) | 34.6410 | 1.49766 | ||||||||
\(536\) | 16.4317 | 0.709740 | ||||||||
\(537\) | 24.0000 | 1.03568 | ||||||||
\(538\) | −13.8564 | −0.597392 | ||||||||
\(539\) | −15.8114 | + | 5.00000i | −0.681045 | + | 0.215365i | ||||
\(540\) | − | 16.4317i | − | 0.707107i | ||||||
\(541\) | 45.0333 | 1.93613 | 0.968067 | − | 0.250692i | \(-0.0806582\pi\) | ||||
0.968067 | + | 0.250692i | \(0.0806582\pi\) | |||||||
\(542\) | − | 24.2487i | − | 1.04157i | ||||||
\(543\) | 13.8564i | 0.594635i | ||||||||
\(544\) | 27.3861i | 1.17417i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3923 | − | 18.9737i | 0.444750 | − | 0.811998i | ||||
\(547\) | − | 9.48683i | − | 0.405628i | −0.979217 | − | 0.202814i | \(-0.934991\pi\) | ||
0.979217 | − | 0.202814i | \(-0.0650086\pi\) | |||||||
\(548\) | 3.16228 | 0.135086 | ||||||||
\(549\) | − | 37.9473i | − | 1.61955i | ||||||
\(550\) | 5.00000 | + | 15.8114i | 0.213201 | + | 0.674200i | ||||
\(551\) | 18.9737 | 0.808305 | ||||||||
\(552\) | 36.0000i | 1.53226i | ||||||||
\(553\) | 10.9545i | 0.465831i | ||||||||
\(554\) | −18.9737 | −0.806114 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.48683i | − | 0.402331i | ||||||
\(557\) | 14.0000i | 0.593199i | 0.955002 | + | 0.296600i | \(0.0958526\pi\) | ||||
−0.955002 | + | 0.296600i | \(0.904147\pi\) | |||||||
\(558\) | 16.4317 | 0.695608 | ||||||||
\(559\) | 30.0000 | + | 16.4317i | 1.26886 | + | 0.694986i | ||||
\(560\) | −10.9545 | −0.462910 | ||||||||
\(561\) | 9.48683 | + | 30.0000i | 0.400534 | + | 1.26660i | ||||
\(562\) | 14.0000 | 0.590554 | ||||||||
\(563\) | 10.9545 | 0.461675 | 0.230838 | − | 0.972992i | \(-0.425853\pi\) | ||||
0.230838 | + | 0.972992i | \(0.425853\pi\) | |||||||
\(564\) | 10.9545i | 0.461266i | ||||||||
\(565\) | 21.9089i | 0.921714i | ||||||||
\(566\) | 3.16228 | 0.132920 | ||||||||
\(567\) | 31.1769 | 1.30931 | ||||||||
\(568\) | 18.9737i | 0.796117i | ||||||||
\(569\) | −5.47723 | −0.229617 | −0.114809 | − | 0.993388i | \(-0.536625\pi\) | ||||
−0.114809 | + | 0.993388i | \(0.536625\pi\) | |||||||
\(570\) | −18.9737 | −0.794719 | ||||||||
\(571\) | 22.1359i | 0.926360i | 0.886264 | + | 0.463180i | \(0.153292\pi\) | ||||
−0.886264 | + | 0.463180i | \(0.846708\pi\) | |||||||
\(572\) | −2.31495 | + | 11.7321i | −0.0967928 | + | 0.490542i | ||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 6.92820 | 0.289178 | ||||||||
\(575\) | 34.6410i | 1.44463i | ||||||||
\(576\) | 21.0000 | 0.875000 | ||||||||
\(577\) | 21.9089i | 0.912080i | 0.889959 | + | 0.456040i | \(0.150733\pi\) | ||||
−0.889959 | + | 0.456040i | \(0.849267\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | − | 36.0000i | − | 1.49611i | ||||||
\(580\) | −17.3205 | −0.719195 | ||||||||
\(581\) | − | 6.92820i | − | 0.287430i | ||||||
\(582\) | − | 18.9737i | − | 0.786484i | ||||||
\(583\) | 6.92820 | + | 21.9089i | 0.286937 | + | 0.907374i | ||||
\(584\) | 20.7846i | 0.860073i | ||||||||
\(585\) | −16.4317 | + | 30.0000i | −0.679366 | + | 1.24035i | ||||
\(586\) | −2.00000 | −0.0826192 | ||||||||
\(587\) | −6.32456 | −0.261042 | −0.130521 | − | 0.991446i | \(-0.541665\pi\) | ||||
−0.130521 | + | 0.991446i | \(0.541665\pi\) | |||||||
\(588\) | 8.66025i | 0.357143i | ||||||||
\(589\) | 18.9737i | 0.781796i | ||||||||
\(590\) | − | 20.0000i | − | 0.823387i | ||||||
\(591\) | 24.2487 | 0.997459 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.00000i | − | 0.0821302i | −0.999156 | − | 0.0410651i | \(-0.986925\pi\) | ||
0.999156 | − | 0.0410651i | \(-0.0130751\pi\) | |||||||
\(594\) | 16.4317 | − | 5.19615i | 0.674200 | − | 0.213201i | ||||
\(595\) | −60.0000 | −2.45976 | ||||||||
\(596\) | − | 22.0000i | − | 0.901155i | ||||||
\(597\) | 41.5692i | 1.70131i | ||||||||
\(598\) | 12.0000 | − | 21.9089i | 0.490716 | − | 0.895922i | ||||
\(599\) | 17.3205i | 0.707697i | 0.935303 | + | 0.353848i | \(0.115127\pi\) | ||||
−0.935303 | + | 0.353848i | \(0.884873\pi\) | |||||||
\(600\) | 25.9808 | 1.06066 | ||||||||
\(601\) | − | 12.6491i | − | 0.515968i | −0.966149 | − | 0.257984i | \(-0.916942\pi\) | ||
0.966149 | − | 0.257984i | \(-0.0830582\pi\) | |||||||
\(602\) | 32.8634 | 1.33941 | ||||||||
\(603\) | − | 16.4317i | − | 0.669150i | ||||||
\(604\) | 10.3923 | 0.422857 | ||||||||
\(605\) | 28.4605 | − | 20.0000i | 1.15708 | − | 0.813116i | ||||
\(606\) | 9.48683 | 0.385376 | ||||||||
\(607\) | − | 28.4605i | − | 1.15518i | −0.816328 | − | 0.577588i | \(-0.803994\pi\) | ||
0.816328 | − | 0.577588i | \(-0.196006\pi\) | |||||||
\(608\) | 17.3205i | 0.702439i | ||||||||
\(609\) | − | 32.8634i | − | 1.33169i | ||||||
\(610\) | 40.0000 | 1.61955 | ||||||||
\(611\) | 10.9545 | − | 20.0000i | 0.443170 | − | 0.809113i | ||||
\(612\) | 16.4317 | 0.664211 | ||||||||
\(613\) | −13.8564 | −0.559655 | −0.279827 | − | 0.960050i | \(-0.590277\pi\) | ||||
−0.279827 | + | 0.960050i | \(0.590277\pi\) | |||||||
\(614\) | 3.46410i | 0.139800i | ||||||||
\(615\) | −10.9545 | −0.441726 | ||||||||
\(616\) | 10.3923 | + | 32.8634i | 0.418718 | + | 1.32410i | ||||
\(617\) | 34.7851 | 1.40039 | 0.700197 | − | 0.713950i | \(-0.253096\pi\) | ||||
0.700197 | + | 0.713950i | \(0.253096\pi\) | |||||||
\(618\) | −13.8564 | −0.557386 | ||||||||
\(619\) | − | 5.47723i | − | 0.220148i | −0.993923 | − | 0.110074i | \(-0.964891\pi\) | ||
0.993923 | − | 0.110074i | \(-0.0351088\pi\) | |||||||
\(620\) | − | 17.3205i | − | 0.695608i | ||||||
\(621\) | 36.0000 | 1.44463 | ||||||||
\(622\) | −6.92820 | −0.277796 | ||||||||
\(623\) | 10.9545 | 0.438881 | ||||||||
\(624\) | −5.47723 | − | 3.00000i | −0.219265 | − | 0.120096i | ||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 12.0000i | 0.479616i | ||||||||
\(627\) | 6.00000 | + | 18.9737i | 0.239617 | + | 0.757735i | ||||
\(628\) | −16.0000 | −0.638470 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 32.8634i | 1.30931i | ||||||||
\(631\) | 49.2950i | 1.96240i | 0.192983 | + | 0.981202i | \(0.438184\pi\) | ||||
−0.192983 | + | 0.981202i | \(0.561816\pi\) | |||||||
\(632\) | 9.48683 | 0.377366 | ||||||||
\(633\) | 5.47723 | 0.217700 | ||||||||
\(634\) | 3.16228i | 0.125590i | ||||||||
\(635\) | − | 10.0000i | − | 0.396838i | ||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 8.66025 | − | 15.8114i | 0.343132 | − | 0.626470i | ||||
\(638\) | −5.47723 | − | 17.3205i | −0.216845 | − | 0.685725i | ||||
\(639\) | 18.9737 | 0.750587 | ||||||||
\(640\) | − | 9.48683i | − | 0.375000i | ||||||
\(641\) | − | 41.5692i | − | 1.64189i | −0.571011 | − | 0.820943i | \(-0.693448\pi\) | ||
0.571011 | − | 0.820943i | \(-0.306552\pi\) | |||||||
\(642\) | 18.9737 | 0.748831 | ||||||||
\(643\) | − | 38.3406i | − | 1.51200i | −0.654569 | − | 0.756002i | \(-0.727150\pi\) | ||
0.654569 | − | 0.756002i | \(-0.272850\pi\) | |||||||
\(644\) | 24.0000i | 0.945732i | ||||||||
\(645\) | −51.9615 | −2.04598 | ||||||||
\(646\) | − | 18.9737i | − | 0.746509i | ||||||
\(647\) | 31.1769i | 1.22569i | 0.790203 | + | 0.612845i | \(0.209975\pi\) | ||||
−0.790203 | + | 0.612845i | \(0.790025\pi\) | |||||||
\(648\) | − | 27.0000i | − | 1.06066i | ||||||
\(649\) | −20.0000 | + | 6.32456i | −0.785069 | + | 0.248261i | ||||
\(650\) | −15.8114 | − | 8.66025i | −0.620174 | − | 0.339683i | ||||
\(651\) | 32.8634 | 1.28802 | ||||||||
\(652\) | − | 5.47723i | − | 0.214505i | ||||||
\(653\) | − | 6.92820i | − | 0.271122i | −0.990769 | − | 0.135561i | \(-0.956716\pi\) | ||
0.990769 | − | 0.135561i | \(-0.0432836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.6410 | 1.35354 | ||||||||
\(656\) | − | 2.00000i | − | 0.0780869i | ||||||
\(657\) | 20.7846 | 0.810885 | ||||||||
\(658\) | − | 21.9089i | − | 0.854098i | ||||||
\(659\) | −43.8178 | −1.70690 | −0.853450 | − | 0.521175i | \(-0.825494\pi\) | ||||
−0.853450 | + | 0.521175i | \(0.825494\pi\) | |||||||
\(660\) | −5.47723 | − | 17.3205i | −0.213201 | − | 0.674200i | ||||
\(661\) | − | 32.8634i | − | 1.27824i | −0.769109 | − | 0.639118i | \(-0.779299\pi\) | ||
0.769109 | − | 0.639118i | \(-0.220701\pi\) | |||||||
\(662\) | −5.47723 | −0.212878 | ||||||||
\(663\) | −30.0000 | − | 16.4317i | −1.16510 | − | 0.638153i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | −37.9473 | −1.47153 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 37.9473i | − | 1.46933i | ||||||
\(668\) | 10.0000i | 0.386912i | ||||||||
\(669\) | −28.4605 | −1.10035 | ||||||||
\(670\) | 17.3205 | 0.669150 | ||||||||
\(671\) | −12.6491 | − | 40.0000i | −0.488314 | − | 1.54418i | ||||
\(672\) | 30.0000 | 1.15728 | ||||||||
\(673\) | 18.9737i | 0.731381i | 0.930736 | + | 0.365691i | \(0.119167\pi\) | ||||
−0.930736 | + | 0.365691i | \(0.880833\pi\) | |||||||
\(674\) | 25.2982 | 0.974451 | ||||||||
\(675\) | − | 25.9808i | − | 1.00000i | ||||||
\(676\) | −7.00000 | − | 10.9545i | −0.269231 | − | 0.421325i | ||||
\(677\) | 38.3406 | 1.47355 | 0.736774 | − | 0.676139i | \(-0.236348\pi\) | ||||
0.736774 | + | 0.676139i | \(0.236348\pi\) | |||||||
\(678\) | 12.0000i | 0.460857i | ||||||||
\(679\) | − | 37.9473i | − | 1.45628i | ||||||
\(680\) | 51.9615i | 1.99263i | ||||||||
\(681\) | −6.92820 | −0.265489 | ||||||||
\(682\) | 17.3205 | − | 5.47723i | 0.663237 | − | 0.209734i | ||||
\(683\) | 12.6491 | 0.484005 | 0.242002 | − | 0.970276i | \(-0.422196\pi\) | ||||
0.242002 | + | 0.970276i | \(0.422196\pi\) | |||||||
\(684\) | 10.3923 | 0.397360 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | 6.92820i | 0.264520i | ||||||||
\(687\) | −37.9473 | −1.44778 | ||||||||
\(688\) | − | 9.48683i | − | 0.361682i | ||||||
\(689\) | −21.9089 | − | 12.0000i | −0.834663 | − | 0.457164i | ||||
\(690\) | 37.9473i | 1.44463i | ||||||||
\(691\) | 16.4317i | 0.625090i | 0.949903 | + | 0.312545i | \(0.101182\pi\) | ||||
−0.949903 | + | 0.312545i | \(0.898818\pi\) | |||||||
\(692\) | −16.4317 | −0.624639 | ||||||||
\(693\) | 32.8634 | − | 10.3923i | 1.24838 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 30.0000i | − | 1.13796i | ||||||
\(696\) | −28.4605 | −1.07879 | ||||||||
\(697\) | − | 10.9545i | − | 0.414929i | ||||||
\(698\) | 17.3205i | 0.655591i | ||||||||
\(699\) | 47.4342i | 1.79412i | ||||||||
\(700\) | 17.3205 | 0.654654 | ||||||||
\(701\) | −16.4317 | −0.620616 | −0.310308 | − | 0.950636i | \(-0.600432\pi\) | ||||
−0.310308 | + | 0.950636i | \(0.600432\pi\) | |||||||
\(702\) | −9.00000 | + | 16.4317i | −0.339683 | + | 0.620174i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 22.1359 | − | 7.00000i | 0.834280 | − | 0.263822i | ||||
\(705\) | 34.6410i | 1.30466i | ||||||||
\(706\) | 15.8114i | 0.595069i | ||||||||
\(707\) | 18.9737 | 0.713578 | ||||||||
\(708\) | 10.9545i | 0.411693i | ||||||||
\(709\) | 21.9089i | 0.822806i | 0.911454 | + | 0.411403i | \(0.134961\pi\) | ||||
−0.911454 | + | 0.411403i | \(0.865039\pi\) | |||||||
\(710\) | 20.0000i | 0.750587i | ||||||||
\(711\) | − | 9.48683i | − | 0.355784i | ||||||
\(712\) | − | 9.48683i | − | 0.355534i | ||||||
\(713\) | 37.9473 | 1.42114 | ||||||||
\(714\) | −32.8634 | −1.22988 | ||||||||
\(715\) | −7.32051 | + | 37.1000i | −0.273771 | + | 1.38746i | ||||
\(716\) | − | 13.8564i | − | 0.517838i | ||||||
\(717\) | 13.8564 | 0.517477 | ||||||||
\(718\) | 32.0000 | 1.19423 | ||||||||
\(719\) | 38.1051i | 1.42108i | 0.703656 | + | 0.710541i | \(0.251550\pi\) | ||||
−0.703656 | + | 0.710541i | \(0.748450\pi\) | |||||||
\(720\) | 9.48683 | 0.353553 | ||||||||
\(721\) | −27.7128 | −1.03208 | ||||||||
\(722\) | 7.00000i | 0.260513i | ||||||||
\(723\) | 42.0000i | 1.56200i | ||||||||
\(724\) | 8.00000 | 0.297318 | ||||||||
\(725\) | −27.3861 | −1.01710 | ||||||||
\(726\) | 15.5885 | − | 10.9545i | 0.578542 | − | 0.406558i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | −32.8634 | − | 18.0000i | −1.21800 | − | 0.667124i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 21.9089i | 0.810885i | ||||||||
\(731\) | − | 51.9615i | − | 1.92187i | ||||||
\(732\) | −21.9089 | −0.809776 | ||||||||
\(733\) | −13.8564 | −0.511798 | −0.255899 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255899 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(734\) | 16.0000i | 0.590571i | ||||||||
\(735\) | 27.3861i | 1.01015i | ||||||||
\(736\) | 34.6410 | 1.27688 | ||||||||
\(737\) | −5.47723 | − | 17.3205i | −0.201756 | − | 0.638009i | ||||
\(738\) | −6.00000 | −0.220863 | ||||||||
\(739\) | −38.1051 | −1.40172 | −0.700860 | − | 0.713299i | \(-0.747200\pi\) | ||||
−0.700860 | + | 0.713299i | \(0.747200\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.9737 | − | 10.3923i | −0.697015 | − | 0.381771i | ||||
\(742\) | −24.0000 | −0.881068 | ||||||||
\(743\) | − | 10.0000i | − | 0.366864i | −0.983032 | − | 0.183432i | \(-0.941279\pi\) | ||
0.983032 | − | 0.183432i | \(-0.0587208\pi\) | |||||||
\(744\) | − | 28.4605i | − | 1.04341i | ||||||
\(745\) | − | 69.5701i | − | 2.54885i | ||||||
\(746\) | 31.6228 | 1.15779 | ||||||||
\(747\) | 6.00000i | 0.219529i | ||||||||
\(748\) | 17.3205 | − | 5.47723i | 0.633300 | − | 0.200267i | ||||
\(749\) | 37.9473 | 1.38657 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.0000 | 1.60558 | 0.802791 | − | 0.596260i | \(-0.203347\pi\) | ||||
0.802791 | + | 0.596260i | \(0.203347\pi\) | |||||||
\(752\) | −6.32456 | −0.230633 | ||||||||
\(753\) | −42.0000 | −1.53057 | ||||||||
\(754\) | 17.3205 | + | 9.48683i | 0.630776 | + | 0.345490i | ||||
\(755\) | 32.8634 | 1.19602 | ||||||||
\(756\) | − | 18.0000i | − | 0.654654i | ||||||
\(757\) | −24.0000 | −0.872295 | −0.436147 | − | 0.899875i | \(-0.643657\pi\) | ||||
−0.436147 | + | 0.899875i | \(0.643657\pi\) | |||||||
\(758\) | −27.3861 | −0.994709 | ||||||||
\(759\) | 37.9473 | − | 12.0000i | 1.37740 | − | 0.435572i | ||||
\(760\) | 32.8634i | 1.19208i | ||||||||
\(761\) | 14.0000i | 0.507500i | 0.967270 | + | 0.253750i | \(0.0816640\pi\) | ||||
−0.967270 | + | 0.253750i | \(0.918336\pi\) | |||||||
\(762\) | − | 5.47723i | − | 0.198419i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 10.3923i | − | 0.375980i | ||||||
\(765\) | 51.9615 | 1.87867 | ||||||||
\(766\) | − | 25.2982i | − | 0.914062i | ||||||
\(767\) | 10.9545 | − | 20.0000i | 0.395542 | − | 0.722158i | ||||
\(768\) | − | 29.4449i | − | 1.06250i | ||||||
\(769\) | −38.1051 | −1.37411 | −0.687053 | − | 0.726607i | \(-0.741096\pi\) | ||||
−0.687053 | + | 0.726607i | \(0.741096\pi\) | |||||||
\(770\) | 10.9545 | + | 34.6410i | 0.394771 | + | 1.24838i | ||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | −20.7846 | −0.748054 | ||||||||
\(773\) | −41.1096 | −1.47861 | −0.739305 | − | 0.673371i | \(-0.764846\pi\) | ||||
−0.739305 | + | 0.673371i | \(0.764846\pi\) | |||||||
\(774\) | −28.4605 | −1.02299 | ||||||||
\(775\) | − | 27.3861i | − | 0.983739i | ||||||
\(776\) | −32.8634 | −1.17973 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.7846 | 0.745164 | ||||||||
\(779\) | − | 6.92820i | − | 0.248229i | ||||||
\(780\) | 17.3205 | + | 9.48683i | 0.620174 | + | 0.339683i | ||||
\(781\) | 20.0000 | − | 6.32456i | 0.715656 | − | 0.226310i | ||||
\(782\) | −37.9473 | −1.35699 | ||||||||
\(783\) | 28.4605i | 1.01710i | ||||||||
\(784\) | −5.00000 | −0.178571 | ||||||||
\(785\) | −50.5964 | −1.80586 | ||||||||
\(786\) | 18.9737 | 0.676768 | ||||||||
\(787\) | 10.3923 | 0.370446 | 0.185223 | − | 0.982697i | \(-0.440699\pi\) | ||||
0.185223 | + | 0.982697i | \(0.440699\pi\) | |||||||
\(788\) | − | 14.0000i | − | 0.498729i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.0000 | 0.355784 | ||||||||
\(791\) | 24.0000i | 0.853342i | ||||||||
\(792\) | −9.00000 | − | 28.4605i | −0.319801 | − | 1.01130i | ||||
\(793\) | 40.0000 | + | 21.9089i | 1.42044 | + | 0.778008i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.9473 | 1.34585 | ||||||||
\(796\) | 24.0000 | 0.850657 | ||||||||
\(797\) | − | 6.92820i | − | 0.245410i | −0.992443 | − | 0.122705i | \(-0.960843\pi\) | ||
0.992443 | − | 0.122705i | \(-0.0391568\pi\) | |||||||
\(798\) | −20.7846 | −0.735767 | ||||||||
\(799\) | −34.6410 | −1.22551 | ||||||||
\(800\) | − | 25.0000i | − | 0.883883i | ||||||
\(801\) | −9.48683 | −0.335201 | ||||||||
\(802\) | − | 22.1359i | − | 0.781647i | ||||||
\(803\) | 21.9089 | − | 6.92820i | 0.773148 | − | 0.244491i | ||||
\(804\) | −9.48683 | −0.334575 | ||||||||
\(805\) | 75.8947i | 2.67494i | ||||||||
\(806\) | −9.48683 | + | 17.3205i | −0.334159 | + | 0.610089i | ||||
\(807\) | 24.0000 | 0.844840 | ||||||||
\(808\) | − | 16.4317i | − | 0.578064i | ||||||
\(809\) | 38.3406 | 1.34798 | 0.673991 | − | 0.738739i | \(-0.264578\pi\) | ||||
0.673991 | + | 0.738739i | \(0.264578\pi\) | |||||||
\(810\) | − | 28.4605i | − | 1.00000i | ||||||
\(811\) | −10.3923 | −0.364923 | −0.182462 | − | 0.983213i | \(-0.558407\pi\) | ||||
−0.182462 | + | 0.983213i | \(0.558407\pi\) | |||||||
\(812\) | −18.9737 | −0.665845 | ||||||||
\(813\) | 42.0000i | 1.47300i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 17.3205i | − | 0.606711i | ||||||
\(816\) | 9.48683i | 0.332106i | ||||||||
\(817\) | − | 32.8634i | − | 1.14974i | ||||||
\(818\) | − | 20.7846i | − | 0.726717i | ||||||
\(819\) | −18.0000 | + | 32.8634i | −0.628971 | + | 1.14834i | ||||
\(820\) | 6.32456i | 0.220863i | ||||||||
\(821\) | − | 26.0000i | − | 0.907406i | −0.891153 | − | 0.453703i | \(-0.850103\pi\) | ||
0.891153 | − | 0.453703i | \(-0.149897\pi\) | |||||||
\(822\) | 5.47723 | 0.191040 | ||||||||
\(823\) | −20.0000 | −0.697156 | −0.348578 | − | 0.937280i | \(-0.613335\pi\) | ||||
−0.348578 | + | 0.937280i | \(0.613335\pi\) | |||||||
\(824\) | 24.0000i | 0.836080i | ||||||||
\(825\) | −8.66025 | − | 27.3861i | −0.301511 | − | 0.953463i | ||||
\(826\) | − | 21.9089i | − | 0.762308i | ||||||
\(827\) | 20.0000i | 0.695468i | 0.937593 | + | 0.347734i | \(0.113049\pi\) | ||||
−0.937593 | + | 0.347734i | \(0.886951\pi\) | |||||||
\(828\) | − | 20.7846i | − | 0.722315i | ||||||
\(829\) | −42.0000 | −1.45872 | −0.729360 | − | 0.684130i | \(-0.760182\pi\) | ||||
−0.729360 | + | 0.684130i | \(0.760182\pi\) | |||||||
\(830\) | −6.32456 | −0.219529 | ||||||||
\(831\) | 32.8634 | 1.14002 | ||||||||
\(832\) | −12.1244 | + | 22.1359i | −0.420336 | + | 0.767426i | ||||
\(833\) | −27.3861 | −0.948873 | ||||||||
\(834\) | − | 16.4317i | − | 0.568982i | ||||||
\(835\) | 31.6228i | 1.09435i | ||||||||
\(836\) | 10.9545 | − | 3.46410i | 0.378868 | − | 0.119808i | ||||
\(837\) | −28.4605 | −0.983739 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.2982 | 0.873392 | 0.436696 | − | 0.899609i | \(-0.356149\pi\) | ||||
0.436696 | + | 0.899609i | \(0.356149\pi\) | |||||||
\(840\) | 56.9210 | 1.96396 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −32.8634 | −1.13255 | ||||||||
\(843\) | −24.2487 | −0.835170 | ||||||||
\(844\) | − | 3.16228i | − | 0.108850i | ||||||
\(845\) | −22.1359 | − | 34.6410i | −0.761500 | − | 1.19169i | ||||
\(846\) | 18.9737i | 0.652328i | ||||||||
\(847\) | 31.1769 | − | 21.9089i | 1.07125 | − | 0.752799i | ||||
\(848\) | 6.92820i | 0.237915i | ||||||||
\(849\) | −5.47723 | −0.187978 | ||||||||
\(850\) | 27.3861i | 0.939336i | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − | 10.9545i | − | 0.375293i | ||||||
\(853\) | −24.2487 | −0.830260 | −0.415130 | − | 0.909762i | \(-0.636264\pi\) | ||||
−0.415130 | + | 0.909762i | \(0.636264\pi\) | |||||||
\(854\) | 43.8178 | 1.49941 | ||||||||
\(855\) | 32.8634 | 1.12390 | ||||||||
\(856\) | − | 32.8634i | − | 1.12325i | ||||||
\(857\) | 27.3861 | 0.935492 | 0.467746 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467746 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(858\) | −4.00961 | + | 20.3205i | −0.136886 | + | 0.693731i | ||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | 30.0000i | 1.02299i | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | −14.0000 | −0.476842 | ||||||||
\(863\) | −50.5964 | −1.72232 | −0.861161 | − | 0.508332i | \(-0.830262\pi\) | ||||
−0.861161 | + | 0.508332i | \(0.830262\pi\) | |||||||
\(864\) | −25.9808 | −0.883883 | ||||||||
\(865\) | −51.9615 | −1.76674 | ||||||||
\(866\) | − | 18.0000i | − | 0.611665i | ||||||
\(867\) | 22.5167i | 0.764706i | ||||||||
\(868\) | − | 18.9737i | − | 0.644008i | ||||||
\(869\) | −3.16228 | − | 10.0000i | −0.107273 | − | 0.339227i | ||||
\(870\) | −30.0000 | −1.01710 | ||||||||
\(871\) | 17.3205 | + | 9.48683i | 0.586883 | + | 0.321449i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.8634i | 1.11226i | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 12.0000i | − | 0.405442i | ||||||
\(877\) | 24.2487 | 0.818821 | 0.409410 | − | 0.912350i | \(-0.365734\pi\) | ||||
0.409410 | + | 0.912350i | \(0.365734\pi\) | |||||||
\(878\) | 28.4605 | 0.960495 | ||||||||
\(879\) | 3.46410 | 0.116841 | ||||||||
\(880\) | 10.0000 | − | 3.16228i | 0.337100 | − | 0.106600i | ||||
\(881\) | − | 34.6410i | − | 1.16709i | −0.812082 | − | 0.583543i | \(-0.801666\pi\) | ||
0.812082 | − | 0.583543i | \(-0.198334\pi\) | |||||||
\(882\) | 15.0000i | 0.505076i | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | −9.48683 | + | 17.3205i | −0.319077 | + | 0.582552i | ||||
\(885\) | 34.6410i | 1.16445i | ||||||||
\(886\) | −10.3923 | −0.349136 | ||||||||
\(887\) | 10.9545 | 0.367814 | 0.183907 | − | 0.982944i | \(-0.441125\pi\) | ||||
0.183907 | + | 0.982944i | \(0.441125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.9545i | − | 0.367400i | ||||||
\(890\) | − | 10.0000i | − | 0.335201i | ||||||
\(891\) | −28.4605 | + | 9.00000i | −0.953463 | + | 0.301511i | ||||
\(892\) | 16.4317i | 0.550173i | ||||||||
\(893\) | −21.9089 | −0.733153 | ||||||||
\(894\) | − | 38.1051i | − | 1.27443i | ||||||
\(895\) | − | 43.8178i | − | 1.46467i | ||||||
\(896\) | − | 10.3923i | − | 0.347183i | ||||||
\(897\) | −20.7846 | + | 37.9473i | −0.693978 | + | 1.26702i | ||||
\(898\) | 15.8114i | 0.527633i | ||||||||
\(899\) | 30.0000i | 1.00056i | ||||||||
\(900\) | −15.0000 | −0.500000 | ||||||||
\(901\) | 37.9473i | 1.26421i | ||||||||
\(902\) | −6.32456 | + | 2.00000i | −0.210585 | + | 0.0665927i | ||||
\(903\) | −56.9210 | −1.89421 | ||||||||
\(904\) | 20.7846 | 0.691286 | ||||||||
\(905\) | 25.2982 | 0.840941 | ||||||||
\(906\) | 18.0000 | 0.598010 | ||||||||
\(907\) | 36.0000 | 1.19536 | 0.597680 | − | 0.801735i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801735i | \(0.296089\pi\) | |||||||
\(908\) | 4.00000i | 0.132745i | ||||||||
\(909\) | −16.4317 | −0.545004 | ||||||||
\(910\) | −34.6410 | − | 18.9737i | −1.14834 | − | 0.628971i | ||||
\(911\) | 17.3205i | 0.573854i | 0.957952 | + | 0.286927i | \(0.0926337\pi\) | ||||
−0.957952 | + | 0.286927i | \(0.907366\pi\) | |||||||
\(912\) | 6.00000i | 0.198680i | ||||||||
\(913\) | 2.00000 | + | 6.32456i | 0.0661903 | + | 0.209312i | ||||
\(914\) | − | 3.46410i | − | 0.114582i | ||||||
\(915\) | −69.2820 | −2.29039 | ||||||||
\(916\) | 21.9089i | 0.723891i | ||||||||
\(917\) | 37.9473 | 1.25313 | ||||||||
\(918\) | 28.4605 | 0.939336 | ||||||||
\(919\) | − | 3.16228i | − | 0.104314i | −0.998639 | − | 0.0521570i | \(-0.983390\pi\) | ||
0.998639 | − | 0.0521570i | \(-0.0166096\pi\) | |||||||
\(920\) | 65.7267 | 2.16695 | ||||||||
\(921\) | − | 6.00000i | − | 0.197707i | ||||||
\(922\) | −14.0000 | −0.461065 | ||||||||
\(923\) | −10.9545 | + | 20.0000i | −0.360570 | + | 0.658308i | ||||
\(924\) | −6.00000 | − | 18.9737i | −0.197386 | − | 0.624188i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.4317 | −0.539978 | ||||||||
\(927\) | 24.0000 | 0.788263 | ||||||||
\(928\) | 27.3861i | 0.898994i | ||||||||
\(929\) | 15.8114 | 0.518755 | 0.259377 | − | 0.965776i | \(-0.416483\pi\) | ||||
0.259377 | + | 0.965776i | \(0.416483\pi\) | |||||||
\(930\) | − | 30.0000i | − | 0.983739i | ||||||
\(931\) | −17.3205 | −0.567657 | ||||||||
\(932\) | 27.3861 | 0.897062 | ||||||||
\(933\) | 12.0000 | 0.392862 | ||||||||
\(934\) | 20.7846 | 0.680093 | ||||||||
\(935\) | 54.7723 | − | 17.3205i | 1.79124 | − | 0.566441i | ||||
\(936\) | 28.4605 | + | 15.5885i | 0.930261 | + | 0.509525i | ||||
\(937\) | − | 6.32456i | − | 0.206614i | −0.994650 | − | 0.103307i | \(-0.967058\pi\) | ||
0.994650 | − | 0.103307i | \(-0.0329424\pi\) | |||||||
\(938\) | 18.9737 | 0.619512 | ||||||||
\(939\) | − | 20.7846i | − | 0.678280i | ||||||
\(940\) | 20.0000 | 0.652328 | ||||||||
\(941\) | − | 38.0000i | − | 1.23876i | −0.785090 | − | 0.619382i | \(-0.787383\pi\) | ||
0.785090 | − | 0.619382i | \(-0.212617\pi\) | |||||||
\(942\) | −27.7128 | −0.902932 | ||||||||
\(943\) | −13.8564 | −0.451227 | ||||||||
\(944\) | −6.32456 | −0.205847 | ||||||||
\(945\) | − | 56.9210i | − | 1.85164i | ||||||
\(946\) | −30.0000 | + | 9.48683i | −0.975384 | + | 0.308444i | ||||
\(947\) | −12.6491 | −0.411041 | −0.205520 | − | 0.978653i | \(-0.565889\pi\) | ||||
−0.205520 | + | 0.978653i | \(0.565889\pi\) | |||||||
\(948\) | −5.47723 | −0.177892 | ||||||||
\(949\) | −12.0000 | + | 21.9089i | −0.389536 | + | 0.711193i | ||||
\(950\) | 17.3205i | 0.561951i | ||||||||
\(951\) | − | 5.47723i | − | 0.177611i | ||||||
\(952\) | 56.9210i | 1.84482i | ||||||||
\(953\) | 5.47723 | 0.177425 | 0.0887124 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887124 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(954\) | 20.7846 | 0.672927 | ||||||||
\(955\) | − | 32.8634i | − | 1.06343i | ||||||
\(956\) | − | 8.00000i | − | 0.258738i | ||||||
\(957\) | 9.48683 | + | 30.0000i | 0.306666 | + | 0.969762i | ||||
\(958\) | −8.00000 | −0.258468 | ||||||||
\(959\) | 10.9545 | 0.353738 | ||||||||
\(960\) | − | 38.3406i | − | 1.23744i | ||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.8634 | −1.05901 | ||||||||
\(964\) | 24.2487 | 0.780998 | ||||||||
\(965\) | −65.7267 | −2.11582 | ||||||||
\(966\) | 41.5692i | 1.33747i | ||||||||
\(967\) | −31.1769 | −1.00258 | −0.501291 | − | 0.865279i | \(-0.667141\pi\) | ||||
−0.501291 | + | 0.865279i | \(0.667141\pi\) | |||||||
\(968\) | −18.9737 | − | 27.0000i | −0.609837 | − | 0.867813i | ||||
\(969\) | 32.8634i | 1.05572i | ||||||||
\(970\) | −34.6410 | −1.11226 | ||||||||
\(971\) | 34.6410i | 1.11168i | 0.831288 | + | 0.555842i | \(0.187604\pi\) | ||||
−0.831288 | + | 0.555842i | \(0.812396\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | − | 32.8634i | − | 1.05355i | ||||||
\(974\) | 27.3861 | 0.877508 | ||||||||
\(975\) | 27.3861 | + | 15.0000i | 0.877058 | + | 0.480384i | ||||
\(976\) | − | 12.6491i | − | 0.404888i | ||||||
\(977\) | −22.1359 | −0.708192 | −0.354096 | − | 0.935209i | \(-0.615211\pi\) | ||||
−0.354096 | + | 0.935209i | \(0.615211\pi\) | |||||||
\(978\) | − | 9.48683i | − | 0.303355i | ||||||
\(979\) | −10.0000 | + | 3.16228i | −0.319601 | + | 0.101067i | ||||
\(980\) | 15.8114 | 0.505076 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.9089i | 0.699141i | ||||||||
\(983\) | −25.2982 | −0.806888 | −0.403444 | − | 0.915004i | \(-0.632187\pi\) | ||||
−0.403444 | + | 0.915004i | \(0.632187\pi\) | |||||||
\(984\) | 10.3923i | 0.331295i | ||||||||
\(985\) | − | 44.2719i | − | 1.41062i | ||||||
\(986\) | − | 30.0000i | − | 0.955395i | ||||||
\(987\) | 37.9473i | 1.20788i | ||||||||
\(988\) | −6.00000 | + | 10.9545i | −0.190885 | + | 0.348508i | ||||
\(989\) | −65.7267 | −2.08999 | ||||||||
\(990\) | −9.48683 | − | 30.0000i | −0.301511 | − | 0.953463i | ||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | −27.3861 | −0.869510 | ||||||||
\(993\) | 9.48683 | 0.301056 | ||||||||
\(994\) | 21.9089i | 0.694908i | ||||||||
\(995\) | 75.8947 | 2.40602 | ||||||||
\(996\) | 3.46410 | 0.109764 | ||||||||
\(997\) | 56.9210i | 1.80271i | 0.433085 | + | 0.901353i | \(0.357425\pi\) | ||||
−0.433085 | + | 0.901353i | \(0.642575\pi\) | |||||||
\(998\) | −38.3406 | −1.21365 | ||||||||
\(999\) | 0 | 0 |
(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 | 429.2.e.b.428.4 | yes | 8 | |
3.2 | odd | 2 | inner | 429.2.e.b.428.5 | yes | 8 | |
11.10 | odd | 2 | inner | 429.2.e.b.428.8 | yes | 8 | |
13.12 | even | 2 | inner | 429.2.e.b.428.7 | yes | 8 | |
33.32 | even | 2 | inner | 429.2.e.b.428.1 | ✓ | 8 | |
39.38 | odd | 2 | inner | 429.2.e.b.428.2 | yes | 8 | |
143.142 | odd | 2 | inner | 429.2.e.b.428.3 | yes | 8 | |
429.428 | even | 2 | inner | 429.2.e.b.428.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.e.b.428.1 | ✓ | 8 | 33.32 | even | 2 | inner | |
429.2.e.b.428.2 | yes | 8 | 39.38 | odd | 2 | inner | |
429.2.e.b.428.3 | yes | 8 | 143.142 | odd | 2 | inner | |
429.2.e.b.428.4 | yes | 8 | 1.1 | even | 1 | trivial | |
429.2.e.b.428.5 | yes | 8 | 3.2 | odd | 2 | inner | |
429.2.e.b.428.6 | yes | 8 | 429.428 | even | 2 | inner | |
429.2.e.b.428.7 | yes | 8 | 13.12 | even | 2 | inner | |
429.2.e.b.428.8 | yes | 8 | 11.10 | odd | 2 | inner |