Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,2,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("108.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.862384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.2.b.b.107.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 2.82843i | 1.26491i | 0.774597 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205i | 0.654654i | 0.944911 | + | 0.327327i | \(0.106148\pi\) | ||||
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 1.22474 | − | 2.12132i | 0.327327 | − | 0.566947i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 1.19208i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | −4.89898 | + | 2.82843i | −1.09545 | + | 0.632456i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | − | 3.46410i | −1.27920 | − | 0.738549i | ||||
\(23\) | −4.89898 | −1.02151 | −0.510754 | − | 0.859727i | \(-0.670634\pi\) | ||||
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 1.22474 | + | 0.707107i | 0.240192 | + | 0.138675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.00000 | + | 1.73205i | −0.566947 | + | 0.327327i | ||||
\(29\) | − | 5.65685i | − | 1.05045i | −0.850963 | − | 0.525226i | \(-0.823981\pi\) | ||
0.850963 | − | 0.525226i | \(-0.176019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | − | 3.46410i | 0.342997 | − | 0.594089i | ||||
\(35\) | −4.89898 | −0.828079 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | −3.67423 | + | 6.36396i | −0.596040 | + | 1.03237i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.00000 | 1.26491 | ||||||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.46410i | − | 0.528271i | −0.964486 | − | 0.264135i | \(-0.914913\pi\) | ||
0.964486 | − | 0.264135i | \(-0.0850865\pi\) | |||||||
\(44\) | 4.89898 | + | 8.48528i | 0.738549 | + | 1.27920i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 3.46410i | 0.884652 | + | 0.510754i | ||||
\(47\) | 4.89898 | 0.714590 | 0.357295 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357295 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 3.67423 | + | 2.12132i | 0.519615 | + | 0.300000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8564i | 1.86840i | ||||||||
\(56\) | 4.89898 | 0.654654 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | + | 6.92820i | −0.525226 | + | 0.909718i | ||||
\(59\) | −4.89898 | −0.637793 | −0.318896 | − | 0.947790i | \(-0.603312\pi\) | ||||
−0.318896 | + | 0.947790i | \(0.603312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0000 | 1.40841 | 0.704203 | − | 0.709999i | \(-0.251305\pi\) | ||||
0.704203 | + | 0.709999i | \(0.251305\pi\) | |||||||
\(62\) | 2.44949 | − | 4.24264i | 0.311086 | − | 0.538816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | − | 2.82843i | − | 0.350823i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.1244i | − | 1.48123i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) | ||
0.671932 | − | 0.740613i | \(-0.265465\pi\) | |||||||
\(68\) | −4.89898 | + | 2.82843i | −0.594089 | + | 0.342997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.00000 | + | 3.46410i | 0.717137 | + | 0.414039i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | 1.22474 | + | 0.707107i | 0.142374 | + | 0.0821995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.00000 | − | 5.19615i | 1.03237 | − | 0.596040i | ||||
\(77\) | 8.48528i | 0.966988i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73205i | 0.194871i | 0.995242 | + | 0.0974355i | \(0.0310640\pi\) | ||||
−0.995242 | + | 0.0974355i | \(0.968936\pi\) | |||||||
\(80\) | −9.79796 | − | 5.65685i | −1.09545 | − | 0.632456i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.00000 | + | 6.92820i | −0.441726 | + | 0.765092i | ||||
\(83\) | −9.79796 | −1.07547 | −0.537733 | − | 0.843115i | \(-0.680719\pi\) | ||||
−0.537733 | + | 0.843115i | \(0.680719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | −2.44949 | + | 4.24264i | −0.264135 | + | 0.457496i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 13.8564i | − | 1.47710i | ||||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.73205i | − | 0.181568i | ||||||
\(92\) | −4.89898 | − | 8.48528i | −0.510754 | − | 0.884652i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | − | 3.46410i | −0.618853 | − | 0.357295i | ||||
\(95\) | 14.6969 | 1.50787 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.0000 | −1.31995 | −0.659975 | − | 0.751288i | \(-0.729433\pi\) | ||||
−0.659975 | + | 0.751288i | \(0.729433\pi\) | |||||||
\(98\) | −4.89898 | − | 2.82843i | −0.494872 | − | 0.285714i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 5.19615i | −0.300000 | − | 0.519615i | ||||
\(101\) | 11.3137i | 1.12576i | 0.826540 | + | 0.562878i | \(0.190306\pi\) | ||||
−0.826540 | + | 0.562878i | \(0.809694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.66025i | 0.853320i | 0.904412 | + | 0.426660i | \(0.140310\pi\) | ||||
−0.904412 | + | 0.426660i | \(0.859690\pi\) | |||||||
\(104\) | 2.82843i | 0.277350i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | + | 6.92820i | −0.388514 | + | 0.672927i | ||||
\(107\) | 14.6969 | 1.42081 | 0.710403 | − | 0.703795i | \(-0.248513\pi\) | ||||
0.710403 | + | 0.703795i | \(0.248513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 9.79796 | − | 16.9706i | 0.934199 | − | 1.61808i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.00000 | − | 3.46410i | −0.566947 | − | 0.327327i | ||||
\(113\) | 2.82843i | 0.266076i | 0.991111 | + | 0.133038i | \(0.0424732\pi\) | ||||
−0.991111 | + | 0.133038i | \(0.957527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.8564i | − | 1.29212i | ||||||
\(116\) | 9.79796 | − | 5.65685i | 0.909718 | − | 0.525226i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | + | 3.46410i | 0.552345 | + | 0.318896i | ||||
\(119\) | −4.89898 | −0.449089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | −13.4722 | − | 7.77817i | −1.21972 | − | 0.704203i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | + | 3.46410i | −0.538816 | + | 0.311086i | ||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | + | 3.46410i | −0.175412 | + | 0.303822i | ||||
\(131\) | 9.79796 | 0.856052 | 0.428026 | − | 0.903767i | \(-0.359209\pi\) | ||||
0.428026 | + | 0.903767i | \(0.359209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.00000 | 0.780399 | ||||||||
\(134\) | −8.57321 | + | 14.8492i | −0.740613 | + | 1.28278i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.00000 | 0.685994 | ||||||||
\(137\) | 19.7990i | 1.69154i | 0.533546 | + | 0.845771i | \(0.320859\pi\) | ||||
−0.533546 | + | 0.845771i | \(0.679141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.66025i | 0.734553i | 0.930112 | + | 0.367277i | \(0.119710\pi\) | ||||
−0.930112 | + | 0.367277i | \(0.880290\pi\) | |||||||
\(140\) | −4.89898 | − | 8.48528i | −0.414039 | − | 0.717137i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.89898 | −0.409673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | 1.22474 | + | 0.707107i | 0.101361 | + | 0.0585206i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | − | 22.6274i | − | 1.85371i | −0.375419 | − | 0.926855i | \(-0.622501\pi\) | ||
0.375419 | − | 0.926855i | \(-0.377499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5167i | 1.83238i | 0.400744 | + | 0.916190i | \(0.368752\pi\) | ||||
−0.400744 | + | 0.916190i | \(0.631248\pi\) | |||||||
\(152\) | −14.6969 | −1.19208 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | − | 10.3923i | 0.483494 | − | 0.837436i | ||||
\(155\) | −9.79796 | −0.786991 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 1.22474 | − | 2.12132i | 0.0974355 | − | 0.168763i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.00000 | + | 13.8564i | 0.632456 | + | 1.09545i | ||||
\(161\) | − | 8.48528i | − | 0.668734i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.19615i | − | 0.406994i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) | ||
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 9.79796 | − | 5.65685i | 0.765092 | − | 0.441726i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | + | 6.92820i | 0.931381 | + | 0.537733i | ||||
\(167\) | −4.89898 | −0.379094 | −0.189547 | − | 0.981872i | \(-0.560702\pi\) | ||||
−0.189547 | + | 0.981872i | \(0.560702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 9.79796 | + | 5.65685i | 0.751469 | + | 0.433861i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.00000 | − | 3.46410i | 0.457496 | − | 0.264135i | ||||
\(173\) | − | 5.65685i | − | 0.430083i | −0.976605 | − | 0.215041i | \(-0.931011\pi\) | ||
0.976605 | − | 0.215041i | \(-0.0689886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.19615i | − | 0.392792i | ||||||
\(176\) | −9.79796 | + | 16.9706i | −0.738549 | + | 1.27920i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | − | 3.46410i | 0.149906 | − | 0.259645i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | −1.22474 | + | 2.12132i | −0.0907841 | + | 0.157243i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.8564i | 1.02151i | ||||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.8564i | 1.01328i | ||||||||
\(188\) | 4.89898 | + | 8.48528i | 0.357295 | + | 0.618853i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | − | 10.3923i | −1.30586 | − | 0.753937i | ||||
\(191\) | −24.4949 | −1.77239 | −0.886194 | − | 0.463314i | \(-0.846660\pi\) | ||||
−0.886194 | + | 0.463314i | \(0.846660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | 15.9217 | + | 9.19239i | 1.14311 | + | 0.659975i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | + | 6.92820i | 0.285714 | + | 0.494872i | ||||
\(197\) | 2.82843i | 0.201517i | 0.994911 | + | 0.100759i | \(0.0321270\pi\) | ||||
−0.994911 | + | 0.100759i | \(0.967873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.19615i | − | 0.368345i | −0.982894 | − | 0.184173i | \(-0.941039\pi\) | ||
0.982894 | − | 0.184173i | \(-0.0589606\pi\) | |||||||
\(200\) | 8.48528i | 0.600000i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.00000 | − | 13.8564i | 0.562878 | − | 0.974933i | ||||
\(203\) | 9.79796 | 0.687682 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000 | 1.11749 | ||||||||
\(206\) | 6.12372 | − | 10.6066i | 0.426660 | − | 0.738997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | − | 25.4558i | − | 1.76082i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.1244i | − | 0.834675i | −0.908752 | − | 0.417338i | \(-0.862963\pi\) | ||
0.908752 | − | 0.417338i | \(-0.137037\pi\) | |||||||
\(212\) | 9.79796 | − | 5.65685i | 0.672927 | − | 0.388514i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | − | 10.3923i | −1.23045 | − | 0.710403i | ||||
\(215\) | 9.79796 | 0.668215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 12.2474 | + | 7.07107i | 0.829502 | + | 0.478913i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24.0000 | + | 13.8564i | −1.61808 | + | 0.934199i | ||||
\(221\) | − | 2.82843i | − | 0.190261i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.2487i | − | 1.62381i | −0.583787 | − | 0.811907i | \(-0.698430\pi\) | ||
0.583787 | − | 0.811907i | \(-0.301570\pi\) | |||||||
\(224\) | 4.89898 | + | 8.48528i | 0.327327 | + | 0.566947i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | − | 3.46410i | 0.133038 | − | 0.230429i | ||||
\(227\) | 19.5959 | 1.30063 | 0.650313 | − | 0.759666i | \(-0.274638\pi\) | ||||
0.650313 | + | 0.759666i | \(0.274638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −9.79796 | + | 16.9706i | −0.646058 | + | 1.11901i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.0000 | −1.05045 | ||||||||
\(233\) | − | 22.6274i | − | 1.48237i | −0.671300 | − | 0.741186i | \(-0.734264\pi\) | ||
0.671300 | − | 0.741186i | \(-0.265736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8564i | 0.903892i | ||||||||
\(236\) | −4.89898 | − | 8.48528i | −0.318896 | − | 0.552345i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | + | 3.46410i | 0.388922 | + | 0.224544i | ||||
\(239\) | −19.5959 | −1.26755 | −0.633777 | − | 0.773516i | \(-0.718496\pi\) | ||||
−0.633777 | + | 0.773516i | \(0.718496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.0000 | −1.61039 | −0.805196 | − | 0.593009i | \(-0.797940\pi\) | ||||
−0.805196 | + | 0.593009i | \(0.797940\pi\) | |||||||
\(242\) | −15.9217 | − | 9.19239i | −1.02348 | − | 0.590909i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0000 | + | 19.0526i | 0.704203 | + | 1.21972i | ||||
\(245\) | 11.3137i | 0.722806i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.19615i | 0.330623i | ||||||||
\(248\) | 9.79796 | 0.622171 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.00000 | − | 6.92820i | 0.252982 | − | 0.438178i | ||||
\(251\) | −29.3939 | −1.85533 | −0.927663 | − | 0.373420i | \(-0.878185\pi\) | ||||
−0.927663 | + | 0.373420i | \(0.878185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0000 | −1.50887 | ||||||||
\(254\) | −7.34847 | + | 12.7279i | −0.461084 | + | 0.798621i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 28.2843i | 1.76432i | 0.470946 | + | 0.882162i | \(0.343913\pi\) | ||||
−0.470946 | + | 0.882162i | \(0.656087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.73205i | − | 0.107624i | ||||||
\(260\) | 4.89898 | − | 2.82843i | 0.303822 | − | 0.175412i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0000 | − | 6.92820i | −0.741362 | − | 0.428026i | ||||
\(263\) | 19.5959 | 1.20834 | 0.604168 | − | 0.796857i | \(-0.293506\pi\) | ||||
0.604168 | + | 0.796857i | \(0.293506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0000 | 0.982872 | ||||||||
\(266\) | −11.0227 | − | 6.36396i | −0.675845 | − | 0.390199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.0000 | − | 12.1244i | 1.28278 | − | 0.740613i | ||||
\(269\) | 2.82843i | 0.172452i | 0.996276 | + | 0.0862261i | \(0.0274808\pi\) | ||||
−0.996276 | + | 0.0862261i | \(0.972519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.19615i | − | 0.315644i | −0.987468 | − | 0.157822i | \(-0.949553\pi\) | ||
0.987468 | − | 0.157822i | \(-0.0504472\pi\) | |||||||
\(272\) | −9.79796 | − | 5.65685i | −0.594089 | − | 0.342997i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | − | 24.2487i | 0.845771 | − | 1.46492i | ||||
\(275\) | −14.6969 | −0.886259 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | 0.841178 | 0.420589 | − | 0.907251i | \(-0.361823\pi\) | ||||
0.420589 | + | 0.907251i | \(0.361823\pi\) | |||||||
\(278\) | 6.12372 | − | 10.6066i | 0.367277 | − | 0.636142i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.8564i | 0.828079i | ||||||||
\(281\) | − | 5.65685i | − | 0.337460i | −0.985662 | − | 0.168730i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168730i | \(-0.0539665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2487i | 1.44144i | 0.693228 | + | 0.720718i | \(0.256188\pi\) | ||||
−0.693228 | + | 0.720718i | \(0.743812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | + | 3.46410i | 0.354787 | + | 0.204837i | ||||
\(287\) | 9.79796 | 0.578355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | −19.5959 | − | 11.3137i | −1.15071 | − | 0.664364i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | 2.82843i | 0.165238i | 0.996581 | + | 0.0826192i | \(0.0263285\pi\) | ||||
−0.996581 | + | 0.0826192i | \(0.973671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 13.8564i | − | 0.806751i | ||||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.0000 | + | 27.7128i | −0.926855 | + | 1.60536i | ||||
\(299\) | 4.89898 | 0.283315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 15.9217 | − | 27.5772i | 0.916190 | − | 1.58689i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.0000 | + | 10.3923i | 1.03237 | + | 0.596040i | ||||
\(305\) | 31.1127i | 1.78151i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3923i | 0.593120i | 0.955014 | + | 0.296560i | \(0.0958395\pi\) | ||||
−0.955014 | + | 0.296560i | \(0.904160\pi\) | |||||||
\(308\) | −14.6969 | + | 8.48528i | −0.837436 | + | 0.483494i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0000 | + | 6.92820i | 0.681554 | + | 0.393496i | ||||
\(311\) | 24.4949 | 1.38898 | 0.694489 | − | 0.719503i | \(-0.255630\pi\) | ||||
0.694489 | + | 0.719503i | \(0.255630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0000 | 0.621757 | 0.310878 | − | 0.950450i | \(-0.399377\pi\) | ||||
0.310878 | + | 0.950450i | \(0.399377\pi\) | |||||||
\(314\) | 12.2474 | + | 7.07107i | 0.691164 | + | 0.399043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | + | 1.73205i | −0.168763 | + | 0.0974355i | ||||
\(317\) | − | 5.65685i | − | 0.317721i | −0.987301 | − | 0.158860i | \(-0.949218\pi\) | ||
0.987301 | − | 0.158860i | \(-0.0507819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 27.7128i | − | 1.55162i | ||||||
\(320\) | − | 22.6274i | − | 1.26491i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | + | 10.3923i | −0.334367 | + | 0.579141i | ||||
\(323\) | 14.6969 | 0.817760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | −3.67423 | + | 6.36396i | −0.203497 | + | 0.352467i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −16.0000 | −0.883452 | ||||||||
\(329\) | 8.48528i | 0.467809i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5167i | 1.23763i | 0.785538 | + | 0.618814i | \(0.212386\pi\) | ||||
−0.785538 | + | 0.618814i | \(0.787614\pi\) | |||||||
\(332\) | −9.79796 | − | 16.9706i | −0.537733 | − | 0.931381i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000 | + | 3.46410i | 0.328305 | + | 0.189547i | ||||
\(335\) | 34.2929 | 1.87362 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | 14.6969 | + | 8.48528i | 0.799408 | + | 0.461538i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.00000 | − | 13.8564i | −0.433861 | − | 0.751469i | ||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | −9.79796 | −0.528271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.00000 | + | 6.92820i | −0.215041 | + | 0.372463i | ||||
\(347\) | −19.5959 | −1.05196 | −0.525982 | − | 0.850496i | \(-0.676302\pi\) | ||||
−0.525982 | + | 0.850496i | \(0.676302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0000 | 1.23116 | 0.615581 | − | 0.788074i | \(-0.288921\pi\) | ||||
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | −3.67423 | + | 6.36396i | −0.196396 | + | 0.340168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.0000 | − | 13.8564i | 1.27920 | − | 0.738549i | ||||
\(353\) | 11.3137i | 0.602168i | 0.953598 | + | 0.301084i | \(0.0973484\pi\) | ||||
−0.953598 | + | 0.301084i | \(0.902652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.89898 | + | 2.82843i | −0.259645 | + | 0.149906i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.6969 | −0.775675 | −0.387837 | − | 0.921728i | \(-0.626778\pi\) | ||||
−0.387837 | + | 0.921728i | \(0.626778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | −0.421053 | ||||||||
\(362\) | −13.4722 | − | 7.77817i | −0.708083 | − | 0.408812i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.00000 | − | 1.73205i | 0.157243 | − | 0.0907841i | ||||
\(365\) | − | 2.82843i | − | 0.148047i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.0526i | − | 0.994535i | −0.867597 | − | 0.497268i | \(-0.834337\pi\) | ||
0.867597 | − | 0.497268i | \(-0.165663\pi\) | |||||||
\(368\) | 9.79796 | − | 16.9706i | 0.510754 | − | 0.884652i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | + | 3.46410i | −0.103975 | + | 0.180090i | ||||
\(371\) | 9.79796 | 0.508685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724071\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 9.79796 | − | 16.9706i | 0.506640 | − | 0.877527i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 13.8564i | − | 0.714590i | ||||||
\(377\) | 5.65685i | 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5885i | 0.800725i | 0.916357 | + | 0.400363i | \(0.131116\pi\) | ||||
−0.916357 | + | 0.400363i | \(0.868884\pi\) | |||||||
\(380\) | 14.6969 | + | 25.4558i | 0.753937 | + | 1.30586i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 30.0000 | + | 17.3205i | 1.53493 | + | 0.886194i | ||||
\(383\) | −19.5959 | −1.00130 | −0.500652 | − | 0.865648i | \(-0.666906\pi\) | ||||
−0.500652 | + | 0.865648i | \(0.666906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | −1.22315 | ||||||||
\(386\) | 1.22474 | + | 0.707107i | 0.0623379 | + | 0.0359908i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.0000 | − | 22.5167i | −0.659975 | − | 1.14311i | ||||
\(389\) | − | 14.1421i | − | 0.717035i | −0.933523 | − | 0.358517i | \(-0.883282\pi\) | ||
0.933523 | − | 0.358517i | \(-0.116718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13.8564i | − | 0.700749i | ||||||
\(392\) | − | 11.3137i | − | 0.571429i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | − | 3.46410i | 0.100759 | − | 0.174519i | ||||
\(395\) | −4.89898 | −0.246494 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0000 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(398\) | −3.67423 | + | 6.36396i | −0.184173 | + | 0.318997i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.00000 | − | 10.3923i | 0.300000 | − | 0.519615i | ||||
\(401\) | − | 22.6274i | − | 1.12996i | −0.825105 | − | 0.564980i | \(-0.808884\pi\) | ||
0.825105 | − | 0.564980i | \(-0.191116\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.46410i | − | 0.172559i | ||||||
\(404\) | −19.5959 | + | 11.3137i | −0.974933 | + | 0.562878i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | − | 6.92820i | −0.595550 | − | 0.343841i | ||||
\(407\) | −4.89898 | −0.242833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | −0.0494468 | −0.0247234 | − | 0.999694i | \(-0.507871\pi\) | ||||
−0.0247234 | + | 0.999694i | \(0.507871\pi\) | |||||||
\(410\) | −19.5959 | − | 11.3137i | −0.967773 | − | 0.558744i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.0000 | + | 8.66025i | −0.738997 | + | 0.426660i | ||||
\(413\) | − | 8.48528i | − | 0.417533i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.7128i | − | 1.36037i | ||||||
\(416\) | −4.89898 | + | 2.82843i | −0.240192 | + | 0.138675i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.0000 | + | 31.1769i | −0.880409 | + | 1.52491i | ||||
\(419\) | −4.89898 | −0.239331 | −0.119665 | − | 0.992814i | \(-0.538182\pi\) | ||||
−0.119665 | + | 0.992814i | \(0.538182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0000 | −1.21843 | −0.609213 | − | 0.793007i | \(-0.708514\pi\) | ||||
−0.609213 | + | 0.793007i | \(0.708514\pi\) | |||||||
\(422\) | −8.57321 | + | 14.8492i | −0.417338 | + | 0.722850i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.0000 | −0.777029 | ||||||||
\(425\) | − | 8.48528i | − | 0.411597i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.0526i | 0.922018i | ||||||||
\(428\) | 14.6969 | + | 25.4558i | 0.710403 | + | 1.23045i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | − | 6.92820i | −0.578691 | − | 0.334108i | ||||
\(431\) | −14.6969 | −0.707927 | −0.353963 | − | 0.935259i | \(-0.615166\pi\) | ||||
−0.353963 | + | 0.935259i | \(0.615166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 7.34847 | + | 4.24264i | 0.352738 | + | 0.203653i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | − | 17.3205i | −0.478913 | − | 0.829502i | ||||
\(437\) | 25.4558i | 1.21772i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3205i | 0.826663i | 0.910581 | + | 0.413331i | \(0.135635\pi\) | ||||
−0.910581 | + | 0.413331i | \(0.864365\pi\) | |||||||
\(440\) | 39.1918 | 1.86840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.00000 | + | 3.46410i | −0.0951303 | + | 0.164771i | ||||
\(443\) | −9.79796 | −0.465515 | −0.232758 | − | 0.972535i | \(-0.574775\pi\) | ||||
−0.232758 | + | 0.972535i | \(0.574775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | −17.1464 | + | 29.6985i | −0.811907 | + | 1.40626i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 13.8564i | − | 0.654654i | ||||||
\(449\) | − | 31.1127i | − | 1.46830i | −0.678988 | − | 0.734150i | \(-0.737581\pi\) | ||
0.678988 | − | 0.734150i | \(-0.262419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.7128i | − | 1.30495i | ||||||
\(452\) | −4.89898 | + | 2.82843i | −0.230429 | + | 0.133038i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.0000 | − | 13.8564i | −1.12638 | − | 0.650313i | ||||
\(455\) | 4.89898 | 0.229668 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | 12.2474 | + | 7.07107i | 0.572286 | + | 0.330409i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.0000 | − | 13.8564i | 1.11901 | − | 0.646058i | ||||
\(461\) | − | 14.1421i | − | 0.658665i | −0.944214 | − | 0.329332i | \(-0.893176\pi\) | ||
0.944214 | − | 0.329332i | \(-0.106824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.1244i | − | 0.563467i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909093\pi\) | |||||||
\(464\) | 19.5959 | + | 11.3137i | 0.909718 | + | 0.525226i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0000 | + | 27.7128i | −0.741186 | + | 1.28377i | ||||
\(467\) | 14.6969 | 0.680093 | 0.340047 | − | 0.940409i | \(-0.389557\pi\) | ||||
0.340047 | + | 0.940409i | \(0.389557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 9.79796 | − | 16.9706i | 0.451946 | − | 0.782794i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.8564i | 0.637793i | ||||||||
\(473\) | − | 16.9706i | − | 0.780307i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.5885i | 0.715247i | ||||||||
\(476\) | −4.89898 | − | 8.48528i | −0.224544 | − | 0.388922i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0000 | + | 13.8564i | 1.09773 | + | 0.633777i | ||||
\(479\) | −9.79796 | −0.447680 | −0.223840 | − | 0.974626i | \(-0.571859\pi\) | ||||
−0.223840 | + | 0.974626i | \(0.571859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.00000 | 0.0455961 | ||||||||
\(482\) | 30.6186 | + | 17.6777i | 1.39464 | + | 0.805196i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.0000 | + | 22.5167i | 0.590909 | + | 1.02348i | ||||
\(485\) | − | 36.7696i | − | 1.66962i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.9808i | − | 1.17730i | −0.808388 | − | 0.588650i | \(-0.799659\pi\) | ||
0.808388 | − | 0.588650i | \(-0.200341\pi\) | |||||||
\(488\) | − | 31.1127i | − | 1.40841i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.00000 | − | 13.8564i | 0.361403 | − | 0.625969i | ||||
\(491\) | 24.4949 | 1.10544 | 0.552720 | − | 0.833367i | \(-0.313590\pi\) | ||||
0.552720 | + | 0.833367i | \(0.313590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0000 | 0.720604 | ||||||||
\(494\) | 3.67423 | − | 6.36396i | 0.165312 | − | 0.286328i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | − | 6.92820i | −0.538816 | − | 0.311086i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | −9.79796 | + | 5.65685i | −0.438178 | + | 0.252982i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.0000 | + | 20.7846i | 1.60676 | + | 0.927663i | ||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | −1.42398 | ||||||||
\(506\) | 29.3939 | + | 16.9706i | 1.30672 | + | 0.754434i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.0000 | − | 10.3923i | 0.798621 | − | 0.461084i | ||||
\(509\) | 19.7990i | 0.877575i | 0.898591 | + | 0.438787i | \(0.144592\pi\) | ||||
−0.898591 | + | 0.438787i | \(0.855408\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.73205i | − | 0.0766214i | ||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.0000 | − | 34.6410i | 0.882162 | − | 1.52795i | ||||
\(515\) | −24.4949 | −1.07937 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000 | 1.05552 | ||||||||
\(518\) | −1.22474 | + | 2.12132i | −0.0538122 | + | 0.0932055i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.00000 | −0.350823 | ||||||||
\(521\) | 19.7990i | 0.867409i | 0.901055 | + | 0.433705i | \(0.142794\pi\) | ||||
−0.901055 | + | 0.433705i | \(0.857206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5885i | 0.681636i | 0.940129 | + | 0.340818i | \(0.110704\pi\) | ||||
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | 9.79796 | + | 16.9706i | 0.428026 | + | 0.741362i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | − | 13.8564i | −1.04645 | − | 0.604168i | ||||
\(527\) | −9.79796 | −0.426806 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −19.5959 | − | 11.3137i | −0.851192 | − | 0.491436i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.00000 | + | 15.5885i | 0.390199 | + | 0.675845i | ||||
\(533\) | 5.65685i | 0.245026i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.5692i | 1.79719i | ||||||||
\(536\) | −34.2929 | −1.48123 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.00000 | − | 3.46410i | 0.0862261 | − | 0.149348i | ||||
\(539\) | 19.5959 | 0.844056 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | −0.0429934 | −0.0214967 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214967 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(542\) | −3.67423 | + | 6.36396i | −0.157822 | + | 0.273356i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | + | 13.8564i | 0.342997 | + | 0.594089i | ||||
\(545\) | − | 28.2843i | − | 1.21157i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5167i | 0.962743i | 0.876517 | + | 0.481371i | \(0.159861\pi\) | ||||
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | −34.2929 | + | 19.7990i | −1.46492 | + | 0.845771i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.0000 | + | 10.3923i | 0.767523 | + | 0.443129i | ||||
\(551\) | −29.3939 | −1.25222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.00000 | −0.127573 | ||||||||
\(554\) | −17.1464 | − | 9.89949i | −0.728482 | − | 0.420589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.0000 | + | 8.66025i | −0.636142 | + | 0.367277i | ||||
\(557\) | 2.82843i | 0.119844i | 0.998203 | + | 0.0599222i | \(0.0190852\pi\) | ||||
−0.998203 | + | 0.0599222i | \(0.980915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46410i | 0.146516i | ||||||||
\(560\) | 9.79796 | − | 16.9706i | 0.414039 | − | 0.717137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.00000 | + | 6.92820i | −0.168730 | + | 0.292249i | ||||
\(563\) | 9.79796 | 0.412935 | 0.206467 | − | 0.978453i | \(-0.433803\pi\) | ||||
0.206467 | + | 0.978453i | \(0.433803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00000 | −0.336563 | ||||||||
\(566\) | 17.1464 | − | 29.6985i | 0.720718 | − | 1.24832i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.7990i | 0.830017i | 0.909818 | + | 0.415008i | \(0.136221\pi\) | ||||
−0.909818 | + | 0.415008i | \(0.863779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 32.9090i | − | 1.37720i | −0.725143 | − | 0.688599i | \(-0.758226\pi\) | ||
0.725143 | − | 0.688599i | \(-0.241774\pi\) | |||||||
\(572\) | −4.89898 | − | 8.48528i | −0.204837 | − | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 6.92820i | −0.500870 | − | 0.289178i | ||||
\(575\) | 14.6969 | 0.612905 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0000 | 1.45707 | 0.728535 | − | 0.685009i | \(-0.240202\pi\) | ||||
0.728535 | + | 0.685009i | \(0.240202\pi\) | |||||||
\(578\) | −11.0227 | − | 6.36396i | −0.458484 | − | 0.264706i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.0000 | + | 27.7128i | 0.664364 | + | 1.15071i | ||||
\(581\) | − | 16.9706i | − | 0.704058i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.7128i | − | 1.14775i | ||||||
\(584\) | 2.82843i | 0.117041i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.00000 | − | 3.46410i | 0.0826192 | − | 0.143101i | ||||
\(587\) | 4.89898 | 0.202203 | 0.101101 | − | 0.994876i | \(-0.467763\pi\) | ||||
0.101101 | + | 0.994876i | \(0.467763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | 0.741677 | ||||||||
\(590\) | −9.79796 | + | 16.9706i | −0.403376 | + | 0.698667i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | − | 3.46410i | 0.0821995 | − | 0.142374i | ||||
\(593\) | 28.2843i | 1.16150i | 0.814083 | + | 0.580748i | \(0.197240\pi\) | ||||
−0.814083 | + | 0.580748i | \(0.802760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.8564i | − | 0.568057i | ||||||
\(596\) | 39.1918 | − | 22.6274i | 1.60536 | − | 0.926855i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | − | 3.46410i | −0.245358 | − | 0.141658i | ||||
\(599\) | 9.79796 | 0.400334 | 0.200167 | − | 0.979762i | \(-0.435852\pi\) | ||||
0.200167 | + | 0.979762i | \(0.435852\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | −7.34847 | − | 4.24264i | −0.299501 | − | 0.172917i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −39.0000 | + | 22.5167i | −1.58689 | + | 0.916190i | ||||
\(605\) | 36.7696i | 1.49489i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12.1244i | − | 0.492112i | −0.969256 | − | 0.246056i | \(-0.920865\pi\) | ||
0.969256 | − | 0.246056i | \(-0.0791348\pi\) | |||||||
\(608\) | −14.6969 | − | 25.4558i | −0.596040 | − | 1.03237i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.0000 | − | 38.1051i | 0.890754 | − | 1.54283i | ||||
\(611\) | −4.89898 | −0.198191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | 0.444286 | 0.222143 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222143 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(614\) | 7.34847 | − | 12.7279i | 0.296560 | − | 0.513657i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | 0.966988 | ||||||||
\(617\) | 2.82843i | 0.113868i | 0.998378 | + | 0.0569341i | \(0.0181325\pi\) | ||||
−0.998378 | + | 0.0569341i | \(0.981868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.0526i | − | 0.765787i | −0.923792 | − | 0.382893i | \(-0.874928\pi\) | ||
0.923792 | − | 0.382893i | \(-0.125072\pi\) | |||||||
\(620\) | −9.79796 | − | 16.9706i | −0.393496 | − | 0.681554i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.0000 | − | 17.3205i | −1.20289 | − | 0.694489i | ||||
\(623\) | −4.89898 | −0.196273 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | −13.4722 | − | 7.77817i | −0.538457 | − | 0.310878i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | − | 17.3205i | −0.399043 | − | 0.691164i | ||||
\(629\) | − | 2.82843i | − | 0.112777i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3731i | 1.44799i | 0.689806 | + | 0.723994i | \(0.257696\pi\) | ||||
−0.689806 | + | 0.723994i | \(0.742304\pi\) | |||||||
\(632\) | 4.89898 | 0.194871 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.00000 | + | 6.92820i | −0.158860 | + | 0.275154i | ||||
\(635\) | 29.3939 | 1.16646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | −19.5959 | + | 33.9411i | −0.775810 | + | 1.34374i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0000 | + | 27.7128i | −0.632456 | + | 1.09545i | ||||
\(641\) | 45.2548i | 1.78746i | 0.448607 | + | 0.893729i | \(0.351920\pi\) | ||||
−0.448607 | + | 0.893729i | \(0.648080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.3205i | − | 0.683054i | −0.939872 | − | 0.341527i | \(-0.889056\pi\) | ||
0.939872 | − | 0.341527i | \(-0.110944\pi\) | |||||||
\(644\) | 14.6969 | − | 8.48528i | 0.579141 | − | 0.334367i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.0000 | − | 10.3923i | −0.708201 | − | 0.408880i | ||||
\(647\) | 29.3939 | 1.15559 | 0.577796 | − | 0.816181i | \(-0.303913\pi\) | ||||
0.577796 | + | 0.816181i | \(0.303913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | −3.67423 | − | 2.12132i | −0.144115 | − | 0.0832050i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.00000 | − | 5.19615i | 0.352467 | − | 0.203497i | ||||
\(653\) | − | 5.65685i | − | 0.221370i | −0.993856 | − | 0.110685i | \(-0.964696\pi\) | ||
0.993856 | − | 0.110685i | \(-0.0353044\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.7128i | 1.08283i | ||||||||
\(656\) | 19.5959 | + | 11.3137i | 0.765092 | + | 0.441726i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | − | 10.3923i | 0.233904 | − | 0.405134i | ||||
\(659\) | −9.79796 | −0.381674 | −0.190837 | − | 0.981622i | \(-0.561120\pi\) | ||||
−0.190837 | + | 0.981622i | \(0.561120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0000 | −1.43913 | −0.719567 | − | 0.694423i | \(-0.755660\pi\) | ||||
−0.719567 | + | 0.694423i | \(0.755660\pi\) | |||||||
\(662\) | 15.9217 | − | 27.5772i | 0.618814 | − | 1.07182i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.7128i | 1.07547i | ||||||||
\(665\) | 25.4558i | 0.987135i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7128i | 1.07304i | ||||||||
\(668\) | −4.89898 | − | 8.48528i | −0.189547 | − | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −42.0000 | − | 24.2487i | −1.62260 | − | 0.936809i | ||||
\(671\) | 53.8888 | 2.08035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | 0.424019 | 0.212009 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212009 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(674\) | −13.4722 | − | 7.77817i | −0.518930 | − | 0.299604i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | − | 20.7846i | −0.461538 | − | 0.799408i | ||||
\(677\) | − | 14.1421i | − | 0.543526i | −0.962364 | − | 0.271763i | \(-0.912393\pi\) | ||
0.962364 | − | 0.271763i | \(-0.0876068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 22.5167i | − | 0.864110i | ||||||
\(680\) | 22.6274i | 0.867722i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | − | 20.7846i | 0.459504 | − | 0.795884i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56.0000 | −2.13965 | ||||||||
\(686\) | 13.4722 | − | 23.3345i | 0.514371 | − | 0.890916i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.0000 | + | 6.92820i | 0.457496 | + | 0.264135i | ||||
\(689\) | 5.65685i | 0.215509i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 45.0333i | − | 1.71315i | −0.516024 | − | 0.856574i | \(-0.672588\pi\) | ||
0.516024 | − | 0.856574i | \(-0.327412\pi\) | |||||||
\(692\) | 9.79796 | − | 5.65685i | 0.372463 | − | 0.215041i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | + | 13.8564i | 0.911028 | + | 0.525982i | ||||
\(695\) | −24.4949 | −0.929144 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | 0.606043 | ||||||||
\(698\) | −28.1691 | − | 16.2635i | −1.06622 | − | 0.615581i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.00000 | − | 5.19615i | 0.340168 | − | 0.196396i | ||||
\(701\) | 2.82843i | 0.106828i | 0.998572 | + | 0.0534141i | \(0.0170103\pi\) | ||||
−0.998572 | + | 0.0534141i | \(0.982990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.19615i | 0.195977i | ||||||||
\(704\) | −39.1918 | −1.47710 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.00000 | − | 13.8564i | 0.301084 | − | 0.521493i | ||||
\(707\) | −19.5959 | −0.736980 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0000 | −0.938895 | −0.469447 | − | 0.882960i | \(-0.655547\pi\) | ||||
−0.469447 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.00000 | 0.299813 | ||||||||
\(713\) | − | 16.9706i | − | 0.635553i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13.8564i | − | 0.518200i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.0000 | + | 10.3923i | 0.671754 | + | 0.387837i | ||||
\(719\) | 29.3939 | 1.09621 | 0.548103 | − | 0.836411i | \(-0.315350\pi\) | ||||
0.548103 | + | 0.836411i | \(0.315350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0000 | −0.558629 | ||||||||
\(722\) | 9.79796 | + | 5.65685i | 0.364642 | + | 0.210526i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0000 | + | 19.0526i | 0.408812 | + | 0.708083i | ||||
\(725\) | 16.9706i | 0.630271i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3205i | 0.642382i | 0.947014 | + | 0.321191i | \(0.104083\pi\) | ||||
−0.947014 | + | 0.321191i | \(0.895917\pi\) | |||||||
\(728\) | −4.89898 | −0.181568 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.00000 | + | 3.46410i | −0.0740233 | + | 0.128212i | ||||
\(731\) | 9.79796 | 0.362391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.0000 | 1.40356 | 0.701781 | − | 0.712393i | \(-0.252388\pi\) | ||||
0.701781 | + | 0.712393i | \(0.252388\pi\) | |||||||
\(734\) | −13.4722 | + | 23.3345i | −0.497268 | + | 0.861293i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | + | 13.8564i | −0.884652 | + | 0.510754i | ||||
\(737\) | − | 59.3970i | − | 2.18792i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923i | 0.382287i | 0.981562 | + | 0.191144i | \(0.0612196\pi\) | ||||
−0.981562 | + | 0.191144i | \(0.938780\pi\) | |||||||
\(740\) | 4.89898 | − | 2.82843i | 0.180090 | − | 0.103975i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0000 | − | 6.92820i | −0.440534 | − | 0.254342i | ||||
\(743\) | −34.2929 | −1.25808 | −0.629041 | − | 0.777372i | \(-0.716552\pi\) | ||||
−0.629041 | + | 0.777372i | \(0.716552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 64.0000 | 2.34478 | ||||||||
\(746\) | 30.6186 | + | 17.6777i | 1.12103 | + | 0.647225i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.0000 | + | 13.8564i | −0.877527 | + | 0.506640i | ||||
\(749\) | 25.4558i | 0.930136i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.4449i | 1.07446i | 0.843436 | + | 0.537229i | \(0.180529\pi\) | ||||
−0.843436 | + | 0.537229i | \(0.819471\pi\) | |||||||
\(752\) | −9.79796 | + | 16.9706i | −0.357295 | + | 0.618853i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.00000 | − | 6.92820i | 0.145671 | − | 0.252310i | ||||
\(755\) | −63.6867 | −2.31780 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | 11.0227 | − | 19.0919i | 0.400363 | − | 0.693448i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 41.5692i | − | 1.50787i | ||||||
\(761\) | 2.82843i | 0.102530i | 0.998685 | + | 0.0512652i | \(0.0163254\pi\) | ||||
−0.998685 | + | 0.0512652i | \(0.983675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.3205i | − | 0.627044i | ||||||
\(764\) | −24.4949 | − | 42.4264i | −0.886194 | − | 1.53493i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | + | 13.8564i | 0.867155 | + | 0.500652i | ||||
\(767\) | 4.89898 | 0.176892 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00000 | −0.0360609 | −0.0180305 | − | 0.999837i | \(-0.505740\pi\) | ||||
−0.0180305 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(770\) | 29.3939 | + | 16.9706i | 1.05928 | + | 0.611577i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | − | 1.73205i | −0.0359908 | − | 0.0623379i | ||||
\(773\) | 28.2843i | 1.01731i | 0.860969 | + | 0.508657i | \(0.169858\pi\) | ||||
−0.860969 | + | 0.508657i | \(0.830142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.3923i | − | 0.373303i | ||||||
\(776\) | 36.7696i | 1.31995i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | + | 17.3205i | −0.358517 | + | 0.620970i | ||||
\(779\) | −29.3939 | −1.05314 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.79796 | + | 16.9706i | −0.350374 | + | 0.606866i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | + | 13.8564i | −0.285714 | + | 0.494872i | ||||
\(785\) | − | 28.2843i | − | 1.00951i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.66025i | 0.308705i | 0.988016 | + | 0.154352i | \(0.0493291\pi\) | ||||
−0.988016 | + | 0.154352i | \(0.950671\pi\) | |||||||
\(788\) | −4.89898 | + | 2.82843i | −0.174519 | + | 0.100759i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.00000 | + | 3.46410i | 0.213470 | + | 0.123247i | ||||
\(791\) | −4.89898 | −0.174188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0000 | −0.390621 | ||||||||
\(794\) | 12.2474 | + | 7.07107i | 0.434646 | + | 0.250943i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.00000 | − | 5.19615i | 0.318997 | − | 0.184173i | ||||
\(797\) | − | 22.6274i | − | 0.801504i | −0.916187 | − | 0.400752i | \(-0.868749\pi\) | ||
0.916187 | − | 0.400752i | \(-0.131251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8564i | 0.490204i | ||||||||
\(800\) | −14.6969 | + | 8.48528i | −0.519615 | + | 0.300000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.0000 | + | 27.7128i | −0.564980 | + | 0.978573i | ||||
\(803\) | −4.89898 | −0.172881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | −2.44949 | + | 4.24264i | −0.0862796 | + | 0.149441i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.0000 | 1.12576 | ||||||||
\(809\) | − | 22.6274i | − | 0.795538i | −0.917486 | − | 0.397769i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397769i | \(-0.130215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 9.79796 | + | 16.9706i | 0.343841 | + | 0.595550i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | + | 3.46410i | 0.210300 | + | 0.121417i | ||||
\(815\) | 14.6969 | 0.514811 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0000 | −0.629740 | ||||||||
\(818\) | 1.22474 | + | 0.707107i | 0.0428222 | + | 0.0247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.0000 | + | 27.7128i | 0.558744 | + | 0.967773i | ||||
\(821\) | − | 31.1127i | − | 1.08584i | −0.839784 | − | 0.542920i | \(-0.817319\pi\) | ||
0.839784 | − | 0.542920i | \(-0.182681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.2295i | 1.75089i | 0.483318 | + | 0.875445i | \(0.339431\pi\) | ||||
−0.483318 | + | 0.875445i | \(0.660569\pi\) | |||||||
\(824\) | 24.4949 | 0.853320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | + | 10.3923i | −0.208767 | + | 0.361595i | ||||
\(827\) | 14.6969 | 0.511063 | 0.255531 | − | 0.966801i | \(-0.417750\pi\) | ||||
0.255531 | + | 0.966801i | \(0.417750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0000 | 0.382046 | 0.191023 | − | 0.981586i | \(-0.438820\pi\) | ||||
0.191023 | + | 0.981586i | \(0.438820\pi\) | |||||||
\(830\) | −19.5959 | + | 33.9411i | −0.680184 | + | 1.17811i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 11.3137i | 0.391997i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13.8564i | − | 0.479521i | ||||||
\(836\) | 44.0908 | − | 25.4558i | 1.52491 | − | 0.880409i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.00000 | + | 3.46410i | 0.207267 | + | 0.119665i | ||||
\(839\) | 48.9898 | 1.69132 | 0.845658 | − | 0.533726i | \(-0.179208\pi\) | ||||
0.845658 | + | 0.533726i | \(0.179208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | 30.6186 | + | 17.6777i | 1.05519 | + | 0.609213i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.0000 | − | 12.1244i | 0.722850 | − | 0.417338i | ||||
\(845\) | − | 33.9411i | − | 1.16761i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.5167i | 0.773682i | ||||||||
\(848\) | 19.5959 | + | 11.3137i | 0.672927 | + | 0.388514i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | + | 10.3923i | −0.205798 | + | 0.356453i | ||||
\(851\) | 4.89898 | 0.167935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.0000 | −1.67773 | −0.838864 | − | 0.544341i | \(-0.816780\pi\) | ||||
−0.838864 | + | 0.544341i | \(0.816780\pi\) | |||||||
\(854\) | 13.4722 | − | 23.3345i | 0.461009 | − | 0.798491i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 41.5692i | − | 1.42081i | ||||||
\(857\) | − | 56.5685i | − | 1.93234i | −0.257897 | − | 0.966172i | \(-0.583030\pi\) | ||
0.257897 | − | 0.966172i | \(-0.416970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.1244i | − | 0.413678i | −0.978375 | − | 0.206839i | \(-0.933682\pi\) | ||
0.978375 | − | 0.206839i | \(-0.0663176\pi\) | |||||||
\(860\) | 9.79796 | + | 16.9706i | 0.334108 | + | 0.578691i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | + | 10.3923i | 0.613082 | + | 0.353963i | ||||
\(863\) | −14.6969 | −0.500290 | −0.250145 | − | 0.968208i | \(-0.580478\pi\) | ||||
−0.250145 | + | 0.968208i | \(0.580478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0000 | 0.544016 | ||||||||
\(866\) | −31.8434 | − | 18.3848i | −1.08208 | − | 0.624740i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.00000 | − | 10.3923i | −0.203653 | − | 0.352738i | ||||
\(869\) | 8.48528i | 0.287843i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1244i | 0.410818i | ||||||||
\(872\) | 28.2843i | 0.957826i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.0000 | − | 31.1769i | 0.608859 | − | 1.05457i | ||||
\(875\) | −9.79796 | −0.331231 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | −0.0337676 | −0.0168838 | − | 0.999857i | \(-0.505375\pi\) | ||||
−0.0168838 | + | 0.999857i | \(0.505375\pi\) | |||||||
\(878\) | 12.2474 | − | 21.2132i | 0.413331 | − | 0.715911i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −48.0000 | − | 27.7128i | −1.61808 | − | 0.934199i | ||||
\(881\) | 19.7990i | 0.667045i | 0.942742 | + | 0.333522i | \(0.108237\pi\) | ||||
−0.942742 | + | 0.333522i | \(0.891763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.19615i | − | 0.174864i | −0.996170 | − | 0.0874322i | \(-0.972134\pi\) | ||
0.996170 | − | 0.0874322i | \(-0.0278661\pi\) | |||||||
\(884\) | 4.89898 | − | 2.82843i | 0.164771 | − | 0.0951303i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | + | 6.92820i | 0.403148 | + | 0.232758i | ||||
\(887\) | −48.9898 | −1.64492 | −0.822458 | − | 0.568826i | \(-0.807398\pi\) | ||||
−0.822458 | + | 0.568826i | \(0.807398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 9.79796 | + | 5.65685i | 0.328428 | + | 0.189618i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.0000 | − | 24.2487i | 1.40626 | − | 0.811907i | ||||
\(893\) | − | 25.4558i | − | 0.851847i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.79796 | + | 16.9706i | −0.327327 | + | 0.566947i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0000 | + | 38.1051i | −0.734150 | + | 1.27158i | ||||
\(899\) | 19.5959 | 0.653560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | −19.5959 | + | 33.9411i | −0.652473 | + | 1.13012i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.00000 | 0.266076 | ||||||||
\(905\) | 31.1127i | 1.03422i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.73205i | 0.0575118i | 0.999586 | + | 0.0287559i | \(0.00915455\pi\) | ||||
−0.999586 | + | 0.0287559i | \(0.990845\pi\) | |||||||
\(908\) | 19.5959 | + | 33.9411i | 0.650313 | + | 1.12638i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | − | 3.46410i | −0.198898 | − | 0.114834i | ||||
\(911\) | −9.79796 | −0.324621 | −0.162310 | − | 0.986740i | \(-0.551895\pi\) | ||||
−0.162310 | + | 0.986740i | \(0.551895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0000 | −1.58857 | ||||||||
\(914\) | −2.44949 | − | 1.41421i | −0.0810219 | − | 0.0467780i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | − | 17.3205i | −0.330409 | − | 0.572286i | ||||
\(917\) | 16.9706i | 0.560417i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.3923i | − | 0.342811i | −0.985201 | − | 0.171405i | \(-0.945169\pi\) | ||
0.985201 | − | 0.171405i | \(-0.0548307\pi\) | |||||||
\(920\) | −39.1918 | −1.29212 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0000 | + | 17.3205i | −0.329332 | + | 0.570421i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | −8.57321 | + | 14.8492i | −0.281733 | + | 0.487976i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.0000 | − | 27.7128i | −0.525226 | − | 0.909718i | ||||
\(929\) | 45.2548i | 1.48476i | 0.669977 | + | 0.742381i | \(0.266304\pi\) | ||||
−0.669977 | + | 0.742381i | \(0.733696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 20.7846i | − | 0.681188i | ||||||
\(932\) | 39.1918 | − | 22.6274i | 1.28377 | − | 0.741186i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.0000 | − | 10.3923i | −0.588978 | − | 0.340047i | ||||
\(935\) | −39.1918 | −1.28171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0000 | −1.20874 | −0.604369 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604369 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(938\) | −25.7196 | − | 14.8492i | −0.839776 | − | 0.484845i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.0000 | + | 13.8564i | −0.782794 | + | 0.451946i | ||||
\(941\) | − | 48.0833i | − | 1.56747i | −0.621096 | − | 0.783735i | \(-0.713312\pi\) | ||
0.621096 | − | 0.783735i | \(-0.286688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.7128i | 0.902453i | ||||||||
\(944\) | 9.79796 | − | 16.9706i | 0.318896 | − | 0.552345i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | + | 20.7846i | −0.390154 | + | 0.675766i | ||||
\(947\) | 34.2929 | 1.11437 | 0.557184 | − | 0.830389i | \(-0.311882\pi\) | ||||
0.557184 | + | 0.830389i | \(0.311882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.00000 | 0.0324614 | ||||||||
\(950\) | 11.0227 | − | 19.0919i | 0.357624 | − | 0.619422i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.8564i | 0.449089i | ||||||||
\(953\) | 2.82843i | 0.0916217i | 0.998950 | + | 0.0458109i | \(0.0145872\pi\) | ||||
−0.998950 | + | 0.0458109i | \(0.985413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 69.2820i | − | 2.24191i | ||||||
\(956\) | −19.5959 | − | 33.9411i | −0.633777 | − | 1.09773i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | + | 6.92820i | 0.387702 | + | 0.223840i | ||||
\(959\) | −34.2929 | −1.10737 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −1.22474 | − | 0.707107i | −0.0394874 | − | 0.0227980i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.0000 | − | 43.3013i | −0.805196 | − | 1.39464i | ||||
\(965\) | − | 2.82843i | − | 0.0910503i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.6936i | − | 1.72667i | −0.504632 | − | 0.863334i | \(-0.668372\pi\) | ||
0.504632 | − | 0.863334i | \(-0.331628\pi\) | |||||||
\(968\) | − | 36.7696i | − | 1.18182i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.0000 | + | 45.0333i | −0.834810 | + | 1.44593i | ||||
\(971\) | −14.6969 | −0.471647 | −0.235824 | − | 0.971796i | \(-0.575779\pi\) | ||||
−0.235824 | + | 0.971796i | \(0.575779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0000 | −0.480878 | ||||||||
\(974\) | −18.3712 | + | 31.8198i | −0.588650 | + | 1.01957i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.0000 | + | 38.1051i | −0.704203 | + | 1.21972i | ||||
\(977\) | − | 5.65685i | − | 0.180979i | −0.995897 | − | 0.0904894i | \(-0.971157\pi\) | ||
0.995897 | − | 0.0904894i | \(-0.0288431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.8564i | 0.442853i | ||||||||
\(980\) | −19.5959 | + | 11.3137i | −0.625969 | + | 0.361403i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.0000 | − | 17.3205i | −0.957338 | − | 0.552720i | ||||
\(983\) | 34.2929 | 1.09377 | 0.546886 | − | 0.837207i | \(-0.315813\pi\) | ||||
0.546886 | + | 0.837207i | \(0.315813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | −0.254901 | ||||||||
\(986\) | −19.5959 | − | 11.3137i | −0.624061 | − | 0.360302i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.00000 | + | 5.19615i | −0.286328 | + | 0.165312i | ||||
\(989\) | 16.9706i | 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.3731i | 1.15543i | 0.816239 | + | 0.577714i | \(0.196055\pi\) | ||||
−0.816239 | + | 0.577714i | \(0.803945\pi\) | |||||||
\(992\) | 9.79796 | + | 16.9706i | 0.311086 | + | 0.538816i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.6969 | 0.465924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.0000 | −1.07679 | −0.538395 | − | 0.842692i | \(-0.680969\pi\) | ||||
−0.538395 | + | 0.842692i | \(0.680969\pi\) | |||||||
\(998\) | 17.1464 | − | 29.6985i | 0.542761 | − | 0.940089i | ||||
\(999\) | 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 | 108.2.b.b.107.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 108.2.b.b.107.4 | yes | 4 | |
4.3 | odd | 2 | inner | 108.2.b.b.107.3 | yes | 4 | |
8.3 | odd | 2 | 1728.2.c.d.1727.1 | 4 | |||
8.5 | even | 2 | 1728.2.c.d.1727.2 | 4 | |||
9.2 | odd | 6 | 324.2.h.a.215.1 | 4 | |||
9.4 | even | 3 | 324.2.h.b.107.2 | 4 | |||
9.5 | odd | 6 | 324.2.h.b.107.1 | 4 | |||
9.7 | even | 3 | 324.2.h.a.215.2 | 4 | |||
12.11 | even | 2 | inner | 108.2.b.b.107.2 | yes | 4 | |
24.5 | odd | 2 | 1728.2.c.d.1727.4 | 4 | |||
24.11 | even | 2 | 1728.2.c.d.1727.3 | 4 | |||
36.7 | odd | 6 | 324.2.h.b.215.1 | 4 | |||
36.11 | even | 6 | 324.2.h.b.215.2 | 4 | |||
36.23 | even | 6 | 324.2.h.a.107.1 | 4 | |||
36.31 | odd | 6 | 324.2.h.a.107.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.b.b.107.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
108.2.b.b.107.2 | yes | 4 | 12.11 | even | 2 | inner | |
108.2.b.b.107.3 | yes | 4 | 4.3 | odd | 2 | inner | |
108.2.b.b.107.4 | yes | 4 | 3.2 | odd | 2 | inner | |
324.2.h.a.107.1 | 4 | 36.23 | even | 6 | |||
324.2.h.a.107.2 | 4 | 36.31 | odd | 6 | |||
324.2.h.a.215.1 | 4 | 9.2 | odd | 6 | |||
324.2.h.a.215.2 | 4 | 9.7 | even | 3 | |||
324.2.h.b.107.1 | 4 | 9.5 | odd | 6 | |||
324.2.h.b.107.2 | 4 | 9.4 | even | 3 | |||
324.2.h.b.215.1 | 4 | 36.7 | odd | 6 | |||
324.2.h.b.215.2 | 4 | 36.11 | even | 6 | |||
1728.2.c.d.1727.1 | 4 | 8.3 | odd | 2 | |||
1728.2.c.d.1727.2 | 4 | 8.5 | even | 2 | |||
1728.2.c.d.1727.3 | 4 | 24.11 | even | 2 | |||
1728.2.c.d.1727.4 | 4 | 24.5 | odd | 2 |