Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.a (trivial) |
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: | yes |
Analytic conductor: | \(29.8959905168\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1248) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.763932 | 0.175258 | 0.0876290 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876290 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.70820 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.4721 | −1.77011 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.47214 | −1.39281 | −0.696405 | − | 0.717649i | \(-0.745218\pi\) | ||||
−0.696405 | + | 0.717649i | \(0.745218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23607 | 0.505389 | 0.252694 | − | 0.967546i | \(-0.418683\pi\) | ||||
0.252694 | + | 0.967546i | \(0.418683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47214 | −0.376997 | −0.188499 | − | 0.982073i | \(-0.560362\pi\) | ||||
−0.188499 | + | 0.982073i | \(0.560362\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9443 | 1.59639 | 0.798193 | − | 0.602402i | \(-0.205789\pi\) | ||||
0.798193 | + | 0.602402i | \(0.205789\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.472136 | 0.0648529 | 0.0324264 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324264 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.47214 | 0.872703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.472136 | 0.0614669 | 0.0307334 | − | 0.999528i | \(-0.490216\pi\) | ||||
0.0307334 | + | 0.999528i | \(0.490216\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2361 | 1.37270 | 0.686352 | − | 0.727269i | \(-0.259211\pi\) | ||||
0.686352 | + | 0.727269i | \(0.259211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.47214 | 0.530745 | 0.265372 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265372 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.47214 | −0.991589 | −0.495794 | − | 0.868440i | \(-0.665123\pi\) | ||||
−0.495794 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.4721 | −1.80805 | −0.904026 | − | 0.427478i | \(-0.859402\pi\) | ||||
−0.904026 | + | 0.427478i | \(0.859402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4721 | −1.56972 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1803 | −1.29111 | −0.645557 | − | 0.763712i | \(-0.723375\pi\) | ||||
−0.645557 | + | 0.763712i | \(0.723375\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | −0.339232 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47214 | −0.253636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.47214 | 0.454077 | 0.227038 | − | 0.973886i | \(-0.427096\pi\) | ||||
0.227038 | + | 0.973886i | \(0.427096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9443 | −1.48701 | −0.743505 | − | 0.668730i | \(-0.766838\pi\) | ||||
−0.743505 | + | 0.668730i | \(0.766838\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4721 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.52786 | −0.534399 | −0.267199 | − | 0.963641i | \(-0.586098\pi\) | ||||
−0.267199 | + | 0.963641i | \(0.586098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9443 | −1.81453 | −0.907266 | − | 0.420557i | \(-0.861835\pi\) | ||||
−0.907266 | + | 0.420557i | \(0.861835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.9443 | 1.95306 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.4721 | 1.32666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.47214 | −0.219367 | −0.109683 | − | 0.993967i | \(-0.534984\pi\) | ||||
−0.109683 | + | 0.993967i | \(0.534984\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.4164 | −1.34694 | −0.673469 | − | 0.739216i | \(-0.735196\pi\) | ||||
−0.673469 | + | 0.739216i | \(0.735196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.47214 | 0.214361 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.2361 | 0.959962 | 0.479981 | − | 0.877279i | \(-0.340644\pi\) | ||||
0.479981 | + | 0.877279i | \(0.340644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8885 | 1.85656 | 0.928281 | − | 0.371879i | \(-0.121287\pi\) | ||||
0.928281 | + | 0.371879i | \(0.121287\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4721 | −1.20185 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.7082 | −1.77841 | −0.889203 | − | 0.457513i | \(-0.848740\pi\) | ||||
−0.889203 | + | 0.457513i | \(0.848740\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.2361 | −1.89092 | −0.945462 | − | 0.325732i | \(-0.894389\pi\) | ||||
−0.945462 | + | 0.325732i | \(0.894389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.4721 | 1.48372 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164 | 1.07075 | 0.535373 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535373 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.9443 | −1.65064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.23607 | 0.566773 | 0.283386 | − | 0.959006i | \(-0.408542\pi\) | ||||
0.283386 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.8885 | −1.53902 | −0.769511 | − | 0.638634i | \(-0.779500\pi\) | ||||
−0.769511 | + | 0.638634i | \(0.779500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.7082 | 1.33861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.4164 | 1.45125 | 0.725625 | − | 0.688090i | \(-0.241551\pi\) | ||||
0.725625 | + | 0.688090i | \(0.241551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4164 | −1.29455 | −0.647276 | − | 0.762256i | \(-0.724092\pi\) | ||||
−0.647276 | + | 0.762256i | \(0.724092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.4164 | 2.01569 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.94427 | −0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4721 | 0.757737 | 0.378869 | − | 0.925450i | \(-0.376313\pi\) | ||||
0.378869 | + | 0.925450i | \(0.376313\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.8885 | −1.14368 | −0.571841 | − | 0.820364i | \(-0.693771\pi\) | ||||
−0.571841 | + | 0.820364i | \(0.693771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.2361 | −1.94049 | −0.970245 | − | 0.242126i | \(-0.922155\pi\) | ||||
−0.970245 | + | 0.242126i | \(0.922155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.4721 | −1.30945 | −0.654727 | − | 0.755865i | \(-0.727217\pi\) | ||||
−0.654727 | + | 0.755865i | \(0.727217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.4721 | 1.01574 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.4721 | −0.731406 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.52786 | −0.105685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.944272 | −0.0650064 | −0.0325032 | − | 0.999472i | \(-0.510348\pi\) | ||||
−0.0325032 | + | 0.999472i | \(0.510348\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.4721 | −1.25397 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.47214 | −0.300828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.6525 | −1.78478 | −0.892391 | − | 0.451263i | \(-0.850974\pi\) | ||||
−0.892391 | + | 0.451263i | \(0.850974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.94427 | 0.460908 | 0.230454 | − | 0.973083i | \(-0.425979\pi\) | ||||
0.230454 | + | 0.973083i | \(0.425979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.41641 | −0.616889 | −0.308445 | − | 0.951242i | \(-0.599808\pi\) | ||||
−0.308445 | + | 0.951242i | \(0.599808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.4164 | −2.31031 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.52786 | −0.228199 | −0.114099 | − | 0.993469i | \(-0.536398\pi\) | ||||
−0.114099 | + | 0.993469i | \(0.536398\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3607 | 1.44038 | 0.720189 | − | 0.693778i | \(-0.244055\pi\) | ||||
0.720189 | + | 0.693778i | \(0.244055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2361 | −0.717846 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.763932 | −0.0486078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0557 | 0.697831 | 0.348916 | − | 0.937154i | \(-0.386550\pi\) | ||||
0.348916 | + | 0.937154i | \(0.386550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9443 | 0.813799 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.52786 | 0.220062 | 0.110031 | − | 0.993928i | \(-0.464905\pi\) | ||||
0.110031 | + | 0.993928i | \(0.464905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.4164 | −1.70357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.94427 | −0.551527 | −0.275764 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275764 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.52786 | −0.0938559 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.5279 | −0.702866 | −0.351433 | − | 0.936213i | \(-0.614306\pi\) | ||||
−0.351433 | + | 0.936213i | \(0.614306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1246 | 1.28323 | 0.641614 | − | 0.767027i | \(-0.278265\pi\) | ||||
0.641614 | + | 0.767027i | \(0.278265\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.9443 | −0.659964 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.94427 | 0.176904 | 0.0884521 | − | 0.996080i | \(-0.471808\pi\) | ||||
0.0884521 | + | 0.996080i | \(0.471808\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.70820 | −0.579143 | −0.289571 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289571 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5279 | −0.804148 | −0.402074 | − | 0.915607i | \(-0.631711\pi\) | ||||
−0.402074 | + | 0.915607i | \(0.631711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4721 | 0.618151 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1803 | 0.711583 | 0.355792 | − | 0.934565i | \(-0.384211\pi\) | ||||
0.355792 | + | 0.934565i | \(0.384211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.52786 | −0.0889557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.47214 | 0.374293 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.4164 | 0.653702 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.2361 | −0.641276 | −0.320638 | − | 0.947202i | \(-0.603897\pi\) | ||||
−0.320638 | + | 0.947202i | \(0.603897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4164 | 1.55464 | 0.777321 | − | 0.629104i | \(-0.216578\pi\) | ||||
0.777321 | + | 0.629104i | \(0.216578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.88854 | −0.219793 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.76393 | 0.267569 | 0.133785 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133785 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94427 | −0.500783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.41641 | 0.190094 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.47214 | −0.303539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 35.4164 | 1.95257 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.18034 | 0.449632 | 0.224816 | − | 0.974401i | \(-0.427822\pi\) | ||||
0.224816 | + | 0.974401i | \(0.427822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.3607 | −1.98660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9443 | 0.596172 | 0.298086 | − | 0.954539i | \(-0.403652\pi\) | ||||
0.298086 | + | 0.954539i | \(0.403652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4164 | 0.618233 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0000 | 1.07366 | 0.536828 | − | 0.843692i | \(-0.319622\pi\) | ||||
0.536828 | + | 0.843692i | \(0.319622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.3607 | 1.62517 | 0.812585 | − | 0.582843i | \(-0.198060\pi\) | ||||
0.812585 | + | 0.582843i | \(0.198060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.5967 | −1.46883 | −0.734413 | − | 0.678702i | \(-0.762543\pi\) | ||||
−0.734413 | + | 0.678702i | \(0.762543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4721 | −0.768101 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.8328 | −0.888402 | −0.444201 | − | 0.895927i | \(-0.646512\pi\) | ||||
−0.444201 | + | 0.895927i | \(0.646512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4164 | −0.969285 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.4164 | 1.43504 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0000 | 1.46159 | 0.730794 | − | 0.682598i | \(-0.239150\pi\) | ||||
0.730794 | + | 0.682598i | \(0.239150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52786 | 0.0793227 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.9443 | −1.80935 | −0.904673 | − | 0.426107i | \(-0.859885\pi\) | ||||
−0.904673 | + | 0.426107i | \(0.859885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.47214 | −0.230327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5967 | 1.21208 | 0.606042 | − | 0.795433i | \(-0.292756\pi\) | ||||
0.606042 | + | 0.795433i | \(0.292756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0000 | −1.53293 | −0.766464 | − | 0.642287i | \(-0.777986\pi\) | ||||
−0.766464 | + | 0.642287i | \(0.777986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.9443 | 1.06742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8885 | 0.602773 | 0.301387 | − | 0.953502i | \(-0.402551\pi\) | ||||
0.301387 | + | 0.953502i | \(0.402551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.9443 | −1.46377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.9443 | −1.45634 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4721 | −0.826713 | −0.413356 | − | 0.910569i | \(-0.635644\pi\) | ||||
−0.413356 | + | 0.910569i | \(0.635644\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.18034 | −0.208756 | −0.104378 | − | 0.994538i | \(-0.533285\pi\) | ||||
−0.104378 | + | 0.994538i | \(0.533285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.70820 | 0.284346 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9443 | 0.839896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3607 | −0.512303 | −0.256151 | − | 0.966637i | \(-0.582455\pi\) | ||||
−0.256151 | + | 0.966637i | \(0.582455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.52786 | 0.0751813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53.3050 | 2.61664 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.5279 | −1.44253 | −0.721265 | − | 0.692659i | \(-0.756439\pi\) | ||||
−0.721265 | + | 0.692659i | \(0.756439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.05573 | −0.441349 | −0.220675 | − | 0.975347i | \(-0.570826\pi\) | ||||
−0.220675 | + | 0.975347i | \(0.570826\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.4721 | 1.18707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.4164 | −0.552479 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0000 | 0.481683 | 0.240842 | − | 0.970564i | \(-0.422577\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.472136 | 0.0226894 | 0.0113447 | − | 0.999936i | \(-0.496389\pi\) | ||||
0.0113447 | + | 0.999936i | \(0.496389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.94427 | −0.236517 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5279 | 0.645650 | 0.322825 | − | 0.946459i | \(-0.395368\pi\) | ||||
0.322825 | + | 0.946459i | \(0.395368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.5279 | 1.02282 | 0.511410 | − | 0.859337i | \(-0.329123\pi\) | ||||
0.511410 | + | 0.859337i | \(0.329123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.4164 | 1.86852 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.5410 | 1.72448 | 0.862239 | − | 0.506502i | \(-0.169062\pi\) | ||||
0.862239 | + | 0.506502i | \(0.169062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.47214 | −0.304761 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4721 | 0.490941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.3607 | −1.60732 | −0.803662 | − | 0.595085i | \(-0.797118\pi\) | ||||
−0.803662 | + | 0.595085i | \(0.797118\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.6525 | 1.05503 | 0.527515 | − | 0.849545i | \(-0.323124\pi\) | ||||
0.527515 | + | 0.849545i | \(0.323124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.7082 | −0.822970 | −0.411485 | − | 0.911417i | \(-0.634990\pi\) | ||||
−0.411485 | + | 0.911417i | \(0.634990\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.88854 | −0.0873914 | −0.0436957 | − | 0.999045i | \(-0.513913\pi\) | ||||
−0.0436957 | + | 0.999045i | \(0.513913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.3607 | 1.67898 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.94427 | 0.227338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.18034 | 0.191807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3050 | 1.06483 | 0.532415 | − | 0.846483i | \(-0.321285\pi\) | ||||
0.532415 | + | 0.846483i | \(0.321285\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.47214 | 0.386296 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.4721 | −0.657146 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2918 | 1.19140 | 0.595698 | − | 0.803209i | \(-0.296876\pi\) | ||||
0.595698 | + | 0.803209i | \(0.296876\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0557 | 0.498938 | 0.249469 | − | 0.968383i | \(-0.419744\pi\) | ||||
0.249469 | + | 0.968383i | \(0.419744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4721 | 0.649164 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.1803 | 1.79872 | 0.899360 | − | 0.437210i | \(-0.144033\pi\) | ||||
0.899360 | + | 0.437210i | \(0.144033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.7771 | 1.77357 | 0.886786 | − | 0.462180i | \(-0.152932\pi\) | ||||
0.886786 | + | 0.462180i | \(0.152932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.3607 | 2.15202 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1803 | −0.717181 | −0.358590 | − | 0.933495i | \(-0.616743\pi\) | ||||
−0.358590 | + | 0.933495i | \(0.616743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.4164 | −1.21283 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.8885 | 1.49331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8885 | −0.962657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9443 | −0.829964 | −0.414982 | − | 0.909830i | \(-0.636212\pi\) | ||||
−0.414982 | + | 0.909830i | \(0.636212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.0557 | 1.00816 | 0.504078 | − | 0.863658i | \(-0.331832\pi\) | ||||
0.504078 | + | 0.863658i | \(0.331832\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.5279 | −1.11201 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.23607 | −0.140170 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.8885 | 0.773389 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.94427 | −0.299111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 61.3050 | 2.62602 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.944272 | 0.0403742 | 0.0201871 | − | 0.999796i | \(-0.493574\pi\) | ||||
0.0201871 | + | 0.999796i | \(0.493574\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.41641 | 0.145544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.9443 | 1.23084 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7082 | −0.580835 | −0.290418 | − | 0.956900i | \(-0.593794\pi\) | ||||
−0.290418 | + | 0.956900i | \(0.593794\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.47214 | 0.104560 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.52786 | −0.0643918 | −0.0321959 | − | 0.999482i | \(-0.510250\pi\) | ||||
−0.0321959 | + | 0.999482i | \(0.510250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.47214 | −0.272285 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.3607 | −1.27279 | −0.636393 | − | 0.771365i | \(-0.719574\pi\) | ||||
−0.636393 | + | 0.771365i | \(0.719574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4721 | −1.44261 | −0.721307 | − | 0.692615i | \(-0.756458\pi\) | ||||
−0.721307 | + | 0.692615i | \(0.756458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.4164 | −1.47697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.9443 | −0.788660 | −0.394330 | − | 0.918969i | \(-0.629023\pi\) | ||||
−0.394330 | + | 0.918969i | \(0.629023\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.3050 | −2.21146 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.944272 | −0.0391077 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.58359 | −0.271734 | −0.135867 | − | 0.990727i | \(-0.543382\pi\) | ||||
−0.135867 | + | 0.990727i | \(0.543382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.36068 | −0.179679 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.2361 | −0.625670 | −0.312835 | − | 0.949807i | \(-0.601279\pi\) | ||||
−0.312835 | + | 0.949807i | \(0.601279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46.8328 | −1.91996 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.9443 | 1.01920 | 0.509598 | − | 0.860413i | \(-0.329794\pi\) | ||||
0.509598 | + | 0.860413i | \(0.329794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.8885 | 1.95341 | 0.976707 | − | 0.214576i | \(-0.0688371\pi\) | ||||
0.976707 | + | 0.214576i | \(0.0688371\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.6525 | 0.920954 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0000 | 1.13648 | 0.568242 | − | 0.822861i | \(-0.307624\pi\) | ||||
0.568242 | + | 0.822861i | \(0.307624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.9443 | −0.442758 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3607 | 1.22626 | 0.613128 | − | 0.789983i | \(-0.289911\pi\) | ||||
0.613128 | + | 0.789983i | \(0.289911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.59675 | −0.144800 | −0.0723998 | − | 0.997376i | \(-0.523066\pi\) | ||||
−0.0723998 | + | 0.997376i | \(0.523066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.6525 | 1.55357 | 0.776787 | − | 0.629763i | \(-0.216848\pi\) | ||||
0.776787 | + | 0.629763i | \(0.216848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.4164 | −1.57919 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.8885 | −1.51072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6525 | 0.742543 | 0.371272 | − | 0.928524i | \(-0.378922\pi\) | ||||
0.371272 | + | 0.928524i | \(0.378922\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.47214 | −0.137571 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.4164 | −0.845897 | −0.422949 | − | 0.906154i | \(-0.639005\pi\) | ||||
−0.422949 | + | 0.906154i | \(0.639005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1246 | 1.14856 | 0.574281 | − | 0.818658i | \(-0.305282\pi\) | ||||
0.574281 | + | 0.818658i | \(0.305282\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0000 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.944272 | −0.0370659 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.3607 | −0.405445 | −0.202722 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202722 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.8885 | 1.94931 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.8328 | −1.35689 | −0.678447 | − | 0.734649i | \(-0.737347\pi\) | ||||
−0.678447 | + | 0.734649i | \(0.737347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2492 | −1.40993 | −0.704966 | − | 0.709241i | \(-0.749038\pi\) | ||||
−0.704966 | + | 0.709241i | \(0.749038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.9443 | −1.12073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.05573 | 0.272383 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5836 | 0.716345 | 0.358172 | − | 0.933655i | \(-0.383400\pi\) | ||||
0.358172 | + | 0.933655i | \(0.383400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.3607 | 1.32059 | 0.660294 | − | 0.751007i | \(-0.270432\pi\) | ||||
0.660294 | + | 0.751007i | \(0.270432\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4721 | 0.555390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.0000 | −0.382639 | −0.191320 | − | 0.981528i | \(-0.561277\pi\) | ||||
−0.191320 | + | 0.981528i | \(0.561277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.3607 | −1.38927 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.472136 | −0.0179869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.5967 | −1.04983 | −0.524915 | − | 0.851155i | \(-0.675903\pi\) | ||||
−0.524915 | + | 0.851155i | \(0.675903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −70.8328 | −2.68684 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4721 | 0.548171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.47214 | −0.244101 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −48.3607 | −1.81879 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0000 | −0.525781 | −0.262891 | − | 0.964826i | \(-0.584676\pi\) | ||||
−0.262891 | + | 0.964826i | \(0.584676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.9443 | 1.38357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47214 | −0.242044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.47214 | −0.241370 | −0.120685 | − | 0.992691i | \(-0.538509\pi\) | ||||
−0.120685 | + | 0.992691i | \(0.538509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.8885 | −1.26208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.4721 | 0.908872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4721 | 0.388390 | 0.194195 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194195 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0557 | −0.408911 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.88854 | −0.291370 | −0.145685 | − | 0.989331i | \(-0.546539\pi\) | ||||
−0.145685 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.4721 | −0.827772 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.8197 | 0.876220 | 0.438110 | − | 0.898921i | \(-0.355648\pi\) | ||||
0.438110 | + | 0.898921i | \(0.355648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.52786 | 0.276171 | 0.138085 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138085 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 70.2492 | 2.57373 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8885 | −0.653633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3607 | −0.451048 | −0.225524 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225524 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 75.1935 | 2.73657 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.5836 | 0.384667 | 0.192334 | − | 0.981330i | \(-0.438394\pi\) | ||||
0.192334 | + | 0.981330i | \(0.438394\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.1803 | 1.16654 | 0.583268 | − | 0.812280i | \(-0.301774\pi\) | ||||
0.583268 | + | 0.812280i | \(0.301774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −61.3050 | −2.21939 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.472136 | −0.0170478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.832816 | 0.0300321 | 0.0150161 | − | 0.999887i | \(-0.495220\pi\) | ||||
0.0150161 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.7082 | −0.780790 | −0.390395 | − | 0.920647i | \(-0.627662\pi\) | ||||
−0.390395 | + | 0.920647i | \(0.627662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.2361 | −1.12203 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.47214 | 0.0885735 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.94427 | −0.320051 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.4164 | −1.54960 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7082 | 0.631229 | 0.315615 | − | 0.948887i | \(-0.397789\pi\) | ||||
0.315615 | + | 0.948887i | \(0.397789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.47214 | 0.230123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.52786 | 0.125278 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.0000 | 1.20434 | 0.602171 | − | 0.798367i | \(-0.294303\pi\) | ||||
0.602171 | + | 0.798367i | \(0.294303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.9443 | 1.73152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9443 | 0.597950 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.7771 | 2.38883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0557 | 0.459015 | 0.229507 | − | 0.973307i | \(-0.426288\pi\) | ||||
0.229507 | + | 0.973307i | \(0.426288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.81966 | 0.134126 | 0.0670632 | − | 0.997749i | \(-0.478637\pi\) | ||||
0.0670632 | + | 0.997749i | \(0.478637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4164 | −0.820241 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.88854 | −0.0660718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.12461 | 0.318451 | 0.159226 | − | 0.987242i | \(-0.449100\pi\) | ||||
0.159226 | + | 0.987242i | \(0.449100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3050 | 0.603213 | 0.301606 | − | 0.953433i | \(-0.402477\pi\) | ||||
0.301606 | + | 0.953433i | \(0.402477\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.7771 | −1.31364 | −0.656819 | − | 0.754048i | \(-0.728098\pi\) | ||||
−0.656819 | + | 0.754048i | \(0.728098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.5279 | 1.37286 | 0.686430 | − | 0.727196i | \(-0.259177\pi\) | ||||
0.686430 | + | 0.727196i | \(0.259177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.5279 | 0.538009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.3607 | 2.22729 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3607 | −0.495786 | −0.247893 | − | 0.968787i | \(-0.579738\pi\) | ||||
−0.247893 | + | 0.968787i | \(0.579738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.23607 | −0.111324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.6525 | −0.778348 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.8328 | 1.87964 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5279 | −0.394707 | −0.197353 | − | 0.980332i | \(-0.563235\pi\) | ||||
−0.197353 | + | 0.980332i | \(0.563235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.4164 | 1.27812 | 0.639060 | − | 0.769157i | \(-0.279324\pi\) | ||||
0.639060 | + | 0.769157i | \(0.279324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.9443 | −1.12404 | −0.562022 | − | 0.827122i | \(-0.689976\pi\) | ||||
−0.562022 | + | 0.827122i | \(0.689976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.8885 | −1.63014 | −0.815072 | − | 0.579359i | \(-0.803303\pi\) | ||||
−0.815072 | + | 0.579359i | \(0.803303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.47214 | 0.220059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8885 | −0.606827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2361 | −0.380720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.94427 | −0.167147 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.3050 | 0.922023 | 0.461011 | − | 0.887394i | \(-0.347487\pi\) | ||||
0.461011 | + | 0.887394i | \(0.347487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.63932 | −0.189994 | −0.0949968 | − | 0.995478i | \(-0.530284\pi\) | ||||
−0.0949968 | + | 0.995478i | \(0.530284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.63932 | −0.122473 | −0.0612364 | − | 0.998123i | \(-0.519504\pi\) | ||||
−0.0612364 | + | 0.998123i | \(0.519504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.3050 | 0.581043 | 0.290522 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290522 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.36068 | 0.279779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.8328 | −2.10027 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.5279 | −0.851402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.11146 | 0.0703428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.3607 | 1.87349 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.3607 | 0.676065 | 0.338033 | − | 0.941134i | \(-0.390239\pi\) | ||||
0.338033 | + | 0.941134i | \(0.390239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.5279 | 1.50841 | 0.754203 | − | 0.656642i | \(-0.228024\pi\) | ||||
0.754203 | + | 0.656642i | \(0.228024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.9443 | 1.09030 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.8885 | −1.64746 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.8885 | −0.458141 | −0.229070 | − | 0.973410i | \(-0.573569\pi\) | ||||
−0.229070 | + | 0.973410i | \(0.573569\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.47214 | −0.147202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.3607 | −1.52433 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.54102 | −0.280222 | −0.140111 | − | 0.990136i | \(-0.544746\pi\) | ||||
−0.140111 | + | 0.990136i | \(0.544746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65248 | 0.0869314 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.9443 | 0.946579 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.3050 | 1.02269 | 0.511344 | − | 0.859376i | \(-0.329148\pi\) | ||||
0.511344 | + | 0.859376i | \(0.329148\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.2361 | 1.01827 | 0.509133 | − | 0.860688i | \(-0.329966\pi\) | ||||
0.509133 | + | 0.860688i | \(0.329966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.9443 | −0.682039 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.4164 | −1.34585 | −0.672926 | − | 0.739710i | \(-0.734963\pi\) | ||||
−0.672926 | + | 0.739710i | \(0.734963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.47214 | 0.275017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.5279 | −1.02129 | −0.510644 | − | 0.859792i | \(-0.670593\pi\) | ||||
−0.510644 | + | 0.859792i | \(0.670593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.8885 | −1.09661 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.3607 | 1.17415 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.58359 | 0.0510836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.4164 | 1.65515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2361 | 0.489959 | 0.244979 | − | 0.969528i | \(-0.421219\pi\) | ||||
0.244979 | + | 0.969528i | \(0.421219\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.8328 | 1.63130 | 0.815651 | − | 0.578544i | \(-0.196379\pi\) | ||||
0.815651 | + | 0.578544i | \(0.196379\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.8328 | 2.27080 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.7082 | 0.438564 | 0.219282 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219282 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3607 | 0.778571 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5836 | 0.720305 | 0.360152 | − | 0.932893i | \(-0.382725\pi\) | ||||
0.360152 | + | 0.932893i | \(0.382725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 88.1378 | 2.80830 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | 0.508770 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.9443 | −1.30064 | −0.650319 | − | 0.759661i | \(-0.725365\pi\) | ||||
−0.650319 | + | 0.759661i | \(0.725365\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 59.7771 | 1.89506 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.8885 | −1.89669 | −0.948345 | − | 0.317242i | \(-0.897243\pi\) | ||||
−0.948345 | + | 0.317242i | \(0.897243\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3744.2.a.s.1.1 | 2 | ||
3.2 | odd | 2 | 1248.2.a.n.1.2 | yes | 2 | ||
4.3 | odd | 2 | 3744.2.a.r.1.1 | 2 | |||
8.3 | odd | 2 | 7488.2.a.cs.1.2 | 2 | |||
8.5 | even | 2 | 7488.2.a.ct.1.2 | 2 | |||
12.11 | even | 2 | 1248.2.a.l.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 2496.2.a.be.1.1 | 2 | |||
24.11 | even | 2 | 2496.2.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1248.2.a.l.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
1248.2.a.n.1.2 | yes | 2 | 3.2 | odd | 2 | ||
2496.2.a.be.1.1 | 2 | 24.5 | odd | 2 | |||
2496.2.a.bh.1.1 | 2 | 24.11 | even | 2 | |||
3744.2.a.r.1.1 | 2 | 4.3 | odd | 2 | |||
3744.2.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7488.2.a.cs.1.2 | 2 | 8.3 | odd | 2 | |||
7488.2.a.ct.1.2 | 2 | 8.5 | even | 2 |