Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6720,2,Mod(1,6720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6720.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: | \(53.6594701583\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3360) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6720.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | 1.16243 | 0.581215 | − | 0.813750i | \(-0.302578\pi\) | ||||
0.581215 | + | 0.813750i | \(0.302578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.47214 | −1.39281 | −0.696405 | − | 0.717649i | \(-0.745218\pi\) | ||||
−0.696405 | + | 0.717649i | \(0.745218\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.47214 | 0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9443 | 1.70921 | 0.854604 | − | 0.519280i | \(-0.173800\pi\) | ||||
0.854604 | + | 0.519280i | \(0.173800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4721 | 1.59699 | 0.798493 | − | 0.602004i | \(-0.205631\pi\) | ||||
0.798493 | + | 0.602004i | \(0.205631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.47214 | 0.360598 | 0.180299 | − | 0.983612i | \(-0.442293\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.47214 | −0.626224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.47214 | 0.302019 | 0.151010 | − | 0.988532i | \(-0.451748\pi\) | ||||
0.151010 | + | 0.988532i | \(0.451748\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.47214 | −0.779154 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.4164 | −1.82959 | −0.914796 | − | 0.403917i | \(-0.867648\pi\) | ||||
−0.914796 | + | 0.403917i | \(0.867648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.47214 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9443 | −1.45634 | −0.728172 | − | 0.685394i | \(-0.759630\pi\) | ||||
−0.728172 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.9443 | −1.85988 | −0.929938 | − | 0.367717i | \(-0.880140\pi\) | ||||
−0.929938 | + | 0.367717i | \(0.880140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47214 | 0.485071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.47214 | −0.908308 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.94427 | −0.736091 | −0.368046 | − | 0.929808i | \(-0.619973\pi\) | ||||
−0.368046 | + | 0.929808i | \(0.619973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47214 | 0.671129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.47214 | −0.454077 | −0.227038 | − | 0.973886i | \(-0.572904\pi\) | ||||
−0.227038 | + | 0.973886i | \(0.572904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.94427 | 0.690981 | 0.345490 | − | 0.938422i | \(-0.387713\pi\) | ||||
0.345490 | + | 0.938422i | \(0.387713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8885 | 1.76261 | 0.881305 | − | 0.472547i | \(-0.156665\pi\) | ||||
0.881305 | + | 0.472547i | \(0.156665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.47214 | −0.625685 | −0.312842 | − | 0.949805i | \(-0.601281\pi\) | ||||
−0.312842 | + | 0.949805i | \(0.601281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.47214 | −0.804140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.47214 | 0.603530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.47214 | 0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.47214 | 0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9443 | 0.986812 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4721 | 0.922020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.944272 | 0.0825014 | 0.0412507 | − | 0.999149i | \(-0.486866\pi\) | ||||
0.0412507 | + | 0.999149i | \(0.486866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.9443 | 0.935032 | 0.467516 | − | 0.883985i | \(-0.345149\pi\) | ||||
0.467516 | + | 0.883985i | \(0.345149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.47214 | 0.208191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.47214 | 0.703573 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.52786 | −0.289014 | −0.144507 | − | 0.989504i | \(-0.546160\pi\) | ||||
−0.144507 | + | 0.989504i | \(0.546160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.9443 | 1.70442 | 0.852210 | − | 0.523199i | \(-0.175262\pi\) | ||||
0.852210 | + | 0.523199i | \(0.175262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.47214 | −0.361551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.47214 | −0.519854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4721 | −1.31462 | −0.657310 | − | 0.753620i | \(-0.728306\pi\) | ||||
−0.657310 | + | 0.753620i | \(0.728306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.47214 | 0.510076 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.47214 | −0.193633 | −0.0968163 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968163 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4721 | 0.810358 | 0.405179 | − | 0.914237i | \(-0.367209\pi\) | ||||
0.405179 | + | 0.914237i | \(0.367209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4164 | 0.997234 | 0.498617 | − | 0.866822i | \(-0.333841\pi\) | ||||
0.498617 | + | 0.866822i | \(0.333841\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4721 | −0.921967 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.47214 | 0.622884 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.4164 | 1.69435 | 0.847176 | − | 0.531313i | \(-0.178301\pi\) | ||||
0.847176 | + | 0.531313i | \(0.178301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9443 | −1.36364 | −0.681819 | − | 0.731521i | \(-0.738811\pi\) | ||||
−0.681819 | + | 0.731521i | \(0.738811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.47214 | −0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9443 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4164 | −0.809288 | −0.404644 | − | 0.914474i | \(-0.632605\pi\) | ||||
−0.404644 | + | 0.914474i | \(0.632605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.47214 | 0.174371 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.47214 | 0.594627 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.9443 | −0.764381 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.47214 | −0.449845 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.4164 | −1.05631 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4721 | −0.714194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.47214 | 0.572494 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.0000 | −1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.8885 | −1.73363 | −0.866813 | − | 0.498634i | \(-0.833835\pi\) | ||||
−0.866813 | + | 0.498634i | \(0.833835\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.944272 | 0.0626735 | 0.0313368 | − | 0.999509i | \(-0.490024\pi\) | ||||
0.0313368 | + | 0.999509i | \(0.490024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.4721 | −1.35284 | −0.676418 | − | 0.736518i | \(-0.736469\pi\) | ||||
−0.676418 | + | 0.736518i | \(0.736469\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.94427 | 0.192886 | 0.0964428 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964428 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.47214 | −0.161264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9443 | −0.840821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3607 | 1.31702 | 0.658511 | − | 0.752571i | \(-0.271186\pi\) | ||||
0.658511 | + | 0.752571i | \(0.271186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.9443 | −1.07380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.05573 | −0.445354 | −0.222677 | − | 0.974892i | \(-0.571479\pi\) | ||||
−0.222677 | + | 0.974892i | \(0.571479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.47214 | 0.280056 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.47214 | 0.528477 | 0.264239 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264239 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.47214 | 0.526433 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.47214 | −0.524412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.52786 | 0.587513 | 0.293757 | − | 0.955880i | \(-0.405094\pi\) | ||||
0.293757 | + | 0.955880i | \(0.405094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.94427 | −0.424983 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.0000 | −1.34136 | −0.670682 | − | 0.741745i | \(-0.733998\pi\) | ||||
−0.670682 | + | 0.741745i | \(0.733998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.3607 | −1.47981 | −0.739903 | − | 0.672714i | \(-0.765129\pi\) | ||||
−0.739903 | + | 0.672714i | \(0.765129\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.47214 | −0.270666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.47214 | 0.268705 | 0.134352 | − | 0.990934i | \(-0.457105\pi\) | ||||
0.134352 | + | 0.990934i | \(0.457105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.47214 | 0.387477 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.8885 | −1.90231 | −0.951156 | − | 0.308712i | \(-0.900102\pi\) | ||||
−0.951156 | + | 0.308712i | \(0.900102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.88854 | −0.350038 | −0.175019 | − | 0.984565i | \(-0.555999\pi\) | ||||
−0.175019 | + | 0.984565i | \(0.555999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.9443 | −0.646020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.47214 | −0.262161 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.05573 | 0.295359 | 0.147679 | − | 0.989035i | \(-0.452820\pi\) | ||||
0.147679 | + | 0.989035i | \(0.452820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.9443 | −1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.4721 | −0.603604 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.94427 | 0.398938 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.4721 | 0.714152 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9443 | −1.42364 | −0.711822 | − | 0.702360i | \(-0.752130\pi\) | ||||
−0.711822 | + | 0.702360i | \(0.752130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8885 | 1.01764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.8885 | 1.92164 | 0.960822 | − | 0.277168i | \(-0.0893958\pi\) | ||||
0.960822 | + | 0.277168i | \(0.0893958\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.472136 | 0.0266867 | 0.0133434 | − | 0.999911i | \(-0.495753\pi\) | ||||
0.0133434 | + | 0.999911i | \(0.495753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8885 | 0.892390 | 0.446195 | − | 0.894936i | \(-0.352779\pi\) | ||||
0.446195 | + | 0.894936i | \(0.352779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.47214 | −0.361239 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.47214 | 0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0000 | −0.774202 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.47214 | −0.136293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.47214 | −0.464270 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.47214 | −0.135067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.94427 | 0.378279 | 0.189139 | − | 0.981950i | \(-0.439430\pi\) | ||||
0.189139 | + | 0.981950i | \(0.439430\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.47214 | 0.348448 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.52786 | −0.511483 | −0.255741 | − | 0.966745i | \(-0.582320\pi\) | ||||
−0.255741 | + | 0.966745i | \(0.582320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.5279 | −0.831188 | −0.415594 | − | 0.909550i | \(-0.636426\pi\) | ||||
−0.415594 | + | 0.909550i | \(0.636426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.4164 | −0.926982 | −0.463491 | − | 0.886102i | \(-0.653403\pi\) | ||||
−0.463491 | + | 0.886102i | \(0.653403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.4164 | 0.818218 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.47214 | 0.236691 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4164 | −0.813647 | −0.406823 | − | 0.913507i | \(-0.633364\pi\) | ||||
−0.406823 | + | 0.913507i | \(0.633364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.47214 | −0.443452 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9443 | 1.09328 | 0.546641 | − | 0.837367i | \(-0.315906\pi\) | ||||
0.546641 | + | 0.837367i | \(0.315906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9443 | 0.569736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58359 | 0.133773 | 0.0668867 | − | 0.997761i | \(-0.478693\pi\) | ||||
0.0668867 | + | 0.997761i | \(0.478693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.8885 | −1.95136 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0557 | 0.978827 | 0.489414 | − | 0.872052i | \(-0.337211\pi\) | ||||
0.489414 | + | 0.872052i | \(0.337211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.4164 | −1.19652 | −0.598261 | − | 0.801301i | \(-0.704142\pi\) | ||||
−0.598261 | + | 0.801301i | \(0.704142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4721 | 0.532329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.4721 | −1.24079 | −0.620393 | − | 0.784291i | \(-0.713027\pi\) | ||||
−0.620393 | + | 0.784291i | \(0.713027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.9443 | 1.46377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.944272 | 0.0476322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9443 | 0.651297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.41641 | 0.0710875 | 0.0355437 | − | 0.999368i | \(-0.488684\pi\) | ||||
0.0355437 | + | 0.999368i | \(0.488684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.9443 | −1.34553 | −0.672766 | − | 0.739855i | \(-0.734894\pi\) | ||||
−0.672766 | + | 0.739855i | \(0.734894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.9443 | 1.44182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.05573 | 0.249990 | 0.124995 | − | 0.992157i | \(-0.460109\pi\) | ||||
0.124995 | + | 0.992157i | \(0.460109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9443 | 0.539841 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9443 | 0.831762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0557 | −0.735520 | −0.367760 | − | 0.929921i | \(-0.619875\pi\) | ||||
−0.367760 | + | 0.929921i | \(0.619875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.8885 | −1.16426 | −0.582128 | − | 0.813097i | \(-0.697780\pi\) | ||||
−0.582128 | + | 0.813097i | \(0.697780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.47214 | 0.120199 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47214 | −0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4721 | 0.603569 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.4721 | 1.66046 | 0.830232 | − | 0.557418i | \(-0.188208\pi\) | ||||
0.830232 | + | 0.557418i | \(0.188208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3607 | 0.882358 | 0.441179 | − | 0.897419i | \(-0.354560\pi\) | ||||
0.441179 | + | 0.897419i | \(0.354560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.47214 | 0.406208 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.4721 | −1.45436 | −0.727178 | − | 0.686449i | \(-0.759168\pi\) | ||||
−0.727178 | + | 0.686449i | \(0.759168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.52786 | −0.0725910 | −0.0362955 | − | 0.999341i | \(-0.511556\pi\) | ||||
−0.0362955 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.94427 | 0.329190 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.52786 | −0.166862 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.8328 | 1.54948 | 0.774738 | − | 0.632282i | \(-0.217882\pi\) | ||||
0.774738 | + | 0.632282i | \(0.217882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.9443 | 0.984048 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.47214 | 0.209657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.9443 | −1.63462 | −0.817312 | − | 0.576195i | \(-0.804537\pi\) | ||||
−0.817312 | + | 0.576195i | \(0.804537\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.47214 | −0.208741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.8328 | −1.34288 | −0.671439 | − | 0.741060i | \(-0.734323\pi\) | ||||
−0.671439 | + | 0.741060i | \(0.734323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.05573 | −0.142012 | −0.0710059 | − | 0.997476i | \(-0.522621\pi\) | ||||
−0.0710059 | + | 0.997476i | \(0.522621\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.47214 | −0.300138 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.8885 | −1.38308 | −0.691538 | − | 0.722340i | \(-0.743067\pi\) | ||||
−0.691538 | + | 0.722340i | \(0.743067\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.47214 | −0.114153 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4721 | −0.758996 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.88854 | −0.451819 | −0.225910 | − | 0.974148i | \(-0.572535\pi\) | ||||
−0.225910 | + | 0.974148i | \(0.572535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.8885 | −1.72757 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.47214 | 0.294492 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.47214 | 0.203069 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0557 | 0.863497 | 0.431749 | − | 0.901994i | \(-0.357897\pi\) | ||||
0.431749 | + | 0.901994i | \(0.357897\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.47214 | −0.111794 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.8885 | 1.70641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4164 | 0.691520 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0557 | 0.494922 | 0.247461 | − | 0.968898i | \(-0.420404\pi\) | ||||
0.247461 | + | 0.968898i | \(0.420404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4721 | 0.467861 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.5279 | 0.959880 | 0.479940 | − | 0.877301i | \(-0.340658\pi\) | ||||
0.479940 | + | 0.877301i | \(0.340658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.94427 | −0.309016 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000 | 0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0000 | −0.975133 | −0.487566 | − | 0.873086i | \(-0.662115\pi\) | ||||
−0.487566 | + | 0.873086i | \(0.662115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.47214 | −0.374785 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8885 | −0.788263 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.0000 | −1.48957 | −0.744784 | − | 0.667306i | \(-0.767447\pi\) | ||||
−0.744784 | + | 0.667306i | \(0.767447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.9443 | 1.09074 | 0.545368 | − | 0.838196i | \(-0.316390\pi\) | ||||
0.545368 | + | 0.838196i | \(0.316390\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.9443 | −1.26083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.9443 | 2.12001 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.47214 | 0.279815 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0000 | −0.690451 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9443 | 0.642504 | 0.321252 | − | 0.946994i | \(-0.395896\pi\) | ||||
0.321252 | + | 0.946994i | \(0.395896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.4164 | 0.575753 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.4164 | −0.659158 | −0.329579 | − | 0.944128i | \(-0.606907\pi\) | ||||
−0.329579 | + | 0.944128i | \(0.606907\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4721 | −0.532298 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.47214 | 0.359622 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0000 | −0.423714 | −0.211857 | − | 0.977301i | \(-0.567951\pi\) | ||||
−0.211857 | + | 0.977301i | \(0.567951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.8328 | 1.98082 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.8328 | 1.37642 | 0.688212 | − | 0.725510i | \(-0.258396\pi\) | ||||
0.688212 | + | 0.725510i | \(0.258396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.94427 | −0.206911 | −0.103456 | − | 0.994634i | \(-0.532990\pi\) | ||||
−0.103456 | + | 0.994634i | \(0.532990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.4164 | 0.978234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.47214 | −0.269907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.3607 | 1.76350 | 0.881749 | − | 0.471719i | \(-0.156366\pi\) | ||||
0.881749 | + | 0.471719i | \(0.156366\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.9443 | −0.787297 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.9443 | 0.702967 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.88854 | 0.243046 | 0.121523 | − | 0.992589i | \(-0.461222\pi\) | ||||
0.121523 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.9443 | −0.614725 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.4721 | −0.512169 | −0.256085 | − | 0.966654i | \(-0.582433\pi\) | ||||
−0.256085 | + | 0.966654i | \(0.582433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.47214 | −0.183340 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.4164 | −0.467242 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.47214 | −0.101009 | −0.0505044 | − | 0.998724i | \(-0.516083\pi\) | ||||
−0.0505044 | + | 0.998724i | \(0.516083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.05573 | −0.369391 | −0.184695 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184695 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.47214 | 0.100673 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.88854 | 0.401364 | 0.200682 | − | 0.979656i | \(-0.435684\pi\) | ||||
0.200682 | + | 0.979656i | \(0.435684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.47214 | 0.343308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0557 | 0.447267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5279 | 0.950281 | 0.475141 | − | 0.879910i | \(-0.342397\pi\) | ||||
0.475141 | + | 0.879910i | \(0.342397\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.9443 | −0.441316 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.9443 | −1.56784 | −0.783919 | − | 0.620864i | \(-0.786782\pi\) | ||||
−0.783919 | + | 0.620864i | \(0.786782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.9443 | 1.80646 | 0.903231 | − | 0.429154i | \(-0.141188\pi\) | ||||
0.903231 | + | 0.429154i | \(0.141188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.47214 | −0.259718 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.94427 | 0.278216 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.8885 | 1.51072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.8885 | −1.34908 | −0.674541 | − | 0.738238i | \(-0.735658\pi\) | ||||
−0.674541 | + | 0.738238i | \(0.735658\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.4164 | −0.609864 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.94427 | 0.274282 | 0.137141 | − | 0.990552i | \(-0.456209\pi\) | ||||
0.137141 | + | 0.990552i | \(0.456209\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4721 | −0.412340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.4164 | 1.23511 | 0.617553 | − | 0.786529i | \(-0.288124\pi\) | ||||
0.617553 | + | 0.786529i | \(0.288124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.47214 | −0.253663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.8885 | 1.56096 | 0.780480 | − | 0.625181i | \(-0.214975\pi\) | ||||
0.780480 | + | 0.625181i | \(0.214975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.944272 | −0.0368958 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.47214 | 0.330530 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.8328 | 0.889440 | 0.444720 | − | 0.895670i | \(-0.353303\pi\) | ||||
0.444720 | + | 0.895670i | \(0.353303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.63932 | 0.0637622 | 0.0318811 | − | 0.999492i | \(-0.489850\pi\) | ||||
0.0318811 | + | 0.999492i | \(0.489850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.0000 | −0.776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.8328 | 2.12314 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.8885 | −1.00091 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7771 | −0.993634 | −0.496817 | − | 0.867855i | \(-0.665498\pi\) | ||||
−0.496817 | + | 0.867855i | \(0.665498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8885 | −0.918111 | −0.459056 | − | 0.888408i | \(-0.651812\pi\) | ||||
−0.459056 | + | 0.888408i | \(0.651812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.47214 | 0.171625 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.944272 | 0.0361846 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.3607 | −1.23825 | −0.619123 | − | 0.785294i | \(-0.712512\pi\) | ||||
−0.619123 | + | 0.785294i | \(0.712512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9443 | −0.418159 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4721 | −0.781061 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.94427 | −0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.88854 | −0.376178 | −0.188089 | − | 0.982152i | \(-0.560229\pi\) | ||||
−0.188089 | + | 0.982152i | \(0.560229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.9443 | −1.85390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4164 | 0.657809 | 0.328904 | − | 0.944363i | \(-0.393321\pi\) | ||||
0.328904 | + | 0.944363i | \(0.393321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.47214 | −0.0931060 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.94427 | −0.261166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.8328 | 1.53351 | 0.766754 | − | 0.641941i | \(-0.221870\pi\) | ||||
0.766754 | + | 0.641941i | \(0.221870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9443 | −0.485448 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.8885 | −1.56874 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.3607 | 0.760384 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.8885 | −0.666204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.00000 | −0.223142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.47214 | −0.314647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0557 | 0.410034 | 0.205017 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205017 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.8328 | −1.73217 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.58359 | 0.0954272 | 0.0477136 | − | 0.998861i | \(-0.484807\pi\) | ||||
0.0477136 | + | 0.998861i | \(0.484807\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0000 | 0.588570 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4164 | 0.712319 | 0.356159 | − | 0.934425i | \(-0.384086\pi\) | ||||
0.356159 | + | 0.934425i | \(0.384086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.52786 | 0.129251 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.9443 | −0.619958 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.47214 | 0.236487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9443 | −1.05619 | −0.528096 | − | 0.849185i | \(-0.677094\pi\) | ||||
−0.528096 | + | 0.849185i | \(0.677094\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.05573 | −0.257125 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.9443 | −0.762240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.4721 | 0.744072 | 0.372036 | − | 0.928218i | \(-0.378660\pi\) | ||||
0.372036 | + | 0.928218i | \(0.378660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.111456 | −0.00404028 | −0.00202014 | − | 0.999998i | \(-0.500643\pi\) | ||||
−0.00202014 | + | 0.999998i | \(0.500643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | 0.506834 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.47214 | 0.161690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.8885 | −0.645918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.47214 | 0.305117 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.0557 | 0.757322 | 0.378661 | − | 0.925535i | \(-0.376385\pi\) | ||||
0.378661 | + | 0.925535i | \(0.376385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.47214 | 0.232486 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.47214 | 0.303936 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.47214 | −0.302769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4721 | 0.587916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.7771 | 0.847562 | 0.423781 | − | 0.905765i | \(-0.360703\pi\) | ||||
0.423781 | + | 0.905765i | \(0.360703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.52786 | 0.339201 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.7771 | −1.98070 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.00000 | 0.0709327 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.0557 | −0.391124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.94427 | −0.245364 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.47214 | −0.228113 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0000 | −0.774437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8328 | −0.451178 | −0.225589 | − | 0.974223i | \(-0.572431\pi\) | ||||
−0.225589 | + | 0.974223i | \(0.572431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7771 | 0.975385 | 0.487693 | − | 0.873015i | \(-0.337839\pi\) | ||||
0.487693 | + | 0.873015i | \(0.337839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.3607 | −0.854366 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.47214 | 0.0865951 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.47214 | −0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.3050 | −1.09255 | −0.546275 | − | 0.837606i | \(-0.683955\pi\) | ||||
−0.546275 | + | 0.837606i | \(0.683955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.05573 | 0.106516 | 0.0532580 | − | 0.998581i | \(-0.483039\pi\) | ||||
0.0532580 | + | 0.998581i | \(0.483039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.4164 | −0.396987 | −0.198494 | − | 0.980102i | \(-0.563605\pi\) | ||||
−0.198494 | + | 0.980102i | \(0.563605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.4164 | −1.16060 | −0.580300 | − | 0.814403i | \(-0.697065\pi\) | ||||
−0.580300 | + | 0.814403i | \(0.697065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.47214 | 0.155137 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.47214 | −0.154950 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.4721 | −0.362403 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.47214 | 0.223710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.8885 | 1.72234 | 0.861172 | − | 0.508314i | \(-0.169731\pi\) | ||||
0.861172 | + | 0.508314i | \(0.169731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −31.8885 | −1.09830 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.00000 | −0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0000 | 0.377964 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.88854 | −0.202094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.8328 | 1.87964 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.5279 | 1.07949 | 0.539747 | − | 0.841827i | \(-0.318520\pi\) | ||||
0.539747 | + | 0.841827i | \(0.318520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.3607 | 0.627189 | 0.313594 | − | 0.949557i | \(-0.398467\pi\) | ||||
0.313594 | + | 0.949557i | \(0.398467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.94427 | −0.168696 | −0.0843482 | − | 0.996436i | \(-0.526881\pi\) | ||||
−0.0843482 | + | 0.996436i | \(0.526881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.9443 | −0.372980 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.3607 | 1.64622 | 0.823108 | − | 0.567884i | \(-0.192238\pi\) | ||||
0.823108 | + | 0.567884i | \(0.192238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00000 | 0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.00000 | 0.101885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0557 | 0.374609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.47214 | −0.151359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.3050 | −1.59737 | −0.798687 | − | 0.601746i | \(-0.794472\pi\) | ||||
−0.798687 | + | 0.601746i | \(0.794472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.05573 | 0.170525 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.8328 | −1.10617 | −0.553083 | − | 0.833126i | \(-0.686549\pi\) | ||||
−0.553083 | + | 0.833126i | \(0.686549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.3050 | 0.851579 | 0.425790 | − | 0.904822i | \(-0.359996\pi\) | ||||
0.425790 | + | 0.904822i | \(0.359996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.5836 | −0.825436 | −0.412718 | − | 0.910859i | \(-0.635421\pi\) | ||||
−0.412718 | + | 0.910859i | \(0.635421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.0000 | 0.534821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.9443 | −0.966421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.8328 | −1.82878 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.94427 | 0.297977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.4721 | −0.348491 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.4164 | −0.445976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3607 | −1.20734 | −0.603668 | − | 0.797236i | \(-0.706295\pi\) | ||||
−0.603668 | + | 0.797236i | \(0.706295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.94427 | 0.230327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.583592 | −0.0193353 | −0.00966764 | − | 0.999953i | \(-0.503077\pi\) | ||||
−0.00966764 | + | 0.999953i | \(0.503077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4721 | 0.412316 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.944272 | −0.0311826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.7214 | 1.87107 | 0.935533 | − | 0.353241i | \(-0.114920\pi\) | ||||
0.935533 | + | 0.353241i | \(0.114920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.9443 | −0.821942 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −68.9443 | −2.26933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.47214 | −0.278562 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.8885 | 0.587537 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.11146 | 0.134893 | 0.0674463 | − | 0.997723i | \(-0.478515\pi\) | ||||
0.0674463 | + | 0.997723i | \(0.478515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.8885 | 1.10946 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.3050 | 1.02269 | 0.511344 | − | 0.859376i | \(-0.329148\pi\) | ||||
0.511344 | + | 0.859376i | \(0.329148\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.472136 | 0.0154076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −70.8328 | −2.30663 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.3607 | 1.83148 | 0.915738 | − | 0.401776i | \(-0.131607\pi\) | ||||
0.915738 | + | 0.401776i | \(0.131607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.8885 | 1.22991 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.8885 | 0.515221 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.7771 | 1.35329 | 0.676646 | − | 0.736308i | \(-0.263433\pi\) | ||||
0.676646 | + | 0.736308i | \(0.263433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.4164 | −0.757737 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9443 | −0.353409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8885 | 0.351243 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.47214 | −0.208562 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.9443 | 0.609838 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.05573 | 0.0982656 | 0.0491328 | − | 0.998792i | \(-0.484354\pi\) | ||||
0.0491328 | + | 0.998792i | \(0.484354\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.47214 | 0.143223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.8328 | −0.794472 | −0.397236 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397236 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.2492 | −0.964800 | −0.482400 | − | 0.875951i | \(-0.660235\pi\) | ||||
−0.482400 | + | 0.875951i | \(0.660235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.9443 | 0.476164 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.47214 | −0.0786890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.7771 | −2.15519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9443 | 1.17357 | 0.586787 | − | 0.809742i | \(-0.300393\pi\) | ||||
0.586787 | + | 0.809742i | \(0.300393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.0000 | 1.01549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.4164 | 0.361924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.4164 | 0.551583 | 0.275792 | − | 0.961217i | \(-0.411060\pi\) | ||||
0.275792 | + | 0.961217i | \(0.411060\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.47214 | −0.268047 |
(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 | 6720.2.a.cv.1.2 | 2 | ||
4.3 | odd | 2 | 6720.2.a.cp.1.2 | 2 | |||
8.3 | odd | 2 | 3360.2.a.bh.1.1 | yes | 2 | ||
8.5 | even | 2 | 3360.2.a.bd.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bd.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
3360.2.a.bh.1.1 | yes | 2 | 8.3 | odd | 2 | ||
6720.2.a.cp.1.2 | 2 | 4.3 | odd | 2 | |||
6720.2.a.cv.1.2 | 2 | 1.1 | even | 1 | trivial |