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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) 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 | ||||||||
\(11\) | 6.47214 | 1.95142 | 0.975711 | − | 0.219061i | \(-0.0702993\pi\) | ||||
0.975711 | + | 0.219061i | \(0.0702993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47214 | −0.567147 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.52786 | −0.274412 | −0.137206 | − | 0.990543i | \(-0.543812\pi\) | ||||
−0.137206 | + | 0.990543i | \(0.543812\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.47214 | −1.12665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.94427 | 1.14163 | 0.570816 | − | 0.821078i | \(-0.306627\pi\) | ||||
0.570816 | + | 0.821078i | \(0.306627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.47214 | 0.716115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427 | 1.36399 | 0.681994 | − | 0.731357i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9443 | −1.88812 | −0.944058 | − | 0.329779i | \(-0.893026\pi\) | ||||
−0.944058 | + | 0.329779i | \(0.893026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.52786 | 0.484589 | 0.242295 | − | 0.970203i | \(-0.422100\pi\) | ||||
0.242295 | + | 0.970203i | \(0.422100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.47214 | 0.872703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.47214 | 0.327442 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.47214 | −0.554700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.52786 | −0.656037 | −0.328018 | − | 0.944671i | \(-0.606381\pi\) | ||||
−0.328018 | + | 0.944671i | \(0.606381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4721 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760422\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.47214 | −0.737568 | ||||||||
\(78\) | 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 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.47214 | 0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52786 | 0.158432 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47214 | −0.253636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.47214 | 0.860215 | 0.430108 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430108 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.47214 | 0.650474 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000 | 1.39305 | 0.696526 | − | 0.717532i | \(-0.254728\pi\) | ||||
0.696526 | + | 0.717532i | \(0.254728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9443 | −1.25137 | −0.625685 | − | 0.780076i | \(-0.715180\pi\) | ||||
−0.625685 | + | 0.780076i | \(0.715180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.94427 | −0.659121 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.472136 | 0.0444148 | 0.0222074 | − | 0.999753i | \(-0.492931\pi\) | ||||
0.0222074 | + | 0.999753i | \(0.492931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47214 | −0.413449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8885 | 2.80805 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.94427 | 0.438733 | 0.219367 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219367 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.94427 | −0.787499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.47214 | 0.214361 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.41641 | 0.629052 | 0.314526 | − | 0.949249i | \(-0.398155\pi\) | ||||
0.314526 | + | 0.949249i | \(0.398155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.9443 | 1.09010 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.9443 | −2.42044 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.9443 | 1.22428 | 0.612141 | − | 0.790748i | \(-0.290308\pi\) | ||||
0.612141 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.52786 | −0.122721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.472136 | 0.0376806 | 0.0188403 | − | 0.999823i | \(-0.494003\pi\) | ||||
0.0188403 | + | 0.999823i | \(0.494003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.52786 | −0.279778 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9443 | −1.32718 | −0.663589 | − | 0.748097i | \(-0.730968\pi\) | ||||
−0.663589 | + | 0.748097i | \(0.730968\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.47214 | −0.503855 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.47214 | −0.189049 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.94427 | 0.223849 | 0.111924 | − | 0.993717i | \(-0.464299\pi\) | ||||
0.111924 | + | 0.993717i | \(0.464299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.47214 | 0.483750 | 0.241875 | − | 0.970307i | \(-0.422238\pi\) | ||||
0.241875 | + | 0.970307i | \(0.422238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.05573 | −0.0784717 | −0.0392358 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392358 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.94427 | 0.510553 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9443 | −0.946579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.583592 | −0.0422272 | −0.0211136 | − | 0.999777i | \(-0.506721\pi\) | ||||
−0.0211136 | + | 0.999777i | \(0.506721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.47214 | 0.320256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5279 | −1.10631 | −0.553157 | − | 0.833077i | \(-0.686577\pi\) | ||||
−0.553157 | + | 0.833077i | \(0.686577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.4164 | −1.94350 | −0.971749 | − | 0.236017i | \(-0.924158\pi\) | ||||
−0.971749 | + | 0.236017i | \(0.924158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9443 | −1.16649 | −0.583246 | − | 0.812296i | \(-0.698218\pi\) | ||||
−0.583246 | + | 0.812296i | \(0.698218\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.52786 | 0.378763 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.94427 | 0.609994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.52786 | 0.103718 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.4721 | 0.842789 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.94427 | 0.601657 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9443 | 0.866813 | 0.433406 | − | 0.901199i | \(-0.357312\pi\) | ||||
0.433406 | + | 0.901199i | \(0.357312\pi\) | |||||||
\(224\) | 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 | ||||||||
\(229\) | −23.8885 | −1.57860 | −0.789300 | − | 0.614008i | \(-0.789556\pi\) | ||||
−0.789300 | + | 0.614008i | \(0.789556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.47214 | 0.425835 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.41641 | −0.616889 | −0.308445 | − | 0.951242i | \(-0.599808\pi\) | ||||
−0.308445 | + | 0.951242i | \(0.599808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9443 | −0.844391 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.9443 | 0.840821 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.4721 | 0.677386 | 0.338693 | − | 0.940897i | \(-0.390015\pi\) | ||||
0.338693 | + | 0.940897i | \(0.390015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9443 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0557 | 0.703459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9443 | 1.07380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.9443 | 1.06951 | 0.534756 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534756 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.8885 | −1.62760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9443 | 1.18171 | 0.590856 | − | 0.806777i | \(-0.298790\pi\) | ||||
0.590856 | + | 0.806777i | \(0.298790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.94427 | −0.431496 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.05573 | −0.435075 | −0.217537 | − | 0.976052i | \(-0.569802\pi\) | ||||
−0.217537 | + | 0.976052i | \(0.569802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.52786 | 0.216715 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.8885 | −0.724857 | −0.362429 | − | 0.932012i | \(-0.618052\pi\) | ||||
−0.362429 | + | 0.932012i | \(0.618052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.52786 | 0.0928111 | 0.0464056 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464056 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.47214 | −0.270666 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.47214 | 0.390284 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9443 | −1.13825 | −0.569125 | − | 0.822251i | \(-0.692718\pi\) | ||||
−0.569125 | + | 0.822251i | \(0.692718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.52786 | −0.0914708 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.9443 | −0.652881 | −0.326440 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326440 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000 | 0.713326 | 0.356663 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356663 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.47214 | 0.146437 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.47214 | −0.496645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.05573 | −0.295359 | −0.147679 | − | 0.989035i | \(-0.547180\pi\) | ||||
−0.147679 | + | 0.989035i | \(0.547180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.94427 | −0.520756 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.47214 | −0.375551 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.94427 | −0.515539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.0000 | −0.804279 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0557 | −0.859276 | −0.429638 | − | 0.903001i | \(-0.641359\pi\) | ||||
−0.429638 | + | 0.903001i | \(0.641359\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.8885 | −1.46800 | −0.734002 | − | 0.679147i | \(-0.762350\pi\) | ||||
−0.734002 | + | 0.679147i | \(0.762350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4164 | −0.984434 | −0.492217 | − | 0.870473i | \(-0.663813\pi\) | ||||
−0.492217 | + | 0.870473i | \(0.663813\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.3607 | −0.806576 | −0.403288 | − | 0.915073i | \(-0.632133\pi\) | ||||
−0.403288 | + | 0.915073i | \(0.632133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.9443 | 0.724740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.9443 | 0.722479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.94427 | 0.275107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.00000 | −0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.9443 | 0.713641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.94427 | 0.380544 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8885 | −1.30129 | −0.650646 | − | 0.759381i | \(-0.725502\pi\) | ||||
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.472136 | −0.0256429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.88854 | −0.535495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.00000 | −0.429463 | −0.214731 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214731 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8885 | 0.636379 | 0.318190 | − | 0.948027i | \(-0.396925\pi\) | ||||
0.318190 | + | 0.948027i | \(0.396925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.47214 | 0.238705 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.88854 | 0.419865 | 0.209932 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209932 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.52786 | −0.293389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | −0.105851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4721 | −0.974922 | −0.487461 | − | 0.873145i | \(-0.662077\pi\) | ||||
−0.487461 | + | 0.873145i | \(0.662077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.8885 | −1.62123 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.4721 | −0.652821 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.05573 | −0.159508 | −0.0797539 | − | 0.996815i | \(-0.525413\pi\) | ||||
−0.0797539 | + | 0.996815i | \(0.525413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.52786 | −0.183158 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.8885 | −1.94620 | −0.973102 | − | 0.230375i | \(-0.926005\pi\) | ||||
−0.973102 | + | 0.230375i | \(0.926005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.94427 | −0.253303 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.47214 | −0.329851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.94427 | 0.454663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.94427 | 0.352089 | 0.176044 | − | 0.984382i | \(-0.443670\pi\) | ||||
0.176044 | + | 0.984382i | \(0.443670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.9443 | −0.651297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4164 | 0.673350 | 0.336675 | − | 0.941621i | \(-0.390698\pi\) | ||||
0.336675 | + | 0.941621i | \(0.390698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.47214 | −0.123762 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.83282 | 0.340367 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.9443 | 2.22780 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.8885 | 0.587851 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.52786 | −0.174017 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427 | 0.440119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.9443 | −0.831762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.41641 | −0.363183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.8885 | −1.46015 | −0.730075 | − | 0.683367i | \(-0.760515\pi\) | ||||
−0.730075 | + | 0.683367i | \(0.760515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.9443 | −0.629372 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.9443 | 1.39744 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.4721 | 0.889771 | 0.444886 | − | 0.895587i | \(-0.353244\pi\) | ||||
0.444886 | + | 0.895587i | \(0.353244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4721 | 0.791600 | 0.395800 | − | 0.918337i | \(-0.370467\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.88854 | 0.473033 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.52786 | −0.0729210 | −0.0364605 | − | 0.999335i | \(-0.511608\pi\) | ||||
−0.0364605 | + | 0.999335i | \(0.511608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.00000 | −0.380091 | −0.190046 | − | 0.981775i | \(-0.560864\pi\) | ||||
−0.190046 | + | 0.981775i | \(0.560864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9443 | −0.706840 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.9443 | −0.609522 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0000 | −0.751746 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.47214 | 0.209657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.94427 | 0.324839 | 0.162420 | − | 0.986722i | \(-0.448070\pi\) | ||||
0.162420 | + | 0.986722i | \(0.448070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.88854 | −0.181108 | −0.0905538 | − | 0.995892i | \(-0.528864\pi\) | ||||
−0.0905538 | + | 0.995892i | \(0.528864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9443 | −0.973363 | −0.486681 | − | 0.873580i | \(-0.661793\pi\) | ||||
−0.486681 | + | 0.873580i | \(0.661793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.52786 | 0.0708530 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.94427 | −0.413892 | −0.206946 | − | 0.978352i | \(-0.566352\pi\) | ||||
−0.206946 | + | 0.978352i | \(0.566352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.472136 | −0.0217549 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.8885 | 2.66172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.47214 | −0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.52786 | 0.161530 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8885 | 0.817348 | 0.408674 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408674 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0557 | −1.41602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.47214 | 0.384700 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9443 | 0.949076 | 0.474538 | − | 0.880235i | \(-0.342615\pi\) | ||||
0.474538 | + | 0.880235i | \(0.342615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.9443 | 0.766246 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3050 | −0.961479 | −0.480740 | − | 0.876863i | \(-0.659632\pi\) | ||||
−0.480740 | + | 0.876863i | \(0.659632\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.47214 | 0.290901 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.52786 | 0.247959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.8885 | −0.621737 | −0.310868 | − | 0.950453i | \(-0.600620\pi\) | ||||
−0.310868 | + | 0.950453i | \(0.600620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | −0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.0000 | −1.42681 | −0.713405 | − | 0.700752i | \(-0.752848\pi\) | ||||
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00000 | −0.310881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.8885 | 1.05884 | 0.529421 | − | 0.848360i | \(-0.322409\pi\) | ||||
0.529421 | + | 0.848360i | \(0.322409\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4721 | 0.551735 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.47214 | 0.109147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −83.7771 | −3.68451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.94427 | −0.129239 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8885 | −0.871333 | −0.435666 | − | 0.900108i | \(-0.643487\pi\) | ||||
−0.435666 | + | 0.900108i | \(0.643487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.94427 | −0.391106 | −0.195553 | − | 0.980693i | \(-0.562650\pi\) | ||||
−0.195553 | + | 0.980693i | \(0.562650\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.05573 | 0.133110 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.94427 | −0.388148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9443 | −0.559630 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.47214 | −0.279293 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.47214 | 0.278775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8885 | 0.511128 | 0.255564 | − | 0.966792i | \(-0.417739\pi\) | ||||
0.255564 | + | 0.966792i | \(0.417739\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.05573 | 0.0453056 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.88854 | 0.251776 | 0.125888 | − | 0.992044i | \(-0.459822\pi\) | ||||
0.125888 | + | 0.992044i | \(0.459822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.94427 | −0.210633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.94427 | −0.294768 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.4721 | −0.867432 | −0.433716 | − | 0.901050i | \(-0.642798\pi\) | ||||
−0.433716 | + | 0.901050i | \(0.642798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.0000 | −1.69182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.8885 | 0.585332 | 0.292666 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292666 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.472136 | 0.0198629 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.8885 | −1.67221 | −0.836107 | − | 0.548566i | \(-0.815174\pi\) | ||||
−0.836107 | + | 0.548566i | \(0.815174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.583592 | 0.0243799 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3607 | 0.431321 | 0.215660 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215660 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.9443 | 0.702967 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.8328 | 0.945639 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.47214 | −0.184900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.77709 | 0.155632 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.5279 | 0.638731 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.8885 | 0.980985 | 0.490492 | − | 0.871445i | \(-0.336817\pi\) | ||||
0.490492 | + | 0.871445i | \(0.336817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.4164 | 1.12208 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.3607 | −0.505044 | −0.252522 | − | 0.967591i | \(-0.581260\pi\) | ||||
−0.252522 | + | 0.967591i | \(0.581260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.9443 | 1.58857 | 0.794285 | − | 0.607545i | \(-0.207846\pi\) | ||||
0.794285 | + | 0.607545i | \(0.207846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.8885 | 1.25580 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.8328 | −1.57618 | −0.788088 | − | 0.615563i | \(-0.788929\pi\) | ||||
−0.788088 | + | 0.615563i | \(0.788929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.8885 | 2.34192 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.94427 | 0.280477 | 0.140238 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140238 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4721 | 0.663143 | 0.331572 | − | 0.943430i | \(-0.392421\pi\) | ||||
0.331572 | + | 0.943430i | \(0.392421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4164 | 1.58428 | 0.792140 | − | 0.610340i | \(-0.208967\pi\) | ||||
0.792140 | + | 0.610340i | \(0.208967\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.8885 | −0.553773 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.8328 | −1.22744 | −0.613718 | − | 0.789526i | \(-0.710327\pi\) | ||||
−0.613718 | + | 0.789526i | \(0.710327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.9443 | 0.673474 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.94427 | 0.196207 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.47214 | −0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.52786 | −0.218679 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.8328 | 0.664856 | 0.332428 | − | 0.943129i | \(-0.392132\pi\) | ||||
0.332428 | + | 0.943129i | \(0.392132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0557 | −0.593740 | −0.296870 | − | 0.954918i | \(-0.595943\pi\) | ||||
−0.296870 | + | 0.954918i | \(0.595943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.94427 | −0.352180 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.88854 | 0.0742463 | 0.0371232 | − | 0.999311i | \(-0.488181\pi\) | ||||
0.0371232 | + | 0.999311i | \(0.488181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −57.8885 | −2.27232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.52786 | −0.0598817 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.5836 | 0.883764 | 0.441882 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441882 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4721 | −0.486584 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3050 | 0.829923 | 0.414962 | − | 0.909839i | \(-0.363795\pi\) | ||||
0.414962 | + | 0.909839i | \(0.363795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8885 | 1.39590 | 0.697951 | − | 0.716145i | \(-0.254095\pi\) | ||||
0.697951 | + | 0.716145i | \(0.254095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.94427 | −0.347367 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.47214 | 0.0958653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9443 | −0.500454 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.9443 | 0.499708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.83282 | 0.340480 | 0.170240 | − | 0.985403i | \(-0.445546\pi\) | ||||
0.170240 | + | 0.985403i | \(0.445546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.0557 | −0.809237 | −0.404619 | − | 0.914485i | \(-0.632596\pi\) | ||||
−0.404619 | + | 0.914485i | \(0.632596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.47214 | −0.325131 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.944272 | −0.0361846 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.88854 | −0.0722631 | −0.0361316 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361316 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.52786 | 0.134793 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.8885 | 0.911405 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.7771 | −0.601059 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.3607 | 1.68756 | 0.843780 | − | 0.536689i | \(-0.180325\pi\) | ||||
0.843780 | + | 0.536689i | \(0.180325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.47214 | −0.245856 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.41641 | 0.281320 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.41641 | 0.356161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1672 | −0.647473 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.9443 | 0.487509 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.0000 | −0.526524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7771 | −0.968079 | −0.484039 | − | 0.875046i | \(-0.660831\pi\) | ||||
−0.484039 | + | 0.875046i | \(0.660831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9443 | −0.485448 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.11146 | 0.228876 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.9443 | −1.08245 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.4721 | −0.391089 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.83282 | 0.254821 | 0.127411 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127411 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9443 | 0.704545 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.8328 | 1.44023 | 0.720115 | − | 0.693855i | \(-0.244089\pi\) | ||||
0.720115 | + | 0.693855i | \(0.244089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.8885 | −0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.5836 | −0.390914 | −0.195457 | − | 0.980712i | \(-0.562619\pi\) | ||||
−0.195457 | + | 0.980712i | \(0.562619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.8885 | −0.953617 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.88854 | −0.216614 | −0.108307 | − | 0.994118i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994118i | \(0.534543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.0557 | −0.406142 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.8328 | −1.27789 | −0.638946 | − | 0.769252i | \(-0.720629\pi\) | ||||
−0.638946 | + | 0.769252i | \(0.720629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.9443 | 0.547516 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.9443 | −0.619958 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9443 | 0.472973 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9443 | 0.764267 | 0.382134 | − | 0.924107i | \(-0.375189\pi\) | ||||
0.382134 | + | 0.924107i | \(0.375189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.9443 | −0.617484 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.8885 | −1.15901 | −0.579504 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579504 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.8885 | 0.939695 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.8885 | −1.01096 | −0.505479 | − | 0.862839i | \(-0.668684\pi\) | ||||
−0.505479 | + | 0.862839i | \(0.668684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.0000 | 1.44432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.8328 | −1.90520 | −0.952600 | − | 0.304226i | \(-0.901602\pi\) | ||||
−0.952600 | + | 0.304226i | \(0.901602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9443 | −0.682261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.9443 | 1.54460 | 0.772299 | − | 0.635259i | \(-0.219107\pi\) | ||||
0.772299 | + | 0.635259i | \(0.219107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.52786 | −0.0548825 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.94427 | 0.249124 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.94427 | 0.177147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.7771 | −1.28020 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.472136 | 0.0168513 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0557 | 1.10702 | 0.553509 | − | 0.832843i | \(-0.313289\pi\) | ||||
0.553509 | + | 0.832843i | \(0.313289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.05573 | 0.251191 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.472136 | −0.0167872 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.94427 | −0.317620 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.52786 | −0.125120 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.9443 | 0.671041 | 0.335520 | − | 0.942033i | \(-0.391088\pi\) | ||||
0.335520 | + | 0.942033i | \(0.391088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.8885 | 0.915871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −80.7214 | −2.84859 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.8885 | 0.418497 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.9443 | 1.36921 | 0.684604 | − | 0.728915i | \(-0.259975\pi\) | ||||
0.684604 | + | 0.728915i | \(0.259975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.4164 | 1.94593 | 0.972967 | − | 0.230946i | \(-0.0741820\pi\) | ||||
0.972967 | + | 0.230946i | \(0.0741820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.52786 | −0.0535845 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9443 | −0.593532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.1115 | −0.773582 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.47214 | 0.156269 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.7771 | −1.17883 | −0.589414 | − | 0.807831i | \(-0.700641\pi\) | ||||
−0.589414 | + | 0.807831i | \(0.700641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.9443 | −1.56666 | −0.783329 | − | 0.621607i | \(-0.786480\pi\) | ||||
−0.783329 | + | 0.621607i | \(0.786480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.47214 | −0.225331 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9443 | 0.450116 | 0.225058 | − | 0.974345i | \(-0.427743\pi\) | ||||
0.225058 | + | 0.974345i | \(0.427743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0557 | 0.453444 | 0.226722 | − | 0.973959i | \(-0.427199\pi\) | ||||
0.226722 | + | 0.973959i | \(0.427199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.9443 | 0.657170 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.52786 | 0.0528107 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.8328 | −1.89304 | −0.946520 | − | 0.322647i | \(-0.895427\pi\) | ||||
−0.946520 | + | 0.322647i | \(0.895427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9443 | 0.376941 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.00000 | 0.240807 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.8885 | −1.06134 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.7771 | −0.952186 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.3050 | 1.07186 | 0.535931 | − | 0.844262i | \(-0.319961\pi\) | ||||
0.535931 | + | 0.844262i | \(0.319961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.47214 | −0.0845453 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.8328 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283427\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.4721 | 1.72209 | 0.861044 | − | 0.508531i | \(-0.169811\pi\) | ||||
0.861044 | + | 0.508531i | \(0.169811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.8885 | −0.745095 | −0.372547 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372547 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.94427 | 0.100108 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −83.7771 | −2.84194 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.8885 | 0.606130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.47214 | 0.286738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.8328 | 1.91911 | 0.959554 | − | 0.281525i | \(-0.0908402\pi\) | ||||
0.959554 | + | 0.281525i | \(0.0908402\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.05573 | 0.170525 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.8885 | −0.939589 | −0.469794 | − | 0.882776i | \(-0.655672\pi\) | ||||
−0.469794 | + | 0.882776i | \(0.655672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.8885 | −1.27505 | −0.637526 | − | 0.770429i | \(-0.720042\pi\) | ||||
−0.637526 | + | 0.770429i | \(0.720042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.94427 | 0.300658 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8328 | 1.03526 | 0.517632 | − | 0.855603i | \(-0.326814\pi\) | ||||
0.517632 | + | 0.855603i | \(0.326814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.94427 | −0.165826 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.47214 | 0.216825 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.0000 | 1.07084 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.47214 | 0.216340 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.8885 | −0.597281 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.05573 | −0.101914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.05573 | −0.235060 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.94427 | 0.297647 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.05573 | −0.0350936 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.8885 | 1.78934 | 0.894670 | − | 0.446728i | \(-0.147411\pi\) | ||||
0.894670 | + | 0.446728i | \(0.147411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.2492 | −1.53231 | −0.766153 | − | 0.642659i | \(-0.777831\pi\) | ||||
−0.766153 | + | 0.642659i | \(0.777831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −109.666 | −3.62940 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0557 | 1.15638 | 0.578191 | − | 0.815902i | \(-0.303759\pi\) | ||||
0.578191 | + | 0.815902i | \(0.303759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.0557 | 0.496103 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.7214 | 0.813713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.94427 | 0.228326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.1115 | −0.528600 | −0.264300 | − | 0.964441i | \(-0.585141\pi\) | ||||
−0.264300 | + | 0.964441i | \(0.585141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47214 | −0.0810210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.8885 | 0.847553 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9443 | −0.423323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.4721 | −1.71419 | −0.857095 | − | 0.515158i | \(-0.827733\pi\) | ||||
−0.857095 | + | 0.515158i | \(0.827733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.4164 | 0.568363 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.8885 | −0.581300 | −0.290650 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290650 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.7771 | 1.81060 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.3607 | 0.465677 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.4164 | −1.08246 | −0.541232 | − | 0.840873i | \(-0.682042\pi\) | ||||
−0.541232 | + | 0.840873i | \(0.682042\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.583592 | −0.0188846 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.9443 | −0.418429 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.52786 | −0.113921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6656 | −0.924698 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.9443 | −0.417123 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8885 | −0.832519 | −0.416260 | − | 0.909246i | \(-0.636659\pi\) | ||||
−0.416260 | + | 0.909246i | \(0.636659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.94427 | −0.158833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.9443 | 1.31396 | 0.656982 | − | 0.753906i | \(-0.271833\pi\) | ||||
0.656982 | + | 0.753906i | \(0.271833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.41641 | −0.237759 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.47214 | 0.143223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.5836 | 0.978456 | 0.489228 | − | 0.872156i | \(-0.337279\pi\) | ||||
0.489228 | + | 0.872156i | \(0.337279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9443 | −0.413701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.8328 | 0.728254 | 0.364127 | − | 0.931349i | \(-0.381367\pi\) | ||||
0.364127 | + | 0.931349i | \(0.381367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.5279 | −0.494759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.9443 | −0.412021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.7771 | −1.13765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.94427 | −0.157060 | −0.0785300 | − | 0.996912i | \(-0.525023\pi\) | ||||
−0.0785300 | + | 0.996912i | \(0.525023\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.944272 | −0.0299656 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.4164 | −0.869159 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.41641 | 0.171539 | 0.0857697 | − | 0.996315i | \(-0.472665\pi\) | ||||
0.0857697 | + | 0.996315i | \(0.472665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.94427 | −0.219707 |
(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.cs.1.2 | 2 | ||
4.3 | odd | 2 | 6720.2.a.cx.1.1 | 2 | |||
8.3 | odd | 2 | 105.2.a.b.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 1680.2.a.v.1.1 | 2 | |||
24.5 | odd | 2 | 5040.2.a.bw.1.2 | 2 | |||
24.11 | even | 2 | 315.2.a.d.1.2 | 2 | |||
40.3 | even | 4 | 525.2.d.c.274.3 | 4 | |||
40.19 | odd | 2 | 525.2.a.g.1.2 | 2 | |||
40.27 | even | 4 | 525.2.d.c.274.2 | 4 | |||
40.29 | even | 2 | 8400.2.a.cx.1.1 | 2 | |||
56.3 | even | 6 | 735.2.i.i.226.2 | 4 | |||
56.11 | odd | 6 | 735.2.i.k.226.2 | 4 | |||
56.19 | even | 6 | 735.2.i.i.361.2 | 4 | |||
56.27 | even | 2 | 735.2.a.k.1.1 | 2 | |||
56.51 | odd | 6 | 735.2.i.k.361.2 | 4 | |||
120.59 | even | 2 | 1575.2.a.r.1.1 | 2 | |||
120.83 | odd | 4 | 1575.2.d.d.1324.1 | 4 | |||
120.107 | odd | 4 | 1575.2.d.d.1324.4 | 4 | |||
168.83 | odd | 2 | 2205.2.a.w.1.2 | 2 | |||
280.139 | even | 2 | 3675.2.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.a.b.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
315.2.a.d.1.2 | 2 | 24.11 | even | 2 | |||
525.2.a.g.1.2 | 2 | 40.19 | odd | 2 | |||
525.2.d.c.274.2 | 4 | 40.27 | even | 4 | |||
525.2.d.c.274.3 | 4 | 40.3 | even | 4 | |||
735.2.a.k.1.1 | 2 | 56.27 | even | 2 | |||
735.2.i.i.226.2 | 4 | 56.3 | even | 6 | |||
735.2.i.i.361.2 | 4 | 56.19 | even | 6 | |||
735.2.i.k.226.2 | 4 | 56.11 | odd | 6 | |||
735.2.i.k.361.2 | 4 | 56.51 | odd | 6 | |||
1575.2.a.r.1.1 | 2 | 120.59 | even | 2 | |||
1575.2.d.d.1324.1 | 4 | 120.83 | odd | 4 | |||
1575.2.d.d.1324.4 | 4 | 120.107 | odd | 4 | |||
1680.2.a.v.1.1 | 2 | 8.5 | even | 2 | |||
2205.2.a.w.1.2 | 2 | 168.83 | odd | 2 | |||
3675.2.a.y.1.2 | 2 | 280.139 | even | 2 | |||
5040.2.a.bw.1.2 | 2 | 24.5 | odd | 2 | |||
6720.2.a.cs.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6720.2.a.cx.1.1 | 2 | 4.3 | odd | 2 | |||
8400.2.a.cx.1.1 | 2 | 40.29 | even | 2 |