Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | 2.28825 | 1.32112 | 0.660560 | − | 0.750774i | \(-0.270319\pi\) | ||||
0.660560 | + | 0.750774i | \(0.270319\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.03631 | −1.11947 | −0.559735 | − | 0.828671i | \(-0.689097\pi\) | ||||
−0.559735 | + | 0.828671i | \(0.689097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.08036 | 0.262027 | 0.131013 | − | 0.991381i | \(-0.458177\pi\) | ||||
0.131013 | + | 0.991381i | \(0.458177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.47214 | −1.41234 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.40492 | 1.54403 | 0.772016 | − | 0.635603i | \(-0.219248\pi\) | ||||
0.772016 | + | 0.635603i | \(0.219248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.74806 | −0.336415 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.9814 | −2.08570 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.86474 | −1.12856 | −0.564278 | − | 0.825585i | \(-0.690845\pi\) | ||||
−0.564278 | + | 0.825585i | \(0.690845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.23607 | −1.47895 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.48528 | −1.29399 | −0.646997 | − | 0.762493i | \(-0.723975\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.48528 | −1.23771 | −0.618853 | − | 0.785507i | \(-0.712402\pi\) | ||||
−0.618853 | + | 0.785507i | \(0.712402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.86474 | 0.942944 | 0.471472 | − | 0.881881i | \(-0.343723\pi\) | ||||
0.471472 | + | 0.881881i | \(0.343723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.28825 | −0.303086 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4721 | −1.36336 | −0.681678 | − | 0.731652i | \(-0.738749\pi\) | ||||
−0.681678 | + | 0.731652i | \(0.738749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70820 | 0.218713 | 0.109357 | − | 0.994003i | \(-0.465121\pi\) | ||||
0.109357 | + | 0.994003i | \(0.465121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.32456 | −0.796819 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62054 | −0.197981 | −0.0989905 | − | 0.995088i | \(-0.531561\pi\) | ||||
−0.0989905 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.9443 | 2.03985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.52786 | −0.181324 | −0.0906621 | − | 0.995882i | \(-0.528898\pi\) | ||||
−0.0906621 | + | 0.995882i | \(0.528898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7295 | 1.60691 | 0.803457 | − | 0.595363i | \(-0.202992\pi\) | ||||
0.803457 | + | 0.595363i | \(0.202992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.8098 | 1.68774 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4164 | −1.28445 | −0.642223 | − | 0.766518i | \(-0.721988\pi\) | ||||
−0.642223 | + | 0.766518i | \(0.721988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.24419 | 0.575625 | 0.287812 | − | 0.957687i | \(-0.407072\pi\) | ||||
0.287812 | + | 0.957687i | \(0.407072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2333 | 1.09713 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.9443 | −1.58409 | −0.792045 | − | 0.610463i | \(-0.790983\pi\) | ||||
−0.792045 | + | 0.610463i | \(0.790983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4164 | 1.19676 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.15298 | −0.949120 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.44897 | −0.451725 | −0.225862 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225862 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.7082 | −1.17672 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.763932 | 0.0760141 | 0.0380070 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380070 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3500 | 1.51248 | 0.756241 | − | 0.654293i | \(-0.227034\pi\) | ||||
0.756241 | + | 0.654293i | \(0.227034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4304 | 1.58838 | 0.794192 | − | 0.607666i | \(-0.207894\pi\) | ||||
0.794192 | + | 0.607666i | \(0.207894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.7082 | −1.49096 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.1089 | −1.13911 | −0.569556 | − | 0.821952i | \(-0.692885\pi\) | ||||
−0.569556 | + | 0.821952i | \(0.692885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.02546 | −0.834404 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.05573 | −0.280118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.7295 | −1.23794 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1058 | 0.896747 | 0.448374 | − | 0.893846i | \(-0.352003\pi\) | ||||
0.448374 | + | 0.893846i | \(0.352003\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.4164 | −1.70952 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.08036 | 0.0923016 | 0.0461508 | − | 0.998934i | \(-0.485305\pi\) | ||||
0.0461508 | + | 0.998934i | \(0.485305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7082 | 1.33235 | 0.666176 | − | 0.745794i | \(-0.267930\pi\) | ||||
0.666176 | + | 0.745794i | \(0.267930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.4164 | −1.63516 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.1344 | 1.76735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.28825 | 0.188731 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.6525 | 1.52807 | 0.764035 | − | 0.645175i | \(-0.223215\pi\) | ||||
0.764035 | + | 0.645175i | \(0.223215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.41577 | 0.195303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3863 | 1.54720 | 0.773599 | − | 0.633676i | \(-0.218455\pi\) | ||||
0.773599 | + | 0.633676i | \(0.218455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.7082 | 1.24574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.9443 | −1.65064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.70401 | 0.364007 | 0.182004 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182004 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.29180 | 0.253215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23607 | −0.170996 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1893 | 1.00276 | 0.501382 | − | 0.865226i | \(-0.332825\pi\) | ||||
0.501382 | + | 0.865226i | \(0.332825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.9628 | −1.80116 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5279 | −1.01112 | −0.505560 | − | 0.862791i | \(-0.668714\pi\) | ||||
−0.505560 | + | 0.862791i | \(0.668714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.90879 | 0.288946 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.65685 | −0.413670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.94427 | 0.359643 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9443 | −1.51547 | −0.757737 | − | 0.652560i | \(-0.773695\pi\) | ||||
−0.757737 | + | 0.652560i | \(0.773695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.44897 | −0.320244 | −0.160122 | − | 0.987097i | \(-0.551189\pi\) | ||||
−0.160122 | + | 0.987097i | \(0.551189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6491 | 0.901212 | 0.450606 | − | 0.892723i | \(-0.351208\pi\) | ||||
0.450606 | + | 0.892723i | \(0.351208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.6491 | −0.887794 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.5579 | 1.15085 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.23607 | 0.362186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4164 | −0.785938 | −0.392969 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392969 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.49613 | −0.239551 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137 | 0.768025 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.4164 | 2.12292 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.36068 | −0.293331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.6668 | 1.91967 | 0.959836 | − | 0.280560i | \(-0.0905202\pi\) | ||||
0.959836 | + | 0.280560i | \(0.0905202\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3500 | −1.01882 | −0.509408 | − | 0.860525i | \(-0.670136\pi\) | ||||
−0.509408 | + | 0.860525i | \(0.670136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.70820 | −0.377209 | −0.188604 | − | 0.982053i | \(-0.560396\pi\) | ||||
−0.188604 | + | 0.982053i | \(0.560396\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.8885 | 2.22970 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.6491 | −0.828671 | −0.414335 | − | 0.910124i | \(-0.635986\pi\) | ||||
−0.414335 | + | 0.910124i | \(0.635986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.1235 | −1.69691 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.88854 | 0.380898 | 0.190449 | − | 0.981697i | \(-0.439006\pi\) | ||||
0.190449 | + | 0.981697i | \(0.439006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.8328 | 1.59962 | 0.799811 | − | 0.600252i | \(-0.204933\pi\) | ||||
0.799811 | + | 0.600252i | \(0.204933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.2588 | −1.23545 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.03631 | 0.256824 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8885 | 1.88655 | 0.943274 | − | 0.332015i | \(-0.107728\pi\) | ||||
0.943274 | + | 0.332015i | \(0.107728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.7727 | −2.43762 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.70401 | −0.293428 | −0.146714 | − | 0.989179i | \(-0.546870\pi\) | ||||
−0.146714 | + | 0.989179i | \(0.546870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.4164 | 1.20648 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.56564 | −0.589843 | −0.294921 | − | 0.955522i | \(-0.595293\pi\) | ||||
−0.294921 | + | 0.955522i | \(0.595293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −34.1962 | −2.09277 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.94427 | −0.179515 | −0.0897577 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897577 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1246 | −1.16174 | −0.580869 | − | 0.813997i | \(-0.697287\pi\) | ||||
−0.580869 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.1235 | 1.58107 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.24109 | 0.194738 | 0.0973691 | − | 0.995248i | \(-0.468957\pi\) | ||||
0.0973691 | + | 0.995248i | \(0.468957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.94427 | −0.535480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41641 | 0.0844958 | 0.0422479 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422479 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5579 | −0.984265 | −0.492133 | − | 0.870520i | \(-0.663782\pi\) | ||||
−0.492133 | + | 0.870520i | \(0.663782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706 | 1.00174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8328 | −0.931342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1803 | −0.596782 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.86474 | 0.401042 | 0.200521 | − | 0.979689i | \(-0.435736\pi\) | ||||
0.200521 | + | 0.979689i | \(0.435736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.15298 | 0.531110 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.8885 | −1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.74806 | 0.100424 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.03631 | −0.230364 | −0.115182 | − | 0.993344i | \(-0.536745\pi\) | ||||
−0.115182 | + | 0.993344i | \(0.536745\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.1246 | 1.99817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.70820 | 0.210273 | 0.105136 | − | 0.994458i | \(-0.466472\pi\) | ||||
0.105136 | + | 0.994458i | \(0.466472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.4589 | −1.55207 | −0.776036 | − | 0.630689i | \(-0.782772\pi\) | ||||
−0.776036 | + | 0.630689i | \(0.782772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.1893 | −0.740784 | −0.370392 | − | 0.928875i | \(-0.620777\pi\) | ||||
−0.370392 | + | 0.928875i | \(0.620777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.4164 | −1.31107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 37.5967 | 2.09845 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08036 | −0.0601130 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.57649 | 0.253081 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4164 | −1.06722 | −0.533611 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533611 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.3500 | −0.841176 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.27740 | −0.396425 | −0.198213 | − | 0.980159i | \(-0.563514\pi\) | ||||
−0.198213 | + | 0.980159i | \(0.563514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.7082 | −1.50490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.9443 | 1.13420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.8639 | −1.87159 | −0.935795 | − | 0.352544i | \(-0.885317\pi\) | ||||
−0.935795 | + | 0.352544i | \(0.885317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.41641 | −0.0758186 | −0.0379093 | − | 0.999281i | \(-0.512070\pi\) | ||||
−0.0379093 | + | 0.999281i | \(0.512070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.05573 | 0.376607 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8902 | −0.845750 | −0.422875 | − | 0.906188i | \(-0.638979\pi\) | ||||
−0.422875 | + | 0.906188i | \(0.638979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.99226 | −0.370069 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1246 | −0.587135 | −0.293567 | − | 0.955938i | \(-0.594842\pi\) | ||||
−0.293567 | + | 0.955938i | \(0.594842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 37.5648 | 1.97164 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.48528 | −0.442928 | −0.221464 | − | 0.975169i | \(-0.571084\pi\) | ||||
−0.221464 | + | 0.975169i | \(0.571084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.4164 | −0.698430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.4164 | −1.00805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3237 | 1.77721 | 0.888606 | − | 0.458670i | \(-0.151674\pi\) | ||||
0.888606 | + | 0.458670i | \(0.151674\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.0509 | −0.929670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.1246 | 1.18471 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.6777 | −1.20987 | −0.604936 | − | 0.796274i | \(-0.706801\pi\) | ||||
−0.604936 | + | 0.796274i | \(0.706801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.9737 | −0.964486 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.94427 | 0.149281 | 0.0746403 | − | 0.997211i | \(-0.476219\pi\) | ||||
0.0746403 | + | 0.997211i | \(0.476219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.7000 | −1.54079 | −0.770395 | − | 0.637566i | \(-0.779941\pi\) | ||||
−0.770395 | + | 0.637566i | \(0.779941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.47214 | 0.324012 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.47214 | 0.223328 | 0.111664 | − | 0.993746i | \(-0.464382\pi\) | ||||
0.111664 | + | 0.993746i | \(0.464382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1452 | 0.804252 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.9442 | 1.78169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.41641 | −0.465611 | −0.232806 | − | 0.972523i | \(-0.574791\pi\) | ||||
−0.232806 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47214 | 0.121941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.6197 | 1.45749 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.9442 | 1.76020 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.05573 | −0.149282 | −0.0746410 | − | 0.997210i | \(-0.523781\pi\) | ||||
−0.0746410 | + | 0.997210i | \(0.523781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.9737 | −0.922531 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.83153 | −0.233814 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 48.3607 | 2.33488 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4721 | 0.504425 | 0.252213 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252213 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9774 | 1.82508 | 0.912540 | − | 0.408989i | \(-0.134118\pi\) | ||||
0.912540 | + | 0.408989i | \(0.134118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.40492 | −0.354225 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.8328 | 1.66248 | 0.831240 | − | 0.555914i | \(-0.187632\pi\) | ||||
0.831240 | + | 0.555914i | \(0.187632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.23607 | 0.106479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.24419 | −0.249159 | −0.124580 | − | 0.992210i | \(-0.539758\pi\) | ||||
−0.124580 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.6814 | 2.01876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.52786 | −0.355262 | −0.177631 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177631 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.4164 | 1.47934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.3060 | −0.860089 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9473 | 1.77510 | 0.887551 | − | 0.460710i | \(-0.152405\pi\) | ||||
0.887551 | + | 0.460710i | \(0.152405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.88854 | −0.0881497 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8885 | −0.553705 | −0.276852 | − | 0.960912i | \(-0.589291\pi\) | ||||
−0.276852 | + | 0.960912i | \(0.589291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.5285 | −1.55820 | −0.779100 | − | 0.626900i | \(-0.784324\pi\) | ||||
−0.779100 | + | 0.626900i | \(0.784324\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7264 | −0.542632 | −0.271316 | − | 0.962490i | \(-0.587459\pi\) | ||||
−0.271316 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.58359 | 0.211651 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.3607 | 2.04403 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.4295 | 2.04287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3500 | 0.702829 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.76393 | 0.309052 | 0.154526 | − | 0.987989i | \(-0.450615\pi\) | ||||
0.154526 | + | 0.987989i | \(0.450615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7082 | 1.26339 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −47.9256 | −2.18069 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7658 | −0.805044 | −0.402522 | − | 0.915410i | \(-0.631866\pi\) | ||||
−0.402522 | + | 0.915410i | \(0.631866\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.4164 | 0.878040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8885 | −1.34885 | −0.674426 | − | 0.738343i | \(-0.735609\pi\) | ||||
−0.674426 | + | 0.738343i | \(0.735609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.83153 | 0.217601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.32145 | 0.193844 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1246 | 1.03520 | 0.517600 | − | 0.855623i | \(-0.326826\pi\) | ||||
0.517600 | + | 0.855623i | \(0.326826\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7639 | 0.480897 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.1853 | −1.74719 | −0.873593 | − | 0.486656i | \(-0.838216\pi\) | ||||
−0.873593 | + | 0.486656i | \(0.838216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.53244 | 0.334527 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.4164 | −1.65845 | −0.829227 | − | 0.558913i | \(-0.811219\pi\) | ||||
−0.829227 | + | 0.558913i | \(0.811219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.8328 | −1.71786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.74806 | 0.0771789 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.4295 | 1.95401 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.1803 | 1.32477 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.8885 | 1.57231 | 0.786153 | − | 0.618032i | \(-0.212070\pi\) | ||||
0.786153 | + | 0.618032i | \(0.212070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.62365 | −0.158451 | −0.0792255 | − | 0.996857i | \(-0.525245\pi\) | ||||
−0.0792255 | + | 0.996857i | \(0.525245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.32145 | −0.188245 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.8328 | 1.38404 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.4164 | −1.01619 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.2179 | 1.04899 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.9551 | −1.33581 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.23607 | −0.225533 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.70820 | −0.0734414 | −0.0367207 | − | 0.999326i | \(-0.511691\pi\) | ||||
−0.0367207 | + | 0.999326i | \(0.511691\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.7295 | 0.589188 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.20788 | −0.0516453 | −0.0258227 | − | 0.999667i | \(-0.508221\pi\) | ||||
−0.0258227 | + | 0.999667i | \(0.508221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.81966 | 0.163019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.47214 | −0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.2905 | 1.37313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.5687 | 0.490184 | 0.245092 | − | 0.969500i | \(-0.421182\pi\) | ||||
0.245092 | + | 0.969500i | \(0.421182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.2492 | 1.44859 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.9443 | −0.546508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.3531 | 0.731347 | 0.365673 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365673 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 30.2874 | 1.27195 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0557 | −0.882702 | −0.441351 | − | 0.897335i | \(-0.645501\pi\) | ||||
−0.441351 | + | 0.897335i | \(0.645501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1246 | −0.632945 | −0.316473 | − | 0.948602i | \(-0.602499\pi\) | ||||
−0.316473 | + | 0.948602i | \(0.602499\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −47.9256 | −2.00212 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65685 | 0.235498 | 0.117749 | − | 0.993043i | \(-0.462432\pi\) | ||||
0.117749 | + | 0.993043i | \(0.462432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1803 | −0.423080 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.8328 | −0.615369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.9442 | −1.48866 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.0246 | −1.52817 | −0.764084 | − | 0.645117i | \(-0.776809\pi\) | ||||
−0.764084 | + | 0.645117i | \(0.776809\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.9443 | 1.19061 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.8098 | 0.608167 | 0.304084 | − | 0.952645i | \(-0.401650\pi\) | ||||
0.304084 | + | 0.952645i | \(0.401650\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.6119 | −1.49843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.8328 | −1.50244 | −0.751221 | − | 0.660051i | \(-0.770535\pi\) | ||||
−0.751221 | + | 0.660051i | \(0.770535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.62365 | −0.147566 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9343 | −0.524985 | −0.262493 | − | 0.964934i | \(-0.584545\pi\) | ||||
−0.262493 | + | 0.964934i | \(0.584545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.9443 | −1.17288 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.2492 | 1.38558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2117 | 0.816341 | 0.408170 | − | 0.912906i | \(-0.366167\pi\) | ||||
0.408170 | + | 0.912906i | \(0.366167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5393 | 1.14895 | 0.574475 | − | 0.818522i | \(-0.305206\pi\) | ||||
0.574475 | + | 0.818522i | \(0.305206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.875388 | 0.0351848 | 0.0175924 | − | 0.999845i | \(-0.494400\pi\) | ||||
0.0175924 | + | 0.999845i | \(0.494400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.9443 | −0.519436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.2688 | 1.69346 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.9814 | 0.478491 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.41641 | −0.295712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7082 | 0.466096 | 0.233048 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233048 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.1235 | −1.03832 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.03631 | −0.159924 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.41641 | −0.135151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.8885 | −1.89148 | −0.945742 | − | 0.324919i | \(-0.894663\pi\) | ||||
−0.945742 | + | 0.324919i | \(0.894663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7264 | 0.462443 | 0.231221 | − | 0.972901i | \(-0.425728\pi\) | ||||
0.231221 | + | 0.972901i | \(0.425728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.8639 | −1.37064 | −0.685320 | − | 0.728242i | \(-0.740338\pi\) | ||||
−0.685320 | + | 0.728242i | \(0.740338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.8328 | 2.15238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.8885 | 1.01465 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.24109 | 0.126834 | 0.0634168 | − | 0.997987i | \(-0.479800\pi\) | ||||
0.0634168 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.7000 | 1.19772 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0557 | −1.05394 | −0.526971 | − | 0.849883i | \(-0.676672\pi\) | ||||
−0.526971 | + | 0.849883i | \(0.676672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.97831 | −0.387525 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.1158 | 1.28225 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 65.5967 | 2.53612 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.94427 | −0.345290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.8090 | −1.65016 | −0.825082 | − | 0.565013i | \(-0.808871\pi\) | ||||
−0.825082 | + | 0.565013i | \(0.808871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0022 | 1.15308 | 0.576540 | − | 0.817069i | \(-0.304403\pi\) | ||||
0.576540 | + | 0.817069i | \(0.304403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5836 | 0.482914 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.1246 | −1.34598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.1058 | −0.386689 | −0.193344 | − | 0.981131i | \(-0.561933\pi\) | ||||
−0.193344 | + | 0.981131i | \(0.561933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.0618 | −0.498338 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.7082 | −1.05560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1246 | −0.575367 | −0.287684 | − | 0.957725i | \(-0.592885\pi\) | ||||
−0.287684 | + | 0.957725i | \(0.592885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 33.1158 | 1.25797 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.48218 | −0.245530 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.9443 | −1.09477 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.1246 | 1.55326 | 0.776628 | − | 0.629960i | \(-0.216929\pi\) | ||||
0.776628 | + | 0.629960i | \(0.216929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.86474 | 0.258908 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.16073 | −0.0812625 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.58359 | 0.247252 | 0.123626 | − | 0.992329i | \(-0.460548\pi\) | ||||
0.123626 | + | 0.992329i | \(0.460548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.5279 | −0.957370 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.6197 | −1.10927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4744 | 0.503212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5967 | −0.805423 | −0.402711 | − | 0.915327i | \(-0.631932\pi\) | ||||
−0.402711 | + | 0.915327i | \(0.631932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.4164 | −1.61691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 56.8236 | 2.11329 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.48528 | −0.314702 | −0.157351 | − | 0.987543i | \(-0.550295\pi\) | ||||
−0.157351 | + | 0.987543i | \(0.550295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9443 | −0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.16718 | −0.339061 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9411 | 1.25364 | 0.626822 | − | 0.779162i | \(-0.284355\pi\) | ||||
0.626822 | + | 0.779162i | \(0.284355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.48528 | 0.312559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.8328 | 1.28135 | 0.640673 | − | 0.767814i | \(-0.278655\pi\) | ||||
0.640673 | + | 0.767814i | \(0.278655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.23607 | 0.339295 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.86474 | −0.251843 | −0.125921 | − | 0.992040i | \(-0.540189\pi\) | ||||
−0.125921 | + | 0.992040i | \(0.540189\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.7264 | 0.429045 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.4721 | −1.69805 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.4164 | 1.73025 | 0.865125 | − | 0.501557i | \(-0.167239\pi\) | ||||
0.865125 | + | 0.501557i | \(0.167239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 68.3923 | 2.49236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.825324 | 0.0299969 | 0.0149985 | − | 0.999888i | \(-0.495226\pi\) | ||||
0.0149985 | + | 0.999888i | \(0.495226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −88.7214 | −3.22038 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5410 | 0.889611 | 0.444806 | − | 0.895627i | \(-0.353273\pi\) | ||||
0.444806 | + | 0.895627i | \(0.353273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.65685 | −0.204792 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.2688 | 1.52624 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.5410 | 1.02922 | 0.514608 | − | 0.857426i | \(-0.327938\pi\) | ||||
0.514608 | + | 0.857426i | \(0.327938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.7639 | −0.387654 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.3500 | −0.552102 | −0.276051 | − | 0.961143i | \(-0.589026\pi\) | ||||
−0.276051 | + | 0.961143i | \(0.589026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44.4295 | 1.59390 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.81758 | −0.279378 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.62365 | 0.129169 | 0.0645845 | − | 0.997912i | \(-0.479428\pi\) | ||||
0.0645845 | + | 0.997912i | \(0.479428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.8885 | −0.779253 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.2492 | 1.21776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.89484 | −0.244843 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.1120 | −0.499874 | −0.249937 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249937 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.16718 | −0.324312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.4164 | −1.18071 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −71.8885 | −2.53689 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.73722 | −0.237161 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4721 | −0.579129 | −0.289565 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289565 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.7618 | −1.53479 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48528 | 0.296862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.5279 | 0.892016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0557 | 0.734850 | 0.367425 | − | 0.930053i | \(-0.380239\pi\) | ||||
0.367425 | + | 0.930053i | \(0.380239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00310 | −0.0698238 | −0.0349119 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349119 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.5942 | −0.716131 | −0.358065 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358065 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.41641 | 0.257272 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.08036 | 0.0374324 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.99226 | 0.241688 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3050 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.24109 | 0.111629 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.4326 | −1.59544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37.8885 | −1.30033 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.8328 | −1.74253 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.4884 | −0.359115 | −0.179558 | − | 0.983747i | \(-0.557467\pi\) | ||||
−0.179558 | + | 0.983747i | \(0.557467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.8059 | −1.39390 | −0.696951 | − | 0.717119i | \(-0.745460\pi\) | ||||
−0.696951 | + | 0.717119i | \(0.745460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.8328 | 1.32342 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.5942 | 0.701035 | 0.350518 | − | 0.936556i | \(-0.386006\pi\) | ||||
0.350518 | + | 0.936556i | \(0.386006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.2294 | −1.23041 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.7771 | 2.02780 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.54102 | 0.221634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.94820 | −0.336696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.44897 | −0.150231 | −0.0751155 | − | 0.997175i | \(-0.523933\pi\) | ||||
−0.0751155 | + | 0.997175i | \(0.523933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.7082 | 0.529825 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.6525 | −1.03271 | −0.516354 | − | 0.856375i | \(-0.672711\pi\) | ||||
−0.516354 | + | 0.856375i | \(0.672711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9675 | 0.503695 | 0.251848 | − | 0.967767i | \(-0.418962\pi\) | ||||
0.251848 | + | 0.967767i | \(0.418962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.3268 | −1.21973 | −0.609867 | − | 0.792504i | \(-0.708777\pi\) | ||||
−0.609867 | + | 0.792504i | \(0.708777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.5836 | −0.958663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 56.0689 | 1.87838 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.48528 | 0.283949 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −68.3923 | −2.28355 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8885 | −0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.41641 | 0.247076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 54.9179 | 1.82755 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.86784 | −0.294452 | −0.147226 | − | 0.989103i | \(-0.547034\pi\) | ||||
−0.147226 | + | 0.989103i | \(0.547034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.70820 | 0.0566575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5279 | −1.24335 | −0.621677 | − | 0.783274i | \(-0.713548\pi\) | ||||
−0.621677 | + | 0.783274i | \(0.713548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.4589 | −0.908759 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8328 | −0.885133 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.23607 | −0.304339 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.16693 | 0.202987 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.3237 | 1.12734 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.4721 | 0.540433 | 0.270217 | − | 0.962800i | \(-0.412905\pi\) | ||||
0.270217 | + | 0.962800i | \(0.412905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.48528 | 0.277796 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.6768 | −1.68821 | −0.844104 | − | 0.536180i | \(-0.819867\pi\) | ||||
−0.844104 | + | 0.536180i | \(0.819867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −62.8328 | −2.05047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0557 | −0.686397 | −0.343199 | − | 0.939263i | \(-0.611510\pi\) | ||||
−0.343199 | + | 0.939263i | \(0.611510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.4295 | −1.44682 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.6969 | 0.932525 | 0.466263 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466263 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.4164 | −1.79889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.1803 | −0.978665 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0764 | 0.877090 | 0.438545 | − | 0.898709i | \(-0.355494\pi\) | ||||
0.438545 | + | 0.898709i | \(0.355494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −53.5825 | −1.73208 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.05573 | −0.0986746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.7394 | 1.18391 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.5579 | −0.532466 | −0.266233 | − | 0.963909i | \(-0.585779\pi\) | ||||
−0.266233 | + | 0.963909i | \(0.585779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.47214 | −0.0794164 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.36068 | 0.139941 | 0.0699704 | − | 0.997549i | \(-0.477710\pi\) | ||||
0.0699704 | + | 0.997549i | \(0.477710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.4295 | −1.42434 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.1304 | −1.50784 | −0.753918 | − | 0.656969i | \(-0.771838\pi\) | ||||
−0.753918 | + | 0.656969i | \(0.771838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78.2492 | 2.50086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.47214 | 0.142784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.4009 | 1.06532 | 0.532662 | − | 0.846328i | \(-0.321192\pi\) | ||||
0.532662 | + | 0.846328i | \(0.321192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.9179 | 1.74806 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.8328 | −1.99797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8328 | −0.471180 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44.4295 | −1.40993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7000 | 0.972280 | 0.486140 | − | 0.873881i | \(-0.338405\pi\) | ||||
0.486140 | + | 0.873881i | \(0.338405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.0000 | 0.379663 |
(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 | 1900.2.a.j.1.4 | 4 | ||
4.3 | odd | 2 | 7600.2.a.ce.1.1 | 4 | |||
5.2 | odd | 4 | 380.2.c.a.229.1 | ✓ | 4 | ||
5.3 | odd | 4 | 380.2.c.a.229.4 | yes | 4 | ||
5.4 | even | 2 | inner | 1900.2.a.j.1.1 | 4 | ||
15.2 | even | 4 | 3420.2.f.a.1369.3 | 4 | |||
15.8 | even | 4 | 3420.2.f.a.1369.4 | 4 | |||
20.3 | even | 4 | 1520.2.d.f.609.1 | 4 | |||
20.7 | even | 4 | 1520.2.d.f.609.4 | 4 | |||
20.19 | odd | 2 | 7600.2.a.ce.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.a.229.1 | ✓ | 4 | 5.2 | odd | 4 | ||
380.2.c.a.229.4 | yes | 4 | 5.3 | odd | 4 | ||
1520.2.d.f.609.1 | 4 | 20.3 | even | 4 | |||
1520.2.d.f.609.4 | 4 | 20.7 | even | 4 | |||
1900.2.a.j.1.1 | 4 | 5.4 | even | 2 | inner | ||
1900.2.a.j.1.4 | 4 | 1.1 | even | 1 | trivial | ||
3420.2.f.a.1369.3 | 4 | 15.2 | even | 4 | |||
3420.2.f.a.1369.4 | 4 | 15.8 | even | 4 | |||
7600.2.a.ce.1.1 | 4 | 4.3 | odd | 2 | |||
7600.2.a.ce.1.4 | 4 | 20.19 | odd | 2 |