Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 3 x^{18} - 35 x^{17} + 103 x^{16} + 501 x^{15} - 1437 x^{14} - 3775 x^{13} + 10450 x^{12} + 16076 x^{11} - 42255 x^{10} - 38701 x^{9} + 93907 x^{8} + 49522 x^{7} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.13995\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | −1.13995 | −0.658149 | −0.329075 | − | 0.944304i | \(-0.606737\pi\) | ||||
−0.329075 | + | 0.944304i | \(0.606737\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.77941 | −1.24299 | −0.621494 | − | 0.783419i | \(-0.713474\pi\) | ||||
−0.621494 | + | 0.783419i | \(0.713474\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.98761 | 0.751245 | 0.375623 | − | 0.926773i | \(-0.377429\pi\) | ||||
0.375623 | + | 0.926773i | \(0.377429\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.70052 | −0.566840 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.06951 | −1.52851 | −0.764257 | − | 0.644911i | \(-0.776894\pi\) | ||||
−0.764257 | + | 0.644911i | \(0.776894\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.33485 | 1.20227 | 0.601135 | − | 0.799147i | \(-0.294715\pi\) | ||||
0.601135 | + | 0.799147i | \(0.294715\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.16838 | 0.818072 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00702 | −0.486774 | −0.243387 | − | 0.969929i | \(-0.578259\pi\) | ||||
−0.243387 | + | 0.969929i | \(0.578259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.26577 | −0.494432 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.07948 | −0.850630 | −0.425315 | − | 0.905045i | \(-0.639837\pi\) | ||||
−0.425315 | + | 0.905045i | \(0.639837\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.72511 | 0.545021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.35835 | 1.03121 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0668313 | 0.0124103 | 0.00620513 | − | 0.999981i | \(-0.498025\pi\) | ||||
0.00620513 | + | 0.999981i | \(0.498025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.97371 | 0.354489 | 0.177244 | − | 0.984167i | \(-0.443282\pi\) | ||||
0.177244 | + | 0.984167i | \(0.443282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.77898 | 1.00599 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.52437 | −0.933790 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4620 | −1.71995 | −0.859974 | − | 0.510339i | \(-0.829520\pi\) | ||||
−0.859974 | + | 0.510339i | \(0.829520\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.94150 | −0.791273 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.38189 | −0.840510 | −0.420255 | − | 0.907406i | \(-0.638059\pi\) | ||||
−0.420255 | + | 0.907406i | \(0.638059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.33887 | −1.42416 | −0.712082 | − | 0.702097i | \(-0.752247\pi\) | ||||
−0.712082 | + | 0.702097i | \(0.752247\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.72644 | 0.704575 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.29606 | 0.334915 | 0.167457 | − | 0.985879i | \(-0.446444\pi\) | ||||
0.167457 | + | 0.985879i | \(0.446444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.04941 | −0.435630 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.28790 | 0.320370 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0902 | 1.89993 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.13995 | −0.150990 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.209025 | −0.0272128 | −0.0136064 | − | 0.999907i | \(-0.504331\pi\) | ||||
−0.0136064 | + | 0.999907i | \(0.504331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.06405 | 1.03250 | 0.516248 | − | 0.856439i | \(-0.327328\pi\) | ||||
0.516248 | + | 0.856439i | \(0.327328\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.37997 | −0.425836 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0483 | −1.49441 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.60660 | 0.807124 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.65039 | 0.559841 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7455 | −1.39394 | −0.696968 | − | 0.717102i | \(-0.745468\pi\) | ||||
−0.696968 | + | 0.717102i | \(0.745468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29444 | 0.853750 | 0.426875 | − | 0.904311i | \(-0.359615\pi\) | ||||
0.426875 | + | 0.904311i | \(0.359615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.10648 | −0.358705 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0762 | −1.14829 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.32647 | −0.824293 | −0.412146 | − | 0.911118i | \(-0.635221\pi\) | ||||
−0.412146 | + | 0.911118i | \(0.635221\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00668 | −0.111853 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.9906 | 1.86497 | 0.932483 | − | 0.361214i | \(-0.117638\pi\) | ||||
0.932483 | + | 0.361214i | \(0.117638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.57833 | 0.605055 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0761842 | −0.00816780 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.39417 | 0.465781 | 0.232891 | − | 0.972503i | \(-0.425182\pi\) | ||||
0.232891 | + | 0.972503i | \(0.425182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.61598 | 0.903200 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.24993 | −0.233306 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.77941 | −0.285161 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.09743 | 0.314497 | 0.157248 | − | 0.987559i | \(-0.449738\pi\) | ||||
0.157248 | + | 0.987559i | \(0.449738\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.62080 | 0.866423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4465 | 1.03947 | 0.519734 | − | 0.854328i | \(-0.326031\pi\) | ||||
0.519734 | + | 0.854328i | \(0.326031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.95839 | −0.291499 | −0.145749 | − | 0.989322i | \(-0.546559\pi\) | ||||
−0.145749 | + | 0.989322i | \(0.546559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.29750 | 0.614573 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.89044 | 0.279429 | 0.139715 | − | 0.990192i | \(-0.455381\pi\) | ||||
0.139715 | + | 0.990192i | \(0.455381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.26906 | 0.313120 | 0.156560 | − | 0.987668i | \(-0.449960\pi\) | ||||
0.156560 | + | 0.987668i | \(0.449960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.9262 | 1.13198 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.43144 | −0.228731 | −0.114365 | − | 0.993439i | \(-0.536483\pi\) | ||||
−0.114365 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.3385 | 1.05732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.37149 | −0.681494 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.98918 | −0.365687 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.6999 | 1.33636 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.13507 | 0.553181 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.32286 | 0.565534 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.83797 | −0.518036 | −0.259018 | − | 0.965872i | \(-0.583399\pi\) | ||||
−0.259018 | + | 0.965872i | \(0.583399\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.6458 | 0.937312 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.59502 | −0.488839 | −0.244420 | − | 0.969670i | \(-0.578597\pi\) | ||||
−0.244420 | + | 0.969670i | \(0.578597\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.98761 | 0.172348 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.8930 | −1.28179 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.71128 | −0.829691 | −0.414846 | − | 0.909892i | \(-0.636164\pi\) | ||||
−0.414846 | + | 0.909892i | \(0.636164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6029 | 1.06896 | 0.534482 | − | 0.845180i | \(-0.320507\pi\) | ||||
0.534482 | + | 0.845180i | \(0.320507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.61739 | −0.220424 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.9755 | −1.83769 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.185751 | −0.0154258 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47617 | 0.286710 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.41435 | 0.525484 | 0.262742 | − | 0.964866i | \(-0.415373\pi\) | ||||
0.262742 | + | 0.964866i | \(0.415373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.91735 | 0.156032 | 0.0780159 | − | 0.996952i | \(-0.475141\pi\) | ||||
0.0780159 | + | 0.996952i | \(0.475141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.41298 | 0.275923 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.48574 | −0.440626 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.62141 | 0.688064 | 0.344032 | − | 0.938958i | \(-0.388207\pi\) | ||||
0.344032 | + | 0.938958i | \(0.388207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.13995 | −0.0904037 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.10841 | −0.639032 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1421 | 0.951044 | 0.475522 | − | 0.879704i | \(-0.342259\pi\) | ||||
0.475522 | + | 0.879704i | \(0.342259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.0621 | −1.25044 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.51915 | 0.194938 | 0.0974690 | − | 0.995239i | \(-0.468925\pi\) | ||||
0.0974690 | + | 0.995239i | \(0.468925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.79089 | 0.445453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.70052 | −0.130042 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.0305 | −1.59892 | −0.799458 | − | 0.600722i | \(-0.794880\pi\) | ||||
−0.799458 | + | 0.600722i | \(0.794880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.41644 | 0.409445 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.238278 | 0.0179101 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.6751 | 1.91905 | 0.959524 | − | 0.281628i | \(-0.0908744\pi\) | ||||
0.959524 | + | 0.281628i | \(0.0908744\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.05364 | 0.524293 | 0.262147 | − | 0.965028i | \(-0.415570\pi\) | ||||
0.262147 | + | 0.965028i | \(0.415570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.19260 | −0.679537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.0782 | 2.13787 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1746 | 0.744042 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.6503 | 0.774695 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.95352 | −0.213710 | −0.106855 | − | 0.994275i | \(-0.534078\pi\) | ||||
−0.106855 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0586 | −1.51583 | −0.757915 | − | 0.652353i | \(-0.773782\pi\) | ||||
−0.757915 | + | 0.652353i | \(0.773782\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.7344 | 0.983543 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.53411 | 0.180548 | 0.0902741 | − | 0.995917i | \(-0.471226\pi\) | ||||
0.0902741 | + | 0.995917i | \(0.471226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.52575 | 0.249934 | 0.124967 | − | 0.992161i | \(-0.460118\pi\) | ||||
0.124967 | + | 0.992161i | \(0.460118\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.53117 | −0.531208 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.132834 | 0.00932315 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.9585 | 1.04474 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.93723 | 0.482171 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.06951 | −0.350665 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7194 | 1.49523 | 0.747613 | − | 0.664134i | \(-0.231200\pi\) | ||||
0.747613 | + | 0.664134i | \(0.231200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3893 | 0.917418 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.9565 | 1.77022 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.92296 | 0.266308 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.31528 | −0.561895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.70013 | −0.585234 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.9341 | 1.73667 | 0.868337 | − | 0.495974i | \(-0.165189\pi\) | ||||
0.868337 | + | 0.495974i | \(0.165189\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.63409 | −0.308940 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.7955 | −0.716522 | −0.358261 | − | 0.933622i | \(-0.616630\pi\) | ||||
−0.358261 | + | 0.933622i | \(0.616630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4067 | 1.67892 | 0.839461 | − | 0.543419i | \(-0.182871\pi\) | ||||
0.839461 | + | 0.543419i | \(0.182871\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.4863 | 0.755746 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.15393 | −0.0755967 | −0.0377983 | − | 0.999285i | \(-0.512034\pi\) | ||||
−0.0377983 | + | 0.999285i | \(0.512034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.38168 | −0.416295 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.35180 | 0.542508 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3725 | −1.38247 | −0.691235 | − | 0.722630i | \(-0.742933\pi\) | ||||
−0.691235 | + | 0.722630i | \(0.742933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4746 | 1.19005 | 0.595026 | − | 0.803707i | \(-0.297142\pi\) | ||||
0.595026 | + | 0.803707i | \(0.297142\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9275 | −0.957598 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.47556 | 0.541483 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.33485 | 0.275820 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.3684 | −1.22743 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.441653 | 0.0278769 | 0.0139384 | − | 0.999903i | \(-0.495563\pi\) | ||||
0.0139384 | + | 0.999903i | \(0.495563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.6810 | 1.30020 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.35901 | −0.398217 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.96951 | −0.559503 | −0.279751 | − | 0.960072i | \(-0.590252\pi\) | ||||
−0.279751 | + | 0.960072i | \(0.590252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.7944 | −1.29210 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.113648 | −0.00703463 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.7301 | 1.46326 | 0.731630 | − | 0.681702i | \(-0.238760\pi\) | ||||
0.731630 | + | 0.681702i | \(0.238760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.77941 | −0.170738 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.00912 | −0.306553 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.91159 | 0.543349 | 0.271675 | − | 0.962389i | \(-0.412423\pi\) | ||||
0.271675 | + | 0.962389i | \(0.412423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.32240 | 0.262567 | 0.131284 | − | 0.991345i | \(-0.458090\pi\) | ||||
0.131284 | + | 0.991345i | \(0.458090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.82177 | −0.594440 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.8149 | −0.833073 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4927 | −0.630448 | −0.315224 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315224 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.35633 | −0.200938 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8927 | 1.36566 | 0.682831 | − | 0.730576i | \(-0.260749\pi\) | ||||
0.682831 | + | 0.730576i | \(0.260749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5026 | 0.683760 | 0.341880 | − | 0.939744i | \(-0.388936\pi\) | ||||
0.341880 | + | 0.939744i | \(0.388936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.16838 | 0.187679 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6971 | −0.631429 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9719 | −0.763051 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.53091 | −0.206986 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.9918 | −1.81056 | −0.905279 | − | 0.424817i | \(-0.860339\pi\) | ||||
−0.905279 | + | 0.424817i | \(0.860339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.580967 | 0.0338252 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.1642 | −1.57623 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.6839 | −1.02269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5620 | −1.06990 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9085 | −0.684126 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.4133 | −1.28338 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.9957 | 1.08414 | 0.542072 | − | 0.840332i | \(-0.317640\pi\) | ||||
0.542072 | + | 0.840332i | \(0.317640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.37241 | 0.191850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.2956 | 1.83131 | 0.915657 | − | 0.401960i | \(-0.131671\pi\) | ||||
0.915657 | + | 0.401960i | \(0.131671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.05599 | 0.172735 | 0.0863673 | − | 0.996263i | \(-0.472474\pi\) | ||||
0.0863673 | + | 0.996263i | \(0.472474\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.39430 | 0.529309 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.55848 | −0.143698 | −0.0718492 | − | 0.997416i | \(-0.522890\pi\) | ||||
−0.0718492 | + | 0.997416i | \(0.522890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.338802 | −0.0189693 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.29495 | −0.183906 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00702 | −0.111674 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.8129 | 0.655262 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.72656 | −0.206079 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.56367 | 0.251603 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.5751 | 1.51567 | 0.757833 | − | 0.652448i | \(-0.226258\pi\) | ||||
0.757833 | + | 0.652448i | \(0.226258\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.7909 | 0.974934 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.3624 | −1.00325 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7108 | 1.23713 | 0.618567 | − | 0.785732i | \(-0.287714\pi\) | ||||
0.618567 | + | 0.785732i | \(0.287714\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.77171 | 0.150539 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0057 | −0.541841 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9743 | −1.07851 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.9253 | −0.695877 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.1150 | 1.72402 | 0.862011 | − | 0.506889i | \(-0.169205\pi\) | ||||
0.862011 | + | 0.506889i | \(0.169205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.9106 | −0.905205 | −0.452602 | − | 0.891712i | \(-0.649504\pi\) | ||||
−0.452602 | + | 0.891712i | \(0.649504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.2276 | 1.23980 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79709 | 0.521447 | 0.260723 | − | 0.965414i | \(-0.416039\pi\) | ||||
0.260723 | + | 0.965414i | \(0.416039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.6456 | 1.73265 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.54745 | 0.240677 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8739 | 0.785012 | 0.392506 | − | 0.919749i | \(-0.371608\pi\) | ||||
0.392506 | + | 0.919749i | \(0.371608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.7572 | −0.879522 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.2742 | −1.06120 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.63231 | −0.294004 | −0.147002 | − | 0.989136i | \(-0.546962\pi\) | ||||
−0.147002 | + | 0.989136i | \(0.546962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.15200 | 0.476434 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.98761 | 0.103192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.6421 | 1.48303 | 0.741515 | − | 0.670937i | \(-0.234108\pi\) | ||||
0.741515 | + | 0.670937i | \(0.234108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.20773 | −0.372206 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.289703 | 0.0149205 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.83077 | −0.248140 | −0.124070 | − | 0.992273i | \(-0.539595\pi\) | ||||
−0.124070 | + | 0.992273i | \(0.539595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.65498 | 0.340945 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.4181 | −0.992219 | −0.496110 | − | 0.868260i | \(-0.665239\pi\) | ||||
−0.496110 | + | 0.868260i | \(0.665239\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.0059 | 1.42731 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.8809 | 0.807272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.905582 | −0.0459148 | −0.0229574 | − | 0.999736i | \(-0.507308\pi\) | ||||
−0.0229574 | + | 0.999736i | \(0.507308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.18760 | 0.414065 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.37803 | 0.321729 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.3633 | 1.02459 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.7294 | −1.09057 | −0.545284 | − | 0.838252i | \(-0.683578\pi\) | ||||
−0.545284 | + | 0.838252i | \(0.683578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.26577 | −0.113430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5204 | 0.725116 | 0.362558 | − | 0.931961i | \(-0.381903\pi\) | ||||
0.362558 | + | 0.931961i | \(0.381903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.55573 | 0.426191 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.79797 | 0.139032 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.0374 | 2.62896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7946 | 0.731548 | 0.365774 | − | 0.930704i | \(-0.380804\pi\) | ||||
0.365774 | + | 0.930704i | \(0.380804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0704 | 0.546060 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.415461 | −0.0204435 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −47.2239 | −2.31813 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.3667 | −0.703538 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.50447 | −0.317764 | −0.158882 | − | 0.987298i | \(-0.550789\pi\) | ||||
−0.158882 | + | 0.987298i | \(0.550789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6865 | −1.54431 | −0.772153 | − | 0.635437i | \(-0.780820\pi\) | ||||
−0.772153 | + | 0.635437i | \(0.780820\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.90449 | −0.189843 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.46935 | −0.265302 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0282 | 0.775658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.0510 | 1.20947 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.76860 | −0.326032 | −0.163016 | − | 0.986623i | \(-0.552122\pi\) | ||||
−0.163016 | + | 0.986623i | \(0.552122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.2217 | 1.45236 | 0.726182 | − | 0.687502i | \(-0.241293\pi\) | ||||
0.726182 | + | 0.687502i | \(0.241293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.211747 | 0.0101525 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.07948 | −0.195148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2835 | −0.586260 | −0.293130 | − | 0.956073i | \(-0.594697\pi\) | ||||
−0.293130 | + | 0.956073i | \(0.594697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.18558 | 0.246933 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.7324 | −1.36512 | −0.682558 | − | 0.730831i | \(-0.739133\pi\) | ||||
−0.682558 | + | 0.730831i | \(0.739133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2132 | −0.578961 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.31202 | −0.345847 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.1318 | −0.666919 | −0.333459 | − | 0.942764i | \(-0.608216\pi\) | ||||
−0.333459 | + | 0.942764i | \(0.608216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.2835 | 1.28473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.18568 | −0.102692 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.9473 | −1.12267 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.0631 | −1.59340 | −0.796702 | − | 0.604372i | \(-0.793424\pi\) | ||||
−0.796702 | + | 0.604372i | \(0.793424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.7543 | −0.501969 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.63906 | −0.448936 | −0.224468 | − | 0.974482i | \(-0.572064\pi\) | ||||
−0.224468 | + | 0.974482i | \(0.572064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.06975 | −0.189137 | −0.0945686 | − | 0.995518i | \(-0.530147\pi\) | ||||
−0.0945686 | + | 0.995518i | \(0.530147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.25346 | 0.289997 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.4052 | 1.36071 | 0.680355 | − | 0.732883i | \(-0.261826\pi\) | ||||
0.680355 | + | 0.732883i | \(0.261826\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.1313 | 0.606348 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.82796 | −0.452849 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.3435 | 2.17686 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.72511 | 0.125036 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70052 | −0.0778614 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.1649 | 1.56103 | 0.780516 | − | 0.625136i | \(-0.214956\pi\) | ||||
0.780516 | + | 0.625136i | \(0.214956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45.3513 | −2.06784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.24316 | 0.420578 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.60902 | −0.390916 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6269 | 0.844064 | 0.422032 | − | 0.906581i | \(-0.361317\pi\) | ||||
0.422032 | + | 0.906581i | \(0.361317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8414 | −0.625929 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.9630 | −1.08144 | −0.540718 | − | 0.841204i | \(-0.681847\pi\) | ||||
−0.540718 | + | 0.841204i | \(0.681847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.134132 | −0.00604100 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.9607 | −1.07695 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.3455 | −1.04719 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.5389 | −1.54617 | −0.773087 | − | 0.634300i | \(-0.781288\pi\) | ||||
−0.773087 | + | 0.634300i | \(0.781288\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.87170 | −0.128298 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.99944 | 0.222914 | 0.111457 | − | 0.993769i | \(-0.464448\pi\) | ||||
0.111457 | + | 0.993769i | \(0.464448\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.0352 | −1.29205 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.60131 | −0.293175 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.22713 | −0.0543914 | −0.0271957 | − | 0.999630i | \(-0.508658\pi\) | ||||
−0.0271957 | + | 0.999630i | \(0.508658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.4985 | 0.641376 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.35835 | 0.236577 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.22257 | 0.362330 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6399 | −0.511922 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.9736 | 1.05233 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8537 | −1.26410 | −0.632051 | − | 0.774927i | \(-0.717787\pi\) | ||||
−0.632051 | + | 0.774927i | \(0.717787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.6998 | −1.12378 | −0.561888 | − | 0.827213i | \(-0.689925\pi\) | ||||
−0.561888 | + | 0.827213i | \(0.689925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.17446 | −0.269476 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.96128 | −0.172556 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.35786 | −0.276429 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.355452 | 0.0154253 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.3297 | −1.01052 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.03371 | −0.347328 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.2683 | −1.26302 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.4590 | 0.665867 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.5450 | −1.18425 | −0.592127 | − | 0.805845i | \(-0.701712\pi\) | ||||
−0.592127 | + | 0.805845i | \(0.701712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.04079 | −0.345063 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.08606 | −0.389204 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.21661 | 0.0520183 | 0.0260092 | − | 0.999662i | \(-0.491720\pi\) | ||||
0.0260092 | + | 0.999662i | \(0.491720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.7131 | −0.585260 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0668313 | 0.00284711 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.5622 | −0.619246 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −33.1477 | −1.40704 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0693 | −0.765621 | −0.382810 | − | 0.923827i | \(-0.625044\pi\) | ||||
−0.382810 | + | 0.923827i | \(0.625044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.4825 | −1.71223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.5985 | −0.489691 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.8866 | −1.17528 | −0.587640 | − | 0.809123i | \(-0.699943\pi\) | ||||
−0.587640 | + | 0.809123i | \(0.699943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.75796 | 0.284310 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00088 | −0.0840291 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.1878 | 1.05593 | 0.527964 | − | 0.849266i | \(-0.322955\pi\) | ||||
0.527964 | + | 0.849266i | \(0.322955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.05094 | 0.295073 | 0.147536 | − | 0.989057i | \(-0.452866\pi\) | ||||
0.147536 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.36686 | 0.140653 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.1170 | −0.463611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5720 | −0.648271 | −0.324136 | − | 0.946011i | \(-0.605073\pi\) | ||||
−0.324136 | + | 0.946011i | \(0.605073\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.0057 | 0.997642 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.7708 | 1.40105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.06951 | −0.209958 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.4884 | 0.847090 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.5421 | 1.54953 | 0.774765 | − | 0.632249i | \(-0.217868\pi\) | ||||
0.774765 | + | 0.632249i | \(0.217868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.97371 | 0.0813253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.88876 | −0.118828 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.7456 | 0.687660 | 0.343830 | − | 0.939032i | \(-0.388276\pi\) | ||||
0.343830 | + | 0.939032i | \(0.388276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0875 | 0.454545 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.01917 | −0.164494 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.3428 | 0.667750 | 0.333875 | − | 0.942617i | \(-0.391644\pi\) | ||||
0.333875 | + | 0.942617i | \(0.391644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.1231 | −1.55507 | −0.777537 | − | 0.628837i | \(-0.783531\pi\) | ||||
−0.777537 | + | 0.628837i | \(0.783531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2346 | −0.457510 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.8571 | −1.66108 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5423 | −0.833785 | −0.416892 | − | 0.908956i | \(-0.636881\pi\) | ||||
−0.416892 | + | 0.908956i | \(0.636881\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.151424 | −0.00613602 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.95306 | 0.402658 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.4726 | −0.948049 | −0.474024 | − | 0.880512i | \(-0.657199\pi\) | ||||
−0.474024 | + | 0.880512i | \(0.657199\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.0519 | −0.687597 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.2521 | −1.53997 | −0.769985 | − | 0.638062i | \(-0.779736\pi\) | ||||
−0.769985 | + | 0.638062i | \(0.779736\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.47558 | 0.260276 | 0.130138 | − | 0.991496i | \(-0.458458\pi\) | ||||
0.130138 | + | 0.991496i | \(0.458458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.8593 | −0.877182 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.73389 | 0.349916 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1993 | −1.24797 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.77898 | 0.230790 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.9975 | 0.837226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.6841 | 1.53999 | 0.769995 | − | 0.638050i | \(-0.220259\pi\) | ||||
0.769995 | + | 0.638050i | \(0.220259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.7590 | −0.984082 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.2261 | 0.643913 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.2187 | −0.523745 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.9735 | 0.790139 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.270432 | −0.0106814 | −0.00534071 | − | 0.999986i | \(-0.501700\pi\) | ||||
−0.00534071 | + | 0.999986i | \(0.501700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3941 | 1.00145 | 0.500723 | − | 0.865608i | \(-0.333068\pi\) | ||||
0.500723 | + | 0.865608i | \(0.333068\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.5891 | −1.16507 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.15234 | −0.0846173 | −0.0423086 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423086 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.05966 | 0.0415952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.47197 | −0.175270 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.3821 | −0.601949 | −0.300975 | − | 0.953632i | \(-0.597312\pi\) | ||||
−0.300975 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5508 | 0.607622 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4043 | −0.483939 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.9048 | 1.74924 | 0.874622 | − | 0.484806i | \(-0.161110\pi\) | ||||
0.874622 | + | 0.484806i | \(0.161110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.93215 | 0.347420 | 0.173710 | − | 0.984797i | \(-0.444424\pi\) | ||||
0.173710 | + | 0.984797i | \(0.444424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.91770 | 0.385171 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.52437 | −0.214226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.272637 | −0.0105565 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.5635 | −1.14299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.8808 | −1.57819 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.1820 | −0.431033 | −0.215517 | − | 0.976500i | \(-0.569144\pi\) | ||||
−0.215517 | + | 0.976500i | \(0.569144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.6021 | 0.562033 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.17661 | −0.352686 | −0.176343 | − | 0.984329i | \(-0.556427\pi\) | ||||
−0.176343 | + | 0.984329i | \(0.556427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.15648 | 0.236264 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3063 | 0.471578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.50041 | −0.133939 | −0.0669697 | − | 0.997755i | \(-0.521333\pi\) | ||||
−0.0669697 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.9916 | 1.03130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.9623 | −1.10498 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.33485 | 0.165144 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.1390 | −1.26067 | −0.630333 | − | 0.776325i | \(-0.717082\pi\) | ||||
−0.630333 | + | 0.776325i | \(0.717082\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.1348 | 0.650896 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.0286 | −1.32871 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8016 | 0.409139 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.31542 | 0.0497539 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5170 | 0.661609 | 0.330805 | − | 0.943699i | \(-0.392680\pi\) | ||||
0.330805 | + | 0.943699i | \(0.392680\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.4620 | −0.394583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.27478 | 0.273984 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7636 | 0.780896 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9394 | −0.861506 | −0.430753 | − | 0.902470i | \(-0.641752\pi\) | ||||
−0.430753 | + | 0.902470i | \(0.641752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4588 | 0.467242 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.05171 | −0.301539 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.0790 | 2.28422 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.3635 | 0.909872 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.3926 | −0.536754 | −0.268377 | − | 0.963314i | \(-0.586487\pi\) | ||||
−0.268377 | + | 0.963314i | \(0.586487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.88012 | −0.218987 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.0600 | −0.783231 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.182122 | 0.00676385 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.5404 | 0.502186 | 0.251093 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251093 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0366 | 0.742095 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.7433 | 0.693246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.11689 | 0.152061 | 0.0760304 | − | 0.997105i | \(-0.475775\pi\) | ||||
0.0760304 | + | 0.997105i | \(0.475775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.66169 | −0.356377 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.4922 | −1.23370 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.4171 | 1.74427 | 0.872133 | − | 0.489269i | \(-0.162736\pi\) | ||||
0.872133 | + | 0.489269i | \(0.162736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.94150 | −0.181530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9829 | 0.512984 | 0.256492 | − | 0.966546i | \(-0.417433\pi\) | ||||
0.256492 | + | 0.966546i | \(0.417433\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8281 | −0.653170 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.8929 | −1.05714 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.74507 | 0.209920 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.8396 | 1.23482 | 0.617412 | − | 0.786640i | \(-0.288181\pi\) | ||||
0.617412 | + | 0.786640i | \(0.288181\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.503461 | −0.0183471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.32910 | −0.193946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1805 | 0.660782 | 0.330391 | − | 0.943844i | \(-0.392819\pi\) | ||||
0.330391 | + | 0.943844i | \(0.392819\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.5752 | −0.855726 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0272 | −0.907236 | −0.453618 | − | 0.891196i | \(-0.649867\pi\) | ||||
−0.453618 | + | 0.891196i | \(0.649867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.49762 | 0.235230 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.48606 | −0.342969 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.906093 | −0.0327171 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.3351 | −1.88725 | −0.943626 | − | 0.331013i | \(-0.892610\pi\) | ||||
−0.943626 | + | 0.331013i | \(0.892610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.2248 | 0.368236 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.6396 | −1.56961 | −0.784804 | − | 0.619744i | \(-0.787236\pi\) | ||||
−0.784804 | + | 0.619744i | \(0.787236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.37857 | 0.193204 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.7046 | 0.850396 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.38189 | −0.192826 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.5440 | 2.13065 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.358105 | 0.0127976 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.9624 | −0.855256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.4911 | 0.587845 | 0.293922 | − | 0.955829i | \(-0.405039\pi\) | ||||
0.293922 | + | 0.955829i | \(0.405039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.0510 | −0.963043 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.83275 | −0.171833 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.9564 | 1.24134 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.16838 | 0.112371 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.8373 | 1.16316 | 0.581578 | − | 0.813490i | \(-0.302435\pi\) | ||||
0.581578 | + | 0.813490i | \(0.302435\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.60824 | −0.163028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.47237 | −0.264023 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.9792 | −1.30497 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.5366 | 0.794309 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.1587 | −0.357605 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.3229 | −1.31220 | −0.656101 | − | 0.754673i | \(-0.727796\pi\) | ||||
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.8831 | 0.768419 | 0.384209 | − | 0.923246i | \(-0.374474\pi\) | ||||
0.384209 | + | 0.923246i | \(0.374474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.92731 | −0.172808 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.7479 | −1.18214 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.33887 | −0.326726 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.6516 | −0.511970 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.3194 | 0.534650 | 0.267325 | − | 0.963606i | \(-0.413860\pi\) | ||||
0.267325 | + | 0.963606i | \(0.413860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.8197 | 0.795444 | 0.397722 | − | 0.917506i | \(-0.369801\pi\) | ||||
0.397722 | + | 0.917506i | \(0.369801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.7483 | 0.548286 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.3269 | 1.19366 | 0.596832 | − | 0.802366i | \(-0.296426\pi\) | ||||
0.596832 | + | 0.802366i | \(0.296426\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.89533 | 0.135291 | 0.0676453 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676453 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.9612 | 0.414929 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.12024 | 0.212054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.00176 | −0.242306 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.5758 | 0.365554 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.0342 | −1.52023 | −0.760115 | − | 0.649788i | \(-0.774858\pi\) | ||||
−0.760115 | + | 0.649788i | \(0.774858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9955 | −0.999846 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.0964 | −0.898809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.0952 | −0.553693 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.2177 | 1.00393 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.1124 | −0.450016 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.6796 | 1.46304 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2699 | 0.899463 | 0.449732 | − | 0.893164i | \(-0.351520\pi\) | ||||
0.449732 | + | 0.893164i | \(0.351520\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.72644 | 0.161641 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.6281 | 0.977919 | 0.488959 | − | 0.872307i | \(-0.337377\pi\) | ||||
0.488959 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6100 | 1.14676 | 0.573380 | − | 0.819290i | \(-0.305632\pi\) | ||||
0.573380 | + | 0.819290i | \(0.305632\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.1941 | 0.415575 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.0673 | −0.342696 | −0.171348 | − | 0.985211i | \(-0.554812\pi\) | ||||
−0.171348 | + | 0.985211i | \(0.554812\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.4522 | 1.98743 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7872 | 0.502201 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.1416 | 1.25994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.6386 | 0.970381 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.26724 | −0.178269 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.5674 | 0.424855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.4279 | −0.554732 | −0.277366 | − | 0.960764i | \(-0.589461\pi\) | ||||
−0.277366 | + | 0.960764i | \(0.589461\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.3290 | 1.19162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.3567 | −1.46072 | −0.730362 | − | 0.683060i | \(-0.760649\pi\) | ||||
−0.730362 | + | 0.683060i | \(0.760649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2453 | 0.815920 | 0.407960 | − | 0.913000i | \(-0.366240\pi\) | ||||
0.407960 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.662272 | −0.0222620 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5718 | 0.388544 | 0.194272 | − | 0.980948i | \(-0.437766\pi\) | ||||
0.194272 | + | 0.980948i | \(0.437766\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6036 | −0.389172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.10336 | 0.170969 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.29606 | 0.0768347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.3616 | −2.38535 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.1587 | 0.673080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.131906 | 0.00439930 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00702 | −0.0668636 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.1597 | 0.704151 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.6049 | −0.651691 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4306 | −0.545568 | −0.272784 | − | 0.962075i | \(-0.587944\pi\) | ||||
−0.272784 | + | 0.962075i | \(0.587944\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.7645 | −0.589212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.2515 | 0.670963 | 0.335482 | − | 0.942047i | \(-0.391101\pi\) | ||||
0.335482 | + | 0.942047i | \(0.391101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86.1342 | −2.85063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.5500 | 0.844656 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1207 | −0.367238 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.8886 | −0.985934 | −0.492967 | − | 0.870048i | \(-0.664088\pi\) | ||||
−0.492967 | + | 0.870048i | \(0.664088\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.6542 | −0.713529 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −50.9150 | −1.67589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5101 | −0.937407 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.03080 | 0.165233 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.8483 | 1.11053 | 0.555263 | − | 0.831675i | \(-0.312618\pi\) | ||||
0.555263 | + | 0.831675i | \(0.312618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.04941 | −0.0999404 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.8153 | −1.20528 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.2794 | −0.924836 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.3480 | 1.08943 | 0.544715 | − | 0.838621i | \(-0.316638\pi\) | ||||
0.544715 | + | 0.838621i | \(0.316638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.48367 | −0.113685 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.45689 | 0.210489 | 0.105244 | − | 0.994446i | \(-0.466438\pi\) | ||||
0.105244 | + | 0.994446i | \(0.466438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.9553 | 0.714963 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −29.6015 | −0.962937 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.36475 | −0.0443485 | −0.0221742 | − | 0.999754i | \(-0.507059\pi\) | ||||
−0.0221742 | + | 0.999754i | \(0.507059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.6203 | 1.02644 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.91653 | 0.0945749 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.51534 | 0.243446 | 0.121723 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121723 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.20905 | 0.265639 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.386216 | 0.0124846 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.3022 | −0.623302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1045 | −0.874338 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.91525 | −0.158392 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 58.5304 | 1.88416 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.4244 | 1.29996 | 0.649981 | − | 0.759950i | \(-0.274777\pi\) | ||||
0.649981 | + | 0.759950i | \(0.274777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.28790 | 0.0734980 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.3407 | −1.03786 | −0.518932 | − | 0.854816i | \(-0.673670\pi\) | ||||
−0.518932 | + | 0.854816i | \(0.673670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.0496 | 0.803055 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.4661 | −0.431260 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.2386 | 1.31934 | 0.659670 | − | 0.751556i | \(-0.270696\pi\) | ||||
0.659670 | + | 0.751556i | \(0.270696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.2763 | −0.711953 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.55911 | −0.177489 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.1516 | 1.82285 | 0.911426 | − | 0.411465i | \(-0.134983\pi\) | ||||
0.911426 | + | 0.411465i | \(0.134983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.04334 | −0.224419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.20234 | −0.165592 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.0977 | 1.21144 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.489719 | 0.0155564 | 0.00777822 | − | 0.999970i | \(-0.497524\pi\) | ||||
0.00777822 | + | 0.999970i | \(0.497524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.4342 | −0.997535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.79950 | −0.310665 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7390 | 0.625142 | 0.312571 | − | 0.949894i | \(-0.398810\pi\) | ||||
0.312571 | + | 0.949894i | \(0.398810\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −56.0592 | −1.77363 |
(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 | 4028.2.a.e.1.7 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.e.1.7 | ✓ | 19 | 1.1 | even | 1 | trivial |