Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, 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("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 19x^{8} + 44x^{7} + 86x^{6} - 236x^{5} - 58x^{4} + 368x^{3} - 194x^{2} - 12x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.97399\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.783186 | 0.452173 | 0.226086 | − | 0.974107i | \(-0.427407\pi\) | ||||
0.226086 | + | 0.974107i | \(0.427407\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.56843 | 1.59585 | 0.797924 | − | 0.602758i | \(-0.205931\pi\) | ||||
0.797924 | + | 0.602758i | \(0.205931\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.38662 | −0.795540 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.51888 | 0.759470 | 0.379735 | − | 0.925095i | \(-0.376015\pi\) | ||||
0.379735 | + | 0.925095i | \(0.376015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.52509 | 1.80974 | 0.904868 | − | 0.425693i | \(-0.139970\pi\) | ||||
0.904868 | + | 0.425693i | \(0.139970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.79474 | 0.721599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.93892 | −0.470258 | −0.235129 | − | 0.971964i | \(-0.575551\pi\) | ||||
−0.235129 | + | 0.971964i | \(0.575551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.56828 | 1.50687 | 0.753434 | − | 0.657524i | \(-0.228396\pi\) | ||||
0.753434 | + | 0.657524i | \(0.228396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.783186 | 0.170905 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.76749 | 0.577061 | 0.288531 | − | 0.957471i | \(-0.406833\pi\) | ||||
0.288531 | + | 0.957471i | \(0.406833\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.73367 | 1.54673 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.21872 | −0.811894 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.34745 | 0.435910 | 0.217955 | − | 0.975959i | \(-0.430061\pi\) | ||||
0.217955 | + | 0.975959i | \(0.430061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.50115 | −1.34725 | −0.673623 | − | 0.739075i | \(-0.735263\pi\) | ||||
−0.673623 | + | 0.739075i | \(0.735263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97275 | 0.343411 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.56843 | 0.603174 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.05146 | 0.994854 | 0.497427 | − | 0.867506i | \(-0.334278\pi\) | ||||
0.497427 | + | 0.867506i | \(0.334278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.11036 | 0.818313 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.71634 | −1.20509 | −0.602545 | − | 0.798085i | \(-0.705846\pi\) | ||||
−0.602545 | + | 0.798085i | \(0.705846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9178 | −1.66495 | −0.832473 | − | 0.554065i | \(-0.813076\pi\) | ||||
−0.832473 | + | 0.554065i | \(0.813076\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.51648 | −1.26956 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.18136 | −1.19337 | −0.596687 | − | 0.802474i | \(-0.703517\pi\) | ||||
−0.596687 | + | 0.802474i | \(0.703517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.51854 | −0.212638 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.04735 | −0.281225 | −0.140613 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140613 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.98842 | 1.21200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.14418 | 0.681364 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.911427 | 0.118658 | 0.0593288 | − | 0.998238i | \(-0.481104\pi\) | ||||
0.0593288 | + | 0.998238i | \(0.481104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.08843 | 0.267396 | 0.133698 | − | 0.991022i | \(-0.457315\pi\) | ||||
0.133698 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.38662 | −0.300686 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.2843 | 2.88806 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87592 | 0.229180 | 0.114590 | − | 0.993413i | \(-0.463445\pi\) | ||||
0.114590 | + | 0.993413i | \(0.463445\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.16746 | 0.260931 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3355 | −1.46395 | −0.731975 | − | 0.681331i | \(-0.761401\pi\) | ||||
−0.731975 | + | 0.681331i | \(0.761401\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1203 | 1.65265 | 0.826327 | − | 0.563190i | \(-0.190426\pi\) | ||||
0.826327 | + | 0.563190i | \(0.190426\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.05690 | 0.699390 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.51888 | 0.287053 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33547 | −0.937814 | −0.468907 | − | 0.883248i | \(-0.655352\pi\) | ||||
−0.468907 | + | 0.883248i | \(0.655352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.85582 | 0.428424 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.44004 | 0.706886 | 0.353443 | − | 0.935456i | \(-0.385011\pi\) | ||||
0.353443 | + | 0.935456i | \(0.385011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.91891 | −0.750461 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.83849 | 0.197107 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.56223 | −0.165596 | −0.0827980 | − | 0.996566i | \(-0.526386\pi\) | ||||
−0.0827980 | + | 0.996566i | \(0.526386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.52509 | 0.684016 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.87480 | −0.609188 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.4384 | 2.40473 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.9273 | 1.92178 | 0.960891 | − | 0.276928i | \(-0.0893165\pi\) | ||||
0.960891 | + | 0.276928i | \(0.0893165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.01160 | −0.604189 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.33962 | −0.431808 | −0.215904 | − | 0.976415i | \(-0.569270\pi\) | ||||
−0.215904 | + | 0.976415i | \(0.569270\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.28597 | 0.126710 | 0.0633552 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633552 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.79474 | 0.272739 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.1882 | −1.56497 | −0.782485 | − | 0.622670i | \(-0.786048\pi\) | ||||
−0.782485 | + | 0.622670i | \(0.786048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.27087 | −0.313292 | −0.156646 | − | 0.987655i | \(-0.550068\pi\) | ||||
−0.156646 | + | 0.987655i | \(0.550068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.73942 | 0.449846 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6115 | −0.998247 | −0.499124 | − | 0.866531i | \(-0.666345\pi\) | ||||
−0.499124 | + | 0.866531i | \(0.666345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.87558 | 0.920902 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.5729 | −1.43972 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.93892 | −0.177741 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.65526 | −0.423206 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.04333 | −0.544908 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.75488 | 0.872503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00575 | −0.355453 | −0.177726 | − | 0.984080i | \(-0.556874\pi\) | ||||
−0.177726 | + | 0.984080i | \(0.556874\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.55065 | −0.752843 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6188 | 1.97621 | 0.988105 | − | 0.153782i | \(-0.0491452\pi\) | ||||
0.988105 | + | 0.153782i | \(0.0491452\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.56828 | 0.569542 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.0542 | −1.29566 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.65295 | 0.226657 | 0.113329 | − | 0.993558i | \(-0.463849\pi\) | ||||
0.113329 | + | 0.993558i | \(0.463849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0524 | 1.02227 | 0.511135 | − | 0.859500i | \(-0.329225\pi\) | ||||
0.511135 | + | 0.859500i | \(0.329225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.40752 | −0.539611 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.4359 | 1.37444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.37670 | 0.695647 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.783186 | 0.0645961 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.867450 | −0.0710643 | −0.0355321 | − | 0.999369i | \(-0.511313\pi\) | ||||
−0.0355321 | + | 0.999369i | \(0.511313\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6652 | −1.35619 | −0.678097 | − | 0.734973i | \(-0.737195\pi\) | ||||
−0.678097 | + | 0.734973i | \(0.737195\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.62748 | 0.374109 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.7673 | −2.15000 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9584 | 0.874578 | 0.437289 | − | 0.899321i | \(-0.355939\pi\) | ||||
0.437289 | + | 0.899321i | \(0.355939\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.60346 | −0.127162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.76749 | 0.218109 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.05160 | 0.239020 | 0.119510 | − | 0.992833i | \(-0.461868\pi\) | ||||
0.119510 | + | 0.992833i | \(0.461868\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.03961 | 0.548033 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.8209 | −1.14688 | −0.573440 | − | 0.819248i | \(-0.694391\pi\) | ||||
−0.573440 | + | 0.819248i | \(0.694391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.5769 | 2.27514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.6760 | −1.19877 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.00098 | −0.304189 | −0.152095 | − | 0.988366i | \(-0.548602\pi\) | ||||
−0.152095 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.73367 | 0.584610 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.713817 | 0.0536537 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.78093 | 0.282600 | 0.141300 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141300 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3282 | −1.58531 | −0.792656 | − | 0.609669i | \(-0.791302\pi\) | ||||
−0.792656 | + | 0.609669i | \(0.791302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.63563 | 0.120909 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.5942 | 1.58764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.88391 | −0.357147 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.21872 | −0.306867 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.3082 | 1.46945 | 0.734726 | − | 0.678365i | \(-0.237311\pi\) | ||||
0.734726 | + | 0.678365i | \(0.237311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2843 | −0.812263 | −0.406132 | − | 0.913815i | \(-0.633123\pi\) | ||||
−0.406132 | + | 0.913815i | \(0.633123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.2359 | 1.30590 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4452 | 1.52791 | 0.763953 | − | 0.645272i | \(-0.223256\pi\) | ||||
0.763953 | + | 0.645272i | \(0.223256\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.8094 | 1.68780 | 0.843901 | − | 0.536499i | \(-0.180254\pi\) | ||||
0.843901 | + | 0.536499i | \(0.180254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.46920 | 0.103629 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.34745 | 0.164759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.5352 | −1.92314 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.60494 | −0.459075 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.5447 | 1.14442 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2738 | −1.46455 | −0.732273 | − | 0.681011i | \(-0.761540\pi\) | ||||
−0.732273 | + | 0.681011i | \(0.761540\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.66096 | −0.661958 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −38.9593 | −2.65700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.50115 | −0.509211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0588 | 0.747285 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6517 | −0.851043 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8047 | −0.790499 | −0.395249 | − | 0.918574i | \(-0.629342\pi\) | ||||
−0.395249 | + | 0.918574i | \(0.629342\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.4573 | −1.23049 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.4000 | −1.22125 | −0.610626 | − | 0.791919i | \(-0.709082\pi\) | ||||
−0.610626 | + | 0.791919i | \(0.709082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.65784 | −0.638208 | −0.319104 | − | 0.947720i | \(-0.603382\pi\) | ||||
−0.319104 | + | 0.947720i | \(0.603382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.97275 | 0.129797 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.53080 | −0.296823 | −0.148411 | − | 0.988926i | \(-0.547416\pi\) | ||||
−0.148411 | + | 0.988926i | \(0.547416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1946 | −1.90444 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.52822 | −0.424053 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.2524 | −1.24533 | −0.622666 | − | 0.782488i | \(-0.713950\pi\) | ||||
−0.622666 | + | 0.782488i | \(0.713950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9588 | 1.28566 | 0.642829 | − | 0.766010i | \(-0.277761\pi\) | ||||
0.642829 | + | 0.766010i | \(0.277761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.6760 | 1.00562 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.56843 | 0.227978 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.8587 | 2.72703 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.04375 | 0.319635 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.57278 | −0.604229 | −0.302114 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302114 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.97096 | 0.438261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.41879 | −0.339338 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.5779 | 0.784588 | 0.392294 | − | 0.919840i | \(-0.371682\pi\) | ||||
0.392294 | + | 0.919840i | \(0.371682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.05146 | 0.376019 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.60247 | −0.346784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9051 | 0.980751 | 0.490375 | − | 0.871511i | \(-0.336860\pi\) | ||||
0.490375 | + | 0.871511i | \(0.336860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.30582 | −0.448793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.22352 | −0.0748779 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.00098 | 0.243944 | 0.121972 | − | 0.992534i | \(-0.461078\pi\) | ||||
0.121972 | + | 0.992534i | \(0.461078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.80466 | 0.231117 | 0.115558 | − | 0.993301i | \(-0.463134\pi\) | ||||
0.115558 | + | 0.993301i | \(0.463134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.11036 | 0.309293 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.4801 | 1.17470 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6170 | −0.758085 | −0.379042 | − | 0.925379i | \(-0.623747\pi\) | ||||
−0.379042 | + | 0.925379i | \(0.623747\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.9024 | 1.07179 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.1161 | 0.782442 | 0.391221 | − | 0.920297i | \(-0.372053\pi\) | ||||
0.391221 | + | 0.920297i | \(0.372053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4251 | −0.738593 | −0.369297 | − | 0.929312i | \(-0.620401\pi\) | ||||
−0.369297 | + | 0.929312i | \(0.620401\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.3566 | 1.08735 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.71634 | −0.455481 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2406 | −0.778857 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.8236 | 0.868977 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8515 | 1.15974 | 0.579869 | − | 0.814709i | \(-0.303104\pi\) | ||||
0.579869 | + | 0.814709i | \(0.303104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.25236 | 0.189360 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.6264 | −0.616609 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.0581 | 1.04433 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9178 | −0.629291 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.39873 | −0.195252 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.45240 | 0.426723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.17681 | 0.124237 | 0.0621186 | − | 0.998069i | \(-0.480214\pi\) | ||||
0.0621186 | + | 0.998069i | \(0.480214\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00715 | 0.0572950 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.14523 | 0.178350 | 0.0891748 | − | 0.996016i | \(-0.471577\pi\) | ||||
0.0891748 | + | 0.996016i | \(0.471577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3476 | −0.697926 | −0.348963 | − | 0.937136i | \(-0.613466\pi\) | ||||
−0.348963 | + | 0.937136i | \(0.613466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.51648 | −0.479849 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.6070 | 0.988906 | 0.494453 | − | 0.869204i | \(-0.335368\pi\) | ||||
0.494453 | + | 0.869204i | \(0.335368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.91293 | 0.331061 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6783 | −0.707636 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.7354 | −0.708617 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 50.4629 | 2.79918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.56170 | −0.141662 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.18136 | −0.451053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0587 | 1.21246 | 0.606229 | − | 0.795290i | \(-0.292681\pi\) | ||||
0.606229 | + | 0.795290i | \(0.292681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.4425 | −0.791446 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.69409 | 0.365737 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0594 | 0.765866 | 0.382933 | − | 0.923776i | \(-0.374914\pi\) | ||||
0.382933 | + | 0.923776i | \(0.374914\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.31079 | −0.451380 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.8945 | −1.02319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.73441 | 0.416407 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.30730 | 0.445959 | 0.222980 | − | 0.974823i | \(-0.428422\pi\) | ||||
0.222980 | + | 0.974823i | \(0.428422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.30333 | 0.283881 | 0.141940 | − | 0.989875i | \(-0.454666\pi\) | ||||
0.141940 | + | 0.989875i | \(0.454666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.5276 | −1.46931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6280 | −1.15114 | −0.575571 | − | 0.817752i | \(-0.695220\pi\) | ||||
−0.575571 | + | 0.817752i | \(0.695220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.0182 | −2.33624 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.51854 | −0.0803696 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.8859 | −1.41898 | −0.709492 | − | 0.704713i | \(-0.751076\pi\) | ||||
−0.709492 | + | 0.704713i | \(0.751076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.1423 | 1.27065 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.64594 | −0.191362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 50.3872 | 2.63739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.41052 | −0.125828 | −0.0629140 | − | 0.998019i | \(-0.520039\pi\) | ||||
−0.0629140 | + | 0.998019i | \(0.520039\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.4160 | 0.958697 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.04735 | −0.106293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0549 | −0.572401 | −0.286200 | − | 0.958170i | \(-0.592392\pi\) | ||||
−0.286200 | + | 0.958170i | \(0.592392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.63989 | 0.394522 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.3173 | 0.788882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.96444 | −0.409106 | −0.204553 | − | 0.978855i | \(-0.565574\pi\) | ||||
−0.204553 | + | 0.978855i | \(0.565574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.13725 | −0.160726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.8440 | −1.11618 | −0.558089 | − | 0.829781i | \(-0.688465\pi\) | ||||
−0.558089 | + | 0.829781i | \(0.688465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.98842 | 0.458093 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.0566 | 1.32453 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.6875 | 1.35311 | 0.676555 | − | 0.736392i | \(-0.263472\pi\) | ||||
0.676555 | + | 0.736392i | \(0.263472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.36595 | −0.271368 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7147 | 0.893588 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.7445 | −1.49661 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8082 | 1.14471 | 0.572355 | − | 0.820006i | \(-0.306030\pi\) | ||||
0.572355 | + | 0.820006i | \(0.306030\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.14418 | 0.257531 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.202861 | −0.0101304 | −0.00506520 | − | 0.999987i | \(-0.501612\pi\) | ||||
−0.00506520 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.9457 | −2.43816 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.7592 | 0.683700 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.2429 | 0.755561 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5826 | −1.01774 | −0.508872 | − | 0.860842i | \(-0.669937\pi\) | ||||
−0.508872 | + | 0.860842i | \(0.669937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.07776 | 0.102488 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.911427 | 0.0448484 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.9808 | 1.12808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.43926 | 0.462243 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.4778 | 0.560727 | 0.280363 | − | 0.959894i | \(-0.409545\pi\) | ||||
0.280363 | + | 0.959894i | \(0.409545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6170 | −0.614917 | −0.307459 | − | 0.951561i | \(-0.599479\pi\) | ||||
−0.307459 | + | 0.951561i | \(0.599479\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.5258 | 0.949377 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.9950 | −0.727364 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.08843 | 0.101066 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.8724 | 0.621484 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7873 | 0.808618 | 0.404309 | − | 0.914623i | \(-0.367512\pi\) | ||||
0.404309 | + | 0.914623i | \(0.367512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.91585 | −0.140127 | −0.0700633 | − | 0.997543i | \(-0.522320\pi\) | ||||
−0.0700633 | + | 0.997543i | \(0.522320\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.56051 | 0.314552 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.1776 | 0.869555 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.3281 | −1.63839 | −0.819195 | − | 0.573516i | \(-0.805579\pi\) | ||||
−0.819195 | + | 0.573516i | \(0.805579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.38662 | −0.113649 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.70289 | 0.365975 | 0.182988 | − | 0.983115i | \(-0.441423\pi\) | ||||
0.182988 | + | 0.983115i | \(0.441423\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.57470 | −0.264266 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.679375 | −0.0321333 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.5705 | −1.53710 | −0.768549 | − | 0.639792i | \(-0.779021\pi\) | ||||
−0.768549 | + | 0.639792i | \(0.779021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.4365 | −0.915229 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.0519 | −0.613233 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.2843 | 1.09159 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2825 | 1.65044 | 0.825222 | − | 0.564809i | \(-0.191050\pi\) | ||||
0.825222 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.17979 | 0.381800 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.63944 | −0.0763561 | −0.0381781 | − | 0.999271i | \(-0.512155\pi\) | ||||
−0.0381781 | + | 0.999271i | \(0.512155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.05450 | 0.188429 | 0.0942144 | − | 0.995552i | \(-0.469966\pi\) | ||||
0.0942144 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.9638 | −0.972172 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.80041 | 0.268411 | 0.134206 | − | 0.990954i | \(-0.457152\pi\) | ||||
0.134206 | + | 0.990954i | \(0.457152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.87592 | 0.0866220 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.58249 | 0.395460 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5005 | −1.26448 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 50.7969 | 2.33072 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.88625 | 0.223726 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.83014 | −0.357768 | −0.178884 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178884 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.4863 | 1.80042 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.16746 | 0.0986227 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 67.5408 | 3.06687 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8721 | 0.537976 | 0.268988 | − | 0.963144i | \(-0.413311\pi\) | ||||
0.268988 | + | 0.963144i | \(0.413311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.38997 | 0.108078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3134 | 0.465436 | 0.232718 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232718 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.55153 | −0.204990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.4520 | −0.964194 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.3355 | −0.553321 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.2726 | 0.817993 | 0.408996 | − | 0.912536i | \(-0.365879\pi\) | ||||
0.408996 | + | 0.912536i | \(0.365879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.6076 | −0.518587 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.13596 | −0.139826 | −0.0699128 | − | 0.997553i | \(-0.522272\pi\) | ||||
−0.0699128 | + | 0.997553i | \(0.522272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4856 | −0.689101 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.1642 | 1.02876 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.9768 | 0.841133 | 0.420567 | − | 0.907262i | \(-0.361831\pi\) | ||||
0.420567 | + | 0.907262i | \(0.361831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.1203 | 0.624645 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.7098 | −1.22342 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.58889 | 0.202211 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.6078 | −0.906332 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.13351 | −0.137546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.60942 | −0.158132 | −0.0790658 | − | 0.996869i | \(-0.525194\pi\) | ||||
−0.0790658 | + | 0.996869i | \(0.525194\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.26279 | −0.142672 | −0.0713360 | − | 0.997452i | \(-0.522726\pi\) | ||||
−0.0713360 | + | 0.997452i | \(0.522726\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.05690 | 0.264345 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.5442 | 0.633554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3410 | −0.667000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.17523 | −0.0943969 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −50.3498 | −2.18089 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −57.7663 | −2.49745 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.96117 | 0.127784 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.51888 | 0.108496 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.8816 | −1.75764 | −0.878818 | − | 0.477158i | \(-0.841667\pi\) | ||||
−0.878818 | + | 0.477158i | \(0.841667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.7039 | −0.716835 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.6718 | −0.499967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4933 | 1.68861 | 0.844305 | − | 0.535863i | \(-0.180014\pi\) | ||||
0.844305 | + | 0.535863i | \(0.180014\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.98428 | −0.212724 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.4187 | 0.656859 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.33547 | −0.354460 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9123 | 0.717885 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.9287 | −1.64946 | −0.824731 | − | 0.565525i | \(-0.808674\pi\) | ||||
−0.824731 | + | 0.565525i | \(0.808674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −71.2396 | −3.01311 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.82501 | −0.161492 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.1618 | 1.43975 | 0.719873 | − | 0.694105i | \(-0.244200\pi\) | ||||
0.719873 | + | 0.694105i | \(0.244200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.8664 | −1.59305 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.85582 | 0.161929 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.5861 | −0.904935 | −0.452467 | − | 0.891781i | \(-0.649456\pi\) | ||||
−0.452467 | + | 0.891781i | \(0.649456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.03105 | −0.336089 | −0.168045 | − | 0.985779i | \(-0.553745\pi\) | ||||
−0.168045 | + | 0.985779i | \(0.553745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.9051 | 0.664445 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.4028 | 0.892560 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.8009 | 1.90672 | 0.953359 | − | 0.301839i | \(-0.0976005\pi\) | ||||
0.953359 | + | 0.301839i | \(0.0976005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.83772 | −0.367283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.44004 | 0.267178 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.15702 | −0.213582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −55.5708 | −2.29757 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.87142 | −0.159791 | −0.0798954 | − | 0.996803i | \(-0.525459\pi\) | ||||
−0.0798954 | + | 0.996803i | \(0.525459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.2697 | −2.03012 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.7956 | 0.690877 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.4013 | −1.65908 | −0.829540 | − | 0.558447i | \(-0.811397\pi\) | ||||
−0.829540 | + | 0.558447i | \(0.811397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.91891 | −0.283648 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6472 | 0.763177 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8607 | −0.688911 | −0.344455 | − | 0.938803i | \(-0.611936\pi\) | ||||
−0.344455 | + | 0.938803i | \(0.611936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.7796 | −1.29632 | −0.648159 | − | 0.761505i | \(-0.724461\pi\) | ||||
−0.648159 | + | 0.761505i | \(0.724461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.47711 | −0.182322 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.6120 | −0.675372 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.3989 | −1.43680 | −0.718399 | − | 0.695631i | \(-0.755125\pi\) | ||||
−0.718399 | + | 0.695631i | \(0.755125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.83849 | 0.0744993 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.3842 | −2.15969 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6414 | −0.550971 | −0.275485 | − | 0.961305i | \(-0.588839\pi\) | ||||
−0.275485 | + | 0.961305i | \(0.588839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.5652 | −0.869591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.2668 | −1.62108 | −0.810540 | − | 0.585684i | \(-0.800826\pi\) | ||||
−0.810540 | + | 0.585684i | \(0.800826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1769 | 0.650205 | 0.325102 | − | 0.945679i | \(-0.394601\pi\) | ||||
0.325102 | + | 0.945679i | \(0.394601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.6753 | −0.468512 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.56223 | −0.0625894 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.85875 | −0.154350 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9576 | 0.517475 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.7333 | −0.467838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.79309 | −0.190810 | −0.0954049 | − | 0.995439i | \(-0.530415\pi\) | ||||
−0.0954049 | + | 0.995439i | \(0.530415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.6613 | −0.662227 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2942 | −0.567249 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.52509 | 0.258534 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.4401 | 1.16463 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.63323 | 0.183002 | 0.0915008 | − | 0.995805i | \(-0.470834\pi\) | ||||
0.0915008 | + | 0.995805i | \(0.470834\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.95425 | −0.234813 | −0.117406 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117406 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.5124 | −1.20142 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.8071 | 0.660754 | 0.330377 | − | 0.943849i | \(-0.392824\pi\) | ||||
0.330377 | + | 0.943849i | \(0.392824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.29577 | 0.0901169 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.87480 | −0.230251 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.80213 | −0.266188 | −0.133094 | − | 0.991103i | \(-0.542491\pi\) | ||||
−0.133094 | + | 0.991103i | \(0.542491\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 80.7134 | 3.15373 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.6998 | −1.31475 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.8568 | −1.78633 | −0.893163 | − | 0.449733i | \(-0.851519\pi\) | ||||
−0.893163 | + | 0.449733i | \(0.851519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.22646 | 0.125495 | 0.0627474 | − | 0.998029i | \(-0.480014\pi\) | ||||
0.0627474 | + | 0.998029i | \(0.480014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.90861 | −0.384818 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.4384 | 0.908903 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.49654 | 0.251547 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.24525 | −0.357442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.26049 | 0.203079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0871 | 0.388828 | 0.194414 | − | 0.980920i | \(-0.437719\pi\) | ||||
0.194414 | + | 0.980920i | \(0.437719\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −32.6262 | −1.25578 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.3792 | −1.24443 | −0.622216 | − | 0.782845i | \(-0.713768\pi\) | ||||
−0.622216 | + | 0.782845i | \(0.713768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.9273 | 0.726365 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.4106 | −0.552217 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7666 | 1.36857 | 0.684285 | − | 0.729215i | \(-0.260114\pi\) | ||||
0.684285 | + | 0.729215i | \(0.260114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.46687 | 0.361711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.56388 | −0.288580 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3592 | −0.508943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.9942 | −0.798657 | −0.399329 | − | 0.916808i | \(-0.630757\pi\) | ||||
−0.399329 | + | 0.916808i | \(0.630757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.01160 | −0.228362 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 43.0081 | 1.63139 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.9614 | 0.566703 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.54846 | −0.134215 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0388 | 0.945704 | 0.472852 | − | 0.881142i | \(-0.343225\pi\) | ||||
0.472852 | + | 0.881142i | \(0.343225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.7477 | 1.49911 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.8648 | −0.861137 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.33962 | −0.163208 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.5877 | −1.22386 | −0.611929 | − | 0.790913i | \(-0.709606\pi\) | ||||
−0.611929 | + | 0.790913i | \(0.709606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.8936 | 0.746068 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.7594 | −0.777444 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 58.6503 | 2.19340 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.0782 | −0.563105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.02299 | 0.336501 | 0.168250 | − | 0.985744i | \(-0.446188\pi\) | ||||
0.168250 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.28597 | 0.0478920 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.6314 | 0.581339 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.1544 | 0.674237 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.8802 | −0.626054 | −0.313027 | − | 0.949744i | \(-0.601343\pi\) | ||||
−0.313027 | + | 0.949744i | \(0.601343\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.709766 | 0.0262876 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.1688 | 0.782955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.9470 | 1.03225 | 0.516123 | − | 0.856514i | \(-0.327375\pi\) | ||||
0.516123 | + | 0.856514i | \(0.327375\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.79474 | 0.103086 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.72522 | 0.174056 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.6219 | −0.390733 | −0.195367 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195367 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.5663 | 1.23309 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.1417 | −1.58272 | −0.791358 | − | 0.611353i | \(-0.790626\pi\) | ||||
−0.791358 | + | 0.611353i | \(0.790626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.09543 | −0.113408 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3699 | −0.562356 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.1882 | −0.591503 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.11267 | 0.150073 | 0.0750367 | − | 0.997181i | \(-0.476093\pi\) | ||||
0.0750367 | + | 0.997181i | \(0.476093\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.49727 | −0.273216 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −59.4685 | −2.16428 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.08900 | 0.148617 | 0.0743087 | − | 0.997235i | \(-0.476325\pi\) | ||||
0.0743087 | + | 0.997235i | \(0.476325\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.45956 | 0.198169 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32450 | 0.0480131 | 0.0240065 | − | 0.999712i | \(-0.492358\pi\) | ||||
0.0240065 | + | 0.999712i | \(0.492358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.27087 | −0.118413 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.5128 | 0.597022 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.94715 | 0.214739 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.8450 | 0.643506 | 0.321753 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321753 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.85084 | 0.354769 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2378 | 0.476131 | 0.238066 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238066 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −58.0114 | −2.08383 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.73942 | 0.170026 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −50.6831 | −1.81591 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.0715 | −1.11183 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.90324 | −0.353913 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.1044 | 1.39569 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.2795 | 0.901118 | 0.450559 | − | 0.892747i | \(-0.351225\pi\) | ||||
0.450559 | + | 0.892747i | \(0.351225\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.4566 | 0.443468 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6115 | −0.377302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6272 | 0.483916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.72181 | −0.202932 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.5312 | −1.29400 | −0.647000 | − | 0.762490i | \(-0.723977\pi\) | ||||
−0.647000 | + | 0.762490i | \(0.723977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.8630 | 0.561194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.72845 | 0.131738 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.5673 | 1.25514 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.87558 | 0.348068 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.13351 | 0.110305 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.75351 | 0.307757 | 0.153879 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153879 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4106 | 0.822057 | 0.411029 | − | 0.911622i | \(-0.365170\pi\) | ||||
0.411029 | + | 0.911622i | \(0.365170\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.97976 | 0.104505 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.8894 | 0.381440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −71.7111 | −2.50885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.5729 | −0.544162 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.1296 | −0.807229 | −0.403614 | − | 0.914929i | \(-0.632246\pi\) | ||||
−0.403614 | + | 0.914929i | \(0.632246\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.2133 | 1.40175 | 0.700874 | − | 0.713285i | \(-0.252793\pi\) | ||||
0.700874 | + | 0.713285i | \(0.252793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.2566 | 0.531166 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.4702 | 1.19865 | 0.599323 | − | 0.800507i | \(-0.295436\pi\) | ||||
0.599323 | + | 0.800507i | \(0.295436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.4776 | −0.815412 | −0.407706 | − | 0.913113i | \(-0.633671\pi\) | ||||
−0.407706 | + | 0.913113i | \(0.633671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.88149 | −0.342785 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.93892 | −0.0671798 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.8875 | −1.83025 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.6453 | 1.09382 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.16748 | 0.0748296 | 0.0374148 | − | 0.999300i | \(-0.488088\pi\) | ||||
0.0374148 | + | 0.999300i | \(0.488088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4895 | −0.809982 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.2724 | 0.353799 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 105.543 | 3.63078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.65526 | −0.159957 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.73113 | −0.333972 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.7473 | 0.574092 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.1247 | 0.654818 | 0.327409 | − | 0.944883i | \(-0.393825\pi\) | ||||
0.327409 | + | 0.944883i | \(0.393825\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −55.9386 | −1.91306 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.73619 | 0.332582 | 0.166291 | − | 0.986077i | \(-0.446821\pi\) | ||||
0.166291 | + | 0.986077i | \(0.446821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.3577 | 1.27463 | 0.637314 | − | 0.770604i | \(-0.280045\pi\) | ||||
0.637314 | + | 0.770604i | \(0.280045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.04333 | −0.205956 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6964 | −0.602392 | −0.301196 | − | 0.953562i | \(-0.597386\pi\) | ||||
−0.301196 | + | 0.953562i | \(0.597386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2772 | −0.485440 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.3698 | −0.352178 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.9960 | −0.712241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2406 | 0.414756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −45.1724 | −1.52885 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.75488 | 0.329775 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9379 | −0.504417 | −0.252209 | − | 0.967673i | \(-0.581157\pi\) | ||||
−0.252209 | + | 0.967673i | \(0.581157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5474 | 0.524402 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1360 | −0.408873 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5340 | −0.354496 | −0.177248 | − | 0.984166i | \(-0.556719\pi\) | ||||
−0.177248 | + | 0.984166i | \(0.556719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.54720 | 0.0856233 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.9916 | −0.536944 | −0.268472 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268472 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00575 | −0.134349 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.71232 | 0.325375 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −53.7375 | −1.79826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4920 | 0.450987 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.1429 | 0.472217 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.6086 | −0.587279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.96966 | 0.132248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.55065 | −0.284548 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −76.1081 | −2.52992 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.0247 | 1.42861 | 0.714306 | − | 0.699833i | \(-0.246742\pi\) | ||||
0.714306 | + | 0.699833i | \(0.246742\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3570 | 0.343521 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.3708 | −1.17189 | −0.585943 | − | 0.810352i | \(-0.699276\pi\) | ||||
−0.585943 | + | 0.810352i | \(0.699276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.2217 | 0.536859 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.83661 | 0.192953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.6188 | 0.746937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.0087 | 1.45171 | 0.725857 | − | 0.687846i | \(-0.241444\pi\) | ||||
0.725857 | + | 0.687846i | \(0.241444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.70485 | 0.0561766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −80.4901 | −2.64936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.8000 | 1.53877 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.06912 | −0.100803 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.4669 | −1.52453 | −0.762265 | − | 0.647265i | \(-0.775913\pi\) | ||||
−0.762265 | + | 0.647265i | \(0.775913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.56828 | 0.215267 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.46330 | 0.0806448 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.4279 | −0.569953 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.4077 | 1.51607 | 0.758037 | − | 0.652211i | \(-0.226159\pi\) | ||||
0.758037 | + | 0.652211i | \(0.226159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.67045 | −0.315583 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.9398 | 0.715216 | 0.357608 | − | 0.933872i | \(-0.383592\pi\) | ||||
0.357608 | + | 0.933872i | \(0.383592\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.3549 | −0.695410 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.0542 | −0.489713 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.5392 | −1.70730 | −0.853648 | − | 0.520851i | \(-0.825615\pi\) | ||||
−0.853648 | + | 0.520851i | \(0.825615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 92.1362 | 2.99087 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.7895 | 0.447156 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.7325 | −1.93493 | −0.967463 | − | 0.253011i | \(-0.918579\pi\) | ||||
−0.967463 | + | 0.253011i | \(0.918579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 72.4684 | 2.34502 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.63092 | 0.149697 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.65295 | 0.0856684 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.2673 | 0.815074 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.6350 | 1.24500 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40.2673 | −1.29625 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.91826 | 0.318950 | 0.159475 | − | 0.987202i | \(-0.449020\pi\) | ||||
0.159475 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.97419 | −0.320417 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.4899 | −0.529188 | −0.264594 | − | 0.964360i | \(-0.585238\pi\) | ||||
−0.264594 | + | 0.964360i | \(0.585238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0524 | 0.386382 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.5218 | 1.26571 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.8390 | −0.666699 | −0.333350 | − | 0.942803i | \(-0.608179\pi\) | ||||
−0.333350 | + | 0.942803i | \(0.608179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.93506 | −0.125765 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.80631 | 0.249236 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.8056 | 1.39718 | 0.698591 | − | 0.715521i | \(-0.253811\pi\) | ||||
0.698591 | + | 0.715521i | \(0.253811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 76.5255 | 2.43831 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.40752 | −0.203954 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.2148 | −0.960776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.6400 | −1.67216 | −0.836082 | − | 0.548605i | \(-0.815159\pi\) | ||||
−0.836082 | + | 0.548605i | \(0.815159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2761 | 0.548240 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 84.9620 | 2.69348 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.2608 | −0.705006 | −0.352503 | − | 0.935811i | \(-0.614669\pi\) | ||||
−0.352503 | + | 0.935811i | \(0.614669\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.5294 | −0.807716 |
(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 | 3584.2.a.p.1.7 | yes | 10 | |
4.3 | odd | 2 | 3584.2.a.o.1.4 | ✓ | 10 | ||
8.3 | odd | 2 | 3584.2.a.o.1.7 | yes | 10 | ||
8.5 | even | 2 | inner | 3584.2.a.p.1.4 | yes | 10 | |
16.3 | odd | 4 | 3584.2.b.h.1793.4 | 10 | |||
16.5 | even | 4 | 3584.2.b.g.1793.4 | 10 | |||
16.11 | odd | 4 | 3584.2.b.h.1793.7 | 10 | |||
16.13 | even | 4 | 3584.2.b.g.1793.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.o.1.4 | ✓ | 10 | 4.3 | odd | 2 | ||
3584.2.a.o.1.7 | yes | 10 | 8.3 | odd | 2 | ||
3584.2.a.p.1.4 | yes | 10 | 8.5 | even | 2 | inner | |
3584.2.a.p.1.7 | yes | 10 | 1.1 | even | 1 | trivial | |
3584.2.b.g.1793.4 | 10 | 16.5 | even | 4 | |||
3584.2.b.g.1793.7 | 10 | 16.13 | even | 4 | |||
3584.2.b.h.1793.4 | 10 | 16.3 | odd | 4 | |||
3584.2.b.h.1793.7 | 10 | 16.11 | odd | 4 |