Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.546295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | 0.546295 | 0.315403 | 0.157702 | − | 0.987487i | \(-0.449592\pi\) | ||||
0.157702 | + | 0.987487i | \(0.449592\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70156 | −0.900521 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70156 | −0.513040 | −0.256520 | − | 0.966539i | \(-0.582576\pi\) | ||||
−0.256520 | + | 0.966539i | \(0.582576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.546295 | −0.151515 | −0.0757574 | − | 0.997126i | \(-0.524137\pi\) | ||||
−0.0757574 | + | 0.997126i | \(0.524137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.11473 | 0.755434 | 0.377717 | − | 0.925921i | \(-0.376709\pi\) | ||||
0.377717 | + | 0.925921i | \(0.376709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.75362 | −1.09055 | −0.545277 | − | 0.838256i | \(-0.683576\pi\) | ||||
−0.545277 | + | 0.838256i | \(0.683576\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.40312 | 1.12663 | 0.563315 | − | 0.826242i | \(-0.309526\pi\) | ||||
0.563315 | + | 0.826242i | \(0.309526\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.11473 | −0.599431 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.298438 | −0.0554185 | −0.0277093 | − | 0.999616i | \(-0.508821\pi\) | ||||
−0.0277093 | + | 0.999616i | \(0.508821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.32206 | 1.31508 | 0.657540 | − | 0.753420i | \(-0.271597\pi\) | ||||
0.657540 | + | 0.753420i | \(0.271597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.929554 | −0.161815 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.40312 | 0.888268 | 0.444134 | − | 0.895960i | \(-0.353511\pi\) | ||||
0.444134 | + | 0.895960i | \(0.353511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.298438 | −0.0477883 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.32206 | −1.14351 | −0.571756 | − | 0.820423i | \(-0.693738\pi\) | ||||
−0.571756 | + | 0.820423i | \(0.693738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.25161 | 1.20362 | 0.601811 | − | 0.798639i | \(-0.294446\pi\) | ||||
0.601811 | + | 0.798639i | \(0.294446\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.70156 | 0.238266 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.40312 | 0.192734 | 0.0963670 | − | 0.995346i | \(-0.469278\pi\) | ||||
0.0963670 | + | 0.995346i | \(0.469278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.59688 | −0.343965 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.70532 | −1.00315 | −0.501573 | − | 0.865115i | \(-0.667245\pi\) | ||||
−0.501573 | + | 0.865115i | \(0.667245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89049 | 1.26635 | 0.633174 | − | 0.774009i | \(-0.281752\pi\) | ||||
0.633174 | + | 0.774009i | \(0.281752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.95170 | 0.355343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.40312 | −0.641233 | −0.320616 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320616 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.3663 | −1.33033 | −0.665165 | − | 0.746696i | \(-0.731639\pi\) | ||||
−0.665165 | + | 0.746696i | \(0.731639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1047 | 1.24937 | 0.624687 | − | 0.780875i | \(-0.285226\pi\) | ||||
0.624687 | + | 0.780875i | \(0.285226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.40312 | 0.711458 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89049 | 1.08562 | 0.542811 | − | 0.839855i | \(-0.317360\pi\) | ||||
0.542811 | + | 0.839855i | \(0.317360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.163035 | −0.0174792 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.8293 | −1.78390 | −0.891951 | − | 0.452133i | \(-0.850663\pi\) | ||||
−0.891951 | + | 0.452133i | \(0.850663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.29991 | 0.538125 | 0.269062 | − | 0.963123i | \(-0.413286\pi\) | ||||
0.269062 | + | 0.963123i | \(0.413286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.59688 | 0.462003 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.383260 | −0.0381358 | −0.0190679 | − | 0.999818i | \(-0.506070\pi\) | ||||
−0.0190679 | + | 0.999818i | \(0.506070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.8514 | −1.85749 | −0.928743 | − | 0.370723i | \(-0.879110\pi\) | ||||
−0.928743 | + | 0.370723i | \(0.879110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29844 | 0.411716 | 0.205858 | − | 0.978582i | \(-0.434002\pi\) | ||||
0.205858 | + | 0.978582i | \(0.434002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.95170 | 0.280163 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.40312 | −0.508283 | −0.254142 | − | 0.967167i | \(-0.581793\pi\) | ||||
−0.254142 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.47585 | 0.136442 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10469 | −0.736790 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | −0.360668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4031 | −1.54428 | −0.772139 | − | 0.635454i | \(-0.780813\pi\) | ||||
−0.772139 | + | 0.635454i | \(0.780813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.18518 | −0.192394 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.89049 | 0.864136 | 0.432068 | − | 0.901841i | \(-0.357784\pi\) | ||||
0.432068 | + | 0.901841i | \(0.357784\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.0000 | −1.70872 | −0.854358 | − | 0.519685i | \(-0.826049\pi\) | ||||
−0.854358 | + | 0.519685i | \(0.826049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.93880 | −0.588541 | −0.294270 | − | 0.955722i | \(-0.595077\pi\) | ||||
−0.294270 | + | 0.955722i | \(0.595077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.50781 | 0.379626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.929554 | 0.0777332 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.29844 | −0.512560 | −0.256280 | − | 0.966603i | \(-0.582497\pi\) | ||||
−0.256280 | + | 0.966603i | \(0.582497\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.41464 | −0.680284 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3051 | 1.46091 | 0.730455 | − | 0.682961i | \(-0.239308\pi\) | ||||
0.730455 | + | 0.682961i | \(0.239308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.766519 | 0.0607889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8062 | −0.846411 | −0.423205 | − | 0.906034i | \(-0.639095\pi\) | ||||
−0.423205 | + | 0.906034i | \(0.639095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6663 | −1.28967 | −0.644837 | − | 0.764320i | \(-0.723075\pi\) | ||||
−0.644837 | + | 0.764320i | \(0.723075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7016 | −0.977043 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.8422 | 0.982067 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.91665 | 0.373806 | 0.186903 | − | 0.982378i | \(-0.440155\pi\) | ||||
0.186903 | + | 0.982378i | \(0.440155\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.20937 | −0.316396 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8062 | −0.807697 | −0.403848 | − | 0.914826i | \(-0.632328\pi\) | ||||
−0.403848 | + | 0.914826i | \(0.632328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.56844 | −0.190911 | −0.0954553 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954553 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.40312 | 0.399410 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.29991 | −0.387568 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7016 | 0.846695 | 0.423348 | − | 0.905967i | \(-0.360855\pi\) | ||||
0.423348 | + | 0.905967i | \(0.360855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2094 | −1.16678 | −0.583388 | − | 0.812194i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812194i | \(0.698273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.2094 | −1.72485 | −0.862423 | − | 0.506188i | \(-0.831054\pi\) | ||||
−0.862423 | + | 0.506188i | \(0.831054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.13688 | −0.364144 | −0.182072 | − | 0.983285i | \(-0.558280\pi\) | ||||
−0.182072 | + | 0.983285i | \(0.558280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.37036 | −0.308261 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.5969 | −1.01455 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.08857 | 0.559498 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7016 | 0.943254 | 0.471627 | − | 0.881798i | \(-0.343667\pi\) | ||||
0.471627 | + | 0.881798i | \(0.343667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.95170 | −0.202247 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.20937 | −0.419591 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.70156 | −0.114459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.48509 | 0.501239 | 0.250619 | − | 0.968086i | \(-0.419366\pi\) | ||||
0.250619 | + | 0.968086i | \(0.419366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.5567 | −1.76263 | −0.881317 | − | 0.472526i | \(-0.843342\pi\) | ||||
−0.881317 | + | 0.472526i | \(0.843342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.75362 | 0.314128 | 0.157064 | − | 0.987588i | \(-0.449797\pi\) | ||||
0.157064 | + | 0.987588i | \(0.449797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.06643 | 0.394057 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.70156 | 0.627542 | 0.313771 | − | 0.949499i | \(-0.398408\pi\) | ||||
0.313771 | + | 0.949499i | \(0.398408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.95170 | −0.190136 | −0.0950678 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950678 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8422 | 0.823827 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.59688 | 0.165235 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.40312 | 0.342409 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.93880 | −0.437973 | −0.218986 | − | 0.975728i | \(-0.570275\pi\) | ||||
−0.218986 | + | 0.975728i | \(0.570275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.19375 | −0.578006 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.46295 | 0.340769 | 0.170385 | − | 0.985378i | \(-0.445499\pi\) | ||||
0.170385 | + | 0.985378i | \(0.445499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.806248 | 0.0499055 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.19375 | −0.562648 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7198 | 1.62913 | 0.814567 | − | 0.580070i | \(-0.196975\pi\) | ||||
0.814567 | + | 0.580070i | \(0.196975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.7327 | −1.38091 | −0.690456 | − | 0.723374i | \(-0.742590\pi\) | ||||
−0.690456 | + | 0.723374i | \(0.742590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4031 | −1.52633 | −0.763163 | − | 0.646206i | \(-0.776355\pi\) | ||||
−0.763163 | + | 0.646206i | \(0.776355\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.7810 | −1.18426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9109 | −1.06848 | −0.534238 | − | 0.845334i | \(-0.679402\pi\) | ||||
−0.534238 | + | 0.845334i | \(0.679402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2347 | 1.14338 | 0.571692 | − | 0.820468i | \(-0.306287\pi\) | ||||
0.571692 | + | 0.820468i | \(0.306287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.29844 | −0.429320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.89531 | 0.169726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.3313 | −0.778823 | −0.389411 | − | 0.921064i | \(-0.627322\pi\) | ||||
−0.389411 | + | 0.921064i | \(0.627322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.29991 | 0.307532 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.95170 | −0.170701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.209373 | −0.0120281 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4199 | 1.22250 | 0.611248 | − | 0.791439i | \(-0.290668\pi\) | ||||
0.611248 | + | 0.791439i | \(0.290668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.2984 | −0.585858 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1030 | −1.53687 | −0.768436 | − | 0.639926i | \(-0.778965\pi\) | ||||
−0.768436 | + | 0.639926i | \(0.778965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1735 | 1.47941 | 0.739707 | − | 0.672930i | \(-0.234964\pi\) | ||||
0.739707 | + | 0.672930i | \(0.234964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.4031 | 0.977457 | 0.488728 | − | 0.872436i | \(-0.337461\pi\) | ||||
0.488728 | + | 0.872436i | \(0.337461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.507811 | 0.0284319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.37036 | 0.243930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8062 | −0.823842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.34821 | 0.129857 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8062 | −0.593965 | −0.296983 | − | 0.954883i | \(-0.595980\pi\) | ||||
−0.296983 | + | 0.954883i | \(0.595980\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.5969 | −0.799904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5969 | −0.795142 | −0.397571 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397571 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.95170 | −0.160314 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4589 | −0.674689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.8062 | −1.65377 | −0.826883 | − | 0.562374i | \(-0.809888\pi\) | ||||
−0.826883 | + | 0.562374i | \(0.809888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0274 | −0.804397 | −0.402198 | − | 0.915553i | \(-0.631754\pi\) | ||||
−0.402198 | + | 0.915553i | \(0.631754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.70156 | 0.0908227 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7105 | 1.10231 | 0.551155 | − | 0.834403i | \(-0.314187\pi\) | ||||
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.8062 | 1.62589 | 0.812946 | − | 0.582339i | \(-0.197862\pi\) | ||||
0.812946 | + | 0.582339i | \(0.197862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.59688 | 0.189309 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.42755 | −0.232386 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.29991 | 0.276653 | 0.138327 | − | 0.990387i | \(-0.455828\pi\) | ||||
0.138327 | + | 0.990387i | \(0.455828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.7810 | 1.02976 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.40312 | −0.279763 | −0.139882 | − | 0.990168i | \(-0.544672\pi\) | ||||
−0.139882 | + | 0.990168i | \(0.544672\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.163035 | 0.00839673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.6125 | 1.93202 | 0.966012 | − | 0.258497i | \(-0.0832272\pi\) | ||||
0.966012 | + | 0.258497i | \(0.0832272\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.50723 | −0.487070 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.8776 | −0.709112 | −0.354556 | − | 0.935035i | \(-0.615368\pi\) | ||||
−0.354556 | + | 0.935035i | \(0.615368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.8062 | 0.549312 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.1047 | 0.563030 | 0.281515 | − | 0.959557i | \(-0.409163\pi\) | ||||
0.281515 | + | 0.959557i | \(0.409163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8293 | 0.851094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.40312 | 0.272552 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.5567 | −1.33285 | −0.666423 | − | 0.745574i | \(-0.732175\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732175\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.29844 | −0.314529 | −0.157264 | − | 0.987557i | \(-0.550268\pi\) | ||||
−0.157264 | + | 0.987557i | \(0.550268\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.19375 | −0.455717 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.13688 | 0.254002 | 0.127001 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127001 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.9259 | −0.538935 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.79063 | −0.185628 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5829 | 1.05439 | 0.527197 | − | 0.849743i | \(-0.323243\pi\) | ||||
0.527197 | + | 0.849743i | \(0.323243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.5078 | −1.09696 | −0.548482 | − | 0.836163i | \(-0.684794\pi\) | ||||
−0.548482 | + | 0.836163i | \(0.684794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.2922 | −1.08389 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.507811 | 0.0245173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.89531 | −0.139462 | −0.0697312 | − | 0.997566i | \(-0.522214\pi\) | ||||
−0.0697312 | + | 0.997566i | \(0.522214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.85911 | −0.0893431 | −0.0446715 | − | 0.999002i | \(-0.514224\pi\) | ||||
−0.0446715 | + | 0.999002i | \(0.514224\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.6844 | −1.22865 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.5620 | 1.88819 | 0.944095 | − | 0.329673i | \(-0.106939\pi\) | ||||
0.944095 | + | 0.329673i | \(0.106939\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.4187 | 1.73031 | 0.865153 | − | 0.501507i | \(-0.167221\pi\) | ||||
0.865153 | + | 0.501507i | \(0.167221\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.46295 | −0.258389 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.1047 | −1.46792 | −0.733960 | − | 0.679192i | \(-0.762330\pi\) | ||||
−0.733960 | + | 0.679192i | \(0.762330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4589 | 0.586668 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.44080 | −0.161663 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2094 | 1.13247 | 0.566233 | − | 0.824245i | \(-0.308400\pi\) | ||||
0.566233 | + | 0.824245i | \(0.308400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.70156 | −0.452830 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.93880 | −0.323172 | −0.161586 | − | 0.986859i | \(-0.551661\pi\) | ||||
−0.161586 | + | 0.986859i | \(0.551661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8062 | −1.43169 | −0.715844 | − | 0.698260i | \(-0.753958\pi\) | ||||
−0.715844 | + | 0.698260i | \(0.753958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.0197 | −1.48169 | −0.740847 | − | 0.671673i | \(-0.765576\pi\) | ||||
−0.740847 | + | 0.671673i | \(0.765576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.80625 | 0.312952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.79063 | −0.173561 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.5137 | 1.94250 | 0.971250 | − | 0.238063i | \(-0.0765125\pi\) | ||||
0.971250 | + | 0.238063i | \(0.0765125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.95170 | −0.134586 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.2094 | −1.64080 | −0.820402 | − | 0.571788i | \(-0.806250\pi\) | ||||
−0.820402 | + | 0.571788i | \(0.806250\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.90340 | −0.266961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.5078 | 1.46706 | 0.733528 | − | 0.679659i | \(-0.237872\pi\) | ||||
0.733528 | + | 0.679659i | \(0.237872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.929554 | −0.0418650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.507811 | −0.0227327 | −0.0113664 | − | 0.999935i | \(-0.503618\pi\) | ||||
−0.0113664 | + | 0.999935i | \(0.503618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.10469 | −0.406767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.34420 | 0.416637 | 0.208319 | − | 0.978061i | \(-0.433201\pi\) | ||||
0.208319 | + | 0.978061i | \(0.433201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.93880 | −0.308163 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.93880 | 0.307557 | 0.153778 | − | 0.988105i | \(-0.450856\pi\) | ||||
0.153778 | + | 0.988105i | \(0.450856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.8062 | 0.653712 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.0406 | −0.617506 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.68594 | 0.117900 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3365 | −1.15382 | −0.576912 | − | 0.816806i | \(-0.695742\pi\) | ||||
−0.576912 | + | 0.816806i | \(0.695742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3011 | 1.10634 | 0.553170 | − | 0.833068i | \(-0.313418\pi\) | ||||
0.553170 | + | 0.833068i | \(0.313418\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8062 | 0.993456 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.19375 | 0.269294 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.8164 | 0.903354 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.90340 | −0.254750 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5078 | 0.623739 | 0.311870 | − | 0.950125i | \(-0.399045\pi\) | ||||
0.311870 | + | 0.950125i | \(0.399045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.40312 | −0.0602138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.6125 | −1.77922 | −0.889611 | − | 0.456719i | \(-0.849024\pi\) | ||||
−0.889611 | + | 0.456719i | \(0.849024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.7198 | −1.14037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41866 | 0.0604369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.4031 | −1.07636 | −0.538182 | − | 0.842828i | \(-0.680889\pi\) | ||||
−0.538182 | + | 0.842828i | \(0.680889\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.18518 | 0.0924232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.89531 | −0.122240 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.7939 | 0.665633 | 0.332817 | − | 0.942992i | \(-0.392001\pi\) | ||||
0.332817 | + | 0.942992i | \(0.392001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.4031 | −1.48418 | −0.742088 | − | 0.670302i | \(-0.766164\pi\) | ||||
−0.742088 | + | 0.670302i | \(0.766164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6125 | 0.904455 | 0.452227 | − | 0.891903i | \(-0.350630\pi\) | ||||
0.452227 | + | 0.891903i | \(0.350630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.39250 | 0.267051 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9923 | −0.707400 | −0.353700 | − | 0.935359i | \(-0.615077\pi\) | ||||
−0.353700 | + | 0.935359i | \(0.615077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.85509 | −0.368005 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.38750 | −0.0988803 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.98710 | 0.164565 | 0.0822826 | − | 0.996609i | \(-0.473779\pi\) | ||||
0.0822826 | + | 0.996609i | \(0.473779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.8062 | −1.43417 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2255 | −0.544022 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7105 | −0.850480 | −0.425240 | − | 0.905081i | \(-0.639810\pi\) | ||||
−0.425240 | + | 0.905081i | \(0.639810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.80625 | −0.114852 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.1047 | −0.453725 | −0.226863 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226863 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.1916 | 1.43550 | 0.717748 | − | 0.696303i | \(-0.245173\pi\) | ||||
0.717748 | + | 0.696303i | \(0.245173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.6125 | 0.880129 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3587 | 1.15104 | 0.575521 | − | 0.817787i | \(-0.304799\pi\) | ||||
0.575521 | + | 0.817787i | \(0.304799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.50781 | −0.182366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.40312 | 0.379789 | 0.189894 | − | 0.981805i | \(-0.439185\pi\) | ||||
0.189894 | + | 0.981805i | \(0.439185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4031 | −1.02269 | −0.511346 | − | 0.859375i | \(-0.670853\pi\) | ||||
−0.511346 | + | 0.859375i | \(0.670853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.89049 | −0.397533 | −0.198766 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.8293 | −0.675336 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.41875 | 0.176468 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.8293 | 0.671028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.50781 | 0.0998344 | 0.0499172 | − | 0.998753i | \(-0.484104\pi\) | ||||
0.0499172 | + | 0.998753i | \(0.484104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.48509 | 0.297506 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5969 | 0.577443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.59688 | −0.181566 | −0.0907828 | − | 0.995871i | \(-0.528937\pi\) | ||||
−0.0907828 | + | 0.995871i | \(0.528937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.5712 | −1.79715 | −0.898577 | − | 0.438817i | \(-0.855398\pi\) | ||||
−0.898577 | + | 0.438817i | \(0.855398\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.5217 | 1.12130 | 0.560652 | − | 0.828052i | \(-0.310551\pi\) | ||||
0.560652 | + | 0.828052i | \(0.310551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1111 | 0.514655 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4031 | 0.837569 | 0.418784 | − | 0.908086i | \(-0.362456\pi\) | ||||
0.418784 | + | 0.908086i | \(0.362456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.7069 | 1.19799 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.1047 | 1.60121 | 0.800606 | − | 0.599192i | \(-0.204511\pi\) | ||||
0.800606 | + | 0.599192i | \(0.204511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8422 | 0.499503 | 0.249752 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249752 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.929554 | −0.0361009 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.61250 | −0.0624361 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.08907 | 0.158092 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.8293 | −0.649688 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.6125 | −1.60404 | −0.802022 | − | 0.597295i | \(-0.796242\pi\) | ||||
−0.802022 | + | 0.597295i | \(0.796242\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.3233 | 1.05012 | 0.525059 | − | 0.851066i | \(-0.324043\pi\) | ||||
0.525059 | + | 0.851066i | \(0.324043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5078 | −0.555941 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.19375 | −0.351789 | −0.175895 | − | 0.984409i | \(-0.556282\pi\) | ||||
−0.175895 | + | 0.984409i | \(0.556282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.59688 | 0.0990770 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.766519 | −0.0292021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.7198 | 1.01647 | 0.508234 | − | 0.861219i | \(-0.330298\pi\) | ||||
0.508234 | + | 0.861219i | \(0.330298\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.8062 | −0.863848 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3141 | 0.502865 | 0.251433 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251433 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.6844 | −0.968705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.1047 | −1.31838 | −0.659192 | − | 0.751975i | \(-0.729102\pi\) | ||||
−0.659192 | + | 0.751975i | \(0.729102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.0000 | −1.12509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.5620 | 1.48161 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.29991 | 0.197929 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.95170 | −0.110080 | −0.0550399 | − | 0.998484i | \(-0.517529\pi\) | ||||
−0.0550399 | + | 0.998484i | \(0.517529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.61250 | −0.0599694 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.7810 | 0.733636 | 0.366818 | − | 0.930293i | \(-0.380447\pi\) | ||||
0.366818 | + | 0.930293i | \(0.380447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.1938 | −0.451620 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4589 | −0.460810 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2830 | 0.601426 | 0.300713 | − | 0.953715i | \(-0.402775\pi\) | ||||
0.300713 | + | 0.953715i | \(0.402775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6125 | 0.501423 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5078 | −0.754392 | −0.377196 | − | 0.926133i | \(-0.623112\pi\) | ||||
−0.377196 | + | 0.926133i | \(0.623112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.41866 | 0.0521158 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.40312 | 0.344967 | 0.172484 | − | 0.985012i | \(-0.444821\pi\) | ||||
0.172484 | + | 0.985012i | \(0.444821\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.7198 | −0.977626 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.5078 | 0.894303 | 0.447151 | − | 0.894458i | \(-0.352439\pi\) | ||||
0.447151 | + | 0.894458i | \(0.352439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.79063 | −0.138138 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5969 | −0.530532 | −0.265266 | − | 0.964175i | \(-0.585460\pi\) | ||||
−0.265266 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.02250 | −0.182305 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.7069 | 1.11312 | 0.556562 | − | 0.830806i | \(-0.312120\pi\) | ||||
0.556562 | + | 0.830806i | \(0.312120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.20937 | 0.151992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0403 | −0.398122 | −0.199061 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199061 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.98438 | 0.107480 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.6936 | 1.13994 | 0.569970 | − | 0.821665i | \(-0.306955\pi\) | ||||
0.569970 | + | 0.821665i | \(0.306955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.8062 | 1.24706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.19375 | 0.328978 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.929554 | 0.0332196 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.9569 | 0.568803 | 0.284401 | − | 0.958705i | \(-0.408205\pi\) | ||||
0.284401 | + | 0.958705i | \(0.408205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.74071 | −0.311178 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.40312 | −0.191871 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.4343 | −1.43226 | −0.716129 | − | 0.697968i | \(-0.754088\pi\) | ||||
−0.716129 | + | 0.697968i | \(0.754088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.7016 | 0.909256 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.4654 | 1.60644 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.3405 | 0.682513 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5969 | 0.513834 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5078 | 0.580384 | 0.290192 | − | 0.956968i | \(-0.406281\pi\) | ||||
0.290192 | + | 0.956968i | \(0.406281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.4042 | −1.84016 | −0.920080 | − | 0.391731i | \(-0.871876\pi\) | ||||
−0.920080 | + | 0.391731i | \(0.871876\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4187 | −0.435544 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.0145 | 0.665232 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.3141 | −1.58147 | −0.790736 | − | 0.612158i | \(-0.790302\pi\) | ||||
−0.790736 | + | 0.612158i | \(0.790302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8062 | 0.516113 | 0.258057 | − | 0.966130i | \(-0.416918\pi\) | ||||
0.258057 | + | 0.966130i | \(0.416918\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.8062 | −0.375770 | −0.187885 | − | 0.982191i | \(-0.560163\pi\) | ||||
−0.187885 | + | 0.982191i | \(0.560163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.4122 | −1.33411 | −0.667055 | − | 0.745008i | \(-0.732446\pi\) | ||||
−0.667055 | + | 0.745008i | \(0.732446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.8776 | −0.481408 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.8062 | −0.788299 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.7069 | 1.06012 | 0.530060 | − | 0.847960i | \(-0.322170\pi\) | ||||
0.530060 | + | 0.847960i | \(0.322170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9109 | −0.996929 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.78465 | −0.337001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5078 | 0.360627 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.1938 | 1.00075 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.47585 | 0.0505321 | 0.0252661 | − | 0.999681i | \(-0.491957\pi\) | ||||
0.0252661 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.2439 | −0.862316 | −0.431158 | − | 0.902276i | \(-0.641895\pi\) | ||||
−0.431158 | + | 0.902276i | \(0.641895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.6232 | −1.11309 | −0.556544 | − | 0.830818i | \(-0.687873\pi\) | ||||
−0.556544 | + | 0.830818i | \(0.687873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.4187 | −0.967385 | −0.483693 | − | 0.875238i | \(-0.660705\pi\) | ||||
−0.483693 | + | 0.875238i | \(0.660705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.98710 | −0.135409 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.8953 | −0.640980 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.37036 | 0.148084 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.3180 | −0.484592 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.0156 | −1.18239 | −0.591197 | − | 0.806527i | \(-0.701344\pi\) | ||||
−0.591197 | + | 0.806527i | \(0.701344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.28282 | −0.245643 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.5620 | −1.33288 | −0.666438 | − | 0.745560i | \(-0.732182\pi\) | ||||
−0.666438 | + | 0.745560i | \(0.732182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.19375 | −0.309394 | −0.154697 | − | 0.987962i | \(-0.549440\pi\) | ||||
−0.154697 | + | 0.987962i | \(0.549440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.6844 | 0.862397 | 0.431199 | − | 0.902257i | \(-0.358091\pi\) | ||||
0.431199 | + | 0.902257i | \(0.358091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8953 | −0.365007 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.2250 | −1.31261 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.61250 | −0.0538397 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.18518 | −0.0728798 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.37036 | 0.145598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.19375 | 0.305274 | 0.152637 | − | 0.988282i | \(-0.451224\pi\) | ||||
0.152637 | + | 0.988282i | \(0.451224\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.03540 | 0.0343420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.8062 | −1.02066 | −0.510328 | − | 0.859980i | \(-0.670476\pi\) | ||||
−0.510328 | + | 0.859980i | \(0.670476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.8293 | −0.556968 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.9109 | 1.38251 | 0.691257 | − | 0.722609i | \(-0.257057\pi\) | ||||
0.691257 | + | 0.722609i | \(0.257057\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7016 | 0.385580 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.95170 | 0.0971563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.9283 | 1.67271 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.13688 | 0.168535 | 0.0842677 | − | 0.996443i | \(-0.473145\pi\) | ||||
0.0842677 | + | 0.996443i | \(0.473145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.8062 | −0.484735 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.0431 | −1.76551 | −0.882755 | − | 0.469834i | \(-0.844314\pi\) | ||||
−0.882755 | + | 0.469834i | \(0.844314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2984 | 0.466612 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.7681 | 0.774817 | 0.387409 | − | 0.921908i | \(-0.373370\pi\) | ||||
0.387409 | + | 0.921908i | \(0.373370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.5620 | −1.28832 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.8062 | −0.741103 | −0.370552 | − | 0.928812i | \(-0.620831\pi\) | ||||
−0.370552 | + | 0.928812i | \(0.620831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.20937 | 0.201565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.50723 | 0.308293 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.6125 | 0.829670 | 0.414835 | − | 0.909897i | \(-0.363839\pi\) | ||||
0.414835 | + | 0.909897i | \(0.363839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.277414 | 0.00896753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6125 | 0.729435 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.6125 | −0.696453 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.20937 | 0.135364 | 0.0676822 | − | 0.997707i | \(-0.478440\pi\) | ||||
0.0676822 | + | 0.997707i | \(0.478440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.08857 | −0.259842 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.9597 | 1.89211 | 0.946053 | − | 0.324011i | \(-0.105031\pi\) | ||||
0.946053 | + | 0.324011i | \(0.105031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.6361 | 0.915213 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.6125 | −0.370758 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.5398 | −1.19733 | −0.598667 | − | 0.800998i | \(-0.704303\pi\) | ||||
−0.598667 | + | 0.800998i | \(0.704303\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.6125 | −0.687237 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.2094 | −1.53142 | −0.765711 | − | 0.643185i | \(-0.777613\pi\) | ||||
−0.765711 | + | 0.643185i | \(0.777613\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.90340 | −0.187339 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.07933 | 0.0658531 | 0.0329266 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329266 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.8293 | −0.532455 |
(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 | 9800.2.a.co.1.3 | 4 | ||
5.2 | odd | 4 | 1960.2.g.d.1569.4 | yes | 8 | ||
5.3 | odd | 4 | 1960.2.g.d.1569.6 | yes | 8 | ||
5.4 | even | 2 | 9800.2.a.cp.1.2 | 4 | |||
7.6 | odd | 2 | inner | 9800.2.a.co.1.2 | 4 | ||
35.13 | even | 4 | 1960.2.g.d.1569.3 | ✓ | 8 | ||
35.27 | even | 4 | 1960.2.g.d.1569.5 | yes | 8 | ||
35.34 | odd | 2 | 9800.2.a.cp.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.g.d.1569.3 | ✓ | 8 | 35.13 | even | 4 | ||
1960.2.g.d.1569.4 | yes | 8 | 5.2 | odd | 4 | ||
1960.2.g.d.1569.5 | yes | 8 | 35.27 | even | 4 | ||
1960.2.g.d.1569.6 | yes | 8 | 5.3 | odd | 4 | ||
9800.2.a.co.1.2 | 4 | 7.6 | odd | 2 | inner | ||
9800.2.a.co.1.3 | 4 | 1.1 | even | 1 | trivial | ||
9800.2.a.cp.1.2 | 4 | 5.4 | even | 2 | |||
9800.2.a.cp.1.3 | 4 | 35.34 | odd | 2 |