Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(1,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, 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("4900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.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: | \(39.1266969904\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 700) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.19869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.1 |
$q$-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 | ||||||||
\(3\) | −0.364448 | −0.210414 | −0.105207 | − | 0.994450i | \(-0.533551\pi\) | ||||
−0.105207 | + | 0.994450i | \(0.533551\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86718 | −0.955726 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36445 | 0.411397 | 0.205698 | − | 0.978615i | \(-0.434053\pi\) | ||||
0.205698 | + | 0.978615i | \(0.434053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.63555 | −0.730971 | −0.365485 | − | 0.930817i | \(-0.619097\pi\) | ||||
−0.365485 | + | 0.930817i | \(0.619097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23163 | 0.541249 | 0.270624 | − | 0.962685i | \(-0.412770\pi\) | ||||
0.270624 | + | 0.962685i | \(0.412770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.23163 | 1.42963 | 0.714816 | − | 0.699312i | \(-0.246510\pi\) | ||||
0.714816 | + | 0.699312i | \(0.246510\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.59607 | −1.37538 | −0.687688 | − | 0.726006i | \(-0.741374\pi\) | ||||
−0.687688 | + | 0.726006i | \(0.741374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13828 | 0.411512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.50273 | 1.02183 | 0.510916 | − | 0.859631i | \(-0.329306\pi\) | ||||
0.510916 | + | 0.859631i | \(0.329306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50273 | −0.808714 | −0.404357 | − | 0.914601i | \(-0.632505\pi\) | ||||
−0.404357 | + | 0.914601i | \(0.632505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.497270 | −0.0865637 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.09334 | 0.344144 | 0.172072 | − | 0.985084i | \(-0.444954\pi\) | ||||
0.172072 | + | 0.985084i | \(0.444954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.960522 | 0.153807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.32497 | −1.45632 | −0.728158 | − | 0.685410i | \(-0.759623\pi\) | ||||
−0.728158 | + | 0.685410i | \(0.759623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86718 | 0.284742 | 0.142371 | − | 0.989813i | \(-0.454527\pi\) | ||||
0.142371 | + | 0.989813i | \(0.454527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.86718 | −1.00168 | −0.500840 | − | 0.865540i | \(-0.666976\pi\) | ||||
−0.500840 | + | 0.865540i | \(0.666976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.813312 | −0.113886 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1383 | 1.39260 | 0.696300 | − | 0.717751i | \(-0.254828\pi\) | ||||
0.696300 | + | 0.717751i | \(0.254828\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.27110 | −0.300815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.63555 | 0.212931 | 0.106465 | − | 0.994316i | \(-0.466047\pi\) | ||||
0.106465 | + | 0.994316i | \(0.466047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0394782 | −0.00505467 | −0.00252733 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252733 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.72890 | 0.822065 | 0.411033 | − | 0.911621i | \(-0.365168\pi\) | ||||
0.411033 | + | 0.911621i | \(0.365168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.40393 | 0.289399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.27110 | −0.744243 | −0.372122 | − | 0.928184i | \(-0.621370\pi\) | ||||
−0.372122 | + | 0.928184i | \(0.621370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.32497 | 0.599106 | 0.299553 | − | 0.954080i | \(-0.403162\pi\) | ||||
0.299553 | + | 0.954080i | \(0.403162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82224 | 0.869138 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7738 | −1.62164 | −0.810819 | − | 0.585296i | \(-0.800978\pi\) | ||||
−0.810819 | + | 0.585296i | \(0.800978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00546 | −0.215008 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.867178 | −0.0919206 | −0.0459603 | − | 0.998943i | \(-0.514635\pi\) | ||||
−0.0459603 | + | 0.998943i | \(0.514635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.64101 | 0.170165 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0988 | −1.63459 | −0.817293 | − | 0.576222i | \(-0.804526\pi\) | ||||
−0.817293 | + | 0.576222i | \(0.804526\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.91211 | −0.393182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6949 | 1.56170 | 0.780849 | − | 0.624719i | \(-0.214787\pi\) | ||||
0.780849 | + | 0.624719i | \(0.214787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3699 | −1.31738 | −0.658688 | − | 0.752416i | \(-0.728888\pi\) | ||||
−0.658688 | + | 0.752416i | \(0.728888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.40393 | −0.522417 | −0.261209 | − | 0.965282i | \(-0.584121\pi\) | ||||
−0.261209 | + | 0.965282i | \(0.584121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.8277 | −1.51602 | −0.758009 | − | 0.652244i | \(-0.773828\pi\) | ||||
−0.758009 | + | 0.652244i | \(0.773828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.762915 | −0.0724127 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4238 | −1.73316 | −0.866581 | − | 0.499036i | \(-0.833688\pi\) | ||||
−0.866581 | + | 0.499036i | \(0.833688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.55660 | 0.698608 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.13828 | −0.830753 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.39847 | 0.306429 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.32497 | −0.472515 | −0.236257 | − | 0.971691i | \(-0.575921\pi\) | ||||
−0.236257 | + | 0.971691i | \(0.575921\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.680489 | −0.0599137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2371 | −1.41864 | −0.709320 | − | 0.704886i | \(-0.750998\pi\) | ||||
−0.709320 | + | 0.704886i | \(0.750998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.40939 | −0.376719 | −0.188360 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188360 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.3699 | 1.89739 | 0.948695 | − | 0.316192i | \(-0.102404\pi\) | ||||
0.948695 | + | 0.316192i | \(0.102404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.50273 | 0.210768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.59607 | −0.300719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.5082 | 1.84394 | 0.921971 | − | 0.387258i | \(-0.126578\pi\) | ||||
0.921971 | + | 0.387258i | \(0.126578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5027 | 1.09884 | 0.549418 | − | 0.835547i | \(-0.314849\pi\) | ||||
0.549418 | + | 0.835547i | \(0.314849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.39847 | −0.517285 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5566 | −1.24155 | −0.620776 | − | 0.783988i | \(-0.713182\pi\) | ||||
−0.620776 | + | 0.783988i | \(0.713182\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.69488 | −0.293023 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.40393 | −0.344942 | −0.172471 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172471 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.09880 | −0.704087 | −0.352043 | − | 0.935984i | \(-0.614513\pi\) | ||||
−0.352043 | + | 0.935984i | \(0.614513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.05387 | −0.465682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.8672 | −1.36634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.9605 | −1.51757 | −0.758785 | − | 0.651341i | \(-0.774207\pi\) | ||||
−0.758785 | + | 0.651341i | \(0.774207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.596074 | −0.0448036 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1921 | −0.986027 | −0.493014 | − | 0.870022i | \(-0.664105\pi\) | ||||
−0.493014 | + | 0.870022i | \(0.664105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2316 | −0.760511 | −0.380255 | − | 0.924882i | \(-0.624164\pi\) | ||||
−0.380255 | + | 0.924882i | \(0.624164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0143878 | 0.00106357 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.04494 | 0.222668 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0055 | 1.01340 | 0.506700 | − | 0.862123i | \(-0.330865\pi\) | ||||
0.506700 | + | 0.862123i | \(0.330865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4094 | 1.03721 | 0.518605 | − | 0.855014i | \(-0.326451\pi\) | ||||
0.518605 | + | 0.855014i | \(0.326451\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5566 | 0.823373 | 0.411687 | − | 0.911325i | \(-0.364940\pi\) | ||||
0.411687 | + | 0.911325i | \(0.364940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.40939 | 0.383461 | 0.191731 | − | 0.981448i | \(-0.438590\pi\) | ||||
0.191731 | + | 0.981448i | \(0.438590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.45233 | −0.172974 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9121 | 1.31448 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.50273 | 0.588146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9660 | −0.754929 | −0.377465 | − | 0.926024i | \(-0.623204\pi\) | ||||
−0.377465 | + | 0.926024i | \(0.623204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.28549 | 0.156599 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.45779 | 0.0985085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.88157 | −0.395637 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.5566 | −1.44354 | −0.721768 | − | 0.692135i | \(-0.756670\pi\) | ||||
−0.721768 | + | 0.692135i | \(0.756670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4238 | 0.824595 | 0.412297 | − | 0.911049i | \(-0.364726\pi\) | ||||
0.412297 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.36445 | 0.552738 | 0.276369 | − | 0.961052i | \(-0.410869\pi\) | ||||
0.276369 | + | 0.961052i | \(0.410869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0055 | −0.917528 | −0.458764 | − | 0.888558i | \(-0.651708\pi\) | ||||
−0.458764 | + | 0.888558i | \(0.651708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.94067 | −0.126060 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9605 | 1.09708 | 0.548542 | − | 0.836123i | \(-0.315183\pi\) | ||||
0.548542 | + | 0.836123i | \(0.315183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3304 | −0.665441 | −0.332721 | − | 0.943025i | \(-0.607967\pi\) | ||||
−0.332721 | + | 0.943025i | \(0.607967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.26564 | −0.594391 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4238 | −1.04502 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.38429 | 0.341216 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5082 | −1.23135 | −0.615673 | − | 0.788002i | \(-0.711116\pi\) | ||||
−0.615673 | + | 0.788002i | \(0.711116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.4633 | −1.77549 | −0.887744 | − | 0.460337i | \(-0.847729\pi\) | ||||
−0.887744 | + | 0.460337i | \(0.847729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.7773 | −0.976591 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.5621 | 1.76121 | 0.880606 | − | 0.473849i | \(-0.157136\pi\) | ||||
0.880606 | + | 0.473849i | \(0.157136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.316041 | 0.0193414 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.19761 | 0.560788 | 0.280394 | − | 0.959885i | \(-0.409535\pi\) | ||||
0.280394 | + | 0.959885i | \(0.409535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.86172 | −0.234583 | −0.117291 | − | 0.993098i | \(-0.537421\pi\) | ||||
−0.117291 | + | 0.993098i | \(0.537421\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6410 | 0.639356 | 0.319678 | − | 0.947526i | \(-0.396425\pi\) | ||||
0.319678 | + | 0.947526i | \(0.396425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9101 | 0.772909 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73436 | 0.103463 | 0.0517315 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517315 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.91211 | 0.351439 | 0.175719 | − | 0.984440i | \(-0.443775\pi\) | ||||
0.175719 | + | 0.984440i | \(0.443775\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0198 | −0.707050 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.86718 | 0.343940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.3250 | −1.42108 | −0.710540 | − | 0.703657i | \(-0.751549\pi\) | ||||
−0.710540 | + | 0.703657i | \(0.751549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.91757 | 0.169295 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.3843 | 1.00536 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.71997 | −0.328604 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.5226 | 1.34250 | 0.671252 | − | 0.741229i | \(-0.265757\pi\) | ||||
0.671252 | + | 0.741229i | \(0.265757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.87264 | 0.277195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.81877 | 0.500067 | 0.250033 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250033 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0933442 | 0.00527612 | 0.00263806 | − | 0.999997i | \(-0.499160\pi\) | ||||
0.00263806 | + | 0.999997i | \(0.499160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.54221 | 0.198950 | 0.0994751 | − | 0.995040i | \(-0.468284\pi\) | ||||
0.0994751 | + | 0.995040i | \(0.468284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50819 | 0.420378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.96945 | 0.109924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9067 | 0.773787 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.76837 | 0.318992 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6499 | −1.08006 | −0.540029 | − | 0.841646i | \(-0.681587\pi\) | ||||
−0.540029 | + | 0.841646i | \(0.681587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00199 | −0.328907 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0449 | −1.25534 | −0.627669 | − | 0.778480i | \(-0.715991\pi\) | ||||
−0.627669 | + | 0.778480i | \(0.715991\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.71451 | 0.364682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.14374 | −0.332702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.5621 | −1.21119 | −0.605597 | − | 0.795771i | \(-0.707066\pi\) | ||||
−0.605597 | + | 0.795771i | \(0.707066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3250 | −0.766798 | −0.383399 | − | 0.923583i | \(-0.625247\pi\) | ||||
−0.383399 | + | 0.923583i | \(0.625247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63555 | −0.300804 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.7003 | −1.74046 | −0.870232 | − | 0.492643i | \(-0.836031\pi\) | ||||
−0.870232 | + | 0.492643i | \(0.836031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.1581 | −1.38057 | −0.690287 | − | 0.723536i | \(-0.742516\pi\) | ||||
−0.690287 | + | 0.723536i | \(0.742516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.8332 | 1.04385 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.33043 | 0.174802 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.2316 | 1.31708 | 0.658540 | − | 0.752546i | \(-0.271174\pi\) | ||||
0.658540 | + | 0.752546i | \(0.271174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.7363 | 1.39184 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.69488 | −0.294870 | −0.147435 | − | 0.989072i | \(-0.547102\pi\) | ||||
−0.147435 | + | 0.989072i | \(0.547102\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.5027 | −0.746929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9660 | 0.768751 | 0.384375 | − | 0.923177i | \(-0.374417\pi\) | ||||
0.384375 | + | 0.923177i | \(0.374417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.94067 | 0.0994238 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.4776 | 1.25075 | 0.625374 | − | 0.780325i | \(-0.284946\pi\) | ||||
0.625374 | + | 0.780325i | \(0.284946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.35353 | −0.272135 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.2460 | −1.58424 | −0.792118 | − | 0.610368i | \(-0.791022\pi\) | ||||
−0.792118 | + | 0.610368i | \(0.791022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7200 | −0.744421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.91757 | 0.298502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.13282 | 0.0568547 | 0.0284274 | − | 0.999596i | \(-0.490950\pi\) | ||||
0.0284274 | + | 0.999596i | \(0.490950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.82224 | −0.190874 | −0.0954368 | − | 0.995435i | \(-0.530425\pi\) | ||||
−0.0954368 | + | 0.995435i | \(0.530425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8672 | 0.591146 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85626 | 0.141580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.6609 | −1.66442 | −0.832211 | − | 0.554459i | \(-0.812925\pi\) | ||||
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.60699 | 0.0792671 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.15267 | −0.399238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.497270 | 0.0242933 | 0.0121466 | − | 0.999926i | \(-0.496134\pi\) | ||||
0.0121466 | + | 0.999926i | \(0.496134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28003 | −0.0623850 | −0.0311925 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311925 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.6894 | 0.957332 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.31058 | 0.0632755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2910 | −0.495698 | −0.247849 | − | 0.968799i | \(-0.579724\pi\) | ||||
−0.247849 | + | 0.968799i | \(0.579724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8870 | −1.43628 | −0.718139 | − | 0.695899i | \(-0.755006\pi\) | ||||
−0.718139 | + | 0.695899i | \(0.755006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.1043 | −1.96628 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.04841 | 0.240947 | 0.120474 | − | 0.992717i | \(-0.461559\pi\) | ||||
0.120474 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7738 | −0.559392 | −0.279696 | − | 0.960089i | \(-0.590234\pi\) | ||||
−0.279696 | + | 0.960089i | \(0.590234\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.20307 | −0.387992 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.3843 | −0.537258 | −0.268629 | − | 0.963244i | \(-0.586571\pi\) | ||||
−0.268629 | + | 0.963244i | \(0.586571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.7234 | −0.599123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.92104 | −0.231211 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.2515 | 1.74255 | 0.871275 | − | 0.490795i | \(-0.163294\pi\) | ||||
0.871275 | + | 0.490795i | \(0.163294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.77184 | 0.222731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0449 | 0.700713 | 0.350356 | − | 0.936616i | \(-0.386061\pi\) | ||||
0.350356 | + | 0.936616i | \(0.386061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.2031 | −1.45013 | −0.725065 | − | 0.688681i | \(-0.758190\pi\) | ||||
−0.725065 | + | 0.688681i | \(0.758190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.7684 | −0.868497 | −0.434248 | − | 0.900793i | \(-0.642986\pi\) | ||||
−0.434248 | + | 0.900793i | \(0.642986\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.66957 | 0.261240 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.54767 | 0.117142 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.0683 | −1.33094 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.714508 | 0.0326467 | 0.0163234 | − | 0.999867i | \(-0.494804\pi\) | ||||
0.0163234 | + | 0.999867i | \(0.494804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.51712 | −0.251559 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6949 | 0.756517 | 0.378259 | − | 0.925700i | \(-0.376523\pi\) | ||||
0.378259 | + | 0.925700i | \(0.376523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.60500 | 0.0725807 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.19761 | 0.279694 | 0.139847 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139847 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.2800 | 0.553065 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4687 | 0.647708 | 0.323854 | − | 0.946107i | \(-0.395021\pi\) | ||||
0.323854 | + | 0.946107i | \(0.395021\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.31604 | 0.148150 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.6949 | 1.36862 | 0.684308 | − | 0.729193i | \(-0.260104\pi\) | ||||
0.684308 | + | 0.729193i | \(0.260104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.20632 | 0.0979861 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.4742 | −1.97128 | −0.985641 | − | 0.168852i | \(-0.945994\pi\) | ||||
−0.985641 | + | 0.168852i | \(0.945994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.3250 | 0.588312 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.36991 | −0.412088 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.27457 | 0.319318 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6499 | 0.554204 | 0.277102 | − | 0.960841i | \(-0.410626\pi\) | ||||
0.277102 | + | 0.960841i | \(0.410626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2711 | −0.449124 | −0.224562 | − | 0.974460i | \(-0.572095\pi\) | ||||
−0.224562 | + | 0.974460i | \(0.572095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0484 | −0.437715 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5082 | 0.891660 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.68942 | −0.203503 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5764 | 1.06452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.80785 | 0.207474 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.13828 | −0.0919319 | −0.0459660 | − | 0.998943i | \(-0.514637\pi\) | ||||
−0.0459660 | + | 0.998943i | \(0.514637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.72890 | 0.160022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0198 | 1.36907 | 0.684535 | − | 0.728980i | \(-0.260005\pi\) | ||||
0.684535 | + | 0.728980i | \(0.260005\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.113191 | 0.00483088 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.2910 | 1.46084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.33043 | 0.352972 | 0.176486 | − | 0.984303i | \(-0.443527\pi\) | ||||
0.176486 | + | 0.984303i | \(0.443527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.92104 | −0.208138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10972 | −0.0468525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.4633 | −0.820278 | −0.410139 | − | 0.912023i | \(-0.634520\pi\) | ||||
−0.410139 | + | 0.912023i | \(0.634520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8925 | 0.792014 | 0.396007 | − | 0.918247i | \(-0.370396\pi\) | ||||
0.396007 | + | 0.918247i | \(0.370396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6301 | −0.779645 | −0.389823 | − | 0.920890i | \(-0.627464\pi\) | ||||
−0.389823 | + | 0.920890i | \(0.627464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.10426 | −0.213234 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5926 | −0.774020 | −0.387010 | − | 0.922075i | \(-0.626492\pi\) | ||||
−0.387010 | + | 0.922075i | \(0.626492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.25147 | −0.218244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8332 | 0.572911 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1383 | 0.418452 | 0.209226 | − | 0.977867i | \(-0.432906\pi\) | ||||
0.209226 | + | 0.977867i | \(0.432906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.0593 | −1.15616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.21178 | −0.173249 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.0055 | −0.698331 | −0.349165 | − | 0.937061i | \(-0.613535\pi\) | ||||
−0.349165 | + | 0.937061i | \(0.613535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.97144 | −0.0806857 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.18669 | −0.334499 | −0.167250 | − | 0.985915i | \(-0.553489\pi\) | ||||
−0.167250 | + | 0.985915i | \(0.553489\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.3359 | 1.44138 | 0.720690 | − | 0.693257i | \(-0.243825\pi\) | ||||
0.720690 | + | 0.693257i | \(0.243825\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.2929 | −0.785669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2316 | 1.14589 | 0.572943 | − | 0.819595i | \(-0.305802\pi\) | ||||
0.572943 | + | 0.819595i | \(0.305802\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0988 | 0.732199 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.1581 | −1.25846 | −0.629232 | − | 0.777217i | \(-0.716631\pi\) | ||||
−0.629232 | + | 0.777217i | \(0.716631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.1527 | 1.57623 | 0.788114 | − | 0.615530i | \(-0.211058\pi\) | ||||
0.788114 | + | 0.615530i | \(0.211058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.3843 | 1.58299 | 0.791494 | − | 0.611177i | \(-0.209304\pi\) | ||||
0.791494 | + | 0.611177i | \(0.209304\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.1043 | −0.565985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.09880 | −0.123754 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.67156 | 0.186267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7003 | 0.903686 | 0.451843 | − | 0.892097i | \(-0.350767\pi\) | ||||
0.451843 | + | 0.892097i | \(0.350767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.99653 | 0.158848 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.9804 | 0.711292 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.41285 | 0.332288 | 0.166144 | − | 0.986102i | \(-0.446868\pi\) | ||||
0.166144 | + | 0.986102i | \(0.446868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.7398 | 1.17282 | 0.586412 | − | 0.810013i | \(-0.300540\pi\) | ||||
0.586412 | + | 0.810013i | \(0.300540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.6859 | 0.852563 | 0.426281 | − | 0.904591i | \(-0.359823\pi\) | ||||
0.426281 | + | 0.904591i | \(0.359823\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.23163 | 0.0875990 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0702 | 1.17674 | 0.588370 | − | 0.808592i | \(-0.299770\pi\) | ||||
0.588370 | + | 0.808592i | \(0.299770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.4687 | 0.447437 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.37537 | 0.0925311 | 0.0462656 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462656 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4633 | 0.562555 | 0.281278 | − | 0.959626i | \(-0.409242\pi\) | ||||
0.281278 | + | 0.959626i | \(0.409242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.14353 | 0.0832476 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.2964 | −1.40540 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.85626 | 0.303741 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0538660 | −0.00207947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.99653 | 0.346791 | 0.173395 | − | 0.984852i | \(-0.444526\pi\) | ||||
0.173395 | + | 0.984852i | \(0.444526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.49181 | −0.287934 | −0.143967 | − | 0.989583i | \(-0.545986\pi\) | ||||
−0.143967 | + | 0.989583i | \(0.545986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.52782 | −0.173506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.3250 | −1.61952 | −0.809760 | − | 0.586761i | \(-0.800403\pi\) | ||||
−0.809760 | + | 0.586761i | \(0.800403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.04841 | −0.116304 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.7200 | −1.01795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.6465 | −1.08976 | −0.544882 | − | 0.838513i | \(-0.683425\pi\) | ||||
−0.544882 | + | 0.838513i | \(0.683425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8098 | −0.788229 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.10426 | 0.193061 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4292 | −0.771601 | −0.385801 | − | 0.922582i | \(-0.626075\pi\) | ||||
−0.385801 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.0449 | 0.491999 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.8277 | 1.08265 | 0.541323 | − | 0.840814i | \(-0.317923\pi\) | ||||
0.541323 | + | 0.840814i | \(0.317923\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.2676 | −0.572581 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.7003 | 1.11229 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.18123 | −0.230842 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.3106 | −1.16769 | −0.583844 | − | 0.811866i | \(-0.698452\pi\) | ||||
−0.583844 | + | 0.811866i | \(0.698452\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.76490 | 0.140018 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.17230 | 0.303094 | 0.151547 | − | 0.988450i | \(-0.451575\pi\) | ||||
0.151547 | + | 0.988450i | \(0.451575\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0899 | −0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.16684 | 0.154116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4183 | 0.791103 | 0.395552 | − | 0.918444i | \(-0.370553\pi\) | ||||
0.395552 | + | 0.918444i | \(0.370553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.18123 | 0.338195 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.35006 | 0.160020 | 0.0800098 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800098 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.98561 | 0.219887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53328 | 0.239683 | 0.119841 | − | 0.992793i | \(-0.461761\pi\) | ||||
0.119841 | + | 0.992793i | \(0.461761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.3592 | 1.54984 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4831 | 1.25831 | 0.629153 | − | 0.777281i | \(-0.283402\pi\) | ||||
0.629153 | + | 0.777281i | \(0.283402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.10972 | 0.259093 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.2425 | −1.60802 | −0.804011 | − | 0.594614i | \(-0.797305\pi\) | ||||
−0.804011 | + | 0.594614i | \(0.797305\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.28003 | 0.119058 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8188 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.31058 | −0.155646 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.158128 | 0.00570225 | 0.00285113 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285113 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3734 | 0.373588 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7991 | 0.640191 | 0.320095 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320095 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −58.1097 | −2.08200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.55660 | −0.306179 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.7664 | 0.420496 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.5226 | 1.48012 | 0.740060 | − | 0.672541i | \(-0.234797\pi\) | ||||
0.740060 | + | 0.672541i | \(0.234797\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.4094 | −0.370584 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.104047 | 0.00369481 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.0933 | −0.888852 | −0.444426 | − | 0.895816i | \(-0.646592\pi\) | ||||
−0.444426 | + | 0.895816i | \(0.646592\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.3250 | −0.542158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.48635 | 0.0878509 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.45779 | −0.192601 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.35205 | −0.117998 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6949 | 0.446328 | 0.223164 | − | 0.974781i | \(-0.428361\pi\) | ||||
0.223164 | + | 0.974781i | \(0.428361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.9749 | −0.631184 | −0.315592 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315592 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.40740 | 0.0493595 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6356 | 0.407076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0683 | 0.700387 | 0.350193 | − | 0.936677i | \(-0.386116\pi\) | ||||
0.350193 | + | 0.936677i | \(0.386116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6105 | −0.369857 | −0.184929 | − | 0.982752i | \(-0.559205\pi\) | ||||
−0.184929 | + | 0.982752i | \(0.559205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.7793 | 1.20939 | 0.604697 | − | 0.796455i | \(-0.293294\pi\) | ||||
0.604697 | + | 0.796455i | \(0.293294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.2282 | 0.910942 | 0.455471 | − | 0.890251i | \(-0.349471\pi\) | ||||
0.455471 | + | 0.890251i | \(0.349471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.87810 | −0.134530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.62810 | −0.332796 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.9210 | −1.17108 | −0.585542 | − | 0.810642i | \(-0.699118\pi\) | ||||
−0.585542 | + | 0.810642i | \(0.699118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28003 | 0.0441391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.632082 | −0.0217701 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.15466 | −0.0739477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8079 | −0.473327 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.6698 | 1.97458 | 0.987288 | − | 0.158942i | \(-0.0508082\pi\) | ||||
0.987288 | + | 0.158942i | \(0.0508082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.4039 | −1.20938 | −0.604688 | − | 0.796463i | \(-0.706702\pi\) | ||||
−0.604688 | + | 0.796463i | \(0.706702\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4434 | 0.458683 | 0.229342 | − | 0.973346i | \(-0.426343\pi\) | ||||
0.229342 | + | 0.973346i | \(0.426343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.06478 | −0.240488 | −0.120244 | − | 0.992744i | \(-0.538368\pi\) | ||||
−0.120244 | + | 0.992744i | \(0.538368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.38061 | 0.148773 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.26564 | 0.246470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7344 | −0.600906 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.1581 | 1.56222 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0055 | 0.506698 | 0.253349 | − | 0.967375i | \(-0.418468\pi\) | ||||
0.253349 | + | 0.967375i | \(0.418468\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.86519 | 0.299015 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3699 | 1.32641 | 0.663203 | − | 0.748440i | \(-0.269197\pi\) | ||||
0.663203 | + | 0.748440i | \(0.269197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.2229 | 1.95936 | 0.979679 | − | 0.200574i | \(-0.0642808\pi\) | ||||
0.979679 | + | 0.200574i | \(0.0642808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.2460 | −0.847678 | −0.423839 | − | 0.905738i | \(-0.639318\pi\) | ||||
−0.423839 | + | 0.905738i | \(0.639318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6730 | 0.357560 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.7937 | −1.43204 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.33567 | −0.211542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.7773 | −0.826369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.6248 | 0.753743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.1867 | 0.902719 | 0.451360 | − | 0.892342i | \(-0.350939\pi\) | ||||
0.451360 | + | 0.892342i | \(0.350939\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45.0000 | −1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.7882 | −1.35137 | −0.675687 | − | 0.737189i | \(-0.736153\pi\) | ||||
−0.675687 | + | 0.737189i | \(0.736153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.1581 | −0.667137 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0737 | −1.55282 | −0.776409 | − | 0.630229i | \(-0.782961\pi\) | ||||
−0.776409 | + | 0.630229i | \(0.782961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.57276 | −0.282482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5278 | 0.544020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.3339 | 1.25905 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.9911 | −0.590268 | −0.295134 | − | 0.955456i | \(-0.595364\pi\) | ||||
−0.295134 | + | 0.955456i | \(0.595364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.21398 | −0.105221 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.7003 | 1.23162 | 0.615808 | − | 0.787896i | \(-0.288830\pi\) | ||||
0.615808 | + | 0.787896i | \(0.288830\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.0340191 | −0.00111017 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.83316 | −0.157556 | −0.0787782 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787782 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.5082 | 2.00298 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.83663 | 0.0921780 | 0.0460890 | − | 0.998937i | \(-0.485324\pi\) | ||||
0.0460890 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5422 | 0.342215 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29095 | −0.0418619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7991 | −0.576571 | −0.288285 | − | 0.957545i | \(-0.593085\pi\) | ||||
−0.288285 | + | 0.957545i | \(0.593085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.73634 | −0.0884535 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7254 | −0.345982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.4940 | 0.499288 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1581 | 0.487453 | 0.243726 | − | 0.969844i | \(-0.421630\pi\) | ||||
0.243726 | + | 0.969844i | \(0.421630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.06825 | −0.162816 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3843 | 1.52063 | 0.760317 | − | 0.649552i | \(-0.225044\pi\) | ||||
0.760317 | + | 0.649552i | \(0.225044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.7200 | −0.758869 | −0.379434 | − | 0.925219i | \(-0.623881\pi\) | ||||
−0.379434 | + | 0.925219i | \(0.623881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.18322 | −0.0378158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.3808 | 1.44890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4543 | 1.09892 | 0.549461 | − | 0.835519i | \(-0.314833\pi\) | ||||
0.549461 | + | 0.835519i | \(0.314833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.3160 | −0.391627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6609 | −1.32340 | −0.661700 | − | 0.749768i | \(-0.730165\pi\) | ||||
−0.661700 | + | 0.749768i | \(0.730165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.16138 | 0.227260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7882 | 0.785051 | 0.392525 | − | 0.919741i | \(-0.371601\pi\) | ||||
0.392525 | + | 0.919741i | \(0.371601\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.47616 | 0.141619 |
(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 | 4900.2.a.bb.1.2 | 3 | ||
5.2 | odd | 4 | 4900.2.e.s.2549.4 | 6 | |||
5.3 | odd | 4 | 4900.2.e.s.2549.3 | 6 | |||
5.4 | even | 2 | 4900.2.a.bd.1.2 | 3 | |||
7.3 | odd | 6 | 700.2.i.d.401.2 | ✓ | 6 | ||
7.5 | odd | 6 | 700.2.i.d.501.2 | yes | 6 | ||
7.6 | odd | 2 | 4900.2.a.bc.1.2 | 3 | |||
35.3 | even | 12 | 700.2.r.d.149.4 | 12 | |||
35.12 | even | 12 | 700.2.r.d.249.4 | 12 | |||
35.13 | even | 4 | 4900.2.e.t.2549.4 | 6 | |||
35.17 | even | 12 | 700.2.r.d.149.3 | 12 | |||
35.19 | odd | 6 | 700.2.i.e.501.2 | yes | 6 | ||
35.24 | odd | 6 | 700.2.i.e.401.2 | yes | 6 | ||
35.27 | even | 4 | 4900.2.e.t.2549.3 | 6 | |||
35.33 | even | 12 | 700.2.r.d.249.3 | 12 | |||
35.34 | odd | 2 | 4900.2.a.ba.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.2 | ✓ | 6 | 7.3 | odd | 6 | ||
700.2.i.d.501.2 | yes | 6 | 7.5 | odd | 6 | ||
700.2.i.e.401.2 | yes | 6 | 35.24 | odd | 6 | ||
700.2.i.e.501.2 | yes | 6 | 35.19 | odd | 6 | ||
700.2.r.d.149.3 | 12 | 35.17 | even | 12 | |||
700.2.r.d.149.4 | 12 | 35.3 | even | 12 | |||
700.2.r.d.249.3 | 12 | 35.33 | even | 12 | |||
700.2.r.d.249.4 | 12 | 35.12 | even | 12 | |||
4900.2.a.ba.1.2 | 3 | 35.34 | odd | 2 | |||
4900.2.a.bb.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4900.2.a.bc.1.2 | 3 | 7.6 | odd | 2 | |||
4900.2.a.bd.1.2 | 3 | 5.4 | even | 2 | |||
4900.2.e.s.2549.3 | 6 | 5.3 | odd | 4 | |||
4900.2.e.s.2549.4 | 6 | 5.2 | odd | 4 | |||
4900.2.e.t.2549.3 | 6 | 35.27 | even | 4 | |||
4900.2.e.t.2549.4 | 6 | 35.13 | even | 4 |