Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3720,2,Mod(1,3720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3720 = 2^{3} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3720.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: | \(29.7043495519\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3720.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17009 | 0.442251 | 0.221126 | − | 0.975245i | \(-0.429027\pi\) | ||||
0.221126 | + | 0.975245i | \(0.429027\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.41855 | −1.63375 | −0.816877 | − | 0.576812i | \(-0.804297\pi\) | ||||
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.17009 | −0.324524 | −0.162262 | − | 0.986748i | \(-0.551879\pi\) | ||||
−0.162262 | + | 0.986748i | \(0.551879\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.12783 | 1.72875 | 0.864376 | − | 0.502846i | \(-0.167714\pi\) | ||||
0.864376 | + | 0.502846i | \(0.167714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.17009 | 0.255334 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.97107 | −1.45357 | −0.726784 | − | 0.686866i | \(-0.758986\pi\) | ||||
−0.726784 | + | 0.686866i | \(0.758986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.21953 | 1.71202 | 0.856012 | − | 0.516955i | \(-0.172935\pi\) | ||||
0.856012 | + | 0.516955i | \(0.172935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.41855 | −0.943249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.17009 | −0.197781 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.09171 | −0.343875 | −0.171937 | − | 0.985108i | \(-0.555003\pi\) | ||||
−0.171937 | + | 0.985108i | \(0.555003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.17009 | −0.187364 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.26180 | −0.821754 | −0.410877 | − | 0.911691i | \(-0.634777\pi\) | ||||
−0.410877 | + | 0.911691i | \(0.634777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.52586 | −0.222569 | −0.111285 | − | 0.993789i | \(-0.535497\pi\) | ||||
−0.111285 | + | 0.993789i | \(0.535497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.63090 | −0.804414 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.12783 | 0.998095 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.474142 | 0.0651284 | 0.0325642 | − | 0.999470i | \(-0.489633\pi\) | ||||
0.0325642 | + | 0.999470i | \(0.489633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.41855 | 0.730637 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.6381 | 1.90572 | 0.952858 | − | 0.303416i | \(-0.0981272\pi\) | ||||
0.952858 | + | 0.303416i | \(0.0981272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9421 | −1.52903 | −0.764517 | − | 0.644603i | \(-0.777023\pi\) | ||||
−0.764517 | + | 0.644603i | \(0.777023\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.17009 | 0.147417 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17009 | 0.145131 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3268 | −1.62813 | −0.814066 | − | 0.580772i | \(-0.802751\pi\) | ||||
−0.814066 | + | 0.580772i | \(0.802751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.97107 | −0.839218 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.14116 | −0.966178 | −0.483089 | − | 0.875571i | \(-0.660485\pi\) | ||||
−0.483089 | + | 0.875571i | \(0.660485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.74539 | −1.02357 | −0.511785 | − | 0.859113i | \(-0.671016\pi\) | ||||
−0.511785 | + | 0.859113i | \(0.671016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.34017 | −0.722530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.46800 | 1.06523 | 0.532617 | − | 0.846357i | \(-0.321209\pi\) | ||||
0.532617 | + | 0.846357i | \(0.321209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.86603 | −0.424352 | −0.212176 | − | 0.977231i | \(-0.568055\pi\) | ||||
−0.212176 | + | 0.977231i | \(0.568055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12783 | −0.773121 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.21953 | 0.988438 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.04226 | −0.216479 | −0.108240 | − | 0.994125i | \(-0.534521\pi\) | ||||
−0.108240 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.36910 | −0.143521 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.73820 | −0.278023 | −0.139011 | − | 0.990291i | \(-0.544392\pi\) | ||||
−0.139011 | + | 0.990291i | \(0.544392\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.41855 | −0.544585 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.92881 | −0.879782 | −0.439891 | − | 0.898051i | \(-0.644983\pi\) | ||||
−0.439891 | + | 0.898051i | \(0.644983\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.17009 | −0.114189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.6514 | −1.51308 | −0.756540 | − | 0.653948i | \(-0.773112\pi\) | ||||
−0.756540 | + | 0.653948i | \(0.773112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0228 | −1.34314 | −0.671570 | − | 0.740941i | \(-0.734380\pi\) | ||||
−0.671570 | + | 0.740941i | \(0.734380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.09171 | −0.198536 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.23513 | 0.492480 | 0.246240 | − | 0.969209i | \(-0.420805\pi\) | ||||
0.246240 | + | 0.969209i | \(0.420805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.97107 | 0.650056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.17009 | −0.108175 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.34017 | 0.764542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3607 | 1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.26180 | −0.474440 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.18342 | −0.726161 | −0.363080 | − | 0.931758i | \(-0.618275\pi\) | ||||
−0.363080 | + | 0.931758i | \(0.618275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.21953 | 0.630774 | 0.315387 | − | 0.948963i | \(-0.397866\pi\) | ||||
0.315387 | + | 0.948963i | \(0.397866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68035 | −0.405837 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.38962 | 0.716774 | 0.358387 | − | 0.933573i | \(-0.383327\pi\) | ||||
0.358387 | + | 0.933573i | \(0.383327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.3402 | −1.55559 | −0.777797 | − | 0.628516i | \(-0.783663\pi\) | ||||
−0.777797 | + | 0.628516i | \(0.783663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.52586 | −0.128500 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.34017 | 0.530192 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.21953 | −0.765641 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.63090 | −0.464429 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0989 | 0.991180 | 0.495590 | − | 0.868557i | \(-0.334952\pi\) | ||||
0.495590 | + | 0.868557i | \(0.334952\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.3318 | 1.81733 | 0.908667 | − | 0.417523i | \(-0.137102\pi\) | ||||
0.908667 | + | 0.417523i | \(0.137102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.12783 | 0.576251 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8371 | 1.18413 | 0.592065 | − | 0.805890i | \(-0.298313\pi\) | ||||
0.592065 | + | 0.805890i | \(0.298313\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.474142 | 0.0376019 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.15676 | −0.642842 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.59478 | −0.124913 | −0.0624564 | − | 0.998048i | \(-0.519893\pi\) | ||||
−0.0624564 | + | 0.998048i | \(0.519893\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.41855 | 0.421834 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.91548 | 0.302989 | 0.151494 | − | 0.988458i | \(-0.451591\pi\) | ||||
0.151494 | + | 0.988458i | \(0.451591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6309 | −0.894684 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.23513 | −0.0939054 | −0.0469527 | − | 0.998897i | \(-0.514951\pi\) | ||||
−0.0469527 | + | 0.998897i | \(0.514951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.17009 | 0.0884502 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6381 | 1.10027 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.4186 | −1.15244 | −0.576218 | − | 0.817296i | \(-0.695472\pi\) | ||||
−0.576218 | + | 0.817296i | \(0.695472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.26180 | −0.539765 | −0.269882 | − | 0.962893i | \(-0.586985\pi\) | ||||
−0.269882 | + | 0.962893i | \(0.586985\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9421 | −0.882788 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.09171 | 0.153785 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −38.6225 | −2.82436 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.17009 | 0.0851113 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.8732 | 1.29326 | 0.646630 | − | 0.762803i | \(-0.276178\pi\) | ||||
0.646630 | + | 0.762803i | \(0.276178\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.6742 | 1.56014 | 0.780072 | − | 0.625690i | \(-0.215183\pi\) | ||||
0.780072 | + | 0.625690i | \(0.215183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.17009 | 0.0837916 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0638 | −1.57198 | −0.785991 | − | 0.618238i | \(-0.787847\pi\) | ||||
−0.785991 | + | 0.618238i | \(0.787847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3896 | −1.16183 | −0.580915 | − | 0.813964i | \(-0.697305\pi\) | ||||
−0.580915 | + | 0.813964i | \(0.697305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.3268 | −0.940003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7877 | 0.757145 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.26180 | 0.367500 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.97107 | −0.484523 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.6742 | 1.49924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6020 | −0.798712 | −0.399356 | − | 0.916796i | \(-0.630766\pi\) | ||||
−0.399356 | + | 0.916796i | \(0.630766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.14116 | −0.557823 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.00000 | 0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17009 | −0.0794306 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.74539 | −0.590959 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.34017 | −0.561021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5441 | 0.773051 | 0.386525 | − | 0.922279i | \(-0.373675\pi\) | ||||
0.386525 | + | 0.922279i | \(0.373675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.7031 | −0.975881 | −0.487941 | − | 0.872877i | \(-0.662252\pi\) | ||||
−0.487941 | + | 0.872877i | \(0.662252\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.60197 | −0.634516 | −0.317258 | − | 0.948339i | \(-0.602762\pi\) | ||||
−0.317258 | + | 0.948339i | \(0.602762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.34017 | −0.417153 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4163 | −0.682393 | −0.341197 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341197 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.52586 | 0.0995360 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.46800 | 0.615013 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.02052 | −0.583489 | −0.291744 | − | 0.956496i | \(-0.594236\pi\) | ||||
−0.291744 | + | 0.956496i | \(0.594236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.97334 | 0.255945 | 0.127973 | − | 0.991778i | \(-0.459153\pi\) | ||||
0.127973 | + | 0.991778i | \(0.459153\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.63090 | 0.359745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.68035 | 0.297803 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.86603 | −0.245000 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.94214 | 0.375065 | 0.187532 | − | 0.982258i | \(-0.439951\pi\) | ||||
0.187532 | + | 0.982258i | \(0.439951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.7731 | 2.37477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.12783 | −0.446362 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.7359 | 0.856824 | 0.428412 | − | 0.903583i | \(-0.359073\pi\) | ||||
0.428412 | + | 0.903583i | \(0.359073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.44748 | −0.152079 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.21953 | 0.570675 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.8638 | 1.03986 | 0.519932 | − | 0.854208i | \(-0.325957\pi\) | ||||
0.519932 | + | 0.854208i | \(0.325957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.474142 | −0.0291263 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.04226 | −0.124984 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.5018 | −1.06711 | −0.533553 | − | 0.845766i | \(-0.679144\pi\) | ||||
−0.533553 | + | 0.845766i | \(0.679144\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.02666 | 0.366094 | 0.183047 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183047 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.36910 | −0.0828618 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.41855 | −0.326751 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2485 | 0.976276 | 0.488138 | − | 0.872767i | \(-0.337676\pi\) | ||||
0.488138 | + | 0.872767i | \(0.337676\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.1711 | −1.20331 | −0.601654 | − | 0.798757i | \(-0.705492\pi\) | ||||
−0.601654 | + | 0.798757i | \(0.705492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.9021 | 1.00473 | 0.502364 | − | 0.864656i | \(-0.332464\pi\) | ||||
0.502364 | + | 0.864656i | \(0.332464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.15676 | −0.363422 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.8059 | 1.98858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.73820 | −0.160516 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.3691 | 0.781031 | 0.390516 | − | 0.920596i | \(-0.372297\pi\) | ||||
0.390516 | + | 0.920596i | \(0.372297\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6381 | −0.852262 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.41855 | −0.314416 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.15676 | 0.471717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.02052 | −0.404656 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.9421 | 0.683805 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.48360 | −0.541257 | −0.270629 | − | 0.962684i | \(-0.587232\pi\) | ||||
−0.270629 | + | 0.962684i | \(0.587232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.92881 | −0.507942 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.6381 | −0.716640 | −0.358320 | − | 0.933599i | \(-0.616650\pi\) | ||||
−0.358320 | + | 0.933599i | \(0.616650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.30018 | −0.299584 | −0.149792 | − | 0.988718i | \(-0.547860\pi\) | ||||
−0.149792 | + | 0.988718i | \(0.547860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.17009 | −0.0659269 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.25953 | −0.463901 | −0.231951 | − | 0.972728i | \(-0.574511\pi\) | ||||
−0.231951 | + | 0.972728i | \(0.574511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −49.9565 | −2.79703 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6514 | −0.873577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.5113 | −1.58641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.17009 | −0.0649047 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0228 | −0.775462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.78539 | −0.0984315 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.3112 | −1.50116 | −0.750581 | − | 0.660779i | \(-0.770226\pi\) | ||||
−0.750581 | + | 0.660779i | \(0.770226\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.09171 | −0.114625 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.3268 | 0.728123 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.77205 | −0.368897 | −0.184449 | − | 0.982842i | \(-0.559050\pi\) | ||||
−0.184449 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.23513 | 0.284333 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.41855 | 0.293431 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.7792 | −0.798004 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.97107 | 0.375310 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.71769 | −0.199576 | −0.0997879 | − | 0.995009i | \(-0.531816\pi\) | ||||
−0.0997879 | + | 0.995009i | \(0.531816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.60424 | −0.353517 | −0.176758 | − | 0.984254i | \(-0.556561\pi\) | ||||
−0.176758 | + | 0.984254i | \(0.556561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.17009 | −0.0624546 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.2206 | −1.71493 | −0.857464 | − | 0.514544i | \(-0.827961\pi\) | ||||
−0.857464 | + | 0.514544i | \(0.827961\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.14116 | 0.432088 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.34017 | 0.441409 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.93722 | 0.155021 | 0.0775103 | − | 0.996992i | \(-0.475303\pi\) | ||||
0.0775103 | + | 0.996992i | \(0.475303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.3607 | 0.963686 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.74539 | 0.457755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3074 | 0.903437 | 0.451719 | − | 0.892160i | \(-0.350811\pi\) | ||||
0.451719 | + | 0.892160i | \(0.350811\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.26180 | −0.273918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.554787 | 0.0288031 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.5958 | 1.58419 | 0.792096 | − | 0.610397i | \(-0.208990\pi\) | ||||
0.792096 | + | 0.610397i | \(0.208990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.7877 | −0.555592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.5585 | 1.72378 | 0.861892 | − | 0.507092i | \(-0.169280\pi\) | ||||
0.861892 | + | 0.507092i | \(0.169280\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.18342 | −0.419249 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.2784 | 1.85374 | 0.926871 | − | 0.375380i | \(-0.122488\pi\) | ||||
0.926871 | + | 0.375380i | \(0.122488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.34017 | 0.323125 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.00000 | −0.304997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.54533 | 0.483968 | 0.241984 | − | 0.970280i | \(-0.422202\pi\) | ||||
0.241984 | + | 0.970280i | \(0.422202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −49.6886 | −2.51286 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.21953 | 0.364177 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.46800 | −0.476387 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.05786 | 0.203658 | 0.101829 | − | 0.994802i | \(-0.467531\pi\) | ||||
0.101829 | + | 0.994802i | \(0.467531\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.68035 | −0.234310 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.0833 | 1.60216 | 0.801082 | − | 0.598555i | \(-0.204258\pi\) | ||||
0.801082 | + | 0.598555i | \(0.204258\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.17009 | 0.0582862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3340 | 0.561807 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.89496 | 0.143147 | 0.0715733 | − | 0.997435i | \(-0.477198\pi\) | ||||
0.0715733 | + | 0.997435i | \(0.477198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.38962 | 0.413830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.1278 | 0.842805 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.86603 | 0.189776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.3402 | −0.898122 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.6381 | −1.78989 | −0.894944 | − | 0.446179i | \(-0.852785\pi\) | ||||
−0.894944 | + | 0.446179i | \(0.852785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.26406 | −0.402766 | −0.201383 | − | 0.979513i | \(-0.564544\pi\) | ||||
−0.201383 | + | 0.979513i | \(0.564544\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.52586 | −0.0741897 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.12783 | 0.345750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.9733 | −0.676217 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.34017 | 0.306106 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.19902 | 0.298596 | 0.149298 | − | 0.988792i | \(-0.452299\pi\) | ||||
0.149298 | + | 0.988792i | \(0.452299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1061 | −0.485667 | −0.242834 | − | 0.970068i | \(-0.578077\pi\) | ||||
−0.242834 | + | 0.970068i | \(0.578077\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.21953 | −0.442043 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.8843 | 1.33389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.20394 | 0.343825 | 0.171913 | − | 0.985112i | \(-0.445005\pi\) | ||||
0.171913 | + | 0.985112i | \(0.445005\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.63090 | −0.268138 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.7031 | 1.07866 | 0.539329 | − | 0.842095i | \(-0.318678\pi\) | ||||
0.539329 | + | 0.842095i | \(0.318678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.04226 | 0.0968124 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0989 | 0.572258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.56585 | 0.215476 | 0.107738 | − | 0.994179i | \(-0.465639\pi\) | ||||
0.107738 | + | 0.994179i | \(0.465639\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.5113 | 1.34254 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.3318 | 1.04924 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.36910 | 0.0641845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.8710 | 1.06986 | 0.534929 | − | 0.844897i | \(-0.320338\pi\) | ||||
0.534929 | + | 0.844897i | \(0.320338\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.12783 | 0.332698 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.0566 | −1.49303 | −0.746513 | − | 0.665371i | \(-0.768274\pi\) | ||||
−0.746513 | + | 0.665371i | \(0.768274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0989 | 0.469336 | 0.234668 | − | 0.972076i | \(-0.424600\pi\) | ||||
0.234668 | + | 0.972076i | \(0.424600\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.630898 | −0.0291945 | −0.0145972 | − | 0.999893i | \(-0.504647\pi\) | ||||
−0.0145972 | + | 0.999893i | \(0.504647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5936 | −0.720044 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.8371 | 0.683658 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.5113 | 1.49487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.474142 | 0.0217095 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.9639 | 0.500953 | 0.250476 | − | 0.968123i | \(-0.419413\pi\) | ||||
0.250476 | + | 0.968123i | \(0.419413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.44748 | 0.111595 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.15676 | −0.371145 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.73820 | 0.124335 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.0784 | −1.68018 | −0.840091 | − | 0.542446i | \(-0.817498\pi\) | ||||
−0.840091 | + | 0.542446i | \(0.817498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.59478 | −0.0721185 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.6430 | 1.15725 | 0.578626 | − | 0.815593i | \(-0.303589\pi\) | ||||
0.578626 | + | 0.815593i | \(0.303589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 65.7152 | 2.95967 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.41855 | 0.243546 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.52586 | −0.427293 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1629 | −0.589252 | −0.294626 | − | 0.955613i | \(-0.595195\pi\) | ||||
−0.294626 | + | 0.955613i | \(0.595195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.91548 | 0.174931 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.362959 | −0.0161836 | −0.00809178 | − | 0.999967i | \(-0.502576\pi\) | ||||
−0.00809178 | + | 0.999967i | \(0.502576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6309 | −0.516546 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.8154 | 1.58749 | 0.793744 | − | 0.608252i | \(-0.208129\pi\) | ||||
0.793744 | + | 0.608252i | \(0.208129\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2329 | −0.452675 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.92881 | 0.393450 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.26794 | 0.363624 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.23513 | −0.0542163 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.7854 | 1.04206 | 0.521028 | − | 0.853539i | \(-0.325549\pi\) | ||||
0.521028 | + | 0.853539i | \(0.325549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.24128 | 0.272912 | 0.136456 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136456 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.17009 | 0.0510668 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.12783 | −0.310493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.5958 | 1.11286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.6381 | 0.635239 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.15676 | 0.266679 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.6514 | 0.676670 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.4186 | −0.665360 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.5113 | 1.31421 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.04331 | 0.0448552 | 0.0224276 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224276 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.26180 | −0.311633 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0228 | 0.600670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.6358 | −1.52368 | −0.761839 | − | 0.647767i | \(-0.775703\pi\) | ||||
−0.761839 | + | 0.647767i | \(0.775703\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.9421 | −0.509678 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.8781 | −1.57106 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0784 | 0.471101 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.09171 | 0.0887881 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.64527 | −0.281569 | −0.140785 | − | 0.990040i | \(-0.544963\pi\) | ||||
−0.140785 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.02052 | 0.296936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −38.6225 | −1.63064 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.2800 | −0.896847 | −0.448424 | − | 0.893821i | \(-0.648014\pi\) | ||||
−0.448424 | + | 0.893821i | \(0.648014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.23513 | −0.220244 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.17009 | 0.0491390 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.7226 | 1.37180 | 0.685902 | − | 0.727694i | \(-0.259408\pi\) | ||||
0.685902 | + | 0.727694i | \(0.259408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.1773 | −0.551452 | −0.275726 | − | 0.961236i | \(-0.588918\pi\) | ||||
−0.275726 | + | 0.961236i | \(0.588918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.8732 | 0.746664 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.97107 | −0.290714 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.8059 | −0.449856 | −0.224928 | − | 0.974375i | \(-0.572215\pi\) | ||||
−0.224928 | + | 0.974375i | \(0.572215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.6742 | 0.900749 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.52359 | −0.187670 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.56916 | −0.106404 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.17009 | 0.0483771 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.6886 | 1.55557 | 0.777787 | − | 0.628528i | \(-0.216342\pi\) | ||||
0.777787 | + | 0.628528i | \(0.216342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.0638 | −0.907584 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8576 | −0.815455 | −0.407727 | − | 0.913104i | \(-0.633679\pi\) | ||||
−0.407727 | + | 0.913104i | \(0.633679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.34017 | −0.341914 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.3896 | −0.670783 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.1350 | 1.68073 | 0.840366 | − | 0.542020i | \(-0.182340\pi\) | ||||
0.840366 | + | 0.542020i | \(0.182340\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.3874 | 0.709245 | 0.354622 | − | 0.935010i | \(-0.384609\pi\) | ||||
0.354622 | + | 0.935010i | \(0.384609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3268 | −0.542711 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.3607 | −0.746468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5558 | −0.874924 | −0.437462 | − | 0.899237i | \(-0.644123\pi\) | ||||
−0.437462 | + | 0.899237i | \(0.644123\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7877 | 0.437138 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.78539 | 0.0722290 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.0544 | 1.33505 | 0.667527 | − | 0.744586i | \(-0.267353\pi\) | ||||
0.667527 | + | 0.744586i | \(0.267353\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.26180 | 0.212176 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.9315 | −1.56732 | −0.783661 | − | 0.621189i | \(-0.786650\pi\) | ||||
−0.783661 | + | 0.621189i | \(0.786650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.6719 | 1.31320 | 0.656598 | − | 0.754241i | \(-0.271995\pi\) | ||||
0.656598 | + | 0.754241i | \(0.271995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.97107 | −0.279739 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.38962 | −0.0957382 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.6742 | 0.865584 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.9093 | −0.594474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.68035 | −0.186322 | −0.0931608 | − | 0.995651i | \(-0.529697\pi\) | ||||
−0.0931608 | + | 0.995651i | \(0.529697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.6020 | −0.461137 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.18342 | 0.324749 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.58864 | 0.261051 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.14116 | −0.322059 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0111 | −0.632399 | −0.316199 | − | 0.948693i | \(-0.602407\pi\) | ||||
−0.316199 | + | 0.948693i | \(0.602407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.24128 | 0.246132 | 0.123066 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123066 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.73206 | 0.303979 | 0.151989 | − | 0.988382i | \(-0.451432\pi\) | ||||
0.151989 | + | 0.988382i | \(0.451432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −79.3172 | −3.11347 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.17009 | −0.0458593 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.16063 | 0.319350 | 0.159675 | − | 0.987170i | \(-0.448955\pi\) | ||||
0.159675 | + | 0.987170i | \(0.448955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.21953 | −0.282091 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.74539 | −0.341190 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.2544 | −1.56809 | −0.784045 | − | 0.620704i | \(-0.786847\pi\) | ||||
−0.784045 | + | 0.620704i | \(0.786847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.7464 | −1.93491 | −0.967456 | − | 0.253039i | \(-0.918570\pi\) | ||||
−0.967456 | + | 0.253039i | \(0.918570\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.34017 | −0.323905 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.68035 | 0.181496 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −64.2700 | −2.48855 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5441 | 0.446321 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.7091 | 2.49807 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.4606 | −1.79093 | −0.895463 | − | 0.445136i | \(-0.853155\pi\) | ||||
−0.895463 | + | 0.445136i | \(0.853155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6248 | 0.754241 | 0.377120 | − | 0.926164i | \(-0.376914\pi\) | ||||
0.377120 | + | 0.926164i | \(0.376914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.20394 | −0.122956 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.7031 | −0.563425 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.23740 | −0.238668 | −0.119334 | − | 0.992854i | \(-0.538076\pi\) | ||||
−0.119334 | + | 0.992854i | \(0.538076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.38962 | −0.320551 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.60197 | −0.366338 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.554787 | −0.0211357 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2823 | −1.53241 | −0.766206 | − | 0.642595i | \(-0.777858\pi\) | ||||
−0.766206 | + | 0.642595i | \(0.777858\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.34017 | −0.240843 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.3402 | 0.695682 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.5052 | −1.42061 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.4163 | −0.393980 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.7998 | 1.20106 | 0.600530 | − | 0.799602i | \(-0.294956\pi\) | ||||
0.600530 | + | 0.799602i | \(0.294956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.36683 | 0.315561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.52586 | 0.0574671 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.68649 | −0.213561 | −0.106780 | − | 0.994283i | \(-0.534054\pi\) | ||||
−0.106780 | + | 0.994283i | \(0.534054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.46800 | 0.355078 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.97107 | 0.261069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.34017 | −0.237109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.02052 | −0.336877 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.6286 | 0.732024 | 0.366012 | − | 0.930610i | \(-0.380723\pi\) | ||||
0.366012 | + | 0.930610i | \(0.380723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4475 | −0.389084 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.97334 | 0.147770 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.21953 | 0.342405 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1783 | 1.04508 | 0.522538 | − | 0.852616i | \(-0.324985\pi\) | ||||
0.522538 | + | 0.852616i | \(0.324985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.7670 | −1.58179 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.63931 | 0.171357 | 0.0856784 | − | 0.996323i | \(-0.472694\pi\) | ||||
0.0856784 | + | 0.996323i | \(0.472694\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.63090 | 0.207699 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 72.2122 | 2.65997 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.0761 | −1.17994 | −0.589969 | − | 0.807426i | \(-0.700860\pi\) | ||||
−0.589969 | + | 0.807426i | \(0.700860\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.68035 | 0.171937 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5503 | 0.460424 | 0.230212 | − | 0.973140i | \(-0.426058\pi\) | ||||
0.230212 | + | 0.973140i | \(0.426058\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.0989 | −0.443269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.86603 | −0.141451 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.3135 | −0.669161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.4908 | 1.65998 | 0.829991 | − | 0.557777i | \(-0.188345\pi\) | ||||
0.829991 | + | 0.557777i | \(0.188345\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.94214 | 0.216544 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.3318 | −0.812736 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.93495 | 0.0703271 | 0.0351635 | − | 0.999382i | \(-0.488805\pi\) | ||||
0.0351635 | + | 0.999382i | \(0.488805\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.7731 | 1.37108 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.2134 | −1.38523 | −0.692617 | − | 0.721305i | \(-0.743542\pi\) | ||||
−0.692617 | + | 0.721305i | \(0.743542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4079 | −0.594005 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.12783 | −0.257707 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.1278 | −0.618450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.6042 | 1.10362 | 0.551808 | − | 0.833971i | \(-0.313938\pi\) | ||||
0.551808 | + | 0.833971i | \(0.313938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.7359 | 0.494688 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.7959 | 1.21555 | 0.607777 | − | 0.794108i | \(-0.292062\pi\) | ||||
0.607777 | + | 0.794108i | \(0.292062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.44748 | −0.0878029 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.0472 | 0.754094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.1133 | 1.57850 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.21953 | 0.329479 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.8371 | −0.529559 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5897 | −0.555712 | −0.277856 | − | 0.960623i | \(-0.589624\pi\) | ||||
−0.277856 | + | 0.960623i | \(0.589624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.8638 | 0.600366 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.12556 | 0.217800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.9733 | 0.496208 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.474142 | −0.0168161 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.4245 | 1.53818 | 0.769088 | − | 0.639143i | \(-0.220711\pi\) | ||||
0.769088 | + | 0.639143i | \(0.220711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8760 | −0.384767 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.04226 | −0.0721597 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47.3874 | 1.67226 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.15676 | 0.287488 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5018 | −0.616094 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.9471 | −1.72089 | −0.860444 | − | 0.509546i | \(-0.829813\pi\) | ||||
−0.860444 | + | 0.509546i | \(0.829813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.1773 | −1.16501 | −0.582506 | − | 0.812827i | \(-0.697928\pi\) | ||||
−0.582506 | + | 0.812827i | \(0.697928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.02666 | 0.211364 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.59478 | 0.0558627 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0000 | 0.839654 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.36910 | −0.0478403 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62985 | −0.0568823 | −0.0284411 | − | 0.999595i | \(-0.509054\pi\) | ||||
−0.0284411 | + | 0.999595i | \(0.509054\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.2434 | 1.19365 | 0.596824 | − | 0.802372i | \(-0.296429\pi\) | ||||
0.596824 | + | 0.802372i | \(0.296429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.41855 | −0.188650 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.5234 | 1.72210 | 0.861049 | − | 0.508522i | \(-0.169808\pi\) | ||||
0.861049 | + | 0.508522i | \(0.169808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.4740 | 1.23206 | 0.616031 | − | 0.787722i | \(-0.288740\pi\) | ||||
0.616031 | + | 0.787722i | \(0.288740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2485 | 0.563653 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.1361 | −1.39063 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.91548 | −0.135501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.2544 | −0.906404 | −0.453202 | − | 0.891408i | \(-0.649718\pi\) | ||||
−0.453202 | + | 0.891408i | \(0.649718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.9998 | 1.93103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.1711 | −0.694731 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.6309 | 0.400115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.4836 | 0.738185 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9021 | 0.580080 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5814 | 0.499846 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.5729 | −1.56039 | −0.780193 | − | 0.625539i | \(-0.784879\pi\) | ||||
−0.780193 | + | 0.625539i | \(0.784879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.24742 | 0.110930 | 0.0554649 | − | 0.998461i | \(-0.482336\pi\) | ||||
0.0554649 | + | 0.998461i | \(0.482336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.1978 | −0.962096 | −0.481048 | − | 0.876694i | \(-0.659744\pi\) | ||||
−0.481048 | + | 0.876694i | \(0.659744\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.15676 | −0.209822 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.4079 | −1.17126 | −0.585629 | − | 0.810579i | \(-0.699152\pi\) | ||||
−0.585629 | + | 0.810579i | \(0.699152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.23513 | 0.0419958 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.8059 | 1.14811 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.3028 | −1.74033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5936 | 0.528368 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.73820 | −0.0926742 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.17009 | −0.0395561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.5897 | 1.53945 | 0.769727 | − | 0.638373i | \(-0.220392\pi\) | ||||
0.769727 | + | 0.638373i | \(0.220392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.3691 | 0.450929 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.1662 | 0.780489 | 0.390245 | − | 0.920711i | \(-0.372390\pi\) | ||||
0.390245 | + | 0.920711i | \(0.372390\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.4863 | 0.588459 | 0.294230 | − | 0.955735i | \(-0.404937\pi\) | ||||
0.294230 | + | 0.955735i | \(0.404937\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.6381 | −0.492054 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.1012 | −0.372741 | −0.186370 | − | 0.982480i | \(-0.559672\pi\) | ||||
−0.186370 | + | 0.982480i | \(0.559672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.57531 | −0.321145 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.41855 | −0.181528 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.10343 | 0.204244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4186 | 0.515385 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.15676 | 0.272346 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.21953 | −0.307489 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.37960 | 0.112591 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.02052 | −0.233628 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.26180 | 0.241390 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.4463 | 1.67504 | 0.837520 | − | 0.546406i | \(-0.184005\pi\) | ||||
0.837520 | + | 0.546406i | \(0.184005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.4596 | 1.43988 | 0.719940 | − | 0.694036i | \(-0.244169\pi\) | ||||
0.719940 | + | 0.694036i | \(0.244169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.9483 | 0.693287 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.9421 | 0.394795 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.44748 | 0.278960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4596 | −0.575939 | −0.287969 | − | 0.957640i | \(-0.592980\pi\) | ||||
−0.287969 | + | 0.957640i | \(0.592980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.48360 | −0.312495 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.52586 | 0.313547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.09171 | −0.0687750 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.92881 | −0.293261 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.13501 | −0.299710 | −0.149855 | − | 0.988708i | \(-0.547881\pi\) | ||||
−0.149855 | + | 0.988708i | \(0.547881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5236 | 0.738181 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.6381 | −0.413752 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38.6225 | 1.26309 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9893 | 0.620354 | 0.310177 | − | 0.950679i | \(-0.399612\pi\) | ||||
0.310177 | + | 0.950679i | \(0.399612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.30018 | −0.172965 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.12064 | 0.101730 | 0.0508649 | − | 0.998706i | \(-0.483802\pi\) | ||||
0.0508649 | + | 0.998706i | \(0.483802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6803 | 1.19448 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.17009 | −0.0380629 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.60424 | −0.214609 | −0.107304 | − | 0.994226i | \(-0.534222\pi\) | ||||
−0.107304 | + | 0.994226i | \(0.534222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2329 | 0.332173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.25953 | −0.267834 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8554 | 0.416426 | 0.208213 | − | 0.978084i | \(-0.433235\pi\) | ||||
0.208213 | + | 0.978084i | \(0.433235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8732 | −0.578364 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −49.9565 | −1.61486 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.81658 | 0.316994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.6514 | −0.504360 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.6742 | −0.697717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.7982 | 1.18335 | 0.591674 | − | 0.806177i | \(-0.298467\pi\) | ||||
0.591674 | + | 0.806177i | \(0.298467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.5113 | −0.915915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.4707 | −1.20249 | −0.601245 | − | 0.799065i | \(-0.705329\pi\) | ||||
−0.601245 | + | 0.799065i | \(0.705329\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.4596 | −0.687963 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.17009 | −0.0374728 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.5113 | 1.36006 | 0.680029 | − | 0.733186i | \(-0.261967\pi\) | ||||
0.680029 | + | 0.733186i | \(0.261967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.0661 | 0.353674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0228 | −0.447713 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.8950 | 0.411285 | 0.205643 | − | 0.978627i | \(-0.434072\pi\) | ||||
0.205643 | + | 0.978627i | \(0.434072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0638 | 0.703012 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.78539 | −0.0568295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.8264 | 1.33000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.55025 | −0.271608 | −0.135804 | − | 0.990736i | \(-0.543362\pi\) | ||||
−0.135804 | + | 0.990736i | \(0.543362\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.3112 | −0.866696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.3896 | 0.519586 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5897 | 0.747093 | 0.373546 | − | 0.927612i | \(-0.378142\pi\) | ||||
0.373546 | + | 0.927612i | \(0.378142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.09171 | −0.0661787 |
(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 | 3720.2.a.o.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 7440.2.a.bo.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3720.2.a.o.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7440.2.a.bo.1.1 | 3 | 4.3 | odd | 2 |