Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6900,2,Mod(1,6900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6900.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: | \(55.0967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.73549\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6900.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73549 | 1.41188 | 0.705941 | − | 0.708270i | \(-0.250524\pi\) | ||||
0.705941 | + | 0.708270i | \(0.250524\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.84469 | 1.46073 | 0.730364 | − | 0.683058i | \(-0.239351\pi\) | ||||
0.730364 | + | 0.683058i | \(0.239351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.84469 | 0.788974 | 0.394487 | − | 0.918902i | \(-0.370922\pi\) | ||||
0.394487 | + | 0.918902i | \(0.370922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.890804 | −0.216052 | −0.108026 | − | 0.994148i | \(-0.534453\pi\) | ||||
−0.108026 | + | 0.994148i | \(0.534453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.84469 | 1.57028 | 0.785139 | − | 0.619319i | \(-0.212591\pi\) | ||||
0.785139 | + | 0.619319i | \(0.212591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.73549 | −0.815151 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.890804 | −0.165418 | −0.0827091 | − | 0.996574i | \(-0.526357\pi\) | ||||
−0.0827091 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.73549 | 1.38933 | 0.694667 | − | 0.719331i | \(-0.255552\pi\) | ||||
0.694667 | + | 0.719331i | \(0.255552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.84469 | −0.843352 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.95388 | 0.321216 | 0.160608 | − | 0.987018i | \(-0.448654\pi\) | ||||
0.160608 | + | 0.987018i | \(0.448654\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.84469 | −0.455514 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3618 | 1.93059 | 0.965293 | − | 0.261169i | \(-0.0841080\pi\) | ||||
0.965293 | + | 0.261169i | \(0.0841080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.47098 | 0.529319 | 0.264660 | − | 0.964342i | \(-0.414740\pi\) | ||||
0.264660 | + | 0.964342i | \(0.414740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.62629 | 0.966544 | 0.483272 | − | 0.875470i | \(-0.339448\pi\) | ||||
0.483272 | + | 0.875470i | \(0.339448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95388 | 0.993412 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.890804 | 0.124737 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.3618 | −1.69802 | −0.849011 | − | 0.528376i | \(-0.822801\pi\) | ||||
−0.849011 | + | 0.528376i | \(0.822801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.84469 | −0.906601 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.890804 | 0.115973 | 0.0579864 | − | 0.998317i | \(-0.481532\pi\) | ||||
0.0579864 | + | 0.998317i | \(0.481532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.62629 | 1.10448 | 0.552242 | − | 0.833684i | \(-0.313773\pi\) | ||||
0.552242 | + | 0.833684i | \(0.313773\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.73549 | 0.470627 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.73549 | −0.945040 | −0.472520 | − | 0.881320i | \(-0.656656\pi\) | ||||
−0.472520 | + | 0.881320i | \(0.656656\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3618 | −1.46707 | −0.733537 | − | 0.679650i | \(-0.762132\pi\) | ||||
−0.733537 | + | 0.679650i | \(0.762132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.5341 | −1.93516 | −0.967582 | − | 0.252555i | \(-0.918729\pi\) | ||||
−0.967582 | + | 0.252555i | \(0.918729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.0973 | 2.06238 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4710 | 1.51560 | 0.757802 | − | 0.652485i | \(-0.226273\pi\) | ||||
0.757802 | + | 0.652485i | \(0.226273\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.58018 | 0.502740 | 0.251370 | − | 0.967891i | \(-0.419119\pi\) | ||||
0.251370 | + | 0.967891i | \(0.419119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.890804 | 0.0955042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1604 | −1.60699 | −0.803497 | − | 0.595309i | \(-0.797030\pi\) | ||||
−0.803497 | + | 0.595309i | \(0.797030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6263 | 1.11394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.73549 | −0.802133 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.2526 | 1.75173 | 0.875867 | − | 0.482552i | \(-0.160290\pi\) | ||||
0.875867 | + | 0.482552i | \(0.160290\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.84469 | 0.486909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.67241 | −0.265915 | −0.132957 | − | 0.991122i | \(-0.542447\pi\) | ||||
−0.132957 | + | 0.991122i | \(0.542447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.21839 | −0.612716 | −0.306358 | − | 0.951916i | \(-0.599111\pi\) | ||||
−0.306358 | + | 0.951916i | \(0.599111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.7986 | 1.43063 | 0.715316 | − | 0.698801i | \(-0.246283\pi\) | ||||
0.715316 | + | 0.698801i | \(0.246283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5341 | −1.20054 | −0.600272 | − | 0.799796i | \(-0.704941\pi\) | ||||
−0.600272 | + | 0.799796i | \(0.704941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.95388 | −0.185454 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.3618 | −1.16290 | −0.581449 | − | 0.813583i | \(-0.697514\pi\) | ||||
−0.581449 | + | 0.813583i | \(0.697514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.84469 | 0.262991 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.32759 | −0.305040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4710 | 1.13373 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.3618 | −1.11462 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7866 | −1.04590 | −0.522948 | − | 0.852365i | \(-0.675168\pi\) | ||||
−0.522948 | + | 0.852365i | \(0.675168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.47098 | −0.305603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4710 | −1.52645 | −0.763223 | − | 0.646135i | \(-0.776384\pi\) | ||||
−0.763223 | + | 0.646135i | \(0.776384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.5683 | 2.21705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.1604 | −1.29524 | −0.647618 | − | 0.761965i | \(-0.724235\pi\) | ||||
−0.647618 | + | 0.761965i | \(0.724235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.51710 | −0.467954 | −0.233977 | − | 0.972242i | \(-0.575174\pi\) | ||||
−0.233977 | + | 0.972242i | \(0.575174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.62629 | −0.558035 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.7816 | 1.15248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.95388 | −0.573547 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.15531 | 0.0946470 | 0.0473235 | − | 0.998880i | \(-0.484931\pi\) | ||||
0.0473235 | + | 0.998880i | \(0.484931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4710 | −1.25901 | −0.629505 | − | 0.776996i | \(-0.716742\pi\) | ||||
−0.629505 | + | 0.776996i | \(0.716742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.890804 | −0.0720172 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6774 | −1.49062 | −0.745311 | − | 0.666717i | \(-0.767699\pi\) | ||||
−0.745311 | + | 0.666717i | \(0.767699\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.3618 | 0.980353 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.73549 | −0.294398 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0922364 | −0.00722451 | −0.00361226 | − | 0.999993i | \(-0.501150\pi\) | ||||
−0.00361226 | + | 0.999993i | \(0.501150\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.37371 | 0.415830 | 0.207915 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207915 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.90776 | −0.377520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.84469 | 0.523426 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.890804 | −0.0669569 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.56322 | −0.714788 | −0.357394 | − | 0.933954i | \(-0.616335\pi\) | ||||
−0.357394 | + | 0.933954i | \(0.616335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.16035 | −0.532225 | −0.266112 | − | 0.963942i | \(-0.585739\pi\) | ||||
−0.266112 | + | 0.963942i | \(0.585739\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.62629 | −0.637674 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.31566 | −0.315593 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.73549 | −0.271717 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0050 | 1.01337 | 0.506684 | − | 0.862132i | \(-0.330871\pi\) | ||||
0.506684 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.7236 | −1.92360 | −0.961802 | − | 0.273745i | \(-0.911737\pi\) | ||||
−0.961802 | + | 0.273745i | \(0.911737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.16035 | −0.652648 | −0.326324 | − | 0.945258i | \(-0.605810\pi\) | ||||
−0.326324 | + | 0.945258i | \(0.605810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.310629 | −0.0220199 | −0.0110099 | − | 0.999939i | \(-0.503505\pi\) | ||||
−0.0110099 | + | 0.999939i | \(0.503505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.73549 | 0.545619 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.32759 | −0.233551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.1604 | 2.29375 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.95388 | 0.409882 | 0.204941 | − | 0.978774i | \(-0.434300\pi\) | ||||
0.204941 | + | 0.978774i | \(0.434300\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3618 | 0.847015 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.8958 | 1.96158 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5341 | 1.11727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.53406 | −0.170459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9078 | 0.797403 | 0.398701 | − | 0.917081i | \(-0.369461\pi\) | ||||
0.398701 | + | 0.917081i | \(0.369461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.37874 | −0.489744 | −0.244872 | − | 0.969555i | \(-0.578746\pi\) | ||||
−0.244872 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.1604 | 1.53048 | 0.765240 | − | 0.643746i | \(-0.222621\pi\) | ||||
0.765240 | + | 0.643746i | \(0.222621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0973 | −1.19071 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9420 | 1.50298 | 0.751489 | − | 0.659746i | \(-0.229336\pi\) | ||||
0.751489 | + | 0.659746i | \(0.229336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4710 | −0.875034 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.361783 | 0.0234018 | 0.0117009 | − | 0.999932i | \(-0.496275\pi\) | ||||
0.0117009 | + | 0.999932i | \(0.496275\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5341 | 1.83804 | 0.919020 | − | 0.394211i | \(-0.128982\pi\) | ||||
0.919020 | + | 0.394211i | \(0.128982\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.4710 | 1.23891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.58018 | −0.290257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.8497 | −1.94722 | −0.973609 | − | 0.228224i | \(-0.926708\pi\) | ||||
−0.973609 | + | 0.228224i | \(0.926708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.84469 | −0.304583 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7524 | 0.795476 | 0.397738 | − | 0.917499i | \(-0.369795\pi\) | ||||
0.397738 | + | 0.917499i | \(0.369795\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.29870 | 0.453519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.890804 | −0.0551394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.36178 | −0.392284 | −0.196142 | − | 0.980575i | \(-0.562841\pi\) | ||||
−0.196142 | + | 0.980575i | \(0.562841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.1604 | 0.927798 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5802 | 0.645085 | 0.322542 | − | 0.946555i | \(-0.395463\pi\) | ||||
0.322542 | + | 0.946555i | \(0.395463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.26451 | −0.259051 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.6263 | −0.643133 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.3787 | 1.76520 | 0.882599 | − | 0.470127i | \(-0.155792\pi\) | ||||
0.882599 | + | 0.470127i | \(0.155792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.73549 | 0.463112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7524 | −1.11868 | −0.559339 | − | 0.828939i | \(-0.688945\pi\) | ||||
−0.559339 | + | 0.828939i | \(0.688945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8958 | 0.766578 | 0.383289 | − | 0.923628i | \(-0.374791\pi\) | ||||
0.383289 | + | 0.923628i | \(0.374791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 46.1773 | 2.72576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2065 | −0.953322 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2526 | −1.01136 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.79857 | −0.514018 | −0.257009 | − | 0.966409i | \(-0.582737\pi\) | ||||
−0.257009 | + | 0.966409i | \(0.582737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.84469 | −0.281117 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.84469 | −0.164512 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9658 | 0.747337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.67241 | 0.153526 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0050 | −0.571018 | −0.285509 | − | 0.958376i | \(-0.592163\pi\) | ||||
−0.285509 | + | 0.958376i | \(0.592163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.21839 | 0.353752 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5290 | −1.05068 | −0.525342 | − | 0.850891i | \(-0.676063\pi\) | ||||
−0.525342 | + | 0.850891i | \(0.676063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.39067 | −0.135128 | −0.0675642 | − | 0.997715i | \(-0.521523\pi\) | ||||
−0.0675642 | + | 0.997715i | \(0.521523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3157 | 0.916379 | 0.458190 | − | 0.888855i | \(-0.348498\pi\) | ||||
0.458190 | + | 0.888855i | \(0.348498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.31566 | −0.241631 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.7986 | −0.825975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.09727 | −0.339261 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.5341 | 0.693135 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.7524 | 1.36465 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8958 | −1.36840 | −0.684200 | − | 0.729295i | \(-0.739848\pi\) | ||||
−0.684200 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.95388 | 0.107072 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.4710 | 1.49644 | 0.748220 | − | 0.663451i | \(-0.230909\pi\) | ||||
0.748220 | + | 0.663451i | \(0.230909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.3618 | 0.671400 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.4760 | 2.02944 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.172274 | −0.00930193 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.25259 | 0.0672424 | 0.0336212 | − | 0.999435i | \(-0.489296\pi\) | ||||
0.0336212 | + | 0.999435i | \(0.489296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.64325 | 0.516192 | 0.258096 | − | 0.966119i | \(-0.416905\pi\) | ||||
0.258096 | + | 0.966119i | \(0.416905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.84469 | −0.151838 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7524 | 0.678744 | 0.339372 | − | 0.940652i | \(-0.389785\pi\) | ||||
0.339372 | + | 0.940652i | \(0.389785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.32759 | 0.176115 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.62629 | −0.349722 | −0.174861 | − | 0.984593i | \(-0.555948\pi\) | ||||
−0.174861 | + | 0.984593i | \(0.555948\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.8497 | 1.46577 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.4710 | −0.654557 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.60933 | 0.501603 | 0.250802 | − | 0.968039i | \(-0.419306\pi\) | ||||
0.250802 | + | 0.968039i | \(0.419306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.3618 | 0.643529 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.1773 | −2.39741 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.8839 | −1.54733 | −0.773665 | − | 0.633595i | \(-0.781579\pi\) | ||||
−0.773665 | + | 0.633595i | \(0.781579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.53406 | −0.130511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.52902 | 0.129907 | 0.0649535 | − | 0.997888i | \(-0.479310\pi\) | ||||
0.0649535 | + | 0.997888i | \(0.479310\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7866 | 0.603848 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.2115 | −1.28825 | −0.644124 | − | 0.764921i | \(-0.722778\pi\) | ||||
−0.644124 | + | 0.764921i | \(0.722778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.47098 | 0.176440 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.0681 | 1.77802 | 0.889012 | − | 0.457884i | \(-0.151392\pi\) | ||||
0.889012 | + | 0.457884i | \(0.151392\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.890804 | 0.0450499 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4710 | 0.881294 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.84972 | −0.444155 | −0.222077 | − | 0.975029i | \(-0.571284\pi\) | ||||
−0.222077 | + | 0.975029i | \(0.571284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.5683 | −1.28001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0681 | −1.15197 | −0.575983 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575983 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.0050 | 1.09615 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.46594 | 0.469209 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.29870 | 0.262004 | 0.131002 | − | 0.991382i | \(-0.458181\pi\) | ||||
0.131002 | + | 0.991382i | \(0.458181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.1604 | 0.747805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.32759 | 0.163740 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.51710 | 0.270173 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.53406 | 0.123797 | 0.0618984 | − | 0.998082i | \(-0.480285\pi\) | ||||
0.0618984 | + | 0.998082i | \(0.480285\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4079 | 1.09209 | 0.546047 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546047 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.62629 | 0.322181 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.2234 | 1.55940 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.7816 | −0.665382 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.5733 | 1.52083 | 0.760416 | − | 0.649436i | \(-0.224995\pi\) | ||||
0.760416 | + | 0.649436i | \(0.224995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.20647 | −0.346321 | −0.173160 | − | 0.984894i | \(-0.555398\pi\) | ||||
−0.173160 | + | 0.984894i | \(0.555398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.84469 | −0.327426 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.72357 | −0.225443 | −0.112722 | − | 0.993627i | \(-0.535957\pi\) | ||||
−0.112722 | + | 0.993627i | \(0.535957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.95388 | 0.331137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.87888 | 0.374337 | 0.187168 | − | 0.982328i | \(-0.440069\pi\) | ||||
0.187168 | + | 0.982328i | \(0.440069\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.15531 | −0.0546445 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.70633 | −0.222105 | −0.111053 | − | 0.993815i | \(-0.535422\pi\) | ||||
−0.111053 | + | 0.993815i | \(0.535422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 59.8890 | 2.82006 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4710 | 0.726890 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.04612 | 0.282825 | 0.141413 | − | 0.989951i | \(-0.454836\pi\) | ||||
0.141413 | + | 0.989951i | \(0.454836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.890804 | 0.0415792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.2526 | −0.896682 | −0.448341 | − | 0.893863i | \(-0.647985\pi\) | ||||
−0.448341 | + | 0.893863i | \(0.647985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4418 | 1.22886 | 0.614428 | − | 0.788973i | \(-0.289387\pi\) | ||||
0.614428 | + | 0.788973i | \(0.289387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.20143 | −0.425792 | −0.212896 | − | 0.977075i | \(-0.568289\pi\) | ||||
−0.212896 | + | 0.977075i | \(0.568289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.8958 | −1.33429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.6774 | 0.860611 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.8158 | 0.773191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.3618 | −0.566007 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.7524 | −0.582674 | −0.291337 | − | 0.956620i | \(-0.594100\pi\) | ||||
−0.291337 | + | 0.956620i | \(0.594100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.55818 | 0.253431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.73549 | 0.169971 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5341 | 1.38363 | 0.691815 | − | 0.722075i | \(-0.256811\pi\) | ||||
0.691815 | + | 0.722075i | \(0.256811\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0922364 | 0.00417107 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.67241 | −0.120604 | −0.0603021 | − | 0.998180i | \(-0.519206\pi\) | ||||
−0.0603021 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.793532 | 0.0357389 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.1773 | −2.07134 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.8036 | −0.931297 | −0.465649 | − | 0.884970i | \(-0.654179\pi\) | ||||
−0.465649 | + | 0.884970i | \(0.654179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.37371 | −0.240080 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.32759 | −0.148370 | −0.0741849 | − | 0.997245i | \(-0.523636\pi\) | ||||
−0.0741849 | + | 0.997245i | \(0.523636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.90776 | 0.217961 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2184 | 0.718868 | 0.359434 | − | 0.933171i | \(-0.382970\pi\) | ||||
0.359434 | + | 0.933171i | \(0.382970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −61.7628 | −2.73223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.84469 | −0.302200 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.1023 | 1.41186 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.18923 | 0.139723 | 0.0698614 | − | 0.997557i | \(-0.477744\pi\) | ||||
0.0698614 | + | 0.997557i | \(0.477744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8155 | −1.04138 | −0.520690 | − | 0.853746i | \(-0.674325\pi\) | ||||
−0.520690 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.89080 | −0.300168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.890804 | 0.0386576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1654 | 1.52318 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.56322 | 0.412683 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.6894 | 1.45110 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7816 | 0.678504 | 0.339252 | − | 0.940695i | \(-0.389826\pi\) | ||||
0.339252 | + | 0.940695i | \(0.389826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.16035 | 0.307280 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.62629 | 0.368161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.09727 | −0.259753 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.3207 | 2.13985 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.7405 | −1.34489 | −0.672445 | − | 0.740147i | \(-0.734756\pi\) | ||||
−0.672445 | + | 0.740147i | \(0.734756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.87384 | 0.417619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31566 | 0.182208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.9250 | −0.924029 | −0.462014 | − | 0.886872i | \(-0.652873\pi\) | ||||
−0.462014 | + | 0.886872i | \(0.652873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.73549 | 0.156876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.6313 | −0.613377 | −0.306689 | − | 0.951810i | \(-0.599221\pi\) | ||||
−0.306689 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24755 | 0.0522084 | 0.0261042 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261042 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.0050 | −0.585069 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.0922 | −0.753190 | −0.376595 | − | 0.926378i | \(-0.622905\pi\) | ||||
−0.376595 | + | 0.926378i | \(0.622905\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.7236 | 1.11059 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1092 | 0.709809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −59.8890 | −2.48035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5290 | −0.517128 | −0.258564 | − | 0.965994i | \(-0.583249\pi\) | ||||
−0.258564 | + | 0.965994i | \(0.583249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.9470 | 2.18164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.16035 | 0.376806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.9470 | 1.02445 | 0.512225 | − | 0.858851i | \(-0.328821\pi\) | ||||
0.512225 | + | 0.858851i | \(0.328821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.310629 | 0.0127132 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.5391 | −1.41123 | −0.705615 | − | 0.708596i | \(-0.749329\pi\) | ||||
−0.705615 | + | 0.708596i | \(0.749329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.9300 | 1.54720 | 0.773599 | − | 0.633675i | \(-0.218454\pi\) | ||||
0.773599 | + | 0.633675i | \(0.218454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.73549 | −0.315013 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.0973 | −1.05926 | −0.529628 | − | 0.848230i | \(-0.677668\pi\) | ||||
−0.529628 | + | 0.848230i | \(0.677668\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.32759 | 0.134841 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.8497 | 0.762578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.84972 | −0.115099 | −0.0575496 | − | 0.998343i | \(-0.518329\pi\) | ||||
−0.0575496 | + | 0.998343i | \(0.518329\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.52213 | 0.383347 | 0.191673 | − | 0.981459i | \(-0.438609\pi\) | ||||
0.191673 | + | 0.981459i | \(0.438609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9762 | −0.963683 | −0.481841 | − | 0.876258i | \(-0.660032\pi\) | ||||
−0.481841 | + | 0.876258i | \(0.660032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −56.6313 | −2.26889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.1604 | −1.32430 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.74053 | −0.0693993 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8789 | −0.711747 | −0.355873 | − | 0.934534i | \(-0.615817\pi\) | ||||
−0.355873 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.95388 | −0.236646 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7816 | 0.783776 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3618 | −0.489025 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.93692 | 0.116001 | 0.0580007 | − | 0.998317i | \(-0.481527\pi\) | ||||
0.0580007 | + | 0.998317i | \(0.481527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.895840 | 0.0353285 | 0.0176642 | − | 0.999844i | \(-0.494377\pi\) | ||||
0.0176642 | + | 0.999844i | \(0.494377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.4659 | 0.843913 | 0.421957 | − | 0.906616i | \(-0.361343\pi\) | ||||
0.421957 | + | 0.906616i | \(0.361343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.31566 | 0.169405 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.8958 | −1.13252 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.84469 | 0.189587 | 0.0947936 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947936 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.5341 | −0.645055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0973 | −0.704970 | −0.352485 | − | 0.935818i | \(-0.614663\pi\) | ||||
−0.352485 | + | 0.935818i | \(0.614663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.747413 | 0.0290710 | 0.0145355 | − | 0.999894i | \(-0.495373\pi\) | ||||
0.0145355 | + | 0.999894i | \(0.495373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.53406 | 0.0984146 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.890804 | 0.0344921 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.9078 | −0.460381 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.7917 | 1.61335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1892 | 0.739691 | 0.369845 | − | 0.929093i | \(-0.379411\pi\) | ||||
0.369845 | + | 0.929093i | \(0.379411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.17731 | 0.160547 | 0.0802735 | − | 0.996773i | \(-0.474421\pi\) | ||||
0.0802735 | + | 0.996773i | \(0.474421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.4469 | 2.47324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.37874 | 0.282754 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0050 | 0.995055 | 0.497528 | − | 0.867448i | \(-0.334241\pi\) | ||||
0.497528 | + | 0.867448i | \(0.334241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.1604 | −0.883622 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.1654 | −1.33969 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8497 | 1.02141 | 0.510706 | − | 0.859756i | \(-0.329384\pi\) | ||||
0.510706 | + | 0.859756i | \(0.329384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0973 | 0.687459 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0119 | −0.417106 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.9420 | −0.867745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9027 | 0.449560 | 0.224780 | − | 0.974410i | \(-0.427834\pi\) | ||||
0.224780 | + | 0.974410i | \(0.427834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3737 | 0.504399 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.98277 | −0.375441 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.3737 | −1.47871 | −0.739355 | − | 0.673315i | \(-0.764870\pi\) | ||||
−0.739355 | + | 0.673315i | \(0.764870\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4710 | 0.505201 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.73549 | −0.289696 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.361783 | −0.0135110 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.6382 | 0.881557 | 0.440778 | − | 0.897616i | \(-0.354702\pi\) | ||||
0.440778 | + | 0.897616i | \(0.354702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2287 | −0.865083 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.5341 | −1.06119 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.5513 | −0.465502 | −0.232751 | − | 0.972536i | \(-0.574773\pi\) | ||||
−0.232751 | + | 0.972536i | \(0.574773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09196 | −0.114360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.1142 | −1.44472 | −0.722359 | − | 0.691519i | \(-0.756942\pi\) | ||||
−0.722359 | + | 0.691519i | \(0.756942\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.4760 | −1.38045 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7456 | 1.31492 | 0.657461 | − | 0.753489i | \(-0.271630\pi\) | ||||
0.657461 | + | 0.753489i | \(0.271630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.4710 | −0.715284 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.4368 | −0.749753 | −0.374876 | − | 0.927075i | \(-0.622315\pi\) | ||||
−0.374876 | + | 0.927075i | \(0.622315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.58018 | 0.167580 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 55.2799 | 2.01988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.534057 | −0.0194880 | −0.00974401 | − | 0.999953i | \(-0.503102\pi\) | ||||
−0.00974401 | + | 0.999953i | \(0.503102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.8497 | 1.12423 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5171 | 1.07282 | 0.536409 | − | 0.843958i | \(-0.319781\pi\) | ||||
0.536409 | + | 0.843958i | \(0.319781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.84469 | 0.175851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1434 | 1.38270 | 0.691348 | − | 0.722522i | \(-0.257017\pi\) | ||||
0.691348 | + | 0.722522i | \(0.257017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.8208 | −1.69503 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.53406 | 0.0914995 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.8786 | 0.752902 | 0.376451 | − | 0.926437i | \(-0.377144\pi\) | ||||
0.376451 | + | 0.926437i | \(0.377144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7524 | −0.459268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.31063 | −0.298913 | −0.149456 | − | 0.988768i | \(-0.547752\pi\) | ||||
−0.149456 | + | 0.988768i | \(0.547752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.29870 | −0.261840 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 84.6125 | 3.03156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.8890 | −2.14300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.890804 | 0.0318347 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.95388 | 0.0696484 | 0.0348242 | − | 0.999393i | \(-0.488913\pi\) | ||||
0.0348242 | + | 0.999393i | \(0.488913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.36178 | 0.226485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.1773 | −1.64188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5391 | 0.871409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1773 | 0.573030 | 0.286515 | − | 0.958076i | \(-0.407503\pi\) | ||||
0.286515 | + | 0.958076i | \(0.407503\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.90273 | −0.208823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1604 | −0.535665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −80.1023 | −2.82675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.5802 | −0.372440 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.8670 | −0.944592 | −0.472296 | − | 0.881440i | \(-0.656575\pi\) | ||||
−0.472296 | + | 0.881440i | \(0.656575\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.13835 | 0.0750878 | 0.0375439 | − | 0.999295i | \(-0.488047\pi\) | ||||
0.0375439 | + | 0.999295i | \(0.488047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.26451 | 0.149563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.7578 | 0.831179 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.6263 | 0.371313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1604 | 0.529100 | 0.264550 | − | 0.964372i | \(-0.414777\pi\) | ||||
0.264550 | + | 0.964372i | \(0.414777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.1264 | 0.806137 | 0.403068 | − | 0.915170i | \(-0.367944\pi\) | ||||
0.403068 | + | 0.915170i | \(0.367944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4299 | −1.64930 | −0.824650 | − | 0.565644i | \(-0.808628\pi\) | ||||
−0.824650 | + | 0.565644i | \(0.808628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.1723 | −1.04793 | −0.523963 | − | 0.851741i | \(-0.675547\pi\) | ||||
−0.523963 | + | 0.851741i | \(0.675547\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3787 | −1.01914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.19454 | −0.214628 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.73549 | −0.267378 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.8497 | 0.650765 | 0.325382 | − | 0.945583i | \(-0.394507\pi\) | ||||
0.325382 | + | 0.945583i | \(0.394507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2065 | −0.972637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.7524 | 0.645869 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.5852 | 1.60069 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.8958 | −0.442584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.95388 | −0.0669782 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.7578 | −1.01889 | −0.509443 | − | 0.860504i | \(-0.670149\pi\) | ||||
−0.509443 | + | 0.860504i | \(0.670149\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.2865 | 0.522177 | 0.261089 | − | 0.965315i | \(-0.415919\pi\) | ||||
0.261089 | + | 0.965315i | \(0.415919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.5171 | 1.14359 | 0.571794 | − | 0.820397i | \(-0.306248\pi\) | ||||
0.571794 | + | 0.820397i | \(0.306248\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.1773 | −1.57372 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.0443 | 1.05676 | 0.528380 | − | 0.849008i | \(-0.322800\pi\) | ||||
0.528380 | + | 0.849008i | \(0.322800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.2065 | 0.550401 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.2627 | 2.21388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0050 | −0.745612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2526 | 0.583912 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.6313 | −0.358994 | −0.179497 | − | 0.983758i | \(-0.557447\pi\) | ||||
−0.179497 | + | 0.983758i | \(0.557447\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.79857 | 0.296768 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5341 | 0.691810 | 0.345905 | − | 0.938270i | \(-0.387572\pi\) | ||||
0.345905 | + | 0.938270i | \(0.387572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0390 | −1.21281 | −0.606404 | − | 0.795157i | \(-0.707388\pi\) | ||||
−0.606404 | + | 0.795157i | \(0.707388\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.9759 | 0.838608 | 0.419304 | − | 0.907846i | \(-0.362274\pi\) | ||||
0.419304 | + | 0.907846i | \(0.362274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.0289 | −1.47668 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.84469 | 0.162303 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.3549 | 1.51774 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.84469 | 0.0949813 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.89080 | −0.229821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0119 | 0.366860 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.9658 | −0.431475 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.6194 | −1.38195 | −0.690975 | − | 0.722879i | \(-0.742818\pi\) | ||||
−0.690975 | + | 0.722879i | \(0.742818\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.67241 | −0.0886383 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.81553 | 0.126414 | 0.0632070 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632070 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.1895 | 0.734366 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −65.2627 | −2.15516 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.7917 | −1.31261 | −0.656303 | − | 0.754497i | \(-0.727881\pi\) | ||||
−0.656303 | + | 0.754497i | \(0.727881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0050 | 0.329677 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.1654 | −1.15748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.21839 | −0.204239 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.6141 | 0.413855 | 0.206928 | − | 0.978356i | \(-0.433654\pi\) | ||||
0.206928 | + | 0.978356i | \(0.433654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.5971 | 1.55993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.5290 | 0.606613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1262 | 0.722830 | 0.361415 | − | 0.932405i | \(-0.382294\pi\) | ||||
0.361415 | + | 0.932405i | \(0.382294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.39067 | 0.0780164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0392 | −0.359869 | −0.179934 | − | 0.983679i | \(-0.557589\pi\) | ||||
−0.179934 | + | 0.983679i | \(0.557589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.3618 | −0.402555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.68937 | −0.314862 | −0.157431 | − | 0.987530i | \(-0.550321\pi\) | ||||
−0.157431 | + | 0.987530i | \(0.550321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.0342 | −1.52679 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3157 | −0.529072 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1845 | 0.459480 | 0.229740 | − | 0.973252i | \(-0.426212\pi\) | ||||
0.229740 | + | 0.973252i | \(0.426212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.31566 | 0.139506 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.6313 | −1.82872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8378 | 0.930252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7986 | 0.476877 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8447 | −0.413057 | −0.206529 | − | 0.978441i | \(-0.566217\pi\) | ||||
−0.206529 | + | 0.978441i | \(0.566217\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.09727 | 0.195873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1945 | −0.776440 | −0.388220 | − | 0.921567i | \(-0.626910\pi\) | ||||
−0.388220 | + | 0.921567i | \(0.626910\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.6091 | −0.660696 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.4879 | −0.591482 | −0.295741 | − | 0.955268i | \(-0.595566\pi\) | ||||
−0.295741 | + | 0.955268i | \(0.595566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.4471 | −2.34738 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5341 | −0.400182 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.8325 | 0.919614 | 0.459807 | − | 0.888019i | \(-0.347919\pi\) | ||||
0.459807 | + | 0.888019i | \(0.347919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.7524 | −0.787879 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.47098 | −0.110371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8958 | 1.29910 | 0.649550 | − | 0.760319i | \(-0.274957\pi\) | ||||
0.649550 | + | 0.760319i | \(0.274957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.8958 | 0.790046 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.65518 | 0.147431 | 0.0737155 | − | 0.997279i | \(-0.476514\pi\) | ||||
0.0737155 | + | 0.997279i | \(0.476514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.95388 | −0.0618181 |
(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 | 6900.2.a.x.1.3 | 3 | ||
5.2 | odd | 4 | 6900.2.f.r.6349.6 | 6 | |||
5.3 | odd | 4 | 6900.2.f.r.6349.1 | 6 | |||
5.4 | even | 2 | 1380.2.a.j.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 4140.2.a.s.1.1 | 3 | |||
20.19 | odd | 2 | 5520.2.a.bv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.a.j.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
4140.2.a.s.1.1 | 3 | 15.14 | odd | 2 | |||
5520.2.a.bv.1.3 | 3 | 20.19 | odd | 2 | |||
6900.2.a.x.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6900.2.f.r.6349.1 | 6 | 5.3 | odd | 4 | |||
6900.2.f.r.6349.6 | 6 | 5.2 | odd | 4 |