Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7440,2,Mod(1,7440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7440, 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("7440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7440.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: | \(59.4086991038\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 930) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7440.1 |
$q$-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 | ||||||||
\(7\) | −3.37228 | −1.27460 | −0.637301 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637301 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.627719 | −0.189264 | −0.0946322 | − | 0.995512i | \(-0.530167\pi\) | ||||
−0.0946322 | + | 0.995512i | \(0.530167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.74456 | −1.15073 | −0.575363 | − | 0.817898i | \(-0.695139\pi\) | ||||
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.627719 | 0.144009 | 0.0720043 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720043 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.37228 | −0.703169 | −0.351585 | − | 0.936156i | \(-0.614357\pi\) | ||||
−0.351585 | + | 0.936156i | \(0.614357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.74456 | −1.62382 | −0.811912 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.627719 | 0.109272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.744563 | −0.122405 | −0.0612027 | − | 0.998125i | \(-0.519494\pi\) | ||||
−0.0612027 | + | 0.998125i | \(0.519494\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.744563 | 0.116281 | 0.0581406 | − | 0.998308i | \(-0.481483\pi\) | ||||
0.0581406 | + | 0.998308i | \(0.481483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.627719 | −0.0957262 | −0.0478631 | − | 0.998854i | \(-0.515241\pi\) | ||||
−0.0478631 | + | 0.998854i | \(0.515241\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.74456 | 0.983796 | 0.491898 | − | 0.870653i | \(-0.336303\pi\) | ||||
0.491898 | + | 0.870653i | \(0.336303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.74456 | 0.664372 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37228 | 0.188497 | 0.0942487 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942487 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.627719 | −0.0846416 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.627719 | −0.0831434 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4891 | 1.47103 | 0.735516 | − | 0.677507i | \(-0.236940\pi\) | ||||
0.735516 | + | 0.677507i | \(0.236940\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.37228 | −0.424868 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7446 | −1.31266 | −0.656329 | − | 0.754475i | \(-0.727892\pi\) | ||||
−0.656329 | + | 0.754475i | \(0.727892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.37228 | 0.405975 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.37228 | −0.400216 | −0.200108 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200108 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.11684 | −0.950005 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.11684 | 0.241237 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.62772 | 0.520659 | 0.260330 | − | 0.965520i | \(-0.416169\pi\) | ||||
0.260330 | + | 0.965520i | \(0.416169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.74456 | −0.514620 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.74456 | 0.937516 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.37228 | −0.145462 | −0.0727308 | − | 0.997352i | \(-0.523171\pi\) | ||||
−0.0727308 | + | 0.997352i | \(0.523171\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.74456 | 0.707022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.627719 | 0.0644026 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.627719 | −0.0630881 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.11684 | 0.807656 | 0.403828 | − | 0.914835i | \(-0.367679\pi\) | ||||
0.403828 | + | 0.914835i | \(0.367679\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.37228 | 0.329101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.627719 | −0.0606839 | −0.0303419 | − | 0.999540i | \(-0.509660\pi\) | ||||
−0.0303419 | + | 0.999540i | \(0.509660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.74456 | 0.454447 | 0.227223 | − | 0.973843i | \(-0.427035\pi\) | ||||
0.227223 | + | 0.973843i | \(0.427035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.744563 | 0.0706708 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.62772 | −0.247195 | −0.123597 | − | 0.992332i | \(-0.539443\pi\) | ||||
−0.123597 | + | 0.992332i | \(0.539443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37228 | −0.314467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.0000 | 1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.744563 | −0.0671350 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4891 | −1.19697 | −0.598483 | − | 0.801135i | \(-0.704230\pi\) | ||||
−0.598483 | + | 0.801135i | \(0.704230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.627719 | 0.0552675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2337 | 1.41834 | 0.709172 | − | 0.705036i | \(-0.249069\pi\) | ||||
0.709172 | + | 0.705036i | \(0.249069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.11684 | −0.183554 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.48913 | −0.298096 | −0.149048 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149048 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7446 | 0.911342 | 0.455671 | − | 0.890148i | \(-0.349399\pi\) | ||||
0.455671 | + | 0.890148i | \(0.349399\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.74456 | −0.567995 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.25544 | 0.104985 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.74456 | −0.726196 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.37228 | −0.360620 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1168 | −0.992651 | −0.496325 | − | 0.868137i | \(-0.665318\pi\) | ||||
−0.496325 | + | 0.868137i | \(0.665318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.74456 | −0.383575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.37228 | 0.747989 | 0.373995 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373995 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.37228 | −0.108829 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3723 | 0.896261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.2337 | −1.89813 | −0.949064 | − | 0.315082i | \(-0.897968\pi\) | ||||
−0.949064 | + | 0.315082i | \(0.897968\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.627719 | 0.0488678 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6277 | 0.977162 | 0.488581 | − | 0.872518i | \(-0.337515\pi\) | ||||
0.488581 | + | 0.872518i | \(0.337515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.627719 | 0.0480028 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37228 | −0.254921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.74456 | 0.206294 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8614 | 1.10464 | 0.552320 | − | 0.833632i | \(-0.313743\pi\) | ||||
0.552320 | + | 0.833632i | \(0.313743\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4891 | −0.849301 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.744563 | −0.0547413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.97825 | 0.217791 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.37228 | 0.245297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4891 | 1.11493 | 0.557466 | − | 0.830200i | \(-0.311774\pi\) | ||||
0.557466 | + | 0.830200i | \(0.311774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4891 | 1.38854 | 0.694271 | − | 0.719713i | \(-0.255727\pi\) | ||||
0.694271 | + | 0.719713i | \(0.255727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6277 | 0.895155 | 0.447578 | − | 0.894245i | \(-0.352287\pi\) | ||||
0.447578 | + | 0.894245i | \(0.352287\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.7446 | 0.757863 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.4891 | 2.06973 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.744563 | 0.0520025 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.37228 | −0.234390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.394031 | −0.0272557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.627719 | 0.0432139 | 0.0216070 | − | 0.999767i | \(-0.493122\pi\) | ||||
0.0216070 | + | 0.999767i | \(0.493122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.37228 | 0.231065 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.627719 | −0.0428101 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.37228 | −0.228925 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.11684 | 0.548485 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48913 | 0.638308 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.25544 | −0.619790 | −0.309895 | − | 0.950771i | \(-0.600294\pi\) | ||||
−0.309895 | + | 0.950771i | \(0.600294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.11684 | −0.405989 | −0.202995 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202995 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.88316 | 0.256606 | 0.128303 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11684 | −0.139278 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.8614 | −0.973603 | −0.486802 | − | 0.873513i | \(-0.661837\pi\) | ||||
−0.486802 | + | 0.873513i | \(0.661837\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.74456 | 0.439967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.62772 | −0.300603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.4891 | 1.90749 | 0.953746 | − | 0.300612i | \(-0.0971910\pi\) | ||||
0.953746 | + | 0.300612i | \(0.0971910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.51087 | 0.290571 | 0.145285 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145285 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.25544 | −0.0798816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.11684 | 0.133085 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.74456 | 0.297116 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3723 | 0.834140 | 0.417070 | − | 0.908874i | \(-0.363057\pi\) | ||||
0.417070 | + | 0.908874i | \(0.363057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.51087 | 0.156018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.74456 | −0.541275 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.9783 | 1.17025 | 0.585125 | − | 0.810943i | \(-0.301046\pi\) | ||||
0.585125 | + | 0.810943i | \(0.301046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37228 | 0.0842986 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.37228 | 0.0839823 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8832 | 0.843342 | 0.421671 | − | 0.906749i | \(-0.361444\pi\) | ||||
0.421671 | + | 0.906749i | \(0.361444\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.74456 | −0.408200 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.627719 | −0.0378529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.2554 | 0.916610 | 0.458305 | − | 0.888795i | \(-0.348457\pi\) | ||||
0.458305 | + | 0.888795i | \(0.348457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7446 | 0.998897 | 0.499448 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499448 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.627719 | −0.0371828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.51087 | −0.148212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.51087 | 0.324169 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.48913 | −0.437519 | −0.218760 | − | 0.975779i | \(-0.570201\pi\) | ||||
−0.218760 | + | 0.975779i | \(0.570201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.74456 | −0.159795 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.627719 | 0.0364239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.74456 | 0.390048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.11684 | 0.122013 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.11684 | −0.466301 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.4891 | 0.657865 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.9783 | −1.76802 | −0.884011 | − | 0.467466i | \(-0.845167\pi\) | ||||
−0.884011 | + | 0.467466i | \(0.845167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.37228 | −0.190007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.7446 | −1.38979 | −0.694897 | − | 0.719110i | \(-0.744550\pi\) | ||||
−0.694897 | + | 0.719110i | \(0.744550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.48913 | 0.307332 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.627719 | 0.0350358 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.97825 | −0.165714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.74456 | −0.262375 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.7446 | −1.25395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.48913 | 0.0818497 | 0.0409249 | − | 0.999162i | \(-0.486970\pi\) | ||||
0.0409249 | + | 0.999162i | \(0.486970\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.744563 | −0.0408018 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7446 | −0.587038 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9783 | 1.57855 | 0.789273 | − | 0.614043i | \(-0.210458\pi\) | ||||
0.789273 | + | 0.614043i | \(0.210458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.62772 | 0.142718 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.627719 | −0.0339929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.37228 | 0.181558 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.4674 | −1.95767 | −0.978836 | − | 0.204648i | \(-0.934395\pi\) | ||||
−0.978836 | + | 0.204648i | \(0.934395\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.25544 | 0.388375 | 0.194187 | − | 0.980964i | \(-0.437793\pi\) | ||||
0.194187 | + | 0.980964i | \(0.437793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4891 | 0.824403 | 0.412201 | − | 0.911093i | \(-0.364760\pi\) | ||||
0.412201 | + | 0.911093i | \(0.364760\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.37228 | −0.178982 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0000 | −0.846810 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.37228 | −0.177982 | −0.0889911 | − | 0.996032i | \(-0.528364\pi\) | ||||
−0.0889911 | + | 0.996032i | \(0.528364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6060 | −0.979262 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.6060 | 0.556669 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.11684 | −0.424855 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.2337 | 1.05619 | 0.528095 | − | 0.849185i | \(-0.322907\pi\) | ||||
0.528095 | + | 0.849185i | \(0.322907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.744563 | 0.0387604 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.62772 | −0.240259 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.8614 | 0.769494 | 0.384747 | − | 0.923022i | \(-0.374289\pi\) | ||||
0.384747 | + | 0.923022i | \(0.374289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.4891 | 0.900736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8614 | 1.48251 | 0.741255 | − | 0.671223i | \(-0.234231\pi\) | ||||
0.741255 | + | 0.671223i | \(0.234231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.4891 | 0.691069 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.4891 | −0.689262 | −0.344631 | − | 0.938738i | \(-0.611996\pi\) | ||||
−0.344631 | + | 0.938738i | \(0.611996\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.11684 | 0.107884 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.627719 | −0.0319087 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.9783 | 0.860831 | 0.430416 | − | 0.902631i | \(-0.358367\pi\) | ||||
0.430416 | + | 0.902631i | \(0.358367\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.2337 | −0.818881 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.62772 | 0.232846 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.60597 | −0.0806013 | −0.0403006 | − | 0.999188i | \(-0.512832\pi\) | ||||
−0.0403006 | + | 0.999188i | \(0.512832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.11684 | 0.105975 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6277 | 1.12997 | 0.564987 | − | 0.825100i | \(-0.308881\pi\) | ||||
0.564987 | + | 0.825100i | \(0.308881\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | −0.0996271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.467376 | 0.0231670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2337 | −0.506023 | −0.253012 | − | 0.967463i | \(-0.581421\pi\) | ||||
−0.253012 | + | 0.967463i | \(0.581421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.48913 | 0.172106 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.25544 | 0.455430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.7446 | −0.526163 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4891 | 0.949842 | 0.474921 | − | 0.880028i | \(-0.342477\pi\) | ||||
0.474921 | + | 0.880028i | \(0.342477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.74456 | 0.327932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.74456 | −0.230145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.7446 | −1.87498 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.25544 | −0.0606131 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.9783 | 1.29950 | 0.649748 | − | 0.760149i | \(-0.274874\pi\) | ||||
0.649748 | + | 0.760149i | \(0.274874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1168 | 1.73566 | 0.867832 | − | 0.496857i | \(-0.165513\pi\) | ||||
0.867832 | + | 0.496857i | \(0.165513\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.74456 | 0.419270 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.11684 | −0.101262 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7446 | −0.703720 | −0.351860 | − | 0.936053i | \(-0.614451\pi\) | ||||
−0.351860 | + | 0.936053i | \(0.614451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3505 | −1.63204 | −0.816022 | − | 0.578022i | \(-0.803825\pi\) | ||||
−0.816022 | + | 0.578022i | \(0.803825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.37228 | −0.0650524 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1168 | 0.573107 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.97825 | −0.423710 | −0.211855 | − | 0.977301i | \(-0.567950\pi\) | ||||
−0.211855 | + | 0.977301i | \(0.567950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.467376 | −0.0220079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | −0.375873 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.74456 | 0.316190 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.4674 | 1.61232 | 0.806158 | − | 0.591700i | \(-0.201543\pi\) | ||||
0.806158 | + | 0.591700i | \(0.201543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.74456 | 0.221457 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.7228 | −0.918583 | −0.459291 | − | 0.888286i | \(-0.651897\pi\) | ||||
−0.459291 | + | 0.888286i | \(0.651897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.51087 | −0.116690 | −0.0583451 | − | 0.998296i | \(-0.518582\pi\) | ||||
−0.0583451 | + | 0.998296i | \(0.518582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.51087 | −0.301287 | −0.150644 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150644 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.2337 | 1.67312 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.37228 | −0.431852 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.394031 | 0.0181176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.627719 | 0.0288017 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.37228 | 0.0628324 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.86141 | −0.404888 | −0.202444 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202444 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.48913 | 0.0678983 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.3723 | −0.517457 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.4891 | 1.69879 | 0.849397 | − | 0.527754i | \(-0.176966\pi\) | ||||
0.849397 | + | 0.527754i | \(0.176966\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2337 | 1.09589 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.6060 | −1.24584 | −0.622920 | − | 0.782286i | \(-0.714054\pi\) | ||||
−0.622920 | + | 0.782286i | \(0.714054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.4891 | 1.86858 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.627719 | −0.0282139 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.3723 | 0.510117 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.4891 | −1.49918 | −0.749590 | − | 0.661903i | \(-0.769749\pi\) | ||||
−0.749590 | + | 0.661903i | \(0.769749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6277 | −0.564165 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.48913 | −0.244748 | −0.122374 | − | 0.992484i | \(-0.539051\pi\) | ||||
−0.122374 | + | 0.992484i | \(0.539051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.11684 | 0.361195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.2554 | −1.20808 | −0.604038 | − | 0.796956i | \(-0.706442\pi\) | ||||
−0.604038 | + | 0.796956i | \(0.706442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3723 | 1.21088 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.627719 | −0.0277145 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.23369 | −0.186197 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.9783 | 1.62005 | 0.810023 | − | 0.586398i | \(-0.199454\pi\) | ||||
0.810023 | + | 0.586398i | \(0.199454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8614 | 0.562390 | 0.281195 | − | 0.959651i | \(-0.409269\pi\) | ||||
0.281195 | + | 0.959651i | \(0.409269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.37228 | 0.147178 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.74456 | −0.206676 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6277 | −0.505553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.74456 | −0.119104 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.48913 | −0.0645012 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.627719 | −0.0271386 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.74456 | −0.118217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4891 | −0.665930 | −0.332965 | − | 0.942939i | \(-0.608049\pi\) | ||||
−0.332965 | + | 0.942939i | \(0.608049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.8614 | −0.637764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.74456 | 0.203235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.74456 | 0.117349 | 0.0586745 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586745 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.4891 | 0.490344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.48913 | −0.233845 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6060 | −0.663633 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.744563 | 0.0316049 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.8832 | 0.503505 | 0.251753 | − | 0.967792i | \(-0.418993\pi\) | ||||
0.251753 | + | 0.967792i | \(0.418993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.25544 | 0.0530993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97825 | −0.125742 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.97825 | 0.294098 | 0.147049 | − | 0.989129i | \(-0.453022\pi\) | ||||
0.147049 | + | 0.989129i | \(0.453022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.62772 | −0.110549 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.37228 | −0.141623 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.37228 | −0.0575290 | −0.0287645 | − | 0.999586i | \(-0.509157\pi\) | ||||
−0.0287645 | + | 0.999586i | \(0.509157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7446 | 1.11923 | 0.559613 | − | 0.828754i | \(-0.310950\pi\) | ||||
0.559613 | + | 0.828754i | \(0.310950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.37228 | −0.140634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.23369 | −0.0929896 | −0.0464948 | − | 0.998919i | \(-0.514805\pi\) | ||||
−0.0464948 | + | 0.998919i | \(0.514805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.4891 | −0.643706 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.4674 | −1.67887 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.861407 | −0.0356758 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.627719 | 0.0258647 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.4891 | −0.801675 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.9783 | 1.84704 | 0.923518 | − | 0.383556i | \(-0.125301\pi\) | ||||
0.923518 | + | 0.383556i | \(0.125301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0000 | 0.655936 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.6277 | −0.516818 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.1168 | −0.413363 | −0.206682 | − | 0.978408i | \(-0.566266\pi\) | ||||
−0.206682 | + | 0.978408i | \(0.566266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5109 | 0.510329 | 0.255165 | − | 0.966898i | \(-0.417870\pi\) | ||||
0.255165 | + | 0.966898i | \(0.417870\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7446 | −0.437552 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6060 | −0.431194 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.62772 | 0.187833 | 0.0939167 | − | 0.995580i | \(-0.470061\pi\) | ||||
0.0939167 | + | 0.995580i | \(0.470061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.4891 | −1.19496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4891 | −0.545712 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.4891 | 1.43339 | 0.716696 | − | 0.697386i | \(-0.245653\pi\) | ||||
0.716696 | + | 0.697386i | \(0.245653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.744563 | −0.0300237 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.88316 | 0.317364 | 0.158682 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158682 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.2337 | −0.652487 | −0.326244 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326244 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.37228 | 0.135325 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.62772 | 0.185406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.394031 | 0.0157361 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.53262 | 0.140855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.3505 | 1.84519 | 0.922593 | − | 0.385775i | \(-0.126066\pi\) | ||||
0.922593 | + | 0.385775i | \(0.126066\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.627719 | −0.0249496 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4891 | −0.535300 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.74456 | −0.346472 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.37228 | −0.133405 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.0951 | 0.989654 | 0.494827 | − | 0.868992i | \(-0.335231\pi\) | ||||
0.494827 | + | 0.868992i | \(0.335231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.627719 | 0.0247164 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −50.5842 | −1.98867 | −0.994335 | − | 0.106287i | \(-0.966104\pi\) | ||||
−0.994335 | + | 0.106287i | \(0.966104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.72281 | 0.0676263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.37228 | 0.132170 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.9783 | 1.60360 | 0.801801 | − | 0.597591i | \(-0.203875\pi\) | ||||
0.801801 | + | 0.597591i | \(0.203875\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.2337 | 0.634303 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.11684 | −0.316668 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.97825 | −0.193632 | −0.0968158 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968158 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.48913 | −0.368527 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.11684 | −0.0820877 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.4891 | 1.14182 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.25544 | 0.357836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.21194 | −0.278414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.510875 | −0.0196928 | −0.00984639 | − | 0.999952i | \(-0.503134\pi\) | ||||
−0.00984639 | + | 0.999952i | \(0.503134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.6060 | −1.59905 | −0.799524 | − | 0.600635i | \(-0.794915\pi\) | ||||
−0.799524 | + | 0.600635i | \(0.794915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.74456 | −0.258833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.11684 | 0.234398 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.8614 | 0.492128 | 0.246064 | − | 0.969254i | \(-0.420863\pi\) | ||||
0.246064 | + | 0.969254i | \(0.420863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.48913 | −0.133313 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.88316 | −0.148152 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.74456 | −0.104560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1386 | 0.728066 | 0.364033 | − | 0.931386i | \(-0.381399\pi\) | ||||
0.364033 | + | 0.931386i | \(0.381399\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.11684 | 0.0804123 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.7446 | 0.407564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.53262 | −0.133808 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.8614 | 0.562110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.6060 | 1.72251 | 0.861257 | − | 0.508170i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508170i | \(0.169678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.467376 | −0.0176274 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.74456 | −0.254015 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.3723 | −1.02944 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.1168 | 1.50662 | 0.753310 | − | 0.657666i | \(-0.228456\pi\) | ||||
0.753310 | + | 0.657666i | \(0.228456\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.62772 | 0.173553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.37228 | −0.126293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25544 | 0.0469507 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.4891 | −1.10129 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.7446 | −1.44493 | −0.722464 | − | 0.691408i | \(-0.756991\pi\) | ||||
−0.722464 | + | 0.691408i | \(0.756991\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.9783 | −1.00472 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.51087 | −0.167761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.74456 | −0.324765 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3723 | −0.718478 | −0.359239 | − | 0.933246i | \(-0.616964\pi\) | ||||
−0.359239 | + | 0.933246i | \(0.616964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.97825 | 0.110155 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.37228 | −0.161274 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.74456 | 0.248439 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9783 | 0.845269 | 0.422634 | − | 0.906300i | \(-0.361105\pi\) | ||||
0.422634 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.25544 | 0.0461196 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.3723 | 1.29768 | 0.648842 | − | 0.760924i | \(-0.275254\pi\) | ||||
0.648842 | + | 0.760924i | \(0.275254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1168 | −0.443927 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.11684 | 0.0773478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.7446 | 1.41381 | 0.706905 | − | 0.707309i | \(-0.250091\pi\) | ||||
0.706905 | + | 0.707309i | \(0.250091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.11684 | −0.0768366 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.8614 | −1.69872 | −0.849362 | − | 0.527810i | \(-0.823013\pi\) | ||||
−0.849362 | + | 0.527810i | \(0.823013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | −0.579239 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.74456 | −0.171540 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.48913 | 0.198201 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.37228 | −0.337973 | −0.168987 | − | 0.985618i | \(-0.554049\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3723 | −0.481591 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.6060 | 0.777113 | 0.388556 | − | 0.921425i | \(-0.372974\pi\) | ||||
0.388556 | + | 0.921425i | \(0.372974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.51087 | −0.0900771 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.467376 | 0.0167455 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.11684 | 0.0757466 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.74456 | 0.312505 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.37228 | 0.334511 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.88316 | 0.352296 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.9783 | −0.675644 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.86141 | 0.315075 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.9783 | −0.815982 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.37228 | −0.0486698 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.5109 | −0.726532 | −0.363266 | − | 0.931685i | \(-0.618338\pi\) | ||||
−0.363266 | + | 0.931685i | \(0.618338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.37228 | −0.0484872 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.09509 | 0.179802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.3723 | 0.400820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.00000 | 0.0704033 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.60597 | 0.337728 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.6277 | 1.42663 | 0.713316 | − | 0.700842i | \(-0.247192\pi\) | ||||
0.713316 | + | 0.700842i | \(0.247192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8832 | −0.486904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.2337 | −0.848869 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.394031 | −0.0137854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.74456 | 0.235674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2554 | 0.532418 | 0.266209 | − | 0.963915i | \(-0.414229\pi\) | ||||
0.266209 | + | 0.963915i | \(0.414229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.2554 | 0.601487 | 0.300743 | − | 0.953705i | \(-0.402765\pi\) | ||||
0.300743 | + | 0.953705i | \(0.402765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.627719 | 0.0218544 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4891 | 0.608156 | 0.304078 | − | 0.952647i | \(-0.401652\pi\) | ||||
0.304078 | + | 0.952647i | \(0.401652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.0951 | −1.07998 | −0.539989 | − | 0.841672i | \(-0.681571\pi\) | ||||
−0.539989 | + | 0.841672i | \(0.681571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.2554 | −0.529205 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.7446 | −0.718756 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6277 | 0.437000 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8614 | −0.582120 | −0.291060 | − | 0.956705i | \(-0.594008\pi\) | ||||
−0.291060 | + | 0.956705i | \(0.594008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.7446 | −0.576713 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.7663 | 1.22895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.0000 | 0.411839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.51087 | 0.0860717 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.0951 | −1.33859 | −0.669295 | − | 0.742997i | \(-0.733404\pi\) | ||||
−0.669295 | + | 0.742997i | \(0.733404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.627719 | 0.0214675 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.48913 | 0.255824 | 0.127912 | − | 0.991786i | \(-0.459173\pi\) | ||||
0.127912 | + | 0.991786i | \(0.459173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4891 | 0.596721 | 0.298361 | − | 0.954453i | \(-0.403560\pi\) | ||||
0.298361 | + | 0.954453i | \(0.403560\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.51087 | 0.0855704 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.35053 | 0.216175 | 0.108087 | − | 0.994141i | \(-0.465527\pi\) | ||||
0.108087 | + | 0.994141i | \(0.465527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.51087 | −0.187159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.90491 | −0.0985422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4891 | 0.728131 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.37228 | −0.114004 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.9783 | −1.51881 | −0.759404 | − | 0.650620i | \(-0.774509\pi\) | ||||
−0.759404 | + | 0.650620i | \(0.774509\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.48913 | 0.252602 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.02175 | −0.101805 | −0.0509027 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509027 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.8614 | −1.50971 | −0.754853 | − | 0.655894i | \(-0.772292\pi\) | ||||
−0.754853 | + | 0.655894i | \(0.772292\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.74456 | 0.0922575 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.7446 | 1.03230 | 0.516151 | − | 0.856498i | \(-0.327364\pi\) | ||||
0.516151 | + | 0.856498i | \(0.327364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.4891 | 1.52566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.627719 | −0.0210294 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.23369 | 0.141675 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.74456 | −0.225194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.74456 | −0.291647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.51087 | −0.216909 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.11684 | −0.0704442 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.8614 | 0.494010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4891 | 0.580717 | 0.290358 | − | 0.956918i | \(-0.406225\pi\) | ||||
0.290358 | + | 0.956918i | \(0.406225\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.11684 | 0.269219 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.51087 | 0.0831890 | 0.0415945 | − | 0.999135i | \(-0.486756\pi\) | ||||
0.0415945 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.53262 | −0.249293 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.4891 | −0.379819 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −54.7446 | −1.80782 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.2337 | 0.403552 | 0.201776 | − | 0.979432i | \(-0.435329\pi\) | ||||
0.201776 | + | 0.979432i | \(0.435329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.9783 | 1.02077 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.74456 | 0.222000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.744563 | −0.0244811 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.1168 | −0.528776 | −0.264388 | − | 0.964416i | \(-0.585170\pi\) | ||||
−0.264388 | + | 0.964416i | \(0.585170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.74456 | 0.0899494 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.97825 | 0.0973992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.2554 | −1.02107 | −0.510535 | − | 0.859857i | \(-0.670553\pi\) | ||||
−0.510535 | + | 0.859857i | \(0.670553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7228 | −0.642945 | −0.321473 | − | 0.946919i | \(-0.604178\pi\) | ||||
−0.321473 | + | 0.946919i | \(0.604178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.51087 | −0.0817653 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.37228 | 0.109700 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.74456 | 0.0891863 | 0.0445932 | − | 0.999005i | \(-0.485801\pi\) | ||||
0.0445932 | + | 0.999005i | \(0.485801\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.2337 | 0.526968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.7446 | 0.802397 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.7228 | 0.379739 | 0.189870 | − | 0.981809i | \(-0.439193\pi\) | ||||
0.189870 | + | 0.981809i | \(0.439193\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.0000 | −0.517748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.48913 | −0.177438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.7663 | 0.379954 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.627719 | −0.0202280 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4891 | 0.498613 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.97825 | 0.0956752 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7011 | 1.56289 | 0.781446 | − | 0.623973i | \(-0.214483\pi\) | ||||
0.781446 | + | 0.623973i | \(0.214483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.2337 | −1.16160 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | 0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.0000 | −1.47167 | −0.735835 | − | 0.677161i | \(-0.763210\pi\) | ||||
−0.735835 | + | 0.677161i | \(0.763210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.861407 | 0.0275307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.74456 | 0.151482 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.97825 | 0.0949914 | 0.0474957 | − | 0.998871i | \(-0.484876\pi\) | ||||
0.0474957 | + | 0.998871i | \(0.484876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.4891 | 0.620975 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.7446 | 0.723967 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11684 | 0.0673117 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.6060 | 1.51225 | 0.756127 | − | 0.654425i | \(-0.227089\pi\) | ||||
0.756127 | + | 0.654425i | \(0.227089\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.48913 | −0.0472560 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.6277 | 0.400326 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.00000 | 0.190022 | 0.0950110 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950110 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.744563 | 0.0235569 |
(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 | 7440.2.a.bg.1.1 | 2 | ||
4.3 | odd | 2 | 930.2.a.r.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 2790.2.a.bd.1.2 | 2 | |||
20.3 | even | 4 | 4650.2.d.bh.3349.1 | 4 | |||
20.7 | even | 4 | 4650.2.d.bh.3349.4 | 4 | |||
20.19 | odd | 2 | 4650.2.a.by.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.r.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
2790.2.a.bd.1.2 | 2 | 12.11 | even | 2 | |||
4650.2.a.by.1.1 | 2 | 20.19 | odd | 2 | |||
4650.2.d.bh.3349.1 | 4 | 20.3 | even | 4 | |||
4650.2.d.bh.3349.4 | 4 | 20.7 | even | 4 | |||
7440.2.a.bg.1.1 | 2 | 1.1 | even | 1 | trivial |