Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 847) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.879640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.120360 | −0.0851073 | −0.0425536 | − | 0.999094i | \(-0.513549\pi\) | ||||
−0.0425536 | + | 0.999094i | \(0.513549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.98551 | −0.992757 | ||||||||
\(5\) | 2.80853 | 1.25601 | 0.628005 | − | 0.778209i | \(-0.283872\pi\) | ||||
0.628005 | + | 0.778209i | \(0.283872\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.479696 | 0.169598 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.338034 | −0.106896 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.07967 | 0.299448 | 0.149724 | − | 0.988728i | \(-0.452162\pi\) | ||||
0.149724 | + | 0.988728i | \(0.452162\pi\) | |||||||
\(14\) | −0.120360 | −0.0321675 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.91329 | 0.978323 | ||||||||
\(17\) | −6.95828 | −1.68763 | −0.843816 | − | 0.536633i | \(-0.819696\pi\) | ||||
−0.843816 | + | 0.536633i | \(0.819696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.54411 | 1.73074 | 0.865369 | − | 0.501135i | \(-0.167084\pi\) | ||||
0.865369 | + | 0.501135i | \(0.167084\pi\) | |||||||
\(20\) | −5.57636 | −1.24691 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82552 | −1.00619 | −0.503095 | − | 0.864231i | \(-0.667806\pi\) | ||||
−0.503095 | + | 0.864231i | \(0.667806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.88781 | 0.577563 | ||||||||
\(26\) | −0.129949 | −0.0254852 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.98551 | −0.375227 | ||||||||
\(29\) | −1.22726 | −0.227897 | −0.113949 | − | 0.993487i | \(-0.536350\pi\) | ||||
−0.113949 | + | 0.993487i | \(0.536350\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.07409 | −1.45015 | −0.725074 | − | 0.688671i | \(-0.758195\pi\) | ||||
−0.725074 | + | 0.688671i | \(0.758195\pi\) | |||||||
\(32\) | −1.43040 | −0.252861 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.837498 | 0.143630 | ||||||||
\(35\) | 2.80853 | 0.474727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53525 | 0.252394 | 0.126197 | − | 0.992005i | \(-0.459723\pi\) | ||||
0.126197 | + | 0.992005i | \(0.459723\pi\) | |||||||
\(38\) | −0.908009 | −0.147298 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.34724 | 0.213017 | ||||||||
\(41\) | −9.29986 | −1.45239 | −0.726197 | − | 0.687487i | \(-0.758714\pi\) | ||||
−0.726197 | + | 0.687487i | \(0.758714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.23402 | −0.798181 | −0.399091 | − | 0.916912i | \(-0.630674\pi\) | ||||
−0.399091 | + | 0.916912i | \(0.630674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.580799 | 0.0856341 | ||||||||
\(47\) | 1.89387 | 0.276249 | 0.138124 | − | 0.990415i | \(-0.455893\pi\) | ||||
0.138124 | + | 0.990415i | \(0.455893\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.347577 | −0.0491548 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.14371 | −0.297279 | ||||||||
\(53\) | 3.82552 | 0.525476 | 0.262738 | − | 0.964867i | \(-0.415375\pi\) | ||||
0.262738 | + | 0.964867i | \(0.415375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.479696 | 0.0641021 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.147713 | 0.0193957 | ||||||||
\(59\) | 6.66349 | 0.867513 | 0.433756 | − | 0.901030i | \(-0.357188\pi\) | ||||
0.433756 | + | 0.901030i | \(0.357188\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.79952 | −1.25470 | −0.627350 | − | 0.778737i | \(-0.715861\pi\) | ||||
−0.627350 | + | 0.778737i | \(0.715861\pi\) | |||||||
\(62\) | 0.971796 | 0.123418 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.65442 | −0.956802 | ||||||||
\(65\) | 3.03229 | 0.376110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.06100 | −0.251792 | −0.125896 | − | 0.992043i | \(-0.540181\pi\) | ||||
−0.125896 | + | 0.992043i | \(0.540181\pi\) | |||||||
\(68\) | 13.8158 | 1.67541 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.338034 | −0.0404028 | ||||||||
\(71\) | −12.5212 | −1.48599 | −0.742996 | − | 0.669296i | \(-0.766596\pi\) | ||||
−0.742996 | + | 0.669296i | \(0.766596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.56708 | 0.300454 | 0.150227 | − | 0.988652i | \(-0.452000\pi\) | ||||
0.150227 | + | 0.988652i | \(0.452000\pi\) | |||||||
\(74\) | −0.184783 | −0.0214806 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9789 | −1.71820 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3283 | −1.72457 | −0.862287 | − | 0.506420i | \(-0.830969\pi\) | ||||
−0.862287 | + | 0.506420i | \(0.830969\pi\) | |||||||
\(80\) | 10.9906 | 1.22878 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.11933 | 0.123609 | ||||||||
\(83\) | −2.04602 | −0.224580 | −0.112290 | − | 0.993675i | \(-0.535819\pi\) | ||||
−0.112290 | + | 0.993675i | \(0.535819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.5425 | −2.11968 | ||||||||
\(86\) | 0.629967 | 0.0679310 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.76119 | −0.504685 | −0.252342 | − | 0.967638i | \(-0.581201\pi\) | ||||
−0.252342 | + | 0.967638i | \(0.581201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07967 | 0.113181 | ||||||||
\(92\) | 9.58114 | 0.998902 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.227945 | −0.0235108 | ||||||||
\(95\) | 21.1878 | 2.17383 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.11512 | 0.925500 | 0.462750 | − | 0.886489i | \(-0.346863\pi\) | ||||
0.462750 | + | 0.886489i | \(0.346863\pi\) | |||||||
\(98\) | −0.120360 | −0.0121582 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.73379 | −0.573379 | ||||||||
\(101\) | 4.74385 | 0.472031 | 0.236015 | − | 0.971749i | \(-0.424158\pi\) | ||||
0.236015 | + | 0.971749i | \(0.424158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.350901 | 0.0345753 | 0.0172876 | − | 0.999851i | \(-0.494497\pi\) | ||||
0.0172876 | + | 0.999851i | \(0.494497\pi\) | |||||||
\(104\) | 0.517915 | 0.0507858 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.460439 | −0.0447218 | ||||||||
\(107\) | −2.54774 | −0.246299 | −0.123149 | − | 0.992388i | \(-0.539299\pi\) | ||||
−0.123149 | + | 0.992388i | \(0.539299\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.81522 | −0.365432 | −0.182716 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182716 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.91329 | 0.369771 | ||||||||
\(113\) | −2.31468 | −0.217747 | −0.108873 | − | 0.994056i | \(-0.534724\pi\) | ||||
−0.108873 | + | 0.994056i | \(0.534724\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5526 | −1.26379 | ||||||||
\(116\) | 2.43675 | 0.226246 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.802017 | −0.0738316 | ||||||||
\(119\) | −6.95828 | −0.637865 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.17947 | 0.106784 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.0312 | 1.43964 | ||||||||
\(125\) | −5.93213 | −0.530586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.84644 | 0.873730 | 0.436865 | − | 0.899527i | \(-0.356089\pi\) | ||||
0.436865 | + | 0.899527i | \(0.356089\pi\) | |||||||
\(128\) | 3.78208 | 0.334291 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.364966 | −0.0320097 | ||||||||
\(131\) | −16.3782 | −1.43097 | −0.715484 | − | 0.698629i | \(-0.753794\pi\) | ||||
−0.715484 | + | 0.698629i | \(0.753794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.54411 | 0.654158 | ||||||||
\(134\) | 0.248062 | 0.0214293 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.33786 | −0.286219 | ||||||||
\(137\) | 14.2142 | 1.21440 | 0.607199 | − | 0.794550i | \(-0.292293\pi\) | ||||
0.607199 | + | 0.794550i | \(0.292293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.17942 | −0.778588 | −0.389294 | − | 0.921114i | \(-0.627281\pi\) | ||||
−0.389294 | + | 0.921114i | \(0.627281\pi\) | |||||||
\(140\) | −5.57636 | −0.471289 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.50705 | 0.126469 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.44680 | −0.286241 | ||||||||
\(146\) | −0.308974 | −0.0255708 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.04827 | −0.250566 | ||||||||
\(149\) | −11.6200 | −0.951947 | −0.475973 | − | 0.879460i | \(-0.657904\pi\) | ||||
−0.475973 | + | 0.879460i | \(0.657904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9150 | 1.45790 | 0.728952 | − | 0.684565i | \(-0.240008\pi\) | ||||
0.728952 | + | 0.684565i | \(0.240008\pi\) | |||||||
\(152\) | 3.61888 | 0.293530 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.6763 | −1.82140 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.42805 | 0.592823 | 0.296412 | − | 0.955060i | \(-0.404210\pi\) | ||||
0.296412 | + | 0.955060i | \(0.404210\pi\) | |||||||
\(158\) | 1.84492 | 0.146774 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.01730 | −0.317596 | ||||||||
\(161\) | −4.82552 | −0.380304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.85296 | 0.615091 | 0.307546 | − | 0.951533i | \(-0.400492\pi\) | ||||
0.307546 | + | 0.951533i | \(0.400492\pi\) | |||||||
\(164\) | 18.4650 | 1.44187 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.246259 | 0.0191134 | ||||||||
\(167\) | 5.40259 | 0.418065 | 0.209032 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209032 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8343 | −0.910331 | ||||||||
\(170\) | 2.35214 | 0.180401 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.3922 | 0.792400 | ||||||||
\(173\) | 19.7211 | 1.49937 | 0.749685 | − | 0.661795i | \(-0.230205\pi\) | ||||
0.749685 | + | 0.661795i | \(0.230205\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.88781 | 0.218298 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.573056 | 0.0429524 | ||||||||
\(179\) | 23.3292 | 1.74370 | 0.871851 | − | 0.489770i | \(-0.162919\pi\) | ||||
0.871851 | + | 0.489770i | \(0.162919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.08500 | 0.229306 | 0.114653 | − | 0.993406i | \(-0.463424\pi\) | ||||
0.114653 | + | 0.993406i | \(0.463424\pi\) | |||||||
\(182\) | −0.129949 | −0.00963250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.31478 | −0.170648 | ||||||||
\(185\) | 4.31180 | 0.317010 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.76030 | −0.274248 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.55017 | −0.185008 | ||||||||
\(191\) | −12.5715 | −0.909640 | −0.454820 | − | 0.890583i | \(-0.650296\pi\) | ||||
−0.454820 | + | 0.890583i | \(0.650296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6685 | −1.48775 | −0.743877 | − | 0.668317i | \(-0.767015\pi\) | ||||
−0.743877 | + | 0.668317i | \(0.767015\pi\) | |||||||
\(194\) | −1.09709 | −0.0787668 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.98551 | −0.141822 | ||||||||
\(197\) | −6.27954 | −0.447399 | −0.223699 | − | 0.974658i | \(-0.571813\pi\) | ||||
−0.223699 | + | 0.974658i | \(0.571813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.86896 | −0.486927 | −0.243464 | − | 0.969910i | \(-0.578284\pi\) | ||||
−0.243464 | + | 0.969910i | \(0.578284\pi\) | |||||||
\(200\) | 1.38527 | 0.0979536 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.570969 | −0.0401733 | ||||||||
\(203\) | −1.22726 | −0.0861370 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.1189 | −1.82422 | ||||||||
\(206\) | −0.0422344 | −0.00294261 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.22508 | 0.292957 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2586 | 0.706232 | 0.353116 | − | 0.935580i | \(-0.385122\pi\) | ||||
0.353116 | + | 0.935580i | \(0.385122\pi\) | |||||||
\(212\) | −7.59562 | −0.521669 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.306645 | 0.0209618 | ||||||||
\(215\) | −14.6999 | −1.00252 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.07409 | −0.548105 | ||||||||
\(218\) | 0.459199 | 0.0311009 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.51268 | −0.505358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5221 | −0.905506 | −0.452753 | − | 0.891636i | \(-0.649558\pi\) | ||||
−0.452753 | + | 0.891636i | \(0.649558\pi\) | |||||||
\(224\) | −1.43040 | −0.0955723 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.278595 | 0.0185319 | ||||||||
\(227\) | −13.5764 | −0.901100 | −0.450550 | − | 0.892751i | \(-0.648772\pi\) | ||||
−0.450550 | + | 0.892751i | \(0.648772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.45296 | −0.0960141 | −0.0480070 | − | 0.998847i | \(-0.515287\pi\) | ||||
−0.0480070 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(230\) | 1.63119 | 0.107557 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.588713 | −0.0386509 | ||||||||
\(233\) | −8.20387 | −0.537453 | −0.268727 | − | 0.963216i | \(-0.586603\pi\) | ||||
−0.268727 | + | 0.963216i | \(0.586603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.31897 | 0.346971 | ||||||||
\(236\) | −13.2305 | −0.861229 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.837498 | 0.0542870 | ||||||||
\(239\) | −10.3835 | −0.671655 | −0.335827 | − | 0.941924i | \(-0.609016\pi\) | ||||
−0.335827 | + | 0.941924i | \(0.609016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.20445 | −0.528495 | −0.264248 | − | 0.964455i | \(-0.585124\pi\) | ||||
−0.264248 | + | 0.964455i | \(0.585124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 19.4571 | 1.24561 | ||||||||
\(245\) | 2.80853 | 0.179430 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.14519 | 0.518266 | ||||||||
\(248\) | −3.87311 | −0.245943 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.713990 | 0.0451567 | ||||||||
\(251\) | 16.4452 | 1.03801 | 0.519005 | − | 0.854771i | \(-0.326302\pi\) | ||||
0.519005 | + | 0.854771i | \(0.326302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.18512 | −0.0743608 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.8536 | 0.928352 | ||||||||
\(257\) | 12.0440 | 0.751282 | 0.375641 | − | 0.926765i | \(-0.377423\pi\) | ||||
0.375641 | + | 0.926765i | \(0.377423\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.53525 | 0.0953960 | ||||||||
\(260\) | −6.02066 | −0.373385 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.97127 | 0.121786 | ||||||||
\(263\) | −1.87602 | −0.115681 | −0.0578403 | − | 0.998326i | \(-0.518421\pi\) | ||||
−0.0578403 | + | 0.998326i | \(0.518421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7441 | 0.660003 | ||||||||
\(266\) | −0.908009 | −0.0556736 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.09215 | 0.249968 | ||||||||
\(269\) | 14.0290 | 0.855362 | 0.427681 | − | 0.903930i | \(-0.359331\pi\) | ||||
0.427681 | + | 0.903930i | \(0.359331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35328 | 0.0822056 | 0.0411028 | − | 0.999155i | \(-0.486913\pi\) | ||||
0.0411028 | + | 0.999155i | \(0.486913\pi\) | |||||||
\(272\) | −27.2298 | −1.65105 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.71081 | −0.103354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3835 | −0.804138 | −0.402069 | − | 0.915609i | \(-0.631709\pi\) | ||||
−0.402069 | + | 0.915609i | \(0.631709\pi\) | |||||||
\(278\) | 1.10483 | 0.0662635 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.34724 | 0.0805129 | ||||||||
\(281\) | −2.31887 | −0.138332 | −0.0691661 | − | 0.997605i | \(-0.522034\pi\) | ||||
−0.0691661 | + | 0.997605i | \(0.522034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.2679 | −1.32369 | −0.661845 | − | 0.749641i | \(-0.730226\pi\) | ||||
−0.661845 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(284\) | 24.8610 | 1.47523 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.29986 | −0.548953 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.4177 | 1.84810 | ||||||||
\(290\) | 0.414857 | 0.0243612 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.09698 | −0.298278 | ||||||||
\(293\) | 2.43981 | 0.142535 | 0.0712675 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712675 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.7146 | 1.08961 | ||||||||
\(296\) | 0.736455 | 0.0428056 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.39858 | 0.0810176 | ||||||||
\(299\) | −5.20999 | −0.301301 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.23402 | −0.301684 | ||||||||
\(302\) | −2.15625 | −0.124078 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 29.5223 | 1.69322 | ||||||||
\(305\) | −27.5222 | −1.57592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.89055 | −0.507410 | −0.253705 | − | 0.967282i | \(-0.581649\pi\) | ||||
−0.253705 | + | 0.967282i | \(0.581649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.72931 | 0.155015 | ||||||||
\(311\) | 11.8347 | 0.671085 | 0.335543 | − | 0.942025i | \(-0.391080\pi\) | ||||
0.335543 | + | 0.942025i | \(0.391080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.5406 | −1.66973 | −0.834865 | − | 0.550454i | \(-0.814455\pi\) | ||||
−0.834865 | + | 0.550454i | \(0.814455\pi\) | |||||||
\(314\) | −0.894039 | −0.0504536 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.4346 | 1.71208 | ||||||||
\(317\) | 25.1545 | 1.41282 | 0.706409 | − | 0.707804i | \(-0.250314\pi\) | ||||
0.706409 | + | 0.707804i | \(0.250314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −21.4976 | −1.20175 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.580799 | 0.0323667 | ||||||||
\(323\) | −52.4941 | −2.92085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.11790 | 0.172950 | ||||||||
\(326\) | −0.945181 | −0.0523488 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.46110 | −0.246323 | ||||||||
\(329\) | 1.89387 | 0.104412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.46333 | −0.520152 | −0.260076 | − | 0.965588i | \(-0.583748\pi\) | ||||
−0.260076 | + | 0.965588i | \(0.583748\pi\) | |||||||
\(332\) | 4.06241 | 0.222954 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.650255 | −0.0355804 | ||||||||
\(335\) | −5.78838 | −0.316253 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2248 | −0.938297 | −0.469148 | − | 0.883119i | \(-0.655439\pi\) | ||||
−0.469148 | + | 0.883119i | \(0.655439\pi\) | |||||||
\(338\) | 1.42438 | 0.0774758 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 38.8019 | 2.10433 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.51074 | −0.135370 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.37363 | −0.127607 | ||||||||
\(347\) | 8.73485 | 0.468911 | 0.234456 | − | 0.972127i | \(-0.424669\pi\) | ||||
0.234456 | + | 0.972127i | \(0.424669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.9851 | −1.60506 | −0.802532 | − | 0.596609i | \(-0.796514\pi\) | ||||
−0.802532 | + | 0.596609i | \(0.796514\pi\) | |||||||
\(350\) | −0.347577 | −0.0185788 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.31999 | −0.389604 | −0.194802 | − | 0.980843i | \(-0.562406\pi\) | ||||
−0.194802 | + | 0.980843i | \(0.562406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.1661 | −1.86642 | ||||||||
\(356\) | 9.45340 | 0.501029 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.80789 | −0.148402 | ||||||||
\(359\) | −4.96996 | −0.262304 | −0.131152 | − | 0.991362i | \(-0.541868\pi\) | ||||
−0.131152 | + | 0.991362i | \(0.541868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.9137 | 1.99546 | ||||||||
\(362\) | −0.371311 | −0.0195156 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.14371 | −0.112361 | ||||||||
\(365\) | 7.20971 | 0.377374 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2042 | −0.741455 | −0.370727 | − | 0.928742i | \(-0.620892\pi\) | ||||
−0.370727 | + | 0.928742i | \(0.620892\pi\) | |||||||
\(368\) | −18.8837 | −0.984379 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.518967 | −0.0269798 | ||||||||
\(371\) | 3.82552 | 0.198611 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.97781 | 0.464853 | 0.232427 | − | 0.972614i | \(-0.425333\pi\) | ||||
0.232427 | + | 0.972614i | \(0.425333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.908480 | 0.0468513 | ||||||||
\(377\) | −1.32504 | −0.0682433 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7896 | 0.554223 | 0.277112 | − | 0.960838i | \(-0.410623\pi\) | ||||
0.277112 | + | 0.960838i | \(0.410623\pi\) | |||||||
\(380\) | −42.0687 | −2.15808 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.51310 | 0.0774170 | ||||||||
\(383\) | 23.5100 | 1.20130 | 0.600652 | − | 0.799511i | \(-0.294908\pi\) | ||||
0.600652 | + | 0.799511i | \(0.294908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.48766 | 0.126619 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.0982 | −0.918797 | ||||||||
\(389\) | 11.8745 | 0.602063 | 0.301032 | − | 0.953614i | \(-0.402669\pi\) | ||||
0.301032 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.5773 | 1.69808 | ||||||||
\(392\) | 0.479696 | 0.0242283 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.755804 | 0.0380769 | ||||||||
\(395\) | −43.0501 | −2.16608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7264 | −1.19079 | −0.595397 | − | 0.803431i | \(-0.703005\pi\) | ||||
−0.595397 | + | 0.803431i | \(0.703005\pi\) | |||||||
\(398\) | 0.826747 | 0.0414411 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.3009 | 0.565043 | ||||||||
\(401\) | 3.80121 | 0.189823 | 0.0949117 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949117 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.71738 | −0.434244 | ||||||||
\(404\) | −9.41898 | −0.468612 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.147713 | 0.00733089 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.98291 | −0.295836 | −0.147918 | − | 0.989000i | \(-0.547257\pi\) | ||||
−0.147918 | + | 0.989000i | \(0.547257\pi\) | |||||||
\(410\) | 3.14367 | 0.155255 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.696718 | −0.0343248 | ||||||||
\(413\) | 6.66349 | 0.327889 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.74631 | −0.282075 | ||||||||
\(416\) | −1.54436 | −0.0757185 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.16889 | 0.203664 | 0.101832 | − | 0.994802i | \(-0.467530\pi\) | ||||
0.101832 | + | 0.994802i | \(0.467530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.4555 | 1.14315 | 0.571575 | − | 0.820550i | \(-0.306333\pi\) | ||||
0.571575 | + | 0.820550i | \(0.306333\pi\) | |||||||
\(422\) | −1.23473 | −0.0601055 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.83509 | 0.0891197 | ||||||||
\(425\) | −20.0942 | −0.974713 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.79952 | −0.474232 | ||||||||
\(428\) | 5.05856 | 0.244515 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.76928 | 0.0853221 | ||||||||
\(431\) | −37.2730 | −1.79538 | −0.897689 | − | 0.440630i | \(-0.854755\pi\) | ||||
−0.897689 | + | 0.440630i | \(0.854755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7863 | −1.09504 | −0.547520 | − | 0.836793i | \(-0.684428\pi\) | ||||
−0.547520 | + | 0.836793i | \(0.684428\pi\) | |||||||
\(434\) | 0.971796 | 0.0466477 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.57517 | 0.362785 | ||||||||
\(437\) | −36.4043 | −1.74145 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.42974 | −0.0682379 | −0.0341189 | − | 0.999418i | \(-0.510863\pi\) | ||||
−0.0341189 | + | 0.999418i | \(0.510863\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.904225 | 0.0430096 | ||||||||
\(443\) | 26.4301 | 1.25573 | 0.627866 | − | 0.778321i | \(-0.283928\pi\) | ||||
0.627866 | + | 0.778321i | \(0.283928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.3719 | −0.633890 | ||||||||
\(446\) | 1.62752 | 0.0770651 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.65442 | −0.361637 | ||||||||
\(449\) | −14.0870 | −0.664806 | −0.332403 | − | 0.943137i | \(-0.607859\pi\) | ||||
−0.332403 | + | 0.943137i | \(0.607859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.59583 | 0.216170 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.63406 | 0.0766902 | ||||||||
\(455\) | 3.03229 | 0.142156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4829 | 1.37915 | 0.689575 | − | 0.724214i | \(-0.257797\pi\) | ||||
0.689575 | + | 0.724214i | \(0.257797\pi\) | |||||||
\(458\) | 0.174878 | 0.00817150 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26.9089 | 1.25463 | ||||||||
\(461\) | −31.7282 | −1.47773 | −0.738866 | − | 0.673853i | \(-0.764638\pi\) | ||||
−0.738866 | + | 0.673853i | \(0.764638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7839 | −0.594117 | −0.297059 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(464\) | −4.80264 | −0.222957 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.987417 | 0.0457412 | ||||||||
\(467\) | −29.5768 | −1.36865 | −0.684325 | − | 0.729177i | \(-0.739903\pi\) | ||||
−0.684325 | + | 0.729177i | \(0.739903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.06100 | −0.0951683 | ||||||||
\(470\) | −0.640191 | −0.0295298 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.19645 | 0.147129 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.7860 | 0.999610 | ||||||||
\(476\) | 13.8158 | 0.633245 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.24976 | 0.0571627 | ||||||||
\(479\) | 28.5574 | 1.30482 | 0.652411 | − | 0.757866i | \(-0.273758\pi\) | ||||
0.652411 | + | 0.757866i | \(0.273758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.65757 | 0.0755788 | ||||||||
\(482\) | 0.987487 | 0.0449788 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.6000 | 1.16244 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.05828 | 0.0479552 | 0.0239776 | − | 0.999712i | \(-0.492367\pi\) | ||||
0.0239776 | + | 0.999712i | \(0.492367\pi\) | |||||||
\(488\) | −4.70079 | −0.212795 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.338034 | −0.0152708 | ||||||||
\(491\) | −18.4489 | −0.832586 | −0.416293 | − | 0.909230i | \(-0.636671\pi\) | ||||
−0.416293 | + | 0.909230i | \(0.636671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.53965 | 0.384606 | ||||||||
\(494\) | −0.980354 | −0.0441082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.5962 | −1.41871 | ||||||||
\(497\) | −12.5212 | −0.561652 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.7293 | 1.42040 | 0.710199 | − | 0.704001i | \(-0.248605\pi\) | ||||
0.710199 | + | 0.704001i | \(0.248605\pi\) | |||||||
\(500\) | 11.7783 | 0.526742 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.97934 | −0.0883423 | ||||||||
\(503\) | 29.0283 | 1.29431 | 0.647154 | − | 0.762359i | \(-0.275959\pi\) | ||||
0.647154 | + | 0.762359i | \(0.275959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3232 | 0.592876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.5502 | −0.867401 | ||||||||
\(509\) | −2.88831 | −0.128022 | −0.0640110 | − | 0.997949i | \(-0.520389\pi\) | ||||
−0.0640110 | + | 0.997949i | \(0.520389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.56708 | 0.113561 | ||||||||
\(512\) | −9.35193 | −0.413301 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.44961 | −0.0639396 | ||||||||
\(515\) | 0.985513 | 0.0434269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.184783 | −0.00811890 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.45458 | 0.0637875 | ||||||||
\(521\) | −31.6708 | −1.38752 | −0.693762 | − | 0.720204i | \(-0.744048\pi\) | ||||
−0.693762 | + | 0.720204i | \(0.744048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.0380 | −0.701295 | −0.350647 | − | 0.936508i | \(-0.614038\pi\) | ||||
−0.350647 | + | 0.936508i | \(0.614038\pi\) | |||||||
\(524\) | 32.5191 | 1.42060 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.225798 | 0.00984526 | ||||||||
\(527\) | 56.1818 | 2.44732 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.285644 | 0.0124193 | ||||||||
\(530\) | −1.29316 | −0.0561711 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.9789 | −0.649419 | ||||||||
\(533\) | −10.0408 | −0.434916 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.15538 | −0.309354 | ||||||||
\(536\) | −0.988655 | −0.0427034 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.68853 | −0.0727976 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5946 | 0.584480 | 0.292240 | − | 0.956345i | \(-0.405599\pi\) | ||||
0.292240 | + | 0.956345i | \(0.405599\pi\) | |||||||
\(542\) | −0.162880 | −0.00699630 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.95310 | 0.426735 | ||||||||
\(545\) | −10.7151 | −0.458986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.82486 | −0.377324 | −0.188662 | − | 0.982042i | \(-0.560415\pi\) | ||||
−0.188662 | + | 0.982042i | \(0.560415\pi\) | |||||||
\(548\) | −28.2224 | −1.20560 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.25862 | −0.394430 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.3283 | −0.651828 | ||||||||
\(554\) | 1.61084 | 0.0684380 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.2259 | 0.772949 | ||||||||
\(557\) | −33.9920 | −1.44029 | −0.720145 | − | 0.693824i | \(-0.755925\pi\) | ||||
−0.720145 | + | 0.693824i | \(0.755925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65104 | −0.239014 | ||||||||
\(560\) | 10.9906 | 0.464437 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.279099 | 0.0117731 | ||||||||
\(563\) | 20.2256 | 0.852406 | 0.426203 | − | 0.904628i | \(-0.359851\pi\) | ||||
0.426203 | + | 0.904628i | \(0.359851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.50084 | −0.273492 | ||||||||
\(566\) | 2.68016 | 0.112656 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00637 | −0.252022 | ||||||||
\(569\) | −28.9330 | −1.21293 | −0.606467 | − | 0.795109i | \(-0.707414\pi\) | ||||
−0.606467 | + | 0.795109i | \(0.707414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.51312 | −0.314414 | −0.157207 | − | 0.987566i | \(-0.550249\pi\) | ||||
−0.157207 | + | 0.987566i | \(0.550249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.11933 | 0.0467199 | ||||||||
\(575\) | −13.9352 | −0.581138 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.3748 | 1.43104 | 0.715521 | − | 0.698592i | \(-0.246190\pi\) | ||||
0.715521 | + | 0.698592i | \(0.246190\pi\) | |||||||
\(578\) | −3.78143 | −0.157287 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.84367 | 0.284168 | ||||||||
\(581\) | −2.04602 | −0.0848834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.23142 | 0.0509565 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.293655 | −0.0121308 | ||||||||
\(587\) | −42.0392 | −1.73514 | −0.867571 | − | 0.497313i | \(-0.834320\pi\) | ||||
−0.867571 | + | 0.497313i | \(0.834320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.9118 | −2.50983 | ||||||||
\(590\) | −2.25249 | −0.0927333 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.00789 | 0.246923 | ||||||||
\(593\) | −29.2867 | −1.20266 | −0.601331 | − | 0.799000i | \(-0.705363\pi\) | ||||
−0.601331 | + | 0.799000i | \(0.705363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5425 | −0.801165 | ||||||||
\(596\) | 23.0716 | 0.945051 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.627074 | 0.0256430 | ||||||||
\(599\) | 15.1577 | 0.619327 | 0.309663 | − | 0.950846i | \(-0.399784\pi\) | ||||
0.309663 | + | 0.950846i | \(0.399784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8735 | 1.30015 | 0.650073 | − | 0.759872i | \(-0.274738\pi\) | ||||
0.650073 | + | 0.759872i | \(0.274738\pi\) | |||||||
\(602\) | 0.629967 | 0.0256755 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −35.5705 | −1.44734 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.1463 | −0.817714 | −0.408857 | − | 0.912598i | \(-0.634073\pi\) | ||||
−0.408857 | + | 0.912598i | \(0.634073\pi\) | |||||||
\(608\) | −10.7911 | −0.437635 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.31257 | 0.134122 | ||||||||
\(611\) | 2.04476 | 0.0827220 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.89132 | −0.157169 | −0.0785844 | − | 0.996907i | \(-0.525040\pi\) | ||||
−0.0785844 | + | 0.996907i | \(0.525040\pi\) | |||||||
\(614\) | 1.07007 | 0.0431843 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.6122 | −1.15189 | −0.575943 | − | 0.817490i | \(-0.695365\pi\) | ||||
−0.575943 | + | 0.817490i | \(0.695365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.1546 | −1.05124 | −0.525621 | − | 0.850719i | \(-0.676167\pi\) | ||||
−0.525621 | + | 0.850719i | \(0.676167\pi\) | |||||||
\(620\) | 45.0240 | 1.80821 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.42443 | −0.0571143 | ||||||||
\(623\) | −4.76119 | −0.190753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0996 | −1.24398 | ||||||||
\(626\) | 3.55550 | 0.142106 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.7485 | −0.588529 | ||||||||
\(629\) | −10.6827 | −0.425948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.68272 | −0.226225 | −0.113113 | − | 0.993582i | \(-0.536082\pi\) | ||||
−0.113113 | + | 0.993582i | \(0.536082\pi\) | |||||||
\(632\) | −7.35295 | −0.292485 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.02759 | −0.120241 | ||||||||
\(635\) | 27.6540 | 1.09741 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.07967 | 0.0427782 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.6221 | 0.419874 | ||||||||
\(641\) | 20.7292 | 0.818756 | 0.409378 | − | 0.912365i | \(-0.365746\pi\) | ||||
0.409378 | + | 0.912365i | \(0.365746\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2756 | 0.839029 | 0.419515 | − | 0.907749i | \(-0.362200\pi\) | ||||
0.419515 | + | 0.907749i | \(0.362200\pi\) | |||||||
\(644\) | 9.58114 | 0.377550 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.31818 | 0.248586 | ||||||||
\(647\) | 17.2718 | 0.679023 | 0.339512 | − | 0.940602i | \(-0.389738\pi\) | ||||
0.339512 | + | 0.940602i | \(0.389738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.375270 | −0.0147193 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.5922 | −0.610636 | ||||||||
\(653\) | −41.0788 | −1.60754 | −0.803768 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803768 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.9985 | −1.79731 | ||||||||
\(656\) | −36.3930 | −1.42091 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.227945 | −0.00888624 | ||||||||
\(659\) | −6.00410 | −0.233887 | −0.116943 | − | 0.993139i | \(-0.537310\pi\) | ||||
−0.116943 | + | 0.993139i | \(0.537310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.83502 | −0.0713739 | −0.0356870 | − | 0.999363i | \(-0.511362\pi\) | ||||
−0.0356870 | + | 0.999363i | \(0.511362\pi\) | |||||||
\(662\) | 1.13901 | 0.0442687 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.981469 | −0.0380884 | ||||||||
\(665\) | 21.1878 | 0.821629 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.92218 | 0.229308 | ||||||||
\(668\) | −10.7269 | −0.415037 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.696689 | 0.0269154 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.4403 | 1.71305 | 0.856524 | − | 0.516107i | \(-0.172619\pi\) | ||||
0.856524 | + | 0.516107i | \(0.172619\pi\) | |||||||
\(674\) | 2.07318 | 0.0798559 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.4972 | 0.903737 | ||||||||
\(677\) | −15.5471 | −0.597525 | −0.298762 | − | 0.954327i | \(-0.596574\pi\) | ||||
−0.298762 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.11512 | 0.349806 | ||||||||
\(680\) | −9.37447 | −0.359494 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.8979 | 1.41186 | 0.705930 | − | 0.708282i | \(-0.250529\pi\) | ||||
0.705930 | + | 0.708282i | \(0.250529\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.9208 | 1.52530 | ||||||||
\(686\) | −0.120360 | −0.00459536 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.4823 | −0.780879 | ||||||||
\(689\) | 4.13032 | 0.157352 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6726 | −0.710339 | −0.355169 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355169 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(692\) | −39.1566 | −1.48851 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.05133 | −0.0399078 | ||||||||
\(695\) | −25.7806 | −0.977915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.7110 | 2.45111 | ||||||||
\(698\) | 3.60900 | 0.136603 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.73379 | −0.216717 | ||||||||
\(701\) | 26.1328 | 0.987022 | 0.493511 | − | 0.869739i | \(-0.335713\pi\) | ||||
0.493511 | + | 0.869739i | \(0.335713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.5821 | 0.436828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.881033 | 0.0331581 | ||||||||
\(707\) | 4.74385 | 0.178411 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4449 | −0.617602 | −0.308801 | − | 0.951127i | \(-0.599928\pi\) | ||||
−0.308801 | + | 0.951127i | \(0.599928\pi\) | |||||||
\(710\) | 4.23259 | 0.158846 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.28392 | −0.0855936 | ||||||||
\(713\) | 38.9617 | 1.45913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46.3204 | −1.73107 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.598184 | 0.0223240 | ||||||||
\(719\) | 9.34913 | 0.348664 | 0.174332 | − | 0.984687i | \(-0.444223\pi\) | ||||
0.174332 | + | 0.984687i | \(0.444223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.350901 | 0.0130682 | ||||||||
\(722\) | −4.56328 | −0.169828 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.12531 | −0.227646 | ||||||||
\(725\) | −3.54411 | −0.131625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7523 | 1.02928 | 0.514638 | − | 0.857408i | \(-0.327927\pi\) | ||||
0.514638 | + | 0.857408i | \(0.327927\pi\) | |||||||
\(728\) | 0.517915 | 0.0191952 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.867760 | −0.0321173 | ||||||||
\(731\) | 36.4198 | 1.34704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.45630 | 0.0537896 | 0.0268948 | − | 0.999638i | \(-0.491438\pi\) | ||||
0.0268948 | + | 0.999638i | \(0.491438\pi\) | |||||||
\(734\) | 1.70962 | 0.0631032 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.90240 | 0.254426 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.5966 | −1.01516 | −0.507579 | − | 0.861605i | \(-0.669459\pi\) | ||||
−0.507579 | + | 0.861605i | \(0.669459\pi\) | |||||||
\(740\) | −8.56113 | −0.314713 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.460439 | −0.0169033 | ||||||||
\(743\) | −27.9773 | −1.02639 | −0.513194 | − | 0.858273i | \(-0.671538\pi\) | ||||
−0.513194 | + | 0.858273i | \(0.671538\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.6350 | −1.19566 | ||||||||
\(746\) | −1.08057 | −0.0395624 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.54774 | −0.0930922 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0957 | 1.24417 | 0.622085 | − | 0.782950i | \(-0.286286\pi\) | ||||
0.622085 | + | 0.782950i | \(0.286286\pi\) | |||||||
\(752\) | 7.41125 | 0.270260 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.159482 | 0.00580800 | ||||||||
\(755\) | 50.3148 | 1.83114 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.7629 | −1.44521 | −0.722604 | − | 0.691262i | \(-0.757055\pi\) | ||||
−0.722604 | + | 0.691262i | \(0.757055\pi\) | |||||||
\(758\) | −1.29863 | −0.0471684 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1637 | 0.368677 | ||||||||
\(761\) | 3.82415 | 0.138625 | 0.0693127 | − | 0.997595i | \(-0.477919\pi\) | ||||
0.0693127 | + | 0.997595i | \(0.477919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.81522 | −0.138120 | ||||||||
\(764\) | 24.9608 | 0.903051 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.82966 | −0.102240 | ||||||||
\(767\) | 7.19440 | 0.259775 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.6583 | −0.708897 | −0.354449 | − | 0.935075i | \(-0.615331\pi\) | ||||
−0.354449 | + | 0.935075i | \(0.615331\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 41.0376 | 1.47698 | ||||||||
\(773\) | 17.5966 | 0.632905 | 0.316452 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316452 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.3165 | −0.837552 | ||||||||
\(776\) | 4.37249 | 0.156963 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.42922 | −0.0512400 | ||||||||
\(779\) | −70.1592 | −2.51371 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.04136 | −0.144519 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.91329 | 0.139760 | ||||||||
\(785\) | 20.8619 | 0.744592 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.0967 | −1.92834 | −0.964169 | − | 0.265287i | \(-0.914533\pi\) | ||||
−0.964169 | + | 0.265287i | \(0.914533\pi\) | |||||||
\(788\) | 12.4681 | 0.444158 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.18150 | 0.184349 | ||||||||
\(791\) | −2.31468 | −0.0823006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5803 | −0.375717 | ||||||||
\(794\) | 2.85571 | 0.101345 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.6384 | 0.483401 | ||||||||
\(797\) | −36.5244 | −1.29376 | −0.646881 | − | 0.762591i | \(-0.723927\pi\) | ||||
−0.646881 | + | 0.762591i | \(0.723927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1781 | −0.466206 | ||||||||
\(800\) | −4.13072 | −0.146043 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.457513 | −0.0161554 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5526 | −0.477666 | ||||||||
\(806\) | 1.04922 | 0.0369573 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.27561 | 0.0800555 | ||||||||
\(809\) | −46.9354 | −1.65016 | −0.825081 | − | 0.565015i | \(-0.808870\pi\) | ||||
−0.825081 | + | 0.565015i | \(0.808870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6615 | −0.444605 | −0.222303 | − | 0.974978i | \(-0.571357\pi\) | ||||
−0.222303 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(812\) | 2.43675 | 0.0855131 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.0552 | 0.772561 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.4861 | −1.38144 | ||||||||
\(818\) | 0.720103 | 0.0251778 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51.8594 | 1.81101 | ||||||||
\(821\) | 49.2938 | 1.72037 | 0.860183 | − | 0.509986i | \(-0.170349\pi\) | ||||
0.860183 | + | 0.509986i | \(0.170349\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.2259 | 0.670173 | 0.335087 | − | 0.942187i | \(-0.391234\pi\) | ||||
0.335087 | + | 0.942187i | \(0.391234\pi\) | |||||||
\(824\) | 0.168326 | 0.00586390 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.802017 | −0.0279057 | ||||||||
\(827\) | −43.6419 | −1.51758 | −0.758789 | − | 0.651337i | \(-0.774208\pi\) | ||||
−0.758789 | + | 0.651337i | \(0.774208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.7072 | −1.27489 | −0.637447 | − | 0.770494i | \(-0.720010\pi\) | ||||
−0.637447 | + | 0.770494i | \(0.720010\pi\) | |||||||
\(830\) | 0.691625 | 0.0240067 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.26428 | −0.286512 | ||||||||
\(833\) | −6.95828 | −0.241090 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.1733 | 0.525094 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.501768 | −0.0173333 | ||||||||
\(839\) | −40.4545 | −1.39665 | −0.698323 | − | 0.715783i | \(-0.746070\pi\) | ||||
−0.698323 | + | 0.715783i | \(0.746070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4938 | −0.948063 | ||||||||
\(842\) | −2.82310 | −0.0972904 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.3686 | −0.701117 | ||||||||
\(845\) | −33.2369 | −1.14339 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.9704 | 0.514085 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.41854 | 0.0829552 | ||||||||
\(851\) | −7.40840 | −0.253957 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.4948 | 0.872927 | 0.436463 | − | 0.899722i | \(-0.356231\pi\) | ||||
0.436463 | + | 0.899722i | \(0.356231\pi\) | |||||||
\(854\) | 1.17947 | 0.0403606 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.22214 | −0.0417718 | ||||||||
\(857\) | −49.4756 | −1.69005 | −0.845027 | − | 0.534723i | \(-0.820416\pi\) | ||||
−0.845027 | + | 0.534723i | \(0.820416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6779 | 0.739641 | 0.369821 | − | 0.929103i | \(-0.379419\pi\) | ||||
0.369821 | + | 0.929103i | \(0.379419\pi\) | |||||||
\(860\) | 29.1868 | 0.995262 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.48618 | 0.152800 | ||||||||
\(863\) | −13.6398 | −0.464306 | −0.232153 | − | 0.972679i | \(-0.574577\pi\) | ||||
−0.232153 | + | 0.972679i | \(0.574577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.3873 | 1.88322 | ||||||||
\(866\) | 2.74256 | 0.0931959 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.0312 | 0.544135 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.22521 | −0.0753985 | ||||||||
\(872\) | −1.83014 | −0.0619765 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.38161 | 0.148210 | ||||||||
\(875\) | −5.93213 | −0.200542 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.1290 | 0.983618 | 0.491809 | − | 0.870703i | \(-0.336336\pi\) | ||||
0.491809 | + | 0.870703i | \(0.336336\pi\) | |||||||
\(878\) | 0.172084 | 0.00580754 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.8256 | 1.64498 | 0.822488 | − | 0.568783i | \(-0.192586\pi\) | ||||
0.822488 | + | 0.568783i | \(0.192586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2131 | −0.814837 | −0.407419 | − | 0.913242i | \(-0.633571\pi\) | ||||
−0.407419 | + | 0.913242i | \(0.633571\pi\) | |||||||
\(884\) | 14.9165 | 0.501697 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.18113 | −0.106872 | ||||||||
\(887\) | −6.64749 | −0.223201 | −0.111600 | − | 0.993753i | \(-0.535598\pi\) | ||||
−0.111600 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.84644 | 0.330239 | ||||||||
\(890\) | 1.60944 | 0.0539486 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.8483 | 0.898947 | ||||||||
\(893\) | 14.2875 | 0.478114 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.5205 | 2.19011 | ||||||||
\(896\) | 3.78208 | 0.126350 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.69551 | 0.0565799 | ||||||||
\(899\) | 9.90903 | 0.330485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.6191 | −0.886809 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.11034 | −0.0369295 | ||||||||
\(905\) | 8.66431 | 0.288011 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.37806 | −0.278189 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(908\) | 26.9562 | 0.894573 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.364966 | −0.0120985 | ||||||||
\(911\) | 18.7868 | 0.622434 | 0.311217 | − | 0.950339i | \(-0.399263\pi\) | ||||
0.311217 | + | 0.950339i | \(0.399263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.54856 | −0.117376 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.88486 | 0.0953186 | ||||||||
\(917\) | −16.3782 | −0.540855 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0039 | 0.593894 | 0.296947 | − | 0.954894i | \(-0.404032\pi\) | ||||
0.296947 | + | 0.954894i | \(0.404032\pi\) | |||||||
\(920\) | −6.50113 | −0.214336 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.81881 | 0.125766 | ||||||||
\(923\) | −13.5188 | −0.444977 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.43353 | 0.145773 | ||||||||
\(926\) | 1.53867 | 0.0505637 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.75547 | 0.0576262 | ||||||||
\(929\) | 10.1225 | 0.332109 | 0.166054 | − | 0.986117i | \(-0.446897\pi\) | ||||
0.166054 | + | 0.986117i | \(0.446897\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.54411 | 0.247248 | ||||||||
\(932\) | 16.2889 | 0.533560 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.55986 | 0.116482 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.2113 | −0.921622 | −0.460811 | − | 0.887498i | \(-0.652441\pi\) | ||||
−0.460811 | + | 0.887498i | \(0.652441\pi\) | |||||||
\(938\) | 0.248062 | 0.00809952 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.5609 | −0.344458 | ||||||||
\(941\) | 20.1501 | 0.656875 | 0.328437 | − | 0.944526i | \(-0.393478\pi\) | ||||
0.328437 | + | 0.944526i | \(0.393478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.8766 | 1.46138 | ||||||||
\(944\) | 26.0762 | 0.848707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.125141 | −0.00406653 | −0.00203326 | − | 0.999998i | \(-0.500647\pi\) | ||||
−0.00203326 | + | 0.999998i | \(0.500647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.77161 | 0.0899703 | ||||||||
\(950\) | −2.62216 | −0.0850741 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.33786 | −0.108181 | ||||||||
\(953\) | 29.3495 | 0.950723 | 0.475362 | − | 0.879790i | \(-0.342317\pi\) | ||||
0.475362 | + | 0.879790i | \(0.342317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.3073 | −1.14252 | ||||||||
\(956\) | 20.6166 | 0.666790 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.43717 | −0.111050 | ||||||||
\(959\) | 14.2142 | 0.458999 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.1909 | 1.10293 | ||||||||
\(962\) | −0.199505 | −0.00643231 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.2900 | 0.524667 | ||||||||
\(965\) | −58.0481 | −1.86863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.9463 | −1.67048 | −0.835240 | − | 0.549885i | \(-0.814672\pi\) | ||||
−0.835240 | + | 0.549885i | \(0.814672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.08122 | −0.0989320 | ||||||||
\(971\) | 25.0066 | 0.802500 | 0.401250 | − | 0.915969i | \(-0.368576\pi\) | ||||
0.401250 | + | 0.915969i | \(0.368576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.17942 | −0.294279 | ||||||||
\(974\) | −0.127374 | −0.00408134 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.3484 | −1.22750 | ||||||||
\(977\) | 17.4156 | 0.557176 | 0.278588 | − | 0.960411i | \(-0.410134\pi\) | ||||
0.278588 | + | 0.960411i | \(0.410134\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.57636 | −0.178130 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.22051 | 0.0708592 | ||||||||
\(983\) | 42.3349 | 1.35028 | 0.675138 | − | 0.737692i | \(-0.264084\pi\) | ||||
0.675138 | + | 0.737692i | \(0.264084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6362 | −0.561937 | ||||||||
\(986\) | −1.02783 | −0.0327328 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.1724 | −0.514512 | ||||||||
\(989\) | 25.2569 | 0.803122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.6263 | 1.76703 | 0.883513 | − | 0.468406i | \(-0.155172\pi\) | ||||
0.883513 | + | 0.468406i | \(0.155172\pi\) | |||||||
\(992\) | 11.5491 | 0.366685 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.50705 | 0.0478007 | ||||||||
\(995\) | −19.2916 | −0.611586 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4267 | −0.520240 | −0.260120 | − | 0.965576i | \(-0.583762\pi\) | ||||
−0.260120 | + | 0.965576i | \(0.583762\pi\) | |||||||
\(998\) | −3.81894 | −0.120886 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.cp.1.4 | 6 | ||
3.2 | odd | 2 | 847.2.a.n.1.3 | yes | 6 | ||
11.10 | odd | 2 | 7623.2.a.cs.1.3 | 6 | |||
21.20 | even | 2 | 5929.2.a.bm.1.3 | 6 | |||
33.2 | even | 10 | 847.2.f.z.323.3 | 24 | |||
33.5 | odd | 10 | 847.2.f.y.729.4 | 24 | |||
33.8 | even | 10 | 847.2.f.z.372.4 | 24 | |||
33.14 | odd | 10 | 847.2.f.y.372.3 | 24 | |||
33.17 | even | 10 | 847.2.f.z.729.3 | 24 | |||
33.20 | odd | 10 | 847.2.f.y.323.4 | 24 | |||
33.26 | odd | 10 | 847.2.f.y.148.3 | 24 | |||
33.29 | even | 10 | 847.2.f.z.148.4 | 24 | |||
33.32 | even | 2 | 847.2.a.m.1.4 | ✓ | 6 | ||
231.230 | odd | 2 | 5929.2.a.bj.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.4 | ✓ | 6 | 33.32 | even | 2 | ||
847.2.a.n.1.3 | yes | 6 | 3.2 | odd | 2 | ||
847.2.f.y.148.3 | 24 | 33.26 | odd | 10 | |||
847.2.f.y.323.4 | 24 | 33.20 | odd | 10 | |||
847.2.f.y.372.3 | 24 | 33.14 | odd | 10 | |||
847.2.f.y.729.4 | 24 | 33.5 | odd | 10 | |||
847.2.f.z.148.4 | 24 | 33.29 | even | 10 | |||
847.2.f.z.323.3 | 24 | 33.2 | even | 10 | |||
847.2.f.z.372.4 | 24 | 33.8 | even | 10 | |||
847.2.f.z.729.3 | 24 | 33.17 | even | 10 | |||
5929.2.a.bj.1.4 | 6 | 231.230 | odd | 2 | |||
5929.2.a.bm.1.3 | 6 | 21.20 | even | 2 | |||
7623.2.a.cp.1.4 | 6 | 1.1 | even | 1 | trivial | ||
7623.2.a.cs.1.3 | 6 | 11.10 | odd | 2 |