Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.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: | \(32.3873230598\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 | ||||||||
\(5\) | 2.24698 | 1.00488 | 0.502440 | − | 0.864612i | \(-0.332436\pi\) | ||||
0.502440 | + | 0.864612i | \(0.332436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.35690 | −0.512858 | −0.256429 | − | 0.966563i | \(-0.582546\pi\) | ||||
−0.256429 | + | 0.966563i | \(0.582546\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.445042 | −0.134185 | −0.0670926 | − | 0.997747i | \(-0.521372\pi\) | ||||
−0.0670926 | + | 0.997747i | \(0.521372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.24698 | −0.580168 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.80194 | −0.437034 | −0.218517 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218517 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69202 | −0.617592 | −0.308796 | − | 0.951128i | \(-0.599926\pi\) | ||||
−0.308796 | + | 0.951128i | \(0.599926\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.35690 | 0.296099 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.24698 | −0.468528 | −0.234264 | − | 0.972173i | \(-0.575268\pi\) | ||||
−0.234264 | + | 0.972173i | \(0.575268\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0489173 | 0.00978347 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.65279 | 0.864002 | 0.432001 | − | 0.901873i | \(-0.357808\pi\) | ||||
0.432001 | + | 0.901873i | \(0.357808\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.25667 | 1.48294 | 0.741471 | − | 0.670985i | \(-0.234129\pi\) | ||||
0.741471 | + | 0.670985i | \(0.234129\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.445042 | 0.0774718 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.04892 | −0.515361 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.41789 | 0.233100 | 0.116550 | − | 0.993185i | \(-0.462816\pi\) | ||||
0.116550 | + | 0.993185i | \(0.462816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.03684 | −1.41132 | −0.705658 | − | 0.708552i | \(-0.749349\pi\) | ||||
−0.705658 | + | 0.708552i | \(0.749349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.09783 | −1.38741 | −0.693703 | − | 0.720261i | \(-0.744022\pi\) | ||||
−0.693703 | + | 0.720261i | \(0.744022\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.24698 | 0.334960 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.58211 | −1.10596 | −0.552982 | − | 0.833193i | \(-0.686510\pi\) | ||||
−0.552982 | + | 0.833193i | \(0.686510\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15883 | −0.736976 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80194 | 0.252322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4330 | 1.57044 | 0.785219 | − | 0.619218i | \(-0.212550\pi\) | ||||
0.785219 | + | 0.619218i | \(0.212550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.69202 | 0.356567 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.93362 | −0.902681 | −0.451340 | − | 0.892352i | \(-0.649054\pi\) | ||||
−0.451340 | + | 0.892352i | \(0.649054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.868313 | −0.111176 | −0.0555881 | − | 0.998454i | \(-0.517703\pi\) | ||||
−0.0555881 | + | 0.998454i | \(0.517703\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.35690 | −0.170953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.53319 | −0.798156 | −0.399078 | − | 0.916917i | \(-0.630670\pi\) | ||||
−0.399078 | + | 0.916917i | \(0.630670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.24698 | 0.270505 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54288 | −0.420462 | −0.210231 | − | 0.977652i | \(-0.567422\pi\) | ||||
−0.210231 | + | 0.977652i | \(0.567422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.35690 | 0.392895 | 0.196447 | − | 0.980514i | \(-0.437059\pi\) | ||||
0.196447 | + | 0.980514i | \(0.437059\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0489173 | −0.00564849 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.603875 | 0.0688180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6746 | −1.42600 | −0.713000 | − | 0.701164i | \(-0.752664\pi\) | ||||
−0.713000 | + | 0.701164i | \(0.752664\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.19806 | −0.351033 | −0.175516 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175516 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04892 | −0.439167 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.65279 | −0.498832 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.454731 | −0.0482013 | −0.0241007 | − | 0.999710i | \(-0.507672\pi\) | ||||
−0.0241007 | + | 0.999710i | \(0.507672\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.25667 | −0.856177 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.04892 | −0.620606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4940 | 1.57317 | 0.786587 | − | 0.617480i | \(-0.211846\pi\) | ||||
0.786587 | + | 0.617480i | \(0.211846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.445042 | −0.0447284 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.77240 | −0.972390 | −0.486195 | − | 0.873850i | \(-0.661616\pi\) | ||||
−0.486195 | + | 0.873850i | \(0.661616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1836 | 1.49608 | 0.748042 | − | 0.663652i | \(-0.230994\pi\) | ||||
0.748042 | + | 0.663652i | \(0.230994\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.04892 | 0.297544 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.48858 | 0.433928 | 0.216964 | − | 0.976180i | \(-0.430385\pi\) | ||||
0.216964 | + | 0.976180i | \(0.430385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1347 | 1.64120 | 0.820602 | − | 0.571500i | \(-0.193638\pi\) | ||||
0.820602 | + | 0.571500i | \(0.193638\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41789 | −0.134581 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.0640 | −1.88746 | −0.943730 | − | 0.330716i | \(-0.892710\pi\) | ||||
−0.943730 | + | 0.330716i | \(0.892710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.04892 | −0.470814 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.44504 | 0.224137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8019 | −0.981994 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.03684 | 0.814824 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1250 | −0.995049 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.76809 | 0.511835 | 0.255917 | − | 0.966699i | \(-0.417622\pi\) | ||||
0.255917 | + | 0.966699i | \(0.417622\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.09783 | 0.801020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.07308 | −0.0937555 | −0.0468777 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468777 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65279 | 0.316737 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.24698 | −0.193389 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.0737 | 1.62957 | 0.814787 | − | 0.579761i | \(-0.196854\pi\) | ||||
0.814787 | + | 0.579761i | \(0.196854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.6093 | −1.15432 | −0.577161 | − | 0.816630i | \(-0.695839\pi\) | ||||
−0.577161 | + | 0.816630i | \(0.695839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.58211 | 0.638528 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4547 | 0.868218 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.15883 | 0.425493 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.1914 | 0.834909 | 0.417454 | − | 0.908698i | \(-0.362922\pi\) | ||||
0.417454 | + | 0.908698i | \(0.362922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5767 | −0.942101 | −0.471050 | − | 0.882106i | \(-0.656125\pi\) | ||||
−0.471050 | + | 0.882106i | \(0.656125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.80194 | −0.145678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.5526 | 1.49018 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.67025 | −0.771770 | −0.385885 | − | 0.922547i | \(-0.626104\pi\) | ||||
−0.385885 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.4330 | −0.906693 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.04892 | 0.240288 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4983 | −0.978940 | −0.489470 | − | 0.872020i | \(-0.662810\pi\) | ||||
−0.489470 | + | 0.872020i | \(0.662810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.56033 | 0.662419 | 0.331209 | − | 0.943557i | \(-0.392543\pi\) | ||||
0.331209 | + | 0.943557i | \(0.392543\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.69202 | −0.205864 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.70709 | 0.357873 | 0.178937 | − | 0.983861i | \(-0.442734\pi\) | ||||
0.178937 | + | 0.983861i | \(0.442734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0663757 | −0.00501753 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.93362 | 0.521163 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.7409 | −1.25128 | −0.625638 | − | 0.780113i | \(-0.715161\pi\) | ||||
−0.625638 | + | 0.780113i | \(0.715161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0707 | −1.41751 | −0.708757 | − | 0.705453i | \(-0.750744\pi\) | ||||
−0.708757 | + | 0.705453i | \(0.750744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.868313 | 0.0641876 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.18598 | 0.234238 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.801938 | 0.0586435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.35690 | 0.0986997 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2543 | −1.46555 | −0.732774 | − | 0.680472i | \(-0.761775\pi\) | ||||
−0.732774 | + | 0.680472i | \(0.761775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1836 | −1.02096 | −0.510478 | − | 0.859891i | \(-0.670532\pi\) | ||||
−0.510478 | + | 0.859891i | \(0.670532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.3502 | −0.808668 | −0.404334 | − | 0.914611i | \(-0.632497\pi\) | ||||
−0.404334 | + | 0.914611i | \(0.632497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2784 | −1.43750 | −0.718750 | − | 0.695268i | \(-0.755286\pi\) | ||||
−0.718750 | + | 0.695268i | \(0.755286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.53319 | 0.460816 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.31336 | −0.443111 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.3056 | −1.41820 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.24698 | −0.156176 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.19806 | 0.0828717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.47650 | 0.170489 | 0.0852447 | − | 0.996360i | \(-0.472833\pi\) | ||||
0.0852447 | + | 0.996360i | \(0.472833\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.54288 | 0.242754 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.4426 | −1.39418 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2034 | −0.760539 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.35690 | −0.226838 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2567 | 0.753802 | 0.376901 | − | 0.926253i | \(-0.376990\pi\) | ||||
0.376901 | + | 0.926253i | \(0.376990\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0489173 | 0.00326116 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.9409 | 1.78813 | 0.894066 | − | 0.447936i | \(-0.147841\pi\) | ||||
0.894066 | + | 0.447936i | \(0.147841\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.36658 | −0.618961 | −0.309481 | − | 0.950906i | \(-0.600155\pi\) | ||||
−0.309481 | + | 0.950906i | \(0.600155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.603875 | −0.0397321 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00969 | −0.459220 | −0.229610 | − | 0.973283i | \(-0.573745\pi\) | ||||
−0.229610 | + | 0.973283i | \(0.573745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.0368 | −1.11136 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6746 | 0.823301 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.58211 | −0.555130 | −0.277565 | − | 0.960707i | \(-0.589527\pi\) | ||||
−0.277565 | + | 0.960707i | \(0.589527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2034 | 0.979340 | 0.489670 | − | 0.871908i | \(-0.337117\pi\) | ||||
0.489670 | + | 0.871908i | \(0.337117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.5918 | −0.740573 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.19806 | 0.202669 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.86831 | −0.181046 | −0.0905232 | − | 0.995894i | \(-0.528854\pi\) | ||||
−0.0905232 | + | 0.995894i | \(0.528854\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.04892 | 0.253553 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7724 | −0.671964 | −0.335982 | − | 0.941868i | \(-0.609068\pi\) | ||||
−0.335982 | + | 0.941868i | \(0.609068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.92394 | −0.119548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.65279 | 0.288001 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.87369 | −0.238862 | −0.119431 | − | 0.992843i | \(-0.538107\pi\) | ||||
−0.119431 | + | 0.992843i | \(0.538107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.6896 | 1.57810 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.454731 | 0.0278291 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.67994 | 0.224370 | 0.112185 | − | 0.993687i | \(-0.464215\pi\) | ||||
0.112185 | + | 0.993687i | \(0.464215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.30798 | −0.383182 | −0.191591 | − | 0.981475i | \(-0.561365\pi\) | ||||
−0.191591 | + | 0.981475i | \(0.561365\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0217703 | −0.00131280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.43429 | −0.146262 | −0.0731311 | − | 0.997322i | \(-0.523299\pi\) | ||||
−0.0731311 | + | 0.997322i | \(0.523299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.25667 | 0.494314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.98493 | 0.535996 | 0.267998 | − | 0.963419i | \(-0.413638\pi\) | ||||
0.267998 | + | 0.963419i | \(0.413638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.9734 | 0.949523 | 0.474761 | − | 0.880115i | \(-0.342534\pi\) | ||||
0.474761 | + | 0.880115i | \(0.342534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.04892 | 0.358307 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.2620 | 0.723806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7530 | −0.809001 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.4940 | −0.908272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.03923 | −0.294395 | −0.147197 | − | 0.989107i | \(-0.547025\pi\) | ||||
−0.147197 | + | 0.989107i | \(0.547025\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.5797 | −0.907086 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.445042 | 0.0258239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3448 | 0.711543 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.77240 | 0.561410 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.95108 | −0.111719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8726 | −0.962972 | −0.481486 | − | 0.876454i | \(-0.659903\pi\) | ||||
−0.481486 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.1836 | −0.863764 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3207 | 0.868754 | 0.434377 | − | 0.900731i | \(-0.356968\pi\) | ||||
0.434377 | + | 0.900731i | \(0.356968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4045 | −1.04028 | −0.520142 | − | 0.854080i | \(-0.674121\pi\) | ||||
−0.520142 | + | 0.854080i | \(0.674121\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.04892 | −0.171787 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.3521 | 1.36775 | 0.683875 | − | 0.729599i | \(-0.260293\pi\) | ||||
0.683875 | + | 0.729599i | \(0.260293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.07069 | −0.115936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.48858 | −0.250528 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.85086 | 0.269909 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.1347 | −0.947549 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.2881 | 0.567203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.74333 | −0.150787 | −0.0753936 | − | 0.997154i | \(-0.524021\pi\) | ||||
−0.0753936 | + | 0.997154i | \(0.524021\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.41789 | 0.0777002 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.6799 | −0.802051 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.5743 | −1.44760 | −0.723798 | − | 0.690012i | \(-0.757605\pi\) | ||||
−0.723798 | + | 0.690012i | \(0.757605\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0640 | 1.08973 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.67456 | −0.198989 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4983 | 0.890823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.04892 | 0.271825 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3937 | 0.933744 | 0.466872 | − | 0.884325i | \(-0.345381\pi\) | ||||
0.466872 | + | 0.884325i | \(0.345381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.75600 | −0.522227 | −0.261113 | − | 0.965308i | \(-0.584090\pi\) | ||||
−0.261113 | + | 0.965308i | \(0.584090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7832 | −0.680378 | −0.340189 | − | 0.940357i | \(-0.610491\pi\) | ||||
−0.340189 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.96077 | −0.422514 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.44504 | −0.129405 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.2784 | 0.753587 | 0.376794 | − | 0.926297i | \(-0.377027\pi\) | ||||
0.376794 | + | 0.926297i | \(0.377027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7530 | −0.618580 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8019 | 0.566955 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.54288 | 0.394812 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.1491 | −0.790779 | −0.395389 | − | 0.918514i | \(-0.629390\pi\) | ||||
−0.395389 | + | 0.918514i | \(0.629390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.03684 | −0.470439 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.5133 | −0.805412 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.7385 | 0.970245 | 0.485123 | − | 0.874446i | \(-0.338775\pi\) | ||||
0.485123 | + | 0.874446i | \(0.338775\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1250 | 0.574492 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3937 | −1.40712 | −0.703561 | − | 0.710635i | \(-0.748408\pi\) | ||||
−0.703561 | + | 0.710635i | \(0.748408\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.76809 | −0.295508 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.3448 | 0.886279 | 0.443139 | − | 0.896453i | \(-0.353865\pi\) | ||||
0.443139 | + | 0.896453i | \(0.353865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.35690 | 0.0691538 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.09783 | −0.462469 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.2620 | −1.23013 | −0.615067 | − | 0.788475i | \(-0.710871\pi\) | ||||
−0.615067 | + | 0.788475i | \(0.710871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04892 | 0.204763 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07308 | 0.0541298 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.4795 | −1.43296 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.7536 | −1.89480 | −0.947400 | − | 0.320053i | \(-0.896299\pi\) | ||||
−0.947400 | + | 0.320053i | \(0.896299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.65279 | −0.182868 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.01400 | −0.450138 | −0.225069 | − | 0.974343i | \(-0.572261\pi\) | ||||
−0.225069 | + | 0.974343i | \(0.572261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.24698 | 0.111653 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.631023 | −0.0312786 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0344 | −0.743405 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0737 | −0.940835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.40821 | 0.462948 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.18598 | −0.352746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6093 | 0.666448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8418 | −1.16475 | −0.582373 | − | 0.812922i | \(-0.697876\pi\) | ||||
−0.582373 | + | 0.812922i | \(0.697876\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4045 | 1.28688 | 0.643438 | − | 0.765498i | \(-0.277507\pi\) | ||||
0.643438 | + | 0.765498i | \(0.277507\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.58211 | −0.368655 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.0881460 | −0.00427571 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.17821 | 0.0570176 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.47757 | 0.263845 | 0.131923 | − | 0.991260i | \(-0.457885\pi\) | ||||
0.131923 | + | 0.991260i | \(0.457885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.9071 | −0.908616 | −0.454308 | − | 0.890845i | \(-0.650113\pi\) | ||||
−0.454308 | + | 0.890845i | \(0.650113\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.4547 | −0.501266 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.04892 | 0.289359 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.6480 | 1.36729 | 0.683647 | − | 0.729812i | \(-0.260393\pi\) | ||||
0.683647 | + | 0.729812i | \(0.260393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.15883 | −0.245659 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3502 | 0.681798 | 0.340899 | − | 0.940100i | \(-0.389269\pi\) | ||||
0.340899 | + | 0.940100i | \(0.389269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.02177 | −0.0484366 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.1914 | −0.482035 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7187 | 1.59128 | 0.795642 | − | 0.605767i | \(-0.207134\pi\) | ||||
0.795642 | + | 0.605767i | \(0.207134\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.02177 | 0.189378 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5767 | 0.543922 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.1758 | 1.92612 | 0.963062 | − | 0.269281i | \(-0.0867859\pi\) | ||||
0.963062 | + | 0.269281i | \(0.0867859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.80194 | 0.0841073 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.94571 | −0.137195 | −0.0685976 | − | 0.997644i | \(-0.521852\pi\) | ||||
−0.0685976 | + | 0.997644i | \(0.521852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.2828 | −1.31441 | −0.657205 | − | 0.753711i | \(-0.728262\pi\) | ||||
−0.657205 | + | 0.753711i | \(0.728262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.5526 | −0.860355 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.5060 | 1.04146 | 0.520728 | − | 0.853723i | \(-0.325661\pi\) | ||||
0.520728 | + | 0.853723i | \(0.325661\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.86486 | 0.409341 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.67025 | 0.445582 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.04892 | 0.186169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.131687 | −0.00604219 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4330 | 0.523479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.1933 | 1.60802 | 0.804011 | − | 0.594615i | \(-0.202695\pi\) | ||||
0.804011 | + | 0.594615i | \(0.202695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.04892 | −0.138731 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.8146 | 1.58085 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.9517 | −1.04004 | −0.520020 | − | 0.854154i | \(-0.674075\pi\) | ||||
−0.520020 | + | 0.854154i | \(0.674075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.4983 | 0.565191 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.5657 | 0.612212 | 0.306106 | − | 0.951997i | \(-0.400974\pi\) | ||||
0.306106 | + | 0.951997i | \(0.400974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.38404 | −0.377598 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.80731 | 0.215638 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5676 | −0.920734 | −0.460367 | − | 0.887729i | \(-0.652282\pi\) | ||||
−0.460367 | + | 0.887729i | \(0.652282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.56033 | −0.382448 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0935 | 0.762163 | 0.381081 | − | 0.924542i | \(-0.375552\pi\) | ||||
0.381081 | + | 0.924542i | \(0.375552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.9584 | −0.977135 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.9288 | −1.63684 | −0.818421 | − | 0.574619i | \(-0.805150\pi\) | ||||
−0.818421 | + | 0.574619i | \(0.805150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.55496 | −0.201499 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.69202 | 0.118856 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.1172 | 1.50338 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.37435 | 0.148404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.70709 | −0.206618 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.63401 | −0.378263 | −0.189131 | − | 0.981952i | \(-0.560567\pi\) | ||||
−0.189131 | + | 0.981952i | \(0.560567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7832 | 0.602695 | 0.301348 | − | 0.953514i | \(-0.402564\pi\) | ||||
0.301348 | + | 0.953514i | \(0.402564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0663757 | 0.00289687 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.8780 | −0.648096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9511 | −0.780482 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.93362 | −0.300894 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0858 | 0.436045 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.7409 | 0.722425 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.29590 | 0.0988913 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.377338 | 0.0162230 | 0.00811152 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811152 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0707 | 0.818402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.5013 | 1.64921 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8635 | −1.70444 | −0.852221 | − | 0.523182i | \(-0.824745\pi\) | ||||
−0.852221 | + | 0.523182i | \(0.824745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.868313 | −0.0370587 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.5254 | −0.533601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1981 | 0.731336 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.18598 | −0.135237 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.34242 | 0.0568802 | 0.0284401 | − | 0.999595i | \(-0.490946\pi\) | ||||
0.0284401 | + | 0.999595i | \(0.490946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.801938 | −0.0338578 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.9493 | −1.47294 | −0.736468 | − | 0.676472i | \(-0.763508\pi\) | ||||
−0.736468 | + | 0.676472i | \(0.763508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.0834 | −1.89667 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.35690 | −0.0569843 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0575 | 0.673167 | 0.336584 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336584 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1444 | −1.42890 | −0.714448 | − | 0.699688i | \(-0.753322\pi\) | ||||
−0.714448 | + | 0.699688i | \(0.753322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.2543 | 0.846134 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.109916 | −0.00458383 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2368 | −0.467795 | −0.233897 | − | 0.972261i | \(-0.575148\pi\) | ||||
−0.233897 | + | 0.972261i | \(0.575148\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1836 | 0.589450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.33944 | 0.180030 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.08815 | −0.210729 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.53750 | −0.352380 | −0.176190 | − | 0.984356i | \(-0.556377\pi\) | ||||
−0.176190 | + | 0.984356i | \(0.556377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.2271 | −0.915853 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.3502 | 0.466884 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4383 | 0.633977 | 0.316988 | − | 0.948429i | \(-0.397328\pi\) | ||||
0.316988 | + | 0.948429i | \(0.397328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.49396 | 0.225230 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.2784 | 0.829941 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.82072 | −0.278687 | −0.139344 | − | 0.990244i | \(-0.544499\pi\) | ||||
−0.139344 | + | 0.990244i | \(0.544499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.4142 | 1.81169 | 0.905846 | − | 0.423607i | \(-0.139236\pi\) | ||||
0.905846 | + | 0.423607i | \(0.139236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.53319 | −0.266052 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.2717 | −0.986786 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2218 | 1.06431 | 0.532154 | − | 0.846648i | \(-0.321383\pi\) | ||||
0.532154 | + | 0.846648i | \(0.321383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.31336 | 0.255830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.02177 | −0.0412689 | −0.0206345 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206345 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20.3056 | 0.818800 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5724 | 0.989248 | 0.494624 | − | 0.869107i | \(-0.335306\pi\) | ||||
0.494624 | + | 0.869107i | \(0.335306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4614 | −0.661641 | −0.330820 | − | 0.943694i | \(-0.607325\pi\) | ||||
−0.330820 | + | 0.943694i | \(0.607325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.24698 | 0.0901682 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.617022 | 0.0247205 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.2422 | −1.00969 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.19806 | −0.0478460 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.55496 | −0.101873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39852 | 0.135293 | 0.0676464 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676464 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.47650 | −0.0984321 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9608 | 0.514333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.54288 | −0.140154 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.4634 | 1.16373 | 0.581866 | − | 0.813284i | \(-0.302323\pi\) | ||||
0.581866 | + | 0.813284i | \(0.302323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7235 | −0.541201 | −0.270601 | − | 0.962692i | \(-0.587222\pi\) | ||||
−0.270601 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.4426 | 0.804929 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5200 | 0.846040 | 0.423020 | − | 0.906120i | \(-0.360970\pi\) | ||||
0.423020 | + | 0.906120i | \(0.360970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.08575 | 0.121126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.2034 | 0.439097 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4935 | −1.03677 | −0.518385 | − | 0.855147i | \(-0.673467\pi\) | ||||
−0.518385 | + | 0.855147i | \(0.673467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.41119 | −0.0942130 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.35690 | 0.130965 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9135 | 1.47690 | 0.738450 | − | 0.674308i | \(-0.235558\pi\) | ||||
0.738450 | + | 0.674308i | \(0.235558\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.940066 | −0.0365643 | −0.0182822 | − | 0.999833i | \(-0.505820\pi\) | ||||
−0.0182822 | + | 0.999833i | \(0.505820\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.20775 | 0.318283 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4547 | −0.404809 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.2567 | −0.435208 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.386436 | 0.0149182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1540 | 0.892523 | 0.446261 | − | 0.894903i | \(-0.352755\pi\) | ||||
0.446261 | + | 0.894903i | \(0.352755\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0489173 | −0.00188283 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.41060 | 0.0926468 | 0.0463234 | − | 0.998926i | \(-0.485250\pi\) | ||||
0.0463234 | + | 0.998926i | \(0.485250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.0237 | −0.806815 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.9409 | −1.03238 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.8823 | 1.64085 | 0.820423 | − | 0.571757i | \(-0.193738\pi\) | ||||
0.820423 | + | 0.571757i | \(0.193738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.8582 | 1.63753 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.36658 | 0.357357 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.2820 | 1.87478 | 0.937388 | − | 0.348287i | \(-0.113236\pi\) | ||||
0.937388 | + | 0.348287i | \(0.113236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.603875 | 0.0229393 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.5797 | −1.15995 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2838 | 0.616793 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.00969 | 0.265131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1213 | −1.17543 | −0.587717 | − | 0.809067i | \(-0.699973\pi\) | ||||
−0.587717 | + | 0.809067i | \(0.699973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.81700 | −0.143961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.0368 | 0.641644 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.2601 | 0.498698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.4416 | 1.51882 | 0.759408 | − | 0.650615i | \(-0.225489\pi\) | ||||
0.759408 | + | 0.650615i | \(0.225489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.6746 | −0.475333 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.5526 | −0.694799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.58211 | 0.320505 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.59658 | 0.320598 | 0.160299 | − | 0.987068i | \(-0.448754\pi\) | ||||
0.160299 | + | 0.987068i | \(0.448754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.6025 | −0.767279 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.2034 | −0.565422 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.227602 | 0.00845294 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.4300 | 0.535178 | 0.267589 | − | 0.963533i | \(-0.413773\pi\) | ||||
0.267589 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3937 | 0.606344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.26636 | 0.268389 | 0.134195 | − | 0.990955i | \(-0.457155\pi\) | ||||
0.134195 | + | 0.990955i | \(0.457155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.5918 | 0.427570 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.90754 | 0.107101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.60281 | 0.132532 | 0.0662658 | − | 0.997802i | \(-0.478891\pi\) | ||||
0.0662658 | + | 0.997802i | \(0.478891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.1812 | 1.21730 | 0.608650 | − | 0.793439i | \(-0.291711\pi\) | ||||
0.608650 | + | 0.793439i | \(0.291711\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.8998 | 0.838983 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.19806 | −0.117011 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.09054 | −0.222543 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.4077 | 1.18257 | 0.591287 | − | 0.806461i | \(-0.298620\pi\) | ||||
0.591287 | + | 0.806461i | \(0.298620\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.86831 | 0.104527 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.0127 | −0.946698 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8726 | 0.504209 | 0.252105 | − | 0.967700i | \(-0.418877\pi\) | ||||
0.252105 | + | 0.967700i | \(0.418877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.00000 | −0.0362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.3943 | 1.28304 | 0.641522 | − | 0.767105i | \(-0.278303\pi\) | ||||
0.641522 | + | 0.767105i | \(0.278303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.2500 | −0.841705 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.04892 | −0.146389 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.1909 | 1.16083 | 0.580416 | − | 0.814320i | \(-0.302890\pi\) | ||||
0.580416 | + | 0.814320i | \(0.302890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.7724 | 0.387958 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.9186 | −0.572551 | −0.286275 | − | 0.958147i | \(-0.592417\pi\) | ||||
−0.286275 | + | 0.958147i | \(0.592417\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.403894 | 0.0145083 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.92394 | 0.0690208 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.3274 | 0.871618 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.57673 | 0.0564198 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.65279 | −0.166277 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.7289 | −0.775536 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.0476 | −0.750266 | −0.375133 | − | 0.926971i | \(-0.622403\pi\) | ||||
−0.375133 | + | 0.926971i | \(0.622403\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.87369 | 0.137907 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.2247 | 0.968000 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.6896 | −0.911117 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.0917 | 1.73892 | 0.869459 | − | 0.494005i | \(-0.164468\pi\) | ||||
0.869459 | + | 0.494005i | \(0.164468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6625 | 0.483344 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.454731 | −0.0160671 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.49396 | −0.0527207 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.85086 | 0.241461 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.67994 | −0.129540 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.4370 | 0.613053 | 0.306526 | − | 0.951862i | \(-0.400833\pi\) | ||||
0.306526 | + | 0.951862i | \(0.400833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0411 | 0.422822 | 0.211411 | − | 0.977397i | \(-0.432194\pi\) | ||||
0.211411 | + | 0.977397i | \(0.432194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.30798 | 0.221230 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.0834 | −0.983717 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.4916 | 0.856851 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.4403 | −1.06237 | −0.531186 | − | 0.847255i | \(-0.678254\pi\) | ||||
−0.531186 | + | 0.847255i | \(0.678254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.22282 | −0.0774825 | −0.0387413 | − | 0.999249i | \(-0.512335\pi\) | ||||
−0.0387413 | + | 0.999249i | \(0.512335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0217703 | 0.000757943 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.9028 | 1.28323 | 0.641617 | − | 0.767025i | \(-0.278264\pi\) | ||||
0.641617 | + | 0.767025i | \(0.278264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2978 | 0.739704 | 0.369852 | − | 0.929091i | \(-0.379408\pi\) | ||||
0.369852 | + | 0.929091i | \(0.379408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.43429 | 0.0844445 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.29590 | 0.322084 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.2349 | 0.665651 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.25667 | −0.285392 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.6353 | 1.36836 | 0.684182 | − | 0.729311i | \(-0.260159\pi\) | ||||
0.684182 | + | 0.729311i | \(0.260159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.35152 | −0.253501 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.98493 | −0.309458 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.6571 | 0.503624 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.9734 | −0.548207 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.18598 | −0.109214 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.8133 | 1.70557 | 0.852787 | − | 0.522259i | \(-0.174910\pi\) | ||||
0.852787 | + | 0.522259i | \(0.174910\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.04892 | −0.206869 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6969 | −0.536197 | −0.268098 | − | 0.963392i | \(-0.586395\pi\) | ||||
−0.268098 | + | 0.963392i | \(0.586395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.5478 | −0.871679 | −0.435839 | − | 0.900024i | \(-0.643548\pi\) | ||||
−0.435839 | + | 0.900024i | \(0.643548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2620 | −0.417889 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.6088 | −1.45042 | −0.725210 | − | 0.688528i | \(-0.758257\pi\) | ||||
−0.725210 | + | 0.688528i | \(0.758257\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5767 | 0.359620 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.7530 | 0.467077 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.64071 | 0.191348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.4940 | 0.524391 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.0954 | 0.510319 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6461 | −0.528331 | −0.264165 | − | 0.964477i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964477i | \(0.585096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.03923 | 0.169969 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.0484 | 1.65248 | 0.826242 | − | 0.563315i | \(-0.190474\pi\) | ||||
0.826242 | + | 0.563315i | \(0.190474\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.8165 | −1.94568 | −0.972841 | − | 0.231476i | \(-0.925644\pi\) | ||||
−0.972841 | + | 0.231476i | \(0.925644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.5797 | 0.523706 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.2847 | 1.82270 | 0.911350 | − | 0.411631i | \(-0.135041\pi\) | ||||
0.911350 | + | 0.411631i | \(0.135041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.82669 | −0.262499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.445042 | −0.0149095 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.4112 | 0.683034 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.6165 | −1.25738 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.4166 | 1.28126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.6015 | −0.686335 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.3448 | −0.410810 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.8514 | −1.42443 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7700 | 0.922088 | 0.461044 | − | 0.887377i | \(-0.347475\pi\) | ||||
0.461044 | + | 0.887377i | \(0.347475\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.77240 | −0.324130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.4403 | 1.43924 | 0.719620 | − | 0.694368i | \(-0.244316\pi\) | ||||
0.719620 | + | 0.694368i | \(0.244316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.42327 | 0.0471034 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.95108 | 0.0645008 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.45606 | 0.0480833 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.6661 | 1.53937 | 0.769686 | − | 0.638423i | \(-0.220413\pi\) | ||||
0.769686 | + | 0.638423i | \(0.220413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.8726 | 0.555972 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0693596 | 0.00228053 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.1836 | 0.498694 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.36467 | −0.208818 | −0.104409 | − | 0.994534i | \(-0.533295\pi\) | ||||
−0.104409 | + | 0.994534i | \(0.533295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.8877 | 0.455151 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.3207 | −0.501576 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.80194 | 0.0589297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.95599 | −0.325248 | −0.162624 | − | 0.986688i | \(-0.551996\pi\) | ||||
−0.162624 | + | 0.986688i | \(0.551996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4045 | 0.600608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.6950 | −1.71781 | −0.858904 | − | 0.512137i | \(-0.828854\pi\) | ||||
−0.858904 | + | 0.512137i | \(0.828854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.3056 | 0.661241 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.04892 | 0.0991813 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.11051 | −0.231060 | −0.115530 | − | 0.993304i | \(-0.536857\pi\) | ||||
−0.115530 | + | 0.993304i | \(0.536857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.3521 | −0.789671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.7569 | 1.96811 | 0.984054 | − | 0.177871i | \(-0.0569209\pi\) | ||||
0.984054 | + | 0.177871i | \(0.0569209\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.5109 | −1.47270 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.07069 | 0.0669358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.8810 | −0.835741 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.1726 | 1.19912 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.48858 | 0.144643 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.8702 | −1.02594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6002 | 0.951877 | 0.475938 | − | 0.879479i | \(-0.342109\pi\) | ||||
0.475938 | + | 0.879479i | \(0.342109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.85086 | −0.155832 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.8525 | 1.72821 | 0.864105 | − | 0.503312i | \(-0.167885\pi\) | ||||
0.864105 | + | 0.503312i | \(0.167885\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4663 | 0.592004 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.55065 | −0.241567 | −0.120783 | − | 0.992679i | \(-0.538541\pi\) | ||||
−0.120783 | + | 0.992679i | \(0.538541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.202374 | 0.00646791 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.1347 | 0.547068 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.7375 | 0.916583 | 0.458292 | − | 0.888802i | \(-0.348462\pi\) | ||||
0.458292 | + | 0.888802i | \(0.348462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.5036 | −0.812614 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.2881 | −0.327475 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.4426 | 0.650038 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.4368 | −1.82454 | −0.912270 | − | 0.409589i | \(-0.865672\pi\) | ||||
−0.912270 | + | 0.409589i | \(0.865672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.74333 | 0.0870570 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.5652 | −1.44452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5633 | 0.777928 | 0.388964 | − | 0.921253i | \(-0.372833\pi\) | ||||
0.388964 | + | 0.921253i | \(0.372833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.41789 | −0.0448602 |
(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 | 4056.2.a.ba.1.3 | yes | 3 | |
4.3 | odd | 2 | 8112.2.a.cn.1.3 | 3 | |||
13.5 | odd | 4 | 4056.2.c.n.337.1 | 6 | |||
13.8 | odd | 4 | 4056.2.c.n.337.6 | 6 | |||
13.12 | even | 2 | 4056.2.a.x.1.1 | ✓ | 3 | ||
52.51 | odd | 2 | 8112.2.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.x.1.1 | ✓ | 3 | 13.12 | even | 2 | ||
4056.2.a.ba.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
4056.2.c.n.337.1 | 6 | 13.5 | odd | 4 | |||
4056.2.c.n.337.6 | 6 | 13.8 | odd | 4 | |||
8112.2.a.ci.1.1 | 3 | 52.51 | odd | 2 | |||
8112.2.a.cn.1.3 | 3 | 4.3 | odd | 2 |