Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1569,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.l (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} + 11x^{8} + 22x^{6} + 99x^{4} + 243x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.6 | ||
Root | \(0.517456 + 1.65295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1569 |
Dual form | 2240.2.l.a.1569.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.03491 | −0.597506 | −0.298753 | − | 0.954330i | \(-0.596571\pi\) | ||||
−0.298753 | + | 0.954330i | \(0.596571\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.188470 | + | 2.22811i | −0.0842861 | + | 0.996442i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.92896 | −0.642986 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.68284i | − | 1.11042i | −0.831711 | − | 0.555209i | \(-0.812638\pi\) | ||
0.831711 | − | 0.555209i | \(-0.187362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.30590 | 1.47159 | 0.735796 | − | 0.677204i | \(-0.236808\pi\) | ||||
0.735796 | + | 0.677204i | \(0.236808\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.195049 | − | 2.30590i | 0.0503615 | − | 0.595380i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.49113i | 1.33180i | 0.746043 | + | 0.665898i | \(0.231951\pi\) | ||||
−0.746043 | + | 0.665898i | \(0.768049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.62306i | 0.372356i | 0.982516 | + | 0.186178i | \(0.0596101\pi\) | ||||
−0.982516 | + | 0.186178i | \(0.940390\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.03491i | 0.225836i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.24612i | − | 0.259834i | −0.991525 | − | 0.129917i | \(-0.958529\pi\) | ||
0.991525 | − | 0.129917i | \(-0.0414711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92896 | − | 0.839862i | −0.985792 | − | 0.167972i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.10104 | 0.981695 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.17086i | − | 1.33159i | −0.746133 | − | 0.665797i | \(-0.768091\pi\) | ||
0.746133 | − | 0.665797i | \(-0.231909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06982 | −0.371751 | −0.185876 | − | 0.982573i | \(-0.559512\pi\) | ||||
−0.185876 | + | 0.982573i | \(0.559512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.81141i | 0.663481i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.22811 | + | 0.188470i | 0.376620 | + | 0.0318572i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.85792 | −0.963036 | −0.481518 | − | 0.876436i | \(-0.659914\pi\) | ||||
−0.481518 | + | 0.876436i | \(0.659914\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.49113 | −0.879285 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5922 | 1.61529 | 0.807645 | − | 0.589669i | \(-0.200742\pi\) | ||||
0.807645 | + | 0.589669i | \(0.200742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.363550 | − | 4.29793i | 0.0541948 | − | 0.640698i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.928958i | 0.135503i | 0.997702 | + | 0.0677513i | \(0.0215824\pi\) | ||||
−0.997702 | + | 0.0677513i | \(0.978418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 5.68284i | − | 0.795756i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.61180 | 0.908200 | 0.454100 | − | 0.890951i | \(-0.349961\pi\) | ||||
0.454100 | + | 0.890951i | \(0.349961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.20577 | + | 0.694102i | 1.10647 | + | 0.0935928i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.67972i | − | 0.222485i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.23486i | − | 0.551331i | −0.961254 | − | 0.275666i | \(-0.911102\pi\) | ||
0.961254 | − | 0.275666i | \(-0.0888983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.59587i | 1.10059i | 0.834971 | + | 0.550294i | \(0.185484\pi\) | ||||
−0.834971 | + | 0.550294i | \(0.814516\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.92896i | 0.243026i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 11.8221i | −0.124035 | + | 1.46635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.30254 | 1.13649 | 0.568243 | − | 0.822861i | \(-0.307623\pi\) | ||||
0.568243 | + | 0.822861i | \(0.307623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.28963i | 0.155253i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.74955 | −0.444989 | −0.222495 | − | 0.974934i | \(-0.571420\pi\) | ||||
−0.222495 | + | 0.974934i | \(0.571420\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5922i | 1.23972i | 0.784713 | + | 0.619860i | \(0.212811\pi\) | ||||
−0.784713 | + | 0.619860i | \(0.787189\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.10104 | + | 0.869183i | 0.589017 | + | 0.100365i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.68284 | −0.419698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.63078 | 1.08355 | 0.541774 | − | 0.840524i | \(-0.317753\pi\) | ||||
0.541774 | + | 0.840524i | \(0.317753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.507756 | 0.0564174 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.84632 | 0.531953 | 0.265976 | − | 0.963980i | \(-0.414306\pi\) | ||||
0.265976 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.2349 | − | 1.03491i | −1.32706 | − | 0.112252i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.42120i | 0.795636i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6118 | 1.33685 | 0.668424 | − | 0.743781i | \(-0.266969\pi\) | ||||
0.668424 | + | 0.743781i | \(0.266969\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.30590i | − | 0.556209i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.14208 | 0.222124 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.61636 | − | 0.305898i | −0.371031 | − | 0.0313844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3338i | 1.25230i | 0.779701 | + | 0.626152i | \(0.215371\pi\) | ||||
−0.779701 | + | 0.626152i | \(0.784629\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.10404i | 0.713983i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.316577i | − | 0.0315006i | −0.999876 | − | 0.0157503i | \(-0.994986\pi\) | ||
0.999876 | − | 0.0157503i | \(-0.00501368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.31716i | − | 0.228317i | −0.993463 | − | 0.114158i | \(-0.963583\pi\) | ||
0.993463 | − | 0.114158i | \(-0.0364172\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.30590 | − | 0.195049i | −0.225033 | − | 0.0190349i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.81937 | −0.562580 | −0.281290 | − | 0.959623i | \(-0.590762\pi\) | ||||
−0.281290 | + | 0.959623i | \(0.590762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0135i | 1.34225i | 0.741345 | + | 0.671124i | \(0.234188\pi\) | ||||
−0.741345 | + | 0.671124i | \(0.765812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.06242 | 0.575420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.52235i | 0.801715i | 0.916140 | + | 0.400857i | \(0.131288\pi\) | ||||
−0.916140 | + | 0.400857i | \(0.868712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.77650 | + | 0.234856i | 0.258910 | + | 0.0219004i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.2349 | −0.946213 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.49113 | 0.503371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56329 | −0.233026 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.06982 | −0.186630 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.80026 | − | 10.8240i | 0.250463 | − | 0.968126i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9775i | 1.77271i | 0.463003 | + | 0.886357i | \(0.346772\pi\) | ||||
−0.463003 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.9620 | −0.965146 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.4584i | 1.87483i | 0.348210 | + | 0.937417i | \(0.386790\pi\) | ||||
−0.348210 | + | 0.937417i | \(0.613210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.62306 | 0.140737 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.961390 | + | 11.3657i | −0.0827432 | + | 0.978201i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.35945i | 0.287017i | 0.989649 | + | 0.143509i | \(0.0458384\pi\) | ||||
−0.989649 | + | 0.143509i | \(0.954162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.72710i | 0.570585i | 0.958440 | + | 0.285293i | \(0.0920908\pi\) | ||||
−0.958440 | + | 0.285293i | \(0.907909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.961390i | − | 0.0809636i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 19.5408i | − | 1.63408i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.9775 | + | 1.35149i | 1.32686 | + | 0.112235i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.03491 | 0.0853581 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 3.35945i | − | 0.275217i | −0.990487 | − | 0.137608i | \(-0.956058\pi\) | ||
0.990487 | − | 0.137608i | \(-0.0439415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8635 | −1.37233 | −0.686166 | − | 0.727445i | \(-0.740708\pi\) | ||||
−0.686166 | + | 0.727445i | \(0.740708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.5922i | − | 0.856326i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.390099 | − | 4.61180i | 0.0313335 | − | 0.370428i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.60053 | 0.446971 | 0.223485 | − | 0.974707i | \(-0.428256\pi\) | ||||
0.223485 | + | 0.974707i | \(0.428256\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.84262 | −0.542655 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.24612 | −0.0982082 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.3546 | 1.75095 | 0.875475 | − | 0.483263i | \(-0.160549\pi\) | ||||
0.875475 | + | 0.483263i | \(0.160549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.49224 | − | 0.718335i | −0.661120 | − | 0.0559223i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.7643i | − | 1.60679i | −0.595444 | − | 0.803397i | \(-0.703024\pi\) | ||
0.595444 | − | 0.803397i | \(-0.296976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.1525 | 1.16558 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.13082i | − | 0.239420i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6941 | 0.813058 | 0.406529 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406529 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.839862 | + | 4.92896i | −0.0634876 | + | 0.372594i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.38270i | 0.329424i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.63433i | − | 0.495873i | −0.968776 | − | 0.247936i | \(-0.920248\pi\) | ||
0.968776 | − | 0.247936i | \(-0.0797524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.0790i | − | 0.897828i | −0.893575 | − | 0.448914i | \(-0.851811\pi\) | ||
0.893575 | − | 0.448914i | \(-0.148189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.89596i | − | 0.657608i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.10404 | − | 13.0521i | 0.0811705 | − | 0.959609i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.2229 | 1.47885 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 5.10104i | − | 0.371046i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9902 | −0.939940 | −0.469970 | − | 0.882682i | \(-0.655735\pi\) | ||||
−0.469970 | + | 0.882682i | \(0.655735\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.5046i | 1.40397i | 0.712190 | + | 0.701986i | \(0.247703\pi\) | ||||
−0.712190 | + | 0.701986i | \(0.752297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.03491 | − | 12.2349i | 0.0741115 | − | 0.876156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1040 | 1.21861 | 0.609306 | − | 0.792935i | \(-0.291448\pi\) | ||||
0.609306 | + | 0.792935i | \(0.291448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.84262 | 0.485061 | 0.242530 | − | 0.970144i | \(-0.422023\pi\) | ||||
0.242530 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.62731 | −0.679058 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.17086 | −0.503296 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.376939 | + | 4.45622i | −0.0263266 | + | 0.311236i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.40372i | 0.167070i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.97747 | 0.413470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2946i | 0.708712i | 0.935111 | + | 0.354356i | \(0.115300\pi\) | ||||
−0.935111 | + | 0.354356i | \(0.884700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.88045 | 0.265884 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.99630 | + | 23.6005i | −0.136147 | + | 1.60954i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.06982i | 0.140509i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 10.9620i | − | 0.740740i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.1354i | 1.95986i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.4142i | − | 1.63489i | −0.576003 | − | 0.817447i | \(-0.695389\pi\) | ||
0.576003 | − | 0.817447i | \(-0.304611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.50776 | + | 1.62006i | 0.633850 | + | 0.108004i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1568 | 1.07237 | 0.536183 | − | 0.844102i | \(-0.319866\pi\) | ||||
0.536183 | + | 0.844102i | \(0.319866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.973049i | − | 0.0643009i | −0.999483 | − | 0.0321504i | \(-0.989764\pi\) | ||
0.999483 | − | 0.0321504i | \(-0.0102356\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81141 | 0.250772 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.8249i | − | 1.16775i | −0.811845 | − | 0.583874i | \(-0.801536\pi\) | ||
0.811845 | − | 0.583874i | \(-0.198464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.06982 | − | 0.175080i | −0.135020 | − | 0.0114210i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.96700 | −0.647426 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0031 | 1.35858 | 0.679290 | − | 0.733870i | \(-0.262288\pi\) | ||||
0.679290 | + | 0.733870i | \(0.262288\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9775 | 0.771537 | 0.385768 | − | 0.922596i | \(-0.373936\pi\) | ||||
0.385768 | + | 0.922596i | \(0.373936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8286 | −1.01540 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.188470 | − | 2.22811i | 0.0120409 | − | 0.142349i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.61180i | 0.547955i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.01551 | −0.317845 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9887i | 1.32480i | 0.749152 | + | 0.662399i | \(0.230461\pi\) | ||||
−0.749152 | + | 0.662399i | \(0.769539\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.58926 | −0.288525 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6620 | + | 1.07104i | 0.792925 | + | 0.0670712i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.45992i | 0.153446i | 0.997052 | + | 0.0767228i | \(0.0244457\pi\) | ||||
−0.997052 | + | 0.0767228i | \(0.975554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.85792i | 0.363993i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8323i | 0.856197i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 27.7158i | − | 1.70903i | −0.519425 | − | 0.854516i | \(-0.673854\pi\) | ||
0.519425 | − | 0.854516i | \(-0.326146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.24612 | + | 14.7318i | −0.0765487 | + | 0.904968i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.0521 | −0.798775 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 16.2187i | − | 0.988871i | −0.869214 | − | 0.494435i | \(-0.835375\pi\) | ||
0.869214 | − | 0.494435i | \(-0.164625\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3240 | −1.53832 | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||||
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.49113i | 0.332339i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.09307 | + | 18.1525i | −0.186519 | + | 1.09464i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.3431 | 1.04205 | 0.521024 | − | 0.853542i | \(-0.325550\pi\) | ||||
0.521024 | + | 0.853542i | \(0.325550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.99260 | 0.239031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6603 | −1.29215 | −0.646073 | − | 0.763276i | \(-0.723590\pi\) | ||||
−0.646073 | + | 0.763276i | \(0.723590\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.10473 | −0.184557 | −0.0922786 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922786 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.74261 | + | 0.316577i | 0.221693 | + | 0.0187524i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.00000i | − | 0.118056i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1525 | −0.773679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 12.7643i | − | 0.748259i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6335 | 1.61437 | 0.807184 | − | 0.590300i | \(-0.200991\pi\) | ||||
0.807184 | + | 0.590300i | \(0.200991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.43573 | + | 0.798141i | 0.549369 | + | 0.0464696i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 18.7863i | − | 1.09009i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6.61180i | − | 0.382370i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.5922i | − | 0.610522i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.327629i | 0.0188218i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.1525 | − | 1.62006i | −1.09667 | − | 0.0927643i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4287 | −1.62251 | −0.811256 | − | 0.584691i | \(-0.801216\pi\) | ||||
−0.811256 | + | 0.584691i | \(0.801216\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.39806i | 0.136421i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0968 | 1.70663 | 0.853316 | − | 0.521394i | \(-0.174588\pi\) | ||||
0.853316 | + | 0.521394i | \(0.174588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.56096i | − | 0.427371i | −0.976903 | − | 0.213685i | \(-0.931453\pi\) | ||
0.976903 | − | 0.213685i | \(-0.0685467\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.29793 | − | 0.363550i | −0.242161 | − | 0.0204837i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7539 | −0.940992 | −0.470496 | − | 0.882402i | \(-0.655925\pi\) | ||||
−0.470496 | + | 0.882402i | \(0.655925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.4091 | −1.47863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.02253 | 0.336145 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.91244 | −0.495902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.1525 | − | 4.45622i | −1.45068 | − | 0.247187i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 14.5027i | − | 0.802002i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.928958 | 0.0512151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.1196i | − | 1.21580i | −0.794013 | − | 0.607900i | \(-0.792012\pi\) | ||
0.794013 | − | 0.607900i | \(-0.207988\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.2997 | 0.619219 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.75325 | + | 20.7271i | −0.0957901 | + | 1.13244i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.52235i | 0.464242i | 0.972687 | + | 0.232121i | \(0.0745665\pi\) | ||||
−0.972687 | + | 0.232121i | \(0.925434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.81987i | − | 0.479030i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.62282i | 0.412799i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.87343 | − | 0.243055i | −0.154700 | − | 0.0130856i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0753 | −0.755604 | −0.377802 | − | 0.925886i | \(-0.623320\pi\) | ||||
−0.377802 | + | 0.925886i | \(0.623320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 26.4208i | − | 1.41427i | −0.707078 | − | 0.707135i | \(-0.749987\pi\) | ||
0.707078 | − | 0.707135i | \(-0.250013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0656 | 1.44465 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.9204i | − | 0.581234i | −0.956839 | − | 0.290617i | \(-0.906139\pi\) | ||
0.956839 | − | 0.290617i | \(-0.0938606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.706675 | − | 8.35441i | 0.0375064 | − | 0.443406i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.68284 | −0.300768 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.3063 | −1.91617 | −0.958085 | − | 0.286483i | \(-0.907514\pi\) | ||||
−0.958085 | + | 0.286483i | \(0.907514\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.3657 | 0.861351 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.65277 | 0.139234 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.6005 | − | 1.99630i | −1.23531 | − | 0.104491i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.8249i | 0.617256i | 0.951183 | + | 0.308628i | \(0.0998698\pi\) | ||||
−0.951183 | + | 0.308628i | \(0.900130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.85792 | −0.200835 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 6.61180i | − | 0.343267i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.7384 | 0.711346 | 0.355673 | − | 0.934611i | \(-0.384252\pi\) | ||||
0.355673 | + | 0.934611i | \(0.384252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.89803 | + | 11.2019i | −0.149653 | + | 0.578461i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 38.0478i | − | 1.95956i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10404i | 0.159444i | 0.996817 | + | 0.0797219i | \(0.0254032\pi\) | ||||
−0.996817 | + | 0.0797219i | \(0.974597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 20.6749i | − | 1.05921i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.73135i | 0.139565i | 0.997562 | + | 0.0697826i | \(0.0222306\pi\) | ||||
−0.997562 | + | 0.0697826i | \(0.977769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.694102 | − | 8.20577i | 0.0353747 | − | 0.418205i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.4319 | −1.03861 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.7165i | 0.847558i | 0.905766 | + | 0.423779i | \(0.139297\pi\) | ||||
−0.905766 | + | 0.423779i | \(0.860703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.84262 | 0.346046 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 22.2076i | − | 1.12022i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.81511 | + | 21.4584i | −0.0913280 | + | 1.07969i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.2679 | −1.61948 | −0.809739 | − | 0.586791i | \(-0.800391\pi\) | ||||
−0.809739 | + | 0.586791i | \(0.800391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.67972 | −0.0840914 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1525 | 0.706745 | 0.353372 | − | 0.935483i | \(-0.385035\pi\) | ||||
0.353372 | + | 0.935483i | \(0.385035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9823 | −0.547066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.0956966 | + | 1.13134i | −0.00475520 | + | 0.0562166i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.5738i | 1.06937i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3051 | −1.49849 | −0.749245 | − | 0.662293i | \(-0.769584\pi\) | ||||
−0.749245 | + | 0.662293i | \(0.769584\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.47673i | − | 0.171495i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.23486 | −0.208384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.913384 | + | 10.7981i | −0.0448362 | + | 0.530060i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.96195i | − | 0.340928i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 23.4810i | − | 1.14712i | −0.819163 | − | 0.573560i | \(-0.805562\pi\) | ||
0.819163 | − | 0.573560i | \(-0.194438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.74159i | − | 0.0848797i | −0.999099 | − | 0.0424399i | \(-0.986487\pi\) | ||
0.999099 | − | 0.0424399i | \(-0.0135131\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.79192i | − | 0.0871262i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.61180 | − | 27.0656i | 0.223705 | − | 1.31287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.59587 | 0.415983 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.2229i | 0.976373i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.5487 | −1.47148 | −0.735741 | − | 0.677263i | \(-0.763166\pi\) | ||||
−0.735741 | + | 0.677263i | \(0.763166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.7318i | 0.707966i | 0.935252 | + | 0.353983i | \(0.115173\pi\) | ||||
−0.935252 | + | 0.353983i | \(0.884827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.5353 | − | 1.39867i | −0.792805 | − | 0.0670611i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.02253 | 0.0967508 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.28963 | −0.0615505 | −0.0307752 | − | 0.999526i | \(-0.509798\pi\) | ||||
−0.0307752 | + | 0.999526i | \(0.509798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.92896 | 0.0918552 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0055 | −0.570399 | −0.285200 | − | 0.958468i | \(-0.592060\pi\) | ||||
−0.285200 | + | 0.958468i | \(0.592060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.37694 | + | 28.1005i | −0.112678 | + | 1.33209i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.47673i | 0.164444i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.57880 | −0.121701 | −0.0608505 | − | 0.998147i | \(-0.519381\pi\) | ||||
−0.0608505 | + | 0.998147i | \(0.519381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.36567i | − | 0.346836i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.4522 | 0.819977 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.8221 | + | 1.00000i | 0.554230 | + | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.0809i | − | 1.17324i | −0.809864 | − | 0.586618i | \(-0.800459\pi\) | ||
0.809864 | − | 0.586618i | \(-0.199541\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.0105i | 1.30742i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13.3687i | − | 0.622641i | −0.950305 | − | 0.311320i | \(-0.899229\pi\) | ||
0.950305 | − | 0.311320i | \(-0.100771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.7158i | − | 1.65986i | −0.557871 | − | 0.829928i | \(-0.688382\pi\) | ||
0.557871 | − | 0.829928i | \(-0.311618\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.403717 | + | 4.77280i | −0.0187219 | + | 0.221333i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.5628 | −0.997806 | −0.498903 | − | 0.866658i | \(-0.666264\pi\) | ||||
−0.498903 | + | 0.866658i | \(0.666264\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.30254i | − | 0.429552i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.79605 | −0.267068 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 39.0092i | − | 1.79365i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.36315 | − | 8.00000i | 0.0625455 | − | 0.367065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.7539 | −0.583960 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.5335 | 1.44080 | 0.720400 | − | 0.693559i | \(-0.243958\pi\) | ||||
0.720400 | + | 0.693559i | \(0.243958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0815 | −1.41719 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.28963 | 0.0586800 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.4810 | − | 2.32454i | −1.24785 | − | 0.105552i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.9775i | 1.26778i | 0.773423 | + | 0.633890i | \(0.218543\pi\) | ||||
−0.773423 | + | 0.633890i | \(0.781457\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.1351 | −1.04620 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 31.6293i | − | 1.42741i | −0.700447 | − | 0.713705i | \(-0.747016\pi\) | ||
0.700447 | − | 0.713705i | \(-0.252984\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.3761 | 1.77341 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.8286 | − | 1.33889i | −0.711442 | − | 0.0601788i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.74955i | 0.168190i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.2946i | 1.17711i | 0.808457 | + | 0.588555i | \(0.200303\pi\) | ||||
−0.808457 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4893i | 0.960069i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.29463i | 0.191488i | 0.995406 | + | 0.0957441i | \(0.0305230\pi\) | ||||
−0.995406 | + | 0.0957441i | \(0.969477\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.705368 | + | 0.0596651i | 0.0313885 | + | 0.00265506i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.6815 | −0.696442 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.7625i | 1.80676i | 0.428836 | + | 0.903382i | \(0.358924\pi\) | ||||
−0.428836 | + | 0.903382i | \(0.641076\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5922 | 0.468570 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.27929i | 0.365540i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.16290 | + | 0.436715i | 0.227504 | + | 0.0192439i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.42120 | 0.150464 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.0674 | −0.485807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0660 | 1.31722 | 0.658608 | − | 0.752487i | \(-0.271146\pi\) | ||||
0.658608 | + | 0.752487i | \(0.271146\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.65277 | −0.115998 | −0.0579988 | − | 0.998317i | \(-0.518472\pi\) | ||||
−0.0579988 | + | 0.998317i | \(0.518472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.869183 | − | 5.10104i | 0.0379342 | − | 0.222627i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.3657i | − | 0.495096i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4472 | 0.932486 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.16886i | 0.354498i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6118 | 0.459648 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.09677 | − | 12.9662i | 0.0474177 | − | 0.560578i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.86594i | 0.296287i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.68284i | 0.158631i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.10104i | 0.219311i | 0.993970 | + | 0.109655i | \(0.0349747\pi\) | ||||
−0.993970 | + | 0.109655i | \(0.965025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.5007i | 0.536458i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.2236 | − | 2.64111i | −1.33747 | − | 0.113133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4171 | 1.21503 | 0.607513 | − | 0.794310i | \(-0.292167\pi\) | ||||
0.607513 | + | 0.794310i | \(0.292167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 16.5811i | − | 0.707663i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.6387 | 0.495827 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.63078i | − | 0.409542i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.14258 | + | 13.5078i | −0.0484999 | + | 0.573372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4542 | −0.739558 | −0.369779 | − | 0.929120i | \(-0.620567\pi\) | ||||
−0.369779 | + | 0.929120i | \(0.620567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56.2010 | 2.37705 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.9290 | −0.883621 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7233 | −1.50556 | −0.752779 | − | 0.658274i | \(-0.771287\pi\) | ||||
−0.752779 | + | 0.658274i | \(0.771287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.9887 | − | 1.60620i | −0.798862 | − | 0.0675734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.507756i | − | 0.0213238i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.8579 | 0.748643 | 0.374321 | − | 0.927299i | \(-0.377876\pi\) | ||||
0.374321 | + | 0.927299i | \(0.377876\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8199i | 1.12238i | 0.827688 | + | 0.561188i | \(0.189656\pi\) | ||||
−0.827688 | + | 0.561188i | \(0.810344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4437 | 0.561620 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.04657 | + | 6.14208i | −0.0436450 | + | 0.256143i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.3840i | 1.68121i | 0.541649 | + | 0.840605i | \(0.317800\pi\) | ||||
−0.541649 | + | 0.840605i | \(0.682200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 20.1855i | − | 0.838883i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.84632i | − | 0.201059i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.3502i | − | 1.00848i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.92896 | − | 22.8044i | 0.0797526 | − | 0.942846i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.706675 | 0.0291676 | 0.0145838 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145838 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.35945i | − | 0.138424i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7012 | −0.728129 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.1402i | 0.416408i | 0.978085 | + | 0.208204i | \(0.0667619\pi\) | ||||
−0.978085 | + | 0.208204i | \(0.933238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03491 | + | 12.2349i | −0.0424272 | + | 0.501580i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.08151 | −0.289827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.2359 | −1.15369 | −0.576843 | − | 0.816855i | \(-0.695716\pi\) | ||||
−0.576843 | + | 0.816855i | \(0.695716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6118 | 1.00394 | 0.501968 | − | 0.864886i | \(-0.332610\pi\) | ||||
0.501968 | + | 0.864886i | \(0.332610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.9442 | −0.730745 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.483101 | − | 5.71128i | 0.0196409 | − | 0.232197i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9064i | 0.605033i | 0.953144 | + | 0.302517i | \(0.0978268\pi\) | ||||
−0.953144 | + | 0.302517i | \(0.902173\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.42120 | 0.300722 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.92896i | 0.199404i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.7313 | 0.918110 | 0.459055 | − | 0.888408i | \(-0.348188\pi\) | ||||
0.459055 | + | 0.888408i | \(0.348188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.390099 | − | 4.61180i | 0.0157303 | − | 0.185966i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.0473i | − | 1.29017i | −0.764109 | − | 0.645087i | \(-0.776821\pi\) | ||
0.764109 | − | 0.645087i | \(-0.223179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.21934i | − | 0.370557i | −0.982686 | − | 0.185278i | \(-0.940681\pi\) | ||
0.982686 | − | 0.185278i | \(-0.0593187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 6.35651i | − | 0.255078i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12.6118i | − | 0.505281i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.5893 | + | 8.27929i | 0.943571 | + | 0.331172i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.18615 | −0.247051 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 32.1666i | − | 1.28257i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5536 | −0.459940 | −0.229970 | − | 0.973198i | \(-0.573863\pi\) | ||||
−0.229970 | + | 0.973198i | \(0.573863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.6540i | − | 0.423460i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −44.5120 | − | 3.76514i | −1.76641 | − | 0.149415i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.30590 | −0.210227 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.23272 | 0.286122 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.8579 | 0.863336 | 0.431668 | − | 0.902033i | \(-0.357925\pi\) | ||||
0.431668 | + | 0.902033i | \(0.357925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.58791 | 0.259802 | 0.129901 | − | 0.991527i | \(-0.458534\pi\) | ||||
0.129901 | + | 0.991527i | \(0.458534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.06599 | − | 24.4245i | 0.0813485 | − | 0.961712i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 12.7539i | − | 0.501407i | −0.968064 | − | 0.250703i | \(-0.919338\pi\) | ||
0.968064 | − | 0.250703i | \(-0.0806619\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.5963 | −0.612208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 2.14208i | − | 0.0839549i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.4627 | 1.46603 | 0.733014 | − | 0.680213i | \(-0.238113\pi\) | ||||
0.733014 | + | 0.680213i | \(0.238113\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.8118 | − | 4.04426i | −1.86816 | − | 0.158022i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 20.4319i | − | 0.797123i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.19059i | 0.0463789i | 0.999731 | + | 0.0231895i | \(0.00738209\pi\) | ||||
−0.999731 | + | 0.0231895i | \(0.992618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.2272i | − | 0.942329i | −0.882045 | − | 0.471165i | \(-0.843834\pi\) | ||
0.882045 | − | 0.471165i | \(-0.156166\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 30.1525i | − | 1.17103i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.305898 | + | 3.61636i | −0.0118622 | + | 0.140236i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.93576 | −0.345994 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.2665i | 0.976860i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.6572 | 1.22211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.8585i | − | 0.418566i | −0.977855 | − | 0.209283i | \(-0.932887\pi\) | ||
0.977855 | − | 0.209283i | \(-0.0671130\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.1428 | − | 4.28417i | −0.967746 | − | 0.164898i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5520 | 1.09734 | 0.548672 | − | 0.836038i | \(-0.315134\pi\) | ||||
0.548672 | + | 0.836038i | \(0.315134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.3338 | 0.473326 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.7209 | −0.640746 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.45992 | 0.0941263 | 0.0470631 | − | 0.998892i | \(-0.485014\pi\) | ||||
0.0470631 | + | 0.998892i | \(0.485014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.48522 | − | 0.633154i | −0.285996 | − | 0.0241916i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00702i | 0.0384202i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.0815 | 1.33650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.9072i | − | 0.529056i | −0.964378 | − | 0.264528i | \(-0.914784\pi\) | ||
0.964378 | − | 0.264528i | \(-0.0852161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.10404 | 0.269860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.9887 | − | 1.26785i | −0.568555 | − | 0.0480924i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9823i | 0.415983i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.4472i | 0.697736i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 43.4771i | − | 1.64211i | −0.570851 | − | 0.821054i | \(-0.693387\pi\) | ||
0.570851 | − | 0.821054i | \(-0.306613\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.50776i | − | 0.358592i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.14208 | + | 0.181193i | 0.0806755 | + | 0.00682411i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.316577 | −0.0119061 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3729i | 0.652454i | 0.945291 | + | 0.326227i | \(0.105777\pi\) | ||||
−0.945291 | + | 0.326227i | \(0.894223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.5774 | −0.696706 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.57925i | 0.0965937i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.5390 | + | 3.68284i | 1.62827 | + | 0.137730i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.7364 | −0.811760 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.5800 | −1.25232 | −0.626161 | − | 0.779694i | \(-0.715375\pi\) | ||||
−0.626161 | + | 0.779694i | \(0.715375\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.31716 | −0.0862957 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.3956 | −0.460998 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.02253 | + | 35.3449i | −0.223671 | + | 1.31268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6933i | 0.952912i | 0.879198 | + | 0.476456i | \(0.158079\pi\) | ||||
−0.879198 | + | 0.476456i | \(0.841921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.8579 | 0.550293 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.1630i | 2.15124i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1483 | 1.03968 | 0.519841 | − | 0.854263i | \(-0.325991\pi\) | ||||
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.195049 | + | 2.30590i | −0.00719450 | + | 0.0850543i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 34.2597i | − | 1.26197i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.840432i | − | 0.0309158i | −0.999881 | − | 0.0154579i | \(-0.995079\pi\) | ||
0.999881 | − | 0.0154579i | \(-0.00492060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 8.91244i | − | 0.327407i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.24612i | 0.339207i | 0.985512 | + | 0.169604i | \(0.0542488\pi\) | ||||
−0.985512 | + | 0.169604i | \(0.945751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.48522 | + | 0.633154i | 0.274237 | + | 0.0231970i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.34835 | −0.342038 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.81937i | 0.212635i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.5469 | 1.66203 | 0.831016 | − | 0.556249i | \(-0.187760\pi\) | ||||
0.831016 | + | 0.556249i | \(0.187760\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.7215i | − | 0.791575i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.17826 | − | 37.5738i | 0.115669 | − | 1.36745i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.23910 | 0.154073 | 0.0770364 | − | 0.997028i | \(-0.475454\pi\) | ||||
0.0770364 | + | 0.997028i | \(0.475454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.74948 | 0.172395 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.2236 | −1.13185 | −0.565927 | − | 0.824455i | \(-0.691482\pi\) | ||||
−0.565927 | + | 0.824455i | \(0.691482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0135 | 0.507322 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.6005 | + | 1.99630i | 0.853279 | + | 0.0721764i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.4697i | − | 0.811334i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3587 | 0.806274 | 0.403137 | − | 0.915140i | \(-0.367920\pi\) | ||||
0.403137 | + | 0.915140i | \(0.367920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.54580i | − | 0.0916848i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.0147 | −0.935684 | −0.467842 | − | 0.883812i | \(-0.654968\pi\) | ||||
−0.467842 | + | 0.883812i | \(0.654968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2021 | + | 1.73837i | 0.366469 | + | 0.0624439i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.06242i | − | 0.217488i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.24612i | 0.116304i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8090i | 0.494124i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 36.5788i | − | 1.30722i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.05553 | + | 12.4786i | −0.0376734 | + | 0.445380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2266 | 0.649710 | 0.324855 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324855 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.6834i | 1.02116i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.52235 | 0.303020 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.6088i | 1.61962i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.28963 | − | 15.2461i | 0.0457383 | − | 0.540724i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.9612 | −1.48634 | −0.743170 | − | 0.669102i | \(-0.766679\pi\) | ||||
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.10104 | −0.180462 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.3276 | −0.859575 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.0092 | 1.37661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.234856 | − | 2.77650i | 0.00827759 | − | 0.0978587i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.7849i | 0.590857i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.2946 | −0.994786 | −0.497393 | − | 0.867525i | \(-0.665709\pi\) | ||||
−0.497393 | + | 0.867525i | \(0.665709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.9732i | 1.33342i | 0.745317 | + | 0.666710i | \(0.232298\pi\) | ||||
−0.745317 | + | 0.666710i | \(0.767702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.2081 | 0.919157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.21317 | + | 49.8086i | −0.147581 | + | 1.74472i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.1917i | 0.601463i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.2349i | 0.357635i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 7.31790i | − | 0.255397i | −0.991813 | − | 0.127698i | \(-0.959241\pi\) | ||
0.991813 | − | 0.127698i | \(-0.0407589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.0815i | − | 1.36230i | −0.732146 | − | 0.681148i | \(-0.761481\pi\) | ||
0.732146 | − | 0.681148i | \(-0.238519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.20106 | − | 18.7863i | 0.111447 | − | 0.654054i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.1256 | −1.46485 | −0.732426 | − | 0.680847i | \(-0.761612\pi\) | ||||
−0.732426 | + | 0.680847i | \(0.761612\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.3583i | − | 0.707074i | −0.935421 | − | 0.353537i | \(-0.884979\pi\) | ||
0.935421 | − | 0.353537i | \(-0.115021\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.9486 | −0.622631 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.49113i | − | 0.190257i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.2653 | + | 3.91345i | 1.60108 | + | 0.135430i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.5582 | −0.364946 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7625 | 0.406085 | 0.203043 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203043 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4212 | −0.773145 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.4165 | 0.772065 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.85579 | + | 33.7616i | −0.0982423 | + | 1.16143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56329i | 0.0880755i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.21312 | 0.110274 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.29968i | 0.250230i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7861 | −1.29377 | −0.646885 | − | 0.762587i | \(-0.723929\pi\) | ||||
−0.646885 | + | 0.762587i | \(0.723929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.97581 | + | 0.590064i | 0.238568 | + | 0.0201798i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.37976i | 0.252088i | 0.992025 | + | 0.126044i | \(0.0402280\pi\) | ||||
−0.992025 | + | 0.126044i | \(0.959772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.37694i | − | 0.217578i | −0.994065 | − | 0.108789i | \(-0.965303\pi\) | ||
0.994065 | − | 0.108789i | \(-0.0346973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.06982i | 0.0705394i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.41074i | 0.252264i | 0.992013 | + | 0.126132i | \(0.0402564\pi\) | ||||
−0.992013 | + | 0.126132i | \(0.959744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.01551 | + | 23.8276i | −0.0685295 | + | 0.810164i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.6117 | 0.462278 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 35.4686i | − | 1.20319i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.3583 | 1.67244 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 23.7913i | − | 0.805214i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8240 | − | 2.80026i | −0.365917 | − | 0.0946662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.9549 | 0.538760 | 0.269380 | − | 0.963034i | \(-0.413181\pi\) | ||||
0.269380 | + | 0.963034i | \(0.413181\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.5983 | −0.964595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.1421 | 0.543841 | 0.271920 | − | 0.962320i | \(-0.412341\pi\) | ||||
0.271920 | + | 0.962320i | \(0.412341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.67972 | 0.0565272 | 0.0282636 | − | 0.999601i | \(-0.491002\pi\) | ||||
0.0282636 | + | 0.999601i | \(0.491002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.76514 | − | 0.826006i | −0.328252 | − | 0.0277659i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.9169i | 1.17239i | 0.810168 | + | 0.586197i | \(0.199376\pi\) | ||||
−0.810168 | + | 0.586197i | \(0.800624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.9775 | 0.670023 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.86998i | − | 0.0626468i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.50776 | −0.0504551 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7820 | + | 1.25037i | 0.494108 | + | 0.0417952i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.84262i | 0.228468i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.8424i | 0.495022i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.3063i | 1.20954i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.9620i | 0.364791i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.9134 | + | 2.27653i | 0.894633 | + | 0.0756745i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.8109 | 1.85317 | 0.926585 | − | 0.376086i | \(-0.122730\pi\) | ||||
0.926585 | + | 0.376086i | \(0.122730\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.610664i | 0.0202544i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.0270 | 0.928575 | 0.464287 | − | 0.885685i | \(-0.346311\pi\) | ||||
0.464287 | + | 0.885685i | \(0.346311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 17.8482i | − | 0.590689i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.8212 | + | 1.67662i | 0.655268 | + | 0.0554273i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4584 | 0.708620 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.7368 | −0.684043 | −0.342021 | − | 0.939692i | \(-0.611112\pi\) | ||||
−0.342021 | + | 0.939692i | \(0.611112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.4212 | 0.969462 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.8947 | −0.654842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8734 | + | 4.91984i | 0.949353 | + | 0.161763i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.46971i | 0.146805i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.97747 | −0.130496 | −0.0652482 | − | 0.997869i | \(-0.520784\pi\) | ||||
−0.0652482 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.62306i | − | 0.0531937i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.1475 | −1.01972 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.81141 | + | 45.0590i | −0.124646 | + | 1.47359i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7637i | 1.59304i | 0.604611 | + | 0.796521i | \(0.293329\pi\) | ||||
−0.604611 | + | 0.796521i | \(0.706671\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.82492i | 0.255357i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.87697i | − | 0.0611875i | −0.999532 | − | 0.0305938i | \(-0.990260\pi\) | ||
0.999532 | − | 0.0305938i | \(-0.00973981\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.49224i | − | 0.0811586i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.3657 | + | 0.961390i | 0.369725 | + | 0.0312740i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.1330 | −1.23916 | −0.619578 | − | 0.784935i | \(-0.712696\pi\) | ||||
−0.619578 | + | 0.784935i | \(0.712696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.2010i | 1.82436i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3388 | 0.562248 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.7252i | 1.57836i | 0.614160 | + | 0.789182i | \(0.289495\pi\) | ||||
−0.614160 | + | 0.789182i | \(0.710505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.44826 | − | 28.9437i | 0.0792239 | − | 0.936595i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.3311 | 0.883488 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.35945 | 0.108482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7158 | −0.861801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2253 | 0.361731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.4584 | − | 3.67603i | −1.39898 | − | 0.118335i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37.2671i | − | 1.19843i | −0.800589 | − | 0.599214i | \(-0.795480\pi\) | ||
0.800589 | − | 0.599214i | \(-0.204520\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.22359 | 0.296304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 60.3753i | − | 1.93754i | −0.247967 | − | 0.968768i | \(-0.579763\pi\) | ||
0.247967 | − | 0.968768i | \(-0.420237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.72710 | 0.215661 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.0656 | + | 4.61180i | 0.866792 | + | 0.147696i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.8231i | 1.05010i | 0.851070 | + | 0.525052i | \(0.175954\pi\) | ||||
−0.851070 | + | 0.525052i | \(0.824046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 46.4472i | − | 1.48446i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 27.0314i | − | 0.863047i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 14.5563i | − | 0.464273i | −0.972683 | − | 0.232136i | \(-0.925428\pi\) | ||
0.972683 | − | 0.232136i | \(-0.0745716\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.22359 | + | 38.1097i | −0.102712 | + | 1.21428i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.961390 | −0.0306014 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 13.1991i | − | 0.419708i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.6804 | −1.03813 | −0.519064 | − | 0.854735i | \(-0.673719\pi\) | ||||
−0.519064 | + | 0.854735i | \(0.673719\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.8918i | 0.726449i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.28963 | + | 15.2461i | −0.0408839 | + | 0.483335i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9107 | −0.535566 | −0.267783 | − | 0.963479i | \(-0.586291\pi\) | ||||
−0.267783 | + | 0.963479i | \(0.586291\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.8814 | −0.945407 |
(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 | 2240.2.l.a.1569.6 | yes | 12 | |
4.3 | odd | 2 | inner | 2240.2.l.a.1569.8 | yes | 12 | |
5.4 | even | 2 | 2240.2.l.b.1569.8 | yes | 12 | ||
8.3 | odd | 2 | 2240.2.l.b.1569.5 | yes | 12 | ||
8.5 | even | 2 | 2240.2.l.b.1569.7 | yes | 12 | ||
20.19 | odd | 2 | 2240.2.l.b.1569.6 | yes | 12 | ||
40.19 | odd | 2 | inner | 2240.2.l.a.1569.7 | yes | 12 | |
40.29 | even | 2 | inner | 2240.2.l.a.1569.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.l.a.1569.5 | ✓ | 12 | 40.29 | even | 2 | inner | |
2240.2.l.a.1569.6 | yes | 12 | 1.1 | even | 1 | trivial | |
2240.2.l.a.1569.7 | yes | 12 | 40.19 | odd | 2 | inner | |
2240.2.l.a.1569.8 | yes | 12 | 4.3 | odd | 2 | inner | |
2240.2.l.b.1569.5 | yes | 12 | 8.3 | odd | 2 | ||
2240.2.l.b.1569.6 | yes | 12 | 20.19 | odd | 2 | ||
2240.2.l.b.1569.7 | yes | 12 | 8.5 | even | 2 | ||
2240.2.l.b.1569.8 | yes | 12 | 5.4 | even | 2 |