Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(337,4056)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.c (of order \(2\), degree \(1\), not 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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.649638144.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.8 | ||
Root | \(-2.34138 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.337 |
Dual form | 4056.2.c.p.337.1 |
$q$-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 \(\left(\mathbb{Z}/4056\mathbb{Z}\right)^\times\).
\(n\) | \(1015\) | \(2029\) | \(2705\) | \(3889\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.20740i | 1.88161i | 0.338951 | + | 0.940804i | \(0.389928\pi\) | ||||
−0.338951 | + | 0.940804i | \(0.610072\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.55539i | 1.34381i | 0.740638 | + | 0.671905i | \(0.234524\pi\) | ||||
−0.740638 | + | 0.671905i | \(0.765476\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.08003i | − 1.53169i | −0.643027 | − | 0.765844i | \(-0.722322\pi\) | ||||
0.643027 | − | 0.765844i | \(-0.277678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.20740i | 1.08635i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.25670 | −0.789865 | −0.394933 | − | 0.918710i | \(-0.629232\pi\) | ||||
−0.394933 | + | 0.918710i | \(0.629232\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.33477i | − 0.765050i | −0.923945 | − | 0.382525i | \(-0.875055\pi\) | ||||
0.923945 | − | 0.382525i | \(-0.124945\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.55539i | 0.775849i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.384069 | −0.0800838 | −0.0400419 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400419 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.7022 | −2.54045 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.28744 | −1.35324 | −0.676621 | − | 0.736331i | \(-0.736557\pi\) | ||||
−0.676621 | + | 0.736331i | \(0.736557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47535i | 1.16301i | 0.813544 | + | 0.581504i | \(0.197535\pi\) | ||||
−0.813544 | + | 0.581504i | \(0.802465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.08003i | − 0.884320i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.9589 | −2.52852 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.12737i | − 0.514137i | −0.966393 | − | 0.257068i | \(-0.917243\pi\) | ||||
0.966393 | − | 0.257068i | \(-0.0827565\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.77404i | 1.05793i | 0.848644 | + | 0.528964i | \(0.177419\pi\) | ||||
−0.848644 | + | 0.528964i | \(0.822581\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.15811 | −0.634106 | −0.317053 | − | 0.948408i | \(-0.602693\pi\) | ||||
−0.317053 | + | 0.948408i | \(0.602693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.20740i | 0.627203i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.49484i | 0.801505i | 0.916186 | + | 0.400752i | \(0.131251\pi\) | ||||
−0.916186 | + | 0.400752i | \(0.868749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.64077 | −0.805824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.25670 | −0.456029 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.613974 | 0.0843358 | 0.0421679 | − | 0.999111i | \(-0.486574\pi\) | ||||
0.0421679 | + | 0.999111i | \(0.486574\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.3737 | 2.88204 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.33477i | − 0.441702i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.87891i | 1.02575i | 0.858464 | + | 0.512873i | \(0.171419\pi\) | ||||
−0.858464 | + | 0.512873i | \(0.828581\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.31227 | −1.06428 | −0.532139 | − | 0.846657i | \(-0.678612\pi\) | ||||
−0.532139 | + | 0.846657i | \(0.678612\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.55539i | 0.447936i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.06878i | 0.252742i | 0.991983 | + | 0.126371i | \(0.0403330\pi\) | ||||
−0.991983 | + | 0.126371i | \(0.959667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.384069 | −0.0462364 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 2.82529i | − 0.335301i | −0.985847 | − | 0.167650i | \(-0.946382\pi\) | ||||
0.985847 | − | 0.167650i | \(-0.0536179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 3.21865i | − 0.376715i | −0.982101 | − | 0.188357i | \(-0.939684\pi\) | ||||
0.982101 | − | 0.188357i | \(-0.0603164\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7022 | −1.46673 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.0615 | 2.05830 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64077 | −0.297109 | −0.148555 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148555 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.96926i | 0.216155i | 0.994142 | + | 0.108077i | \(0.0344694\pi\) | ||||
−0.994142 | + | 0.108077i | \(0.965531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.7022i | − 1.48622i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.28744 | −0.781295 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 14.1601i | − 1.50096i | −0.660891 | − | 0.750482i | \(-0.729821\pi\) | ||||
0.660891 | − | 0.750482i | \(-0.270179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47535i | 0.671463i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.0307 | 1.43952 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.86766i | 0.900374i | 0.892934 | + | 0.450187i | \(0.148643\pi\) | ||||
−0.892934 | + | 0.450187i | \(0.851357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 5.08003i | − 0.510563i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.44750 | −0.940062 | −0.470031 | − | 0.882650i | \(-0.655757\pi\) | ||||
−0.470031 | + | 0.882650i | \(0.655757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.15811 | 0.212645 | 0.106322 | − | 0.994332i | \(-0.466092\pi\) | ||||
0.106322 | + | 0.994332i | \(0.466092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.9589 | −1.45984 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.7003 | −1.80782 | −0.903912 | − | 0.427718i | \(-0.859318\pi\) | ||||
−0.903912 | + | 0.427718i | \(0.859318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4754i | 1.38649i | 0.720703 | + | 0.693244i | \(0.243819\pi\) | ||||
−0.720703 | + | 0.693244i | \(0.756181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 3.12737i | − 0.296837i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.74330 | 0.258068 | 0.129034 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129034 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.61593i | − 0.150686i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 11.5788i | − 1.06143i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.8067 | −1.34607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.77404i | 0.610795i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 32.4064i | − 2.89852i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1274 | 0.898659 | 0.449329 | − | 0.893366i | \(-0.351663\pi\) | ||||
0.449329 | + | 0.893366i | \(0.351663\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.15811 | −0.366101 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3430 | −1.16578 | −0.582892 | − | 0.812550i | \(-0.698079\pi\) | ||||
−0.582892 | + | 0.812550i | \(0.698079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8564 | 1.02808 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.20740i | 0.362116i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.8955i | − 1.01630i | −0.861268 | − | 0.508151i | \(-0.830329\pi\) | ||||
0.861268 | − | 0.508151i | \(-0.169671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4207 | 1.13833 | 0.569165 | − | 0.822223i | \(-0.307267\pi\) | ||||
0.569165 | + | 0.822223i | \(0.307267\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.49484i | 0.462749i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 30.6612i | − 2.54627i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.64077 | −0.465243 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.51144i | − 0.451515i | −0.974184 | − | 0.225757i | \(-0.927514\pi\) | ||||
0.974184 | − | 0.225757i | \(-0.0724856\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.08003i | 0.413407i | 0.978404 | + | 0.206704i | \(0.0662736\pi\) | ||||
−0.978404 | + | 0.206704i | \(0.933726\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.25670 | −0.263288 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.2444 | −2.18832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.5670 | −1.00296 | −0.501478 | − | 0.865170i | \(-0.667210\pi\) | ||||
−0.501478 | + | 0.865170i | \(0.667210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.613974 | 0.0486913 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.36551i | − 0.107617i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.81799i | − 0.690678i | −0.938478 | − | 0.345339i | \(-0.887764\pi\) | ||||
0.938478 | − | 0.345339i | \(-0.112236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.3737 | 1.66394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 14.6695i | − 1.13516i | −0.823317 | − | 0.567582i | \(-0.807879\pi\) | ||||
0.823317 | − | 0.567582i | \(-0.192121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.33477i | − 0.255017i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.41481 | 0.183594 | 0.0917972 | − | 0.995778i | \(-0.470739\pi\) | ||||
0.0917972 | + | 0.995778i | \(0.470739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 45.1614i | − 3.41388i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.87891i | 0.592215i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.35728 | 0.400422 | 0.200211 | − | 0.979753i | \(-0.435837\pi\) | ||||
0.200211 | + | 0.979753i | \(0.435837\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6715 | 1.31351 | 0.656756 | − | 0.754103i | \(-0.271928\pi\) | ||||
0.656756 | + | 0.754103i | \(0.271928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.31227 | −0.614461 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.1581 | 0.967403 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.5441i | 1.20983i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.55539i | 0.258616i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.57487 | 0.331026 | 0.165513 | − | 0.986208i | \(-0.447072\pi\) | ||||
0.165513 | + | 0.986208i | \(0.447072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.8428i | 1.21237i | 0.795323 | + | 0.606186i | \(0.207301\pi\) | ||||
−0.795323 | + | 0.606186i | \(0.792699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.85641i | − 0.132263i | −0.997811 | − | 0.0661317i | \(-0.978934\pi\) | ||||
0.997811 | − | 0.0661317i | \(-0.0210658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.9877 | 1.34600 | 0.673002 | − | 0.739641i | \(-0.265005\pi\) | ||||
0.673002 | + | 0.739641i | \(0.265005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.06878i | 0.145921i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 25.9096i | − 1.81850i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.5011 | −1.99060 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.384069 | −0.0266946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.9408 | −1.17182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2424 | 0.842804 | 0.421402 | − | 0.906874i | \(-0.361538\pi\) | ||||
0.421402 | + | 0.906874i | \(0.361538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.82529i | − 0.193586i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 17.4948i | − 1.19314i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.0224 | −1.56286 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3.21865i | − 0.217497i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7085i | 1.38675i | 0.720579 | + | 0.693373i | \(0.243876\pi\) | ||||
−0.720579 | + | 0.693373i | \(0.756124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.7022 | −0.846816 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.63881i | − 0.573378i | −0.958024 | − | 0.286689i | \(-0.907445\pi\) | ||||
0.958024 | − | 0.286689i | \(-0.0925546\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 20.1111i | − 1.32898i | −0.747296 | − | 0.664491i | \(-0.768648\pi\) | ||||
0.747296 | − | 0.664491i | \(-0.231352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0615 | 1.18836 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.41089 | 0.288967 | 0.144484 | − | 0.989507i | \(-0.453848\pi\) | ||||
0.144484 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.1190 | −1.50812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.64077 | −0.171536 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.51734i | 0.227518i | 0.993508 | + | 0.113759i | \(0.0362892\pi\) | ||||
−0.993508 | + | 0.113759i | \(0.963711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.74330i | 0.305543i | 0.988262 | + | 0.152771i | \(0.0488198\pi\) | ||||
−0.988262 | + | 0.152771i | \(0.951180\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 23.7330i | − 1.51624i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.96926i | 0.124797i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.98968 | −0.441185 | −0.220592 | − | 0.975366i | \(-0.570799\pi\) | ||||
−0.220592 | + | 0.975366i | \(0.570799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.95108i | 0.122663i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 13.7022i | − 0.858068i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.71010 | 0.293808 | 0.146904 | − | 0.989151i | \(-0.453069\pi\) | ||||
0.146904 | + | 0.989151i | \(0.453069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1190 | 0.690902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.28744 | −0.451081 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.12933 | −0.254625 | −0.127313 | − | 0.991863i | \(-0.540635\pi\) | ||||
−0.127313 | + | 0.991863i | \(0.540635\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.58324i | 0.158687i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 14.1601i | − 0.866582i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2587 | 0.991308 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.3171i | 1.96313i | 0.191137 | + | 0.981563i | \(0.438783\pi\) | ||||
−0.191137 | + | 0.981563i | \(0.561217\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 64.5278i | 3.89117i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.7369 | 1.42621 | 0.713106 | − | 0.701056i | \(-0.247288\pi\) | ||||
0.713106 | + | 0.701056i | \(0.247288\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.47535i | 0.387669i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.5812i | 1.52604i | 0.646373 | + | 0.763022i | \(0.276285\pi\) | ||||
−0.646373 | + | 0.763022i | \(0.723715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6486 | 0.692439 | 0.346220 | − | 0.938154i | \(-0.387465\pi\) | ||||
0.346220 | + | 0.938154i | \(0.387465\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.0307 | 0.831109 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.0843 | −1.42165 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.39392 | −0.376113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.86766i | 0.519831i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.85016i | 0.575452i | 0.957713 | + | 0.287726i | \(0.0928993\pi\) | ||||
−0.957713 | + | 0.287726i | \(0.907101\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −33.1497 | −1.93005 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.08003i | − 0.294773i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 14.7837i | − 0.852117i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.44750 | −0.542745 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 34.9731i | − 2.00255i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4182i | 0.708744i | 0.935105 | + | 0.354372i | \(0.115305\pi\) | ||||
−0.935105 | + | 0.354372i | \(0.884695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15811 | 0.122771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.42267 | −0.420901 | −0.210450 | − | 0.977605i | \(-0.567493\pi\) | ||||
−0.210450 | + | 0.977605i | \(0.567493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9799 | 1.58152 | 0.790758 | − | 0.612129i | \(-0.209687\pi\) | ||||
0.790758 | + | 0.612129i | \(0.209687\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.9589 | −0.842841 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 8.02484i | − 0.450720i | −0.974276 | − | 0.225360i | \(-0.927644\pi\) | ||||
0.974276 | − | 0.225360i | \(-0.0723558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.0204i | 2.07275i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7003 | −1.04375 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8604i | 0.604286i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.4754i | 0.800489i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.5363 | −1.07707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9252i | 1.04022i | 0.854098 | + | 0.520112i | \(0.174110\pi\) | ||||
−0.854098 | + | 0.520112i | \(0.825890\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.12737i | − 0.171379i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.70420 | −0.475561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8296 | −0.753347 | −0.376674 | − | 0.926346i | \(-0.622932\pi\) | ||||
−0.376674 | + | 0.926346i | \(0.622932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.74330 | 0.148996 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.8950 | 1.78136 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.83260i | 0.260936i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − 1.61593i | − 0.0869988i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.9093 | −0.907737 | −0.453869 | − | 0.891069i | \(-0.649956\pi\) | ||||
−0.453869 | + | 0.891069i | \(0.649956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 15.7462i | − 0.842874i | −0.906858 | − | 0.421437i | \(-0.861526\pi\) | ||||
0.906858 | − | 0.421437i | \(-0.138474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 21.9960i | − 1.17073i | −0.810771 | − | 0.585363i | \(-0.800952\pi\) | ||||
0.810771 | − | 0.585363i | \(-0.199048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.8871 | 0.630904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 11.5788i | − 0.612816i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.5606i | 1.29626i | 0.761530 | + | 0.648130i | \(0.224449\pi\) | ||||
−0.761530 | + | 0.648130i | \(0.775551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.87928 | 0.414699 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.8067 | −0.777152 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5422 | 0.708830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.20778 | 0.428443 | 0.214221 | − | 0.976785i | \(-0.431279\pi\) | ||||
0.214221 | + | 0.976785i | \(0.431279\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.77404i | 0.352642i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.18291i | 0.113331i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1190 | −0.523942 | −0.261971 | − | 0.965076i | \(-0.584373\pi\) | ||||
−0.261971 | + | 0.965076i | \(0.584373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 32.4064i | − 1.67346i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1614i | 1.08699i | 0.839413 | + | 0.543493i | \(0.182899\pi\) | ||||
−0.839413 | + | 0.543493i | \(0.817101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1274 | 0.518841 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.1151i | 1.33442i | 0.744871 | + | 0.667209i | \(0.232511\pi\) | ||||
−0.744871 | + | 0.667209i | \(0.767489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 75.9919i | 3.87291i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.15811 | −0.211369 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.18493 | −0.465695 | −0.232847 | − | 0.972513i | \(-0.574804\pi\) | ||||
−0.232847 | + | 0.972513i | \(0.574804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25080 | 0.0632554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.3430 | −0.673066 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 11.1108i | − 0.559044i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7912i | 0.591783i | 0.955222 | + | 0.295892i | \(0.0956167\pi\) | ||||
−0.955222 | + | 0.295892i | \(0.904383\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.8564 | 0.593563 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.4822i | 1.52221i | 0.648630 | + | 0.761104i | \(0.275342\pi\) | ||||
−0.648630 | + | 0.761104i | \(0.724658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.20740i | 0.209068i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.8871 | −0.787497 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8096i | 0.831182i | 0.909552 | + | 0.415591i | \(0.136425\pi\) | ||||
−0.909552 | + | 0.415591i | \(0.863575\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 11.8955i | − 0.586762i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.0126 | −1.37841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.28548 | −0.406718 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.4207 | 0.657215 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.5788 | −1.20075 | −0.600376 | − | 0.799718i | \(-0.704982\pi\) | ||||
−0.600376 | + | 0.799718i | \(0.704982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.1157i | 0.541748i | 0.962615 | + | 0.270874i | \(0.0873127\pi\) | ||||
−0.962615 | + | 0.270874i | \(0.912687\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.49484i | 0.267168i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 41.3674 | 2.00661 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 29.5533i | − 1.43019i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.5606i | 1.76106i | 0.473988 | + | 0.880531i | \(0.342814\pi\) | ||||
−0.473988 | + | 0.880531i | \(0.657186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.1765 | 0.921566 | 0.460783 | − | 0.887513i | \(-0.347569\pi\) | ||||
0.460783 | + | 0.887513i | \(0.347569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 30.6612i | − 1.47009i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.28078i | 0.0612681i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.8213 | −1.13693 | −0.568463 | − | 0.822709i | \(-0.692462\pi\) | ||||
−0.568463 | + | 0.822709i | \(0.692462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.64077 | −0.268608 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.48020 | 0.307884 | 0.153942 | − | 0.988080i | \(-0.450803\pi\) | ||||
0.153942 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 59.5771 | 2.82423 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.51144i | − 0.260682i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 7.11077i | − 0.335578i | −0.985823 | − | 0.167789i | \(-0.946337\pi\) | ||||
0.985823 | − | 0.167789i | \(-0.0536627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.4123 | 1.62041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.08003i | 0.238681i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 1.71558i | − 0.0802514i | −0.999195 | − | 0.0401257i | \(-0.987224\pi\) | ||||
0.999195 | − | 0.0401257i | \(-0.0127758\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.25670 | −0.152010 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.5129i | 1.51428i | 0.653254 | + | 0.757139i | \(0.273403\pi\) | ||||
−0.653254 | + | 0.757139i | \(0.726597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3.37282i | − 0.156748i | −0.996924 | − | 0.0783741i | \(-0.975027\pi\) | ||||
0.996924 | − | 0.0783741i | \(-0.0249728\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −27.2444 | −1.26343 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3241 | 0.894212 | 0.447106 | − | 0.894481i | \(-0.352455\pi\) | ||||
0.447106 | + | 0.894481i | \(0.352455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.35532 | −0.339637 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.5670 | −0.579057 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.1233i | 0.971252i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 42.3591i | 1.94357i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.613974 | 0.0281119 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.72313i | 0.398570i | 0.979942 | + | 0.199285i | \(0.0638620\pi\) | ||||
−0.979942 | + | 0.199285i | \(0.936138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.36551i | − 0.0621329i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.3098 | −1.69415 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 11.6431i | − 0.527599i | −0.964578 | − | 0.263800i | \(-0.915024\pi\) | ||||
0.964578 | − | 0.263800i | \(-0.0849758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 8.81799i | − 0.398763i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.77208 | −0.350749 | −0.175375 | − | 0.984502i | \(-0.556114\pi\) | ||||
−0.175375 | + | 0.984502i | \(0.556114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.7330 | 1.06888 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.3737 | 0.960679 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0450 | 0.450580 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3434i | 0.910695i | 0.890314 | + | 0.455348i | \(0.150485\pi\) | ||||
−0.890314 | + | 0.455348i | \(0.849515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 14.6695i | − 0.655387i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1522 | −0.943130 | −0.471565 | − | 0.881831i | \(-0.656311\pi\) | ||||
−0.471565 | + | 0.881831i | \(0.656311\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 39.7495i | − 1.76883i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 38.0803i | − 1.68788i | −0.536438 | − | 0.843939i | \(-0.680231\pi\) | ||||
0.536438 | − | 0.843939i | \(-0.319769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4436 | 0.506233 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 3.33477i | − 0.147234i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.08003i | 0.400114i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.9140 | 1.22765 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.41481 | 0.105998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.7433 | 0.908781 | 0.454390 | − | 0.890803i | \(-0.349857\pi\) | ||||
0.454390 | + | 0.890803i | \(0.349857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.94247 | −0.216119 | −0.108060 | − | 0.994144i | \(-0.534464\pi\) | ||||
−0.108060 | + | 0.994144i | \(0.534464\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 45.1614i | − 1.97100i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 21.0883i | − 0.918619i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8525 | −0.993587 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.87891i | 0.341915i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 78.6796i | − 3.40162i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.35728 | 0.231184 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6553i | 1.23427i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 43.7196i | − 1.87965i | −0.341650 | − | 0.939827i | \(-0.610986\pi\) | ||||
0.341650 | − | 0.939827i | \(-0.389014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6715 | 0.758357 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −60.9036 | −2.60883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1028 | 1.67191 | 0.835957 | − | 0.548795i | \(-0.184913\pi\) | ||||
0.835957 | + | 0.548795i | \(0.184913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.31227 | −0.354759 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3020i | 1.03530i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 9.38894i | − 0.399259i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.1581 | 0.558531 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.9916i | 1.01656i | 0.861192 | + | 0.508279i | \(0.169718\pi\) | ||||
−0.861192 | + | 0.508279i | \(0.830282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.5441i | 0.698494i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4763 | −0.441523 | −0.220761 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220761 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.5422i | 0.485583i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.55539i | 0.149312i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.7964 | −1.29105 | −0.645526 | − | 0.763738i | \(-0.723362\pi\) | ||||
−0.645526 | + | 0.763738i | \(0.723362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.52126 | −0.398452 | −0.199226 | − | 0.979954i | \(-0.563843\pi\) | ||||
−0.199226 | + | 0.979954i | \(0.563843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.57487 | 0.191118 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.87853 | 0.203449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 47.7495i | − 1.98784i | −0.110124 | − | 0.993918i | \(-0.535125\pi\) | ||||
0.110124 | − | 0.993918i | \(-0.464875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.8428i | 0.699964i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.00149 | −0.290471 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.11901i | − 0.129176i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 39.4845i | − 1.62970i | −0.579671 | − | 0.814851i | \(-0.696819\pi\) | ||||
0.579671 | − | 0.814851i | \(-0.303181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.5938 | 0.889758 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1.85641i | − 0.0763624i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 20.0166i | − 0.821983i | −0.911639 | − | 0.410992i | \(-0.865183\pi\) | ||||
0.911639 | − | 0.410992i | \(-0.134817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.7168 | 1.99719 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.9877 | 0.777116 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8517 | −0.811120 | −0.405560 | − | 0.914068i | \(-0.632923\pi\) | ||||
−0.405560 | + | 0.914068i | \(0.632923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7022 | 0.477344 | 0.238672 | − | 0.971100i | \(-0.423288\pi\) | ||||
0.238672 | + | 0.971100i | \(0.423288\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.06878i | 0.0842473i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 62.2979i | − 2.53277i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.1955 | −1.75325 | −0.876626 | − | 0.481173i | \(-0.840211\pi\) | ||||
−0.876626 | + | 0.481173i | \(0.840211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − 25.9096i | − 1.04991i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 31.6417i | − 1.27800i | −0.769208 | − | 0.638998i | \(-0.779349\pi\) | ||||
0.769208 | − | 0.638998i | \(-0.220651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.5011 | −1.14928 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 15.8027i | − 0.636193i | −0.948058 | − | 0.318096i | \(-0.896956\pi\) | ||||
0.948058 | − | 0.318096i | \(-0.103044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0663i | 1.44963i | 0.688945 | + | 0.724814i | \(0.258074\pi\) | ||||
−0.688945 | + | 0.724814i | \(0.741926\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.384069 | −0.0154121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.3445 | 2.01701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 72.8358 | 2.91343 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9408 | −0.676549 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1849i | 0.406099i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 17.9063i | − 0.712837i | −0.934326 | − | 0.356418i | \(-0.883998\pi\) | ||||
0.934326 | − | 0.356418i | \(-0.116002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.2424 | 0.486593 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.6099i | 1.69092i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 2.82529i | − 0.111767i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.7101 | −1.37097 | −0.685483 | − | 0.728088i | \(-0.740409\pi\) | ||||
−0.685483 | + | 0.728088i | \(0.740409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 45.5430i | − 1.79604i | −0.439955 | − | 0.898020i | \(-0.645006\pi\) | ||||
0.439955 | − | 0.898020i | \(-0.354994\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 17.4948i | − 0.688859i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8603 | 0.702162 | 0.351081 | − | 0.936345i | \(-0.385814\pi\) | ||||
0.351081 | + | 0.936345i | \(0.385814\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0251 | 1.57112 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.0224 | −0.902318 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.6757 | −1.47436 | −0.737182 | − | 0.675694i | \(-0.763844\pi\) | ||||
−0.737182 | + | 0.675694i | \(0.763844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 56.1394i | − 2.19355i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 3.21865i | − 0.125572i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.7475 | 1.35357 | 0.676785 | − | 0.736181i | \(-0.263373\pi\) | ||||
0.676785 | + | 0.736181i | \(0.263373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.3234i | 1.52950i | 0.644325 | + | 0.764752i | \(0.277139\pi\) | ||||
−0.644325 | + | 0.764752i | \(0.722861\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 49.8847i | 1.93445i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.79888 | 0.108373 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.7085i | 0.800638i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.2266i | 1.63014i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.1436 | −0.429554 | −0.214777 | − | 0.976663i | \(-0.568902\pi\) | ||||
−0.214777 | + | 0.976663i | \(0.568902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.7022 | −0.488910 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.3037 | −0.472868 | −0.236434 | − | 0.971648i | \(-0.575979\pi\) | ||||
−0.236434 | + | 0.971648i | \(0.575979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.5279 | −1.20993 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − 8.63881i | − 0.331040i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5381i | 0.671078i | 0.942026 | + | 0.335539i | \(0.108918\pi\) | ||||
−0.942026 | + | 0.335539i | \(0.891082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.0492 | 1.91228 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 20.1111i | − 0.767288i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 13.1181i | − 0.499035i | −0.968370 | − | 0.249518i | \(-0.919728\pi\) | ||||
0.968370 | − | 0.249518i | \(-0.0802720\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0615 | 0.686099 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 56.4663i | 2.14189i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 22.0610i | − 0.835620i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.41089 | 0.166835 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.768137 | 0.0290121 | 0.0145061 | − | 0.999895i | \(-0.495382\pi\) | ||||
0.0145061 | + | 0.999895i | \(0.495382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.4291 | −0.393340 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.1190 | −0.870712 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 33.5895i | − 1.26326i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.0897i | 1.20515i | 0.798061 | + | 0.602577i | \(0.205859\pi\) | ||||
−0.798061 | + | 0.602577i | \(0.794141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.64077 | −0.0990365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.48698i | − 0.0931381i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.51734i | 0.131358i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.9771 | 0.409378 | 0.204689 | − | 0.978827i | \(-0.434382\pi\) | ||||
0.204689 | + | 0.978827i | \(0.434382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.67291i | 0.285754i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.74330i | 0.176405i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 92.5668 | 3.43784 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.9056 | −1.51710 | −0.758552 | − | 0.651612i | \(-0.774093\pi\) | ||||
−0.758552 | + | 0.651612i | \(0.774093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5417 | 0.500858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.18829i | − 0.228570i | −0.993448 | − | 0.114285i | \(-0.963542\pi\) | ||||
0.993448 | − | 0.114285i | \(-0.0364577\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 23.7330i | − 0.875404i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5095 | 0.387122 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.3488i | 1.96247i | 0.192824 | + | 0.981233i | \(0.438235\pi\) | ||||
−0.192824 | + | 0.981233i | \(0.561765\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.5728i | 1.63522i | 0.575774 | + | 0.817609i | \(0.304701\pi\) | ||||
−0.575774 | + | 0.817609i | \(0.695299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.1888 | 0.849574 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.96926i | 0.0720515i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 66.4867i | − 2.42937i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50945 | 0.0550807 | 0.0275403 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275403 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.98968 | −0.254718 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.3737 | −0.777870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.9794 | −1.88922 | −0.944611 | − | 0.328192i | \(-0.893561\pi\) | ||||
−0.944611 | + | 0.328192i | \(0.893561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.95108i | 0.0708198i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6695i | 0.386771i | 0.981123 | + | 0.193385i | \(0.0619468\pi\) | ||||
−0.981123 | + | 0.193385i | \(0.938053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.4655 | −1.86317 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 13.7022i | − 0.495406i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.01256i | 0.216818i | 0.994106 | + | 0.108409i | \(0.0345757\pi\) | ||||
−0.994106 | + | 0.108409i | \(0.965424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.71010 | 0.169630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.8907i | 1.43477i | 0.696677 | + | 0.717385i | \(0.254661\pi\) | ||||
−0.696677 | + | 0.717385i | \(0.745339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 82.2515i | − 2.95456i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.1190 | 0.398892 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.5899 | 0.809367 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3526 | −0.513576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.28744 | −0.260432 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 52.8745i | − 1.88717i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.50215i | − 0.124838i | −0.998050 | − | 0.0624190i | \(-0.980118\pi\) | ||||
0.998050 | − | 0.0624190i | \(-0.0198815\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.12933 | −0.147008 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.75350i | 0.346794i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.58324i | 0.0916179i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2869 | 0.860287 | 0.430144 | − | 0.902760i | \(-0.358463\pi\) | ||||
0.430144 | + | 0.902760i | \(0.358463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 17.8950i | − 0.633081i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 14.1601i | − 0.500321i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3509 | −0.577010 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.74526 | 0.202494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.2587 | 0.572332 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.1288 | −0.672534 | −0.336267 | − | 0.941767i | \(-0.609164\pi\) | ||||
−0.336267 | + | 0.941767i | \(0.609164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.1857i | 1.93783i | 0.247387 | + | 0.968917i | \(0.420428\pi\) | ||||
−0.247387 | + | 0.968917i | \(0.579572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.3171i | 1.13341i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.1008 | 1.29959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8664i | 0.485122i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 23.3362i | − 0.814440i | −0.913330 | − | 0.407220i | \(-0.866498\pi\) | ||||
0.913330 | − | 0.407220i | \(-0.133502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.05359 | 0.0715835 | 0.0357918 | − | 0.999359i | \(-0.488605\pi\) | ||||
0.0357918 | + | 0.999359i | \(0.488605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64.5278i | 2.24657i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.96289i | − 0.207350i | −0.994611 | − | 0.103675i | \(-0.966940\pi\) | ||||
0.994611 | − | 0.103675i | \(-0.0330602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5631 | −0.505797 | −0.252899 | − | 0.967493i | \(-0.581384\pi\) | ||||
−0.252899 | + | 0.967493i | \(0.581384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.7369 | 0.823424 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3703 | 0.636492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 61.7207 | 2.13593 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.47535i | 0.223821i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.0737i | 1.69421i | 0.531425 | + | 0.847105i | \(0.321657\pi\) | ||||
−0.531425 | + | 0.847105i | \(0.678343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1067 | 0.831267 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.5812i | 0.881062i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 52.6437i | − 1.80886i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.6486 | 0.399780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20112i | 0.0411740i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.6929i | 1.87265i | 0.351138 | + | 0.936324i | \(0.385795\pi\) | ||||
−0.351138 | + | 0.936324i | \(0.614205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.0307 | 0.479841 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.2811 | 0.795266 | 0.397633 | − | 0.917545i | \(-0.369832\pi\) | ||||
0.397633 | + | 0.917545i | \(0.369832\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4229 | 1.48157 | 0.740785 | − | 0.671742i | \(-0.234454\pi\) | ||||
0.740785 | + | 0.671742i | \(0.234454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24.0843 | −0.820792 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 7.28977i | − 0.248147i | −0.992273 | − | 0.124073i | \(-0.960404\pi\) | ||||
0.992273 | − | 0.124073i | \(-0.0395958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.1601i | 0.345453i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.39392 | −0.217149 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4152i | 0.455079i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.86766i | 0.300125i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 115.217 | 3.89506 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 33.2464i | − 1.12265i | −0.827595 | − | 0.561326i | \(-0.810292\pi\) | ||||
0.827595 | − | 0.561326i | \(-0.189708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.85016i | 0.332238i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1888 | −0.545415 | −0.272708 | − | 0.962097i | \(-0.587919\pi\) | ||||
−0.272708 | + | 0.962097i | \(0.587919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0492 | 0.674708 | 0.337354 | − | 0.941378i | \(-0.390468\pi\) | ||||
0.337354 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.1497 | −1.11432 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.3120 | −1.82362 | −0.911810 | − | 0.410612i | \(-0.865315\pi\) | ||||
−0.911810 | + | 0.410612i | \(0.865315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0067i | 1.20763i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.08003i | − 0.170188i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3240 | 0.613191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.5402i | 0.753436i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 47.1887i | − 1.57383i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.99953 | −0.0666139 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 14.7837i | − 0.491970i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 74.3511i | 2.47152i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.8972 | 1.72322 | 0.861610 | − | 0.507571i | \(-0.169457\pi\) | ||||
0.861610 | + | 0.507571i | \(0.169457\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.44750 | −0.313354 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0433 | 0.564669 | 0.282334 | − | 0.959316i | \(-0.408891\pi\) | ||||
0.282334 | + | 0.959316i | \(0.408891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0039 | 0.331081 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 34.9731i | − 1.15617i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 47.4395i | − 1.56659i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0693 | −0.530078 | −0.265039 | − | 0.964238i | \(-0.585385\pi\) | ||||
−0.265039 | + | 0.964238i | \(0.585385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.4182i | 0.409194i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.7246i | 1.30614i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.15811 | 0.0708816 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 11.4025i | − 0.374104i | −0.982350 | − | 0.187052i | \(-0.940107\pi\) | ||||
0.982350 | − | 0.187052i | \(-0.0598933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.8107i | 0.616495i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.42267 | −0.243007 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −69.6078 | −2.27642 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.8213 | −1.10489 | −0.552447 | − | 0.833548i | \(-0.686306\pi\) | ||||
−0.552447 | + | 0.833548i | \(0.686306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.9799 | 0.913088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 48.0429i | − 1.56615i | −0.621925 | − | 0.783077i | \(-0.713649\pi\) | ||||
0.621925 | − | 0.783077i | \(-0.286351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.60170i | − 0.0847229i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.9589 | −0.486614 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 12.0779i | − 0.392481i | −0.980556 | − | 0.196240i | \(-0.937127\pi\) | ||||
0.980556 | − | 0.196240i | \(-0.0628733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 8.02484i | − 0.260223i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.4251 | −0.499669 | −0.249834 | − | 0.968289i | \(-0.580376\pi\) | ||||
−0.249834 | + | 0.968289i | \(0.580376\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.2483i | 0.622862i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.0204i | 1.19670i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.2931 | 1.36572 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.9302 | −0.352587 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.7003 | −0.602608 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −70.8645 | −2.28121 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.7289i | 1.59917i | 0.600550 | + | 0.799587i | \(0.294948\pi\) | ||||
−0.600550 | + | 0.799587i | \(0.705052\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.8604i | 0.348885i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.9897 | −0.994506 | −0.497253 | − | 0.867606i | \(-0.665658\pi\) | ||||
−0.497253 | + | 0.867606i | \(0.665658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.7158i | 1.52970i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 22.8765i | − 0.731886i | −0.930637 | − | 0.365943i | \(-0.880747\pi\) | ||||
0.930637 | − | 0.365943i | \(-0.119253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −71.9336 | −2.29901 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4754i | 0.462162i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 28.0019i | − 0.893121i | −0.894754 | − | 0.446560i | \(-0.852649\pi\) | ||||
0.894754 | − | 0.446560i | \(-0.147351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.81065 | 0.248868 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.5363 | −0.621846 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.59700 | 0.0507816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2855 | −0.517325 | −0.258663 | − | 0.965968i | \(-0.583282\pi\) | ||||
−0.258663 | + | 0.965968i | \(0.583282\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9252i | 0.600574i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 79.8890i | 2.53265i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.3034 | 1.46644 | 0.733222 | − | 0.679989i | \(-0.238015\pi\) | ||||
0.733222 | + | 0.679989i | \(0.238015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 3.12737i | − 0.0989456i |
(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.c.p.337.8 | 8 | ||
13.5 | odd | 4 | 4056.2.a.be.1.4 | 4 | |||
13.8 | odd | 4 | 4056.2.a.bd.1.1 | 4 | |||
13.9 | even | 3 | 312.2.bf.b.49.4 | ✓ | 8 | ||
13.10 | even | 6 | 312.2.bf.b.121.1 | yes | 8 | ||
13.12 | even | 2 | inner | 4056.2.c.p.337.1 | 8 | ||
39.23 | odd | 6 | 936.2.bi.c.433.4 | 8 | |||
39.35 | odd | 6 | 936.2.bi.c.361.1 | 8 | |||
52.23 | odd | 6 | 624.2.bv.g.433.1 | 8 | |||
52.31 | even | 4 | 8112.2.a.cs.1.4 | 4 | |||
52.35 | odd | 6 | 624.2.bv.g.49.4 | 8 | |||
52.47 | even | 4 | 8112.2.a.cq.1.1 | 4 | |||
156.23 | even | 6 | 1872.2.by.m.433.4 | 8 | |||
156.35 | even | 6 | 1872.2.by.m.1297.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bf.b.49.4 | ✓ | 8 | 13.9 | even | 3 | ||
312.2.bf.b.121.1 | yes | 8 | 13.10 | even | 6 | ||
624.2.bv.g.49.4 | 8 | 52.35 | odd | 6 | |||
624.2.bv.g.433.1 | 8 | 52.23 | odd | 6 | |||
936.2.bi.c.361.1 | 8 | 39.35 | odd | 6 | |||
936.2.bi.c.433.4 | 8 | 39.23 | odd | 6 | |||
1872.2.by.m.433.4 | 8 | 156.23 | even | 6 | |||
1872.2.by.m.1297.1 | 8 | 156.35 | even | 6 | |||
4056.2.a.bd.1.1 | 4 | 13.8 | odd | 4 | |||
4056.2.a.be.1.4 | 4 | 13.5 | odd | 4 | |||
4056.2.c.p.337.1 | 8 | 13.12 | even | 2 | inner | ||
4056.2.c.p.337.8 | 8 | 1.1 | even | 1 | trivial | ||
8112.2.a.cq.1.1 | 4 | 52.47 | even | 4 | |||
8112.2.a.cs.1.4 | 4 | 52.31 | even | 4 |