Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(0.500000 - 1.44392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.i.1537.7 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.47363i | − 1.10624i | −0.833102 | − | 0.553120i | \(-0.813437\pi\) | ||||
0.833102 | − | 0.553120i | \(-0.186563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55765 | −0.966700 | −0.483350 | − | 0.875427i | \(-0.660580\pi\) | ||||
−0.483350 | + | 0.875427i | \(0.660580\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.669808i | − 0.201955i | −0.994889 | − | 0.100977i | \(-0.967803\pi\) | ||||
0.994889 | − | 0.100977i | \(-0.0321970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.08402i | 1.13270i | 0.824164 | + | 0.566352i | \(0.191646\pi\) | ||||
−0.824164 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.47363 | −0.638687 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.44549 | 1.56326 | 0.781630 | − | 0.623742i | \(-0.214389\pi\) | ||||
0.781630 | + | 0.623742i | \(0.214389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.44549i | 1.47870i | 0.673323 | + | 0.739348i | \(0.264866\pi\) | ||||
−0.673323 | + | 0.739348i | \(0.735134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.55765i | 0.558124i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.11882 | −0.223765 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.35480i | 0.808666i | 0.914612 | + | 0.404333i | \(0.132496\pi\) | ||||
−0.914612 | + | 0.404333i | \(0.867504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.55765 | −1.17779 | −0.588894 | − | 0.808210i | \(-0.700437\pi\) | ||||
−0.588894 | + | 0.808210i | \(0.700437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.669808 | −0.116599 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.32666i | 1.06940i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.85970i | 0.634531i | 0.948337 | + | 0.317265i | \(0.102765\pi\) | ||||
−0.948337 | + | 0.317265i | \(0.897235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.08402 | 0.653967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.788632 | −0.123164 | −0.0615818 | − | 0.998102i | \(-0.519615\pi\) | ||||
−0.0615818 | + | 0.998102i | \(0.519615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.550984i | 0.0840242i | 0.999117 | + | 0.0420121i | \(0.0133768\pi\) | ||||
−0.999117 | + | 0.0420121i | \(0.986623\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.47363i | 0.368746i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.458440 | −0.0654915 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 6.44549i | − 0.902549i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.64520i | − 0.500707i | −0.968155 | − | 0.250353i | \(-0.919453\pi\) | ||||
0.968155 | − | 0.250353i | \(-0.0805468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65685 | −0.223410 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.44549 | 0.853726 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.65685i | 0.736460i | 0.929735 | + | 0.368230i | \(0.120036\pi\) | ||||
−0.929735 | + | 0.368230i | \(0.879964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.20285i | 0.794193i | 0.917777 | + | 0.397097i | \(0.129982\pi\) | ||||
−0.917777 | + | 0.397097i | \(0.870018\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.55765 | 0.322233 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1023 | 1.25304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.99647i | − 0.366077i | −0.983106 | − | 0.183039i | \(-0.941407\pi\) | ||||
0.983106 | − | 0.183039i | \(-0.0585933\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.82843i | − 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.11529 | 0.607074 | 0.303537 | − | 0.952820i | \(-0.401832\pi\) | ||||
0.303537 | + | 0.952820i | \(0.401832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7721 | 1.72895 | 0.864475 | − | 0.502676i | \(-0.167651\pi\) | ||||
0.864475 | + | 0.502676i | \(0.167651\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.11882i | 0.129191i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.71313i | 0.195230i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.32000 | −0.711055 | −0.355528 | − | 0.934666i | \(-0.615699\pi\) | ||||
−0.355528 | + | 0.934666i | \(0.615699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.907457i | − 0.0996063i | −0.998759 | − | 0.0498032i | \(-0.984141\pi\) | ||||
0.998759 | − | 0.0498032i | \(-0.0158594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 15.9437i | − 1.72934i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.35480 | 0.466884 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.31724 | 0.669626 | 0.334813 | − | 0.942285i | \(-0.391327\pi\) | ||||
0.334813 | + | 0.942285i | \(0.391327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 10.4455i | − 1.09498i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.55765i | 0.679996i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9437 | 1.63579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.6533 | 1.28475 | 0.642375 | − | 0.766390i | \(-0.277949\pi\) | ||||
0.642375 | + | 0.766390i | \(0.277949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.669808i | 0.0673182i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.6417i | − 1.05889i | −0.848346 | − | 0.529443i | \(-0.822401\pi\) | ||||
0.848346 | − | 0.529443i | \(-0.177599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33686 | 0.328790 | 0.164395 | − | 0.986395i | \(-0.447433\pi\) | ||||
0.164395 | + | 0.986395i | \(0.447433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.32666 | 0.617419 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.8874i | 1.92259i | 0.275518 | + | 0.961296i | \(0.411151\pi\) | ||||
−0.275518 | + | 0.961296i | \(0.588849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.91598i | 0.375083i | 0.982257 | + | 0.187541i | \(0.0600519\pi\) | ||||
−0.982257 | + | 0.187541i | \(0.939948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.85970 | 0.366347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.23765 | −0.210500 | −0.105250 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105250 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 6.99647i | − 0.652424i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.08402i | − 0.377568i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.4853 | −1.51120 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5514 | 0.959214 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.788632i | 0.0711086i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.60058i | − 0.858702i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2145 | −1.08386 | −0.541931 | − | 0.840423i | \(-0.682307\pi\) | ||||
−0.541931 | + | 0.840423i | \(0.682307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.550984 | 0.0485114 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.33962i | − 0.466524i | −0.972414 | − | 0.233262i | \(-0.925060\pi\) | ||||
0.972414 | − | 0.233262i | \(-0.0749400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 16.4853i | − 1.42946i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.47363 | 0.212896 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.10587 | 0.436224 | 0.218112 | − | 0.975924i | \(-0.430010\pi\) | ||||
0.218112 | + | 0.975924i | \(0.430010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16.6533i | − 1.41252i | −0.707954 | − | 0.706258i | \(-0.750382\pi\) | ||||
0.707954 | − | 0.706258i | \(-0.249618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.82843i | − 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73551 | 0.228755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7721 | 0.894578 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.458440i | 0.0378115i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 11.1832i | − 0.916166i | −0.888909 | − | 0.458083i | \(-0.848536\pi\) | ||||
0.888909 | − | 0.458083i | \(-0.151464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6506 | 1.19225 | 0.596123 | − | 0.802893i | \(-0.296707\pi\) | ||||
0.596123 | + | 0.802893i | \(0.296707\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.44549 | −0.521087 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.2212i | 1.30292i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.45754i | 0.355750i | 0.984053 | + | 0.177875i | \(0.0569223\pi\) | ||||
−0.984053 | + | 0.177875i | \(0.943078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.64520 | −0.289083 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.23412 | −0.570128 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.78510i | 0.609776i | 0.952388 | + | 0.304888i | \(0.0986191\pi\) | ||||
−0.952388 | + | 0.304888i | \(0.901381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.65685i | 0.128986i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.1814 | −1.56168 | −0.780841 | − | 0.624730i | \(-0.785209\pi\) | ||||
−0.780841 | + | 0.624730i | \(0.785209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.67923 | −0.283018 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.44549i | − 0.492899i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.15639i | 0.468061i | 0.972229 | + | 0.234031i | \(0.0751916\pi\) | ||||
−0.972229 | + | 0.234031i | \(0.924808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.86156 | 0.216313 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65685 | 0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7855i | 1.40409i | 0.712131 | + | 0.702046i | \(0.247730\pi\) | ||||
−0.712131 | + | 0.702046i | \(0.752270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97499i | 0.667106i | 0.942731 | + | 0.333553i | \(0.108248\pi\) | ||||
−0.942731 | + | 0.333553i | \(0.891752\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.20285 | 0.458528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.54745 | 0.701943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.31724i | − 0.315708i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.55765i | − 0.186041i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.60058 | −0.405243 | −0.202622 | − | 0.979257i | \(-0.564946\pi\) | ||||
−0.202622 | + | 0.979257i | \(0.564946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.4514 | −1.40014 | −0.700071 | − | 0.714074i | \(-0.746848\pi\) | ||||
−0.700071 | + | 0.714074i | \(0.746848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 10.1023i | − 0.723444i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.75070i | − 0.124732i | −0.998053 | − | 0.0623659i | \(-0.980135\pi\) | ||||
0.998053 | − | 0.0623659i | \(-0.0198646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.993710 | −0.0704422 | −0.0352211 | − | 0.999380i | \(-0.511214\pi\) | ||||
−0.0352211 | + | 0.999380i | \(0.511214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.99647 | −0.211355 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 11.1380i | − 0.781738i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.95078i | 0.136248i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.31724 | 0.298630 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5.97409i | − 0.411273i | −0.978628 | − | 0.205637i | \(-0.934073\pi\) | ||||
0.978628 | − | 0.205637i | \(-0.0659265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 5.11529i | − 0.350494i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.36293 | 0.0929509 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.7721 | 1.13857 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 14.7721i | − 0.998209i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.3235i | 1.77071i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7659 | 1.59148 | 0.795740 | − | 0.605639i | \(-0.207082\pi\) | ||||
0.795740 | + | 0.605639i | \(0.207082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.11882 | 0.0745883 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 0.907457i | − 0.0602300i | −0.999546 | − | 0.0301150i | \(-0.990413\pi\) | ||||
0.999546 | − | 0.0301150i | \(-0.00958735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 7.55579i | − 0.499301i | −0.968336 | − | 0.249650i | \(-0.919684\pi\) | ||||
0.968336 | − | 0.249650i | \(-0.0803157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.71313 | 0.112716 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.2271 | 1.52166 | 0.760828 | − | 0.648954i | \(-0.224793\pi\) | ||||
0.760828 | + | 0.648954i | \(0.224793\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 6.99647i | − 0.456399i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.32000i | 0.410528i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.9213 | 1.74140 | 0.870698 | − | 0.491817i | \(-0.163667\pi\) | ||||
0.870698 | + | 0.491817i | \(0.163667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3494 | 0.666664 | 0.333332 | − | 0.942809i | \(-0.391827\pi\) | ||||
0.333332 | + | 0.942809i | \(0.391827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.13401i | 0.0724492i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.3235 | −1.67492 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.907457 | −0.0575077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 13.7984i | − 0.870949i | −0.900201 | − | 0.435475i | \(-0.856581\pi\) | ||||
0.900201 | − | 0.435475i | \(-0.143419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.89450i | − 0.119106i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.9437 | −0.998435 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9965 | 1.06021 | 0.530105 | − | 0.847932i | \(-0.322152\pi\) | ||||
0.530105 | + | 0.847932i | \(0.322152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.87175i | − 0.613401i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.35480i | − 0.269555i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.9929 | −1.84944 | −0.924722 | − | 0.380643i | \(-0.875703\pi\) | ||||
−0.924722 | + | 0.380643i | \(0.875703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.01686 | −0.553901 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.31724i | − 0.386609i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.1332i | 1.77628i | 0.459569 | + | 0.888142i | \(0.348004\pi\) | ||||
−0.459569 | + | 0.888142i | \(0.651996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.6506 | −1.61891 | −0.809453 | − | 0.587184i | \(-0.800236\pi\) | ||||
−0.809453 | + | 0.587184i | \(0.800236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.4455 | −0.632190 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.749397i | 0.0451904i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1430i | 1.03003i | 0.857183 | + | 0.515013i | \(0.172213\pi\) | ||||
−0.857183 | + | 0.515013i | \(0.827787\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.55765 | 0.392596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.76588 | −0.164999 | −0.0824993 | − | 0.996591i | \(-0.526290\pi\) | ||||
−0.0824993 | + | 0.996591i | \(0.526290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.34315i | 0.377061i | 0.982067 | + | 0.188530i | \(0.0603724\pi\) | ||||
−0.982067 | + | 0.188530i | \(0.939628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 15.9437i | − 0.944425i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.01704 | 0.119062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.5443 | 1.44378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 12.6533i | − 0.741751i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6078i | 0.678133i | 0.940762 | + | 0.339067i | \(0.110111\pi\) | ||||
−0.940762 | + | 0.339067i | \(0.889889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.9929 | 0.814700 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.669808 | 0.0388662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.5514i | 0.668032i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.40922i | − 0.0812262i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.6417 | −0.611348 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3435 | 0.878567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 14.7855i | − 0.843852i | −0.906630 | − | 0.421926i | \(-0.861354\pi\) | ||||
0.906630 | − | 0.421926i | \(-0.138646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.33686i | − 0.189827i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0761 | −0.854885 | −0.427442 | − | 0.904043i | \(-0.640585\pi\) | ||||
−0.427442 | + | 0.904043i | \(0.640585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.0027 | −1.30019 | −0.650096 | − | 0.759852i | \(-0.725271\pi\) | ||||
−0.650096 | + | 0.759852i | \(0.725271\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6.32666i | − 0.356467i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.55855i | 0.536862i | 0.963299 | + | 0.268431i | \(0.0865051\pi\) | ||||
−0.963299 | + | 0.268431i | \(0.913495\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.91688 | 0.163314 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.8874 | 1.11001 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.5443i | 2.31159i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.56930i | − 0.253459i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.91598 | 0.216554 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.23412 | −0.398830 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8079i | 1.52846i | 0.644945 | + | 0.764229i | \(0.276880\pi\) | ||||
−0.644945 | + | 0.764229i | \(0.723120\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.85970i | − 0.211510i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.41215 | −0.404969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.00980 | −0.163954 | −0.0819771 | − | 0.996634i | \(-0.526123\pi\) | ||||
−0.0819771 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.23765i | 0.121532i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.39236i | 0.237860i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0761 | 1.03001 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.99647 | −0.376677 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.87449i | 0.476408i | 0.971215 | + | 0.238204i | \(0.0765586\pi\) | ||||
−0.971215 | + | 0.238204i | \(0.923441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.70698i | 0.359016i | 0.983757 | + | 0.179508i | \(0.0574506\pi\) | ||||
−0.983757 | + | 0.179508i | \(0.942549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.08402 | −0.217989 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.75882 | −0.466185 | −0.233093 | − | 0.972455i | \(-0.574884\pi\) | ||||
−0.233093 | + | 0.972455i | \(0.574884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 12.6533i | − 0.671569i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.4853i | 0.872494i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.7917 | 1.73068 | 0.865341 | − | 0.501184i | \(-0.167102\pi\) | ||||
0.865341 | + | 0.501184i | \(0.167102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5443 | −1.18654 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 10.5514i | − 0.553803i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 36.5408i | − 1.91263i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6435 | 1.07758 | 0.538791 | − | 0.842439i | \(-0.318881\pi\) | ||||
0.538791 | + | 0.842439i | \(0.318881\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.788632 | 0.0410546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.32313i | 0.484033i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 23.4995i | − 1.21676i | −0.793646 | − | 0.608379i | \(-0.791820\pi\) | ||||
0.793646 | − | 0.608379i | \(-0.208180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.60058 | −0.495772 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.7851 | −0.915979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0004i | 0.565051i | 0.959260 | + | 0.282526i | \(0.0911722\pi\) | ||||
−0.959260 | + | 0.282526i | \(0.908828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2145i | 0.625768i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.2037 | 0.879070 | 0.439535 | − | 0.898225i | \(-0.355143\pi\) | ||||
0.439535 | + | 0.898225i | \(0.355143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.23765 | 0.215971 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 0.550984i | − 0.0280081i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.7311i | 1.71023i | 0.518436 | + | 0.855116i | \(0.326514\pi\) | ||||
−0.518436 | + | 0.855116i | \(0.673486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2306 | 0.921961 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.33962 | −0.269348 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6333i | 0.786597i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.5201i | − 0.728742i | −0.931254 | − | 0.364371i | \(-0.881284\pi\) | ||||
0.931254 | − | 0.364371i | \(-0.118716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.4853 | −0.825296 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.2274 | −1.60936 | −0.804681 | − | 0.593708i | \(-0.797663\pi\) | ||||
−0.804681 | + | 0.593708i | \(0.797663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 26.7816i | − 1.33409i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2.47363i | − 0.122915i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58526 | 0.128146 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5702 | 0.572110 | 0.286055 | − | 0.958213i | \(-0.407656\pi\) | ||||
0.286055 | + | 0.958213i | \(0.407656\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 5.10587i | − 0.251854i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 14.4682i | − 0.711935i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.24471 | −0.110188 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.6533 | −0.815517 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.54193i | 0.466154i | 0.972458 | + | 0.233077i | \(0.0748794\pi\) | ||||
−0.972458 | + | 0.233077i | \(0.925121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3583i | 1.18715i | 0.804778 | + | 0.593576i | \(0.202284\pi\) | ||||
−0.804778 | + | 0.593576i | \(0.797716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.21137 | −0.349803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 15.8647i | − 0.767746i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.73551i | − 0.132072i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.7088 | 1.96087 | 0.980437 | − | 0.196832i | \(-0.0630654\pi\) | ||||
0.980437 | + | 0.196832i | \(0.0630654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.31371 | −0.351474 | −0.175737 | − | 0.984437i | \(-0.556231\pi\) | ||||
−0.175737 | + | 0.984437i | \(0.556231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 10.7721i | − 0.516485i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2306i | 0.872087i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7122 | 0.845356 | 0.422678 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422678 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.458440 | 0.0218305 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1953i | 1.05453i | 0.849701 | + | 0.527264i | \(0.176782\pi\) | ||||
−0.849701 | + | 0.527264i | \(0.823218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 15.6265i | − 0.740766i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.1832 | −0.528949 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.3400 | −1.33745 | −0.668723 | − | 0.743511i | \(-0.733159\pi\) | ||||
−0.668723 | + | 0.743511i | \(0.733159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.528232i | 0.0248735i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 14.6506i | − 0.688344i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.8382 | −1.21131 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3396 | 0.811113 | 0.405557 | − | 0.914070i | \(-0.367078\pi\) | ||||
0.405557 | + | 0.914070i | \(0.367078\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.44549i | 0.300850i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.39404i | − 0.111501i | −0.998445 | − | 0.0557507i | \(-0.982245\pi\) | ||||
0.998445 | − | 0.0557507i | \(-0.0177552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.70238 | 0.125590 | 0.0627951 | − | 0.998026i | \(-0.479999\pi\) | ||||
0.0627951 | + | 0.998026i | \(0.479999\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.2212 | 0.752239 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.2023i | 1.11995i | 0.828510 | + | 0.559975i | \(0.189189\pi\) | ||||
−0.828510 | + | 0.559975i | \(0.810811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.66391i | 0.353887i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.45754 | 0.205393 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.369053 | 0.0169691 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 7.21137i | − 0.330880i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.64520i | 0.166902i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.2251 | 1.01549 | 0.507745 | − | 0.861508i | \(-0.330479\pi\) | ||||
0.507745 | + | 0.861508i | \(0.330479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.7631 | −0.718735 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.23412i | 0.329164i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 31.2996i | − 1.42124i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9839 | 0.633672 | 0.316836 | − | 0.948480i | \(-0.397380\pi\) | ||||
0.316836 | + | 0.948480i | \(0.397380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.78510 | 0.352055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 10.2306i | − 0.461700i | −0.972989 | − | 0.230850i | \(-0.925849\pi\) | ||||
0.972989 | − | 0.230850i | \(-0.0741507\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0688i | 1.26416i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0831 | −0.586858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3.66391i | − 0.164019i | −0.996632 | − | 0.0820097i | \(-0.973866\pi\) | ||||
0.996632 | − | 0.0820097i | \(-0.0261338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1814i | 0.901637i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.6443 | −1.76765 | −0.883825 | − | 0.467817i | \(-0.845041\pi\) | ||||
−0.883825 | + | 0.467817i | \(0.845041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.3235 | −1.17138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.67923i | 0.163400i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 28.6909i | − 1.27170i | −0.771812 | − | 0.635851i | \(-0.780649\pi\) | ||||
0.771812 | − | 0.635851i | \(-0.219351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.7819 | −1.67137 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.44549 | −0.284575 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8.25413i | − 0.363721i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.89450i | − 0.0833201i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.15639 | 0.270235 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1784 | −1.01546 | −0.507732 | − | 0.861515i | \(-0.669516\pi\) | ||||
−0.507732 | + | 0.861515i | \(0.669516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.18193i | 0.357771i | 0.983870 | + | 0.178885i | \(0.0572491\pi\) | ||||
−0.983870 | + | 0.178885i | \(0.942751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2.86156i | − 0.124889i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.2672 | −1.84119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.65685i | − 0.245487i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.22079i | − 0.139508i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.1941 | 2.12685 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.7855 | 0.810653 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.307067i | 0.0132263i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 6.43715i | − 0.276755i | −0.990380 | − | 0.138377i | \(-0.955811\pi\) | ||||
0.990380 | − | 0.138377i | \(-0.0441887\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.97499 | 0.385154 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.68667 | 0.414931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 39.2239i | − 1.67709i | −0.544830 | − | 0.838546i | \(-0.683406\pi\) | ||||
0.544830 | − | 0.838546i | \(-0.316594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6.20285i | − 0.264731i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0688 | −1.19577 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.1643 | 0.687377 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 9.54745i | − 0.405267i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.66224i | − 0.0704315i | −0.999380 | − | 0.0352157i | \(-0.988788\pi\) | ||||
0.999380 | − | 0.0352157i | \(-0.0112118\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.25023 | −0.0951745 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.31724 | −0.182274 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.6368i | 1.71264i | 0.516447 | + | 0.856319i | \(0.327254\pi\) | ||||
−0.516447 | + | 0.856319i | \(0.672746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.53511i | 0.232864i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.55765 | −0.107411 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0004 | 1.13191 | 0.565957 | − | 0.824435i | \(-0.308507\pi\) | ||||
0.565957 | + | 0.824435i | \(0.308507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 20.9706i | − 0.877591i | −0.898587 | − | 0.438795i | \(-0.855405\pi\) | ||||
0.898587 | − | 0.438795i | \(-0.144595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.60058i | 0.233967i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.16451 | −0.131969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6372 | −1.56686 | −0.783429 | − | 0.621481i | \(-0.786531\pi\) | ||||
−0.783429 | + | 0.621481i | \(0.786531\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.4514i | 0.808372i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.32095i | 0.0962894i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.44158 | −0.101120 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.1023 | −0.417680 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.2047i | 1.82452i | 0.409609 | + | 0.912261i | \(0.365665\pi\) | ||||
−0.409609 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 42.2672i | − 1.74159i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.75070 | −0.0720140 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.59611 | 0.147675 | 0.0738373 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738373 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.7784i | 1.67175i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.993710i | 0.0406698i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.0296 | 0.900104 | 0.450052 | − | 0.893002i | \(-0.351405\pi\) | ||||
0.450052 | + | 0.893002i | \(0.351405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.7721 | −0.439405 | −0.219703 | − | 0.975567i | \(-0.570509\pi\) | ||||
−0.219703 | + | 0.975567i | \(0.570509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.99647i | 0.122026i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 26.1001i | − 1.06112i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.47453 | −0.222204 | −0.111102 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111102 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.1380 | −0.451336 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5514i | 0.467318i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8562i | 0.600035i | 0.953934 | + | 0.300018i | \(0.0969925\pi\) | ||||
−0.953934 | + | 0.300018i | \(0.903007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.95078 | 0.0786631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.2235 | −0.894686 | −0.447343 | − | 0.894363i | \(-0.647630\pi\) | ||||
−0.447343 | + | 0.894363i | \(0.647630\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 16.4612i | − 0.661631i | −0.943696 | − | 0.330815i | \(-0.892676\pi\) | ||||
0.943696 | − | 0.330815i | \(-0.107324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843i | 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1573 | −0.647327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.3424 | −1.17369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.31724i | − 0.172414i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.8776i | 0.991937i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.06977 | −0.162015 | −0.0810075 | − | 0.996713i | \(-0.525814\pi\) | ||||
−0.0810075 | + | 0.996713i | \(0.525814\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.97409 | −0.237449 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.2141i | 1.19901i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.87228i | − 0.0741824i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.11529 | −0.202358 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.41958 | −0.332553 | −0.166277 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166277 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 10.4266i | − 0.411186i | −0.978638 | − | 0.205593i | \(-0.934088\pi\) | ||||
0.978638 | − | 0.205593i | \(-0.0659124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.36293i | − 0.0536652i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.6132 | 0.456560 | 0.228280 | − | 0.973595i | \(-0.426690\pi\) | ||||
0.228280 | + | 0.973595i | \(0.426690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.78901 | 0.148731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 16.7721i | − 0.657352i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2.73012i | − 0.106838i | −0.998572 | − | 0.0534190i | \(-0.982988\pi\) | ||||
0.998572 | − | 0.0534190i | \(-0.0170119\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2082 | −0.516088 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.7721 | −0.576316 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 31.5514i | − 1.22907i | −0.788891 | − | 0.614533i | \(-0.789344\pi\) | ||||
0.788891 | − | 0.614533i | \(-0.210656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1368i | 0.588752i | 0.955690 | + | 0.294376i | \(0.0951118\pi\) | ||||
−0.955690 | + | 0.294376i | \(0.904888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.3235 | 1.02232 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40.7784 | −1.58132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3172i | 0.476925i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 23.7659i | − 0.918841i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.15472 | 0.160391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6345 | −0.795401 | −0.397700 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397700 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.11882i | − 0.0430636i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 37.9357i | − 1.45799i | −0.684520 | − | 0.728994i | \(-0.739988\pi\) | ||||
0.684520 | − | 0.728994i | \(-0.260012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.3627 | −1.24197 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.907457 | −0.0347738 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 18.2471i | − 0.698205i | −0.937085 | − | 0.349102i | \(-0.886487\pi\) | ||||
0.937085 | − | 0.349102i | \(-0.113513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.6300i | − 0.482568i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.55579 | −0.288271 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.8871 | 0.567152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.2533i | 1.15089i | 0.817840 | + | 0.575446i | \(0.195171\pi\) | ||||
−0.817840 | + | 0.575446i | \(0.804829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.71313i | − 0.0650765i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.1941 | −1.56258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.08312 | −0.192537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 23.2271i | − 0.878528i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 20.0875i | − 0.758696i | −0.925254 | − | 0.379348i | \(-0.876148\pi\) | ||||
0.925254 | − | 0.379348i | \(-0.123852\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.8776 | −0.938278 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.99647 | −0.263502 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.2176i | 1.02362i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7864i | 1.56932i | 0.619926 | + | 0.784660i | \(0.287163\pi\) | ||||
−0.619926 | + | 0.784660i | \(0.712837\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.32000 | 0.237018 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.5478 | −0.694622 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6.76663i | − 0.253058i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 26.9213i | − 1.00540i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.3683 | 1.05796 | 0.528979 | − | 0.848635i | \(-0.322575\pi\) | ||||
0.528979 | + | 0.848635i | \(0.322575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.53450 | −0.317841 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 10.3494i | − 0.384899i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 4.87226i | − 0.180951i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.4843 | −0.759722 | −0.379861 | − | 0.925044i | \(-0.624028\pi\) | ||||
−0.379861 | + | 0.925044i | \(0.624028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.55136i | 0.131352i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 48.0777i | − 1.77579i | −0.460045 | − | 0.887895i | \(-0.652167\pi\) | ||||
0.460045 | − | 0.887895i | \(-0.347833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.13401 | 0.0418286 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.00706 | −0.0739310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4459i | 0.788899i | 0.918918 | + | 0.394449i | \(0.129065\pi\) | ||||
−0.918918 | + | 0.394449i | \(0.870935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.3235i | 0.967018i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.17431 | 0.0797677 | 0.0398839 | − | 0.999204i | \(-0.487301\pi\) | ||||
0.0398839 | + | 0.999204i | \(0.487301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.6631 | −1.01350 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.907457i | 0.0332021i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 50.8651i | − 1.85857i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.8980 | 1.09099 | 0.545497 | − | 0.838113i | \(-0.316341\pi\) | ||||
0.545497 | + | 0.838113i | \(0.316341\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7984 | −0.502843 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 36.2400i | − 1.31891i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 21.6791i | − 0.787939i | −0.919123 | − | 0.393970i | \(-0.871101\pi\) | ||||
0.919123 | − | 0.393970i | \(-0.128899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.89450 | −0.0687661 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.29449 | −0.155675 | −0.0778375 | − | 0.996966i | \(-0.524802\pi\) | ||||
−0.0778375 | + | 0.996966i | \(0.524802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.0157i | − 0.362592i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.9437i | 0.576446i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.1027 | −0.834191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.8819 | 1.22181 | 0.610907 | − | 0.791703i | \(-0.290805\pi\) | ||||
0.610907 | + | 0.791703i | \(0.290805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 16.9965i | − 0.612113i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.5300i | 1.78147i | 0.454521 | + | 0.890736i | \(0.349810\pi\) | ||||
−0.454521 | + | 0.890736i | \(0.650190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.33686 | 0.263548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.87175 | −0.354147 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5.08312i | − 0.182122i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3.42627i | − 0.122601i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.35480 | −0.155628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0263 | 0.393545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.0953i | − 1.21537i | −0.794180 | − | 0.607683i | \(-0.792099\pi\) | ||||
0.794180 | − | 0.607683i | \(-0.207901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.9929i | 1.06778i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.72312 | 0.203491 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.3326 | −0.899585 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.01686i | 0.319795i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.6901i | 1.44132i | 0.693290 | + | 0.720659i | \(0.256160\pi\) | ||||
−0.693290 | + | 0.720659i | \(0.743840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.2306 | 0.644952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.31724 | −0.223209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.89450i | − 0.349169i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.8945i | 0.630698i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.1332 | 1.02554 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9926 | 0.386478 | 0.193239 | − | 0.981152i | \(-0.438101\pi\) | ||||
0.193239 | + | 0.981152i | \(0.438101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.2498i | 0.746182i | 0.927795 | + | 0.373091i | \(0.121702\pi\) | ||||
−0.927795 | + | 0.373091i | \(0.878298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.6506i | 0.934676i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2574 | 0.674558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.55136 | −0.124246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4455i | 0.364995i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 30.0572i | − 1.04900i | −0.851410 | − | 0.524501i | \(-0.824252\pi\) | ||||
0.851410 | − | 0.524501i | \(-0.175748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.0851 | −1.92015 | −0.960073 | − | 0.279751i | \(-0.909748\pi\) | ||||
−0.960073 | + | 0.279751i | \(0.909748\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.749397 | 0.0260907 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 34.5478i | − 1.20135i | −0.799495 | − | 0.600673i | \(-0.794899\pi\) | ||||
0.799495 | − | 0.600673i | \(-0.205101\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.0046i | 1.07683i | 0.842679 | + | 0.538417i | \(0.180977\pi\) | ||||
−0.842679 | + | 0.538417i | \(0.819023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.1430 | 0.594685 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.95487 | −0.102380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.9212i | 1.72759i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 6.55765i | − 0.226665i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.14195 | 0.177520 | 0.0887599 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887599 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0357 | 0.346059 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.76588i | 0.0952620i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.10104i | 0.313085i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.9867 | −0.927272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.34315 | 0.217696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9169i | 0.374226i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5060i | 0.633632i | 0.948487 | + | 0.316816i | \(0.102614\pi\) | ||||
−0.948487 | + | 0.316816i | \(0.897386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.9437 | −0.545264 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.8878 | −0.781833 | −0.390916 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390916 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 35.5286i | − 1.21222i | −0.795381 | − | 0.606110i | \(-0.792729\pi\) | ||||
0.795381 | − | 0.606110i | \(-0.207271\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2.01704i | − 0.0687407i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.9296 | 1.49538 | 0.747691 | − | 0.664047i | \(-0.231163\pi\) | ||||
0.747691 | + | 0.664047i | \(0.231163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.2286 | 0.517788 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 24.5443i | − 0.833568i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.23319i | 0.143601i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2376 | 0.414657 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.6533 | −0.428250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.5549i | 0.830107i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.5773i | 0.728614i | 0.931279 | + | 0.364307i | \(0.118694\pi\) | ||||
−0.931279 | + | 0.364307i | \(0.881306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.6078 | 0.391520 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6686 | −0.730035 | −0.365018 | − | 0.931001i | \(-0.618937\pi\) | ||||
−0.365018 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.0834930i | 0.00280976i | 0.999999 | + | 0.00140488i | \(0.000447188\pi\) | ||||
−0.999999 | + | 0.00140488i | \(0.999553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 13.9929i | − 0.470368i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8043 | 1.03431 | 0.517154 | − | 0.855892i | \(-0.326991\pi\) | ||||
0.517154 | + | 0.855892i | \(0.326991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2404 | 1.04777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 0.669808i | − 0.0224394i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.2306i | 0.610063i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.4682 | 1.55326 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.5514 | 0.385689 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 28.5573i | − 0.952438i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 23.4951i | − 0.782735i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.40922 | −0.0468960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.2008 | 0.737979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 49.5215i | − 1.64434i | −0.569245 | − | 0.822168i | \(-0.692764\pi\) | ||||
0.569245 | − | 0.822168i | \(-0.307236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6417i | 0.352962i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.0829331 | 0.00274770 | 0.00137385 | − | 0.999999i | \(-0.499563\pi\) | ||||
0.00137385 | + | 0.999999i | \(0.499563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.607822 | −0.0201160 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 15.3435i | − 0.507241i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6569i | 0.450989i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.1161 | 0.663568 | 0.331784 | − | 0.943355i | \(-0.392350\pi\) | ||||
0.331784 | + | 0.943355i | \(0.392350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.7855 | −0.487198 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.8910i | 0.687635i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.31833i | − 0.141986i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.33686 | −0.109597 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.55098 | 0.280549 | 0.140274 | − | 0.990113i | \(-0.455202\pi\) | ||||
0.140274 | + | 0.990113i | \(0.455202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.95487i | − 0.0968420i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0761i | 0.493568i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6792 | −0.349248 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5780 | −1.09695 | −0.548473 | − | 0.836168i | \(-0.684791\pi\) | ||||
−0.548473 | + | 0.836168i | \(0.684791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.0027i | 0.750666i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.9991i | − 0.391159i | −0.980688 | − | 0.195579i | \(-0.937341\pi\) | ||||
0.980688 | − | 0.195579i | \(-0.0626587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.23059 | −0.0726380 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.32666 | −0.205806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 25.2537i | − 0.820635i | −0.911943 | − | 0.410318i | \(-0.865418\pi\) | ||||
0.911943 | − | 0.410318i | \(-0.134582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.3298i | 1.95839i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.55855 | 0.309957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.86469 | −0.125190 | −0.0625948 | − | 0.998039i | \(-0.519938\pi\) | ||||
−0.0625948 | + | 0.998039i | \(0.519938\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.8537i | 0.448296i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.91688i | − 0.0942894i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.0590 | −0.421698 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0027 | 0.387185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 19.8874i | − 0.640864i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.1154i | 1.54889i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.8714 | −1.21786 | −0.608930 | − | 0.793224i | \(-0.708401\pi\) | ||||
−0.608930 | + | 0.793224i | \(0.708401\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.5443 | 1.33460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.74587i | − 0.120211i | −0.998192 | − | 0.0601053i | \(-0.980856\pi\) | ||||
0.998192 | − | 0.0601053i | \(-0.0191437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.5933i | 1.36548i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.56930 | −0.146335 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.6530 | −0.564768 | −0.282384 | − | 0.959301i | \(-0.591125\pi\) | ||||
−0.282384 | + | 0.959301i | \(0.591125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.23134i | − 0.135234i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.91598i | − 0.125028i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.3557 | 0.713035 | 0.356518 | − | 0.934289i | \(-0.383964\pi\) | ||||
0.356518 | + | 0.934289i | \(0.383964\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.33057 | −0.137983 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.23412i | 0.230265i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55842i | 0.0495548i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.8769 | −0.567878 | −0.283939 | − | 0.958842i | \(-0.591641\pi\) | ||||
−0.283939 | + | 0.958842i | \(0.591641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8079 | 0.882456 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45807i | 0.0779260i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 6.06146i | − 0.191968i | −0.995383 | − | 0.0959841i | \(-0.969400\pi\) | ||||
0.995383 | − | 0.0959841i | \(-0.0305998\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.85970 | −0.122116 |
(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 | 3072.2.d.i.1537.2 | 8 | ||
4.3 | odd | 2 | 3072.2.d.f.1537.6 | 8 | |||
8.3 | odd | 2 | 3072.2.d.f.1537.3 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.i.1537.7 | 8 | ||
16.3 | odd | 4 | 3072.2.a.i.1.2 | 4 | |||
16.5 | even | 4 | 3072.2.a.n.1.3 | 4 | |||
16.11 | odd | 4 | 3072.2.a.t.1.3 | 4 | |||
16.13 | even | 4 | 3072.2.a.o.1.2 | 4 | |||
32.3 | odd | 8 | 48.2.j.a.37.2 | yes | 8 | ||
32.5 | even | 8 | 192.2.j.a.145.4 | 8 | |||
32.11 | odd | 8 | 384.2.j.b.289.3 | 8 | |||
32.13 | even | 8 | 384.2.j.a.97.1 | 8 | |||
32.19 | odd | 8 | 384.2.j.b.97.3 | 8 | |||
32.21 | even | 8 | 384.2.j.a.289.1 | 8 | |||
32.27 | odd | 8 | 48.2.j.a.13.2 | ✓ | 8 | ||
32.29 | even | 8 | 192.2.j.a.49.4 | 8 | |||
48.5 | odd | 4 | 9216.2.a.x.1.2 | 4 | |||
48.11 | even | 4 | 9216.2.a.y.1.2 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bn.1.3 | 4 | |||
48.35 | even | 4 | 9216.2.a.bo.1.3 | 4 | |||
96.5 | odd | 8 | 576.2.k.b.145.1 | 8 | |||
96.11 | even | 8 | 1152.2.k.c.289.4 | 8 | |||
96.29 | odd | 8 | 576.2.k.b.433.1 | 8 | |||
96.35 | even | 8 | 144.2.k.b.37.3 | 8 | |||
96.53 | odd | 8 | 1152.2.k.f.289.4 | 8 | |||
96.59 | even | 8 | 144.2.k.b.109.3 | 8 | |||
96.77 | odd | 8 | 1152.2.k.f.865.4 | 8 | |||
96.83 | even | 8 | 1152.2.k.c.865.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.2 | ✓ | 8 | 32.27 | odd | 8 | ||
48.2.j.a.37.2 | yes | 8 | 32.3 | odd | 8 | ||
144.2.k.b.37.3 | 8 | 96.35 | even | 8 | |||
144.2.k.b.109.3 | 8 | 96.59 | even | 8 | |||
192.2.j.a.49.4 | 8 | 32.29 | even | 8 | |||
192.2.j.a.145.4 | 8 | 32.5 | even | 8 | |||
384.2.j.a.97.1 | 8 | 32.13 | even | 8 | |||
384.2.j.a.289.1 | 8 | 32.21 | even | 8 | |||
384.2.j.b.97.3 | 8 | 32.19 | odd | 8 | |||
384.2.j.b.289.3 | 8 | 32.11 | odd | 8 | |||
576.2.k.b.145.1 | 8 | 96.5 | odd | 8 | |||
576.2.k.b.433.1 | 8 | 96.29 | odd | 8 | |||
1152.2.k.c.289.4 | 8 | 96.11 | even | 8 | |||
1152.2.k.c.865.4 | 8 | 96.83 | even | 8 | |||
1152.2.k.f.289.4 | 8 | 96.53 | odd | 8 | |||
1152.2.k.f.865.4 | 8 | 96.77 | odd | 8 | |||
3072.2.a.i.1.2 | 4 | 16.3 | odd | 4 | |||
3072.2.a.n.1.3 | 4 | 16.5 | even | 4 | |||
3072.2.a.o.1.2 | 4 | 16.13 | even | 4 | |||
3072.2.a.t.1.3 | 4 | 16.11 | odd | 4 | |||
3072.2.d.f.1537.3 | 8 | 8.3 | odd | 2 | |||
3072.2.d.f.1537.6 | 8 | 4.3 | odd | 2 | |||
3072.2.d.i.1537.2 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.i.1537.7 | 8 | 8.5 | even | 2 | inner | ||
9216.2.a.x.1.2 | 4 | 48.5 | odd | 4 | |||
9216.2.a.y.1.2 | 4 | 48.11 | even | 4 | |||
9216.2.a.bn.1.3 | 4 | 48.29 | odd | 4 | |||
9216.2.a.bo.1.3 | 4 | 48.35 | even | 4 |