Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (of order \(3\), degree \(2\), 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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.8528759163648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.1 | ||
Root | \(1.06839 + 1.36328i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.2305 |
Dual form | 3456.2.i.f.1153.1 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.34011 | + | 2.32114i | −0.599317 | + | 1.03805i | 0.393605 | + | 0.919279i | \(0.371228\pi\) |
−0.992922 | + | 0.118767i | \(0.962106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.48656 | − | 4.30684i | −0.939830 | − | 1.62783i | −0.765786 | − | 0.643095i | \(-0.777650\pi\) |
−0.174043 | − | 0.984738i | \(-0.555683\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26947 | + | 2.19879i | 0.382760 | + | 0.662960i | 0.991456 | − | 0.130444i | \(-0.0416402\pi\) |
−0.608696 | + | 0.793404i | \(0.708307\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.21483 | + | 3.83620i | −0.614284 | + | 1.06397i | 0.376225 | + | 0.926528i | \(0.377222\pi\) |
−0.990510 | + | 0.137443i | \(0.956111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.43417 | 0.590373 | 0.295186 | − | 0.955440i | \(-0.404618\pi\) | ||||
0.295186 | + | 0.955440i | \(0.404618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.18361 | 0.959786 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.570641 | + | 0.988379i | −0.118987 | + | 0.206091i | −0.919366 | − | 0.393402i | \(-0.871298\pi\) |
0.800380 | + | 0.599494i | \(0.204631\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.09180 | − | 1.89106i | −0.218361 | − | 0.378212i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00434 | + | 5.20366i | 0.557891 | + | 0.966296i | 0.997672 | + | 0.0681908i | \(0.0217227\pi\) |
−0.439781 | + | 0.898105i | \(0.644944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65303 | − | 4.59518i | 0.476498 | − | 0.825319i | −0.523139 | − | 0.852247i | \(-0.675239\pi\) |
0.999637 | + | 0.0269282i | \(0.00857256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.3291 | 2.25302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.241556 | −0.0397115 | −0.0198558 | − | 0.999803i | \(-0.506321\pi\) | ||||
−0.0198558 | + | 0.999803i | \(0.506321\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.21105 | − | 5.56170i | 0.501482 | − | 0.868592i | −0.498517 | − | 0.866880i | \(-0.666122\pi\) |
0.999999 | − | 0.00171211i | \(-0.000544983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.57273 | − | 9.65224i | −0.849833 | − | 1.47195i | −0.881357 | − | 0.472451i | \(-0.843370\pi\) |
0.0315245 | − | 0.999503i | \(-0.489964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.37728 | − | 4.11757i | −0.346762 | − | 0.600609i | 0.638910 | − | 0.769281i | \(-0.279385\pi\) |
−0.985672 | + | 0.168672i | \(0.946052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.86592 | + | 15.3562i | −1.26656 | + | 2.19375i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.38345 | −1.28892 | −0.644458 | − | 0.764640i | \(-0.722917\pi\) | ||||
−0.644458 | + | 0.764640i | \(0.722917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.80494 | −0.917578 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.40906 | + | 9.36876i | −0.704199 | + | 1.21971i | 0.262781 | + | 0.964856i | \(0.415360\pi\) |
−0.966980 | + | 0.254853i | \(0.917973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.16044 | − | 7.20610i | −0.532690 | − | 0.922646i | −0.999271 | − | 0.0381677i | \(-0.987848\pi\) |
0.466581 | − | 0.884478i | \(-0.345485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.93625 | − | 10.2819i | −0.736302 | − | 1.27531i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.13269 | + | 1.96188i | −0.138380 | + | 0.239682i | −0.926884 | − | 0.375349i | \(-0.877523\pi\) |
0.788503 | + | 0.615030i | \(0.210856\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.52639 | −0.537183 | −0.268592 | − | 0.963254i | \(-0.586558\pi\) | ||||
−0.268592 | + | 0.963254i | \(0.586558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.34728 | −0.391769 | −0.195885 | − | 0.980627i | \(-0.562758\pi\) | ||||
−0.195885 | + | 0.980627i | \(0.562758\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.31322 | − | 10.9348i | 0.719459 | − | 1.24614i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.14159 | + | 5.44139i | 0.353457 | + | 0.612205i | 0.986853 | − | 0.161623i | \(-0.0516729\pi\) |
−0.633396 | + | 0.773828i | \(0.718340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.738248 | + | 1.27868i | 0.0810332 | + | 0.140354i | 0.903694 | − | 0.428179i | \(-0.140845\pi\) |
−0.822661 | + | 0.568533i | \(0.807511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.26206 | + | 5.65005i | −0.353820 | + | 0.612834i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8823 | −1.57752 | −0.788762 | − | 0.614698i | \(-0.789278\pi\) | ||||
−0.788762 | + | 0.614698i | \(0.789278\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.0292 | 2.30929 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.60651 | + | 9.71076i | −0.575216 | + | 0.996303i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.89884 | + | 10.2171i | 0.598937 | + | 1.03739i | 0.992978 | + | 0.118296i | \(0.0377432\pi\) |
−0.394042 | + | 0.919093i | \(0.628923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.81211 | − | 10.0669i | −0.578326 | − | 1.00169i | −0.995671 | − | 0.0929424i | \(-0.970373\pi\) |
0.417345 | − | 0.908748i | \(-0.362961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.54962 | + | 16.5404i | −0.940952 | + | 1.62978i | −0.177292 | + | 0.984158i | \(0.556734\pi\) |
−0.763660 | + | 0.645618i | \(0.776600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.99694 | −0.483072 | −0.241536 | − | 0.970392i | \(-0.577651\pi\) | ||||
−0.241536 | + | 0.970392i | \(0.577651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.15690 | 0.206594 | 0.103297 | − | 0.994651i | \(-0.467061\pi\) | ||||
0.103297 | + | 0.994651i | \(0.467061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2451 | + | 17.7451i | −0.963782 | + | 1.66932i | −0.250929 | + | 0.968005i | \(0.580736\pi\) |
−0.712853 | + | 0.701314i | \(0.752597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.52945 | − | 2.64908i | −0.142622 | − | 0.247028i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.05270 | − | 10.4836i | −0.554850 | − | 0.961028i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.27688 | − | 3.94368i | 0.206989 | − | 0.358516i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.54856 | −0.675164 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.71867 | −0.862392 | −0.431196 | − | 0.902258i | \(-0.641908\pi\) | ||||
−0.431196 | + | 0.902258i | \(0.641908\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.49219 | + | 6.04865i | −0.305114 | + | 0.528473i | −0.977287 | − | 0.211921i | \(-0.932028\pi\) |
0.672173 | + | 0.740394i | \(0.265361\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.4028 | − | 18.0181i | −0.902035 | − | 1.56237i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.2072 | − | 19.4114i | −0.957493 | − | 1.65843i | −0.728558 | − | 0.684984i | \(-0.759809\pi\) |
−0.228935 | − | 0.973442i | \(-0.573524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.56822 | − | 4.44830i | 0.217834 | − | 0.377299i | −0.736312 | − | 0.676643i | \(-0.763434\pi\) |
0.954146 | + | 0.299343i | \(0.0967675\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.2467 | −0.940494 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.1046 | −1.33741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.08562 | + | 1.88034i | −0.0889372 | + | 0.154044i | −0.907062 | − | 0.420997i | \(-0.861680\pi\) |
0.818125 | + | 0.575040i | \(0.195014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.10508 | + | 5.37816i | 0.252688 | + | 0.437669i | 0.964265 | − | 0.264940i | \(-0.0853520\pi\) |
−0.711577 | + | 0.702608i | \(0.752019\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.11072 | + | 12.3161i | 0.571147 | + | 0.989255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.97578 | + | 13.8144i | −0.636536 | + | 1.10251i | 0.349651 | + | 0.936880i | \(0.386300\pi\) |
−0.986187 | + | 0.165633i | \(0.947033\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.67572 | 0.447310 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.72991 | −0.370475 | −0.185237 | − | 0.982694i | \(-0.559305\pi\) | ||||
−0.185237 | + | 0.982694i | \(0.559305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.18611 | − | 2.05440i | 0.0917836 | − | 0.158974i | −0.816478 | − | 0.577376i | \(-0.804077\pi\) |
0.908262 | + | 0.418403i | \(0.137410\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31097 | − | 5.73477i | −0.254690 | − | 0.441137i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.19528 | + | 2.07028i | 0.0908752 | + | 0.157400i | 0.907880 | − | 0.419231i | \(-0.137700\pi\) |
−0.817004 | + | 0.576631i | \(0.804367\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.42967 | + | 9.40446i | −0.410444 | + | 0.710910i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.19567 | 0.0893689 | 0.0446845 | − | 0.999001i | \(-0.485772\pi\) | ||||
0.0446845 | + | 0.999001i | \(0.485772\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.17390 | −0.384573 | −0.192287 | − | 0.981339i | \(-0.561590\pi\) | ||||
−0.192287 | + | 0.981339i | \(0.561590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.323712 | − | 0.560686i | 0.0237998 | − | 0.0412224i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.09011 | + | 5.35222i | 0.225971 | + | 0.391393i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.654726 | + | 1.13402i | 0.0473743 | + | 0.0820548i | 0.888740 | − | 0.458411i | \(-0.151581\pi\) |
−0.841366 | + | 0.540466i | \(0.818248\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0726 | − | 17.4463i | 0.725043 | − | 1.25581i | −0.233913 | − | 0.972257i | \(-0.575153\pi\) |
0.958956 | − | 0.283554i | \(-0.0915135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.46023 | −0.531520 | −0.265760 | − | 0.964039i | \(-0.585623\pi\) | ||||
−0.265760 | + | 0.964039i | \(0.585623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.47361 | 0.246238 | 0.123119 | − | 0.992392i | \(-0.460710\pi\) | ||||
0.123119 | + | 0.992392i | \(0.460710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.9409 | − | 25.8784i | 1.04865 | − | 1.81631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.60634 | + | 14.9066i | 0.601093 | + | 1.04112i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.31097 | + | 9.19888i | 0.367368 | + | 0.636300i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.38878 | − | 7.60159i | 0.302136 | − | 0.523315i | −0.674483 | − | 0.738290i | \(-0.735634\pi\) |
0.976620 | + | 0.214975i | \(0.0689670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.8723 | 2.03728 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.3876 | −1.79131 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.39128 | + | 9.33797i | −0.362657 | + | 0.628140i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.42411 | − | 12.8589i | −0.497155 | − | 0.861098i | 0.502840 | − | 0.864380i | \(-0.332289\pi\) |
−0.999995 | + | 0.00328197i | \(0.998955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.49314 | − | 16.4426i | −0.630082 | − | 1.09133i | −0.987535 | − | 0.157403i | \(-0.949688\pi\) |
0.357453 | − | 0.933931i | \(-0.383645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.17194 | − | 2.02986i | 0.0774441 | − | 0.134137i | −0.824702 | − | 0.565567i | \(-0.808657\pi\) |
0.902147 | + | 0.431430i | \(0.141991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.0912 | −0.792120 | −0.396060 | − | 0.918225i | \(-0.629623\pi\) | ||||
−0.396060 | + | 0.918225i | \(0.629623\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7433 | 0.831281 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.54375 | − | 13.0662i | 0.487965 | − | 0.845180i | −0.511939 | − | 0.859022i | \(-0.671073\pi\) |
0.999904 | + | 0.0138417i | \(0.00440610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.01095 | + | 1.75101i | 0.0651208 | + | 0.112793i | 0.896748 | − | 0.442542i | \(-0.145923\pi\) |
−0.831627 | + | 0.555335i | \(0.812590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.7627 | − | 41.1581i | −1.51814 | − | 2.62950i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.26600 | + | 16.0492i | −0.589581 | + | 1.02118i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7796 | 1.18536 | 0.592679 | − | 0.805438i | \(-0.298070\pi\) | ||||
0.592679 | + | 0.805438i | \(0.298070\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.89765 | −0.182174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5006 | − | 19.9197i | 0.717389 | − | 1.24255i | −0.244642 | − | 0.969613i | \(-0.578671\pi\) |
0.962031 | − | 0.272940i | \(-0.0879961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.600642 | + | 1.04034i | 0.0373221 | + | 0.0646437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.77774 | − | 16.9356i | −0.602922 | − | 1.04429i | −0.992376 | − | 0.123245i | \(-0.960670\pi\) |
0.389455 | − | 0.921046i | \(-0.372663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.5749 | − | 21.7803i | 0.772469 | − | 1.33796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2107 | −0.805468 | −0.402734 | − | 0.915317i | \(-0.631940\pi\) | ||||
−0.402734 | + | 0.915317i | \(0.631940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.63055 | 0.524268 | 0.262134 | − | 0.965031i | \(-0.415574\pi\) | ||||
0.262134 | + | 0.965031i | \(0.415574\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.77203 | − | 4.80130i | 0.167160 | − | 0.289529i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.21650 | + | 2.10705i | 0.0730927 | + | 0.126600i | 0.900255 | − | 0.435362i | \(-0.143380\pi\) |
−0.827163 | + | 0.561963i | \(0.810046\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.75715 | + | 8.23962i | 0.283787 | + | 0.491534i | 0.972314 | − | 0.233676i | \(-0.0750756\pi\) |
−0.688527 | + | 0.725211i | \(0.741742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.27042 | + | 9.12864i | −0.313294 | + | 0.542641i | −0.979073 | − | 0.203507i | \(-0.934766\pi\) |
0.665779 | + | 0.746149i | \(0.268099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.9378 | −1.88523 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0748 | −0.651460 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.10888 | − | 5.38474i | 0.181623 | − | 0.314580i | −0.760811 | − | 0.648974i | \(-0.775198\pi\) |
0.942433 | + | 0.334394i | \(0.108532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4975 | − | 25.1104i | −0.844077 | − | 1.46198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.52775 | − | 4.37819i | −0.146184 | − | 0.253197i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.7138 | + | 48.0017i | −1.59740 | + | 2.76677i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.3018 | 1.27700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.45594 | 0.140168 | 0.0700839 | − | 0.997541i | \(-0.477673\pi\) | ||||
0.0700839 | + | 0.997541i | \(0.477673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.06337 | − | 3.57386i | 0.117003 | − | 0.202655i | −0.801576 | − | 0.597893i | \(-0.796005\pi\) |
0.918579 | + | 0.395238i | \(0.129338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.66061 | + | 4.60831i | 0.150386 | + | 0.260477i | 0.931370 | − | 0.364075i | \(-0.118615\pi\) |
−0.780983 | + | 0.624552i | \(0.785282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1291 | + | 17.5440i | 0.568904 | + | 0.985371i | 0.996675 | + | 0.0814836i | \(0.0259658\pi\) |
−0.427770 | + | 0.903887i | \(0.640701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.62784 | + | 13.2118i | −0.427077 | + | 0.739719i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1836 | 0.566631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.67266 | 0.536543 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.8225 | + | 20.4771i | −0.651794 | + | 1.12894i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.88990 | − | 8.46955i | −0.268773 | − | 0.465529i | 0.699772 | − | 0.714366i | \(-0.253285\pi\) |
−0.968545 | + | 0.248837i | \(0.919952\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.03587 | − | 5.25828i | −0.165867 | − | 0.287290i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.61501 | + | 13.1896i | −0.414816 | + | 0.718482i | −0.995409 | − | 0.0957115i | \(-0.969487\pi\) |
0.580593 | + | 0.814194i | \(0.302821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4718 | 0.729538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 53.3706 | 2.88174 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.12881 | + | 5.41925i | −0.167963 | + | 0.290921i | −0.937704 | − | 0.347436i | \(-0.887052\pi\) |
0.769741 | + | 0.638357i | \(0.220386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0277 | + | 17.3685i | 0.536772 | + | 0.929716i | 0.999075 | + | 0.0429941i | \(0.0136897\pi\) |
−0.462304 | + | 0.886722i | \(0.652977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.26961 | + | 16.0554i | 0.493372 | + | 0.854545i | 0.999971 | − | 0.00763681i | \(-0.00243089\pi\) |
−0.506599 | + | 0.862182i | \(0.669098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.06587 | − | 10.5064i | 0.321943 | − | 0.557621i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.2838 | −1.33443 | −0.667213 | − | 0.744867i | \(-0.732513\pi\) | ||||
−0.667213 | + | 0.744867i | \(0.732513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.49741 | −0.0788112 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.48573 | − | 7.76951i | 0.234794 | − | 0.406675i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.32458 | − | 10.9545i | −0.330141 | − | 0.571820i | 0.652399 | − | 0.757876i | \(-0.273763\pi\) |
−0.982539 | + | 0.186056i | \(0.940429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3325 | + | 40.4130i | 1.21136 | + | 2.09814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.39906 | − | 16.2796i | 0.486665 | − | 0.842928i | −0.513218 | − | 0.858258i | \(-0.671547\pi\) |
0.999882 | + | 0.0153303i | \(0.00487998\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.6164 | −1.37081 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.15057 | −0.110467 | −0.0552337 | − | 0.998473i | \(-0.517590\pi\) | ||||
−0.0552337 | + | 0.998473i | \(0.517590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2847 | − | 28.2060i | 0.832111 | − | 1.44126i | −0.0642505 | − | 0.997934i | \(-0.520466\pi\) |
0.896361 | − | 0.443324i | \(-0.146201\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.9209 | + | 29.3078i | 0.862367 | + | 1.49366i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.9569 | + | 20.7100i | 0.606241 | + | 1.05004i | 0.991854 | + | 0.127380i | \(0.0406567\pi\) |
−0.385613 | + | 0.922661i | \(0.626010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.38904 | + | 2.40588i | −0.0702466 | + | 0.121671i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.8403 | −0.847329 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.42557 | −0.222113 | −0.111056 | − | 0.993814i | \(-0.535423\pi\) | ||||
−0.111056 | + | 0.993814i | \(0.535423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.04462 | − | 5.27344i | 0.152041 | − | 0.263343i | −0.779936 | − | 0.625859i | \(-0.784749\pi\) |
0.931978 | + | 0.362515i | \(0.118082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.7520 | + | 20.3551i | 0.585411 | + | 1.01396i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.306648 | − | 0.531130i | −0.0152000 | − | 0.0263272i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.23061 | + | 2.13148i | −0.0608497 | + | 0.105395i | −0.894845 | − | 0.446376i | \(-0.852714\pi\) |
0.833996 | + | 0.551771i | \(0.186048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 53.7997 | 2.64731 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.95734 | −0.194258 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.75667 | + | 16.8991i | −0.476645 | + | 0.825573i | −0.999642 | − | 0.0267617i | \(-0.991480\pi\) |
0.522997 | + | 0.852334i | \(0.324814\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.52846 | − | 16.5038i | −0.464389 | − | 0.804345i | 0.534785 | − | 0.844988i | \(-0.320393\pi\) |
−0.999174 | + | 0.0406435i | \(0.987059\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.65764 | − | 4.60316i | −0.128914 | − | 0.223286i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.6903 | + | 35.8367i | −1.00128 | + | 1.73426i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.6111 | 1.13731 | 0.568654 | − | 0.822577i | \(-0.307464\pi\) | ||||
0.568654 | + | 0.822577i | \(0.307464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.09660 | −0.100756 | −0.0503780 | − | 0.998730i | \(-0.516043\pi\) | ||||
−0.0503780 | + | 0.998730i | \(0.516043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.38734 | + | 4.13499i | −0.114202 | + | 0.197804i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.38026 | − | 7.58684i | −0.209059 | − | 0.362100i | 0.742360 | − | 0.670002i | \(-0.233707\pi\) |
−0.951418 | + | 0.307901i | \(0.900373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.51251 | + | 7.81590i | 0.214396 | + | 0.371345i | 0.953086 | − | 0.302701i | \(-0.0978884\pi\) |
−0.738690 | + | 0.674046i | \(0.764555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.9440 | − | 34.5440i | 0.945437 | − | 1.63754i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.54295 | 0.120009 | 0.0600047 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600047 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.3054 | 0.767789 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.5216 | + | 51.1330i | −1.38400 | + | 2.39715i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9090 | + | 22.3590i | 0.603855 | + | 1.04591i | 0.992231 | + | 0.124407i | \(0.0397029\pi\) |
−0.388376 | + | 0.921501i | \(0.626964\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4517 | − | 21.5669i | −0.579932 | − | 1.00447i | −0.995486 | − | 0.0949039i | \(-0.969746\pi\) |
0.415554 | − | 0.909568i | \(-0.363588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.0655 | + | 19.1660i | −0.514258 | + | 0.890721i | 0.485605 | + | 0.874178i | \(0.338599\pi\) |
−0.999863 | + | 0.0165428i | \(0.994734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7135 | −1.14361 | −0.571803 | − | 0.820391i | \(-0.693756\pi\) | ||||
−0.571803 | + | 0.820391i | \(0.693756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2660 | 0.520215 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.1488 | − | 24.5065i | 0.650564 | − | 1.12681i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.56768 | − | 7.91146i | −0.209580 | − | 0.363003i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6023 | + | 33.9522i | 0.895653 | + | 1.55132i | 0.832995 | + | 0.553281i | \(0.186624\pi\) |
0.0626578 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.535006 | − | 0.926657i | 0.0243942 | − | 0.0422519i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.6204 | −1.43581 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.3140 | −1.32835 | −0.664173 | − | 0.747579i | \(-0.731216\pi\) | ||||
−0.664173 | + | 0.747579i | \(0.731216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.57211 | − | 4.45503i | 0.116078 | − | 0.201052i | −0.802132 | − | 0.597146i | \(-0.796301\pi\) |
0.918210 | + | 0.396094i | \(0.129635\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.31306 | + | 12.6666i | 0.329364 | + | 0.570474i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.2551 | + | 19.4944i | 0.504861 | + | 0.874445i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5877 | + | 30.4627i | −0.787332 | + | 1.36370i | 0.140263 | + | 0.990114i | \(0.455205\pi\) |
−0.927596 | + | 0.373585i | \(0.878128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.2366 | −0.590192 | −0.295096 | − | 0.955468i | \(-0.595352\pi\) | ||||
−0.295096 | + | 0.955468i | \(0.595352\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1555 | 1.38640 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8738 | + | 27.4942i | −0.703593 | + | 1.21866i | 0.263604 | + | 0.964631i | \(0.415089\pi\) |
−0.967197 | + | 0.254028i | \(0.918245\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.32319 | + | 14.4162i | 0.368196 | + | 0.637735i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.5951 | − | 44.3321i | −1.12786 | − | 1.95350i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.03578 | − | 10.4543i | 0.265453 | − | 0.459778i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.83339 | 0.124133 | 0.0620666 | − | 0.998072i | \(-0.480231\pi\) | ||||
0.0620666 | + | 0.998072i | \(0.480231\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.0242 | −1.40032 | −0.700160 | − | 0.713986i | \(-0.746888\pi\) | ||||
−0.700160 | + | 0.713986i | \(0.746888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.45792 | − | 11.1854i | 0.281311 | − | 0.487246i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8487 | + | 18.7906i | 0.471684 | + | 0.816981i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.2239 | + | 24.6365i | 0.616105 | + | 1.06713i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.69646 | − | 11.5986i | 0.289513 | − | 0.501452i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −45.0201 | −1.93915 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.84546 | 0.165329 | 0.0826646 | − | 0.996577i | \(-0.473657\pi\) | ||||
0.0826646 | + | 0.996577i | \(0.473657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.89049 | + | 5.00648i | −0.123815 | + | 0.214454i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4749 | − | 38.9277i | −0.960958 | − | 1.66443i | −0.720102 | − | 0.693868i | \(-0.755905\pi\) |
−0.240856 | − | 0.970561i | \(-0.577428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.5690 | + | 21.7701i | 0.535456 | + | 0.927437i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.6235 | − | 27.0607i | 0.664378 | − | 1.15074i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.8629 | 1.51956 | 0.759780 | − | 0.650180i | \(-0.225307\pi\) | ||||
0.759780 | + | 0.650180i | \(0.225307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.3706 | 2.08816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.11092 | − | 8.85237i | 0.215400 | − | 0.373083i | −0.737997 | − | 0.674805i | \(-0.764228\pi\) |
0.953396 | + | 0.301721i | \(0.0975613\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.4593 | − | 47.5609i | −1.15522 | − | 2.00090i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.4319 | − | 19.8006i | −0.479250 | − | 0.830085i | 0.520467 | − | 0.853882i | \(-0.325758\pi\) |
−0.999717 | + | 0.0237967i | \(0.992425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.63442 | − | 2.83091i | 0.0683985 | − | 0.118470i | −0.829798 | − | 0.558064i | \(-0.811544\pi\) |
0.898197 | + | 0.439594i | \(0.144878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.49211 | 0.103928 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.2432 | −1.67535 | −0.837673 | − | 0.546172i | \(-0.816084\pi\) | ||||
−0.837673 | + | 0.546172i | \(0.816084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.67139 | − | 6.35903i | 0.152315 | − | 0.263817i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.9120 | − | 20.6322i | −0.493346 | − | 0.854500i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3312 | + | 23.0903i | 0.550236 | + | 0.953037i | 0.998257 | + | 0.0590141i | \(0.0187957\pi\) |
−0.448021 | + | 0.894023i | \(0.647871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.0992 | − | 19.2244i | 0.457336 | − | 0.792129i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.4349 | −1.49620 | −0.748101 | − | 0.663585i | \(-0.769034\pi\) | ||||
−0.748101 | + | 0.663585i | \(0.769034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.4452 | 1.33012 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.51357 | − | 11.2818i | 0.266137 | − | 0.460963i | −0.701724 | − | 0.712449i | \(-0.747586\pi\) |
0.967861 | + | 0.251486i | \(0.0809193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.1094 | − | 40.0267i | −0.942653 | − | 1.63272i | −0.760384 | − | 0.649473i | \(-0.774989\pi\) |
−0.182268 | − | 0.983249i | \(-0.558344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.10256 | + | 10.5699i | 0.248104 | + | 0.429729i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.32515 | − | 10.9555i | 0.256730 | − | 0.444669i | −0.708634 | − | 0.705576i | \(-0.750688\pi\) |
0.965364 | + | 0.260907i | \(0.0840215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.0611 | 0.852041 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.2013 | 0.654365 | 0.327182 | − | 0.944961i | \(-0.393901\pi\) | ||||
0.327182 | + | 0.944961i | \(0.393901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.54706 | − | 4.41164i | 0.102541 | − | 0.177606i | −0.810190 | − | 0.586167i | \(-0.800636\pi\) |
0.912731 | + | 0.408561i | \(0.133969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5926 | − | 21.8111i | −0.506140 | − | 0.876660i | −0.999975 | − | 0.00710457i | \(-0.997739\pi\) |
0.493835 | − | 0.869556i | \(-0.335595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37.0058 | + | 64.0959i | 1.48260 | + | 2.56795i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5749 | − | 26.9766i | 0.622998 | − | 1.07906i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.587987 | −0.0234446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4509 | 0.734518 | 0.367259 | − | 0.930119i | \(-0.380296\pi\) | ||||
0.367259 | + | 0.930119i | \(0.380296\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.0241 | − | 22.5584i | 0.516846 | − | 0.895204i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.2731 | − | 68.0230i | −1.55606 | − | 2.69517i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.2431 | + | 29.8659i | 0.681062 | + | 1.17963i | 0.974657 | + | 0.223704i | \(0.0718149\pi\) |
−0.293595 | + | 0.955930i | \(0.594852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.28665 | + | 9.15675i | −0.208485 | + | 0.361107i | −0.951238 | − | 0.308459i | \(-0.900187\pi\) |
0.742752 | + | 0.669566i | \(0.233520\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5011 | 0.570098 | 0.285049 | − | 0.958513i | \(-0.407990\pi\) | ||||
0.285049 | + | 0.958513i | \(0.407990\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.4666 | −1.07816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.29761 | + | 5.71162i | −0.129045 | + | 0.223513i | −0.923307 | − | 0.384063i | \(-0.874525\pi\) |
0.794262 | + | 0.607576i | \(0.207858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.35986 | − | 16.2117i | −0.365720 | − | 0.633445i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5531 | − | 26.9387i | −0.605861 | − | 1.04938i | −0.991915 | − | 0.126906i | \(-0.959495\pi\) |
0.386053 | − | 0.922476i | \(-0.373838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1695 | + | 29.7384i | −0.667816 | + | 1.15669i | 0.310698 | + | 0.950509i | \(0.399437\pi\) |
−0.978514 | + | 0.206182i | \(0.933896\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.7636 | 2.16242 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.85759 | −0.265527 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5631 | − | 18.2959i | 0.407785 | − | 0.706304i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.32809 | + | 10.9606i | 0.243930 | + | 0.422499i | 0.961830 | − | 0.273647i | \(-0.0882299\pi\) |
−0.717900 | + | 0.696146i | \(0.754897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.78910 | + | 11.7591i | 0.260926 | + | 0.451938i | 0.966488 | − | 0.256710i | \(-0.0826387\pi\) |
−0.705562 | + | 0.708648i | \(0.749305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.3356 | − | 50.8107i | 1.12580 | − | 1.94994i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.85174 | 0.147383 | 0.0736914 | − | 0.997281i | \(-0.476522\pi\) | ||||
0.0736914 | + | 0.997281i | \(0.476522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60.0755 | 2.29537 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.7828 | − | 35.9968i | 0.791761 | − | 1.37137i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.3658 | − | 35.2746i | −0.774752 | − | 1.34191i | −0.934934 | − | 0.354822i | \(-0.884542\pi\) |
0.160182 | − | 0.987087i | \(-0.448792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.88342 | + | 11.9224i | 0.261103 | + | 0.452244i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.81624 | − | 13.5381i | 0.296061 | − | 0.512793i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5260 | −0.661948 | −0.330974 | − | 0.943640i | \(-0.607377\pi\) | ||||
−0.330974 | + | 0.943640i | \(0.607377\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.01057 | −0.0381146 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.9043 | + | 50.0636i | −1.08706 | + | 1.88284i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5020 | + | 19.9220i | 0.431965 | + | 0.748185i | 0.997042 | − | 0.0768527i | \(-0.0244871\pi\) |
−0.565078 | + | 0.825038i | \(0.691154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.02786 | + | 5.24440i | 0.113394 | + | 0.196404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0718 | − | 26.1051i | 0.563654 | − | 0.976277i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.6172 | 0.433250 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 94.9826 | 3.53734 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.56030 | − | 11.3628i | 0.243643 | − | 0.422003i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5416 | + | 40.7752i | 0.873109 | + | 1.51227i | 0.858763 | + | 0.512373i | \(0.171233\pi\) |
0.0143459 | + | 0.999897i | \(0.495433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5650 | − | 23.4952i | −0.501718 | − | 0.869001i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5946 | + | 21.8145i | −0.465193 | + | 0.805737i | −0.999210 | − | 0.0397362i | \(-0.987348\pi\) |
0.534018 | + | 0.845473i | \(0.320682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.75168 | −0.211866 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.73735 | 0.358194 | 0.179097 | − | 0.983831i | \(-0.442682\pi\) | ||||
0.179097 | + | 0.983831i | \(0.442682\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0084 | + | 31.1915i | −0.660666 | + | 1.14431i | 0.319775 | + | 0.947493i | \(0.396393\pi\) |
−0.980441 | + | 0.196813i | \(0.936941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.90970 | − | 5.03974i | −0.106603 | − | 0.184642i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4252 | + | 21.5210i | 0.454006 | + | 0.786361i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.3734 | − | 24.8954i | 0.524493 | − | 0.908448i | −0.475101 | − | 0.879931i | \(-0.657588\pi\) |
0.999593 | − | 0.0285164i | \(-0.00907828\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6446 | −0.605761 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.3478 | 1.93896 | 0.969479 | − | 0.245174i | \(-0.0788450\pi\) | ||||
0.969479 | + | 0.245174i | \(0.0788450\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4580 | + | 23.3100i | −0.487853 | + | 0.844986i | −0.999902 | − | 0.0139702i | \(-0.995553\pi\) |
0.512050 | + | 0.858956i | \(0.328886\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.36326 | − | 9.28943i | −0.194163 | − | 0.336300i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.9603 | − | 41.5005i | −0.865157 | − | 1.49850i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.56541 | + | 7.90752i | −0.164633 | + | 0.285152i | −0.936525 | − | 0.350601i | \(-0.885977\pi\) |
0.771892 | + | 0.635754i | \(0.219311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.5628 | −0.739591 | −0.369796 | − | 0.929113i | \(-0.620572\pi\) | ||||
−0.369796 | + | 0.929113i | \(0.620572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.5864 | −0.416194 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.4338 | − | 23.2680i | 0.481315 | − | 0.833663i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.74612 | − | 9.95257i | −0.205612 | − | 0.356131i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3769 | − | 37.0258i | −0.762974 | − | 1.32151i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.17998 | − | 5.50789i | 0.113354 | − | 0.196335i | −0.803767 | − | 0.594945i | \(-0.797174\pi\) |
0.917121 | + | 0.398610i | \(0.130507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 101.900 | 3.62316 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8587 | 1.30889 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.3241 | + | 17.8819i | −0.365699 | + | 0.633409i | −0.988888 | − | 0.148662i | \(-0.952503\pi\) |
0.623189 | + | 0.782071i | \(0.285837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.78670 | − | 10.0229i | −0.204719 | − | 0.354583i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.24928 | − | 7.35996i | −0.149954 | − | 0.259727i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.60611 | + | 13.1742i | −0.268080 | + | 0.464328i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.2805 | 1.59198 | 0.795989 | − | 0.605311i | \(-0.206951\pi\) | ||||
0.795989 | + | 0.605311i | \(0.206951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.29363 | −0.150770 | −0.0753848 | − | 0.997155i | \(-0.524019\pi\) | ||||
−0.0753848 | + | 0.997155i | \(0.524019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.33861 | − | 10.9788i | 0.222032 | − | 0.384570i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3141 | − | 40.3812i | −0.815657 | − | 1.41276i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.49228 | − | 14.7091i | −0.296383 | − | 0.513350i | 0.678923 | − | 0.734210i | \(-0.262447\pi\) |
−0.975306 | + | 0.220860i | \(0.929114\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.98907 | + | 5.17721i | −0.104192 | + | 0.180466i | −0.913408 | − | 0.407045i | \(-0.866559\pi\) |
0.809216 | + | 0.587512i | \(0.199892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.4590 | −0.398469 | −0.199234 | − | 0.979952i | \(-0.563845\pi\) | ||||
−0.199234 | + | 0.979952i | \(0.563845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5859 | 1.20122 | 0.600609 | − | 0.799543i | \(-0.294925\pi\) | ||||
0.600609 | + | 0.799543i | \(0.294925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.5811 | + | 37.3796i | −0.747742 | + | 1.29513i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.17903 | + | 5.50625i | 0.110015 | + | 0.190551i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.1093 | − | 20.9740i | −0.418060 | − | 0.724102i | 0.577684 | − | 0.816261i | \(-0.303957\pi\) |
−0.995744 | + | 0.0921587i | \(0.970623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.55207 | + | 6.15236i | −0.122485 | + | 0.212150i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.7483 | 0.610561 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.6464 | −0.778139 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.137842 | − | 0.238749i | 0.00472515 | − | 0.00818420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7241 | + | 46.2875i | 0.915016 | + | 1.58485i | 0.806878 | + | 0.590719i | \(0.201156\pi\) |
0.108138 | + | 0.994136i | \(0.465511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.79836 | − | 3.11486i | −0.0614310 | − | 0.106402i | 0.833674 | − | 0.552256i | \(-0.186233\pi\) |
−0.895105 | + | 0.445855i | \(0.852900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.9691 | + | 27.6594i | −0.544860 | + | 0.943726i | 0.453755 | + | 0.891126i | \(0.350084\pi\) |
−0.998616 | + | 0.0525994i | \(0.983249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.20625 | 0.0751016 | 0.0375508 | − | 0.999295i | \(-0.488044\pi\) | ||||
0.0375508 | + | 0.999295i | \(0.488044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.40722 | −0.217852 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.97632 | + | 13.8154i | −0.270578 | + | 0.468655i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.01744 | − | 8.69047i | −0.170010 | − | 0.294465i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.7699 | + | 32.5105i | 0.634539 | + | 1.09905i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.07129 | + | 5.31962i | −0.103710 | + | 0.179631i | −0.913210 | − | 0.407488i | \(-0.866405\pi\) |
0.809500 | + | 0.587119i | \(0.199738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.6422 | 1.30189 | 0.650945 | − | 0.759125i | \(-0.274373\pi\) | ||||
0.650945 | + | 0.759125i | \(0.274373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.4651 | −1.29446 | −0.647228 | − | 0.762297i | \(-0.724072\pi\) | ||||
−0.647228 | + | 0.762297i | \(0.724072\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.1015 | − | 43.4770i | 0.842825 | − | 1.45982i | −0.0446713 | − | 0.999002i | \(-0.514224\pi\) |
0.887497 | − | 0.460814i | \(-0.152443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.1660 | + | 41.8568i | 0.810502 | + | 1.40383i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.94561 | − | 17.2263i | −0.332817 | − | 0.576456i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.60234 | + | 2.77533i | −0.0535603 | + | 0.0927691i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.8824 | 1.06334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.8409 | −0.760941 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.93361 | − | 12.0094i | 0.230481 | − | 0.399205i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.5437 | + | 49.4391i | 0.947777 | + | 1.64160i | 0.750093 | + | 0.661332i | \(0.230009\pi\) |
0.197684 | + | 0.980266i | \(0.436658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.15893 | − | 14.1317i | −0.270317 | − | 0.468204i | 0.698626 | − | 0.715487i | \(-0.253795\pi\) |
−0.968943 | + | 0.247284i | \(0.920462\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.87437 | + | 3.24650i | −0.0620326 | + | 0.107444i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.7341 | 1.14702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.5992 | 0.844441 | 0.422220 | − | 0.906493i | \(-0.361251\pi\) | ||||
0.422220 | + | 0.906493i | \(0.361251\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0252 | − | 17.3641i | 0.329983 | − | 0.571548i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.263732 | + | 0.456797i | 0.00867145 | + | 0.0150194i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.3480 | + | 21.3874i | 0.405126 | + | 0.701699i | 0.994336 | − | 0.106281i | \(-0.0338944\pi\) |
−0.589210 | + | 0.807980i | \(0.700561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.0915 | + | 64.2444i | −1.21563 | + | 2.10553i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.5644 | −0.541713 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.3574 | −0.893728 | −0.446864 | − | 0.894602i | \(-0.647459\pi\) | ||||
−0.446864 | + | 0.894602i | \(0.647459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.2953 | − | 21.2962i | 0.400817 | − | 0.694235i | −0.593008 | − | 0.805197i | \(-0.702060\pi\) |
0.993825 | + | 0.110962i | \(0.0353931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.66472 | + | 6.34747i | 0.119340 | + | 0.206702i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.0107 | − | 17.3391i | −0.325305 | − | 0.563445i | 0.656269 | − | 0.754527i | \(-0.272134\pi\) |
−0.981574 | + | 0.191082i | \(0.938800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.41366 | − | 12.8408i | 0.240658 | − | 0.416831i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.59573 | 0.246050 | 0.123025 | − | 0.992404i | \(-0.460741\pi\) | ||||
0.123025 | + | 0.992404i | \(0.460741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.50963 | −0.113569 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55.7345 | + | 96.5350i | −1.79976 | + | 3.11728i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.42287 | + | 2.46448i | 0.0458990 | + | 0.0794994i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.9969 | + | 46.7600i | 0.869061 | + | 1.50526i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.2203 | + | 17.7020i | −0.328662 | + | 0.569259i | −0.982247 | − | 0.187594i | \(-0.939931\pi\) |
0.653585 | + | 0.756853i | \(0.273264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.8189 | −1.53458 | −0.767290 | − | 0.641300i | \(-0.778395\pi\) | ||||
−0.767290 | + | 0.641300i | \(0.778395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.5441 | −0.818907 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.33054 | − | 9.23277i | 0.170539 | − | 0.295382i | −0.768069 | − | 0.640367i | \(-0.778782\pi\) |
0.938608 | + | 0.344984i | \(0.112116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8927 | − | 32.7231i | −0.603813 | − | 1.04584i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.9147 | − | 20.6369i | −0.380020 | − | 0.658214i | 0.611045 | − | 0.791596i | \(-0.290750\pi\) |
−0.991065 | + | 0.133382i | \(0.957416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.99755 | − | 17.3163i | 0.318549 | − | 0.551742i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7201 | 0.404476 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.3401 | 0.360231 | 0.180116 | − | 0.983645i | \(-0.442353\pi\) | ||||
0.180116 | + | 0.983645i | \(0.442353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.65503 | + | 8.06276i | −0.147575 | + | 0.255607i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0454 | − | 27.7914i | −0.508163 | − | 0.880164i | −0.999955 | − | 0.00945137i | \(-0.996991\pi\) |
0.491793 | − | 0.870712i | \(-0.336342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3456.2.i.f.2305.1 | 10 | ||
3.2 | odd | 2 | 1152.2.i.g.769.5 | yes | 10 | ||
4.3 | odd | 2 | 3456.2.i.g.2305.1 | 10 | |||
8.3 | odd | 2 | 3456.2.i.h.2305.5 | 10 | |||
8.5 | even | 2 | 3456.2.i.e.2305.5 | 10 | |||
9.2 | odd | 6 | 1152.2.i.g.385.5 | yes | 10 | ||
9.7 | even | 3 | inner | 3456.2.i.f.1153.1 | 10 | ||
12.11 | even | 2 | 1152.2.i.f.769.1 | yes | 10 | ||
24.5 | odd | 2 | 1152.2.i.e.769.1 | yes | 10 | ||
24.11 | even | 2 | 1152.2.i.h.769.5 | yes | 10 | ||
36.7 | odd | 6 | 3456.2.i.g.1153.1 | 10 | |||
36.11 | even | 6 | 1152.2.i.f.385.1 | yes | 10 | ||
72.11 | even | 6 | 1152.2.i.h.385.5 | yes | 10 | ||
72.29 | odd | 6 | 1152.2.i.e.385.1 | ✓ | 10 | ||
72.43 | odd | 6 | 3456.2.i.h.1153.5 | 10 | |||
72.61 | even | 6 | 3456.2.i.e.1153.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.e.385.1 | ✓ | 10 | 72.29 | odd | 6 | ||
1152.2.i.e.769.1 | yes | 10 | 24.5 | odd | 2 | ||
1152.2.i.f.385.1 | yes | 10 | 36.11 | even | 6 | ||
1152.2.i.f.769.1 | yes | 10 | 12.11 | even | 2 | ||
1152.2.i.g.385.5 | yes | 10 | 9.2 | odd | 6 | ||
1152.2.i.g.769.5 | yes | 10 | 3.2 | odd | 2 | ||
1152.2.i.h.385.5 | yes | 10 | 72.11 | even | 6 | ||
1152.2.i.h.769.5 | yes | 10 | 24.11 | even | 2 | ||
3456.2.i.e.1153.5 | 10 | 72.61 | even | 6 | |||
3456.2.i.e.2305.5 | 10 | 8.5 | even | 2 | |||
3456.2.i.f.1153.1 | 10 | 9.7 | even | 3 | inner | ||
3456.2.i.f.2305.1 | 10 | 1.1 | even | 1 | trivial | ||
3456.2.i.g.1153.1 | 10 | 36.7 | odd | 6 | |||
3456.2.i.g.2305.1 | 10 | 4.3 | odd | 2 | |||
3456.2.i.h.1153.5 | 10 | 72.43 | odd | 6 | |||
3456.2.i.h.2305.5 | 10 | 8.3 | odd | 2 |