Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(104,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 9, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.cs (of order \(18\), degree \(6\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 524.1 | ||
Character | \(\chi\) | \(=\) | 945.524 |
Dual form | 945.2.cs.a.734.1 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{18}\right)\) | \(-1\) |
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 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(3\) | −1.62968 | + | 0.586627i | −0.940898 | + | 0.338689i | ||||
\(4\) | −0.347296 | − | 1.96962i | −0.173648 | − | 0.984808i | ||||
\(5\) | 0.764780 | − | 2.10122i | 0.342020 | − | 0.939693i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.459430 | − | 2.60556i | 0.173648 | − | 0.984808i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.31174 | − | 1.91203i | 0.770579 | − | 0.637344i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20957 | + | 6.07074i | 0.666210 | + | 1.83040i | 0.546259 | + | 0.837616i | \(0.316051\pi\) |
0.119950 | + | 0.992780i | \(0.461727\pi\) | |||||||
\(12\) | 1.72141 | + | 3.00612i | 0.496929 | + | 0.867791i | ||||
\(13\) | 3.66210 | − | 3.07287i | 1.01568 | − | 0.852260i | 0.0266051 | − | 0.999646i | \(-0.491530\pi\) |
0.989079 | + | 0.147386i | \(0.0470859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0137197 | + | 3.87296i | −0.00354242 | + | 0.999994i | ||||
\(16\) | −3.75877 | + | 1.36808i | −0.939693 | + | 0.342020i | ||||
\(17\) | 6.43317 | − | 3.71419i | 1.56027 | − | 0.900823i | 0.563043 | − | 0.826428i | \(-0.309630\pi\) |
0.997229 | − | 0.0743959i | \(-0.0237028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | −4.40419 | − | 0.776578i | −0.984808 | − | 0.173648i | ||||
\(21\) | 0.779764 | + | 4.51575i | 0.170158 | + | 0.985417i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.83022 | − | 3.21394i | −0.766044 | − | 0.642788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | + | 4.47214i | −0.509175 | + | 0.860663i | ||||
\(28\) | −5.29150 | −1.00000 | ||||||||
\(29\) | 3.10864 | − | 3.70474i | 0.577260 | − | 0.687952i | −0.395844 | − | 0.918318i | \(-0.629548\pi\) |
0.973104 | + | 0.230366i | \(0.0739923\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.16215 | − | 8.59719i | −1.24677 | − | 1.49658i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.12348 | − | 2.95804i | −0.866025 | − | 0.500000i | ||||
\(36\) | −4.56883 | − | 3.88919i | −0.761471 | − | 0.648199i | ||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.16544 | + | 7.15609i | −0.667004 | + | 1.14589i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(44\) | 11.1896 | − | 6.46034i | 1.68690 | − | 0.973933i | ||||
\(45\) | −2.24962 | − | 6.31975i | −0.335354 | − | 0.942092i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.0199 | − | 2.29576i | −1.89915 | − | 0.334872i | −0.903544 | − | 0.428495i | \(-0.859044\pi\) |
−0.995608 | + | 0.0936230i | \(0.970155\pi\) | |||||||
\(48\) | 5.32305 | − | 4.43453i | 0.768317 | − | 0.640070i | ||||
\(49\) | −6.57785 | − | 2.39414i | −0.939693 | − | 0.342020i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.30518 | + | 9.82682i | −1.16296 | + | 1.37603i | ||||
\(52\) | −7.32420 | − | 6.14574i | −1.01568 | − | 0.852260i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4458 | 1.94787 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(60\) | 7.63300 | − | 1.31804i | 0.985417 | − | 0.170158i | ||||
\(61\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.91983 | − | 6.90181i | −0.493852 | − | 0.869546i | ||||
\(64\) | 4.00000 | + | 6.92820i | 0.500000 | + | 0.866025i | ||||
\(65\) | −3.65606 | − | 10.0449i | −0.453478 | − | 1.24592i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(68\) | −9.54974 | − | 11.3809i | −1.15808 | − | 1.38014i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0138 | − | 6.93616i | 1.42577 | − | 0.823171i | 0.428990 | − | 0.903309i | \(-0.358869\pi\) |
0.996784 | + | 0.0801380i | \(0.0255361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.68743 | + | 9.85092i | −0.665664 | + | 1.15296i | 0.313441 | + | 0.949608i | \(0.398518\pi\) |
−0.979105 | + | 0.203355i | \(0.934815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.12743 | + | 2.99079i | 0.938475 | + | 0.345347i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.8328 | − | 2.96807i | 1.91827 | − | 0.338243i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.15248 | + | 6.84074i | 0.917225 | + | 0.769644i | 0.973480 | − | 0.228773i | \(-0.0734713\pi\) |
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | 1.68826 | − | 8.84024i | 0.187585 | − | 0.982248i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.15477 | + | 2.56795i | −0.236517 | + | 0.281870i | −0.871227 | − | 0.490881i | \(-0.836675\pi\) |
0.634710 | + | 0.772750i | \(0.281120\pi\) | |||||||
\(84\) | 8.62348 | − | 3.10414i | 0.940898 | − | 0.338689i | ||||
\(85\) | −2.88436 | − | 16.3580i | −0.312853 | − | 1.77428i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.89281 | + | 7.86116i | −0.310141 | + | 0.842805i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.32405 | − | 10.9536i | −0.662941 | − | 1.14825i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.22994 | − | 3.35942i | 0.937159 | − | 0.341098i | 0.172115 | − | 0.985077i | \(-0.444940\pi\) |
0.765043 | + | 0.643979i | \(0.222718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.7154 | + | 9.80919i | 1.67996 | + | 0.985860i | ||||
\(100\) | −5.00000 | + | 8.66025i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.6205 | − | 6.41332i | −1.73620 | − | 0.631923i | −0.737155 | − | 0.675724i | \(-0.763831\pi\) |
−0.999040 | + | 0.0438001i | \(0.986054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0849 | + | 1.81510i | 0.984186 | + | 0.177136i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 9.72725 | + | 3.65796i | 0.936005 | + | 0.351987i | ||||
\(109\) | −4.26636 | −0.408644 | −0.204322 | − | 0.978904i | \(-0.565499\pi\) | ||||
−0.204322 | + | 0.978904i | \(0.565499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.83772 | + | 10.4222i | 0.173648 | + | 0.984808i | ||||
\(113\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.37652 | − | 4.83619i | −0.777741 | − | 0.449029i | ||||
\(117\) | 2.59039 | − | 14.1057i | 0.239482 | − | 1.30407i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.72194 | − | 18.4684i | −0.616199 | − | 1.69299i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.5452 | + | 19.7567i | −2.14047 | + | 1.79607i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.68246 | + | 5.59017i | −0.866025 | + | 0.500000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(132\) | −14.4458 | + | 17.0925i | −1.25734 | + | 1.48771i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.37351 | + | 8.97950i | 0.634611 | + | 0.772832i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(140\) | −4.04684 | + | 11.1186i | −0.342020 | + | 0.939693i | ||||
\(141\) | 22.5651 | − | 3.89647i | 1.90033 | − | 0.328142i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 26.7462 | + | 15.4419i | 2.23663 | + | 1.29132i | ||||
\(144\) | −6.07348 | + | 10.3495i | −0.506123 | + | 0.862461i | ||||
\(145\) | −5.40702 | − | 9.36524i | −0.449029 | − | 0.777741i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1243 | + | 0.0429495i | 0.999994 | + | 0.00354242i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6129 | + | 18.6067i | 1.27906 | + | 1.52432i | 0.716578 | + | 0.697507i | \(0.245707\pi\) |
0.562478 | + | 0.826812i | \(0.309848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9577 | + | 8.35593i | −1.86827 | + | 0.679996i | −0.897000 | + | 0.442031i | \(0.854258\pi\) |
−0.971274 | + | 0.237964i | \(0.923520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.77014 | − | 20.8867i | 0.628179 | − | 1.68859i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 15.5414 | + | 5.71903i | 1.24431 | + | 0.457889i | ||||
\(157\) | −7.13246 | − | 2.59600i | −0.569232 | − | 0.207184i | 0.0413387 | − | 0.999145i | \(-0.486838\pi\) |
−0.610571 | + | 0.791962i | \(0.709060\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.5420 | + | 8.47428i | −1.83274 | + | 0.659721i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.69944 | − | 12.9116i | 0.363653 | − | 0.999129i | −0.614074 | − | 0.789249i | \(-0.710470\pi\) |
0.977727 | − | 0.209881i | \(-0.0673075\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.71104 | − | 9.70381i | 0.131619 | − | 0.746447i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.96495 | + | 24.6310i | 0.681593 | + | 1.87266i | 0.420221 | + | 0.907422i | \(0.361953\pi\) |
0.261372 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1338 | + | 8.50328i | −0.766044 | + | 0.642788i | ||||
\(176\) | −16.6105 | − | 19.7956i | −1.25206 | − | 1.49215i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.52023 | + | 1.45505i | −0.188371 | + | 0.108756i | −0.591220 | − | 0.806511i | \(-0.701353\pi\) |
0.402849 | + | 0.915267i | \(0.368020\pi\) | |||||||
\(180\) | −11.6662 | + | 6.62572i | −0.869546 | + | 0.493852i | ||||
\(181\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.7624 | + | 30.8473i | 2.68833 | + | 2.25578i | ||||
\(188\) | 26.4416i | 1.92845i | ||||||||
\(189\) | 10.4369 | + | 8.94829i | 0.759170 | + | 0.650892i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.80278 | − | 4.53198i | 0.275160 | − | 0.327923i | −0.610712 | − | 0.791853i | \(-0.709117\pi\) |
0.885872 | + | 0.463930i | \(0.153561\pi\) | |||||||
\(192\) | −10.5830 | − | 8.94427i | −0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.8508 | + | 14.2253i | 0.848657 | + | 1.01870i | ||||
\(196\) | −2.43107 | + | 13.7873i | −0.173648 | + | 0.984808i | ||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.22469 | − | 9.80181i | −0.577260 | − | 0.687952i | ||||
\(204\) | 22.2394 | + | 12.9452i | 1.55707 | + | 0.906345i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.56107 | + | 16.5603i | −0.662941 | + | 1.14825i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6715 | + | 4.61204i | 0.872340 | + | 0.317506i | 0.739114 | − | 0.673580i | \(-0.235244\pi\) |
0.133226 | + | 0.991086i | \(0.457467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5097 | + | 18.3514i | −1.06271 | + | 1.25741i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.48990 | − | 19.3903i | 0.235826 | − | 1.31027i | ||||
\(220\) | −5.01696 | − | 28.4526i | −0.338243 | − | 1.91827i | ||||
\(221\) | 12.1457 | − | 33.3700i | 0.817008 | − | 2.24471i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.269600 | + | 1.52898i | −0.0180537 | + | 0.102388i | −0.992503 | − | 0.122220i | \(-0.960999\pi\) |
0.974449 | + | 0.224607i | \(0.0721099\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.9996 | − | 0.106272i | −0.999975 | − | 0.00708479i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.41408 | − | 23.1175i | −0.558462 | − | 1.53436i | −0.821869 | − | 0.569677i | \(-0.807068\pi\) |
0.263407 | − | 0.964685i | \(-0.415154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.6910 | + | 14.7116i | −1.69034 | + | 0.967952i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.7813 | + | 25.6019i | −0.964225 | + | 1.67009i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.2989 | − | 6.36578i | −1.12369 | − | 0.413502i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2413 | − | 3.92174i | 1.43867 | − | 0.253677i | 0.600737 | − | 0.799447i | \(-0.294874\pi\) |
0.837935 | + | 0.545770i | \(0.183763\pi\) | |||||||
\(240\) | −5.24695 | − | 14.5763i | −0.338689 | − | 0.940898i | ||||
\(241\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.43459 | + | 15.3972i | 0.156179 | + | 0.987729i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0612 | + | 11.9905i | −0.642788 | + | 0.766044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.00516 | − | 5.44900i | 0.127072 | − | 0.345316i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | −12.2326 | + | 10.1175i | −0.770579 | + | 0.637344i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.2966 | + | 24.9663i | 0.895291 | + | 1.56345i | ||||
\(256\) | 12.2567 | − | 10.2846i | 0.766044 | − | 0.642788i | ||||
\(257\) | −9.68118 | − | 11.5376i | −0.603895 | − | 0.719694i | 0.374317 | − | 0.927301i | \(-0.377877\pi\) |
−0.978212 | + | 0.207606i | \(0.933433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.5149 | + | 10.6896i | −1.14825 | + | 0.662941i | ||||
\(261\) | 0.102790 | − | 14.5082i | 0.00636255 | − | 0.898035i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −19.0995 | + | 22.7619i | −1.15808 | + | 1.38014i | ||||
\(273\) | 16.7319 | + | 14.1410i | 1.01266 | + | 0.855853i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0478 | − | 30.3537i | 0.666210 | − | 1.83040i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4666 | + | 31.5041i | 0.684037 | + | 1.87938i | 0.344704 | + | 0.938711i | \(0.387979\pi\) |
0.339333 | + | 0.940666i | \(0.389799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9516 | − | 20.9369i | 1.48322 | − | 1.24457i | 0.580558 | − | 0.814219i | \(-0.302835\pi\) |
0.902662 | − | 0.430350i | \(-0.141610\pi\) | |||||||
\(284\) | −17.8339 | − | 21.2536i | −1.05825 | − | 1.26117i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0904 | − | 33.0656i | 1.12297 | − | 1.94503i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0712 | + | 10.8893i | −0.766245 | + | 0.638344i | ||||
\(292\) | 21.3777 | + | 7.78086i | 1.25104 | + | 0.455341i | ||||
\(293\) | 32.4198 | − | 5.71649i | 1.89399 | − | 0.333961i | 0.899336 | − | 0.437257i | \(-0.144050\pi\) |
0.994651 | + | 0.103296i | \(0.0329390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −32.9951 | − | 6.18017i | −1.91457 | − | 0.358610i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.06808 | − | 17.0466i | 0.177136 | − | 0.984186i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0180 | + | 19.0837i | 0.628830 | + | 1.08916i | 0.987787 | + | 0.155811i | \(0.0497990\pi\) |
−0.358957 | + | 0.933354i | \(0.616868\pi\) | |||||||
\(308\) | −11.6919 | − | 32.1233i | −0.666210 | − | 1.83040i | ||||
\(309\) | 32.4780 | + | 0.115051i | 1.84761 | + | 0.00654504i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.70330 | + | 0.983921i | −0.152800 | + | 0.0556145i | −0.417288 | − | 0.908774i | \(-0.637019\pi\) |
0.264488 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | + | 2.95804i | −0.986013 | + | 0.166667i | ||||
\(316\) | 10.6423 | − | 18.4330i | 0.598676 | − | 1.03694i | ||||
\(317\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.3592 | + | 10.6859i | 1.64380 | + | 0.598295i | ||||
\(320\) | 17.6168 | − | 3.10631i | 0.984808 | − | 0.173648i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −17.9982 | − | 0.255046i | −0.999900 | − | 0.0141692i | ||||
\(325\) | −23.9027 | −1.32588 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.95282 | − | 2.50276i | 0.384492 | − | 0.138403i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.9635 | + | 32.8694i | −0.659569 | + | 1.81215i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.31148 | − | 35.7942i | 0.346911 | − | 1.96743i | 0.127051 | − | 0.991896i | \(-0.459449\pi\) |
0.219860 | − | 0.975531i | \(-0.429440\pi\) | |||||||
\(332\) | 5.80623 | + | 3.35223i | 0.318658 | + | 0.183977i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −9.10886 | − | 15.9069i | −0.496929 | − | 0.867791i | ||||
\(337\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31.2173 | + | 11.3622i | −1.69299 | + | 0.616199i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.26013 | + | 16.0390i | −0.500000 | + | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(348\) | 16.4881 | + | 2.96756i | 0.883856 | + | 0.159078i | ||||
\(349\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.05327 | + | 24.5075i | 0.216348 | + | 1.30811i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.91274 | − | 4.66303i | 0.208254 | − | 0.248188i | −0.651799 | − | 0.758392i | \(-0.725986\pi\) |
0.860054 | + | 0.510204i | \(0.170430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.38647 | − | 30.5482i | −0.285884 | − | 1.62133i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.7887 | + | 26.1544i | 1.15318 | + | 1.38424i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1235 | + | 18.5465i | 1.69541 | + | 0.978847i | 0.950004 | + | 0.312239i | \(0.101079\pi\) |
0.745409 | + | 0.666608i | \(0.232254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.7813 | − | 46.0095i | 1.40566 | − | 2.41487i | ||||
\(364\) | −19.3780 | + | 16.2601i | −1.01568 | + | 0.852260i | ||||
\(365\) | 16.3493 | + | 19.4843i | 0.855761 | + | 1.01986i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.5913 | − | 12.2262i | 1.75345 | − | 0.638204i | 0.753633 | − | 0.657296i | \(-0.228300\pi\) |
0.999818 | + | 0.0190919i | \(0.00607750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | − | 14.7902i | 0.645497 | − | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.1196i | − | 1.19072i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.0734 | −1.80160 | −0.900800 | − | 0.434234i | \(-0.857019\pi\) | ||||
−0.900800 | + | 0.434234i | \(0.857019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.47176 | + | 20.5285i | −0.381789 | + | 1.04896i | 0.588813 | + | 0.808269i | \(0.299595\pi\) |
−0.970603 | + | 0.240688i | \(0.922627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.63682 | − | 37.6393i | 0.338243 | − | 1.91827i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.82230 | − | 17.0127i | −0.498652 | − | 0.863690i | ||||
\(389\) | 2.66074 | + | 7.31033i | 0.134905 | + | 0.370648i | 0.988689 | − | 0.149979i | \(-0.0479205\pi\) |
−0.853784 | + | 0.520627i | \(0.825698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.6087 | − | 11.8985i | 1.03694 | − | 0.598676i | ||||
\(396\) | 13.5151 | − | 36.3296i | 0.679161 | − | 1.82563i | ||||
\(397\) | −17.3129 | + | 29.9868i | −0.868910 | + | 1.50500i | −0.00579782 | + | 0.999983i | \(0.501846\pi\) |
−0.863112 | + | 0.505013i | \(0.831488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.7939 | + | 6.84040i | 0.939693 | + | 0.342020i | ||||
\(401\) | −29.1310 | + | 5.13658i | −1.45473 | + | 0.256509i | −0.844433 | − | 0.535662i | \(-0.820062\pi\) |
−0.610300 | + | 0.792170i | \(0.708951\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.2841 | − | 10.3082i | −0.858854 | − | 0.512221i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.51226 | + | 36.9329i | −0.320836 | + | 1.81955i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.74790 | + | 6.49156i | 0.183977 | + | 0.318658i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(420\) | 0.0725979 | − | 20.4938i | 0.00354242 | − | 0.999994i | ||||
\(421\) | 15.9140 | − | 5.79221i | 0.775600 | − | 0.282295i | 0.0762630 | − | 0.997088i | \(-0.475701\pi\) |
0.699337 | + | 0.714793i | \(0.253479\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −34.4882 | + | 19.5873i | −1.67688 | + | 0.952368i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −36.5776 | − | 6.44962i | −1.77428 | − | 0.312853i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −52.6466 | − | 9.47542i | −2.54180 | − | 0.457478i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.8890i | 1.82505i | 0.409021 | + | 0.912525i | \(0.365870\pi\) | ||||
−0.409021 | + | 0.912525i | \(0.634130\pi\) | |||||||
\(432\) | 3.82653 | − | 20.4293i | 0.184104 | − | 0.982907i | ||||
\(433\) | −29.5653 | −1.42082 | −0.710410 | − | 0.703788i | \(-0.751490\pi\) | ||||
−0.710410 | + | 0.703788i | \(0.751490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.3056 | + | 12.0905i | 0.685903 | + | 0.579694i | ||||
\(436\) | 1.48169 | + | 8.40310i | 0.0709602 | + | 0.402435i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.7839 | + | 7.04243i | −0.942092 | + | 0.335354i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.3592 | − | 21.1641i | −1.71973 | − | 1.00103i | ||||
\(448\) | 19.8895 | − | 7.23920i | 0.939693 | − | 0.342020i | ||||
\(449\) | 11.1822 | − | 6.45603i | 0.527719 | − | 0.304679i | −0.212368 | − | 0.977190i | \(-0.568118\pi\) |
0.740087 | + | 0.672511i | \(0.234784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.5120 | − | 27.0851i | 1.52755 | − | 1.27257i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.8524 | + | 4.91112i | −1.30574 | + | 0.230237i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.410194 | + | 38.5968i | −0.0191462 | + | 1.80155i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(464\) | −6.61630 | + | 18.1781i | −0.307154 | + | 0.843898i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.380337 | − | 0.219588i | −0.0175999 | − | 0.0101613i | 0.491174 | − | 0.871061i | \(-0.336568\pi\) |
−0.508774 | + | 0.860900i | \(0.669901\pi\) | |||||||
\(468\) | −28.6825 | − | 0.203214i | −1.32585 | − | 0.00939359i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1465 | + | 0.0465708i | 0.605760 | + | 0.00214587i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −34.0411 | + | 19.6536i | −1.56027 | + | 0.900823i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 47.0903 | + | 39.5135i | 2.14047 | + | 1.79607i | ||||
\(485\) | − | 21.9633i | − | 0.997304i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.64669 | + | 15.5142i | −0.254832 | + | 0.700144i | 0.744635 | + | 0.667472i | \(0.232624\pi\) |
−0.999466 | + | 0.0326716i | \(0.989598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.23832 | − | 35.3793i | 0.280960 | − | 1.59340i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.3948 | − | 27.6208i | 1.50099 | − | 1.24146i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.5531 | − | 34.4893i | −0.563082 | − | 1.54706i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.93548 | + | 6.65866i | −0.355241 | + | 0.298082i | −0.802890 | − | 0.596127i | \(-0.796706\pi\) |
0.447650 | + | 0.894209i | \(0.352261\pi\) | |||||||
\(500\) | 14.3732 | + | 17.1293i | 0.642788 | + | 0.766044i | ||||
\(501\) | −0.0843052 | + | 23.7986i | −0.00376648 | + | 1.06324i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.3190 | + | 19.8141i | −1.53021 | + | 0.883466i | −0.530857 | + | 0.847461i | \(0.678130\pi\) |
−0.999352 | + | 0.0360049i | \(0.988537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.90406 | + | 16.8179i | 0.128974 | + | 0.746908i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.0542 | + | 19.3447i | 1.01986 | + | 0.855761i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.9516 | + | 32.1196i | −1.18763 | + | 1.41536i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.8314 | − | 84.1132i | −0.652285 | − | 3.69929i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.0592 | − | 34.8817i | −1.27556 | − | 1.53113i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8147 | + | 22.1957i | 0.560346 | + | 0.970548i | 0.997466 | + | 0.0711450i | \(0.0226653\pi\) |
−0.437120 | + | 0.899403i | \(0.644001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.5267 | − | 19.8024i | 0.503065 | − | 0.864249i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 38.6825 | + | 22.5165i | 1.68344 | + | 0.979903i | ||||
\(529\) | 21.6129 | − | 7.86646i | 0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.25360 | − | 3.84971i | 0.140403 | − | 0.166127i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 45.2224i | − | 1.94787i | ||||||
\(540\) | 15.1254 | − | 17.6415i | 0.650892 | − | 0.759170i | ||||
\(541\) | 46.4770 | 1.99820 | 0.999102 | − | 0.0423705i | \(-0.0134910\pi\) | ||||
0.999102 | + | 0.0423705i | \(0.0134910\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.26283 | + | 8.96455i | −0.139764 | + | 0.383999i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.5694 | − | 18.0989i | 0.917225 | − | 0.769644i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 23.3048 | + | 4.10927i | 0.984808 | + | 0.173648i | ||||
\(561\) | −78.0069 | − | 28.7055i | −3.29345 | − | 1.21195i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.74803 | − | 1.36619i | 0.326541 | − | 0.0575779i | −0.00797484 | − | 0.999968i | \(-0.502538\pi\) |
0.334515 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(564\) | −15.5113 | − | 43.0914i | −0.653145 | − | 1.81447i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.2581 | − | 8.46033i | −0.934752 | − | 0.355301i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.48464 | + | 1.76932i | −0.0622392 | + | 0.0741738i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.734027 | + | 0.679121i | \(0.237639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.32981 | − | 41.5694i | −0.306743 | − | 1.73963i | −0.615186 | − | 0.788382i | \(-0.710919\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 21.1258 | − | 58.0427i | 0.883315 | − | 2.42689i | ||||
\(573\) | −3.53875 | + | 9.61651i | −0.147833 | + | 0.401735i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 22.4939 | + | 8.36806i | 0.937246 | + | 0.348669i | ||||
\(577\) | −10.4244 | − | 18.0556i | −0.433974 | − | 0.751664i | 0.563238 | − | 0.826295i | \(-0.309556\pi\) |
−0.997211 | + | 0.0746307i | \(0.976222\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −16.5681 | + | 13.9023i | −0.687952 | + | 0.577260i | ||||
\(581\) | 5.70099 | + | 6.79417i | 0.236517 | + | 0.281870i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.6581 | − | 16.2308i | −1.14352 | − | 0.671059i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.0208 | + | 7.93838i | 1.85821 | + | 0.327652i | 0.986677 | − | 0.162690i | \(-0.0520171\pi\) |
0.871530 | + | 0.490342i | \(0.163128\pi\) | |||||||
\(588\) | −4.12612 | − | 23.8951i | −0.170158 | − | 0.985417i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.621055i | 0.0255037i | 0.999919 | + | 0.0127518i | \(0.00405915\pi\) | ||||
−0.999919 | + | 0.0127518i | \(0.995941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −43.9469 | −1.80165 | ||||||||
\(596\) | 31.2257 | − | 37.2134i | 1.27906 | − | 1.52432i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.823864 | + | 2.26355i | −0.0336622 | + | 0.0924860i | −0.955385 | − | 0.295363i | \(-0.904559\pi\) |
0.921723 | + | 0.387849i | \(0.126782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.4311 | + | 42.3159i | 0.994088 | + | 1.72181i | ||||
\(605\) | 23.5063 | + | 64.5831i | 0.955667 | + | 2.62567i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.87654 | + | 3.25280i | −0.157344 | + | 0.132027i | −0.718061 | − | 0.695980i | \(-0.754970\pi\) |
0.560717 | + | 0.828008i | \(0.310526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1537 | + | 11.1490i | 0.776145 | + | 0.451781i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54.7349 | + | 31.6012i | −2.21434 | + | 1.27845i | ||||
\(612\) | −43.8372 | − | 8.05033i | −1.77201 | − | 0.325415i | ||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.86682 | − | 32.5968i | 0.234861 | − | 1.30491i | ||||
\(625\) | 4.34120 | + | 24.6202i | 0.173648 | + | 0.984808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.63605 | + | 14.9498i | −0.105190 | + | 0.596561i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0476 | + | 32.9915i | 0.758275 | + | 1.31337i | 0.943730 | + | 0.330718i | \(0.107291\pi\) |
−0.185455 | + | 0.982653i | \(0.559376\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.3560 | − | 0.0827373i | −0.928319 | − | 0.00328851i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.4456 | + | 11.4453i | −1.24592 | + | 0.453478i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5106 | − | 39.0053i | 0.574029 | − | 1.54303i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.95317 | − | 1.40236i | −0.314131 | − | 0.0553898i | 0.0143597 | − | 0.999897i | \(-0.495429\pi\) |
−0.328491 | + | 0.944507i | \(0.606540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.5449 | − | 16.9409i | −1.83555 | − | 0.668086i | −0.991213 | − | 0.132273i | \(-0.957772\pi\) |
−0.844337 | − | 0.535813i | \(-0.820005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.2989i | 1.26980i | 0.772594 | + | 0.634901i | \(0.218959\pi\) | ||||
−0.772594 | + | 0.634901i | \(0.781041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.68743 | + | 33.6473i | 0.221888 | + | 1.31271i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.66213 | − | 26.5465i | −0.376383 | − | 1.03410i | −0.972844 | − | 0.231462i | \(-0.925649\pi\) |
0.596461 | − | 0.802642i | \(-0.296573\pi\) | |||||||
\(660\) | 24.8671 | + | 43.4257i | 0.967952 | + | 1.69034i | ||||
\(661\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.217887 | + | 61.5075i | −0.00846202 | + | 2.38876i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −27.0630 | − | 4.77193i | −1.04710 | − | 0.184632i | ||||
\(669\) | −0.457576 | − | 2.64990i | −0.0176909 | − | 0.102451i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.5070 | − | 8.62599i | 0.943274 | − | 0.332015i | ||||
\(676\) | −19.7070 | −0.757962 | ||||||||
\(677\) | 32.8096 | − | 39.1010i | 1.26098 | − | 1.50277i | 0.481347 | − | 0.876530i | \(-0.340148\pi\) |
0.779629 | − | 0.626242i | \(-0.215408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.51266 | − | 25.5926i | −0.173180 | − | 0.982152i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2736 | + | 32.7383i | 1.04513 | + | 1.25453i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(692\) | 45.4001 | − | 26.2118i | 1.72585 | − | 0.996422i | ||||
\(693\) | 33.2379 | − | 39.0462i | 1.26260 | − | 1.48324i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.2676 | + | 17.0066i | 0.766044 | + | 0.642788i | ||||
\(701\) | − | 10.5119i | − | 0.397028i | −0.980098 | − | 0.198514i | \(-0.936389\pi\) | ||
0.980098 | − | 0.198514i | \(-0.0636115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −33.2210 | + | 39.5913i | −1.25206 | + | 1.49215i | ||||
\(705\) | 9.07003 | − | 50.3942i | 0.341597 | − | 1.89795i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.09396 | − | 45.9031i | 0.303975 | − | 1.72393i | −0.324314 | − | 0.945949i | \(-0.605134\pi\) |
0.628290 | − | 0.777980i | \(-0.283755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.9261 | + | 0.226195i | 1.19732 | + | 0.00848299i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52.9019 | − | 44.3899i | 1.97842 | − | 1.66009i | ||||
\(716\) | 3.74116 | + | 4.45855i | 0.139814 | + | 0.166624i | ||||
\(717\) | −33.9457 | + | 19.4386i | −1.26773 | + | 0.725946i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 17.1017 | + | 20.6768i | 0.637344 | + | 0.770579i | ||||
\(721\) | −24.8056 | + | 42.9646i | −0.923810 | + | 1.60009i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.8136 | + | 4.19898i | −0.884414 | + | 0.155946i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1896 | + | 34.5622i | 1.52764 | + | 1.28184i | 0.812783 | + | 0.582566i | \(0.197951\pi\) |
0.714854 | + | 0.699274i | \(0.246493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | − | 23.6643i | −0.481481 | − | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.39100 | + | 41.9164i | 0.272993 | + | 1.54822i | 0.745266 | + | 0.666767i | \(0.232322\pi\) |
−0.472274 | + | 0.881452i | \(0.656567\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.36266 | − | 25.4429i | 0.345347 | − | 0.938475i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.3056 | − | 35.1704i | −0.746955 | − | 1.29376i | −0.949276 | − | 0.314445i | \(-0.898182\pi\) |
0.202321 | − | 0.979319i | \(-0.435152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.0371 | − | 18.5760i | 1.86985 | − | 0.680571i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0712494 | + | 10.0564i | −0.00260688 | + | 0.367946i | ||||
\(748\) | 47.9899 | − | 83.1209i | 1.75468 | − | 3.03920i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.4384 | − | 17.9941i | −1.80403 | − | 0.656615i | −0.997892 | − | 0.0648920i | \(-0.979330\pi\) |
−0.806142 | − | 0.591723i | \(-0.798448\pi\) | |||||||
\(752\) | 52.0797 | − | 9.18306i | 1.89915 | − | 0.334872i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.6296i | 1.98818i | ||||||||
\(756\) | 14.0000 | − | 23.6643i | 0.509175 | − | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.96009 | + | 11.1163i | −0.0709602 | + | 0.402435i | ||||
\(764\) | −10.2470 | − | 5.91608i | −0.370722 | − | 0.214036i | ||||
\(765\) | −37.9449 | − | 32.3004i | −1.37190 | − | 1.16783i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.9413 | + | 23.9508i | −0.503065 | + | 0.864249i | ||||
\(769\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5455 | + | 13.1234i | 0.811957 | + | 0.472626i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6373 | + | 8.45084i | −0.526467 | + | 0.303956i | −0.739576 | − | 0.673073i | \(-0.764974\pi\) |
0.213110 | + | 0.977028i | \(0.431641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 23.9027 | − | 28.2820i | 0.855853 | − | 1.01266i | ||||
\(781\) | 68.6529 | + | 57.6066i | 2.45659 | + | 2.06133i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.34339 | + | 23.7041i | 0.298168 | + | 0.847115i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | −10.9095 | + | 13.0015i | −0.389378 | + | 0.464042i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.09210 | + | 40.2213i | 0.252806 | + | 1.43373i | 0.801642 | + | 0.597804i | \(0.203960\pi\) |
−0.548836 | + | 0.835930i | \(0.684929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.8057 | − | 36.7128i | −1.09119 | − | 1.30043i | −0.950618 | − | 0.310364i | \(-0.899549\pi\) |
−0.140576 | − | 0.990070i | \(-0.544895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −92.2863 | + | 33.5895i | −3.26485 | + | 1.18831i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −72.3691 | − | 12.7606i | −2.55385 | − | 0.450313i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.2163i | 1.09751i | 0.835984 | + | 0.548753i | \(0.184897\pi\) | ||||
−0.835984 | + | 0.548753i | \(0.815103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −16.4494 | + | 19.6036i | −0.577260 | + | 0.687952i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 17.7734 | − | 48.2989i | 0.622193 | − | 1.69080i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.5631 | − | 13.2300i | −1.24268 | − | 0.462294i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.0813 | + | 38.6880i | 0.491440 | + | 1.35022i | 0.899363 | + | 0.437203i | \(0.144031\pi\) |
−0.407923 | + | 0.913016i | \(0.633747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.198192 | + | 55.9479i | −0.00690015 | + | 1.94785i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.9379 | + | 13.0803i | 1.24592 | + | 0.453478i | ||||
\(833\) | −51.2087 | + | 9.02947i | −1.77428 | + | 0.312853i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.5360 | − | 19.7491i | −0.814498 | − | 0.683445i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.974388 | + | 5.52603i | 0.0335996 | + | 0.190553i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.1680 | − | 44.6151i | −1.28013 | − | 1.53663i | ||||
\(844\) | 4.68319 | − | 26.5597i | 0.161202 | − | 0.914221i | ||||
\(845\) | −19.0812 | − | 11.0166i | −0.656414 | − | 0.378981i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.6599 | + | 70.4251i | 1.39709 | + | 2.41983i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.3811 | + | 48.7578i | −0.974037 | + | 1.67336i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 41.5316 | + | 24.1748i | 1.42285 | + | 0.828217i | ||||
\(853\) | 12.8652 | − | 4.68254i | 0.440495 | − | 0.160327i | −0.112245 | − | 0.993681i | \(-0.535804\pi\) |
0.552741 | + | 0.833353i | \(0.313582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.3791 | + | 3.94604i | 0.764455 | + | 0.134794i | 0.542263 | − | 0.840209i | \(-0.317568\pi\) |
0.222192 | + | 0.975003i | \(0.428679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.6113 | 1.99284 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.7142 | + | 65.0854i | −0.397835 | + | 2.21042i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.5149 | + | 64.6066i | −0.797688 | + | 2.19163i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.9139 | − | 25.4141i | 0.504758 | − | 0.860136i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.1171 | + | 27.7965i | 0.342020 | + | 0.939693i | ||||
\(876\) | −39.4034 | − | 0.139584i | −1.33132 | − | 0.00471611i | ||||
\(877\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.4806 | + | 28.3344i | −1.66894 | + | 0.955696i | ||||
\(880\) | −54.2983 | + | 19.7630i | −1.83040 | + | 0.666210i | ||||
\(881\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(884\) | −69.9442 | − | 12.3331i | −2.35248 | − | 0.414806i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −58.2334 | + | 10.2681i | −1.95529 | + | 0.344770i | −0.956734 | + | 0.290963i | \(0.906024\pi\) |
−0.998551 | + | 0.0538062i | \(0.982865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.3971 | − | 9.28410i | 1.92287 | − | 0.311029i | ||||
\(892\) | 3.10512 | 0.103967 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.12996 | + | 6.40834i | 0.0377705 | + | 0.214207i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | + | 29.5804i | 0.166667 | + | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(908\) | −42.6104 | + | 24.6011i | −1.41408 | + | 0.816417i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.7065 | + | 8.94092i | 1.67998 | + | 0.296226i | 0.930634 | − | 0.365951i | \(-0.119256\pi\) |
0.749347 | + | 0.662177i | \(0.230367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3505 | − | 7.40697i | −0.673503 | − | 0.245135i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6113 | 1.04276 | 0.521380 | − | 0.853325i | \(-0.325417\pi\) | ||||
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.1508 | − | 24.6370i | −0.960553 | − | 0.811816i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.6818 | − | 62.3177i | 0.746580 | − | 2.05121i | ||||
\(924\) | 37.8986 | + | 45.4920i | 1.24677 | + | 1.49658i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.9964 | + | 18.8650i | −1.74063 | + | 0.619607i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 92.9320 | − | 53.6543i | 3.03920 | − | 1.75468i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.4638 | + | 44.1045i | −0.831864 | + | 1.44083i | 0.0646935 | + | 0.997905i | \(0.479393\pi\) |
−0.896558 | + | 0.442926i | \(0.853940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.82833 | − | 3.18931i | 0.124933 | − | 0.104079i | ||||
\(940\) | 55.5595 | + | 20.2220i | 1.81215 | + | 0.659569i | ||||
\(941\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 26.7842 | − | 15.0866i | 0.871290 | − | 0.490768i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(948\) | −6.53029 | + | 36.2830i | −0.212094 | + | 1.17842i | ||||
\(949\) | 9.44263 | + | 53.5518i | 0.306521 | + | 1.73836i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.61438 | − | 11.4564i | −0.214036 | − | 0.370722i | ||||
\(956\) | −15.4487 | − | 42.4448i | −0.499645 | − | 1.37276i | ||||
\(957\) | −54.1149 | − | 0.191699i | −1.74929 | − | 0.00619674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.8875 | + | 15.3968i | −0.867791 | + | 0.496929i | ||||
\(961\) | −29.1305 | + | 10.6026i | −0.939693 | + | 0.342020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 29.4810 | − | 10.1426i | 0.945603 | − | 0.325323i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 38.9538 | − | 14.0219i | 1.24752 | − | 0.449062i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 27.1109 | + | 15.6525i | 0.866025 | + | 0.500000i | ||||
\(981\) | −9.86271 | + | 8.15743i | −0.314892 | + | 0.260447i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.8310 | + | 54.4851i | 0.632509 | + | 1.73780i | 0.674068 | + | 0.738669i | \(0.264545\pi\) |
−0.0415592 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.214618 | − | 60.5849i | 0.00683137 | − | 1.92844i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3255 | − | 54.2574i | 0.995087 | − | 1.72354i | 0.411807 | − | 0.911271i | \(-0.364898\pi\) |
0.583280 | − | 0.812271i | \(-0.301769\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.7121 | + | 62.0357i | 0.339939 | + | 1.96864i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.4288 | − | 2.05698i | −0.362136 | − | 0.0651779i | ||||
\(997\) | −14.1873 | − | 11.9046i | −0.449318 | − | 0.377022i | 0.389865 | − | 0.920872i | \(-0.372522\pi\) |
−0.839183 | + | 0.543850i | \(0.816966\pi\) | |||||||
\(998\) | 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 | 945.2.cs.a.524.1 | ✓ | 24 | |
5.4 | even | 2 | inner | 945.2.cs.a.524.4 | yes | 24 | |
7.6 | odd | 2 | inner | 945.2.cs.a.524.4 | yes | 24 | |
27.5 | odd | 18 | inner | 945.2.cs.a.734.1 | yes | 24 | |
35.34 | odd | 2 | CM | 945.2.cs.a.524.1 | ✓ | 24 | |
135.59 | odd | 18 | inner | 945.2.cs.a.734.4 | yes | 24 | |
189.167 | even | 18 | inner | 945.2.cs.a.734.4 | yes | 24 | |
945.734 | even | 18 | inner | 945.2.cs.a.734.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.cs.a.524.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
945.2.cs.a.524.1 | ✓ | 24 | 35.34 | odd | 2 | CM | |
945.2.cs.a.524.4 | yes | 24 | 5.4 | even | 2 | inner | |
945.2.cs.a.524.4 | yes | 24 | 7.6 | odd | 2 | inner | |
945.2.cs.a.734.1 | yes | 24 | 27.5 | odd | 18 | inner | |
945.2.cs.a.734.1 | yes | 24 | 945.734 | even | 18 | inner | |
945.2.cs.a.734.4 | yes | 24 | 135.59 | odd | 18 | inner | |
945.2.cs.a.734.4 | yes | 24 | 189.167 | even | 18 | inner |