Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(289,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.bl (of order \(4\), 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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Character | \(\chi\) | \(=\) | 1920.289 |
Dual form | 1920.2.bl.a.1249.2 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.98421 | − | 1.03097i | 0.887367 | − | 0.461064i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.91927 | −1.48134 | −0.740672 | − | 0.671867i | \(-0.765493\pi\) | ||||
−0.740672 | + | 0.671867i | \(0.765493\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93423 | − | 2.93423i | 0.884703 | − | 0.884703i | −0.109305 | − | 0.994008i | \(-0.534862\pi\) |
0.994008 | + | 0.109305i | \(0.0348625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.732828 | − | 0.732828i | 0.203250 | − | 0.203250i | −0.598141 | − | 0.801391i | \(-0.704094\pi\) |
0.801391 | + | 0.598141i | \(0.204094\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.674045 | + | 2.13206i | −0.174038 | + | 0.550495i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.89302i | 0.701659i | 0.936439 | + | 0.350830i | \(0.114100\pi\) | ||||
−0.936439 | + | 0.350830i | \(0.885900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.67534 | − | 1.67534i | −0.384350 | − | 0.384350i | 0.488316 | − | 0.872667i | \(-0.337611\pi\) |
−0.872667 | + | 0.488316i | \(0.837611\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.77134 | − | 2.77134i | 0.604756 | − | 0.604756i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.73133 | −0.361006 | −0.180503 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180503 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.87420 | − | 4.09133i | 0.574841 | − | 0.818265i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.99003 | + | 4.99003i | 0.926625 | + | 0.926625i | 0.997486 | − | 0.0708617i | \(-0.0225749\pi\) |
−0.0708617 | + | 0.997486i | \(0.522575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.8149 | −1.94241 | −0.971203 | − | 0.238254i | \(-0.923425\pi\) | ||||
−0.971203 | + | 0.238254i | \(0.923425\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.14963i | 0.722357i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.77666 | + | 4.04065i | −1.31450 | + | 0.682994i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.41524 | − | 6.41524i | −1.05466 | − | 1.05466i | −0.998417 | − | 0.0562413i | \(-0.982088\pi\) |
−0.0562413 | − | 0.998417i | \(-0.517912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03637i | 0.165953i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.00577512i | 0.000901923i | 1.00000 | 0.000450961i | \(0.000143545\pi\) | |||||
−1.00000 | 0.000450961i | \(0.999856\pi\) | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.23930 | + | 2.23930i | 0.341490 | + | 0.341490i | 0.856927 | − | 0.515437i | \(-0.172370\pi\) |
−0.515437 | + | 0.856927i | \(0.672370\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.03097 | − | 1.98421i | −0.153688 | − | 0.295789i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.6451i | − | 1.69861i | −0.527900 | − | 0.849307i | \(-0.677020\pi\) | ||
0.527900 | − | 0.849307i | \(-0.322980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.36066 | 1.19438 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.04567 | − | 2.04567i | −0.286451 | − | 0.286451i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.55765 | − | 5.55765i | −0.763402 | − | 0.763402i | 0.213533 | − | 0.976936i | \(-0.431503\pi\) |
−0.976936 | + | 0.213533i | \(0.931503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.79703 | − | 8.84724i | 0.377152 | − | 1.19296i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.36929 | 0.313821 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.83290 | + | 3.83290i | −0.499001 | + | 0.499001i | −0.911127 | − | 0.412126i | \(-0.864786\pi\) |
0.412126 | + | 0.911127i | \(0.364786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.30595 | − | 9.30595i | −1.19150 | − | 1.19150i | −0.976645 | − | 0.214859i | \(-0.931071\pi\) |
−0.214859 | − | 0.976645i | \(-0.568929\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.91927i | 0.493781i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.698563 | − | 2.20961i | 0.0866461 | − | 0.274068i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85243 | − | 3.85243i | 0.470649 | − | 0.470649i | −0.431476 | − | 0.902124i | \(-0.642007\pi\) |
0.902124 | + | 0.431476i | \(0.142007\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.22423 | − | 1.22423i | 0.147380 | − | 0.147380i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.15355i | 0.136901i | 0.997655 | + | 0.0684504i | \(0.0218055\pi\) | ||||
−0.997655 | + | 0.0684504i | \(0.978195\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.98713 | −0.934823 | −0.467411 | − | 0.884040i | \(-0.654813\pi\) | ||||
−0.467411 | + | 0.884040i | \(0.654813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.860637 | + | 4.92537i | 0.0993778 | + | 0.568733i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.5000 | + | 11.5000i | −1.31055 | + | 1.31055i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.843960 | 0.0949529 | 0.0474765 | − | 0.998872i | \(-0.484882\pi\) | ||||
0.0474765 | + | 0.998872i | \(0.484882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.20069 | − | 5.20069i | 0.570850 | − | 0.570850i | −0.361516 | − | 0.932366i | \(-0.617741\pi\) |
0.932366 | + | 0.361516i | \(0.117741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98261 | + | 5.74036i | 0.323510 | + | 0.622629i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.05696 | −0.756586 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.40896i | − | 0.573349i | −0.958028 | − | 0.286674i | \(-0.907450\pi\) | ||
0.958028 | − | 0.286674i | \(-0.0925498\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.87215 | + | 2.87215i | −0.301083 | + | 0.301083i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.64726 | − | 7.64726i | 0.792984 | − | 0.792984i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.05147 | − | 1.59701i | −0.518270 | − | 0.163850i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.24154i | − | 0.227594i | −0.993504 | − | 0.113797i | \(-0.963699\pi\) | ||
0.993504 | − | 0.113797i | \(-0.0363013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.93423 | − | 2.93423i | −0.294901 | − | 0.294901i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50655 | − | 7.50655i | 0.746930 | − | 0.746930i | −0.226972 | − | 0.973901i | \(-0.572882\pi\) |
0.973901 | + | 0.226972i | \(0.0728824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.91110 | 0.385372 | 0.192686 | − | 0.981260i | \(-0.438280\pi\) | ||||
0.192686 | + | 0.981260i | \(0.438280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.64176 | − | 8.35610i | 0.257810 | − | 0.815472i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.60233 | + | 2.60233i | 0.251577 | + | 0.251577i | 0.821617 | − | 0.570040i | \(-0.193072\pi\) |
−0.570040 | + | 0.821617i | \(0.693072\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.06635 | + | 2.06635i | 0.197920 | + | 0.197920i | 0.799108 | − | 0.601188i | \(-0.205306\pi\) |
−0.601188 | + | 0.799108i | \(0.705306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.07252 | 0.861125 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.13610i | − | 0.765380i | −0.923877 | − | 0.382690i | \(-0.874998\pi\) | ||
0.923877 | − | 0.382690i | \(-0.125002\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.43532 | + | 1.78495i | −0.320345 | + | 0.166447i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.732828 | − | 0.732828i | −0.0677500 | − | 0.0677500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 11.3385i | − | 1.03940i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 6.21941i | − | 0.565401i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.00408363 | − | 0.00408363i | −0.000368208 | − | 0.000368208i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.48500 | − | 11.0813i | 0.132822 | − | 0.991140i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0862i | 1.42742i | 0.700442 | + | 0.713709i | \(0.252986\pi\) | ||||
−0.700442 | + | 0.713709i | \(0.747014\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.16685 | −0.278826 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0407 | − | 13.0407i | −1.13937 | − | 1.13937i | −0.988563 | − | 0.150808i | \(-0.951813\pi\) |
−0.150808 | − | 0.988563i | \(-0.548187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.56612 | + | 6.56612i | 0.569355 | + | 0.569355i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.13206 | + | 0.674045i | 0.183498 | + | 0.0580125i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.51614 | −0.556711 | −0.278356 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278356 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0953 | − | 15.0953i | 1.28036 | − | 1.28036i | 0.339902 | − | 0.940461i | \(-0.389606\pi\) |
0.940461 | − | 0.339902i | \(-0.110394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.23434 | + | 8.23434i | 0.693456 | + | 0.693456i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.30057i | − | 0.359632i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0458 | + | 4.75671i | 1.24949 | + | 0.395023i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.91188 | + | 5.91188i | −0.487604 | + | 0.487604i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.27402 | + | 4.27402i | −0.350141 | + | 0.350141i | −0.860162 | − | 0.510021i | \(-0.829638\pi\) |
0.510021 | + | 0.860162i | \(0.329638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.39998i | 0.683581i | 0.939776 | + | 0.341790i | \(0.111033\pi\) | ||||
−0.939776 | + | 0.341790i | \(0.888967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.89302 | 0.233886 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.4590 | + | 11.1498i | −1.72363 | + | 0.895573i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.68893 | − | 5.68893i | 0.454026 | − | 0.454026i | −0.442662 | − | 0.896689i | \(-0.645966\pi\) |
0.896689 | + | 0.442662i | \(0.145966\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.85971 | 0.623315 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.78553 | 0.534775 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.63869 | + | 5.63869i | −0.441656 | + | 0.441656i | −0.892568 | − | 0.450912i | \(-0.851099\pi\) |
0.450912 | + | 0.892568i | \(0.351099\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.27814 | + | 8.23374i | 0.333053 | + | 0.640996i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.45583 | −0.499567 | −0.249783 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249783 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9259i | 0.917379i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.67534 | + | 1.67534i | −0.128117 | + | 0.128117i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.33664 | + | 7.33664i | −0.557795 | + | 0.557795i | −0.928679 | − | 0.370884i | \(-0.879055\pi\) |
0.370884 | + | 0.928679i | \(0.379055\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2648 | + | 16.0350i | −0.851537 | + | 1.21213i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.42054i | − | 0.407432i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.04377 | + | 1.04377i | 0.0780153 | + | 0.0780153i | 0.745038 | − | 0.667022i | \(-0.232431\pi\) |
−0.667022 | + | 0.745038i | \(0.732431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1024 | − | 12.1024i | 0.899567 | − | 0.899567i | −0.0958310 | − | 0.995398i | \(-0.530551\pi\) |
0.995398 | + | 0.0958310i | \(0.0305508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.1606 | 0.972859 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.3431 | − | 6.11528i | −1.42213 | − | 0.449604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.48877 | + | 8.48877i | 0.620761 | + | 0.620761i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.77134 | − | 2.77134i | −0.201585 | − | 0.201585i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2273 | −1.53596 | −0.767978 | − | 0.640477i | \(-0.778737\pi\) | ||||
−0.767978 | + | 0.640477i | \(0.778737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 19.2782i | − | 1.38767i | −0.720132 | − | 0.693837i | \(-0.755919\pi\) | ||
0.720132 | − | 0.693837i | \(-0.244081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.06847 | + | 2.05639i | 0.0765148 | + | 0.147261i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.48350 | − | 9.48350i | −0.675672 | − | 0.675672i | 0.283346 | − | 0.959018i | \(-0.408556\pi\) |
−0.959018 | + | 0.283346i | \(0.908556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.65421i | − | 0.613481i | −0.951793 | − | 0.306740i | \(-0.900762\pi\) | ||
0.951793 | − | 0.306740i | \(-0.0992383\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.44815i | 0.384283i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.5572 | − | 19.5572i | −1.37265 | − | 1.37265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.00595398 | + | 0.0114591i | 0.000415844 | + | 0.000800336i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.73133i | 0.120335i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.83169 | −0.680072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.875946 | + | 0.875946i | 0.0603026 | + | 0.0603026i | 0.736615 | − | 0.676312i | \(-0.236423\pi\) |
−0.676312 | + | 0.736615i | \(0.736423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.815681 | − | 0.815681i | −0.0558895 | − | 0.0558895i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.75190 | + | 2.13460i | 0.460476 | + | 0.145578i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.3863 | 2.87737 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.64775 | − | 5.64775i | 0.381640 | − | 0.381640i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.12008 | + | 2.12008i | 0.142612 | + | 0.142612i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.4375i | − | 0.698946i | −0.936946 | − | 0.349473i | \(-0.886361\pi\) | ||
0.936946 | − | 0.349473i | \(-0.113639\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.09133 | − | 2.87420i | −0.272755 | − | 0.191614i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7218 | − | 13.7218i | 0.910747 | − | 0.910747i | −0.0855842 | − | 0.996331i | \(-0.527276\pi\) |
0.996331 | + | 0.0855842i | \(0.0272757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.43878 | + | 8.43878i | −0.557651 | + | 0.557651i | −0.928638 | − | 0.370987i | \(-0.879019\pi\) |
0.370987 | + | 0.928638i | \(0.379019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16.2635i | − | 1.07006i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.6100 | −1.87431 | −0.937153 | − | 0.348919i | \(-0.886549\pi\) | ||||
−0.937153 | + | 0.348919i | \(0.886549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.0058 | − | 23.1064i | −0.783169 | − | 1.50729i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.596770 | + | 0.596770i | −0.0387644 | + | 0.0387644i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4924 | 1.39023 | 0.695115 | − | 0.718899i | \(-0.255354\pi\) | ||||
0.695115 | + | 0.718899i | \(0.255354\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5943 | −1.26218 | −0.631091 | − | 0.775709i | \(-0.717393\pi\) | ||||
−0.631091 | + | 0.775709i | \(0.717393\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.5893 | − | 8.61959i | 1.05985 | − | 0.550685i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.45548 | −0.156238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.35489i | 0.466097i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.58072 | − | 9.58072i | 0.604730 | − | 0.604730i | −0.336834 | − | 0.941564i | \(-0.609356\pi\) |
0.941564 | + | 0.336834i | \(0.109356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.08011 | + | 5.08011i | −0.319384 | + | 0.319384i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.16807 | − | 1.95002i | −0.386260 | − | 0.122115i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2730i | 0.827946i | 0.910289 | + | 0.413973i | \(0.135859\pi\) | ||||
−0.910289 | + | 0.413973i | \(0.864141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.1430 | + | 25.1430i | 1.56231 | + | 1.56231i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.99003 | − | 4.99003i | 0.308875 | − | 0.308875i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0606 | 0.805349 | 0.402675 | − | 0.915343i | \(-0.368081\pi\) | ||||
0.402675 | + | 0.915343i | \(0.368081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.7573 | − | 5.29780i | −1.02940 | − | 0.325441i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.82471 | + | 3.82471i | 0.234069 | + | 0.234069i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.4067 | + | 12.4067i | 0.756451 | + | 0.756451i | 0.975675 | − | 0.219224i | \(-0.0703525\pi\) |
−0.219224 | + | 0.975675i | \(0.570353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.11193 | 0.128291 | 0.0641453 | − | 0.997941i | \(-0.479568\pi\) | ||||
0.0641453 | + | 0.997941i | \(0.479568\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.06183i | − | 0.245833i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.57132 | − | 20.4385i | −0.215359 | − | 1.23249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.2116 | + | 13.2116i | 0.793808 | + | 0.793808i | 0.982111 | − | 0.188303i | \(-0.0602988\pi\) |
−0.188303 | + | 0.982111i | \(0.560299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.8149i | 0.647469i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.78786i | 0.225965i | 0.993597 | + | 0.112982i | \(0.0360404\pi\) | ||||
−0.993597 | + | 0.112982i | \(0.963960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.16274 | + | 3.16274i | 0.188005 | + | 0.188005i | 0.794833 | − | 0.606828i | \(-0.207558\pi\) |
−0.606828 | + | 0.794833i | \(0.707558\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.70118 | − | 2.44267i | 0.278474 | − | 0.144691i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.0226343i | − | 0.00133606i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.63046 | 0.507674 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.58501 | + | 1.58501i | 0.0929147 | + | 0.0929147i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.51339 | − | 8.51339i | −0.497357 | − | 0.497357i | 0.413257 | − | 0.910614i | \(-0.364391\pi\) |
−0.910614 | + | 0.413257i | \(0.864391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.65368 | + | 11.5569i | −0.212726 | + | 0.672868i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.14963 | 0.240786 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.26876 | + | 1.26876i | −0.0733745 | + | 0.0733745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.77642 | − | 8.77642i | −0.505864 | − | 0.505864i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.6159i | 0.609866i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.0591 | − | 8.87083i | −1.60666 | − | 0.507942i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.12093 | + | 7.12093i | −0.406413 | + | 0.406413i | −0.880486 | − | 0.474073i | \(-0.842783\pi\) |
0.474073 | + | 0.880486i | \(0.342783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.76557 | + | 2.76557i | −0.157328 | + | 0.157328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2980i | 1.20770i | 0.797099 | + | 0.603849i | \(0.206367\pi\) | ||||
−0.797099 | + | 0.603849i | \(0.793633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.49789 | 0.423806 | 0.211903 | − | 0.977291i | \(-0.432034\pi\) | ||||
0.211903 | + | 0.977291i | \(0.432034\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.04065 | + | 7.77666i | 0.227665 | + | 0.438165i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.35354 | + | 2.35354i | −0.132188 | + | 0.132188i | −0.770105 | − | 0.637917i | \(-0.779796\pi\) |
0.637917 | + | 0.770105i | \(0.279796\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.2838 | 1.63958 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.68025 | −0.205412 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.84680 | − | 4.84680i | 0.269683 | − | 0.269683i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.891943 | − | 5.10453i | −0.0494761 | − | 0.283149i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.92226 | −0.161601 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.6403i | 2.51623i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.6845 | + | 22.6845i | −1.24685 | + | 1.24685i | −0.289753 | + | 0.957102i | \(0.593573\pi\) |
−0.957102 | + | 0.289753i | \(0.906427\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.41524 | + | 6.41524i | −0.351553 | + | 0.351553i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.67230 | − | 11.6158i | 0.200639 | − | 0.634637i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.90357i | − | 0.485008i | −0.970150 | − | 0.242504i | \(-0.922031\pi\) | ||
0.970150 | − | 0.242504i | \(-0.0779688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.75309 | + | 5.75309i | 0.312465 | + | 0.312465i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.7333 | + | 31.7333i | −1.71845 | + | 1.71845i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.33279 | −0.287944 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16699 | − | 3.69129i | 0.0628287 | − | 0.198732i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.87783 | − | 8.87783i | −0.476587 | − | 0.476587i | 0.427451 | − | 0.904038i | \(-0.359412\pi\) |
−0.904038 | + | 0.427451i | \(0.859412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.23040 | + | 8.23040i | 0.440563 | + | 0.440563i | 0.892201 | − | 0.451638i | \(-0.149160\pi\) |
−0.451638 | + | 0.892201i | \(0.649160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.03637 | 0.0553176 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.7125i | 1.84756i | 0.382922 | + | 0.923781i | \(0.374918\pi\) | ||||
−0.382922 | + | 0.923781i | \(0.625082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.18927 | + | 2.28888i | 0.0631200 | + | 0.121481i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.01753 | + | 8.01753i | 0.424333 | + | 0.424333i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.81082i | 0.148350i | 0.997245 | + | 0.0741748i | \(0.0236323\pi\) | ||||
−0.997245 | + | 0.0741748i | \(0.976368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.3864i | − | 0.704550i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.39778 | + | 4.39778i | 0.230824 | + | 0.230824i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.8482 | + | 8.23449i | −0.829531 | + | 0.431013i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2835i | 0.954392i | 0.878797 | + | 0.477196i | \(0.158347\pi\) | ||||
−0.878797 | + | 0.477196i | \(0.841653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.00577512 | 0.000300641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.7819 | + | 21.7819i | 1.13086 | + | 1.13086i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.4176 | + | 23.4176i | 1.21252 | + | 1.21252i | 0.970195 | + | 0.242324i | \(0.0779098\pi\) |
0.242324 | + | 0.970195i | \(0.422090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.78560 | + | 8.88570i | 0.350407 | + | 0.458856i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.31366 | 0.376673 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.20944 | − | 6.20944i | 0.318957 | − | 0.318957i | −0.529409 | − | 0.848367i | \(-0.677586\pi\) |
0.848367 | + | 0.529409i | \(0.177586\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3746 | − | 11.3746i | −0.582741 | − | 0.582741i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.4005i | − | 0.735832i | −0.929859 | − | 0.367916i | \(-0.880071\pi\) | ||
0.929859 | − | 0.367916i | \(-0.119929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9623 | + | 34.6747i | −0.558692 | + | 1.76719i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.23930 | − | 2.23930i | 0.113830 | − | 0.113830i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.4753 | + | 15.4753i | −0.784630 | + | 0.784630i | −0.980608 | − | 0.195978i | \(-0.937212\pi\) |
0.195978 | + | 0.980608i | \(0.437212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.00875i | − | 0.253304i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.4423 | 0.930292 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.67460 | − | 0.870098i | 0.0842581 | − | 0.0437794i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0440 | − | 15.0440i | 0.755036 | − | 0.755036i | −0.220378 | − | 0.975414i | \(-0.570729\pi\) |
0.975414 | + | 0.220378i | \(0.0707292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.28590 | −0.464876 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7953 | 1.43797 | 0.718985 | − | 0.695026i | \(-0.244607\pi\) | ||||
0.718985 | + | 0.695026i | \(0.244607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.92543 | + | 7.92543i | −0.394794 | + | 0.394794i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.98421 | + | 1.03097i | −0.0985963 | + | 0.0512293i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.6476 | −1.86612 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3562i | 1.15489i | 0.816430 | + | 0.577444i | \(0.195950\pi\) | ||||
−0.816430 | + | 0.577444i | \(0.804050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.60760 | − | 4.60760i | 0.227276 | − | 0.227276i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0222 | − | 15.0222i | 0.739192 | − | 0.739192i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.95752 | − | 15.6810i | 0.243355 | − | 0.769751i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.3479i | 1.04541i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.4332 | + | 22.4332i | 1.09594 | + | 1.09594i | 0.994881 | + | 0.101055i | \(0.0322217\pi\) |
0.101055 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7632 | + | 14.7632i | −0.719513 | + | 0.719513i | −0.968505 | − | 0.248993i | \(-0.919900\pi\) |
0.248993 | + | 0.968505i | \(0.419900\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.6451 | −0.566205 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.8363 | + | 8.31511i | 0.574144 | + | 0.403342i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.4725 | + | 36.4725i | 1.76503 | + | 1.76503i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.04096 | + | 3.04096i | 0.146819 | + | 0.146819i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.92220 | 0.285262 | 0.142631 | − | 0.989776i | \(-0.454444\pi\) | ||||
0.142631 | + | 0.989776i | \(0.454444\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.27026i | 0.253272i | 0.991949 | + | 0.126636i | \(0.0404181\pi\) | ||||
−0.991949 | + | 0.126636i | \(0.959582\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.0025 | + | 7.27551i | −0.671369 | + | 0.348834i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.90057 | + | 2.90057i | 0.138753 | + | 0.138753i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8427i | 0.851587i | 0.904820 | + | 0.425793i | \(0.140005\pi\) | ||||
−0.904820 | + | 0.425793i | \(0.859995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8.36066i | − | 0.398127i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.89855 | + | 5.89855i | 0.280248 | + | 0.280248i | 0.833208 | − | 0.552960i | \(-0.186502\pi\) |
−0.552960 | + | 0.833208i | \(0.686502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.57648 | − | 10.7325i | −0.264350 | − | 0.508771i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 6.04438i | − | 0.285889i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.12803 | 0.383586 | 0.191793 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191793 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0169455 | + | 0.0169455i | 0.000797934 | + | 0.000797934i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.93968 | − | 5.93968i | −0.279071 | − | 0.279071i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.73786 | + | 8.66005i | −0.128353 | + | 0.405990i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.35488 | −0.297269 | −0.148634 | − | 0.988892i | \(-0.547488\pi\) | ||||
−0.148634 | + | 0.988892i | \(0.547488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.04567 | + | 2.04567i | −0.0954838 | + | 0.0954838i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.13085 | − | 2.13085i | −0.0992438 | − | 0.0992438i | 0.655742 | − | 0.754985i | \(-0.272356\pi\) |
−0.754985 | + | 0.655742i | \(0.772356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 18.4540i | − | 0.857630i | −0.903392 | − | 0.428815i | \(-0.858931\pi\) | ||
0.903392 | − | 0.428815i | \(-0.141069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.28970 | − | 23.0579i | 0.338052 | − | 1.06928i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.63243 | − | 5.63243i | 0.260638 | − | 0.260638i | −0.564675 | − | 0.825313i | \(-0.690999\pi\) |
0.825313 | + | 0.564675i | \(0.190999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0987 | + | 15.0987i | −0.697193 | + | 0.697193i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.04537i | 0.370711i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.1412 | 0.604235 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.6697 | + | 2.03910i | −0.535441 | + | 0.0935604i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.55765 | + | 5.55765i | −0.254467 | + | 0.254467i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.4860 | 0.981720 | 0.490860 | − | 0.871239i | \(-0.336683\pi\) | ||||
0.490860 | + | 0.871239i | \(0.336683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.40253 | −0.428718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.79810 | + | 4.79810i | −0.218321 | + | 0.218321i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.31096 | − | 4.44769i | −0.104935 | − | 0.201959i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.3297 | 1.64626 | 0.823128 | − | 0.567856i | \(-0.192227\pi\) | ||||
0.823128 | + | 0.567856i | \(0.192227\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.97431i | − | 0.360611i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.63599 | + | 1.63599i | −0.0738313 | + | 0.0738313i | −0.743058 | − | 0.669227i | \(-0.766625\pi\) |
0.669227 | + | 0.743058i | \(0.266625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.4362 | + | 14.4362i | −0.650175 | + | 0.650175i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.84724 | − | 2.79703i | −0.397654 | − | 0.125717i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.52106i | − | 0.202797i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7955 | − | 18.7955i | −0.841402 | − | 0.841402i | 0.147639 | − | 0.989041i | \(-0.452833\pi\) |
−0.989041 | + | 0.147639i | \(0.952833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.56496 | − | 4.56496i | 0.203947 | − | 0.203947i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8118 | 0.615838 | 0.307919 | − | 0.951413i | \(-0.400367\pi\) | ||||
0.307919 | + | 0.951413i | \(0.400367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.15557 | − | 22.6336i | 0.318419 | − | 1.00718i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.43290 | − | 8.43290i | −0.374518 | − | 0.374518i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.40184 | + | 5.40184i | 0.239432 | + | 0.239432i | 0.816615 | − | 0.577183i | \(-0.195848\pi\) |
−0.577183 | + | 0.816615i | \(0.695848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.3037 | 1.38479 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.36929i | − | 0.104607i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.76046 | − | 4.03223i | 0.341967 | − | 0.177681i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.1694 | − | 34.1694i | −1.50277 | − | 1.50277i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.3756i | − | 0.455437i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 33.6969i | − | 1.47629i | −0.674642 | − | 0.738145i | \(-0.735702\pi\) | ||
0.674642 | − | 0.738145i | \(-0.264298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.31481 | + | 4.31481i | 0.188673 | + | 0.188673i | 0.795122 | − | 0.606449i | \(-0.207407\pi\) |
−0.606449 | + | 0.795122i | \(0.707407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.37307 | − | 19.3039i | −0.147213 | − | 0.842489i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 31.2876i | − | 1.36291i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0025 | −0.869674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.83290 | + | 3.83290i | 0.166334 | + | 0.166334i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.00423217 | + | 0.00423217i | 0.000183316 | + | 0.000183316i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.84650 | + | 2.48065i | 0.339234 | + | 0.107248i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.47612 | −0.0636993 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.5321 | − | 24.5321i | 1.05667 | − | 1.05667i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8010 | + | 22.8010i | 0.980290 | + | 0.980290i | 0.999809 | − | 0.0195198i | \(-0.00621375\pi\) |
−0.0195198 | + | 0.999809i | \(0.506214\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.1154i | 0.734493i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.23041 | + | 1.96973i | 0.266882 | + | 0.0843740i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.56014 | − | 5.56014i | 0.237735 | − | 0.237735i | −0.578177 | − | 0.815911i | \(-0.696236\pi\) |
0.815911 | + | 0.578177i | \(0.196236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.30595 | + | 9.30595i | −0.397168 | + | 0.397168i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16.7200i | − | 0.712297i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.30771 | −0.140658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.0018 | − | 9.35349i | 0.764134 | − | 0.397034i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.2628 | + | 12.2628i | −0.519591 | + | 0.519591i | −0.917447 | − | 0.397857i | \(-0.869754\pi\) |
0.397857 | + | 0.917447i | \(0.369754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.28204 | 0.138816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0049 | −0.506849 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.327630 | + | 0.327630i | −0.0138079 | + | 0.0138079i | −0.713977 | − | 0.700169i | \(-0.753108\pi\) |
0.700169 | + | 0.713977i | \(0.253108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.38807 | − | 16.1438i | −0.352889 | − | 0.679173i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.91927 | 0.164594 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.6010i | 1.49247i | 0.665681 | + | 0.746237i | \(0.268141\pi\) | ||||
−0.665681 | + | 0.746237i | \(0.731859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.57427 | + | 3.57427i | −0.149579 | + | 0.149579i | −0.777930 | − | 0.628351i | \(-0.783730\pi\) |
0.628351 | + | 0.777930i | \(0.283730\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0100 | − | 15.0100i | 0.627051 | − | 0.627051i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.97618 | + | 7.08342i | −0.207521 | + | 0.295399i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 8.80260i | − | 0.366457i | −0.983070 | − | 0.183229i | \(-0.941345\pi\) | ||
0.983070 | − | 0.183229i | \(-0.0586548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.6317 | + | 13.6317i | 0.566515 | + | 0.566515i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.3829 | + | 20.3829i | −0.845625 | + | 0.845625i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.6149 | −1.35077 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.20961 | − | 0.698563i | −0.0913561 | − | 0.0288820i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.9887 | − | 17.9887i | −0.742475 | − | 0.742475i | 0.230579 | − | 0.973054i | \(-0.425938\pi\) |
−0.973054 | + | 0.230579i | \(0.925938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.1186 | + | 18.1186i | 0.746564 | + | 0.746564i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.4117 | 0.551684 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.4791i | − | 1.04630i | −0.852240 | − | 0.523150i | \(-0.824757\pi\) | ||
0.852240 | − | 0.523150i | \(-0.175243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.6897 | − | 22.4980i | −0.479229 | − | 0.922328i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.11945 | + | 6.11945i | 0.250452 | + | 0.250452i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6977i | 0.600532i | 0.953856 | + | 0.300266i | \(0.0970754\pi\) | ||||
−0.953856 | + | 0.300266i | \(0.902925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.2790i | 0.500869i | 0.968134 | + | 0.250434i | \(0.0805735\pi\) | ||||
−0.968134 | + | 0.250434i | \(0.919427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.85243 | − | 3.85243i | −0.156883 | − | 0.156883i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.41202 | − | 12.3406i | −0.260686 | − | 0.501718i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.2195i | − | 1.06421i | −0.846677 | − | 0.532107i | \(-0.821400\pi\) | ||
0.846677 | − | 0.532107i | \(-0.178600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.6581 | 1.12076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.53386 | − | 8.53386i | −0.345243 | − | 0.345243i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.4055 | − | 23.4055i | −0.945340 | − | 0.945340i | 0.0532416 | − | 0.998582i | \(-0.483045\pi\) |
−0.998582 | + | 0.0532416i | \(0.983045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0123129 | − | 0.00389269i | −0.000496503 | − | 0.000156968i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5735 | −1.11007 | −0.555033 | − | 0.831828i | \(-0.687294\pi\) | ||||
−0.555033 | + | 0.831828i | \(0.687294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.2452 | − | 12.2452i | 0.492176 | − | 0.492176i | −0.416815 | − | 0.908991i | \(-0.636854\pi\) |
0.908991 | + | 0.416815i | \(0.136854\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.22423 | − | 1.22423i | −0.0491268 | − | 0.0491268i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.1992i | 0.849327i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.47792 | − | 23.5186i | −0.339117 | − | 0.940744i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.95205 | − | 6.95205i | 0.277638 | − | 0.277638i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.5594 | − | 18.5594i | 0.740011 | − | 0.740011i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.5846i | − | 1.01851i | −0.860617 | − | 0.509253i | \(-0.829922\pi\) | ||
0.860617 | − | 0.509253i | \(-0.170078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.23877 | −0.0492369 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5844 | + | 31.9184i | 0.658131 | + | 1.26664i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.12692 | − | 6.12692i | 0.242758 | − | 0.242758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.15355 | 0.0456336 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.52020 | −0.139040 | −0.0695198 | − | 0.997581i | \(-0.522147\pi\) | ||||
−0.0695198 | + | 0.997581i | \(0.522147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0869 | − | 19.0869i | 0.752715 | − | 0.752715i | −0.222270 | − | 0.974985i | \(-0.571347\pi\) |
0.974985 | + | 0.222270i | \(0.0713466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.28370 | + | 3.26493i | −0.247421 | + | 0.128556i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.02456 | 0.197536 | 0.0987678 | − | 0.995111i | \(-0.468510\pi\) | ||||
0.0987678 | + | 0.995111i | \(0.468510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.4932i | 0.882935i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.9717 | + | 29.9717i | −1.17468 | + | 1.17468i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.07220 | − | 6.07220i | 0.237623 | − | 0.237623i | −0.578242 | − | 0.815865i | \(-0.696261\pi\) |
0.815865 | + | 0.578242i | \(0.196261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.3201 | − | 12.4310i | −1.53636 | − | 0.485718i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.98713i | 0.311608i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.88182 | + | 5.88182i | 0.229123 | + | 0.229123i | 0.812326 | − | 0.583203i | \(-0.198201\pi\) |
−0.583203 | + | 0.812326i | \(0.698201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0275 | − | 24.0275i | 0.934562 | − | 0.934562i | −0.0634242 | − | 0.997987i | \(-0.520202\pi\) |
0.997987 | + | 0.0634242i | \(0.0202021\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.99825 | −0.116442 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.7981 | + | 6.25911i | 0.767736 | + | 0.242718i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.63936 | − | 8.63936i | −0.334517 | − | 0.334517i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.38042 | + | 7.38042i | 0.285344 | + | 0.285344i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −54.6116 | −2.10826 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.5327i | 1.40823i | 0.710084 | + | 0.704117i | \(0.248657\pi\) | ||||
−0.710084 | + | 0.704117i | \(0.751343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.92537 | − | 0.860637i | 0.189578 | − | 0.0331259i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.5460 | − | 20.5460i | −0.789645 | − | 0.789645i | 0.191791 | − | 0.981436i | \(-0.438571\pi\) |
−0.981436 | + | 0.191791i | \(0.938571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.78518i | 0.337144i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4055i | 0.743622i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.2074 | + | 18.2074i | 0.696688 | + | 0.696688i | 0.963695 | − | 0.267007i | \(-0.0860346\pi\) |
−0.267007 | + | 0.963695i | \(0.586035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.9294 | + | 6.71794i | −0.494007 | + | 0.256679i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 11.9342i | − | 0.455320i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.14561 | −0.310323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5350 | − | 11.5350i | −0.438811 | − | 0.438811i | 0.452801 | − | 0.891612i | \(-0.350425\pi\) |
−0.891612 | + | 0.452801i | \(0.850425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.5000 | + | 11.5000i | 0.436850 | + | 0.436850i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.3894 | − | 45.5149i | 0.545823 | − | 1.72648i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0167075 | −0.000632842 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.2304 | − | 20.2304i | 0.765182 | − | 0.765182i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5440 | − | 16.5440i | −0.624859 | − | 0.624859i | 0.321911 | − | 0.946770i | \(-0.395675\pi\) |
−0.946770 | + | 0.321911i | \(0.895675\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.4955i | 0.810717i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.8280 | + | 7.84932i | 0.935078 | + | 0.295623i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.4202 | + | 29.4202i | −1.10646 | + | 1.10646i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.47518 | − | 8.47518i | 0.318292 | − | 0.318292i | −0.529819 | − | 0.848111i | \(-0.677740\pi\) |
0.848111 | + | 0.529819i | \(0.177740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.843960i | − | 0.0316510i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.7240 | 0.701221 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.43376 | − | 8.53325i | −0.165813 | − | 0.319125i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.1974 | + | 15.1974i | −0.567559 | + | 0.567559i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.5303 | −0.430008 | −0.215004 | − | 0.976613i | \(-0.568976\pi\) | ||||
−0.215004 | + | 0.976613i | \(0.568976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3287 | −0.570869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.8553 | − | 13.8553i | 0.515284 | − | 0.515284i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.7582 | − | 6.07348i | 1.29089 | − | 0.225564i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2855 | 1.19740 | 0.598702 | − | 0.800972i | \(-0.295684\pi\) | ||||
0.598702 | + | 0.800972i | \(0.295684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.47833 | + | 6.47833i | −0.239610 | + | 0.239610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6309 | − | 33.6309i | 1.24219 | − | 1.24219i | 0.283094 | − | 0.959092i | \(-0.408639\pi\) |
0.959092 | − | 0.283094i | \(-0.0913609\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.63546 | + | 17.8254i | −0.207867 | + | 0.657500i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 22.6078i | − | 0.832769i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6806 | + | 11.6806i | 0.429676 | + | 0.429676i | 0.888518 | − | 0.458842i | \(-0.151736\pi\) |
−0.458842 | + | 0.888518i | \(0.651736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.73628 | − | 1.73628i | 0.0637840 | − | 0.0637840i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.7641 | −0.431582 | −0.215791 | − | 0.976440i | \(-0.569233\pi\) | ||||
−0.215791 | + | 0.976440i | \(0.569233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.07418 | + | 12.8870i | −0.149266 | + | 0.472142i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.20069 | − | 5.20069i | −0.190283 | − | 0.190283i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1992 | − | 10.1992i | −0.372672 | − | 0.372672i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.89062 | 0.360914 | 0.180457 | − | 0.983583i | \(-0.442242\pi\) | ||||
0.180457 | + | 0.983583i | \(0.442242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.5492i | 0.493760i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.66012 | + | 16.6673i | 0.315174 | + | 0.606587i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.7078 | + | 19.7078i | 0.716291 | + | 0.716291i | 0.967844 | − | 0.251553i | \(-0.0809413\pi\) |
−0.251553 | + | 0.967844i | \(0.580941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 7.18436i | − | 0.260776i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.2102i | − | 1.74762i | −0.486270 | − | 0.873808i | \(-0.661643\pi\) | ||
0.486270 | − | 0.873808i | \(-0.338357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.09857 | − | 8.09857i | −0.293188 | − | 0.293188i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.74036 | − | 2.98261i | 0.207543 | − | 0.107837i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.61771i | 0.202844i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.7814 | −1.11000 | −0.555002 | − | 0.831849i | \(-0.687283\pi\) | ||||
−0.555002 | + | 0.831849i | \(0.687283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.38542 | − | 9.38542i | −0.338008 | − | 0.338008i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.7802 | + | 31.7802i | 1.14306 | + | 1.14306i | 0.987888 | + | 0.155167i | \(0.0495916\pi\) |
0.155167 | + | 0.987888i | \(0.450408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.0841 | + | 44.2471i | −1.11657 | + | 1.58940i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.5576 | −1.27562 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.00967532 | − | 0.00967532i | 0.000346654 | − | 0.000346654i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.38477 | + | 3.38477i | 0.121117 | + | 0.121117i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.05696i | 0.252195i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.42294 | − | 17.1532i | 0.193553 | − | 0.612223i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.8749 | − | 21.8749i | 0.779754 | − | 0.779754i | −0.200035 | − | 0.979789i | \(-0.564105\pi\) |
0.979789 | + | 0.200035i | \(0.0641054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.23522 | + | 9.23522i | −0.328782 | + | 0.328782i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.8876i | 1.13379i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6393 | −0.484346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5953 | − | 8.10312i | 0.553110 | − | 0.287388i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.0370 | + | 16.0370i | −0.568058 | + | 0.568058i | −0.931584 | − | 0.363526i | \(-0.881573\pi\) |
0.363526 | + | 0.931584i | \(0.381573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.6895 | 1.19185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.40896 | −0.191116 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4361 | + | 23.4361i | −0.827041 | + | 0.827041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4639 | − | 6.99568i | 0.474542 | − | 0.246565i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.5457 | −0.617639 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 37.0836i | − | 1.30379i | −0.758309 | − | 0.651895i | \(-0.773974\pi\) | ||
0.758309 | − | 0.651895i | \(-0.226026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8858 | − | 11.8858i | 0.417369 | − | 0.417369i | −0.466927 | − | 0.884296i | \(-0.654639\pi\) |
0.884296 | + | 0.466927i | \(0.154639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.49336 | + | 1.49336i | −0.0523744 | + | 0.0523744i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.37504 | + | 17.0017i | −0.188279 | + | 0.595543i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.50320i | − | 0.262504i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.87215 | + | 2.87215i | 0.100361 | + | 0.100361i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0568 | − | 18.0568i | 0.630186 | − | 0.630186i | −0.317928 | − | 0.948115i | \(-0.602987\pi\) |
0.948115 | + | 0.317928i | \(0.102987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.66750 | −0.336988 | −0.168494 | − | 0.985703i | \(-0.553890\pi\) | ||||
−0.168494 | + | 0.985703i | \(0.553890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.9775 | + | 11.9269i | 0.591080 | + | 0.415240i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.9204 | − | 15.9204i | −0.553607 | − | 0.553607i | 0.373873 | − | 0.927480i | \(-0.378030\pi\) |
−0.927480 | + | 0.373873i | \(0.878030\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.21199 | − | 6.21199i | −0.215751 | − | 0.215751i | 0.590954 | − | 0.806705i | \(-0.298751\pi\) |
−0.806705 | + | 0.590954i | \(0.798751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6840 | −0.648141 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.1875i | 0.838048i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.8097 | + | 6.65576i | −0.443299 | + | 0.230332i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.64726 | − | 7.64726i | −0.264328 | − | 0.264328i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 11.4138i | − | 0.394047i | −0.980399 | − | 0.197023i | \(-0.936873\pi\) | ||
0.980399 | − | 0.197023i | \(-0.0631275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8007i | 0.717266i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.67842 | − | 2.67842i | −0.0922497 | − | 0.0922497i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.2953 | + | 23.6636i | 0.422970 | + | 0.814052i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.3755i | 0.837553i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.47278 | −0.153506 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.1069 | + | 11.1069i | 0.380739 | + | 0.380739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1530 | + | 12.1530i | 0.416110 | + | 0.416110i | 0.883861 | − | 0.467751i | \(-0.154935\pi\) |
−0.467751 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.59701 | + | 5.05147i | −0.0546166 | + | 0.172757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.6445 | −0.807681 | −0.403840 | − | 0.914829i | \(-0.632325\pi\) | ||||
−0.403840 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9186 | + | 18.9186i | −0.645494 | + | 0.645494i | −0.951901 | − | 0.306407i | \(-0.900873\pi\) |
0.306407 | + | 0.951901i | \(0.400873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0160048 | + | 0.0160048i | 0.000545443 | + | 0.000545443i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.1371i | 1.09396i | 0.837146 | + | 0.546980i | \(0.184223\pi\) | ||||
−0.837146 | + | 0.546980i | \(0.815777\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.99361 | + | 22.1213i | −0.237790 | + | 0.752148i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.10266 | + | 6.10266i | −0.207257 | + | 0.207257i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.47637 | − | 2.47637i | 0.0840052 | − | 0.0840052i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.64633i | − | 0.191319i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.24154 | −0.0758645 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.82010 | + | 43.4305i | −0.196755 | + | 1.46822i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5598 | − | 33.5598i | 1.13323 | − | 1.13323i | 0.143597 | − | 0.989636i | \(-0.454133\pi\) |
0.989636 | − | 0.143597i | \(-0.0458670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0397 | 0.406091 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.11390 | 0.104910 | 0.0524550 | − | 0.998623i | \(-0.483295\pi\) | ||||
0.0524550 | + | 0.998623i | \(0.483295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.1043 | + | 36.1043i | −1.21501 | + | 1.21501i | −0.245647 | + | 0.969359i | \(0.579000\pi\) |
−0.969359 | + | 0.245647i | \(0.921000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.58841 | − | 10.7555i | −0.187852 | − | 0.361542i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.4317 | 1.29041 | 0.645206 | − | 0.764009i | \(-0.276772\pi\) | ||||
0.645206 | + | 0.764009i | \(0.276772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 63.0461i | − | 2.11450i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.93423 | + | 2.93423i | −0.0983004 | + | 0.0983004i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.5096 | + | 19.5096i | −0.652863 | + | 0.652863i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.14717 | + | 0.994971i | 0.105198 | + | 0.0332582i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.79430i | − | 0.0599100i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.9664 | − | 53.9664i | −1.79988 | − | 1.79988i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0784 | − | 16.0784i | 0.535649 | − | 0.535649i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.4117 | 0.413037 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.5366 | − | 36.4910i | 0.383488 | − | 1.21300i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.6279 | − | 37.6279i | −1.24941 | − | 1.24941i | −0.955979 | − | 0.293436i | \(-0.905201\pi\) |
−0.293436 | − | 0.955979i | \(-0.594799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.50655 | − | 7.50655i | −0.248977 | − | 0.248977i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8631 | −0.393042 | −0.196521 | − | 0.980500i | \(-0.562964\pi\) | ||||
−0.196521 | + | 0.980500i | \(0.562964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 30.5200i | − | 1.01007i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.1134 | − | 13.5682i | 0.863283 | − | 0.448550i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.1100 | + | 51.1100i | 1.68780 | + | 1.68780i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 46.4906i | − | 1.53358i | −0.641895 | − | 0.766792i | \(-0.721852\pi\) | ||
0.641895 | − | 0.766792i | \(-0.278148\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 10.0705i | − | 0.331835i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.845351 | + | 0.845351i | 0.0278251 | + | 0.0278251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.6855 | + | 7.80814i | −1.46925 | + | 0.256730i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 3.91110i | − | 0.128457i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.18351 | 0.104448 | 0.0522238 | − | 0.998635i | \(-0.483369\pi\) | ||||
0.0522238 | + | 0.998635i | \(0.483369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.0070 | − | 14.0070i | −0.459060 | − | 0.459060i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.0599 | − | 15.0599i | −0.493040 | − | 0.493040i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.5952 | + | 8.09187i | 0.837053 | + | 0.264632i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.2455 | −0.890072 | −0.445036 | − | 0.895513i | \(-0.646809\pi\) | ||||
−0.445036 | + | 0.895513i | \(0.646809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.30181 | + | 5.30181i | −0.173018 | + | 0.173018i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.15297 | − | 4.15297i | −0.135383 | − | 0.135383i | 0.636168 | − | 0.771551i | \(-0.280519\pi\) |
−0.771551 | + | 0.636168i | \(0.780519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.00999862i | − | 0.000325600i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.35610 | − | 2.64176i | −0.271824 | − | 0.0859365i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3519 | + | 18.3519i | −0.596358 | + | 0.596358i | −0.939341 | − | 0.342984i | \(-0.888562\pi\) |
0.342984 | + | 0.939341i | \(0.388562\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.85319 | + | 5.85319i | −0.190003 | + | 0.190003i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.32841i | − | 0.107931i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.0669 | 1.68661 | 0.843307 | − | 0.537433i | \(-0.180606\pi\) | ||||
0.843307 | + | 0.537433i | \(0.180606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.1195 | + | 21.8847i | −1.36296 | + | 0.708173i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.7067 | + | 20.7067i | −0.669354 | + | 0.669354i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.5385 | 0.824681 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 85.9611 | 2.77294 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.60233 | − | 2.60233i | 0.0838589 | − | 0.0838589i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.8752 | − | 38.2520i | −0.639806 | − | 1.23138i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.8074 | 1.05502 | 0.527508 | − | 0.849550i | \(-0.323127\pi\) | ||||
0.527508 | + | 0.849550i | \(0.323127\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.85441i | 0.220195i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.4682 | − | 25.4682i | 0.817314 | − | 0.817314i | −0.168404 | − | 0.985718i | \(-0.553861\pi\) |
0.985718 | + | 0.168404i | \(0.0538613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.1623 | + | 59.1623i | −1.89666 | + | 1.89666i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.24015 | + | 2.97875i | 0.135793 | + | 0.0953964i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.69863i | 0.0863367i | 0.999068 | + | 0.0431684i | \(0.0137452\pi\) | ||||
−0.999068 | + | 0.0431684i | \(0.986255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.8711 | − | 15.8711i | −0.507244 | − | 0.507244i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.06635 | − | 2.06635i | 0.0659734 | − | 0.0659734i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.2037 | −0.803875 | −0.401937 | − | 0.915667i | \(-0.631663\pi\) | ||||
−0.401937 | + | 0.915667i | \(0.631663\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.5945 | − | 9.04009i | −0.911097 | − | 0.288041i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.2726 | − | 32.2726i | −1.02725 | − | 1.02725i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.87696 | − | 3.87696i | −0.123280 | − | 0.123280i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.06410 | −0.287931 | −0.143965 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143965 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.0808i | − | 1.01805i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.92223 | − | 17.1718i | −0.282854 | − | 0.544382i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.5035 | + | 25.5035i | 0.807703 | + | 0.807703i | 0.984286 | − | 0.176583i | \(-0.0565044\pi\) |
−0.176583 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.07252i | − | 0.287042i |
(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 | 1920.2.bl.a.289.2 | 48 | ||
4.3 | odd | 2 | 1920.2.bl.b.289.23 | 48 | |||
5.4 | even | 2 | inner | 1920.2.bl.a.289.23 | 48 | ||
8.3 | odd | 2 | 960.2.bl.a.529.2 | 48 | |||
8.5 | even | 2 | 240.2.bl.a.109.3 | ✓ | 48 | ||
16.3 | odd | 4 | 960.2.bl.a.49.17 | 48 | |||
16.5 | even | 4 | inner | 1920.2.bl.a.1249.23 | 48 | ||
16.11 | odd | 4 | 1920.2.bl.b.1249.2 | 48 | |||
16.13 | even | 4 | 240.2.bl.a.229.22 | yes | 48 | ||
20.19 | odd | 2 | 1920.2.bl.b.289.2 | 48 | |||
24.5 | odd | 2 | 720.2.bm.h.109.22 | 48 | |||
40.19 | odd | 2 | 960.2.bl.a.529.17 | 48 | |||
40.29 | even | 2 | 240.2.bl.a.109.22 | yes | 48 | ||
48.29 | odd | 4 | 720.2.bm.h.469.3 | 48 | |||
80.19 | odd | 4 | 960.2.bl.a.49.2 | 48 | |||
80.29 | even | 4 | 240.2.bl.a.229.3 | yes | 48 | ||
80.59 | odd | 4 | 1920.2.bl.b.1249.23 | 48 | |||
80.69 | even | 4 | inner | 1920.2.bl.a.1249.2 | 48 | ||
120.29 | odd | 2 | 720.2.bm.h.109.3 | 48 | |||
240.29 | odd | 4 | 720.2.bm.h.469.22 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.bl.a.109.3 | ✓ | 48 | 8.5 | even | 2 | ||
240.2.bl.a.109.22 | yes | 48 | 40.29 | even | 2 | ||
240.2.bl.a.229.3 | yes | 48 | 80.29 | even | 4 | ||
240.2.bl.a.229.22 | yes | 48 | 16.13 | even | 4 | ||
720.2.bm.h.109.3 | 48 | 120.29 | odd | 2 | |||
720.2.bm.h.109.22 | 48 | 24.5 | odd | 2 | |||
720.2.bm.h.469.3 | 48 | 48.29 | odd | 4 | |||
720.2.bm.h.469.22 | 48 | 240.29 | odd | 4 | |||
960.2.bl.a.49.2 | 48 | 80.19 | odd | 4 | |||
960.2.bl.a.49.17 | 48 | 16.3 | odd | 4 | |||
960.2.bl.a.529.2 | 48 | 8.3 | odd | 2 | |||
960.2.bl.a.529.17 | 48 | 40.19 | odd | 2 | |||
1920.2.bl.a.289.2 | 48 | 1.1 | even | 1 | trivial | ||
1920.2.bl.a.289.23 | 48 | 5.4 | even | 2 | inner | ||
1920.2.bl.a.1249.2 | 48 | 80.69 | even | 4 | inner | ||
1920.2.bl.a.1249.23 | 48 | 16.5 | even | 4 | inner | ||
1920.2.bl.b.289.2 | 48 | 20.19 | odd | 2 | |||
1920.2.bl.b.289.23 | 48 | 4.3 | odd | 2 | |||
1920.2.bl.b.1249.2 | 48 | 16.11 | odd | 4 | |||
1920.2.bl.b.1249.23 | 48 | 80.59 | odd | 4 |