Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,1,Mod(298,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([0, 11, 10]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2925.298");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.er (of order \(20\), degree \(8\), 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: | \(1.45976516195\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\Q(\zeta_{80})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{32} - x^{24} + x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{40}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\) |
Embedding invariants
Embedding label | 1117.4 | ||
Root | \(0.0784591 - 0.996917i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.1117 |
Dual form | 2925.1.er.a.2053.4 |
$q$-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 \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35505 | + | 0.690434i | 1.35505 | + | 0.690434i | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.771685 | + | 1.06213i | 0.771685 | + | 1.06213i | ||||
\(5\) | 0.852640 | − | 0.522499i | 0.852640 | − | 0.522499i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0.0744338 | + | 0.469957i | 0.0744338 | + | 0.469957i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.51612 | − | 0.119322i | 1.51612 | − | 0.119322i | ||||
\(11\) | −0.444039 | + | 0.144277i | −0.444039 | + | 0.144277i | −0.522499 | − | 0.852640i | \(-0.675000\pi\) |
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.453990 | + | 0.891007i | 0.453990 | + | 0.891007i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.182086 | − | 0.560404i | 0.182086 | − | 0.560404i | ||||
\(17\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | 1.21293 | + | 0.502413i | 1.21293 | + | 0.502413i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.701311 | − | 0.111077i | −0.701311 | − | 0.111077i | ||||
\(23\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.453990 | − | 0.891007i | 0.453990 | − | 0.891007i | ||||
\(26\) | 1.52081i | 1.52081i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(32\) | 0.970111 | − | 0.970111i | 0.970111 | − | 0.970111i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.309017 | + | 0.361812i | 0.309017 | + | 0.361812i | ||||
\(41\) | −0.149238 | − | 0.0484904i | −0.149238 | − | 0.0484904i | 0.233445 | − | 0.972370i | \(-0.425000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(44\) | −0.495900 | − | 0.360293i | −0.495900 | − | 0.360293i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0245474 | − | 0.154986i | 0.0245474 | − | 0.154986i | −0.972370 | − | 0.233445i | \(-0.925000\pi\) |
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 1.00000i | ||||||||
\(50\) | 1.23036 | − | 0.893911i | 1.23036 | − | 0.893911i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.596030 | + | 1.16977i | −0.596030 | + | 1.16977i | ||||
\(53\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.303221 | + | 0.355026i | −0.303221 | + | 0.355026i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.322922 | + | 0.993851i | −0.322922 | + | 0.993851i | 0.649448 | + | 0.760406i | \(0.275000\pi\) |
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.42395 | − | 0.462668i | 1.42395 | − | 0.462668i | ||||
\(65\) | 0.852640 | + | 0.522499i | 0.852640 | + | 0.522499i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.14309 | − | 1.57333i | −1.14309 | − | 1.57333i | −0.760406 | − | 0.649448i | \(-0.775000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.831254 | + | 1.14412i | 0.831254 | + | 1.14412i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(80\) | −0.137556 | − | 0.572963i | −0.137556 | − | 0.572963i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.168746 | − | 0.168746i | −0.168746 | − | 0.168746i | ||||
\(83\) | −0.203192 | − | 1.28290i | −0.203192 | − | 1.28290i | −0.852640 | − | 0.522499i | \(-0.825000\pi\) |
0.649448 | − | 0.760406i | \(-0.275000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.57746 | + | 0.837469i | −2.57746 | + | 0.837469i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.100856 | − | 0.197940i | −0.100856 | − | 0.197940i | ||||
\(89\) | −0.236511 | − | 0.727907i | −0.236511 | − | 0.727907i | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) |
0.760406 | − | 0.649448i | \(-0.225000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.140271 | − | 0.193066i | 0.140271 | − | 0.193066i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(98\) | −0.690434 | + | 1.35505i | −0.690434 | + | 1.35505i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.29671 | − | 0.205378i | 1.29671 | − | 0.205378i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.221232 | + | 1.39680i | −0.221232 | + | 1.39680i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(104\) | −0.384942 | + | 0.279677i | −0.384942 | + | 0.279677i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(110\) | −0.656003 | + | 0.271726i | −0.656003 | + | 0.271726i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.12377 | + | 1.12377i | −1.12377 | + | 1.12377i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.632662 | + | 0.459656i | −0.632662 | + | 0.459656i | ||||
\(122\) | 0.469957 | − | 2.96719i | 0.469957 | − | 2.96719i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.0784591 | − | 0.996917i | −0.0784591 | − | 0.996917i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.280582 | + | 0.550672i | −0.280582 | + | 0.550672i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | 0.893911 | + | 0.141582i | 0.893911 | + | 0.141582i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.794622 | + | 1.29671i | 0.794622 | + | 1.29671i | ||||
\(131\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.347469 | + | 0.681947i | 0.347469 | + | 0.681947i | 0.996917 | − | 0.0784591i | \(-0.0250000\pi\) |
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.11803 | + | 0.363271i | −1.11803 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.462668 | − | 2.92117i | −0.462668 | − | 2.92117i | ||||
\(143\) | −0.330142 | − | 0.330142i | −0.330142 | − | 0.330142i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.84776 | −1.84776 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(158\) | 0.336452 | + | 2.12427i | 0.336452 | + | 2.12427i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.320274 | − | 1.33404i | 0.320274 | − | 1.33404i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(164\) | −0.0636615 | − | 0.195930i | −0.0636615 | − | 0.195930i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | ||||
\(167\) | −1.68429 | + | 0.266765i | −1.68429 | + | 0.266765i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.760406 | + | 0.649448i | \(0.775000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.31075 | − | 0.365986i | −2.31075 | − | 0.365986i | ||||
\(173\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.275113i | 0.275113i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.182086 | − | 1.14965i | 0.182086 | − | 1.14965i | ||||
\(179\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.951057 | + | 0.690983i | 0.951057 | + | 0.690983i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.183559 | − | 0.0935280i | 0.183559 | − | 0.0935280i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.06213 | + | 0.771685i | −1.06213 | + | 0.771685i | ||||
\(197\) | 0.289053 | − | 1.82501i | 0.289053 | − | 1.82501i | −0.233445 | − | 0.972370i | \(-0.575000\pi\) |
0.522499 | − | 0.852640i | \(-0.325000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.907981i | 0.907981i | 0.891007 | + | 0.453990i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(200\) | 0.452527 | + | 0.147035i | 0.452527 | + | 0.147035i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.152583 | + | 0.0366318i | −0.152583 | + | 0.0366318i | ||||
\(206\) | −1.26418 | + | 1.74000i | −1.26418 | + | 1.74000i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.581990 | − | 0.0921781i | 0.581990 | − | 0.0921781i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.416003 | + | 1.73278i | −0.416003 | + | 1.73278i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.611077 | − | 0.0480928i | −0.611077 | − | 0.0480928i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.681947 | + | 0.347469i | 0.681947 | + | 0.347469i | 0.760406 | − | 0.649448i | \(-0.225000\pi\) |
−0.0784591 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0600500 | − | 0.144974i | −0.0600500 | − | 0.144974i | ||||
\(236\) | −1.30480 | + | 0.423954i | −1.30480 | + | 0.423954i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.570989 | − | 1.75732i | −0.570989 | − | 1.75732i | −0.649448 | − | 0.760406i | \(-0.725000\pi\) |
0.0784591 | − | 0.996917i | \(-0.475000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(242\) | −1.17465 | + | 0.186047i | −1.17465 | + | 0.186047i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.52437 | − | 2.09811i | 1.52437 | − | 2.09811i | ||||
\(245\) | 0.522499 | + | 0.852640i | 0.522499 | + | 0.852640i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.581990 | − | 1.40505i | 0.581990 | − | 1.40505i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.760406 | + | 0.552467i | −0.760406 | + | 0.552467i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0977364 | − | 0.0710097i | −0.0977364 | − | 0.0710097i | ||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.103007 | + | 1.30882i | 0.103007 | + | 1.30882i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.16398i | 1.16398i | ||||||||
\(275\) | −0.0730378 | + | 0.461143i | −0.0730378 | + | 0.461143i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.412215 | − | 0.809017i | 0.412215 | − | 0.809017i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
1.00000 | \(0\) | |||||||||
\(278\) | −1.76581 | − | 0.279677i | −1.76581 | − | 0.279677i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.00234 | − | 1.37960i | 1.00234 | − | 1.37960i | 0.0784591 | − | 0.996917i | \(-0.475000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.59811 | − | 0.253116i | 1.59811 | − | 0.253116i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(284\) | 0.788979 | − | 2.42823i | 0.788979 | − | 2.42823i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.219418 | − | 0.675301i | −0.219418 | − | 0.675301i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.40985 | + | 1.40985i | 1.40985 | + | 1.40985i | 0.760406 | + | 0.649448i | \(0.225000\pi\) |
0.649448 | + | 0.760406i | \(0.275000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.243950 | + | 1.01612i | 0.243950 | + | 1.01612i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.50381 | − | 1.27576i | −2.50381 | − | 1.27576i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.50209 | − | 1.28290i | −1.50209 | − | 1.28290i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.280582 | + | 0.550672i | 0.280582 | + | 0.550672i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 0.147035 | + | 0.452527i | 0.147035 | + | 0.452527i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.573745 | + | 1.76580i | −0.573745 | + | 1.76580i | ||||
\(317\) | −1.28290 | + | 0.203192i | −1.28290 | + | 0.203192i | −0.760406 | − | 0.649448i | \(-0.775000\pi\) |
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.972370 | − | 1.13850i | 0.972370 | − | 1.13850i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.0116800 | − | 0.0737448i | 0.0116800 | − | 0.0737448i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(332\) | 1.20582 | − | 1.20582i | 1.20582 | − | 1.20582i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.46648 | − | 0.801408i | −2.46648 | − | 0.801408i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.69480 | − | 0.863541i | 1.69480 | − | 0.863541i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(338\) | −1.35505 | + | 0.690434i | −1.35505 | + | 0.690434i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.685972 | − | 0.498388i | −0.685972 | − | 0.498388i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.290803 | + | 0.570732i | −0.290803 | + | 0.570732i | ||||
\(353\) | 1.96929 | + | 0.311904i | 1.96929 | + | 0.311904i | 0.996917 | + | 0.0784591i | \(0.0250000\pi\) |
0.972370 | + | 0.233445i | \(0.0750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.79671 | − | 0.744220i | −1.79671 | − | 0.744220i | ||||
\(356\) | 0.590622 | − | 0.812922i | 0.590622 | − | 0.812922i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.616129 | − | 1.89625i | 0.616129 | − | 1.89625i | 0.233445 | − | 0.972370i | \(-0.425000\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(362\) | 0.811654 | + | 1.59296i | 0.811654 | + | 1.59296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.142040 | + | 0.896802i | 0.142040 | + | 0.896802i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.04744 | + | 0.533698i | 1.04744 | + | 0.533698i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0746640 | 0.0746640 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.289053 | + | 1.82501i | 0.289053 | + | 1.82501i | 0.522499 | + | 0.852640i | \(0.325000\pi\) |
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.469957 | + | 0.0744338i | −0.469957 | + | 0.0744338i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.65173 | − | 2.27341i | 1.65173 | − | 2.27341i | ||||
\(395\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(398\) | −0.626901 | + | 1.23036i | −0.626901 | + | 1.23036i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.416659 | − | 0.416659i | −0.416659 | − | 0.416659i | ||||
\(401\) | 1.94474i | 1.94474i | 0.233445 | + | 0.972370i | \(0.425000\pi\) | ||||
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | −0.232049 | − | 0.0557101i | −0.232049 | − | 0.0557101i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.65431 | + | 0.842914i | −1.65431 | + | 0.842914i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.843566 | − | 0.987688i | −0.843566 | − | 0.987688i | ||||
\(416\) | 1.30480 | + | 0.423954i | 1.30480 | + | 0.423954i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 0.423954 | − | 2.67674i | 0.423954 | − | 2.67674i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.76007 | + | 2.06078i | −1.76007 | + | 2.06078i | ||||
\(431\) | 0.893911 | − | 1.23036i | 0.893911 | − | 1.23036i | −0.0784591 | − | 0.996917i | \(-0.525000\pi\) |
0.972370 | − | 0.233445i | \(-0.0750000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.16110 | + | 0.183900i | −1.16110 | + | 0.183900i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.80902 | + | 0.587785i | −1.80902 | + | 0.587785i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(440\) | −0.189417 | − | 0.116075i | −0.189417 | − | 0.116075i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.581990 | − | 0.497066i | −0.581990 | − | 0.497066i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.04500 | −1.04500 | −0.522499 | − | 0.852640i | \(-0.675000\pi\) | ||||
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0732636 | 0.0732636 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.684170 | + | 0.941679i | 0.684170 | + | 0.941679i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.62182 | − | 0.526961i | 1.62182 | − | 0.526961i | 0.649448 | − | 0.760406i | \(-0.275000\pi\) |
0.972370 | + | 0.233445i | \(0.0750000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.0187237 | − | 0.237907i | 0.0187237 | − | 0.237907i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.491103 | − | 0.0777831i | −0.491103 | − | 0.0777831i | ||||
\(473\) | 0.377723 | − | 0.741322i | 0.377723 | − | 0.741322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.439596 | − | 2.77550i | 0.439596 | − | 2.77550i | ||||
\(479\) | 1.37960 | − | 1.00234i | 1.37960 | − | 1.00234i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.976431 | − | 0.317262i | −0.976431 | − | 0.317262i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(488\) | 0.837469 | − | 0.426712i | 0.837469 | − | 0.426712i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.119322 | + | 1.51612i | 0.119322 | + | 1.51612i | ||||
\(491\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0.998313 | − | 0.852640i | 0.998313 | − | 0.852640i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.801408 | + | 0.126931i | −0.801408 | + | 0.126931i | ||||
\(509\) | −0.469957 | + | 1.44638i | −0.469957 | + | 1.44638i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.494296 | − | 0.970111i | −0.494296 | − | 0.970111i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.541196 | + | 1.30656i | 0.541196 | + | 1.30656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0114610 | + | 0.0723617i | 0.0114610 | + | 0.0723617i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.182086 | + | 0.439596i | −0.182086 | + | 0.439596i | ||||
\(521\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.76007 | − | 0.896802i | −1.76007 | − | 0.896802i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.809017 | − | 0.587785i | \(-0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0245474 | − | 0.154986i | −0.0245474 | − | 0.154986i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.144277 | − | 0.444039i | −0.144277 | − | 0.444039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.309017 | − | 0.0489435i | −0.309017 | − | 0.0489435i | − | 1.00000i | \(-0.5\pi\) | |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(548\) | −0.456182 | + | 0.895307i | −0.456182 | + | 0.895307i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.417359 | + | 0.574445i | −0.417359 | + | 0.574445i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.11715 | − | 0.811654i | 1.11715 | − | 0.811654i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.24861 | − | 0.907170i | −1.24861 | − | 0.907170i | ||||
\(557\) | −1.20582 | + | 1.20582i | −1.20582 | + | 1.20582i | −0.233445 | + | 0.972370i | \(0.575000\pi\) |
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.69480 | − | 0.550672i | −1.69480 | − | 0.550672i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.31075 | − | 1.17738i | 2.31075 | − | 1.17738i | ||||
\(563\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.34029 | + | 0.760406i | 2.34029 | + | 0.760406i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.654311 | − | 0.654311i | 0.654311 | − | 0.654311i | ||||
\(569\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(572\) | 0.0958891 | − | 0.605420i | 0.0958891 | − | 0.605420i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(578\) | 1.50209 | + | 0.237907i | 1.50209 | + | 0.237907i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.937016 | + | 2.88384i | 0.937016 | + | 2.88384i | ||||
\(587\) | 0.774181 | + | 1.51942i | 0.774181 | + | 1.51942i | 0.852640 | + | 0.522499i | \(0.175000\pi\) |
−0.0784591 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.371002 | + | 1.54533i | −0.371002 | + | 1.54533i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.42589 | − | 1.96257i | −1.42589 | − | 1.96257i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.299263 | + | 0.722486i | −0.299263 | + | 0.722486i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.39680 | + | 1.39680i | 1.39680 | + | 1.39680i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.14965 | − | 2.77550i | −1.14965 | − | 2.77550i | ||||
\(611\) | 0.149238 | − | 0.0484904i | 0.149238 | − | 0.0484904i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.154986 | + | 0.0245474i | −0.154986 | + | 0.0245474i | −0.233445 | − | 0.972370i | \(-0.575000\pi\) |
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(626\) | 0.939913i | 0.939913i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0642564 | + | 0.405699i | −0.0642564 | + | 0.405699i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(632\) | −0.475815 | + | 0.475815i | −0.475815 | + | 0.475815i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.87869 | − | 0.610425i | −1.87869 | − | 0.610425i | ||||
\(635\) | 0.0484904 | + | 0.616129i | 0.0484904 | + | 0.616129i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.891007 | + | 0.453990i | −0.891007 | + | 0.453990i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.836160 | − | 0.346349i | 0.836160 | − | 0.346349i | ||||
\(641\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.487899i | − | 0.487899i | ||||||
\(650\) | 1.35505 | + | 0.690434i | 1.35505 | + | 0.690434i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0543485 | + | 0.0748042i | −0.0543485 | + | 0.0748042i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.58308 | − | 1.58308i | −1.58308 | − | 1.58308i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.542106 | + | 0.746144i | 0.542106 | + | 0.746144i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26007 | + | 0.642040i | 1.26007 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(674\) | 2.89276 | 2.89276 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.31287 | −1.31287 | ||||||||
\(677\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.0730378 | − | 0.461143i | −0.0730378 | − | 0.461143i | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.652583 | + | 0.399903i | 0.652583 | + | 0.399903i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.476708 | + | 0.935593i | 0.476708 | + | 0.935593i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.763472 | + | 0.893911i | −0.763472 | + | 0.893911i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.565536 | + | 0.410886i | −0.565536 | + | 0.410886i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.45314 | + | 1.78231i | 2.45314 | + | 1.78231i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(710\) | −1.92080 | − | 2.24896i | −1.92080 | − | 2.24896i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.324480 | − | 0.165331i | 0.324480 | − | 0.165331i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.453990 | − | 0.108993i | −0.453990 | − | 0.108993i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.14412 | − | 2.14412i | 2.14412 | − | 2.14412i | ||||
\(719\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.237907 | − | 1.50209i | 0.237907 | − | 1.50209i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.54337i | 1.54337i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.734572 | − | 1.44168i | 0.734572 | − | 1.44168i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(734\) | −0.426712 | + | 1.31328i | −0.426712 | + | 1.31328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.37514 | + | 1.37514i | 1.37514 | + | 1.37514i | 0.852640 | + | 0.522499i | \(0.175000\pi\) |
0.522499 | + | 0.852640i | \(0.325000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.57547 | + | 0.965451i | −1.57547 | + | 0.965451i | ||||
\(746\) | 1.05086 | + | 1.44638i | 1.05086 | + | 1.44638i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.17557 | 1.17557 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(752\) | −0.0823852 | − | 0.0419774i | −0.0823852 | − | 0.0419774i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.34500 | + | 1.34500i | 1.34500 | + | 1.34500i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.89625 | + | 0.616129i | −1.89625 | + | 0.616129i | −0.923880 | + | 0.382683i | \(0.875000\pi\) |
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.868367 | + | 2.67256i | −0.868367 | + | 2.67256i | ||||
\(767\) | −1.03213 | + | 0.163474i | −1.03213 | + | 0.163474i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.474419 | − | 0.931099i | 0.474419 | − | 0.931099i | −0.522499 | − | 0.852640i | \(-0.675000\pi\) |
0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.560404 | + | 0.182086i | 0.560404 | + | 0.182086i | ||||
\(785\) | 0.304224 | + | 0.0730378i | 0.304224 | + | 0.0730378i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(788\) | 2.16146 | − | 1.10132i | 2.16146 | − | 1.10132i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.39680 | + | 1.63545i | 1.39680 | + | 1.63545i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.964397 | + | 0.700675i | −0.964397 | + | 0.700675i | ||||
\(797\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.423954 | − | 1.30480i | −0.423954 | − | 1.30480i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.34271 | + | 2.63523i | −1.34271 | + | 2.63523i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.156654 | − | 0.133795i | −0.156654 | − | 0.133795i | ||||
\(821\) | −0.893911 | − | 1.23036i | −0.893911 | − | 1.23036i | −0.972370 | − | 0.233445i | \(-0.925000\pi\) |
0.0784591 | − | 0.996917i | \(-0.475000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.76007 | + | 0.896802i | 1.76007 | + | 0.896802i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(824\) | −0.672904 | −0.672904 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.73278 | + | 0.882893i | 1.73278 | + | 0.882893i | 0.972370 | + | 0.233445i | \(0.0750000\pi\) |
0.760406 | + | 0.649448i | \(0.225000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.04744 | − | 1.44168i | −1.04744 | − | 1.44168i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(830\) | −0.461143 | − | 1.92080i | −0.461143 | − | 1.92080i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.05870 | + | 1.05870i | 1.05870 | + | 1.05870i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.29671 | + | 1.10749i | −1.29671 | + | 1.10749i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.526961 | + | 1.62182i | 0.526961 | + | 1.62182i | 0.760406 | + | 0.649448i | \(0.225000\pi\) |
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.37515 | − | 1.89274i | 1.37515 | − | 1.89274i | ||||
\(845\) | −0.0784591 | + | 0.996917i | −0.0784591 | + | 0.996917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.863541 | − | 0.280582i | −0.863541 | − | 0.280582i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(860\) | −2.16146 | + | 0.895307i | −2.16146 | + | 0.895307i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.06078 | − | 1.05002i | 2.06078 | − | 1.05002i | ||||
\(863\) | −1.77652 | + | 0.905182i | −1.77652 | + | 0.905182i | −0.852640 | + | 0.522499i | \(0.825000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.70032 | − | 0.552467i | −1.70032 | − | 0.552467i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.534180 | − | 0.388105i | −0.534180 | − | 0.388105i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(878\) | −2.85714 | − | 0.452527i | −2.85714 | − | 0.452527i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.143746 | + | 0.234572i | 0.143746 | + | 0.234572i | ||||
\(881\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.610425 | + | 0.0966818i | −0.610425 | + | 0.0966818i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.445436 | − | 1.07538i | −0.445436 | − | 1.07538i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.41603 | − | 0.721502i | −1.41603 | − | 0.721502i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.0992762 | + | 0.0505837i | 0.0992762 | + | 0.0505837i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17195 | + | 0.0922342i | 1.17195 | + | 0.0922342i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.437016 | − | 0.437016i | −0.437016 | − | 0.437016i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(908\) | 0.157189 | + | 0.992455i | 0.157189 | + | 0.992455i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.275319 | + | 0.540344i | 0.275319 | + | 0.540344i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.16110 | − | 1.59811i | 1.16110 | − | 1.59811i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.56148 | + | 0.405699i | 2.56148 | + | 0.405699i | ||||
\(923\) | 0.882893 | − | 1.73278i | 0.882893 | − | 1.73278i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.61305 | + | 1.17195i | −1.61305 | + | 1.17195i | −0.760406 | + | 0.649448i | \(0.775000\pi\) |
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.44168 | − | 0.734572i | 1.44168 | − | 0.734572i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.107642 | − | 0.175655i | 0.107642 | − | 0.175655i | ||||
\(941\) | 1.84956 | + | 0.600958i | 1.84956 | + | 0.600958i | 0.996917 | + | 0.0784591i | \(0.0250000\pi\) |
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.498159 | + | 0.361934i | 0.498159 | + | 0.361934i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.02367 | − | 0.743739i | 1.02367 | − | 0.743739i | ||||
\(947\) | −0.163474 | + | 1.03213i | −0.163474 | + | 1.03213i | 0.760406 | + | 0.649448i | \(0.225000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.42589 | − | 1.96257i | 1.42589 | − | 1.96257i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.56148 | − | 0.405699i | 2.56148 | − | 0.405699i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(968\) | −0.263110 | − | 0.263110i | −0.263110 | − | 0.263110i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.16398 | −1.16398 | ||||||||
\(977\) | −0.931099 | − | 0.474419i | −0.931099 | − | 0.474419i | −0.0784591 | − | 0.996917i | \(-0.525000\pi\) |
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.210041 | + | 0.289096i | 0.210041 | + | 0.289096i | ||||
\(980\) | −0.502413 | + | 1.21293i | −0.502413 | + | 1.21293i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.311904 | − | 1.96929i | −0.311904 | − | 1.96929i | −0.233445 | − | 0.972370i | \(-0.575000\pi\) |
−0.0784591 | − | 0.996917i | \(-0.525000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.474419 | + | 0.774181i | 0.474419 | + | 0.774181i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.76007 | + | 0.278768i | 1.76007 | + | 0.278768i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(998\) | 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 | 2925.1.er.a.1117.4 | yes | 32 | |
3.2 | odd | 2 | inner | 2925.1.er.a.1117.1 | ✓ | 32 | |
13.12 | even | 2 | inner | 2925.1.er.a.1117.1 | ✓ | 32 | |
25.3 | odd | 20 | inner | 2925.1.er.a.2053.1 | yes | 32 | |
39.38 | odd | 2 | CM | 2925.1.er.a.1117.4 | yes | 32 | |
75.53 | even | 20 | inner | 2925.1.er.a.2053.4 | yes | 32 | |
325.103 | odd | 20 | inner | 2925.1.er.a.2053.4 | yes | 32 | |
975.428 | even | 20 | inner | 2925.1.er.a.2053.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2925.1.er.a.1117.1 | ✓ | 32 | 3.2 | odd | 2 | inner | |
2925.1.er.a.1117.1 | ✓ | 32 | 13.12 | even | 2 | inner | |
2925.1.er.a.1117.4 | yes | 32 | 1.1 | even | 1 | trivial | |
2925.1.er.a.1117.4 | yes | 32 | 39.38 | odd | 2 | CM | |
2925.1.er.a.2053.1 | yes | 32 | 25.3 | odd | 20 | inner | |
2925.1.er.a.2053.1 | yes | 32 | 975.428 | even | 20 | inner | |
2925.1.er.a.2053.4 | yes | 32 | 75.53 | even | 20 | inner | |
2925.1.er.a.2053.4 | yes | 32 | 325.103 | odd | 20 | inner |