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 | 2287.4 | ||
Root | \(-0.852640 + 0.522499i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2287 |
Dual form | 2925.1.er.a.298.4 |
$q$-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 \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92080 | − | 0.304224i | 1.92080 | − | 0.304224i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.996917 | + | 0.0784591i | \(0.0250000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.64585 | − | 0.859689i | 2.64585 | − | 0.859689i | ||||
\(5\) | −0.649448 | + | 0.760406i | −0.649448 | + | 0.760406i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 3.08783 | − | 1.57333i | 3.08783 | − | 1.57333i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.01612 | + | 1.65816i | −1.01612 | + | 1.65816i | ||||
\(11\) | −0.0922342 | + | 0.126949i | −0.0922342 | + | 0.126949i | −0.852640 | − | 0.522499i | \(-0.825000\pi\) |
0.760406 | + | 0.649448i | \(0.225000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.156434 | + | 0.987688i | −0.156434 | + | 0.987688i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.20175 | − | 2.32621i | 3.20175 | − | 2.32621i | ||||
\(17\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −1.06463 | + | 2.57024i | −1.06463 | + | 2.57024i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.138542 | + | 0.271904i | −0.138542 | + | 0.271904i | ||||
\(23\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.156434 | − | 0.987688i | −0.156434 | − | 0.987688i | ||||
\(26\) | 1.94474i | 1.94474i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(32\) | 2.99171 | − | 2.99171i | 2.99171 | − | 2.99171i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.809017 | + | 3.36980i | −0.809017 | + | 3.36980i | ||||
\(41\) | −1.00234 | − | 1.37960i | −1.00234 | − | 1.37960i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.0784591 | − | 0.996917i | \(-0.525000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(44\) | −0.134901 | + | 0.415182i | −0.134901 | + | 0.415182i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.51942 | − | 0.774181i | −1.51942 | − | 0.774181i | −0.522499 | − | 0.852640i | \(-0.675000\pi\) |
−0.996917 | + | 0.0784591i | \(0.975000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 1.00000i | ||||||||
\(50\) | −0.600958 | − | 1.84956i | −0.600958 | − | 1.84956i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.435203 | + | 2.74776i | 0.435203 | + | 2.74776i | ||||
\(53\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0366318 | − | 0.152583i | −0.0366318 | − | 0.152583i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.23036 | + | 0.893911i | −1.23036 | + | 0.893911i | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) |
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.51011 | − | 3.45487i | 2.51011 | − | 3.45487i | ||||
\(65\) | −0.649448 | − | 0.760406i | −0.649448 | − | 0.760406i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.89625 | + | 0.616129i | −1.89625 | + | 0.616129i | −0.923880 | + | 0.382683i | \(0.875000\pi\) |
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.34500 | + | 0.437016i | −1.34500 | + | 0.437016i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(80\) | −0.310508 | + | 3.94538i | −0.310508 | + | 3.94538i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.34500 | − | 2.34500i | −2.34500 | − | 2.34500i | ||||
\(83\) | 0.416003 | − | 0.211964i | 0.416003 | − | 0.211964i | −0.233445 | − | 0.972370i | \(-0.575000\pi\) |
0.649448 | + | 0.760406i | \(0.275000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.25803 | − | 3.10791i | 2.25803 | − | 3.10791i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0850703 | + | 0.537113i | −0.0850703 | + | 0.537113i | ||||
\(89\) | 1.49487 | + | 1.08609i | 1.49487 | + | 1.08609i | 0.972370 | + | 0.233445i | \(0.0750000\pi\) |
0.522499 | + | 0.852640i | \(0.325000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.15401 | − | 1.02480i | −3.15401 | − | 1.02480i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(98\) | 0.304224 | + | 1.92080i | 0.304224 | + | 1.92080i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.26301 | − | 2.47879i | −1.26301 | − | 2.47879i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.26007 | + | 0.642040i | 1.26007 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 1.07091 | + | 3.29594i | 1.07091 | + | 3.29594i | ||||
\(105\) | 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 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(110\) | −0.116782 | − | 0.281936i | −0.116782 | − | 0.281936i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.09133 | + | 2.09133i | −2.09133 | + | 2.09133i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.301408 | + | 0.927638i | 0.301408 | + | 0.927638i | ||||
\(122\) | −1.57333 | − | 0.801650i | −1.57333 | − | 0.801650i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.852640 | + | 0.522499i | 0.852640 | + | 0.522499i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.253116 | − | 1.59811i | −0.253116 | − | 1.59811i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(128\) | 1.84956 | − | 3.62996i | 1.84956 | − | 3.62996i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.47879 | − | 1.26301i | −1.47879 | − | 1.26301i | ||||
\(131\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.289053 | + | 1.82501i | −0.289053 | + | 1.82501i | 0.233445 | + | 0.972370i | \(0.425000\pi\) |
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.11803 | − | 1.53884i | 1.11803 | − | 1.53884i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.45487 | + | 1.76034i | −3.45487 | + | 1.76034i | ||||
\(143\) | −0.110958 | − | 0.110958i | −0.110958 | − | 0.110958i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.765367 | 0.765367 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(158\) | −2.45052 | + | 1.24860i | −2.45052 | + | 1.24860i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.331954 | + | 4.21788i | 0.331954 | + | 4.21788i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(164\) | −3.83807 | − | 2.78852i | −3.83807 | − | 2.78852i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | ||||
\(167\) | −0.589686 | − | 1.15732i | −0.589686 | − | 1.15732i | −0.972370 | − | 0.233445i | \(-0.925000\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.49492 | − | 4.89655i | 2.49492 | − | 4.89655i | ||||
\(173\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.621017i | 0.621017i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.20175 | + | 1.63137i | 3.20175 | + | 1.63137i | ||||
\(179\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.68570 | − | 0.742143i | −4.68570 | − | 0.742143i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(192\) | 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 | ||||||||
\(196\) | 0.859689 | + | 2.64585i | 0.859689 | + | 2.64585i | ||||
\(197\) | −0.681947 | − | 0.347469i | −0.681947 | − | 0.347469i | 0.0784591 | − | 0.996917i | \(-0.475000\pi\) |
−0.760406 | + | 0.649448i | \(0.775000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.312869i | − | 0.312869i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(200\) | −2.03700 | − | 2.80369i | −2.03700 | − | 2.80369i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.70002 | + | 0.133795i | 1.70002 | + | 0.133795i | ||||
\(206\) | 2.61567 | + | 0.849882i | 2.61567 | + | 0.849882i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.79671 | + | 3.52623i | 1.79671 | + | 3.52623i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.59811 | + | 1.16110i | 1.59811 | + | 1.16110i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.154986 | + | 1.96929i | 0.154986 | + | 1.96929i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.228096 | − | 0.372219i | −0.228096 | − | 0.372219i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.82501 | − | 0.289053i | 1.82501 | − | 0.289053i | 0.852640 | − | 0.522499i | \(-0.175000\pi\) |
0.972370 | + | 0.233445i | \(0.0750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.57547 | − | 0.652583i | 1.57547 | − | 0.652583i | ||||
\(236\) | −2.48687 | + | 3.42289i | −2.48687 | + | 3.42289i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.619195 | − | 0.449871i | −0.619195 | − | 0.449871i | 0.233445 | − | 0.972370i | \(-0.425000\pi\) |
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(242\) | 0.861154 | + | 1.69011i | 0.861154 | + | 1.69011i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.40238 | − | 0.780582i | −2.40238 | − | 0.780582i | ||||
\(245\) | −0.760406 | − | 0.649448i | −0.760406 | − | 0.649448i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.79671 | + | 0.744220i | 1.79671 | + | 0.744220i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.972370 | − | 2.99265i | −0.972370 | − | 2.99265i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.12866 | − | 3.47366i | 1.12866 | − | 3.47366i | ||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.37206 | − | 1.45360i | −2.37206 | − | 1.45360i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.59341i | 3.59341i | ||||||||
\(275\) | 0.139815 | + | 0.0712394i | 0.139815 | + | 0.0712394i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0489435 | + | 0.309017i | 0.0489435 | + | 0.309017i | 1.00000 | \(0\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(278\) | 1.67936 | − | 3.29594i | 1.67936 | − | 3.29594i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.23532 | − | 0.401381i | −1.23532 | − | 0.401381i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.852640 | + | 0.522499i | \(0.825000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.280582 | + | 0.550672i | 0.280582 | + | 0.550672i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | −4.48752 | + | 3.26037i | −4.48752 | + | 3.26037i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.246884 | − | 0.179372i | −0.246884 | − | 0.179372i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.738925 | + | 0.738925i | 0.738925 | + | 0.738925i | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) |
−0.233445 | + | 0.972370i | \(0.575000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.119322 | − | 1.51612i | 0.119322 | − | 1.51612i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.47011 | − | 0.232843i | 1.47011 | − | 0.232843i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.882893 | − | 0.211964i | 0.882893 | − | 0.211964i | ||||
\(306\) | 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 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.253116 | − | 1.59811i | 0.253116 | − | 1.59811i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(314\) | −2.80369 | − | 2.03700i | −2.80369 | − | 2.03700i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.18296 | + | 2.31256i | −3.18296 | + | 2.31256i | ||||
\(317\) | −0.211964 | − | 0.416003i | −0.211964 | − | 0.416003i | 0.760406 | − | 0.649448i | \(-0.225000\pi\) |
−0.972370 | + | 0.233445i | \(0.925000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.996917 | + | 4.15246i | 0.996917 | + | 4.15246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.26561 | − | 2.68296i | −5.26561 | − | 2.68296i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(332\) | 0.918458 | − | 0.918458i | 0.918458 | − | 0.918458i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.48475 | − | 2.04359i | −1.48475 | − | 2.04359i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.16110 | − | 0.183900i | −1.16110 | − | 0.183900i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | −1.92080 | − | 0.304224i | −1.92080 | − | 0.304224i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.11546 | − | 6.51071i | 2.11546 | − | 6.51071i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.103858 | + | 0.655734i | 0.103858 | + | 0.655734i | ||||
\(353\) | 0.474419 | − | 0.931099i | 0.474419 | − | 0.931099i | −0.522499 | − | 0.852640i | \(-0.675000\pi\) |
0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.763007 | − | 1.84206i | 0.763007 | − | 1.84206i | ||||
\(356\) | 4.88890 | + | 1.58850i | 4.88890 | + | 1.58850i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.845420 | − | 0.614234i | 0.845420 | − | 0.614234i | −0.0784591 | − | 0.996917i | \(-0.525000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(362\) | −0.578669 | + | 3.65357i | −0.578669 | + | 3.65357i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.278768 | + | 0.142040i | −0.278768 | + | 0.142040i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.87869 | − | 0.297556i | 1.87869 | − | 0.297556i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.90974 | −5.90974 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.681947 | + | 0.347469i | −0.681947 | + | 0.347469i | −0.760406 | − | 0.649448i | \(-0.775000\pi\) |
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.57333 | + | 3.08783i | 1.57333 | + | 3.08783i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.41559 | − | 0.459953i | −1.41559 | − | 0.459953i | ||||
\(395\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(398\) | −0.0951823 | − | 0.600958i | −0.0951823 | − | 0.600958i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.79843 | − | 2.79843i | −2.79843 | − | 2.79843i | ||||
\(401\) | 1.99383i | 1.99383i | 0.0784591 | + | 0.996917i | \(0.475000\pi\) | ||||
−0.0784591 | + | 0.996917i | \(0.525000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(410\) | 3.30610 | − | 0.260196i | 3.30610 | − | 0.260196i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.88592 | + | 0.615470i | 3.88592 | + | 0.615470i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.108993 | + | 0.453990i | −0.108993 | + | 0.453990i | ||||
\(416\) | 2.48687 | + | 3.42289i | 2.48687 | + | 3.42289i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(422\) | 3.42289 | + | 1.74405i | 3.42289 | + | 1.74405i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.896802 | + | 3.73545i | 0.896802 | + | 3.73545i | ||||
\(431\) | 1.84956 | + | 0.600958i | 1.84956 | + | 0.600958i | 0.996917 | + | 0.0784591i | \(0.0250000\pi\) |
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.863541 | + | 1.69480i | 0.863541 | + | 1.69480i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.690983 | + | 0.951057i | −0.690983 | + | 0.951057i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(440\) | −0.353175 | − | 0.413515i | −0.353175 | − | 0.413515i | ||||
\(441\) | 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 | ||||||||
\(445\) | −1.79671 | + | 0.431351i | −1.79671 | + | 0.431351i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.52081 | 1.52081 | 0.760406 | − | 0.649448i | \(-0.225000\pi\) | ||||
0.760406 | + | 0.649448i | \(0.225000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.267590 | 0.267590 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.41754 | − | 1.11042i | 3.41754 | − | 1.11042i | ||||
\(455\) | 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 | ||||||||
\(461\) | 0.763472 | − | 1.05083i | 0.763472 | − | 1.05083i | −0.233445 | − | 0.972370i | \(-0.575000\pi\) |
0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.82763 | − | 1.73278i | 2.82763 | − | 1.73278i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.39274 | + | 4.69601i | −2.39274 | + | 4.69601i | ||||
\(473\) | 0.0484904 | + | 0.306156i | 0.0484904 | + | 0.306156i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.32621 | − | 0.675737i | −1.32621 | − | 0.675737i | ||||
\(479\) | 0.401381 | + | 1.23532i | 0.401381 | + | 1.23532i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.59496 | + | 2.19528i | 1.59496 | + | 2.19528i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(488\) | −3.10791 | − | 0.492245i | −3.10791 | − | 0.492245i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.65816 | − | 1.01612i | −1.65816 | − | 1.01612i | ||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 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 | \(0.5\pi\) | |||||||||
\(500\) | 2.70515 | + | 0.649448i | 2.70515 | + | 0.649448i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.04359 | − | 4.01077i | −2.04359 | − | 4.01077i | ||||
\(509\) | 1.57333 | − | 1.14309i | 1.57333 | − | 1.14309i | 0.649448 | − | 0.760406i | \(-0.275000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.473841 | − | 2.99171i | 0.473841 | − | 2.99171i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.30656 | + | 0.541196i | −1.30656 | + | 0.541196i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.238424 | − | 0.121483i | 0.238424 | − | 0.121483i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.20175 | − | 1.32621i | −3.20175 | − | 1.32621i | ||||
\(521\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.896802 | − | 0.142040i | 0.896802 | − | 0.142040i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.51942 | − | 0.774181i | 1.51942 | − | 0.774181i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.126949 | − | 0.0922342i | −0.126949 | − | 0.0922342i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.809017 | − | 1.58779i | 0.809017 | − | 1.58779i | − | 1.00000i | \(-0.5\pi\) | |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(548\) | 0.804150 | + | 5.07720i | 0.804150 | + | 5.07720i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.290229 | + | 0.0943012i | 0.290229 | + | 0.0943012i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.188021 | + | 0.578669i | 0.188021 | + | 0.578669i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.63523 | − | 5.03271i | 1.63523 | − | 5.03271i | ||||
\(557\) | −0.918458 | + | 0.918458i | −0.918458 | + | 0.918458i | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) |
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.16110 | + | 1.59811i | 1.16110 | + | 1.59811i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.49492 | − | 0.395156i | −2.49492 | − | 0.395156i | ||||
\(563\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.706468 | + | 0.972370i | 0.706468 | + | 0.972370i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.88592 | + | 4.88592i | −4.88592 | + | 4.88592i | ||||
\(569\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(572\) | −0.388968 | − | 0.198189i | −0.388968 | − | 0.198189i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(578\) | −0.882893 | + | 1.73278i | −0.882893 | + | 1.73278i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.64412 | + | 1.19453i | 1.64412 | + | 1.19453i | ||||
\(587\) | 0.203192 | − | 1.28290i | 0.203192 | − | 1.28290i | −0.649448 | − | 0.760406i | \(-0.725000\pi\) |
0.852640 | − | 0.522499i | \(-0.175000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.232049 | − | 2.94847i | −0.232049 | − | 2.94847i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.02505 | − | 0.657978i | 2.02505 | − | 0.657978i | ||||
\(597\) | 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 | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.901131 | − | 0.373260i | −0.901131 | − | 0.373260i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.63137 | − | 0.675737i | 1.63137 | − | 0.675737i | ||||
\(611\) | 1.00234 | − | 1.37960i | 1.00234 | − | 1.37960i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.774181 | − | 1.51942i | −0.774181 | − | 1.51942i | −0.852640 | − | 0.522499i | \(-0.825000\pi\) |
0.0784591 | − | 0.996917i | \(-0.475000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(626\) | − | 3.14666i | − | 3.14666i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.41724 | − | 2.25070i | −4.41724 | − | 2.25070i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(632\) | −3.46555 | + | 3.46555i | −3.46555 | + | 3.46555i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.533698 | − | 0.734572i | −0.533698 | − | 0.734572i | ||||
\(635\) | 1.37960 | + | 0.845420i | 1.37960 | + | 0.845420i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.987688 | − | 0.156434i | −0.987688 | − | 0.156434i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.55905 | + | 3.76389i | 1.55905 | + | 3.76389i | ||||
\(641\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(642\) | 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 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.238643i | − | 0.238643i | ||||||
\(650\) | 1.92080 | − | 0.304224i | 1.92080 | − | 0.304224i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.41848 | − | 2.08549i | −6.41848 | − | 2.08549i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −2.55516 | − | 2.55516i | −2.55516 | − | 2.55516i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.135505 | − | 0.0440284i | 0.135505 | − | 0.0440284i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.39680 | + | 0.221232i | −1.39680 | + | 0.221232i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(674\) | −2.28618 | −2.28618 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.78201 | −2.78201 | ||||||||
\(677\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.139815 | − | 0.0712394i | 0.139815 | − | 0.0712394i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.522499 | + | 0.852640i | \(0.325000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.20002 | − | 1.40505i | −1.20002 | − | 1.40505i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.22296 | − | 7.72147i | 1.22296 | − | 7.72147i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.444039 | + | 1.84956i | 0.444039 | + | 1.84956i | ||||
\(696\) | 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 | ||||||||
\(704\) | 0.207076 | + | 0.637314i | 0.207076 | + | 0.637314i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.627999 | − | 1.93278i | 0.627999 | − | 1.93278i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(710\) | 0.905182 | − | 3.77035i | 0.905182 | − | 3.77035i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.32467 | + | 1.00173i | 6.32467 | + | 1.00173i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.156434 | − | 0.0123117i | 0.156434 | − | 0.0123117i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.43702 | − | 1.43702i | 1.43702 | − | 1.43702i | ||||
\(719\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.73278 | + | 0.882893i | 1.73278 | + | 0.882893i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.29170i | 5.29170i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0966818 | + | 0.610425i | 0.0966818 | + | 0.610425i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(734\) | −0.492245 | + | 0.357637i | −0.492245 | + | 0.357637i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.40985 | − | 1.40985i | −1.40985 | − | 1.40985i | −0.760406 | − | 0.649448i | \(-0.775000\pi\) |
−0.649448 | − | 0.760406i | \(-0.725000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.497066 | + | 0.581990i | −0.497066 | + | 0.581990i | ||||
\(746\) | 3.51807 | − | 1.14309i | 3.51807 | − | 1.14309i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(752\) | −6.66570 | + | 1.05574i | −6.66570 | + | 1.05574i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.831254 | + | 0.831254i | 0.831254 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.614234 | + | 0.845420i | −0.614234 | + | 0.845420i | −0.996917 | − | 0.0784591i | \(-0.975000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20417 | + | 0.874883i | −1.20417 | + | 0.874883i | ||||
\(767\) | −0.690434 | − | 1.35505i | −0.690434 | − | 1.35505i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.237907 | + | 1.50209i | 0.237907 | + | 1.50209i | 0.760406 | + | 0.649448i | \(0.225000\pi\) |
−0.522499 | + | 0.852640i | \(0.675000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.32621 | + | 3.20175i | 2.32621 | + | 3.20175i | ||||
\(785\) | 1.77652 | − | 0.139815i | 1.77652 | − | 0.139815i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(788\) | −2.10305 | − | 0.333090i | −2.10305 | − | 0.333090i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.642040 | − | 2.67429i | 0.642040 | − | 2.67429i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.268970 | − | 0.827805i | −0.268970 | − | 0.827805i | ||||
\(797\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.42289 | − | 2.48687i | −3.42289 | − | 2.48687i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.606573 | + | 3.82975i | 0.606573 | + | 3.82975i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.61303 | − | 1.10749i | 4.61303 | − | 1.10749i | ||||
\(821\) | −1.84956 | + | 0.600958i | −1.84956 | + | 0.600958i | −0.852640 | + | 0.522499i | \(0.825000\pi\) |
−0.996917 | + | 0.0784591i | \(0.975000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.896802 | + | 0.142040i | −0.896802 | + | 0.142040i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(824\) | 4.90103 | 4.90103 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.96929 | − | 0.311904i | 1.96929 | − | 0.311904i | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) |
0.996917 | − | 0.0784591i | \(-0.0250000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(830\) | −0.0712394 | + | 0.905182i | −0.0712394 | + | 0.905182i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.01967 | + | 3.01967i | 3.01967 | + | 3.01967i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.26301 | + | 0.303221i | 1.26301 | + | 0.303221i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.05083 | + | 0.763472i | 1.05083 | + | 0.763472i | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) |
0.0784591 | + | 0.996917i | \(0.475000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.22655 | + | 1.69821i | 5.22655 | + | 1.69821i | ||||
\(845\) | 0.852640 | − | 0.522499i | 0.852640 | − | 0.522499i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(860\) | 2.10305 | + | 5.07720i | 2.10305 | + | 5.07720i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.73545 | + | 0.591637i | 3.73545 | + | 0.591637i | ||||
\(863\) | 1.03213 | + | 0.163474i | 1.03213 | + | 0.163474i | 0.649448 | − | 0.760406i | \(-0.275000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.17429 | + | 2.99265i | 2.17429 | + | 2.99265i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0685758 | − | 0.211055i | 0.0685758 | − | 0.211055i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(878\) | −1.03790 | + | 2.03700i | −1.03790 | + | 2.03700i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.472225 | − | 0.403318i | −0.472225 | − | 0.403318i | ||||
\(881\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.734572 | − | 1.44168i | −0.734572 | − | 1.44168i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.31988 | + | 1.37514i | −3.31988 | + | 1.37514i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.92117 | − | 0.462668i | 2.92117 | − | 0.462668i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.513985 | − | 0.0814072i | 0.513985 | − | 0.0814072i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.993851 | − | 1.62182i | −0.993851 | − | 1.62182i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.14412 | − | 1.14412i | −1.14412 | − | 1.14412i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(908\) | 4.58021 | − | 2.33373i | 4.58021 | − | 2.33373i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0114610 | + | 0.0723617i | −0.0114610 | + | 0.0723617i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.863541 | − | 0.280582i | −0.863541 | − | 0.280582i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.14679 | − | 2.25070i | 1.14679 | − | 2.25070i | ||||
\(923\) | −0.311904 | − | 1.96929i | −0.311904 | − | 1.96929i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.322922 | − | 0.993851i | −0.322922 | − | 0.993851i | −0.972370 | − | 0.233445i | \(-0.925000\pi\) |
0.649448 | − | 0.760406i | \(-0.275000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.610425 | − | 0.0966818i | −0.610425 | − | 0.0966818i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.60745 | − | 3.08105i | 3.60745 | − | 3.08105i | ||||
\(941\) | −1.17195 | − | 1.61305i | −1.17195 | − | 1.61305i | −0.649448 | − | 0.760406i | \(-0.725000\pi\) |
−0.522499 | − | 0.852640i | \(-0.675000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.85989 | + | 5.72416i | −1.85989 | + | 5.72416i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.186280 | + | 0.573312i | 0.186280 | + | 0.573312i | ||||
\(947\) | 1.35505 | + | 0.690434i | 1.35505 | + | 0.690434i | 0.972370 | − | 0.233445i | \(-0.0750000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.02505 | − | 0.657978i | −2.02505 | − | 0.657978i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.14679 | + | 2.25070i | 1.14679 | + | 2.25070i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(968\) | 2.39018 | + | 2.39018i | 2.39018 | + | 2.39018i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.59341 | −3.59341 | ||||||||
\(977\) | 1.50209 | − | 0.237907i | 1.50209 | − | 0.237907i | 0.649448 | − | 0.760406i | \(-0.275000\pi\) |
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.275756 | + | 0.0895986i | −0.275756 | + | 0.0895986i | ||||
\(980\) | −2.57024 | − | 1.06463i | −2.57024 | − | 1.06463i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.931099 | − | 0.474419i | 0.931099 | − | 0.474419i | 0.0784591 | − | 0.996917i | \(-0.475000\pi\) |
0.852640 | + | 0.522499i | \(0.175000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.30902 | + | 0.951057i | −1.30902 | + | 0.951057i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.237907 | + | 0.203192i | 0.237907 | + | 0.203192i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.896802 | + | 1.76007i | −0.896802 | + | 1.76007i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(998\) | 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.2287.4 | yes | 32 | |
3.2 | odd | 2 | inner | 2925.1.er.a.2287.1 | yes | 32 | |
13.12 | even | 2 | inner | 2925.1.er.a.2287.1 | yes | 32 | |
25.23 | odd | 20 | inner | 2925.1.er.a.298.1 | ✓ | 32 | |
39.38 | odd | 2 | CM | 2925.1.er.a.2287.4 | yes | 32 | |
75.23 | even | 20 | inner | 2925.1.er.a.298.4 | yes | 32 | |
325.298 | odd | 20 | inner | 2925.1.er.a.298.4 | yes | 32 | |
975.623 | even | 20 | inner | 2925.1.er.a.298.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2925.1.er.a.298.1 | ✓ | 32 | 25.23 | odd | 20 | inner | |
2925.1.er.a.298.1 | ✓ | 32 | 975.623 | even | 20 | inner | |
2925.1.er.a.298.4 | yes | 32 | 75.23 | even | 20 | inner | |
2925.1.er.a.298.4 | yes | 32 | 325.298 | odd | 20 | inner | |
2925.1.er.a.2287.1 | yes | 32 | 3.2 | odd | 2 | inner | |
2925.1.er.a.2287.1 | yes | 32 | 13.12 | even | 2 | inner | |
2925.1.er.a.2287.4 | yes | 32 | 1.1 | even | 1 | trivial | |
2925.1.er.a.2287.4 | yes | 32 | 39.38 | odd | 2 | CM |