Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1375,1,Mod(54,1375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1375, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([11, 25]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1375.54");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1375 = 5^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1375.bz (of order \(50\), degree \(20\), 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: | \(0.686214392370\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{50})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{15} + x^{10} - x^{5} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{50}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{50} - \cdots)\) |
Embedding invariants
Embedding label | 1209.1 | ||
Root | \(0.637424 - 0.770513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1375.1209 |
Dual form | 1375.1.bz.a.439.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1375\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(1002\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{47}{50}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(3\) | 0.0623382 | − | 0.242791i | 0.0623382 | − | 0.242791i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(4\) | 0.929776 | − | 0.368125i | 0.929776 | − | 0.368125i | ||||
\(5\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.821245 | + | 0.451483i | 0.821245 | + | 0.451483i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.187381 | + | 0.982287i | 0.187381 | + | 0.982287i | ||||
\(12\) | −0.0314168 | − | 0.248690i | −0.0314168 | − | 0.248690i | ||||
\(13\) | 0 | 0 | 0.481754 | − | 0.876307i | \(-0.340000\pi\) | ||||
−0.481754 | + | 0.876307i | \(0.660000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.250172 | + | 0.0157395i | −0.250172 | + | 0.0157395i | ||||
\(16\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(17\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(20\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.450043 | + | 0.211774i | 0.450043 | + | 0.211774i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.332404 | − | 0.353975i | 0.332404 | − | 0.353975i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.791759 | − | 0.313480i | −0.791759 | − | 0.313480i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.250172 | + | 0.0157395i | 0.250172 | + | 0.0157395i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.929776 | + | 0.117458i | 0.929776 | + | 0.117458i | ||||
\(37\) | −0.804733 | − | 0.856954i | −0.804733 | − | 0.856954i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(44\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(45\) | 0.175607 | − | 0.920567i | 0.175607 | − | 0.920567i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.60601 | − | 1.01920i | −1.60601 | − | 1.01920i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(48\) | −0.120759 | − | 0.219661i | −0.120759 | − | 0.219661i | ||||
\(49\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.96070 | + | 0.123357i | −1.96070 | + | 0.123357i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.44644 | + | 0.182728i | −1.44644 | + | 0.182728i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(60\) | −0.226810 | + | 0.106729i | −0.226810 | + | 0.106729i | ||||
\(61\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.425779 | − | 0.904827i | 0.425779 | − | 0.904827i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.53799 | + | 1.27233i | 1.53799 | + | 1.27233i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0794717 | − | 0.0960648i | 0.0794717 | − | 0.0960648i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.06320 | + | 1.67534i | −1.06320 | + | 1.67534i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0922765 | + | 0.233064i | 0.0922765 | + | 0.233064i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(80\) | −0.876307 | − | 0.481754i | −0.876307 | − | 0.481754i | ||||
\(81\) | 0.436938 | + | 0.688505i | 0.436938 | + | 0.688505i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.06320 | + | 0.134314i | 1.06320 | + | 0.134314i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.496398 | + | 0.0312307i | 0.496398 | + | 0.0312307i | ||||
\(93\) | −0.125467 | + | 0.172690i | −0.125467 | + | 0.172690i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.05491 | − | 0.872693i | 1.05491 | − | 0.872693i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.289600 | + | 0.891298i | −0.289600 | + | 0.891298i | ||||
\(100\) | −0.535827 | + | 0.844328i | −0.535827 | + | 0.844328i | ||||
\(101\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.734796 | + | 1.85588i | 0.734796 | + | 1.85588i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(108\) | 0.178755 | − | 0.451483i | 0.178755 | − | 0.451483i | ||||
\(109\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.258227 | + | 0.141961i | −0.258227 | + | 0.141961i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.211645 | + | 1.67534i | 0.211645 | + | 1.67534i | 0.637424 | + | 0.770513i | \(0.280000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0623382 | − | 0.493458i | 0.0623382 | − | 0.493458i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.851559 | −0.851559 | ||||||||
\(125\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(132\) | 0.238398 | − | 0.0774602i | 0.238398 | − | 0.0774602i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.439368 | − | 0.206751i | −0.439368 | − | 0.206751i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.193142 | − | 1.52888i | −0.193142 | − | 1.52888i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.347569 | + | 0.326389i | −0.347569 | + | 0.326389i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.907724 | − | 0.233064i | 0.907724 | − | 0.233064i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0922765 | − | 0.233064i | −0.0922765 | − | 0.233064i | ||||
\(148\) | −1.06369 | − | 0.500534i | −1.06369 | − | 0.500534i | ||||
\(149\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0534698 | + | 0.849878i | −0.0534698 | + | 0.849878i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.432756 | − | 0.595638i | 0.432756 | − | 0.595638i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0922765 | + | 0.483730i | −0.0922765 | + | 0.483730i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.63742 | + | 0.770513i | −1.63742 | + | 0.770513i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0623382 | − | 0.242791i | −0.0623382 | − | 0.242791i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.535827 | − | 0.844328i | −0.535827 | − | 0.844328i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(177\) | −0.0458038 | + | 0.362574i | −0.0458038 | + | 0.362574i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.683098 | − | 1.07639i | 0.683098 | − | 1.07639i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(180\) | −0.175607 | − | 0.920567i | −0.175607 | − | 0.920567i | ||||
\(181\) | −1.03137 | + | 1.24672i | −1.03137 | + | 1.24672i | −0.0627905 | + | 0.998027i | \(0.520000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.566335 | + | 1.03016i | −0.566335 | + | 1.03016i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.86842 | − | 0.356420i | −1.86842 | − | 0.356420i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.06320 | − | 0.134314i | 1.06320 | − | 0.134314i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(192\) | −0.193142 | − | 0.159781i | −0.193142 | − | 0.159781i | ||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(197\) | 0 | 0 | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | ||||
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.404787 | − | 0.294095i | 0.404787 | − | 0.294095i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.273983 | + | 0.377105i | 0.273983 | + | 0.377105i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(212\) | −1.77760 | + | 0.836475i | −1.77760 | + | 0.836475i | ||||
\(213\) | 0.340480 | + | 0.362574i | 0.340480 | + | 0.362574i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.637424 | − | 0.770513i | 0.637424 | − | 0.770513i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.659566 | + | 0.702367i | −0.659566 | + | 0.702367i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.929776 | + | 0.117458i | −0.929776 | + | 0.117458i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.116762 | − | 1.85588i | −0.116762 | − | 1.85588i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.473036 | + | 1.84235i | −0.473036 | + | 1.84235i | ||||
\(236\) | −1.27760 | + | 0.702367i | −1.27760 | + | 0.702367i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(240\) | −0.171593 | + | 0.182728i | −0.171593 | + | 0.182728i | ||||
\(241\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.656217 | − | 0.213218i | 0.656217 | − | 0.213218i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.123693 | + | 0.481754i | −0.123693 | + | 0.481754i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(257\) | 0.473036 | − | 0.153699i | 0.473036 | − | 0.153699i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.481754 | − | 0.876307i | \(-0.340000\pi\) | ||||
−0.481754 | + | 0.876307i | \(0.660000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.723208 | + | 1.82662i | 0.723208 | + | 1.82662i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0988884 | − | 0.249764i | 0.0988884 | − | 0.249764i | ||||
\(268\) | 1.89836 | + | 0.616814i | 1.89836 | + | 0.616814i | ||||
\(269\) | −1.80113 | + | 0.462452i | −1.80113 | + | 0.462452i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.728969 | − | 0.684547i | −0.728969 | − | 0.684547i | ||||
\(276\) | 0.0385271 | − | 0.118574i | 0.0385271 | − | 0.118574i | ||||
\(277\) | 0 | 0 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.508698 | − | 0.614910i | −0.508698 | − | 0.614910i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) | ||||
0.998027 | + | 0.0627905i | \(0.0200000\pi\) | |||||||
\(284\) | −0.371808 | + | 1.94908i | −0.371808 | + | 1.94908i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.728969 | − | 0.684547i | −0.728969 | − | 0.684547i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.146121 | − | 0.310524i | −0.146121 | − | 0.310524i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.620759 | + | 1.31918i | 0.620759 | + | 1.31918i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.409991 | + | 0.260188i | 0.409991 | + | 0.260188i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.171593 | + | 0.182728i | 0.171593 | + | 0.182728i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.496398 | − | 0.0627097i | 0.496398 | − | 0.0627097i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.0534698 | + | 0.113629i | −0.0534698 | + | 0.113629i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.51373 | − | 0.288760i | −1.51373 | − | 0.288760i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.742395 | + | 0.614163i | 0.742395 | + | 0.614163i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.659711 | + | 0.479308i | 0.659711 | + | 0.479308i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0672897 | − | 0.106032i | −0.0672897 | − | 0.106032i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.273983 | − | 1.06709i | −0.273983 | − | 1.06709i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.734796 | − | 1.85588i | 0.734796 | − | 1.85588i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.904827 | − | 0.425779i | \(-0.140000\pi\) | ||||
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.419952 | + | 0.0530522i | 0.419952 | + | 0.0530522i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.159566 | − | 0.836475i | 0.159566 | − | 0.836475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.115921 | − | 0.0458965i | −0.115921 | − | 0.0458965i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.770513 | − | 0.637424i | \(-0.220000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.92189 | + | 0.493458i | 1.92189 | + | 0.493458i | ||||
\(356\) | 1.03799 | − | 0.266509i | 1.03799 | − | 0.266509i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0314168 | + | 0.248690i | 0.0314168 | + | 0.248690i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.30113 | + | 0.825723i | −1.30113 | + | 0.825723i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(368\) | 0.473036 | − | 0.153699i | 0.473036 | − | 0.153699i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0530846 | + | 0.206751i | −0.0530846 | + | 0.206751i | ||||
\(373\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.193142 | − | 0.159781i | 0.193142 | − | 0.159781i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.574633 | + | 0.227513i | −0.574633 | + | 0.227513i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.52794 | − | 0.969661i | 1.52794 | − | 0.969661i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.659566 | − | 1.19975i | 0.659566 | − | 1.19975i | ||||
\(389\) | 1.53583 | − | 0.844328i | 1.53583 | − | 0.844328i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
1.00000 | \(0\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0588452 | + | 0.935317i | 0.0588452 | + | 0.935317i | ||||
\(397\) | −0.621636 | − | 1.57007i | −0.621636 | − | 1.57007i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.187381 | − | 0.982287i | \(-0.440000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(401\) | 0.115808 | − | 0.356420i | 0.115808 | − | 0.356420i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.519786 | − | 0.628313i | 0.519786 | − | 0.628313i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.690983 | − | 0.951057i | 0.690983 | − | 0.951057i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.383238 | − | 0.0484142i | −0.383238 | − | 0.0484142i | ||||
\(412\) | 1.36639 | + | 1.45506i | 1.36639 | + | 1.45506i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.781202 | − | 1.23098i | −0.781202 | − | 1.23098i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
0.187381 | − | 0.982287i | \(-0.440000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.03799 | − | 0.266509i | −1.03799 | − | 0.266509i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.858772 | − | 1.56210i | −0.858772 | − | 1.56210i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(432\) | − | 0.485583i | − | 0.485583i | ||||||
\(433\) | 0.905793 | + | 0.749337i | 0.905793 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.929776 | − | 0.117458i | 0.929776 | − | 0.117458i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.36909i | − | 1.36909i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(444\) | −0.187834 | + | 0.227052i | −0.187834 | + | 0.227052i | ||||
\(445\) | −0.200808 | − | 1.05267i | −0.200808 | − | 1.05267i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.56720 | + | 1.13864i | 1.56720 | + | 1.13864i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.813516 | + | 1.47978i | 0.813516 | + | 1.47978i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.123693 | − | 0.481754i | −0.123693 | − | 0.481754i | ||||
\(461\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.15596 | + | 1.23098i | 1.15596 | + | 1.23098i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.203010 | + | 0.0659619i | 0.203010 | + | 0.0659619i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.89836 | + | 0.119435i | 1.89836 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.117638 | − | 0.142201i | −0.117638 | − | 0.142201i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.66591 | − | 0.783916i | −1.66591 | − | 0.783916i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.728969 | + | 0.684547i | −0.728969 | + | 0.684547i | ||||
\(485\) | −1.15596 | − | 0.733597i | −1.15596 | − | 0.733597i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0849998 | + | 0.445585i | 0.0849998 | + | 0.445585i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.937166 | 0.937166 | ||||||||
\(496\) | −0.791759 | + | 0.313480i | −0.791759 | + | 0.313480i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(500\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.238398 | + | 0.0774602i | −0.238398 | + | 0.0774602i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.11716 | − | 0.614163i | −1.11716 | − | 0.614163i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.53799 | − | 1.27233i | 1.53799 | − | 1.27233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.700215 | − | 1.76854i | 0.700215 | − | 1.76854i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.00788530 | − | 0.125333i | −0.00788530 | − | 0.125333i | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.193142 | − | 0.159781i | 0.193142 | − | 0.159781i | ||||
\(529\) | −0.479734 | − | 0.579899i | −0.479734 | − | 0.579899i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.27038 | − | 0.502980i | −1.27038 | − | 0.502980i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.218755 | − | 0.232950i | −0.218755 | − | 0.232950i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(540\) | −0.484624 | − | 0.0304900i | −0.484624 | − | 0.0304900i | ||||
\(541\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.238398 | + | 0.328127i | 0.238398 | + | 0.328127i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.844328 | − | 0.535827i | \(-0.820000\pi\) | ||||
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(548\) | −0.742395 | − | 1.35041i | −0.742395 | − | 1.35041i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.214810 | + | 0.201720i | 0.214810 | + | 0.201720i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.982287 | − | 0.187381i | \(-0.940000\pi\) | ||||
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(564\) | −0.203010 | + | 0.431418i | −0.203010 | + | 0.431418i | ||||
\(565\) | 1.52794 | − | 0.718995i | 1.52794 | − | 0.718995i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0336680 | − | 0.266509i | 0.0336680 | − | 0.266509i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.488570 | + | 0.0931997i | −0.488570 | + | 0.0931997i | ||||
\(576\) | 0.758183 | − | 0.550853i | 0.758183 | − | 0.550853i | ||||
\(577\) | 0.464173 | + | 0.844328i | 0.464173 | + | 0.844328i | 1.00000 | \(0\) | ||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.488570 | − | 1.90285i | −0.488570 | − | 1.90285i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.23879 | + | 0.582932i | −1.23879 | + | 0.582932i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(588\) | −0.171593 | − | 0.182728i | −0.171593 | − | 0.182728i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.17325 | − | 0.0738147i | −1.17325 | − | 0.0738147i | ||||
\(593\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.246226 | − | 0.203696i | 0.246226 | − | 0.203696i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.541587 | + | 1.66683i | −0.541587 | + | 1.66683i | 0.187381 | + | 0.982287i | \(0.440000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.688626 | + | 1.73927i | 0.688626 | + | 1.73927i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.813516 | + | 0.516273i | −0.813516 | + | 0.516273i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0534698 | − | 0.849878i | 0.0534698 | − | 0.849878i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.929776 | − | 0.368125i | \(-0.120000\pi\) | |||||||
\(620\) | 0.263146 | + | 0.809880i | 0.263146 | + | 0.809880i | ||||
\(621\) | 0.224559 | − | 0.0889091i | 0.224559 | − | 0.0889091i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.183098 | − | 0.713118i | 0.183098 | − | 0.713118i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.00788530 | − | 0.125333i | 0.00788530 | − | 0.125333i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
1.00000 | \(0\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0922765 | + | 0.483730i | 0.0922765 | + | 0.483730i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.62954 | + | 0.895846i | −1.62954 | + | 0.895846i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.44644 | − | 1.35830i | 1.44644 | − | 1.35830i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.72108 | + | 0.559214i | 1.72108 | + | 0.559214i | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.734796 | + | 1.85588i | 0.734796 | + | 1.85588i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.450527 | − | 1.38658i | −0.450527 | − | 1.38658i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.23879 | + | 1.31918i | −1.23879 | + | 1.31918i | ||||
\(653\) | 1.39436 | − | 1.15352i | 1.39436 | − | 1.15352i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(660\) | −0.147338 | − | 0.202793i | −0.147338 | − | 0.202793i | ||||
\(661\) | 1.26480 | + | 0.159781i | 1.26480 | + | 0.159781i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.129412 | + | 0.203921i | 0.129412 | + | 0.203921i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0608596 | + | 0.481754i | −0.0608596 | + | 0.481754i | ||||
\(676\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(677\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.567290 | + | 0.469303i | 0.567290 | + | 0.469303i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39436 | + | 0.656137i | −1.39436 | + | 0.656137i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.457871 | − | 0.0873436i | −0.457871 | − | 0.0873436i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.92189 | + | 0.242791i | −1.92189 | + | 0.242791i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(705\) | 0.417819 | + | 0.229698i | 0.417819 | + | 0.229698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.0908852 | + | 0.353975i | 0.0908852 | + | 0.353975i | ||||
\(709\) | −0.159566 | − | 0.339095i | −0.159566 | − | 0.339095i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.289939 | − | 0.308753i | −0.289939 | − | 0.308753i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.238883 | − | 1.25227i | 0.238883 | − | 1.25227i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.72897 | − | 0.684547i | −1.72897 | − | 0.684547i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(720\) | −0.502159 | − | 0.791276i | −0.502159 | − | 0.791276i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.23879 | + | 0.582932i | 1.23879 | + | 0.582932i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.0403423 | + | 0.641222i | 0.0403423 | + | 0.641222i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.193142 | + | 0.159781i | −0.193142 | + | 0.159781i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.961606 | + | 1.74915i | −0.961606 | + | 1.74915i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(740\) | −0.147338 | + | 1.16630i | −0.147338 | + | 1.16630i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.07165 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(752\) | −1.86842 | + | 0.356420i | −1.86842 | + | 0.356420i | ||||
\(753\) | −0.0233620 | + | 0.0909891i | −0.0233620 | + | 0.0909891i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.30209 | − | 0.423073i | 1.30209 | − | 0.423073i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.109255 | + | 0.0600633i | 0.109255 | + | 0.0600633i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.939097 | − | 0.516273i | 0.939097 | − | 0.516273i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.238398 | − | 0.0774602i | −0.238398 | − | 0.0774602i | ||||
\(769\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.00782850 | − | 0.124430i | −0.00782850 | − | 0.124430i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.77760 | + | 0.836475i | 1.77760 | + | 0.836475i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.824805 | − | 0.211774i | 0.824805 | − | 0.211774i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.84489 | − | 0.730444i | −1.84489 | − | 0.730444i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.187381 | − | 0.982287i | 0.187381 | − | 0.982287i | ||||
\(785\) | −0.700215 | − | 0.227513i | −0.700215 | − | 0.227513i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.684547 | − | 0.728969i | \(-0.740000\pi\) | ||||
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.488570 | − | 0.0617207i | 0.488570 | − | 0.0617207i | ||||
\(796\) | 1.23480 | + | 0.317042i | 1.23480 | + | 0.317042i | ||||
\(797\) | −1.42578 | − | 0.904827i | −1.42578 | − | 0.904827i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.812510 | + | 0.590323i | 0.812510 | + | 0.590323i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.268098 | − | 0.422454i | 0.268098 | − | 0.422454i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.466128i | 0.466128i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.23879 | + | 1.31918i | 1.23879 | + | 1.31918i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.246226 | − | 1.94908i | 0.246226 | − | 1.94908i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.211645 | + | 0.134314i | −0.211645 | + | 0.134314i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(828\) | 0.393565 | + | 0.249764i | 0.393565 | + | 0.249764i | ||||
\(829\) | −1.69755 | − | 0.435857i | −1.69755 | − | 0.435857i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.374148 | + | 0.176061i | −0.374148 | + | 0.176061i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.34484 | + | 1.43211i | −1.34484 | + | 1.43211i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.180684 | − | 0.556087i | −0.180684 | − | 0.556087i | ||||
\(852\) | 0.450043 | + | 0.211774i | 0.450043 | + | 0.211774i | ||||
\(853\) | 0 | 0 | −0.368125 | − | 0.929776i | \(-0.620000\pi\) | ||||
0.368125 | + | 0.929776i | \(0.380000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.273190 | − | 0.256543i | 0.273190 | − | 0.256543i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.226810 | − | 1.79538i | −0.226810 | − | 1.79538i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.211645 | + | 0.134314i | −0.211645 | + | 0.134314i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.26034 | − | 0.240423i | 1.26034 | − | 0.240423i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.982287 | − | 0.187381i | \(-0.0600000\pi\) | ||||
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(881\) | 0.110048 | − | 1.74915i | 0.110048 | − | 1.74915i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.52794 | + | 0.969661i | −1.52794 | + | 0.969661i | −0.535827 | + | 0.844328i | \(0.680000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.358983 | − | 0.0684796i | 0.358983 | − | 0.0684796i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.594435 | + | 0.558212i | −0.594435 | + | 0.558212i | ||||
\(892\) | −0.354691 | + | 0.895846i | −0.354691 | + | 0.895846i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.23480 | − | 0.317042i | −1.23480 | − | 0.317042i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.821245 | + | 0.451483i | −0.821245 | + | 0.451483i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.50441 | + | 0.595638i | 1.50441 | + | 0.595638i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.124591 | + | 0.0157395i | 0.124591 | + | 0.0157395i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.791759 | − | 1.68257i | −0.791759 | − | 1.68257i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.15475 | + | 0.220280i | 1.15475 | + | 0.220280i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.234453 | + | 1.85588i | −0.234453 | + | 1.85588i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.683098 | + | 1.07639i | −0.683098 | + | 1.07639i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.0242550 | + | 0.0200654i | 0.0242550 | + | 0.0200654i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.982287 | − | 0.187381i | \(-0.940000\pi\) | ||||
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.164472 | + | 0.349520i | −0.164472 | + | 0.349520i | ||||
\(940\) | 0.238398 | + | 1.88711i | 0.238398 | + | 1.88711i | ||||
\(941\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.929324 | + | 1.12336i | −0.929324 | + | 1.12336i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.961606 | + | 0.0604991i | −0.961606 | + | 0.0604991i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.195393 | − | 0.141961i | 0.195393 | − | 0.141961i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.844328 | − | 0.535827i | \(-0.820000\pi\) | ||||
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.456288 | − | 0.969661i | −0.456288 | − | 0.969661i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.0922765 | + | 0.233064i | −0.0922765 | + | 0.233064i | ||||
\(961\) | −0.200356 | − | 0.188146i | −0.200356 | − | 0.188146i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) | ||||
0.998027 | + | 0.0627905i | \(0.0200000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.238883 | − | 0.288760i | −0.238883 | − | 0.288760i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(972\) | 0.531645 | − | 0.439815i | 0.531645 | − | 0.439815i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.06369 | − | 0.500534i | −1.06369 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.0672897 | + | 1.06954i | 0.0672897 | + | 1.06954i | ||||
\(980\) | −0.968583 | − | 0.248690i | −0.968583 | − | 0.248690i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.567290 | − | 1.43281i | 0.567290 | − | 1.43281i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.27760 | − | 0.702367i | −1.27760 | − | 0.702367i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.0299383 | + | 0.00972753i | −0.0299383 | + | 0.00972753i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.393950 | − | 1.21245i | 0.393950 | − | 1.21245i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.570837 | −0.570837 |
(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 | 1375.1.bz.a.1209.1 | yes | 20 | |
11.10 | odd | 2 | CM | 1375.1.bz.a.1209.1 | yes | 20 | |
125.64 | even | 50 | inner | 1375.1.bz.a.439.1 | ✓ | 20 | |
1375.439 | odd | 50 | inner | 1375.1.bz.a.439.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1375.1.bz.a.439.1 | ✓ | 20 | 125.64 | even | 50 | inner | |
1375.1.bz.a.439.1 | ✓ | 20 | 1375.439 | odd | 50 | inner | |
1375.1.bz.a.1209.1 | yes | 20 | 1.1 | even | 1 | trivial | |
1375.1.bz.a.1209.1 | yes | 20 | 11.10 | odd | 2 | CM |