Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3997,1,Mod(13,3997)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3997, base_ring=CyclotomicField(570))
chi = DirichletCharacter(H, H._module([285, 352]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3997.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3997 = 7 \cdot 571 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3997.cz (of order \(570\), degree \(144\), 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: | \(1.99476285549\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Coefficient field: | \(\Q(\zeta_{570})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{144} - x^{143} + x^{142} + x^{139} - x^{138} + x^{137} - x^{129} + x^{128} - x^{127} + x^{125} - 2 x^{124} + 2 x^{123} - x^{122} + x^{120} - x^{119} + x^{118} + x^{114} - x^{113} + x^{112} - x^{110} + 2 x^{109} - 2 x^{108} + x^{107} - x^{105} + x^{104} - x^{103} - x^{99} + x^{98} - x^{97} + x^{95} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{285}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{285} - \cdots)\) |
Embedding invariants
Embedding label | 237.1 | ||
Root | \(-0.840168 - 0.542326i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3997.237 |
Dual form | 3997.1.cz.a.3373.1 |
$q$-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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).
\(n\) | \(1716\) | \(2285\) |
\(\chi(n)\) | \(e\left(\frac{16}{285}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.579560 | + | 1.85296i | −0.579560 | + | 1.85296i | −0.0605901 | + | 0.998163i | \(0.519298\pi\) |
−0.518970 | + | 0.854793i | \(0.673684\pi\) | |||||||
\(3\) | 0 | 0 | −0.984487 | − | 0.175457i | \(-0.943860\pi\) | ||||
0.984487 | + | 0.175457i | \(0.0561404\pi\) | |||||||
\(4\) | −2.27578 | − | 1.57799i | −2.27578 | − | 1.57799i | ||||
\(5\) | 0 | 0 | 0.565270 | − | 0.824906i | \(-0.308772\pi\) | ||||
−0.565270 | + | 0.824906i | \(0.691228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.995083 | + | 0.0990455i | −0.995083 | + | 0.0990455i | ||||
\(8\) | 2.71079 | − | 2.10989i | 2.71079 | − | 2.10989i | ||||
\(9\) | 0.938430 | + | 0.345471i | 0.938430 | + | 0.345471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0109101 | − | 0.00157421i | −0.0109101 | − | 0.00157421i | 0.137354 | − | 0.990522i | \(-0.456140\pi\) |
−0.148264 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.731980 | − | 0.681326i | \(-0.238596\pi\) | ||||
−0.731980 | + | 0.681326i | \(0.761404\pi\) | |||||||
\(14\) | 0.393183 | − | 1.90125i | 0.393183 | − | 1.90125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.36744 | + | 3.65228i | 1.36744 | + | 3.65228i | ||||
\(17\) | 0 | 0 | −0.834139 | − | 0.551554i | \(-0.814035\pi\) | ||||
0.834139 | + | 0.551554i | \(0.185965\pi\) | |||||||
\(18\) | −1.18402 | + | 1.53865i | −1.18402 | + | 1.53865i | ||||
\(19\) | 0 | 0 | 0.471093 | − | 0.882084i | \(-0.343860\pi\) | ||||
−0.471093 | + | 0.882084i | \(0.656140\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.00924000 | − | 0.0193036i | 0.00924000 | − | 0.0193036i | ||||
\(23\) | 0.154936 | − | 0.104921i | 0.154936 | − | 0.104921i | −0.480787 | − | 0.876837i | \(-0.659649\pi\) |
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.360939 | − | 0.932589i | −0.360939 | − | 0.932589i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.42088 | + | 1.34482i | 2.42088 | + | 1.34482i | ||||
\(29\) | −1.47171 | − | 1.28171i | −1.47171 | − | 1.28171i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
−0.592235 | − | 0.805765i | \(-0.701754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(32\) | −4.13011 | + | 0.227865i | −4.13011 | + | 0.227865i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.59051 | − | 2.26704i | −1.59051 | − | 2.26704i | ||||
\(37\) | 0.611104 | − | 1.31367i | 0.611104 | − | 1.31367i | −0.319482 | − | 0.947592i | \(-0.603509\pi\) |
0.930586 | − | 0.366074i | \(-0.119298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0629058 | − | 1.62968i | −0.0629058 | − | 1.62968i | −0.609854 | − | 0.792514i | \(-0.708772\pi\) |
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(44\) | 0.0223448 | + | 0.0207986i | 0.0223448 | + | 0.0207986i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.104618 | + | 0.347898i | 0.104618 | + | 0.347898i | ||||
\(47\) | 0 | 0 | 0.635724 | − | 0.771917i | \(-0.280702\pi\) | ||||
−0.635724 | + | 0.771917i | \(0.719298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.980380 | − | 0.197117i | 0.980380 | − | 0.197117i | ||||
\(50\) | 1.93723 | − | 0.128313i | 1.93723 | − | 0.128313i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.272892 | − | 0.202901i | −0.272892 | − | 0.202901i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
−0.724425 | + | 0.689353i | \(0.757895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.48849 | + | 2.36801i | −2.48849 | + | 2.36801i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.22790 | − | 1.98418i | 3.22790 | − | 1.98418i | ||||
\(59\) | 0 | 0 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.0935596 | − | 0.995614i | \(-0.470175\pi\) | ||||
−0.0935596 | + | 0.995614i | \(0.529825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.968033 | − | 0.250825i | −0.968033 | − | 0.250825i | ||||
\(64\) | 1.01406 | − | 4.00444i | 1.01406 | − | 4.00444i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.548057 | − | 0.236807i | 0.548057 | − | 0.236807i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.652586 | + | 0.757715i | \(0.273684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.33534 | + | 1.48304i | 1.33534 | + | 1.48304i | 0.716783 | + | 0.697297i | \(0.245614\pi\) |
0.618553 | + | 0.785743i | \(0.287719\pi\) | |||||||
\(72\) | 3.27279 | − | 1.04349i | 3.27279 | − | 1.04349i | ||||
\(73\) | 0 | 0 | 0.996114 | − | 0.0880708i | \(-0.0280702\pi\) | ||||
−0.996114 | + | 0.0880708i | \(0.971930\pi\) | |||||||
\(74\) | 2.07999 | + | 1.89370i | 2.07999 | + | 1.89370i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0110124 | 0.000485878i | 0.0110124 | 0.000485878i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.882997 | + | 0.938222i | −0.882997 | + | 0.938222i | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) |
0.115485 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.761300 | + | 0.648400i | 0.761300 | + | 0.648400i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.537687 | − | 0.843145i | \(-0.680702\pi\) | ||||
0.537687 | + | 0.843145i | \(0.319298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.05618 | + | 0.827935i | 3.05618 | + | 0.827935i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0328964 | + | 0.0187518i | −0.0328964 | + | 0.0187518i | ||||
\(89\) | 0 | 0 | 0.999028 | − | 0.0440782i | \(-0.0140351\pi\) | ||||
−0.999028 | + | 0.0440782i | \(0.985965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.518164 | − | 0.00571202i | −0.518164 | − | 0.00571202i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.329907 | − | 0.944013i | \(-0.607018\pi\) | ||||
0.329907 | + | 0.944013i | \(0.392982\pi\) | |||||||
\(98\) | −0.202940 | + | 1.93084i | −0.202940 | + | 1.93084i | ||||
\(99\) | −0.00969451 | − | 0.00524640i | −0.00969451 | − | 0.00524640i | ||||
\(100\) | −0.650198 | + | 2.69192i | −0.650198 | + | 2.69192i | ||||
\(101\) | 0 | 0 | −0.999757 | − | 0.0220445i | \(-0.992982\pi\) | ||||
0.999757 | + | 0.0220445i | \(0.00701754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.534123 | − | 0.388063i | 0.534123 | − | 0.388063i | ||||
\(107\) | 0.605380 | − | 1.61690i | 0.605380 | − | 1.61690i | −0.170028 | − | 0.985439i | \(-0.554386\pi\) |
0.775409 | − | 0.631460i | \(-0.217544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.909007 | − | 1.57445i | 0.909007 | − | 1.57445i | 0.0935596 | − | 0.995614i | \(-0.470175\pi\) |
0.815447 | − | 0.578832i | \(-0.196491\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.72246 | − | 3.49888i | −1.72246 | − | 3.49888i | ||||
\(113\) | 1.65603 | − | 0.201791i | 1.65603 | − | 0.201791i | 0.761300 | − | 0.648400i | \(-0.224561\pi\) |
0.894729 | + | 0.446609i | \(0.147368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.32675 | + | 5.23923i | 1.32675 | + | 5.23923i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.959094 | − | 0.282660i | −0.959094 | − | 0.282660i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.02580 | − | 1.64835i | 1.02580 | − | 1.64835i | ||||
\(127\) | −1.17712 | + | 0.433342i | −1.17712 | + | 0.433342i | −0.857640 | − | 0.514250i | \(-0.828070\pi\) |
−0.319482 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(128\) | 3.30846 | + | 2.03371i | 3.30846 | + | 2.03371i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.121161 | + | 1.15277i | 0.121161 | + | 1.15277i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.146193 | + | 0.377731i | −0.146193 | + | 0.377731i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) |
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.170028 | − | 0.985439i | \(-0.445614\pi\) | ||||
−0.170028 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.52191 | + | 1.61481i | −3.52191 | + | 1.61481i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0214943 | + | 3.89981i | 0.0214943 | + | 3.89981i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46369 | + | 2.02530i | −3.46369 | + | 2.02530i | ||||
\(149\) | 1.05277 | + | 0.712920i | 1.05277 | + | 0.712920i | 0.959210 | − | 0.282694i | \(-0.0912281\pi\) |
0.0935596 | + | 0.995614i | \(0.470175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.200530 | + | 0.0590991i | −0.200530 | + | 0.0590991i | −0.381410 | − | 0.924406i | \(-0.624561\pi\) |
0.180881 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.00728263 | + | 0.0201238i | −0.00728263 | + | 0.0201238i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.0605901 | − | 0.998163i | \(-0.480702\pi\) | ||||
−0.0605901 | + | 0.998163i | \(0.519298\pi\) | |||||||
\(158\) | −1.22673 | − | 2.17991i | −1.22673 | − | 2.17991i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.143783 | + | 0.119750i | −0.143783 | + | 0.119750i | ||||
\(162\) | −1.64267 | + | 1.03487i | −1.64267 | + | 1.03487i | ||||
\(163\) | 1.68387 | + | 0.167604i | 1.68387 | + | 0.167604i | 0.894729 | − | 0.446609i | \(-0.147368\pi\) |
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0715891 | − | 0.997434i | 0.0715891 | − | 0.997434i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.42846 | + | 3.80805i | −2.42846 | + | 3.80805i | ||||
\(173\) | 0 | 0 | 0.949339 | − | 0.314254i | \(-0.101754\pi\) | ||||
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.451533 | + | 0.892254i | 0.451533 | + | 0.892254i | ||||
\(176\) | −0.00916945 | − | 0.0419993i | −0.00916945 | − | 0.0419993i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.511075 | − | 0.593407i | 0.511075 | − | 0.593407i | −0.441671 | − | 0.897177i | \(-0.645614\pi\) |
0.952745 | + | 0.303771i | \(0.0982456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.198629 | − | 0.611317i | 0.198629 | − | 0.611317i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.249849 | + | 1.96037i | −0.249849 | + | 1.96037i | 0.0275543 | + | 0.999620i | \(0.491228\pi\) |
−0.277403 | + | 0.960754i | \(0.589474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.33696 | − | 1.48485i | 1.33696 | − | 1.48485i | 0.635724 | − | 0.771917i | \(-0.280702\pi\) |
0.701237 | − | 0.712928i | \(-0.252632\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.54217 | − | 1.09843i | −2.54217 | − | 1.09843i | ||||
\(197\) | 1.57458 | − | 0.944136i | 1.57458 | − | 0.944136i | 0.583317 | − | 0.812244i | \(-0.301754\pi\) |
0.991264 | − | 0.131892i | \(-0.0421053\pi\) | |||||||
\(198\) | 0.0153399 | − | 0.0149229i | 0.0153399 | − | 0.0149229i | ||||
\(199\) | 0 | 0 | −0.583317 | − | 0.812244i | \(-0.698246\pi\) | ||||
0.583317 | + | 0.812244i | \(0.301754\pi\) | |||||||
\(200\) | −2.94610 | − | 1.76651i | −2.94610 | − | 1.76651i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.59142 | + | 1.12964i | 1.59142 | + | 1.12964i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.181644 | − | 0.0449346i | 0.181644 | − | 0.0449346i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.276911 | + | 0.920840i | −0.276911 | + | 0.920840i | 0.701237 | + | 0.712928i | \(0.252632\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(212\) | 0.300866 | + | 0.892377i | 0.300866 | + | 0.892377i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.64519 | + | 2.05883i | 2.64519 | + | 2.05883i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.39055 | + | 2.59683i | 2.39055 | + | 2.59683i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.0715891 | − | 0.997434i | \(-0.522807\pi\) | ||||
0.0715891 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(224\) | 4.08724 | − | 0.635814i | 4.08724 | − | 0.635814i | ||||
\(225\) | −0.0165339 | − | 0.999863i | −0.0165339 | − | 0.999863i | ||||
\(226\) | −0.585858 | + | 3.18550i | −0.585858 | + | 3.18550i | ||||
\(227\) | 0 | 0 | −0.644194 | − | 0.764862i | \(-0.722807\pi\) | ||||
0.644194 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.411766 | − | 0.911290i | \(-0.635088\pi\) | ||||
0.411766 | + | 0.911290i | \(0.364912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.69378 | − | 0.369306i | −6.69378 | − | 0.369306i | ||||
\(233\) | −1.73938 | − | 0.684239i | −1.73938 | − | 0.684239i | −0.999939 | − | 0.0110229i | \(-0.996491\pi\) |
−0.739446 | − | 0.673216i | \(-0.764912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0147891 | − | 0.383136i | 0.0147891 | − | 0.383136i | −0.973327 | − | 0.229424i | \(-0.926316\pi\) |
0.988116 | − | 0.153712i | \(-0.0491228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.340293 | − | 0.940319i | \(-0.610526\pi\) | ||||
0.340293 | + | 0.940319i | \(0.389474\pi\) | |||||||
\(242\) | 1.07961 | − | 1.61334i | 1.07961 | − | 1.61334i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.660898 | − | 0.750475i | \(-0.729825\pi\) | ||||
0.660898 | + | 0.750475i | \(0.270175\pi\) | |||||||
\(252\) | 1.80723 | + | 2.09837i | 1.80723 | + | 2.09837i | ||||
\(253\) | −0.00185554 | 0.000900790i | −0.00185554 | 0.000900790i | ||||||
\(254\) | −0.120751 | − | 2.43230i | −0.120751 | − | 2.43230i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.57072 | + | 2.23884i | −2.57072 | + | 2.23884i | ||||
\(257\) | 0 | 0 | −0.934564 | − | 0.355794i | \(-0.884211\pi\) | ||||
0.934564 | + | 0.355794i | \(0.115789\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.477987 | + | 1.36773i | −0.477987 | + | 1.36773i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.938301 | − | 1.71123i | −0.938301 | − | 1.71123i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.956756 | − | 0.727881i | −0.956756 | − | 0.727881i | 0.00551154 | − | 0.999985i | \(-0.498246\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.62093 | − | 0.325908i | −1.62093 | − | 0.325908i | ||||
\(269\) | 0 | 0 | 0.0165339 | − | 0.999863i | \(-0.494737\pi\) | ||||
−0.0165339 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.615191 | − | 0.489807i | −0.615191 | − | 0.489807i | ||||
\(275\) | 0.00246979 | + | 0.0107428i | 0.00246979 | + | 0.0107428i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.188797 | − | 0.653876i | 0.188797 | − | 0.653876i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.997814 | − | 0.0660906i | \(-0.0210526\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0285579 | − | 0.575244i | 0.0285579 | − | 0.575244i | −0.942181 | − | 0.335105i | \(-0.891228\pi\) |
0.970739 | − | 0.240139i | \(-0.0771930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.956036 | − | 0.293250i | \(-0.905263\pi\) | ||||
0.956036 | + | 0.293250i | \(0.0947368\pi\) | |||||||
\(284\) | −0.698705 | − | 5.48221i | −0.698705 | − | 5.48221i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.95454 | − | 1.21300i | −3.95454 | − | 1.21300i | ||||
\(289\) | 0.391577 | + | 0.920146i | 0.391577 | + | 0.920146i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.889752 | − | 0.456444i | \(-0.849123\pi\) | ||||
0.889752 | + | 0.456444i | \(0.150877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.11512 | − | 4.85044i | −1.11512 | − | 4.85044i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.93115 | + | 1.53756i | −1.93115 | + | 1.53756i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.224009 | + | 1.61544i | 0.224009 | + | 1.61544i | ||||
\(302\) | 0.00671078 | − | 0.405824i | 0.00671078 | − | 0.405824i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.942181 | − | 0.335105i | \(-0.108772\pi\) | ||||
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(308\) | −0.0242950 | − | 0.0184831i | −0.0242950 | − | 0.0184831i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.441671 | − | 0.897177i | \(-0.354386\pi\) | ||||
−0.441671 | + | 0.897177i | \(0.645614\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.904357 | − | 0.426776i | \(-0.859649\pi\) | ||||
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.49001 | − | 0.741824i | 3.49001 | − | 0.741824i | ||||
\(317\) | 0.0505274 | + | 1.01778i | 0.0505274 | + | 1.01778i | 0.884667 | + | 0.466224i | \(0.154386\pi\) |
−0.834139 | + | 0.551554i | \(0.814035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0140388 | + | 0.0163004i | 0.0140388 | + | 0.0163004i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.138562 | − | 0.335825i | −0.138562 | − | 0.335825i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.709382 | − | 2.67694i | −0.709382 | − | 2.67694i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.28647 | + | 3.02300i | −1.28647 | + | 3.02300i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.82609 | − | 0.813029i | −1.82609 | − | 0.813029i | −0.926494 | − | 0.376309i | \(-0.877193\pi\) |
−0.899598 | − | 0.436719i | \(-0.856140\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.02731 | − | 1.02166i | 1.02731 | − | 1.02166i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.181137 | − | 1.92757i | −0.181137 | − | 1.92757i | −0.340293 | − | 0.940319i | \(-0.610526\pi\) |
0.159156 | − | 0.987253i | \(-0.449123\pi\) | |||||||
\(338\) | 1.80671 | + | 0.710724i | 1.80671 | + | 0.710724i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.956036 | + | 0.293250i | −0.956036 | + | 0.293250i | ||||
\(344\) | −3.60898 | − | 4.28500i | −3.60898 | − | 4.28500i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.55952 | − | 0.242601i | 1.55952 | − | 0.242601i | 0.685350 | − | 0.728214i | \(-0.259649\pi\) |
0.874174 | + | 0.485613i | \(0.161404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.609854 | − | 0.792514i | \(-0.708772\pi\) | ||||
0.609854 | + | 0.792514i | \(0.291228\pi\) | |||||||
\(350\) | −1.91500 | + | 0.319557i | −1.91500 | + | 0.319557i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0454186 | + | 0.00401566i | 0.0454186 | + | 0.00401566i | ||||
\(353\) | 0 | 0 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.803358 | + | 1.29091i | 0.803358 | + | 1.29091i | ||||
\(359\) | −0.313363 | − | 0.929443i | −0.313363 | − | 0.929443i | −0.982493 | − | 0.186298i | \(-0.940351\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.556143 | − | 0.831087i | −0.556143 | − | 0.831087i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.202517 | − | 0.979279i | \(-0.564912\pi\) | ||||
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(368\) | 0.595065 | + | 0.422397i | 0.595065 | + | 0.422397i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.291646 | + | 0.174874i | 0.291646 | + | 0.174874i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.397675 | + | 0.386864i | −0.397675 | + | 0.386864i | −0.868768 | − | 0.495219i | \(-0.835088\pi\) |
0.471093 | + | 0.882084i | \(0.343860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.781810 | + | 1.73025i | −0.781810 | + | 1.73025i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.48768 | − | 1.59911i | −3.48768 | − | 1.59911i | ||||
\(383\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.97650 | + | 3.33788i | 1.97650 | + | 3.33788i | ||||
\(387\) | 0.503974 | − | 1.55107i | 0.503974 | − | 1.55107i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.923508 | + | 1.52111i | 0.923508 | + | 1.52111i | 0.851919 | + | 0.523673i | \(0.175439\pi\) |
0.0715891 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.24171 | − | 2.60284i | 2.24171 | − | 2.60284i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.836879 | + | 3.46481i | 0.836879 | + | 3.46481i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0137838 | + | 0.0272375i | 0.0137838 | + | 0.0272375i | ||||
\(397\) | 0 | 0 | 0.930586 | − | 0.366074i | \(-0.119298\pi\) | ||||
−0.930586 | + | 0.366074i | \(0.880702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.91251 | − | 2.59351i | 2.91251 | − | 2.59351i | ||||
\(401\) | −0.149362 | − | 1.80254i | −0.149362 | − | 1.80254i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.350638 | − | 0.936511i | \(-0.385965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.01550 | + | 2.29413i | −3.01550 | + | 2.29413i | ||||
\(407\) | −0.00873519 | + | 0.0133702i | −0.00873519 | + | 0.0133702i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.846095 | − | 0.533032i | \(-0.178947\pi\) | ||||
−0.846095 | + | 0.533032i | \(0.821053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0220116 | + | 0.362620i | −0.0220116 | + | 0.362620i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.170028 | − | 0.985439i | \(-0.554386\pi\) | ||||
0.170028 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.70487 | − | 0.188695i | −1.70487 | − | 0.188695i | −0.795863 | − | 0.605477i | \(-0.792982\pi\) |
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(422\) | −1.54579 | − | 1.04679i | −1.54579 | − | 1.04679i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.16785 | + | 0.0257510i | −1.16785 | + | 0.0257510i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.92916 | + | 2.72442i | −3.92916 | + | 2.72442i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.60979 | + | 0.803537i | −1.60979 | + | 0.803537i | −0.609854 | + | 0.792514i | \(0.708772\pi\) |
−0.999939 | + | 0.0110229i | \(0.996491\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.115485 | − | 0.993309i | \(-0.536842\pi\) | ||||
0.115485 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.55315 | + | 2.14868i | −4.55315 | + | 2.14868i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.601081 | − | 0.799188i | \(-0.705263\pi\) | ||||
0.601081 | + | 0.799188i | \(0.294737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.988116 | + | 0.153712i | 0.988116 | + | 0.153712i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.00907 | − | 0.620275i | −1.00907 | − | 0.620275i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) |
−0.926494 | + | 0.376309i | \(0.877193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.612454 | + | 4.08519i | −0.612454 | + | 4.08519i | ||||
\(449\) | 0.492126 | + | 0.206233i | 0.492126 | + | 0.206233i | 0.618553 | − | 0.785743i | \(-0.287719\pi\) |
−0.126427 | + | 0.991976i | \(0.540351\pi\) | |||||||
\(450\) | 1.86228 | + | 0.548844i | 1.86228 | + | 0.548844i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.08718 | − | 2.15396i | −4.08718 | − | 2.15396i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.204493 | + | 0.298419i | 0.204493 | + | 0.298419i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.709053 | + | 0.705155i | \(0.750877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.718655 | − | 1.54486i | −0.718655 | − | 1.54486i | −0.834139 | − | 0.551554i | \(-0.814035\pi\) |
0.115485 | − | 0.993309i | \(-0.463158\pi\) | |||||||
\(464\) | 2.66869 | − | 7.12775i | 2.66869 | − | 7.12775i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.27594 | − | 2.82645i | 2.27594 | − | 2.82645i | ||||
\(467\) | 0 | 0 | 0.159156 | − | 0.987253i | \(-0.449123\pi\) | ||||
−0.159156 | + | 0.987253i | \(0.550877\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.521908 | + | 0.289925i | −0.521908 | + | 0.289925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.00187916 | + | 0.0178790i | −0.00187916 | + | 0.0178790i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.185994 | − | 0.284684i | −0.185994 | − | 0.284684i | ||||
\(478\) | 0.701363 | + | 0.249454i | 0.701363 | + | 0.249454i | ||||
\(479\) | 0 | 0 | −0.999939 | − | 0.0110229i | \(-0.996491\pi\) | ||||
0.999939 | + | 0.0110229i | \(0.00350877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.73665 | + | 2.15671i | 1.73665 | + | 2.15671i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.28409 | + | 1.04571i | 1.28409 | + | 1.04571i | 0.996114 | + | 0.0880708i | \(0.0280702\pi\) |
0.287976 | + | 0.957638i | \(0.407018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.92452 | + | 0.476082i | 1.92452 | + | 0.476082i | 0.993931 | + | 0.110008i | \(0.0350877\pi\) |
0.930586 | + | 0.366074i | \(0.119298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.47566 | − | 1.34349i | −1.47566 | − | 1.34349i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.40901 | + | 0.449244i | −1.40901 | + | 0.449244i | −0.909007 | − | 0.416782i | \(-0.863158\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.371197 | − | 0.928554i | \(-0.621053\pi\) | ||||
0.371197 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(504\) | −3.15335 | + | 1.36251i | −3.15335 | + | 1.36251i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.000593729 | − | 0.00396029i | −0.000593729 | − | 0.00396029i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.36267 | + | 0.871295i | 3.36267 | + | 0.871295i | ||||
\(509\) | 0 | 0 | 0.451533 | − | 0.892254i | \(-0.350877\pi\) | ||||
−0.451533 | + | 0.892254i | \(0.649123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.09859 | − | 2.50453i | −1.09859 | − | 2.50453i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.25733 | − | 1.67837i | −2.25733 | − | 1.67837i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.997814 | − | 0.0660906i | \(-0.0210526\pi\) | ||||
−0.997814 | + | 0.0660906i | \(0.978947\pi\) | |||||||
\(522\) | 3.71463 | − | 0.746871i | 3.71463 | − | 0.746871i | ||||
\(523\) | 0 | 0 | −0.180881 | − | 0.983505i | \(-0.557895\pi\) | ||||
0.180881 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.90323 | − | 1.35098i | 1.90323 | − | 1.35098i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.358200 | + | 0.896042i | −0.358200 | + | 0.896042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.986032 | − | 1.79828i | 0.986032 | − | 1.79828i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0110063 | 0.000607237i | −0.0110063 | 0.000607237i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.940755 | − | 1.76149i | −0.940755 | − | 1.76149i | −0.518970 | − | 0.854793i | \(-0.673684\pi\) |
−0.421786 | − | 0.906696i | \(-0.638596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.43142 | + | 0.754366i | −1.43142 | + | 0.754366i | −0.989750 | − | 0.142811i | \(-0.954386\pi\) |
−0.441671 | + | 0.897177i | \(0.645614\pi\) | |||||||
\(548\) | 0.928758 | − | 0.628941i | 0.928758 | − | 0.628941i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0213374 | − | 0.00164971i | −0.0213374 | − | 0.00164971i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.785728 | − | 1.02107i | 0.785728 | − | 1.02107i | ||||
\(554\) | 1.10218 | + | 0.728792i | 1.10218 | + | 0.728792i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.129401 | + | 0.625723i | −0.129401 | + | 0.625723i | 0.863256 | + | 0.504766i | \(0.168421\pi\) |
−0.992658 | + | 0.120958i | \(0.961404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.04935 | + | 0.386305i | 1.04935 | + | 0.386305i | ||||
\(563\) | 0 | 0 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.821778 | − | 0.569808i | −0.821778 | − | 0.569808i | ||||
\(568\) | 6.74887 | + | 1.20280i | 6.74887 | + | 1.20280i | ||||
\(569\) | −0.501605 | + | 1.60372i | −0.501605 | + | 1.60372i | 0.266796 | + | 0.963753i | \(0.414035\pi\) |
−0.768401 | + | 0.639969i | \(0.778947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.350638 | + | 0.936511i | 0.350638 | + | 0.936511i | ||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.153770 | − | 0.106622i | −0.153770 | − | 0.106622i | ||||
\(576\) | 2.33504 | − | 3.40756i | 2.33504 | − | 3.40756i | ||||
\(577\) | 0 | 0 | 0.461341 | − | 0.887223i | \(-0.347368\pi\) | ||||
−0.461341 | + | 0.887223i | \(0.652632\pi\) | |||||||
\(578\) | −1.93193 | + | 0.192295i | −1.93193 | + | 0.192295i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.00265787 | + | 0.00264326i | 0.00265787 | + | 0.00264326i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.350638 | − | 0.936511i | \(-0.614035\pi\) | ||||
0.350638 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.63352 | + | 0.435558i | 5.63352 | + | 0.435558i | ||||
\(593\) | 0 | 0 | 0.431754 | − | 0.901991i | \(-0.357895\pi\) | ||||
−0.431754 | + | 0.901991i | \(0.642105\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.27089 | − | 3.28370i | −1.27089 | − | 3.28370i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.08145 | + | 0.600754i | 1.08145 | + | 0.600754i | 0.922290 | − | 0.386499i | \(-0.126316\pi\) |
0.159156 | + | 0.987253i | \(0.449123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.471093 | − | 0.882084i | \(-0.656140\pi\) | ||||
0.471093 | + | 0.882084i | \(0.343860\pi\) | |||||||
\(602\) | −3.12316 | − | 0.521163i | −3.12316 | − | 0.521163i | ||||
\(603\) | 0.596123 | − | 0.0328890i | 0.596123 | − | 0.0328890i | ||||
\(604\) | 0.549618 | + | 0.181937i | 0.549618 | + | 0.181937i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.574329 | − | 0.818625i | \(-0.694737\pi\) | ||||
0.574329 | + | 0.818625i | \(0.305263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.385280 | + | 0.963783i | −0.385280 | + | 0.963783i | 0.601081 | + | 0.799188i | \(0.294737\pi\) |
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0308774 | − | 0.0219178i | 0.0308774 | − | 0.0219178i | ||||
\(617\) | −0.207884 | − | 0.691298i | −0.207884 | − | 0.691298i | −0.997024 | − | 0.0770854i | \(-0.975439\pi\) |
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.180881 | − | 0.983505i | \(-0.557895\pi\) | ||||
0.180881 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.739446 | + | 0.673216i | −0.739446 | + | 0.673216i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.809114 | + | 0.153423i | −0.809114 | + | 0.153423i | −0.574329 | − | 0.818625i | \(-0.694737\pi\) |
−0.234785 | + | 0.972047i | \(0.575439\pi\) | |||||||
\(632\) | −0.414073 | + | 4.40635i | −0.414073 | + | 4.40635i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.91518 | − | 0.496238i | −1.91518 | − | 0.496238i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0383402 | + | 0.0165662i | −0.0383402 | + | 0.0165662i | ||||
\(639\) | 0.740771 | + | 1.85305i | 0.740771 | + | 1.85305i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.28474 | + | 1.33529i | 1.28474 | + | 1.33529i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
0.371197 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.952745 | − | 0.303771i | \(-0.0982456\pi\) | ||||
−0.952745 | + | 0.303771i | \(0.901754\pi\) | |||||||
\(644\) | 0.516182 | − | 0.0456379i | 0.516182 | − | 0.0456379i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.889752 | − | 0.456444i | \(-0.150877\pi\) | ||||
−0.889752 | + | 0.456444i | \(0.849123\pi\) | |||||||
\(648\) | 3.43178 | + | 0.151414i | 3.43178 | + | 0.151414i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.56763 | − | 3.03856i | −3.56763 | − | 3.03856i | ||||
\(653\) | 0.492982 | + | 0.139402i | 0.492982 | + | 0.139402i | 0.509516 | − | 0.860461i | \(-0.329825\pi\) |
−0.0165339 | + | 0.999863i | \(0.505263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.28481 | − | 0.732375i | 1.28481 | − | 0.732375i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(662\) | 2.56483 | − | 2.91247i | 2.56483 | − | 2.91247i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.29771 | + | 2.49568i | 1.29771 | + | 2.49568i | ||||
\(667\) | −0.362499 | − | 0.0441713i | −0.362499 | − | 0.0441713i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.25319 | − | 0.696158i | 1.25319 | − | 0.696158i | 0.287976 | − | 0.957638i | \(-0.407018\pi\) |
0.965209 | + | 0.261480i | \(0.0842105\pi\) | |||||||
\(674\) | 3.67669 | + | 0.781504i | 3.67669 | + | 0.781504i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73686 | + | 2.15697i | −1.73686 | + | 2.15697i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.121330 | − | 0.246461i | −0.121330 | − | 0.246461i | 0.828009 | − | 0.560715i | \(-0.189474\pi\) |
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.0107005 | − | 1.94145i | 0.0107005 | − | 1.94145i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.86602 | − | 2.45824i | 5.86602 | − | 2.45824i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.115485 | − | 0.993309i | \(-0.463158\pi\) | ||||
−0.115485 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0101665 | + | 0.00426041i | 0.0101665 | + | 0.00426041i | ||||
\(694\) | −0.454309 | + | 3.03033i | −0.454309 | + | 3.03033i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.380378 | − | 2.74309i | 0.380378 | − | 2.74309i | ||||
\(701\) | 1.66037 | + | 0.258288i | 1.66037 | + | 0.258288i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.746821 | + | 0.665025i | \(0.231579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.0173674 | + | 0.0420925i | −0.0173674 | + | 0.0420925i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.163769 | − | 1.40862i | −0.163769 | − | 1.40862i | −0.782322 | − | 0.622874i | \(-0.785965\pi\) |
0.618553 | − | 0.785743i | \(-0.287719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.15276 | + | 0.575405i | −1.15276 | + | 0.575405i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.09948 | + | 0.543991i | −2.09948 | + | 0.543991i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.90383 | − | 0.0419791i | 1.90383 | − | 0.0419791i | ||||
\(719\) | 0 | 0 | 0.863256 | − | 0.504766i | \(-0.168421\pi\) | ||||
−0.863256 | + | 0.504766i | \(0.831579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.86228 | − | 0.548844i | 1.86228 | − | 0.548844i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.664114 | + | 1.83512i | −0.664114 | + | 1.83512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.999453 | − | 0.0330634i | \(-0.989474\pi\) | ||||
0.999453 | + | 0.0330634i | \(0.0105263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.490424 | + | 0.871484i | 0.490424 | + | 0.871484i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.846095 | − | 0.533032i | \(-0.178947\pi\) | ||||
−0.846095 | + | 0.533032i | \(0.821053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.615997 | + | 0.468638i | −0.615997 | + | 0.468638i | ||||
\(737\) | −0.00635214 | + | 0.00172083i | −0.00635214 | + | 0.00172083i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.25806 | − | 0.831861i | 1.25806 | − | 0.831861i | 0.266796 | − | 0.963753i | \(-0.414035\pi\) |
0.991264 | + | 0.131892i | \(0.0421053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.493061 | + | 0.439058i | −0.493061 | + | 0.439058i | ||||
\(743\) | 1.04669 | − | 1.64131i | 1.04669 | − | 1.64131i | 0.329907 | − | 0.944013i | \(-0.392982\pi\) |
0.716783 | − | 0.697297i | \(-0.245614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.486366 | − | 0.961085i | −0.486366 | − | 0.961085i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.442257 | + | 1.66891i | −0.442257 | + | 1.66891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.89152 | + | 0.0208513i | −1.89152 | + | 0.0208513i | −0.949339 | − | 0.314254i | \(-0.898246\pi\) |
−0.942181 | + | 0.335105i | \(0.891228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.14931 | + | 1.52810i | −1.14931 | + | 1.52810i | −0.340293 | + | 0.940319i | \(0.610526\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(758\) | −2.75296 | − | 2.45144i | −2.75296 | − | 2.45144i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.984487 | − | 0.175457i | \(-0.0561404\pi\) | ||||
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.748595 | + | 1.65674i | −0.748595 | + | 1.65674i | ||||
\(764\) | 3.66205 | − | 4.06712i | 3.66205 | − | 4.06712i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.716783 | − | 0.697297i | \(-0.245614\pi\) | ||||
−0.716783 | + | 0.697297i | \(0.754386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.38569 | + | 1.26947i | −5.38569 | + | 1.26947i | ||||
\(773\) | 0 | 0 | 0.319482 | − | 0.947592i | \(-0.396491\pi\) | ||||
−0.319482 | + | 0.947592i | \(0.603509\pi\) | |||||||
\(774\) | 2.58198 | + | 1.83278i | 2.58198 | + | 1.83278i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.35377 | + | 0.829648i | −3.35377 | + | 0.829648i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0122340 | − | 0.0182822i | −0.0122340 | − | 0.0182822i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.06054 | + | 3.31107i | 2.06054 | + | 3.31107i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.991264 | − | 0.131892i | \(-0.0421053\pi\) | ||||
−0.991264 | + | 0.131892i | \(0.957895\pi\) | |||||||
\(788\) | −5.07323 | − | 0.336028i | −5.07323 | − | 0.336028i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.62790 | + | 0.364821i | −1.62790 | + | 0.364821i | ||||
\(792\) | −0.0373492 | + | 0.00623247i | −0.0373492 | + | 0.00623247i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.180881 | − | 0.983505i | \(-0.442105\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.70322 | + | 3.76945i | 1.70322 | + | 3.76945i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.42658 | + | 0.767916i | 3.42658 | + | 0.767916i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0546983 | − | 0.0543977i | 0.0546983 | − | 0.0543977i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) |
0.731980 | + | 0.681326i | \(0.238596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(812\) | −1.83915 | − | 5.08206i | −1.83915 | − | 5.08206i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0197118 | − | 0.0239348i | −0.0197118 | − | 0.0239348i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.271873 | − | 0.459135i | 0.271873 | − | 0.459135i | −0.693336 | − | 0.720615i | \(-0.743860\pi\) |
0.965209 | + | 0.261480i | \(0.0842105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.17413 | − | 1.36328i | −1.17413 | − | 1.36328i | −0.917973 | − | 0.396642i | \(-0.870175\pi\) |
−0.256156 | − | 0.966635i | \(-0.582456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.21032 | + | 1.05407i | −1.21032 | + | 1.05407i | −0.213300 | + | 0.976987i | \(0.568421\pi\) |
−0.997024 | + | 0.0770854i | \(0.975439\pi\) | |||||||
\(828\) | −0.484287 | − | 0.184371i | −0.484287 | − | 0.184371i | ||||
\(829\) | 0 | 0 | −0.904357 | − | 0.426776i | \(-0.859649\pi\) | ||||
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.980380 | − | 0.197117i | \(-0.936842\pi\) | ||||
0.980380 | + | 0.197117i | \(0.0631579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.385787 | + | 2.78209i | 0.385787 | + | 2.78209i | ||||
\(842\) | 1.33772 | − | 3.04969i | 1.33772 | − | 3.04969i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.08326 | − | 1.65866i | 2.08326 | − | 1.65866i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.982374 | + | 0.186276i | 0.982374 | + | 0.186276i | ||||
\(848\) | 0.367886 | − | 1.27413i | 0.367886 | − | 1.27413i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0431483 | − | 0.267652i | −0.0431483 | − | 0.267652i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.391577 | − | 0.920146i | \(-0.628070\pi\) | ||||
0.391577 | + | 0.920146i | \(0.371930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.77043 | − | 5.66037i | −1.77043 | − | 5.66037i | ||||
\(857\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.956036 | − | 0.293250i | \(-0.905263\pi\) | ||||
0.956036 | + | 0.293250i | \(0.0947368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.555946 | − | 3.44857i | −0.555946 | − | 3.44857i | ||||
\(863\) | −1.19082 | − | 0.678797i | −1.19082 | − | 0.678797i | −0.234785 | − | 0.972047i | \(-0.575439\pi\) |
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0111105 | − | 0.00884605i | 0.0111105 | − | 0.00884605i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.857786 | − | 6.18590i | −0.857786 | − | 6.18590i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.156210 | + | 0.0536269i | −0.156210 | + | 0.0536269i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.480787 | − | 0.876837i | \(-0.659649\pi\) | ||||
0.480787 | + | 0.876837i | \(0.340351\pi\) | |||||||
\(882\) | −0.857494 | + | 1.74185i | −0.857494 | + | 1.74185i | ||||
\(883\) | 0.602771 | − | 1.72480i | 0.602771 | − | 1.72480i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) |
0.685350 | − | 0.728214i | \(-0.259649\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.73416 | − | 1.51028i | 1.73416 | − | 1.51028i | ||||
\(887\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12841 | − | 0.547800i | 1.12841 | − | 0.547800i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.00728513 | − | 0.00827255i | −0.00728513 | − | 0.00827255i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.49363 | − | 1.69602i | −3.49363 | − | 1.69602i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.667356 | + | 0.792363i | −0.667356 | + | 0.792363i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.54015 | + | 2.30156i | −1.54015 | + | 2.30156i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.06339 | − | 4.04106i | 4.06339 | − | 4.04106i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0152873 | − | 0.0529459i | −0.0152873 | − | 0.0529459i | 0.952745 | − | 0.303771i | \(-0.0982456\pi\) |
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.957107 | + | 0.214493i | 0.957107 | + | 0.214493i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.287976 | + | 0.957638i | \(0.407018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.671473 | + | 0.205964i | −0.671473 | + | 0.205964i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.00236730 | − | 0.0329830i | −0.00236730 | − | 0.0329830i | 0.996114 | − | 0.0880708i | \(-0.0280702\pi\) |
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.44568 | − | 0.0957554i | −1.44568 | − | 0.0957554i | ||||
\(926\) | 3.27907 | − | 0.436295i | 3.27907 | − | 0.436295i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.37038 | + | 4.95827i | 6.37038 | + | 4.95827i | ||||
\(929\) | 0 | 0 | −0.528360 | − | 0.849020i | \(-0.677193\pi\) | ||||
0.528360 | + | 0.849020i | \(0.322807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.87873 | + | 4.30190i | 2.87873 | + | 4.30190i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(938\) | −0.234742 | − | 1.13510i | −0.234742 | − | 1.13510i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.973327 | − | 0.229424i | \(-0.0736842\pi\) | ||||
−0.973327 | + | 0.229424i | \(0.926316\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0320399 | − | 0.0138439i | −0.0320399 | − | 0.0138439i | ||||
\(947\) | −0.0549447 | + | 1.99329i | −0.0549447 | + | 1.99329i | 0.0495838 | + | 0.998770i | \(0.484211\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.820894 | − | 0.376382i | −0.820894 | − | 0.376382i | −0.0385714 | − | 0.999256i | \(-0.512281\pi\) |
−0.782322 | + | 0.622874i | \(0.785965\pi\) | |||||||
\(954\) | 0.635302 | − | 0.179646i | 0.635302 | − | 0.179646i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.638241 | + | 0.848595i | −0.638241 | + | 0.848595i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.108062 | − | 0.390354i | 0.108062 | − | 0.390354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.945817 | + | 0.324699i | 0.945817 | + | 0.324699i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.12670 | − | 1.30820i | 1.12670 | − | 1.30820i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.883333 | − | 1.74551i | −0.883333 | − | 1.74551i | −0.627176 | − | 0.778877i | \(-0.715789\pi\) |
−0.256156 | − | 0.966635i | \(-0.582456\pi\) | |||||||
\(968\) | −3.19629 | + | 1.25735i | −3.19629 | + | 1.25735i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.746821 | − | 0.665025i | \(-0.231579\pi\) | ||||
−0.746821 | + | 0.665025i | \(0.768421\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.68186 | + | 1.77331i | −2.68186 | + | 1.77331i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.56050 | + | 1.18719i | −1.56050 | + | 1.18719i | −0.660898 | + | 0.750475i | \(0.729825\pi\) |
−0.899598 | + | 0.436719i | \(0.856140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.39696 | − | 1.16347i | 1.39696 | − | 1.16347i | ||||
\(982\) | −1.99753 | + | 3.29013i | −1.99753 | + | 3.29013i | ||||
\(983\) | 0 | 0 | −0.685350 | − | 0.728214i | \(-0.740351\pi\) | ||||
0.685350 | + | 0.728214i | \(0.259649\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.180733 | − | 0.245897i | −0.180733 | − | 0.245897i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.90678 | − | 0.561956i | 1.90678 | − | 0.561956i | 0.922290 | − | 0.386499i | \(-0.126316\pi\) |
0.984487 | − | 0.175457i | \(-0.0561404\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.34466 | − | 1.95570i | 3.34466 | − | 1.95570i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.968033 | − | 0.250825i | \(-0.0807018\pi\) | ||||
−0.968033 | + | 0.250825i | \(0.919298\pi\) | |||||||
\(998\) | −0.0158249 | − | 2.87119i | −0.0158249 | − | 2.87119i | ||||
\(999\) | 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 | 3997.1.cz.a.237.1 | ✓ | 144 | |
7.6 | odd | 2 | CM | 3997.1.cz.a.237.1 | ✓ | 144 | |
571.518 | even | 285 | inner | 3997.1.cz.a.3373.1 | yes | 144 | |
3997.3373 | odd | 570 | inner | 3997.1.cz.a.3373.1 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3997.1.cz.a.237.1 | ✓ | 144 | 1.1 | even | 1 | trivial | |
3997.1.cz.a.237.1 | ✓ | 144 | 7.6 | odd | 2 | CM | |
3997.1.cz.a.3373.1 | yes | 144 | 571.518 | even | 285 | inner | |
3997.1.cz.a.3373.1 | yes | 144 | 3997.3373 | odd | 570 | inner |