Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,1,Mod(13,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(64))
chi = DirichletCharacter(H, H._module([0, 47, 32]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.bt (of order \(64\), degree \(32\), 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: | \(0.894324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Coefficient field: | \(\Q(\zeta_{64})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{32} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{64}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{64} - \cdots)\) |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.0980171 - 0.995185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.349 |
Dual form | 1792.1.bt.a.1525.1 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{43}{64}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.290285 | + | 0.956940i | −0.290285 | + | 0.956940i | ||||
\(3\) | 0 | 0 | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) | ||||
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(4\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(5\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(8\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(9\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.276306 | + | 0.0988640i | 0.276306 | + | 0.0988640i | 0.471397 | − | 0.881921i | \(-0.343750\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.242980 | − | 0.970031i | \(-0.421875\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(14\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(17\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(18\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(19\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.174814 | + | 0.235710i | −0.174814 | + | 0.235710i | ||||
\(23\) | −0.0569057 | − | 0.187593i | −0.0569057 | − | 0.187593i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | ||||
\(29\) | 0.733452 | − | 1.55075i | 0.733452 | − | 1.55075i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(32\) | −0.995185 | + | 0.0980171i | −0.995185 | + | 0.0980171i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.773010 | + | 0.634393i | 0.773010 | + | 0.634393i | ||||
\(37\) | 1.51251 | − | 1.12175i | 1.51251 | − | 1.12175i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.956940 | − | 0.290285i | \(-0.0937500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.80580 | − | 0.0887133i | 1.80580 | − | 0.0887133i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(44\) | −0.174814 | − | 0.235710i | −0.174814 | − | 0.235710i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.196034 | 0.196034 | ||||||||
\(47\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.195090 | − | 0.980785i | −0.195090 | − | 0.980785i | ||||
\(50\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.574257 | + | 1.21416i | 0.574257 | + | 1.21416i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 1.00000i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.27107 | + | 1.15203i | 1.27107 | + | 1.15203i | ||||
\(59\) | 0 | 0 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(64\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.34150 | − | 1.48012i | −1.34150 | − | 1.48012i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.634393 | − | 0.773010i | \(-0.718750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.192268 | + | 1.95213i | 0.192268 | + | 1.95213i | 0.290285 | + | 0.956940i | \(0.406250\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(72\) | −0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | ||||
\(73\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(74\) | 0.634393 | + | 1.77301i | 0.634393 | + | 1.77301i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.251710 | − | 0.150869i | 0.251710 | − | 0.150869i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.72995 | + | 0.344109i | −1.72995 | + | 0.344109i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.980785 | + | 0.195090i | 0.980785 | + | 0.195090i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.439303 | + | 1.75380i | −0.439303 | + | 1.75380i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.276306 | − | 0.0988640i | 0.276306 | − | 0.0988640i | ||||
\(89\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0569057 | + | 0.187593i | −0.0569057 | + | 0.187593i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(98\) | 0.995185 | + | 0.0980171i | 0.995185 | + | 0.0980171i | ||||
\(99\) | −0.265286 | − | 0.125471i | −0.265286 | − | 0.125471i | ||||
\(100\) | −0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | ||||
\(101\) | 0 | 0 | −0.989177 | − | 0.146730i | \(-0.953125\pi\) | ||||
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.32858 | + | 0.197076i | −1.32858 | + | 0.197076i | ||||
\(107\) | −0.995185 | + | 1.09802i | −0.995185 | + | 1.09802i | 1.00000i | \(0.5\pi\) | ||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.58903 | − | 0.235710i | 1.58903 | − | 0.235710i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.956940 | + | 0.290285i | 0.956940 | + | 0.290285i | ||||
\(113\) | 0.704900 | − | 1.05496i | 0.704900 | − | 1.05496i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.47140 | + | 0.881921i | −1.47140 | + | 0.881921i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.706439 | − | 0.579760i | −0.706439 | − | 0.579760i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(127\) | 1.11114i | 1.11114i | 0.831470 | + | 0.555570i | \(0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(128\) | 0.881921 | + | 0.471397i | 0.881921 | + | 0.471397i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) | ||||
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.80580 | − | 0.854080i | 1.80580 | − | 0.854080i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0924099 | + | 0.938254i | −0.0924099 | + | 0.938254i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.92388 | − | 0.382683i | −1.92388 | − | 0.382683i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.290285 | − | 0.956940i | −0.290285 | − | 0.956940i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.88082 | + | 0.0923988i | −1.88082 | + | 0.0923988i | ||||
\(149\) | −0.0659037 | + | 0.0727135i | −0.0659037 | + | 0.0727135i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.555570 | − | 0.168530i | 0.555570 | − | 0.168530i | − | 1.00000i | \(-0.5\pi\) | |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0713052 | + | 0.284666i | 0.0713052 | + | 0.284666i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.903989 | − | 0.427555i | \(-0.859375\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(158\) | 0.172887 | − | 1.75535i | 0.172887 | − | 1.75535i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.181112 | − | 0.0750191i | −0.181112 | − | 0.0750191i | ||||
\(162\) | −0.471397 | + | 0.881921i | −0.471397 | + | 0.881921i | ||||
\(163\) | −0.457553 | + | 0.163715i | −0.457553 | + | 0.163715i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.881921 | − | 0.471397i | −0.881921 | − | 0.471397i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.55075 | − | 0.929487i | −1.55075 | − | 0.929487i | ||||
\(173\) | 0 | 0 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(176\) | 0.0143994 | + | 0.293107i | 0.0143994 | + | 0.293107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.577920 | + | 0.346392i | −0.577920 | + | 0.346392i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.903989 | − | 0.427555i | \(-0.140625\pi\) | ||||
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.162997 | − | 0.108911i | −0.162997 | − | 0.108911i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.35332 | + | 1.35332i | 1.35332 | + | 1.35332i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.40740 | + | 1.40740i | −1.40740 | + | 1.40740i | −0.634393 | + | 0.773010i | \(0.718750\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(197\) | −0.207775 | − | 0.829484i | −0.207775 | − | 0.829484i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.773010 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(198\) | 0.197076 | − | 0.217440i | 0.197076 | − | 0.217440i | ||||
\(199\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(200\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.733452 | − | 1.55075i | −0.733452 | − | 1.55075i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0382444 | + | 0.192268i | 0.0382444 | + | 0.192268i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.612501 | − | 0.825862i | 0.612501 | − | 0.825862i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(212\) | 0.197076 | − | 1.32858i | 0.197076 | − | 1.32858i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.761850 | − | 1.27107i | −0.761850 | − | 1.27107i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.235710 | + | 1.58903i | −0.235710 | + | 1.58903i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(224\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(225\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(226\) | 0.804910 | + | 0.980785i | 0.804910 | + | 0.980785i | ||||
\(227\) | 0 | 0 | 0.427555 | − | 0.903989i | \(-0.359375\pi\) | ||||
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.416822 | − | 1.66405i | −0.416822 | − | 1.66405i | ||||
\(233\) | −0.512016 | − | 1.68789i | −0.512016 | − | 1.68789i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.195090 | − | 0.980785i | \(-0.437500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.38268 | + | 0.923880i | −1.38268 | + | 0.923880i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(242\) | 0.759864 | − | 0.507725i | 0.759864 | − | 0.507725i | ||||
\(243\) | 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 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(252\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(253\) | 0.00282279 | − | 0.0574591i | 0.00282279 | − | 0.0574591i | ||||
\(254\) | −1.06330 | − | 0.322547i | −1.06330 | − | 0.322547i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0923988 | − | 1.88082i | 0.0923988 | − | 1.88082i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.881921 | + | 1.47140i | −0.881921 | + | 1.47140i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.17221 | + | 1.42834i | −1.17221 | + | 1.42834i | −0.290285 | + | 0.956940i | \(0.593750\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.293107 | + | 1.97597i | 0.293107 | + | 1.97597i | ||||
\(269\) | 0 | 0 | 0.242980 | − | 0.970031i | \(-0.421875\pi\) | ||||
−0.242980 | + | 0.970031i | \(0.578125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.871028 | − | 0.360791i | −0.871028 | − | 0.360791i | ||||
\(275\) | −0.0430597 | − | 0.290285i | −0.0430597 | − | 0.290285i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.882768 | + | 0.800094i | 0.882768 | + | 0.800094i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.273678 | + | 0.512016i | 0.273678 | + | 0.512016i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(284\) | 0.924678 | − | 1.72995i | 0.924678 | − | 1.72995i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 1.00000 | ||||||||
\(289\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.803208 | − | 0.595699i | \(-0.203125\pi\) | ||||
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.457553 | − | 1.82665i | 0.457553 | − | 1.82665i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0504517 | − | 0.0841735i | −0.0504517 | − | 0.0841735i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07701 | − | 1.45218i | 1.07701 | − | 1.45218i | ||||
\(302\) | 0.580569i | 0.580569i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(308\) | −0.293107 | − | 0.0143994i | −0.293107 | − | 0.0143994i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.62958 | + | 0.674993i | 1.62958 | + | 0.674993i | ||||
\(317\) | −0.360073 | + | 0.326351i | −0.360073 | + | 0.326351i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.355971 | − | 0.355971i | 0.355971 | − | 0.355971i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.124363 | − | 0.151537i | 0.124363 | − | 0.151537i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0238449 | − | 0.485375i | −0.0238449 | − | 0.485375i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.75380 | − | 0.829484i | 1.75380 | − | 0.829484i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.61518 | + | 0.968101i | −1.61518 | + | 0.968101i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.51631 | − | 0.301614i | −1.51631 | − | 0.301614i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(338\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.881921 | − | 0.471397i | −0.881921 | − | 0.471397i | ||||
\(344\) | 1.33962 | − | 1.21416i | 1.33962 | − | 1.21416i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.15569 | + | 1.55827i | 1.15569 | + | 1.55827i | 0.773010 | + | 0.634393i | \(0.218750\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(350\) | 0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.284666 | − | 0.0713052i | −0.284666 | − | 0.0713052i | ||||
\(353\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.163715 | − | 0.653587i | −0.163715 | − | 0.653587i | ||||
\(359\) | 1.36347 | − | 0.728789i | 1.36347 | − | 0.728789i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(368\) | 0.151537 | − | 0.124363i | 0.151537 | − | 0.124363i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30287 | + | 0.326351i | 1.30287 | + | 0.326351i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.666487 | + | 1.86271i | −0.666487 | + | 1.86271i | −0.195090 | + | 0.980785i | \(0.562500\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.15203 | − | 0.690501i | −1.15203 | − | 0.690501i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.68789 | + | 0.902197i | −1.68789 | + | 0.902197i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.938254 | − | 1.75535i | −0.938254 | − | 1.75535i | ||||
\(387\) | −1.80580 | − | 0.0887133i | −1.80580 | − | 0.0887133i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.55075 | + | 0.929487i | 1.55075 | + | 0.929487i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.773010 | − | 0.634393i | −0.773010 | − | 0.634393i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.854080 | + | 0.0419583i | 0.854080 | + | 0.0419583i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.150869 | + | 0.251710i | 0.150869 | + | 0.251710i | ||||
\(397\) | 0 | 0 | −0.970031 | − | 0.242980i | \(-0.921875\pi\) | ||||
0.970031 | + | 0.242980i | \(0.0781250\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(401\) | −0.858923 | − | 1.28547i | −0.858923 | − | 1.28547i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.0980171 | − | 0.995185i | \(-0.468750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.69689 | − | 0.251710i | 1.69689 | − | 0.251710i | ||||
\(407\) | 0.528818 | − | 0.160415i | 0.528818 | − | 0.160415i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.195090 | − | 0.0192147i | −0.195090 | − | 0.0192147i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.289486 | − | 0.390327i | −0.289486 | − | 0.390327i | 0.634393 | − | 0.773010i | \(-0.281250\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(422\) | 0.612501 | + | 0.825862i | 0.612501 | + | 0.825862i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.21416 | + | 0.574257i | 1.21416 | + | 0.574257i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.43749 | − | 0.360073i | 1.43749 | − | 0.360073i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.750661 | + | 0.149316i | 0.750661 | + | 0.149316i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.45218 | − | 0.686831i | −1.45218 | − | 0.686831i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0980171 | + | 0.995185i | 0.0980171 | + | 0.995185i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.82665 | + | 0.457553i | −1.82665 | + | 0.457553i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | ||||
\(449\) | −0.275899 | + | 0.275899i | −0.275899 | + | 0.275899i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(450\) | −0.995185 | + | 0.0980171i | −0.995185 | + | 0.0980171i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.17221 | + | 0.485544i | −1.17221 | + | 0.485544i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28547 | + | 1.05496i | −1.28547 | + | 1.05496i | −0.290285 | + | 0.956940i | \(0.593750\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.301614 | + | 1.51631i | 0.301614 | + | 1.51631i | 0.773010 | + | 0.634393i | \(0.218750\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(464\) | 1.71339 | + | 0.0841735i | 1.71339 | + | 0.0841735i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.76384 | 1.76384 | ||||||||
\(467\) | 0 | 0 | 0.595699 | − | 0.803208i | \(-0.296875\pi\) | ||||
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.99518 | + | 0.0980171i | −1.99518 | + | 0.0980171i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.507725 | + | 0.154017i | 0.507725 | + | 0.154017i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.452483 | − | 1.26460i | −0.452483 | − | 1.26460i | ||||
\(478\) | −0.482726 | − | 1.59133i | −0.482726 | − | 1.59133i | ||||
\(479\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.265286 | + | 0.874529i | 0.265286 | + | 0.874529i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.444430 | + | 0.831470i | 0.444430 | + | 0.831470i | 1.00000 | \(0\) | ||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.0727135 | + | 0.0659037i | 0.0727135 | + | 0.0659037i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.63099 | + | 1.08979i | 1.63099 | + | 1.08979i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0238449 | + | 0.0951944i | −0.0238449 | + | 0.0951944i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(504\) | −0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.0541655 | + | 0.0193807i | 0.0541655 | + | 0.0193807i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.617317 | − | 0.923880i | 0.617317 | − | 0.923880i | ||||
\(509\) | 0 | 0 | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) | ||||
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.77301 | + | 0.634393i | 1.77301 | + | 0.634393i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(522\) | −1.15203 | − | 1.27107i | −1.15203 | − | 1.27107i | ||||
\(523\) | 0 | 0 | −0.941544 | − | 0.336890i | \(-0.890625\pi\) | ||||
0.941544 | + | 0.336890i | \(0.109375\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.02656 | − | 1.53636i | −1.02656 | − | 1.53636i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.799517 | − | 0.534220i | 0.799517 | − | 0.534220i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.97597 | − | 0.293107i | −1.97597 | − | 0.293107i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0430597 | − | 0.290285i | 0.0430597 | − | 0.290285i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.633595 | − | 1.33962i | 0.633595 | − | 1.33962i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.346392 | + | 0.968101i | 0.346392 | + | 0.968101i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(548\) | 0.598102 | − | 0.728789i | 0.598102 | − | 0.728789i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.290285 | + | 0.0430597i | 0.290285 | + | 0.0430597i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.831470 | + | 1.55557i | −0.831470 | + | 1.55557i | ||||
\(554\) | −1.02190 | + | 0.612501i | −1.02190 | + | 0.612501i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.709715 | + | 0.956940i | −0.709715 | + | 0.956940i | 0.290285 | + | 0.956940i | \(0.406250\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.569414 | + | 0.113263i | −0.569414 | + | 0.113263i | ||||
\(563\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(568\) | 1.38704 | + | 1.38704i | 1.38704 | + | 1.38704i | ||||
\(569\) | 1.10579 | − | 0.108911i | 1.10579 | − | 0.108911i | 0.471397 | − | 0.881921i | \(-0.343750\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.416822 | + | 1.66405i | 0.416822 | + | 1.66405i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.138617 | + | 0.138617i | −0.138617 | + | 0.138617i | ||||
\(576\) | −0.290285 | + | 0.956940i | −0.290285 | + | 0.956940i | ||||
\(577\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | 0.773010 | + | 0.634393i | 0.773010 | + | 0.634393i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0386337 | + | 0.392255i | 0.0386337 | + | 0.392255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.903989 | − | 0.427555i | \(-0.140625\pi\) | ||||
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.61518 | + | 0.968101i | 1.61518 | + | 0.968101i | ||||
\(593\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0951944 | − | 0.0238449i | 0.0951944 | − | 0.0238449i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.62958 | − | 0.871028i | −1.62958 | − | 0.871028i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.634393 | − | 0.773010i | \(-0.718750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(602\) | 1.07701 | + | 1.45218i | 1.07701 | + | 1.45218i | ||||
\(603\) | 1.18996 | + | 1.60448i | 1.18996 | + | 1.60448i | ||||
\(604\) | −0.555570 | − | 0.168530i | −0.555570 | − | 0.168530i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.91906 | + | 0.284666i | 1.91906 | + | 0.284666i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0988640 | − | 0.276306i | 0.0988640 | − | 0.276306i | ||||
\(617\) | 1.59133 | − | 0.482726i | 1.59133 | − | 0.482726i | 0.634393 | − | 0.773010i | \(-0.281250\pi\) |
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.671559 | − | 0.740951i | \(-0.265625\pi\) | ||||
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0382444 | + | 0.388302i | −0.0382444 | + | 0.388302i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(632\) | −1.11897 | + | 1.36347i | −1.11897 | + | 1.36347i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.207775 | − | 0.439303i | −0.207775 | − | 0.439303i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.237310 | + | 0.443977i | 0.237310 | + | 0.443977i | ||||
\(639\) | − | 1.96157i | − | 1.96157i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.99037i | 1.99037i | 0.0980171 | + | 0.995185i | \(0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) | ||||
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(644\) | 0.108911 | + | 0.162997i | 0.108911 | + | 0.162997i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(648\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.471397 | + | 0.118079i | 0.471397 | + | 0.118079i | ||||
\(653\) | 1.91906 | + | 0.480701i | 1.91906 | + | 0.480701i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.58903 | − | 0.235710i | 1.58903 | − | 0.235710i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.671559 | − | 0.740951i | \(-0.265625\pi\) | ||||
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(662\) | 0.284666 | + | 1.91906i | 0.284666 | + | 1.91906i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.457553 | − | 1.82665i | −0.457553 | − | 1.82665i | ||||
\(667\) | −0.332649 | − | 0.0493438i | −0.332649 | − | 0.0493438i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.360480 | + | 0.149316i | 0.360480 | + | 0.149316i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(674\) | 0.728789 | − | 1.36347i | 0.728789 | − | 1.36347i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | ||||
\(677\) | 0 | 0 | −0.595699 | − | 0.803208i | \(-0.703125\pi\) | ||||
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0330608 | + | 0.672968i | 0.0330608 | + | 0.672968i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.773010 | + | 1.63439i | 0.773010 | + | 1.63439i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.857729 | − | 0.514103i | \(-0.171875\pi\) | ||||
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.265286 | + | 0.125471i | −0.265286 | + | 0.125471i | ||||
\(694\) | −1.82665 | + | 0.653587i | −1.82665 | + | 0.653587i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(701\) | −0.574257 | − | 0.633595i | −0.574257 | − | 0.633595i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.150869 | − | 0.251710i | 0.150869 | − | 0.251710i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.480701 | + | 1.91906i | 0.480701 | + | 1.91906i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75535 | − | 0.172887i | 1.75535 | − | 0.172887i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.672968 | + | 0.0330608i | 0.672968 | + | 0.0330608i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.301614 | + | 1.51631i | 0.301614 | + | 1.51631i | ||||
\(719\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.00000i | − | 1.00000i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.71339 | + | 0.0841735i | −1.71339 | + | 0.0841735i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0750191 | + | 0.181112i | 0.0750191 | + | 0.181112i | ||||
\(737\) | −0.224335 | − | 0.541592i | −0.224335 | − | 0.541592i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.509389 | − | 1.07701i | 0.509389 | − | 1.07701i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.690501 | + | 1.15203i | −0.690501 | + | 1.15203i | ||||
\(743\) | −0.902197 | − | 1.68789i | −0.902197 | − | 1.68789i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.58903 | − | 1.17850i | −1.58903 | − | 1.17850i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.217440 | + | 1.46586i | 0.217440 | + | 1.46586i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.324423 | − | 0.216773i | 0.324423 | − | 0.216773i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.39528 | + | 0.499238i | 1.39528 | + | 0.499238i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(758\) | 0.995185 | − | 0.901983i | 0.995185 | − | 0.901983i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.634393 | − | 0.773010i | \(-0.281250\pi\) | ||||
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.825862 | − | 1.37787i | 0.825862 | − | 1.37787i | ||||
\(764\) | −0.373380 | − | 1.87711i | −0.373380 | − | 1.87711i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.95213 | − | 0.388302i | 1.95213 | − | 0.388302i | ||||
\(773\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(774\) | 0.609090 | − | 1.70229i | 0.609090 | − | 1.70229i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.33962 | + | 1.21416i | −1.33962 | + | 1.21416i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.139870 | + | 0.558393i | −0.139870 | + | 0.558393i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(788\) | −0.288078 | + | 0.805124i | −0.288078 | + | 0.805124i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.368309 | − | 1.21415i | −0.368309 | − | 1.21415i | ||||
\(792\) | −0.284666 | + | 0.0713052i | −0.284666 | + | 0.0713052i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.427555 | − | 0.903989i | \(-0.359375\pi\) | ||||
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.47945 | − | 0.448786i | 1.47945 | − | 0.448786i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.783904 | − | 1.46658i | 0.783904 | − | 1.46658i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | ||||
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(812\) | −0.251710 | + | 1.69689i | −0.251710 | + | 1.69689i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.552613i | 0.552613i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.829484 | − | 1.75380i | −0.829484 | − | 1.75380i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.195090 | − | 0.980785i | \(-0.562500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.42834 | − | 1.17221i | 1.42834 | − | 1.17221i | 0.471397 | − | 0.881921i | \(-0.343750\pi\) |
0.956940 | − | 0.290285i | \(-0.0937500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.207775 | + | 0.829484i | 0.207775 | + | 0.829484i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(828\) | 0.0750191 | − | 0.181112i | 0.0750191 | − | 0.181112i | ||||
\(829\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(830\) | 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 | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.23250 | − | 1.50180i | −1.23250 | − | 1.50180i | ||||
\(842\) | 0.457553 | − | 0.163715i | 0.457553 | − | 0.163715i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.968101 | + | 0.346392i | −0.968101 | + | 0.346392i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.896321 | + | 0.178289i | −0.896321 | + | 0.178289i | ||||
\(848\) | −0.901983 | + | 0.995185i | −0.901983 | + | 0.995185i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.296504 | − | 0.219902i | −0.296504 | − | 0.219902i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) | ||||
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0727135 | + | 1.48012i | −0.0727135 | + | 1.48012i | ||||
\(857\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.595699 | − | 0.803208i | \(-0.703125\pi\) | ||||
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.360791 | + | 0.674993i | −0.360791 | + | 0.674993i | ||||
\(863\) | −0.536376 | − | 0.222174i | −0.536376 | − | 0.222174i | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.512016 | − | 0.0759505i | −0.512016 | − | 0.0759505i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.07880 | − | 1.19028i | 1.07880 | − | 1.19028i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.845855 | − | 0.125471i | 0.845855 | − | 0.125471i | 0.290285 | − | 0.956940i | \(-0.406250\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(882\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(883\) | −0.471397 | − | 0.118079i | −0.471397 | − | 0.118079i | − | 1.00000i | \(-0.5\pi\) | |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0923988 | − | 1.88082i | 0.0923988 | − | 1.88082i | ||||
\(887\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.858923 | + | 0.704900i | 0.858923 | + | 0.704900i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.251710 | + | 0.150869i | 0.251710 | + | 0.150869i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.183930 | − | 0.344109i | −0.183930 | − | 0.344109i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.124363 | − | 1.26268i | −0.124363 | − | 1.26268i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.541185 | − | 1.51251i | 0.541185 | − | 1.51251i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.923880 | + | 1.38268i | −0.923880 | + | 1.38268i | 1.00000i | \(0.5\pi\) | ||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.636379 | − | 1.53636i | −0.636379 | − | 1.53636i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.06330 | − | 0.322547i | 1.06330 | − | 0.322547i | 0.290285 | − | 0.956940i | \(-0.406250\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.70229 | − | 0.805124i | −1.70229 | − | 0.805124i | ||||
\(926\) | −1.53858 | − | 0.151537i | −1.53858 | − | 0.151537i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.577920 | + | 1.61518i | −0.577920 | + | 1.61518i | ||||
\(929\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.512016 | + | 1.68789i | −0.512016 | + | 1.68789i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(938\) | 0.485375 | − | 1.93773i | 0.485375 | − | 1.93773i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.294770 | + | 0.441154i | −0.294770 | + | 0.441154i | ||||
\(947\) | −1.02190 | + | 0.612501i | −1.02190 | + | 0.612501i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.187593 | + | 1.90466i | 0.187593 | + | 1.90466i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(954\) | 1.34150 | − | 0.0659037i | 1.34150 | − | 0.0659037i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.66294 | 1.66294 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.666656 | + | 0.666656i | 0.666656 | + | 0.666656i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.09802 | − | 0.995185i | 1.09802 | − | 0.995185i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.577774 | + | 0.0569057i | −0.577774 | + | 0.0569057i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(968\) | −0.913881 | −0.913881 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.427555 | − | 0.903989i | \(-0.640625\pi\) | ||||
0.427555 | + | 0.903989i | \(0.359375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.924678 | + | 0.183930i | −0.924678 | + | 0.183930i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.382683 | + | 1.92388i | −0.382683 | + | 1.92388i | 1.00000i | \(0.5\pi\) | ||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.60448 | + | 0.0788231i | −1.60448 | + | 0.0788231i | ||||
\(982\) | −0.0841735 | + | 0.0504517i | −0.0841735 | + | 0.0504517i | ||||
\(983\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.119402 | − | 0.333707i | −0.119402 | − | 0.333707i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.591637 | − | 1.42834i | 0.591637 | − | 1.42834i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.51631 | + | 1.24441i | −1.51631 | + | 1.24441i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(998\) | −0.0841735 | − | 0.0504517i | −0.0841735 | − | 0.0504517i | ||||
\(999\) | 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 | 1792.1.bt.a.349.1 | ✓ | 32 | |
7.6 | odd | 2 | CM | 1792.1.bt.a.349.1 | ✓ | 32 | |
256.245 | even | 64 | inner | 1792.1.bt.a.1525.1 | yes | 32 | |
1792.1525 | odd | 64 | inner | 1792.1.bt.a.1525.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.1.bt.a.349.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1792.1.bt.a.349.1 | ✓ | 32 | 7.6 | odd | 2 | CM | |
1792.1.bt.a.1525.1 | yes | 32 | 256.245 | even | 64 | inner | |
1792.1.bt.a.1525.1 | yes | 32 | 1792.1525 | odd | 64 | inner |