Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3840,1,Mod(29,3840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3840, base_ring=CyclotomicField(64))
chi = DirichletCharacter(H, H._module([0, 59, 32, 32]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3840.29");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3840 = 2^{8} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3840.dy (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: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{64})\) |
Coefficient field: | \(\Q(\zeta_{128})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} + 1 \) |
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 | 629.2 | ||
Root | \(-0.998795 + 0.0490677i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3840.629 |
Dual form | 3840.1.dy.a.989.2 |
$q$-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 \(\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(1537\) | \(2561\) | \(2821\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{53}{64}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.146730 | − | 0.989177i | 0.146730 | − | 0.989177i | ||||
\(3\) | 0.998795 | − | 0.0490677i | 0.998795 | − | 0.0490677i | ||||
\(4\) | −0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | ||||
\(5\) | 0.857729 | − | 0.514103i | 0.857729 | − | 0.514103i | ||||
\(6\) | 0.0980171 | − | 0.995185i | 0.0980171 | − | 0.995185i | ||||
\(7\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(8\) | −0.427555 | + | 0.903989i | −0.427555 | + | 0.903989i | ||||
\(9\) | 0.995185 | − | 0.0980171i | 0.995185 | − | 0.0980171i | ||||
\(10\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(11\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(12\) | −0.970031 | − | 0.242980i | −0.970031 | − | 0.242980i | ||||
\(13\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(16\) | 0.831470 | + | 0.555570i | 0.831470 | + | 0.555570i | ||||
\(17\) | −0.404061 | − | 0.269985i | −0.404061 | − | 0.269985i | 0.336890 | − | 0.941544i | \(-0.390625\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(18\) | 0.0490677 | − | 0.998795i | 0.0490677 | − | 0.998795i | ||||
\(19\) | −0.845855 | − | 0.125471i | −0.845855 | − | 0.125471i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(20\) | −0.970031 | + | 0.242980i | −0.970031 | + | 0.242980i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.345845 | − | 1.14010i | 0.345845 | − | 1.14010i | −0.595699 | − | 0.803208i | \(-0.703125\pi\) |
0.941544 | − | 0.336890i | \(-0.109375\pi\) | |||||||
\(24\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(25\) | 0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.989177 | − | 0.146730i | 0.989177 | − | 0.146730i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.903989 | − | 0.427555i | \(-0.140625\pi\) | ||||
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(30\) | −0.427555 | − | 0.903989i | −0.427555 | − | 0.903989i | ||||
\(31\) | −0.222174 | + | 0.536376i | −0.222174 | + | 0.536376i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(32\) | 0.671559 | − | 0.740951i | 0.671559 | − | 0.740951i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.326351 | + | 0.360073i | −0.326351 | + | 0.360073i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(37\) | 0 | 0 | 0.595699 | − | 0.803208i | \(-0.296875\pi\) | ||||
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(38\) | −0.248225 | + | 0.818289i | −0.248225 | + | 0.818289i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0980171 | + | 0.995185i | 0.0980171 | + | 0.995185i | ||||
\(41\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) | ||||
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.803208 | − | 0.595699i | 0.803208 | − | 0.595699i | ||||
\(46\) | −1.07701 | − | 0.509389i | −1.07701 | − | 0.509389i | ||||
\(47\) | −0.262029 | − | 1.31731i | −0.262029 | − | 1.31731i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
0.595699 | − | 0.803208i | \(-0.296875\pi\) | |||||||
\(48\) | 0.857729 | + | 0.514103i | 0.857729 | + | 0.514103i | ||||
\(49\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(50\) | −0.803208 | − | 0.595699i | −0.803208 | − | 0.595699i | ||||
\(51\) | −0.416822 | − | 0.249834i | −0.416822 | − | 0.249834i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.39759 | + | 0.661009i | 1.39759 | + | 0.661009i | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) |
0.427555 | + | 0.903989i | \(0.359375\pi\) | |||||||
\(54\) | − | 1.00000i | − | 1.00000i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.850993 | − | 0.0838155i | −0.850993 | − | 0.0838155i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.970031 | − | 0.242980i | \(-0.921875\pi\) | ||||
0.970031 | + | 0.242980i | \(0.0781250\pi\) | |||||||
\(60\) | −0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | ||||
\(61\) | 0.452483 | − | 0.499238i | 0.452483 | − | 0.499238i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(62\) | 0.497971 | + | 0.298472i | 0.497971 | + | 0.298472i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.740951 | − | 0.671559i | \(-0.765625\pi\) | ||||
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(68\) | 0.308290 | + | 0.375652i | 0.308290 | + | 0.375652i | ||||
\(69\) | 0.289486 | − | 1.15569i | 0.289486 | − | 1.15569i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(72\) | −0.336890 | + | 0.941544i | −0.336890 | + | 0.941544i | ||||
\(73\) | 0 | 0 | 0.634393 | − | 0.773010i | \(-0.281250\pi\) | ||||
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.427555 | − | 0.903989i | 0.427555 | − | 0.903989i | ||||
\(76\) | 0.773010 | + | 0.365607i | 0.773010 | + | 0.365607i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.63099 | − | 0.324423i | −1.63099 | − | 0.324423i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(80\) | 0.998795 | + | 0.0490677i | 0.998795 | + | 0.0490677i | ||||
\(81\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.18566 | + | 1.59868i | 1.18566 | + | 1.59868i | 0.671559 | + | 0.740951i | \(0.265625\pi\) |
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.485375 | − | 0.0238449i | −0.485375 | − | 0.0238449i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(90\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.661906 | + | 0.990612i | −0.661906 | + | 0.990612i | ||||
\(93\) | −0.195588 | + | 0.546632i | −0.195588 | + | 0.546632i | ||||
\(94\) | −1.34150 | + | 0.0659037i | −1.34150 | + | 0.0659037i | ||||
\(95\) | −0.790019 | + | 0.327237i | −0.790019 | + | 0.327237i | ||||
\(96\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(97\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(98\) | 0.941544 | + | 0.336890i | 0.941544 | + | 0.336890i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(101\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(102\) | −0.308290 | + | 0.375652i | −0.308290 | + | 0.375652i | ||||
\(103\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.858923 | − | 1.28547i | 0.858923 | − | 1.28547i | ||||
\(107\) | −0.698564 | + | 0.633141i | −0.698564 | + | 0.633141i | −0.941544 | − | 0.336890i | \(-0.890625\pi\) |
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(108\) | −0.989177 | − | 0.146730i | −0.989177 | − | 0.146730i | ||||
\(109\) | 0.0143994 | − | 0.0970732i | 0.0143994 | − | 0.0970732i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.823301 | + | 1.23216i | 0.823301 | + | 1.23216i | 0.970031 | + | 0.242980i | \(0.0781250\pi\) |
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(114\) | −0.207775 | + | 0.829484i | −0.207775 | + | 0.829484i | ||||
\(115\) | −0.289486 | − | 1.15569i | −0.289486 | − | 1.15569i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.146730 | + | 0.989177i | 0.146730 | + | 0.989177i | ||||
\(121\) | −0.773010 | + | 0.634393i | −0.773010 | + | 0.634393i | ||||
\(122\) | −0.427441 | − | 0.520839i | −0.427441 | − | 0.520839i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.368309 | − | 0.448786i | 0.368309 | − | 0.448786i | ||||
\(125\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −0.857729 | + | 0.514103i | −0.857729 | + | 0.514103i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) | ||||
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(136\) | 0.416822 | − | 0.249834i | 0.416822 | − | 0.249834i | ||||
\(137\) | 0.195798 | + | 1.98797i | 0.195798 | + | 1.98797i | 0.146730 | + | 0.989177i | \(0.453125\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(138\) | −1.10071 | − | 0.455929i | −1.10071 | − | 0.455929i | ||||
\(139\) | −1.86271 | + | 0.666487i | −1.86271 | + | 0.666487i | −0.881921 | + | 0.471397i | \(0.843750\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.326351 | − | 1.30287i | −0.326351 | − | 1.30287i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.881921 | + | 0.471397i | 0.881921 | + | 0.471397i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.146730 | + | 0.989177i | −0.146730 | + | 0.989177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(150\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(151\) | −0.187593 | − | 0.0569057i | −0.187593 | − | 0.0569057i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(152\) | 0.475074 | − | 0.710998i | 0.475074 | − | 0.710998i | ||||
\(153\) | −0.428579 | − | 0.229080i | −0.428579 | − | 0.229080i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0851872 | + | 0.574286i | 0.0851872 | + | 0.574286i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.427555 | − | 0.903989i | \(-0.640625\pi\) | ||||
0.427555 | + | 0.903989i | \(0.359375\pi\) | |||||||
\(158\) | −0.560227 | + | 1.56573i | −0.560227 | + | 1.56573i | ||||
\(159\) | 1.42834 | + | 0.591637i | 1.42834 | + | 0.591637i | ||||
\(160\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(163\) | 0 | 0 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.75535 | − | 0.938254i | 1.75535 | − | 0.938254i | ||||
\(167\) | 0.298472 | + | 0.983931i | 0.298472 | + | 0.983931i | 0.970031 | + | 0.242980i | \(0.0781250\pi\) |
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(170\) | −0.0948062 | + | 0.476623i | −0.0948062 | + | 0.476623i | ||||
\(171\) | −0.854080 | − | 0.0419583i | −0.854080 | − | 0.0419583i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.05072 | − | 1.41673i | −1.05072 | − | 1.41673i | −0.903989 | − | 0.427555i | \(-0.859375\pi\) |
−0.146730 | − | 0.989177i | \(-0.546875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.514103 | − | 0.857729i | \(-0.328125\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(180\) | −0.941544 | + | 0.336890i | −0.941544 | + | 0.336890i | ||||
\(181\) | −0.733452 | + | 1.55075i | −0.733452 | + | 1.55075i | 0.0980171 | + | 0.995185i | \(0.468750\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.427441 | − | 0.520839i | 0.427441 | − | 0.520839i | ||||
\(184\) | 0.882768 | + | 0.800094i | 0.882768 | + | 0.800094i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.512016 | + | 0.273678i | 0.512016 | + | 0.273678i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.131649 | + | 1.33665i | −0.131649 | + | 1.33665i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.207775 | + | 0.829484i | 0.207775 | + | 0.829484i | ||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | −0.671559 | − | 0.740951i | −0.671559 | − | 0.740951i | ||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | ||||
\(197\) | 0.378487 | + | 0.0948062i | 0.378487 | + | 0.0948062i | 0.427555 | − | 0.903989i | \(-0.359375\pi\) |
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.95213 | − | 0.192268i | −1.95213 | − | 0.192268i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(200\) | 0.595699 | + | 0.803208i | 0.595699 | + | 0.803208i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.326351 | + | 0.360073i | 0.326351 | + | 0.360073i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.232430 | − | 1.16851i | 0.232430 | − | 1.16851i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0788231 | − | 0.0584592i | 0.0788231 | − | 0.0584592i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(212\) | −1.14553 | − | 1.03824i | −1.14553 | − | 1.03824i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.523788 | + | 0.783904i | 0.523788 | + | 0.783904i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.290285 | + | 0.956940i | −0.290285 | + | 0.956940i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.0939097 | − | 0.0284872i | −0.0939097 | − | 0.0284872i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(226\) | 1.33962 | − | 0.633595i | 1.33962 | − | 0.633595i | ||||
\(227\) | 1.14697 | − | 0.542476i | 1.14697 | − | 0.542476i | 0.242980 | − | 0.970031i | \(-0.421875\pi\) |
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(228\) | 0.790019 | + | 0.327237i | 0.790019 | + | 0.327237i | ||||
\(229\) | 0.290285 | − | 0.0430597i | 0.290285 | − | 0.0430597i | − | 1.00000i | \(-0.5\pi\) | |
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(230\) | −1.18566 | + | 0.116777i | −1.18566 | + | 0.116777i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0851872 | + | 0.280825i | −0.0851872 | + | 0.280825i | −0.989177 | − | 0.146730i | \(-0.953125\pi\) |
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.901983 | − | 0.995185i | −0.901983 | − | 0.995185i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.64494 | − | 0.244004i | −1.64494 | − | 0.244004i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(240\) | 1.00000 | 1.00000 | ||||||||
\(241\) | −1.59133 | + | 1.06330i | −1.59133 | + | 1.06330i | −0.634393 | + | 0.773010i | \(0.718750\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(242\) | 0.514103 | + | 0.857729i | 0.514103 | + | 0.857729i | ||||
\(243\) | 0.970031 | − | 0.242980i | 0.970031 | − | 0.242980i | ||||
\(244\) | −0.577920 | + | 0.346392i | −0.577920 | + | 0.346392i | ||||
\(245\) | 0.336890 | + | 0.941544i | 0.336890 | + | 0.941544i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.389887 | − | 0.430174i | −0.389887 | − | 0.430174i | ||||
\(249\) | 1.26268 | + | 1.53858i | 1.26268 | + | 1.53858i | ||||
\(250\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(251\) | 0 | 0 | 0.857729 | − | 0.514103i | \(-0.171875\pi\) | ||||
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.485960 | −0.485960 | ||||||||
\(256\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(257\) | −1.60642 | −1.60642 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.23076 | + | 1.49969i | 1.23076 | + | 1.49969i | 0.803208 | + | 0.595699i | \(0.203125\pi\) |
0.427555 | + | 0.903989i | \(0.359375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.53858 | − | 0.151537i | 1.53858 | − | 0.151537i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(270\) | −0.514103 | − | 0.857729i | −0.514103 | − | 0.857729i | ||||
\(271\) | −0.636379 | + | 0.425215i | −0.636379 | + | 0.425215i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(272\) | −0.185969 | − | 0.448969i | −0.185969 | − | 0.448969i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.99518 | + | 0.0980171i | 1.99518 | + | 0.0980171i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.612501 | + | 1.02190i | −0.612501 | + | 1.02190i | ||||
\(277\) | 0 | 0 | −0.671559 | − | 0.740951i | \(-0.734375\pi\) | ||||
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(278\) | 0.385958 | + | 1.94034i | 0.385958 | + | 1.94034i | ||||
\(279\) | −0.168530 | + | 0.555570i | −0.168530 | + | 0.555570i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(282\) | −1.33665 | + | 0.131649i | −1.33665 | + | 0.131649i | ||||
\(283\) | 0 | 0 | 0.989177 | − | 0.146730i | \(-0.0468750\pi\) | ||||
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.773010 | + | 0.365607i | −0.773010 | + | 0.365607i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.595699 | − | 0.803208i | 0.595699 | − | 0.803208i | ||||
\(289\) | −0.292310 | − | 0.705698i | −0.292310 | − | 0.705698i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.18566 | − | 1.59868i | 1.18566 | − | 1.59868i | 0.514103 | − | 0.857729i | \(-0.328125\pi\) |
0.671559 | − | 0.740951i | \(-0.265625\pi\) | |||||||
\(294\) | 0.956940 | + | 0.290285i | 0.956940 | + | 0.290285i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.671559 | + | 0.740951i | −0.671559 | + | 0.740951i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.0838155 | + | 0.177213i | −0.0838155 | + | 0.177213i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.633595 | − | 0.574257i | −0.633595 | − | 0.574257i | ||||
\(305\) | 0.131448 | − | 0.660833i | 0.131448 | − | 0.660833i | ||||
\(306\) | −0.289486 | + | 0.390327i | −0.289486 | + | 0.390327i | ||||
\(307\) | 0 | 0 | −0.857729 | − | 0.514103i | \(-0.828125\pi\) | ||||
0.857729 | + | 0.514103i | \(0.171875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.580569 | 0.580569 | ||||||||
\(311\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.46658 | + | 0.783904i | 1.46658 | + | 0.783904i | ||||
\(317\) | 0.746196 | − | 0.823301i | 0.746196 | − | 0.823301i | −0.242980 | − | 0.970031i | \(-0.578125\pi\) |
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(318\) | 0.794814 | − | 1.32607i | 0.794814 | − | 1.32607i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.941544 | − | 0.336890i | −0.941544 | − | 0.336890i | ||||
\(321\) | −0.666656 | + | 0.666656i | −0.666656 | + | 0.666656i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.307902 | + | 0.279066i | 0.307902 | + | 0.279066i | ||||
\(324\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.00961895 | − | 0.0976628i | 0.00961895 | − | 0.0976628i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.439614 | + | 0.929487i | −0.439614 | + | 0.929487i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(332\) | −0.670535 | − | 1.87402i | −0.670535 | − | 1.87402i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.01708 | − | 0.150869i | 1.01708 | − | 0.150869i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(338\) | −0.336890 | − | 0.941544i | −0.336890 | − | 0.941544i | ||||
\(339\) | 0.882768 | + | 1.19028i | 0.882768 | + | 1.19028i | ||||
\(340\) | 0.457553 | + | 0.163715i | 0.457553 | + | 0.163715i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.166824 | + | 0.838679i | −0.166824 | + | 0.838679i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.345845 | − | 1.14010i | −0.345845 | − | 1.14010i | ||||
\(346\) | −1.55557 | + | 0.831470i | −1.55557 | + | 0.831470i | ||||
\(347\) | −0.892476 | − | 0.661906i | −0.892476 | − | 0.661906i | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) |
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.609090 | − | 1.70229i | 0.609090 | − | 1.70229i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.73975 | + | 0.720627i | 1.73975 | + | 0.720627i | 0.998795 | + | 0.0490677i | \(0.0156250\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(360\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(361\) | −0.257213 | − | 0.0780246i | −0.257213 | − | 0.0780246i | ||||
\(362\) | 1.42635 | + | 0.953057i | 1.42635 | + | 0.953057i | ||||
\(363\) | −0.740951 | + | 0.671559i | −0.740951 | + | 0.671559i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.452483 | − | 0.499238i | −0.452483 | − | 0.499238i | ||||
\(367\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(368\) | 0.920964 | − | 0.755815i | 0.920964 | − | 0.755815i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.345845 | − | 0.466318i | 0.345845 | − | 0.466318i | ||||
\(373\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.0980171 | − | 0.995185i | −0.0980171 | − | 0.995185i | ||||
\(376\) | 1.30287 | + | 0.326351i | 1.30287 | + | 0.326351i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.881921 | + | 1.47140i | 0.881921 | + | 1.47140i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0.850993 | − | 0.0838155i | 0.850993 | − | 0.0838155i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.88309i | − | 1.88309i | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||
0.336890 | − | 0.941544i | \(-0.390625\pi\) | |||||||
\(384\) | −0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.447552 | + | 0.367296i | −0.447552 | + | 0.367296i | ||||
\(392\) | −0.803208 | − | 0.595699i | −0.803208 | − | 0.595699i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.149316 | − | 0.360480i | 0.149316 | − | 0.360480i | ||||
\(395\) | −1.56573 | + | 0.560227i | −1.56573 | + | 0.560227i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(398\) | −0.476623 | + | 1.90278i | −0.476623 | + | 1.90278i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(401\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.740951 | − | 0.671559i | 0.740951 | − | 0.671559i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.404061 | − | 0.269985i | 0.404061 | − | 0.269985i | ||||
\(409\) | 0.172887 | + | 0.0924099i | 0.172887 | + | 0.0924099i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.293107 | + | 1.97597i | 0.293107 | + | 1.97597i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.12175 | − | 0.401370i | −1.12175 | − | 0.401370i | ||||
\(415\) | 1.83886 | + | 0.761681i | 1.83886 | + | 0.761681i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.82776 | + | 0.757083i | −1.82776 | + | 0.757083i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.58903 | + | 1.17850i | 1.58903 | + | 1.17850i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | −0.0462607 | − | 0.0865477i | −0.0462607 | − | 0.0865477i | ||||
\(423\) | −0.389887 | − | 1.28528i | −0.389887 | − | 1.28528i | ||||
\(424\) | −1.19509 | + | 0.980785i | −1.19509 | + | 0.980785i | ||||
\(425\) | −0.428579 | + | 0.229080i | −0.428579 | + | 0.229080i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.852275 | − | 0.403096i | 0.852275 | − | 0.403096i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(432\) | 0.903989 | + | 0.427555i | 0.903989 | + | 0.427555i | ||||
\(433\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0419583 | + | 0.0887133i | −0.0419583 | + | 0.0887133i | ||||
\(437\) | −0.435583 | + | 0.920964i | −0.435583 | + | 0.920964i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.247528 | + | 0.301614i | −0.247528 | + | 0.301614i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.465035 | + | 1.85652i | −0.465035 | + | 1.85652i | 0.0490677 | + | 0.998795i | \(0.484375\pi\) |
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(450\) | −0.857729 | − | 0.514103i | −0.857729 | − | 0.514103i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.430174 | − | 1.41809i | −0.430174 | − | 1.41809i | ||||
\(453\) | −0.190159 | − | 0.0476324i | −0.190159 | − | 0.0476324i | ||||
\(454\) | −0.368309 | − | 1.21415i | −0.368309 | − | 1.21415i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.439614 | − | 0.733452i | 0.439614 | − | 0.733452i | ||||
\(457\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(458\) | − | 0.293461i | − | 0.293461i | ||||||
\(459\) | −0.439303 | − | 0.207775i | −0.439303 | − | 0.207775i | ||||
\(460\) | −0.0584592 | + | 1.18996i | −0.0584592 | + | 1.18996i | ||||
\(461\) | 0 | 0 | −0.857729 | − | 0.514103i | \(-0.828125\pi\) | ||||
0.857729 | + | 0.514103i | \(0.171875\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.113263 | + | 0.569414i | 0.113263 | + | 0.569414i | ||||
\(466\) | 0.265286 | + | 0.125471i | 0.265286 | + | 0.125471i | ||||
\(467\) | 0.313396 | − | 0.232430i | 0.313396 | − | 0.232430i | −0.427555 | − | 0.903989i | \(-0.640625\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.11676 | + | 0.746196i | −1.11676 | + | 0.746196i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.482726 | + | 1.59133i | −0.482726 | + | 1.59133i | ||||
\(475\) | −0.509389 | + | 0.686831i | −0.509389 | + | 0.686831i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.45565 | + | 0.520839i | 1.45565 | + | 0.520839i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(480\) | 0.146730 | − | 0.989177i | 0.146730 | − | 0.989177i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.818289 | + | 1.73013i | 0.818289 | + | 1.73013i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0980171 | − | 0.995185i | −0.0980171 | − | 0.995185i | ||||
\(487\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(488\) | 0.257844 | + | 0.622491i | 0.257844 | + | 0.622491i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(491\) | 0 | 0 | −0.671559 | − | 0.740951i | \(-0.734375\pi\) | ||||
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.482726 | + | 0.322547i | −0.482726 | + | 0.322547i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.70720 | − | 1.02325i | 1.70720 | − | 1.02325i | ||||
\(499\) | 0.284666 | − | 0.0713052i | 0.284666 | − | 0.0713052i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(500\) | −0.242980 | + | 0.970031i | −0.242980 | + | 0.970031i | ||||
\(501\) | 0.346392 | + | 0.968101i | 0.346392 | + | 0.968101i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.98797 | + | 0.195798i | −1.98797 | + | 0.195798i | −0.989177 | + | 0.146730i | \(0.953125\pi\) |
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.857729 | − | 0.514103i | 0.857729 | − | 0.514103i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | ||||
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(510\) | −0.0713052 | + | 0.480701i | −0.0713052 | + | 0.480701i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.970031 | − | 0.242980i | 0.970031 | − | 0.242980i | ||||
\(513\) | −0.855110 | −0.855110 | ||||||||
\(514\) | −0.235710 | + | 1.58903i | −0.235710 | + | 1.58903i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.11897 | − | 1.36347i | −1.11897 | − | 1.36347i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66405 | − | 0.997391i | 1.66405 | − | 0.997391i | ||||
\(527\) | 0.234586 | − | 0.156745i | 0.234586 | − | 0.156745i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.348744 | − | 0.233023i | −0.348744 | − | 0.233023i | ||||
\(530\) | 0.0758597 | − | 1.54416i | 0.0758597 | − | 1.54416i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.273678 | + | 0.902197i | −0.273678 | + | 0.902197i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(541\) | −0.929487 | + | 0.439614i | −0.929487 | + | 0.439614i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(542\) | 0.327237 | + | 0.691883i | 0.327237 | + | 0.691883i | ||||
\(543\) | −0.656477 | + | 1.58488i | −0.656477 | + | 1.58488i | ||||
\(544\) | −0.471397 | + | 0.118079i | −0.471397 | + | 0.118079i | ||||
\(545\) | −0.0375548 | − | 0.0906652i | −0.0375548 | − | 0.0906652i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.941544 | − | 0.336890i | \(-0.890625\pi\) | ||||
0.941544 | + | 0.336890i | \(0.109375\pi\) | |||||||
\(548\) | 0.389711 | − | 1.95921i | 0.389711 | − | 1.95921i | ||||
\(549\) | 0.401370 | − | 0.541185i | 0.401370 | − | 0.541185i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.920964 | + | 0.755815i | 0.920964 | + | 0.755815i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.97597 | − | 0.0970732i | 1.97597 | − | 0.0970732i | ||||
\(557\) | 0.157456 | − | 0.116777i | 0.157456 | − | 0.116777i | −0.514103 | − | 0.857729i | \(-0.671875\pi\) |
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(558\) | 0.524828 | + | 0.248225i | 0.524828 | + | 0.248225i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.334669 | + | 0.200593i | 0.334669 | + | 0.200593i | 0.671559 | − | 0.740951i | \(-0.265625\pi\) |
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(564\) | −0.0659037 | + | 1.34150i | −0.0659037 | + | 1.34150i | ||||
\(565\) | 1.33962 | + | 0.633595i | 1.33962 | + | 0.633595i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(570\) | 0.248225 | + | 0.818289i | 0.248225 | + | 0.818289i | ||||
\(571\) | −1.55827 | − | 0.390327i | −1.55827 | − | 0.390327i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.842446 | − | 0.842446i | −0.842446 | − | 0.842446i | ||||
\(576\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | −0.740951 | + | 0.185599i | −0.740951 | + | 0.185599i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.40740 | − | 1.40740i | −1.40740 | − | 1.40740i | ||||
\(587\) | 0.754140 | − | 1.59449i | 0.754140 | − | 1.59449i | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) |
0.803208 | − | 0.595699i | \(-0.203125\pi\) | |||||||
\(588\) | 0.427555 | − | 0.903989i | 0.427555 | − | 0.903989i | ||||
\(589\) | 0.255227 | − | 0.425820i | 0.255227 | − | 0.425820i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.382683 | + | 0.0761205i | 0.382683 | + | 0.0761205i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.94034 | − | 0.385958i | 1.94034 | − | 0.385958i | 0.941544 | − | 0.336890i | \(-0.109375\pi\) |
0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.95921 | − | 0.0962497i | −1.95921 | − | 0.0962497i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(600\) | 0.634393 | + | 0.773010i | 0.634393 | + | 0.773010i | ||||
\(601\) | −0.0569057 | − | 0.187593i | −0.0569057 | − | 0.187593i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.162997 | + | 0.108911i | 0.162997 | + | 0.108911i | ||||
\(605\) | −0.336890 | + | 0.941544i | −0.336890 | + | 0.941544i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(608\) | −0.661009 | + | 0.542476i | −0.661009 | + | 0.542476i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.634393 | − | 0.226990i | −0.634393 | − | 0.226990i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.343626 | + | 0.343626i | 0.343626 | + | 0.343626i | ||||
\(613\) | 0 | 0 | −0.146730 | − | 0.989177i | \(-0.546875\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.28528 | − | 0.389887i | −1.28528 | − | 0.389887i | −0.427555 | − | 0.903989i | \(-0.640625\pi\) |
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.48012 | − | 1.34150i | 1.48012 | − | 1.34150i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.773010 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(620\) | 0.0851872 | − | 0.574286i | 0.0851872 | − | 0.574286i | ||||
\(621\) | 0.174814 | − | 1.17850i | 0.174814 | − | 1.17850i | ||||
\(622\) | 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 | ||||||||
\(631\) | −0.181112 | − | 1.83886i | −0.181112 | − | 1.83886i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
0.290285 | − | 0.956940i | \(-0.406250\pi\) | |||||||
\(632\) | 0.990612 | − | 1.33569i | 0.990612 | − | 1.33569i | ||||
\(633\) | 0.0758597 | − | 0.0622564i | 0.0758597 | − | 0.0622564i | ||||
\(634\) | −0.704900 | − | 0.858923i | −0.704900 | − | 0.858923i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.19509 | − | 0.980785i | −1.19509 | − | 0.980785i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.471397 | + | 0.881921i | −0.471397 | + | 0.881921i | ||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0.561621 | + | 0.757259i | 0.561621 | + | 0.757259i | ||||
\(643\) | 0 | 0 | −0.0490677 | − | 0.998795i | \(-0.515625\pi\) | ||||
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.321224 | − | 0.263622i | 0.321224 | − | 0.263622i | ||||
\(647\) | −1.39759 | + | 1.14697i | −1.39759 | + | 1.14697i | −0.427555 | + | 0.903989i | \(0.640625\pi\) |
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(648\) | −0.242980 | + | 0.970031i | −0.242980 | + | 0.970031i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.229080 | − | 0.914539i | −0.229080 | − | 0.914539i | −0.970031 | − | 0.242980i | \(-0.921875\pi\) |
0.740951 | − | 0.671559i | \(-0.234375\pi\) | |||||||
\(654\) | −0.0951944 | − | 0.0238449i | −0.0951944 | − | 0.0238449i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.48012 | + | 1.34150i | −1.48012 | + | 1.34150i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(662\) | 0.854922 | + | 0.571240i | 0.854922 | + | 0.571240i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.95213 | + | 0.388302i | −1.95213 | + | 0.388302i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 1.02821i | − | 1.02821i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.336890 | − | 0.941544i | 0.336890 | − | 0.941544i | ||||
\(676\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(677\) | 1.53724 | + | 1.14010i | 1.53724 | + | 1.14010i | 0.941544 | + | 0.336890i | \(0.109375\pi\) |
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(678\) | 1.30692 | − | 0.698564i | 1.30692 | − | 0.698564i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.229080 | − | 0.428579i | 0.229080 | − | 0.428579i | ||||
\(681\) | 1.11897 | − | 0.598102i | 1.11897 | − | 0.598102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.66094 | − | 0.0815966i | −1.66094 | − | 0.0815966i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(684\) | 0.805124 | + | 0.288078i | 0.805124 | + | 0.288078i | ||||
\(685\) | 1.18996 | + | 1.60448i | 1.18996 | + | 1.60448i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.287822 | − | 0.0572514i | 0.287822 | − | 0.0572514i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.17850 | + | 0.174814i | −1.17850 | + | 0.174814i | ||||
\(691\) | 0.881921 | − | 1.47140i | 0.881921 | − | 1.47140i | − | 1.00000i | \(-0.5\pi\) | |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(692\) | 0.594221 | + | 1.66074i | 0.594221 | + | 1.66074i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.785695 | + | 0.785695i | −0.785695 | + | 0.785695i | ||||
\(695\) | −1.25505 | + | 1.52929i | −1.25505 | + | 1.52929i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.59449 | − | 0.852275i | −1.59449 | − | 0.852275i | ||||
\(699\) | −0.0713052 | + | 0.284666i | −0.0713052 | + | 0.284666i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.740951 | − | 0.671559i | \(-0.765625\pi\) | ||||
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.949728 | − | 0.949728i | −0.949728 | − | 0.949728i | ||||
\(706\) | 0.968101 | − | 1.61518i | 0.968101 | − | 1.61518i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.75380 | + | 0.439303i | 1.75380 | + | 0.439303i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.65493 | − | 0.162997i | −1.65493 | − | 0.162997i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.534683 | + | 0.438803i | 0.534683 | + | 0.438803i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(720\) | 0.998795 | − | 0.0490677i | 0.998795 | − | 0.0490677i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.114921 | + | 0.242980i | −0.114921 | + | 0.242980i | ||||
\(723\) | −1.53724 | + | 1.14010i | −1.53724 | + | 1.14010i | ||||
\(724\) | 1.15203 | − | 1.27107i | 1.15203 | − | 1.27107i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(727\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.560227 | + | 0.374332i | −0.560227 | + | 0.374332i | ||||
\(733\) | 0 | 0 | −0.941544 | − | 0.336890i | \(-0.890625\pi\) | ||||
0.941544 | + | 0.336890i | \(0.109375\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(736\) | −0.612501 | − | 1.02190i | −0.612501 | − | 1.02190i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.33962 | − | 0.633595i | 1.33962 | − | 0.633595i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.887682 | − | 1.66074i | 0.887682 | − | 1.66074i | 0.146730 | − | 0.989177i | \(-0.453125\pi\) |
0.740951 | − | 0.671559i | \(-0.234375\pi\) | |||||||
\(744\) | −0.410525 | − | 0.410525i | −0.410525 | − | 0.410525i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.33665 | + | 1.47477i | 1.33665 | + | 1.47477i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.998795 | − | 0.0490677i | −0.998795 | − | 0.0490677i | ||||
\(751\) | 0.783904 | + | 0.523788i | 0.783904 | + | 0.523788i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(752\) | 0.513989 | − | 1.24088i | 0.513989 | − | 1.24088i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.190159 | + | 0.0476324i | −0.190159 | + | 0.0476324i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.336890 | − | 0.941544i | \(-0.609375\pi\) | ||||
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(758\) | 1.58488 | − | 0.656477i | 1.58488 | − | 0.656477i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0419583 | − | 0.854080i | 0.0419583 | − | 0.854080i | ||||
\(761\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.485375 | + | 0.0238449i | −0.485375 | + | 0.0238449i | ||||
\(766\) | −1.86271 | − | 0.276306i | −1.86271 | − | 0.276306i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.427555 | + | 0.903989i | 0.427555 | + | 0.903989i | ||||
\(769\) | −0.942793 | −0.942793 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.60448 | + | 0.0788231i | −1.60448 | + | 0.0788231i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.58488 | − | 0.949938i | 1.58488 | − | 0.949938i | 0.595699 | − | 0.803208i | \(-0.296875\pi\) |
0.989177 | − | 0.146730i | \(-0.0468750\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.368309 | + | 0.448786i | 0.368309 | + | 0.448786i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.297651 | + | 0.496601i | 0.297651 | + | 0.496601i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.989177 | − | 0.146730i | \(-0.953125\pi\) | ||||
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(788\) | −0.334669 | − | 0.200593i | −0.334669 | − | 0.200593i | ||||
\(789\) | 1.30287 | + | 1.43749i | 1.30287 | + | 1.43749i | ||||
\(790\) | 0.324423 | + | 1.63099i | 0.324423 | + | 1.63099i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.52929 | − | 0.226848i | 1.52929 | − | 0.226848i | ||||
\(796\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | ||||
\(797\) | 1.00446 | − | 0.475074i | 1.00446 | − | 0.475074i | 0.146730 | − | 0.989177i | \(-0.453125\pi\) |
0.857729 | + | 0.514103i | \(0.171875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.249778 | + | 0.603018i | −0.249778 | + | 0.603018i | ||||
\(800\) | −0.336890 | − | 0.941544i | −0.336890 | − | 0.941544i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(810\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(811\) | −0.0923988 | + | 1.88082i | −0.0923988 | + | 1.88082i | 0.290285 | + | 0.956940i | \(0.406250\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.614748 | + | 0.455929i | −0.614748 | + | 0.455929i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.207775 | − | 0.439303i | −0.207775 | − | 0.439303i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.116777 | − | 0.157456i | 0.116777 | − | 0.157456i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.903989 | − | 0.427555i | \(-0.859375\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(822\) | 1.99759 | 1.99759 | ||||||||
\(823\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.07784 | + | 0.269985i | 1.07784 | + | 0.269985i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
0.336890 | + | 0.941544i | \(0.390625\pi\) | |||||||
\(828\) | −0.561621 | + | 1.05072i | −0.561621 | + | 1.05072i | ||||
\(829\) | 1.30287 | − | 1.43749i | 1.30287 | − | 1.43749i | 0.471397 | − | 0.881921i | \(-0.343750\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(830\) | 1.02325 | − | 1.70720i | 1.02325 | − | 1.70720i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.343626 | − | 0.343626i | 0.343626 | − | 0.343626i | ||||
\(834\) | 0.480701 | + | 1.91906i | 0.480701 | + | 1.91906i | ||||
\(835\) | 0.761850 | + | 0.690501i | 0.761850 | + | 0.690501i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.141067 | + | 0.563170i | −0.141067 | + | 0.563170i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(842\) | 1.39891 | − | 1.39891i | 1.39891 | − | 1.39891i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0923988 | + | 0.0330608i | −0.0923988 | + | 0.0330608i | ||||
\(845\) | 0.514103 | − | 0.857729i | 0.514103 | − | 0.857729i | ||||
\(846\) | −1.32858 | + | 0.197076i | −1.32858 | + | 0.197076i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.794814 | + | 1.32607i | 0.794814 | + | 1.32607i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.163715 | + | 0.457553i | 0.163715 | + | 0.457553i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) | ||||
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.754140 | + | 0.403096i | −0.754140 | + | 0.403096i | ||||
\(856\) | −0.273678 | − | 0.902197i | −0.273678 | − | 0.902197i | ||||
\(857\) | 0.195588 | + | 0.644767i | 0.195588 | + | 0.644767i | 0.998795 | + | 0.0490677i | \(0.0156250\pi\) |
−0.803208 | + | 0.595699i | \(0.796875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.541185 | + | 0.401370i | 0.541185 | + | 0.401370i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.82776 | + | 0.757083i | −1.82776 | + | 0.757083i | −0.857729 | + | 0.514103i | \(0.828125\pi\) |
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(864\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(865\) | −1.62958 | − | 0.674993i | −1.62958 | − | 0.674993i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.326585 | − | 0.690505i | −0.326585 | − | 0.690505i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.0815966 | + | 0.0545211i | 0.0815966 | + | 0.0545211i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.847082 | + | 0.566002i | 0.847082 | + | 0.566002i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(878\) | 0.262029 | + | 0.289105i | 0.262029 | + | 0.289105i | ||||
\(879\) | 1.10579 | − | 1.65493i | 1.10579 | − | 1.65493i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(882\) | 0.970031 | + | 0.242980i | 0.970031 | + | 0.242980i | ||||
\(883\) | 0 | 0 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.76820 | + | 0.732410i | 1.76820 | + | 0.732410i | ||||
\(887\) | −0.0287642 | − | 0.292048i | −0.0287642 | − | 0.292048i | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) |
0.970031 | − | 0.242980i | \(-0.0781250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0563549 | + | 1.14713i | 0.0563549 | + | 1.14713i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.634393 | + | 0.773010i | −0.634393 | + | 0.773010i | ||||
\(901\) | −0.386248 | − | 0.644416i | −0.386248 | − | 0.644416i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.46586 | + | 0.217440i | −1.46586 | + | 0.217440i | ||||
\(905\) | 0.168144 | + | 1.70720i | 0.168144 | + | 1.70720i | ||||
\(906\) | −0.0750191 | + | 0.181112i | −0.0750191 | + | 0.181112i | ||||
\(907\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(908\) | −1.25505 | + | 0.186170i | −1.25505 | + | 0.186170i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(912\) | −0.661009 | − | 0.542476i | −0.661009 | − | 0.542476i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0988640 | − | 0.666487i | 0.0988640 | − | 0.666487i | ||||
\(916\) | −0.290285 | − | 0.0430597i | −0.290285 | − | 0.0430597i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.269985 | + | 0.404061i | −0.269985 | + | 0.404061i | ||||
\(919\) | −1.21415 | − | 0.368309i | −1.21415 | − | 0.368309i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(920\) | 1.16851 | + | 0.232430i | 1.16851 | + | 0.232430i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(930\) | 0.579870 | − | 0.0284872i | 0.579870 | − | 0.0284872i | ||||
\(931\) | 0.288078 | − | 0.805124i | 0.288078 | − | 0.805124i | ||||
\(932\) | 0.163038 | − | 0.244004i | 0.163038 | − | 0.244004i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.183930 | − | 0.344109i | −0.183930 | − | 0.344109i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.574257 | + | 1.21416i | 0.574257 | + | 1.21416i | ||||
\(941\) | 0 | 0 | −0.595699 | − | 0.803208i | \(-0.703125\pi\) | ||||
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.100782 | + | 0.168144i | −0.100782 | + | 0.168144i | −0.903989 | − | 0.427555i | \(-0.859375\pi\) |
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(948\) | 1.50328 | + | 0.710998i | 1.50328 | + | 0.710998i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.604654 | + | 0.604654i | 0.604654 | + | 0.604654i | ||||
\(951\) | 0.704900 | − | 0.858923i | 0.704900 | − | 0.858923i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.100782 | − | 1.02325i | 0.100782 | − | 1.02325i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
0.903989 | − | 0.427555i | \(-0.140625\pi\) | |||||||
\(954\) | 0.728789 | − | 1.36347i | 0.728789 | − | 1.36347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | ||||
\(961\) | 0.468769 | + | 0.468769i | 0.468769 | + | 0.468769i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.633141 | + | 0.698564i | −0.633141 | + | 0.698564i | ||||
\(964\) | 1.83147 | − | 0.555570i | 1.83147 | − | 0.555570i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(968\) | −0.242980 | − | 0.970031i | −0.242980 | − | 0.970031i | ||||
\(969\) | 0.321224 | + | 0.263622i | 0.321224 | + | 0.263622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.903989 | − | 0.427555i | \(-0.859375\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(972\) | −0.998795 | − | 0.0490677i | −0.998795 | − | 0.0490677i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.653587 | − | 0.163715i | 0.653587 | − | 0.163715i | ||||
\(977\) | −0.313396 | − | 1.57555i | −0.313396 | − | 1.57555i | −0.740951 | − | 0.671559i | \(-0.765625\pi\) |
0.427555 | − | 0.903989i | \(-0.359375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(981\) | 0.00481527 | − | 0.0980171i | 0.00481527 | − | 0.0980171i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.914539 | − | 1.71098i | −0.914539 | − | 1.71098i | −0.671559 | − | 0.740951i | \(-0.734375\pi\) |
−0.242980 | − | 0.970031i | \(-0.578125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.373380 | − | 0.113263i | 0.373380 | − | 0.113263i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | 1.00000 | \(0\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(992\) | 0.248225 | + | 0.524828i | 0.248225 | + | 0.524828i | ||||
\(993\) | −0.393477 | + | 0.949938i | −0.393477 | + | 0.949938i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.77324 | + | 0.838679i | −1.77324 | + | 0.838679i | ||||
\(996\) | −0.761681 | − | 1.83886i | −0.761681 | − | 1.83886i | ||||
\(997\) | 0 | 0 | 0.989177 | − | 0.146730i | \(-0.0468750\pi\) | ||||
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(998\) | −0.0287642 | − | 0.292048i | −0.0287642 | − | 0.292048i | ||||
\(999\) | 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 | 3840.1.dy.a.629.2 | yes | 64 | |
3.2 | odd | 2 | inner | 3840.1.dy.a.629.1 | ✓ | 64 | |
5.4 | even | 2 | inner | 3840.1.dy.a.629.1 | ✓ | 64 | |
15.14 | odd | 2 | CM | 3840.1.dy.a.629.2 | yes | 64 | |
256.221 | even | 64 | inner | 3840.1.dy.a.989.2 | yes | 64 | |
768.221 | odd | 64 | inner | 3840.1.dy.a.989.1 | yes | 64 | |
1280.989 | even | 64 | inner | 3840.1.dy.a.989.1 | yes | 64 | |
3840.989 | odd | 64 | inner | 3840.1.dy.a.989.2 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3840.1.dy.a.629.1 | ✓ | 64 | 3.2 | odd | 2 | inner | |
3840.1.dy.a.629.1 | ✓ | 64 | 5.4 | even | 2 | inner | |
3840.1.dy.a.629.2 | yes | 64 | 1.1 | even | 1 | trivial | |
3840.1.dy.a.629.2 | yes | 64 | 15.14 | odd | 2 | CM | |
3840.1.dy.a.989.1 | yes | 64 | 768.221 | odd | 64 | inner | |
3840.1.dy.a.989.1 | yes | 64 | 1280.989 | even | 64 | inner | |
3840.1.dy.a.989.2 | yes | 64 | 256.221 | even | 64 | inner | |
3840.1.dy.a.989.2 | yes | 64 | 3840.989 | odd | 64 | inner |