Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), 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: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 641.4 | ||
Root | \(1.66798 - 0.466730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.c.385.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.90008 | + | 1.20125i | 1.67436 | + | 0.693543i | 0.999033 | − | 0.0439740i | \(-0.0140019\pi\) |
0.675328 | + | 0.737517i | \(0.264002\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.21229 | − | 2.92673i | −0.542153 | − | 1.30887i | −0.923201 | − | 0.384318i | \(-0.874437\pi\) |
0.381047 | − | 0.924556i | \(-0.375563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.933460 | − | 0.933460i | 0.352815 | − | 0.352815i | −0.508341 | − | 0.861156i | \(-0.669741\pi\) |
0.861156 | + | 0.508341i | \(0.169741\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.84613 | + | 4.84613i | 1.61538 | + | 1.61538i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.05232 | − | 0.435885i | 0.317286 | − | 0.131424i | −0.218356 | − | 0.975869i | \(-0.570069\pi\) |
0.535643 | + | 0.844445i | \(0.320069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.09830 | + | 2.65154i | −0.304615 | + | 0.735405i | 0.695247 | + | 0.718771i | \(0.255295\pi\) |
−0.999862 | + | 0.0166339i | \(0.994705\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.94402i | − | 2.56753i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.61082i | − | 0.390681i | −0.980735 | − | 0.195341i | \(-0.937419\pi\) | ||
0.980735 | − | 0.195341i | \(-0.0625813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.34533 | − | 5.66214i | 0.538056 | − | 1.29898i | −0.388021 | − | 0.921650i | \(-0.626841\pi\) |
0.926078 | − | 0.377333i | \(-0.123159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.82843 | − | 1.58579i | 0.835431 | − | 0.346047i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.67967 | + | 1.67967i | 0.350235 | + | 0.350235i | 0.860197 | − | 0.509962i | \(-0.170341\pi\) |
−0.509962 | + | 0.860197i | \(0.670341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.56057 | + | 3.56057i | −0.712114 | + | 0.712114i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.62898 | + | 11.1753i | 0.890847 | + | 2.15070i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.06575 | + | 2.92673i | 1.31208 | + | 0.543480i | 0.925490 | − | 0.378772i | \(-0.123654\pi\) |
0.386588 | + | 0.922253i | \(0.373654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53073 | 0.274928 | 0.137464 | − | 0.990507i | \(-0.456105\pi\) | ||||
0.137464 | + | 0.990507i | \(0.456105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.57542 | 0.622400 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.86361 | − | 1.60036i | −0.653069 | − | 0.270510i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.08793 | − | 5.04072i | −0.343254 | − | 0.828689i | −0.997383 | − | 0.0723054i | \(-0.976964\pi\) |
0.654128 | − | 0.756384i | \(-0.273036\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.37033 | + | 6.37033i | −1.02007 | + | 1.02007i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.03540 | − | 1.03540i | −0.161703 | − | 0.161703i | 0.621618 | − | 0.783321i | \(-0.286476\pi\) |
−0.783321 | + | 0.621618i | \(0.786476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.98247 | + | 1.64959i | −0.607321 | + | 0.251561i | −0.665083 | − | 0.746770i | \(-0.731604\pi\) |
0.0577615 | + | 0.998330i | \(0.481604\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.30839 | − | 20.0582i | 1.23854 | − | 2.99011i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.97641i | 0.434154i | 0.976154 | + | 0.217077i | \(0.0696523\pi\) | ||||
−0.976154 | + | 0.217077i | \(0.930348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.25731i | 0.751044i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.93500 | − | 4.67151i | 0.270954 | − | 0.654142i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1694 | − | 4.21229i | 1.39687 | − | 0.578603i | 0.447933 | − | 0.894067i | \(-0.352160\pi\) |
0.948937 | + | 0.315464i | \(0.102160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.55144 | − | 2.55144i | −0.344036 | − | 0.344036i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.6033 | − | 13.6033i | 1.80180 | − | 1.80180i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.34842 | − | 8.08380i | −0.435927 | − | 1.05242i | −0.977342 | − | 0.211666i | \(-0.932111\pi\) |
0.541415 | − | 0.840756i | \(-0.317889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6440 | − | 5.23733i | −1.61890 | − | 0.670571i | −0.624978 | − | 0.780643i | \(-0.714892\pi\) |
−0.993924 | + | 0.110072i | \(0.964892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.04733 | 1.13986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.09181 | 1.12770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8681 | − | 4.91593i | −1.44992 | − | 0.600577i | −0.487739 | − | 0.872989i | \(-0.662178\pi\) |
−0.962180 | + | 0.272413i | \(0.912178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.85346 | + | 6.88887i | 0.343516 | + | 0.829322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.88894 | + | 5.88894i | −0.698889 | + | 0.698889i | −0.964171 | − | 0.265282i | \(-0.914535\pi\) |
0.265282 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.71444 | + | 3.71444i | 0.434742 | + | 0.434742i | 0.890238 | − | 0.455496i | \(-0.150538\pi\) |
−0.455496 | + | 0.890238i | \(0.650538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.6031 | + | 6.04879i | −1.68622 | + | 0.698454i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.575417 | − | 1.38918i | 0.0655748 | − | 0.158312i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4058i | 1.17074i | 0.810766 | + | 0.585370i | \(0.199051\pi\) | ||||
−0.810766 | + | 0.585370i | \(0.800949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.4096i | 1.93439i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.13163 | + | 2.73199i | −0.124212 | + | 0.299874i | −0.973738 | − | 0.227673i | \(-0.926888\pi\) |
0.849526 | + | 0.527547i | \(0.176888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.71444 | + | 1.95278i | −0.511353 | + | 0.211809i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.9755 | + | 16.9755i | 1.81996 | + | 1.81996i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.56361 | + | 6.56361i | −0.695741 | + | 0.695741i | −0.963489 | − | 0.267748i | \(-0.913720\pi\) |
0.267748 | + | 0.963489i | \(0.413720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.44988 | + | 3.50033i | 0.151989 | + | 0.366934i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.43925 | + | 1.83880i | 0.460329 | + | 0.190674i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.4148 | −1.99191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01037 | 0.102587 | 0.0512937 | − | 0.998684i | \(-0.483666\pi\) | ||||
0.0512937 | + | 0.998684i | \(0.483666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.21203 | + | 2.98732i | 0.724836 | + | 0.300237i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.16937 | + | 10.0658i | 0.414868 | + | 1.00158i | 0.983812 | + | 0.179204i | \(0.0573521\pi\) |
−0.568944 | + | 0.822376i | \(0.692648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1802 | + | 10.1802i | −1.00308 | + | 1.00308i | −0.00308887 | + | 0.999995i | \(0.500983\pi\) |
−0.999995 | + | 0.00308887i | \(0.999017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.28234 | − | 9.28234i | −0.905864 | − | 0.905864i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.16246 | − | 3.79522i | 0.885769 | − | 0.366897i | 0.107038 | − | 0.994255i | \(-0.465864\pi\) |
0.778731 | + | 0.627357i | \(0.215864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.04072 | + | 9.75516i | −0.387031 | + | 0.934375i | 0.603535 | + | 0.797336i | \(0.293758\pi\) |
−0.990566 | + | 0.137038i | \(0.956242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 17.1266i | − | 1.62559i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.57112i | 0.241871i | 0.992660 | + | 0.120935i | \(0.0385894\pi\) | ||||
−0.992660 | + | 0.120935i | \(0.961411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.87969 | − | 6.95218i | 0.268532 | − | 0.648294i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.1722 | + | 7.52718i | −1.68002 | + | 0.695888i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50364 | − | 1.50364i | −0.137838 | − | 0.137838i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.86079 | + | 6.86079i | −0.623709 | + | 0.623709i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.75897 | − | 4.24653i | −0.158601 | − | 0.382897i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.103618 | + | 0.0429201i | 0.00926790 | + | 0.00383889i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.16126 | −0.546723 | −0.273362 | − | 0.961911i | \(-0.588136\pi\) | ||||
−0.273362 | + | 0.961911i | \(0.588136\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.5311 | −1.19134 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.92409 | + | 0.796984i | 0.168108 | + | 0.0696328i | 0.465151 | − | 0.885232i | \(-0.346000\pi\) |
−0.297042 | + | 0.954864i | \(0.596000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09610 | − | 7.47465i | −0.268466 | − | 0.648135i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.0955 | − | 27.0955i | 2.33201 | − | 2.33201i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1315 | + | 11.1315i | 0.951029 | + | 0.951029i | 0.998856 | − | 0.0478269i | \(-0.0152296\pi\) |
−0.0478269 | + | 0.998856i | \(0.515230\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.95493 | + | 4.12347i | −0.844366 | + | 0.349748i | −0.762574 | − | 0.646902i | \(-0.776064\pi\) |
−0.0817925 | + | 0.996649i | \(0.526064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.57542 | + | 8.63182i | −0.301104 | + | 0.726930i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.26900i | 0.273368i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 24.2276i | − | 2.01199i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.31535 | + | 15.2466i | −0.520881 | + | 1.25752i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0658 | − | 5.41201i | 1.07039 | − | 0.443369i | 0.223261 | − | 0.974759i | \(-0.428330\pi\) |
0.847128 | + | 0.531389i | \(0.178330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0916 | − | 14.0916i | −1.14676 | − | 1.14676i | −0.987186 | − | 0.159572i | \(-0.948988\pi\) |
−0.159572 | − | 0.987186i | \(-0.551012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.80625 | − | 7.80625i | 0.631098 | − | 0.631098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.85570 | − | 4.48005i | −0.149053 | − | 0.359846i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.86629 | − | 1.18726i | −0.228755 | − | 0.0947534i | 0.265362 | − | 0.964149i | \(-0.414509\pi\) |
−0.494117 | + | 0.869395i | \(0.664509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.5520 | 2.74015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.13580 | 0.247136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.20872 | + | 3.81438i | 0.721283 | + | 0.298765i | 0.712964 | − | 0.701200i | \(-0.247352\pi\) |
0.00831846 | + | 0.999965i | \(0.497352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.33445 | − | 10.4643i | −0.337436 | − | 0.814643i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.15971 | − | 6.15971i | 0.476653 | − | 0.476653i | −0.427407 | − | 0.904059i | \(-0.640573\pi\) |
0.904059 | + | 0.427407i | \(0.140573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.36800 | + | 3.36800i | 0.259077 | + | 0.259077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 38.8052 | − | 16.0737i | 2.96751 | − | 1.22918i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.02283 | + | 9.71198i | −0.305850 | + | 0.738388i | 0.693980 | + | 0.719994i | \(0.255855\pi\) |
−0.999831 | + | 0.0183942i | \(0.994145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.64730i | 0.502488i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 27.4660i | − | 2.06447i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.34665 | + | 15.3222i | −0.474371 | + | 1.14523i | 0.487841 | + | 0.872932i | \(0.337785\pi\) |
−0.962212 | + | 0.272301i | \(0.912215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.12619 | − | 1.70912i | 0.306697 | − | 0.127038i | −0.224026 | − | 0.974583i | \(-0.571920\pi\) |
0.530724 | + | 0.847545i | \(0.321920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.3773 | − | 30.3773i | −2.24556 | − | 2.24556i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.2216 | + | 12.2216i | −0.898553 | + | 0.898553i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.702133 | − | 1.69510i | −0.0513450 | − | 0.123958i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.7527 | + | 6.11077i | 1.07310 | + | 0.444493i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7979 | −1.07074 | −0.535371 | − | 0.844617i | \(-0.679828\pi\) | ||||
−0.535371 | + | 0.844617i | \(0.679828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.66722 | −0.479917 | −0.239959 | − | 0.970783i | \(-0.577134\pi\) | ||||
−0.239959 | + | 0.970783i | \(0.577134\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.3670 | + | 10.9216i | 1.88818 | + | 0.782108i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.25199 | − | 15.0936i | −0.445436 | − | 1.07538i | −0.974013 | − | 0.226492i | \(-0.927274\pi\) |
0.528577 | − | 0.848885i | \(-0.322726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.682332 | − | 0.682332i | 0.0483693 | − | 0.0483693i | −0.682508 | − | 0.730878i | \(-0.739111\pi\) |
0.730878 | + | 0.682508i | \(0.239111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.5132 | − | 28.5132i | −2.01116 | − | 2.01116i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.32758 | − | 3.86361i | 0.654668 | − | 0.271172i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.77514 | + | 4.28556i | −0.123981 | + | 0.299317i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.2798i | 1.13152i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.98067i | − | 0.482863i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.43698 | − | 15.5403i | 0.443140 | − | 1.06984i | −0.531700 | − | 0.846933i | \(-0.678447\pi\) |
0.974841 | − | 0.222903i | \(-0.0715533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.1525 | + | 10.0043i | −1.65490 | + | 0.685483i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.65583 | + | 9.65583i | 0.658522 | + | 0.658522i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42888 | − | 1.42888i | 0.0969986 | − | 0.0969986i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.31019 | + | 15.2341i | 0.426403 | + | 1.02943i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.27116 | + | 1.76917i | 0.287309 | + | 0.119007i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.47654 | 0.0988764 | 0.0494382 | − | 0.998777i | \(-0.484257\pi\) | ||||
0.0494382 | + | 0.998777i | \(0.484257\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −34.5099 | −2.30066 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.1225 | − | 10.8203i | −1.73381 | − | 0.718169i | −0.999213 | − | 0.0396690i | \(-0.987370\pi\) |
−0.734600 | − | 0.678500i | \(-0.762630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.61614 | + | 8.73012i | 0.238961 | + | 0.576903i | 0.997176 | − | 0.0751019i | \(-0.0239282\pi\) |
−0.758215 | + | 0.652005i | \(0.773928\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.33751 | − | 3.33751i | 0.219592 | − | 0.219592i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.99248 | + | 9.99248i | 0.654629 | + | 0.654629i | 0.954104 | − | 0.299475i | \(-0.0968115\pi\) |
−0.299475 | + | 0.954104i | \(0.596811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.71115 | − | 3.60828i | 0.568253 | − | 0.235378i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.4999 | + | 30.1775i | −0.811959 | + | 1.96024i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5759i | 0.684097i | 0.939682 | + | 0.342049i | \(0.111121\pi\) | ||||
−0.939682 | + | 0.342049i | \(0.888879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.690846i | − | 0.0445013i | −0.999752 | − | 0.0222507i | \(-0.992917\pi\) | ||
0.999752 | − | 0.0222507i | \(-0.00708319\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.02632 | + | 16.9630i | −0.450739 | + | 1.08818i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.3867 | − | 6.37339i | 0.983021 | − | 0.407181i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.4375 | + | 12.4375i | 0.791379 | + | 0.791379i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.56361 | + | 6.56361i | −0.415952 | + | 0.415952i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.08493 | − | 14.6903i | −0.384077 | − | 0.927244i | −0.991168 | − | 0.132612i | \(-0.957664\pi\) |
0.607091 | − | 0.794632i | \(-0.292336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.49969 | + | 1.03540i | 0.157154 | + | 0.0650953i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.0180 | −1.00309 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7928 | −0.735612 | −0.367806 | − | 0.929902i | \(-0.619891\pi\) | ||||
−0.367806 | + | 0.929902i | \(0.619891\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.65431 | − | 2.75631i | −0.413479 | − | 0.171269i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0582 | + | 48.4249i | 1.24157 | + | 2.99742i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.4934 | − | 20.4934i | 1.26368 | − | 1.26368i | 0.314384 | − | 0.949296i | \(-0.398202\pi\) |
0.949296 | − | 0.314384i | \(-0.101798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.6565 | − | 24.6565i | −1.51464 | − | 1.51464i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.9195 | + | 11.1504i | −1.64745 | + | 0.682395i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.82741 | − | 9.24018i | 0.233361 | − | 0.563384i | −0.763208 | − | 0.646153i | \(-0.776377\pi\) |
0.996569 | + | 0.0827697i | \(0.0263766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.2037i | − | 1.53102i | −0.643426 | − | 0.765508i | \(-0.722488\pi\) | ||
0.643426 | − | 0.765508i | \(-0.277512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.8929i | 0.719791i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.19486 | + | 5.29885i | −0.132355 | + | 0.319533i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.6544 | + | 5.65583i | −0.820413 | + | 0.339826i | −0.753100 | − | 0.657906i | \(-0.771443\pi\) |
−0.0673127 | + | 0.997732i | \(0.521443\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.41813 | + | 7.41813i | 0.444112 | + | 0.444112i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.45247 | − | 4.45247i | 0.265612 | − | 0.265612i | −0.561717 | − | 0.827329i | \(-0.689859\pi\) |
0.827329 | + | 0.561717i | \(0.189859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.32635 | − | 22.5158i | −0.554394 | − | 1.33843i | −0.914149 | − | 0.405379i | \(-0.867140\pi\) |
0.359755 | − | 0.933047i | \(-0.382860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −56.3044 | − | 23.3220i | −3.33518 | − | 1.38148i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.93302 | −0.114102 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4053 | 0.847368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.93015 | + | 1.21371i | 0.171769 | + | 0.0711488i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.76241 | + | 6.66906i | 0.161382 | + | 0.389611i | 0.983799 | − | 0.179274i | \(-0.0573750\pi\) |
−0.822417 | + | 0.568885i | \(0.807375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.5998 | + | 19.5998i | −1.14115 | + | 1.14115i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.74233 | + | 9.74233i | 0.565307 | + | 0.565307i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.29848 | + | 2.60892i | −0.364251 | + | 0.150878i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.17765 | + | 5.25731i | −0.125518 | + | 0.303026i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.1999i | 1.96474i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.3548i | 2.48249i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.76523 | + | 16.3327i | −0.386112 | + | 0.932158i | 0.604643 | + | 0.796497i | \(0.293316\pi\) |
−0.990755 | + | 0.135661i | \(0.956684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −41.7523 | + | 17.2944i | −2.37521 | + | 0.983843i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.48818 | − | 9.48818i | −0.538025 | − | 0.538025i | 0.384923 | − | 0.922949i | \(-0.374228\pi\) |
−0.922949 | + | 0.384923i | \(0.874228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.39347 | − | 8.39347i | 0.474427 | − | 0.474427i | −0.428917 | − | 0.903344i | \(-0.641105\pi\) |
0.903344 | + | 0.428917i | \(0.141105\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.9680 | − | 26.4791i | −0.617977 | − | 1.49193i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.5907 | + | 11.0142i | 1.49348 | + | 0.618621i | 0.972072 | − | 0.234683i | \(-0.0754053\pi\) |
0.521413 | + | 0.853305i | \(0.325405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.71115 | 0.487731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.1309 | 1.73756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.12069 | − | 3.77791i | −0.507489 | − | 0.210209i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.53040 | − | 13.3516i | −0.306772 | − | 0.740612i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.4368 | + | 23.4368i | −1.29606 | + | 1.29606i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.77836 | + | 2.77836i | 0.153176 | + | 0.153176i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.42728 | + | 3.90491i | −0.518170 | + | 0.214633i | −0.626413 | − | 0.779491i | \(-0.715478\pi\) |
0.108243 | + | 0.994124i | \(0.465478\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.3096 | − | 34.5464i | 0.784160 | − | 1.89313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.6943i | 2.22337i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.82843i | − | 0.154074i | −0.997028 | − | 0.0770371i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770371i | \(-0.0245460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.08856 | + | 7.45645i | −0.167748 | + | 0.404979i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.61082 | − | 0.667224i | 0.0872308 | − | 0.0361322i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4417 | + | 11.4417i | 0.617794 | + | 0.617794i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.7026 | − | 16.7026i | 0.899239 | − | 0.899239i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.101243 | − | 0.244423i | −0.00543503 | − | 0.0131213i | 0.921139 | − | 0.389234i | \(-0.127260\pi\) |
−0.926574 | + | 0.376113i | \(0.877260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.72727 | + | 0.715459i | 0.0924586 | + | 0.0382976i | 0.428433 | − | 0.903573i | \(-0.359066\pi\) |
−0.335975 | + | 0.941871i | \(0.609066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34.7159 | −1.85300 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.0270 | 1.17238 | 0.586189 | − | 0.810175i | \(-0.300628\pi\) | ||||
0.586189 | + | 0.810175i | \(0.300628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.3745 | + | 10.0962i | 1.29366 | + | 0.535853i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.55442 | − | 6.16691i | −0.135194 | − | 0.326388i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.40689 | − | 9.40689i | 0.496477 | − | 0.496477i | −0.413863 | − | 0.910339i | \(-0.635821\pi\) |
0.910339 | + | 0.413863i | \(0.135821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1242 | − | 13.1242i | −0.690746 | − | 0.690746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.1384 | + | 11.6553i | −1.47688 | + | 0.611745i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.36818 | − | 15.3741i | 0.333326 | − | 0.804720i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.57941i | − | 0.343442i | −0.985146 | − | 0.171721i | \(-0.945067\pi\) | ||
0.985146 | − | 0.171721i | \(-0.0549328\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 10.0354i | − | 0.522422i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.56069 | − | 13.4247i | 0.288697 | − | 0.696976i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.2298 | − | 5.47997i | 0.685014 | − | 0.283742i | −0.0129074 | − | 0.999917i | \(-0.504109\pi\) |
0.697921 | + | 0.716175i | \(0.254109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.248943 | + | 0.248943i | 0.0128554 | + | 0.0128554i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.5207 | + | 15.5207i | −0.799356 | + | 0.799356i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.55000 | − | 8.57046i | −0.182351 | − | 0.440235i | 0.806099 | − | 0.591781i | \(-0.201575\pi\) |
−0.988450 | + | 0.151546i | \(0.951575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.8681 | − | 7.40122i | −0.915412 | − | 0.379176i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6316 | 1.10532 | 0.552661 | − | 0.833406i | \(-0.313612\pi\) | ||||
0.552661 | + | 0.833406i | \(0.313612\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.76333 | −0.242762 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.2937 | − | 11.3054i | −1.38742 | − | 0.574687i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.31161 | + | 7.99494i | 0.167906 | + | 0.405360i | 0.985326 | − | 0.170681i | \(-0.0545968\pi\) |
−0.817421 | + | 0.576041i | \(0.804597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.70564 | − | 2.70564i | 0.136830 | − | 0.136830i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.62263 | + | 4.62263i | 0.233181 | + | 0.233181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.4549 | − | 12.6148i | 1.53235 | − | 0.634721i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.23136 | + | 2.97276i | −0.0618001 | + | 0.149199i | −0.951763 | − | 0.306834i | \(-0.900730\pi\) |
0.889963 | + | 0.456033i | \(0.150730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 25.3963i | − | 1.27140i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.2175i | 1.10949i | 0.832021 | + | 0.554744i | \(0.187184\pi\) | ||||
−0.832021 | + | 0.554744i | \(0.812816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68121 | + | 4.05880i | −0.0837471 | + | 0.202183i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 50.9531 | − | 21.1055i | 2.53188 | − | 1.04874i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.39435 | − | 4.39435i | −0.217820 | − | 0.217820i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8932 | − | 17.8932i | 0.884760 | − | 0.884760i | −0.109254 | − | 0.994014i | \(-0.534846\pi\) |
0.994014 | + | 0.109254i | \(0.0348462\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.9105 | + | 45.6540i | 0.932786 | + | 2.25195i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.6715 | − | 4.42029i | −0.525111 | − | 0.217508i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.36765 | 0.459840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.8234 | −1.65634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.2254 | − | 9.62029i | −1.13464 | − | 0.469982i | −0.265282 | − | 0.964171i | \(-0.585465\pi\) |
−0.869354 | + | 0.494189i | \(0.835465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.42786 | + | 20.3467i | 0.410749 | + | 0.991635i | 0.984937 | + | 0.172912i | \(0.0553176\pi\) |
−0.574189 | + | 0.818723i | \(0.694682\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4241 | + | 14.4241i | −0.701322 | + | 0.701322i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.73544 | + | 5.73544i | 0.278210 | + | 0.278210i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.6915 | + | 6.91385i | −0.807759 | + | 0.334585i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.92689 | + | 9.48036i | −0.189592 | + | 0.457716i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.2075i | − | 1.55138i | −0.631115 | − | 0.775689i | \(-0.717402\pi\) | ||
0.631115 | − | 0.775689i | \(-0.282598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.4806i | − | 1.41675i | −0.705837 | − | 0.708374i | \(-0.749429\pi\) | ||
0.705837 | − | 0.708374i | \(-0.250571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.1035 | − | 70.2620i | 1.39540 | − | 3.36880i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4499 | − | 5.57112i | 0.643395 | − | 0.266503i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2529 | + | 13.2529i | 0.632526 | + | 0.632526i | 0.948701 | − | 0.316175i | \(-0.102399\pi\) |
−0.316175 | + | 0.948701i | \(0.602399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.4776 | + | 25.4776i | −1.21322 | + | 1.21322i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.1474 | + | 31.7407i | 0.624653 | + | 1.50805i | 0.846183 | + | 0.532893i | \(0.178895\pi\) |
−0.221529 | + | 0.975154i | \(0.571105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.1669 | + | 11.2529i | 1.28784 | + | 0.533439i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.3929 | 2.09971 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.2227 | −1.61507 | −0.807534 | − | 0.589821i | \(-0.799198\pi\) | ||||
−0.807534 | + | 0.589821i | \(0.799198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54089 | − | 0.638259i | −0.0725578 | − | 0.0300544i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.9392 | − | 57.7943i | −1.12476 | − | 2.71541i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.48684 | − | 8.48684i | 0.397869 | − | 0.397869i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.79873 | + | 9.79873i | 0.458365 | + | 0.458365i | 0.898119 | − | 0.439753i | \(-0.144934\pi\) |
−0.439753 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.0015 | − | 7.45645i | 0.840237 | − | 0.348037i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.83552 | − | 4.43134i | 0.0854887 | − | 0.206388i | −0.875354 | − | 0.483483i | \(-0.839372\pi\) |
0.960843 | + | 0.277095i | \(0.0893716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.8164i | − | 1.15332i | −0.816985 | − | 0.576658i | \(-0.804356\pi\) | ||
0.816985 | − | 0.576658i | \(-0.195644\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 15.2216i | − | 0.705887i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.50725 | + | 15.7099i | −0.301120 | + | 0.726967i | 0.698812 | + | 0.715305i | \(0.253712\pi\) |
−0.999932 | + | 0.0116621i | \(0.996288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6672 | + | 6.48958i | −0.723445 | + | 0.299661i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.88628 | − | 6.88628i | −0.317303 | − | 0.317303i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.47180 | + | 3.47180i | −0.159633 | + | 0.159633i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.8097 | + | 28.5111i | 0.541866 | + | 1.30818i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 69.6954 | + | 28.8688i | 3.19113 | + | 1.32181i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7254 | −1.63234 | −0.816168 | − | 0.577815i | \(-0.803905\pi\) | ||||
−0.816168 | + | 0.577815i | \(0.803905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.6589 | 0.713982 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.09407 | + | 3.76689i | 0.413795 | + | 0.171399i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.22486 | − | 2.95708i | −0.0556181 | − | 0.134274i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.34809 | + | 5.34809i | −0.242345 | + | 0.242345i | −0.817820 | − | 0.575475i | \(-0.804817\pi\) |
0.575475 | + | 0.817820i | \(0.304817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.1240 | + | 22.1240i | 1.00048 | + | 1.00048i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.7647 | − | 16.8853i | 1.83968 | − | 0.762022i | 0.884104 | − | 0.467291i | \(-0.154770\pi\) |
0.955580 | − | 0.294731i | \(-0.0952302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.71444 | − | 11.3817i | 0.212328 | − | 0.512604i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 24.7292i | − | 1.11149i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9942i | 0.493157i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.95447 | + | 4.71852i | −0.0874943 | + | 0.211230i | −0.961570 | − | 0.274560i | \(-0.911468\pi\) |
0.874076 | + | 0.485790i | \(0.161468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.2630 | − | 10.4643i | 1.12867 | − | 0.467510i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.81469 | − | 4.81469i | −0.214676 | − | 0.214676i | 0.591574 | − | 0.806251i | \(-0.298507\pi\) |
−0.806251 | + | 0.591574i | \(0.798507\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.4053 | − | 24.4053i | 1.08602 | − | 1.08602i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.72164 | + | 13.8133i | 0.254107 | + | 0.613469i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.71949 | − | 2.36909i | −0.253512 | − | 0.105008i | 0.252308 | − | 0.967647i | \(-0.418810\pi\) |
−0.505821 | + | 0.862639i | \(0.668810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.93456 | 0.306767 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 74.1328 | 3.27304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.1360 | + | 17.4533i | 1.85674 | + | 0.769085i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.29737 | + | 3.13213i | 0.0570584 | + | 0.137751i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.3331 | + | 23.3331i | −1.02421 | + | 1.02421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8240 | + | 13.8240i | 0.605642 | + | 0.605642i | 0.941804 | − | 0.336162i | \(-0.109129\pi\) |
−0.336162 | + | 0.941804i | \(0.609129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.51144 | − | 3.11134i | 0.328452 | − | 0.136049i | −0.212363 | − | 0.977191i | \(-0.568116\pi\) |
0.540815 | + | 0.841141i | \(0.318116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.98508 | + | 19.2777i | −0.348497 | + | 0.841347i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.46574i | − | 0.107409i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.3574i | − | 0.754671i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.9483 | − | 55.4020i | 0.995870 | − | 2.40424i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.88260 | − | 1.60823i | 0.168174 | − | 0.0696600i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.2152 | − | 22.2152i | −0.960445 | − | 0.960445i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.8116 | + | 36.8116i | −1.58854 | + | 1.58854i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.29158 | + | 5.53237i | 0.0987054 | + | 0.238296i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9728 | − | 9.10142i | −0.944683 | − | 0.391300i | −0.143453 | − | 0.989657i | \(-0.545821\pi\) |
−0.801230 | + | 0.598357i | \(0.795821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0194 | 0.601629 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.4493 | 1.43281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.2456 | + | 16.2561i | 1.67802 | + | 0.695060i | 0.999229 | − | 0.0392692i | \(-0.0125030\pi\) |
0.678794 | + | 0.734329i | \(0.262503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.8938 | − | 86.6553i | −1.53191 | − | 3.69836i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.1431 | − | 33.1431i | 1.41194 | − | 1.41194i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.71336 | + | 9.71336i | 0.413054 | + | 0.413054i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −50.1250 | + | 20.7625i | −2.12769 | + | 0.881317i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0835 | − | 38.8291i | 0.681481 | − | 1.64524i | −0.0797936 | − | 0.996811i | \(-0.525426\pi\) |
0.761275 | − | 0.648429i | \(-0.224574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.3714i | − | 0.523256i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.75936i | − | 0.243160i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.3396 | + | 37.0331i | −0.646487 | + | 1.56076i | 0.171289 | + | 0.985221i | \(0.445207\pi\) |
−0.817776 | + | 0.575536i | \(0.804793\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.52498 | − | 3.11695i | 0.316578 | − | 0.131131i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.2511 | + | 16.2511i | 0.682483 | + | 0.682483i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.5518 | − | 18.5518i | 0.777732 | − | 0.777732i | −0.201713 | − | 0.979445i | \(-0.564651\pi\) |
0.979445 | + | 0.201713i | \(0.0646508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94591 | + | 4.69785i | 0.0814340 | + | 0.196599i | 0.959352 | − | 0.282212i | \(-0.0910680\pi\) |
−0.877918 | + | 0.478811i | \(0.841068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.9152 | − | 17.7761i | −1.79281 | − | 0.742606i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.9611 | −0.498814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3839 | −1.51468 | −0.757341 | − | 0.653020i | \(-0.773502\pi\) | ||||
−0.757341 | + | 0.653020i | \(0.773502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.3355 | − | 8.00902i | −0.803555 | − | 0.332843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.49387 | + | 3.60653i | 0.0619762 | + | 0.149624i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.86535 | − | 8.86535i | 0.367165 | − | 0.367165i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 44.0601 | + | 44.0601i | 1.82166 | + | 1.82166i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.2613 | + | 10.8778i | −1.08392 | + | 0.448974i | −0.851883 | − | 0.523733i | \(-0.824539\pi\) |
−0.232037 | + | 0.972707i | \(0.574539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.59008 | − | 8.66722i | 0.147927 | − | 0.357127i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 51.2830i | − | 2.10950i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.36388i | 0.343464i | 0.985144 | + | 0.171732i | \(0.0549362\pi\) | ||||
−0.985144 | + | 0.171732i | \(0.945064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.57789 | + | 6.22359i | −0.105683 | + | 0.255142i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.79847 | − | 1.15916i | 0.114534 | − | 0.0474414i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.8797 | + | 10.8797i | 0.444531 | + | 0.444531i | 0.893531 | − | 0.449001i | \(-0.148220\pi\) |
−0.449001 | + | 0.893531i | \(0.648220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9066 | + | 13.9066i | −0.567264 | + | 0.567264i | −0.931361 | − | 0.364097i | \(-0.881378\pi\) |
0.364097 | + | 0.931361i | \(0.381378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.6911 | − | 81.3376i | −1.37201 | − | 3.31232i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.3970 | + | 11.7624i | 1.15450 | + | 0.478210i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.3665 | 1.71960 | 0.859801 | − | 0.510629i | \(-0.170588\pi\) | ||||
0.859801 | + | 0.510629i | \(0.170588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.6919 | 1.28422 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.89207 | − | 3.26900i | −0.319279 | − | 0.132250i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.50500 | + | 13.2902i | 0.222345 | + | 0.536788i | 0.995208 | − | 0.0977853i | \(-0.0311758\pi\) |
−0.772863 | + | 0.634573i | \(0.781176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.2961 | + | 10.2961i | −0.415178 | + | 0.415178i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.8105 | + | 17.8105i | 0.717025 | + | 0.717025i | 0.967995 | − | 0.250970i | \(-0.0807494\pi\) |
−0.250970 | + | 0.967995i | \(0.580749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.6033 | + | 4.80624i | −0.466376 | + | 0.193179i | −0.603481 | − | 0.797377i | \(-0.706220\pi\) |
0.137105 | + | 0.990556i | \(0.456220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.9957 | + | 26.5460i | −0.441242 | + | 1.06525i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2537i | 0.490935i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8217i | 0.992869i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.38555 | − | 20.2445i | 0.334886 | − | 0.808487i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.11970 | + | 3.36329i | −0.323753 | + | 0.134103i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8865 | + | 12.8865i | 0.513004 | + | 0.513004i | 0.915446 | − | 0.402442i | \(-0.131838\pi\) |
−0.402442 | + | 0.915446i | \(0.631838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.3355 | − | 37.3355i | 1.48395 | − | 1.48395i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.46924 | + | 18.0323i | 0.296408 | + | 0.715592i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.9400 | − | 5.77412i | −0.552321 | − | 0.228779i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57.0772 | −2.25794 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6050 | −0.497868 | −0.248934 | − | 0.968520i | \(-0.580080\pi\) | ||||
−0.248934 | + | 0.968520i | \(0.580080\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2632 | + | 5.90799i | 0.562484 | + | 0.232988i | 0.645763 | − | 0.763538i | \(-0.276539\pi\) |
−0.0832793 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.4036 | + | 39.6018i | 0.645891 | + | 1.55932i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.4412 | + | 19.4412i | −0.764314 | + | 0.764314i | −0.977099 | − | 0.212785i | \(-0.931747\pi\) |
0.212785 | + | 0.977099i | \(0.431747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.04722 | − | 7.04722i | −0.276627 | − | 0.276627i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.86030 | − | 2.42742i | 0.229683 | − | 0.0951380i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.40282 | + | 3.38672i | −0.0548968 | + | 0.132533i | −0.948948 | − | 0.315432i | \(-0.897851\pi\) |
0.894052 | + | 0.447964i | \(0.147851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.59747i | − | 0.257784i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.0013i | 1.40454i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.44977 | − | 15.5711i | 0.251247 | − | 0.606565i | −0.747058 | − | 0.664759i | \(-0.768534\pi\) |
0.998305 | + | 0.0581942i | \(0.0185343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5801 | + | 6.03928i | −0.567100 | + | 0.234901i | −0.647764 | − | 0.761841i | \(-0.724296\pi\) |
0.0806641 | + | 0.996741i | \(0.474296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.2615 | + | 10.2615i | 0.398522 | + | 0.398522i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.1229 | + | 18.1229i | −0.702777 | + | 0.702777i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.95218 | + | 16.7840i | 0.269189 | + | 0.649880i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.28208 | + | 1.77370i | 0.165555 | + | 0.0685750i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.5884 | −0.601784 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1812 | −0.700834 | −0.350417 | − | 0.936594i | \(-0.613960\pi\) | ||||
−0.350417 | + | 0.936594i | \(0.613960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −56.2724 | − | 23.3088i | −2.16592 | − | 0.897155i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7255 | + | 35.5504i | 0.565945 | + | 1.36631i | 0.904946 | + | 0.425527i | \(0.139911\pi\) |
−0.339000 | + | 0.940786i | \(0.610089\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.943139 | − | 0.943139i | 0.0361944 | − | 0.0361944i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −62.7595 | − | 62.7595i | −2.40495 | − | 2.40495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.69296 | − | 2.35810i | 0.217835 | − | 0.0902303i | −0.271097 | − | 0.962552i | \(-0.587386\pi\) |
0.488932 | + | 0.872322i | \(0.337386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.0843 | − | 46.0736i | 0.729173 | − | 1.76038i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.6619i | 1.13167i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.5909i | 1.20352i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.68727 | − | 6.48765i | 0.102229 | − | 0.246802i | −0.864487 | − | 0.502655i | \(-0.832356\pi\) |
0.966716 | + | 0.255854i | \(0.0823565\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.52069 | − | 3.94360i | 0.361661 | − | 0.149805i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.1366 | + | 24.1366i | 0.915552 | + | 0.915552i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.66785 | + | 1.66785i | −0.0631743 | + | 0.0631743i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.9755 | + | 40.9825i | 0.642072 | + | 1.55010i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.6300 | + | 4.81730i | 0.439258 | + | 0.181947i | 0.591342 | − | 0.806421i | \(-0.298598\pi\) |
−0.152084 | + | 0.988368i | \(0.548598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4381 | −1.26114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.5975 | 1.11470 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.2879 | + | 5.50404i | 0.499744 | + | 0.207001i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.857335 | + | 2.06979i | 0.0321979 | + | 0.0777326i | 0.939161 | − | 0.343478i | \(-0.111605\pi\) |
−0.906963 | + | 0.421211i | \(0.861605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −50.4277 | + | 50.4277i | −1.89119 | + | 1.89119i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.57112 | + | 2.57112i | 0.0962893 | + | 0.0962893i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.56749 | − | 3.96298i | 0.357804 | − | 0.148207i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.7043 | + | 30.6709i | −0.474451 | + | 1.14543i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.4245i | 1.09735i | 0.836036 | + | 0.548674i | \(0.184867\pi\) | ||||
−0.836036 | + | 0.548674i | \(0.815133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0056i | 0.707806i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.829880 | − | 2.00351i | 0.0308636 | − | 0.0745113i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35.5789 | + | 14.7373i | −1.32137 | + | 0.547329i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.75350 | − | 1.75350i | −0.0650337 | − | 0.0650337i | 0.673842 | − | 0.738876i | \(-0.264643\pi\) |
−0.738876 | + | 0.673842i | \(0.764643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.82254 | + | 3.82254i | −0.141575 | + | 0.141575i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.65720 | + | 6.41505i | 0.0982801 | + | 0.237269i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.08042 | − | 0.447524i | −0.0399062 | − | 0.0165297i | 0.362641 | − | 0.931929i | \(-0.381875\pi\) |
−0.402547 | + | 0.915399i | \(0.631875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 52.2787 | 1.92833 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6318 | −0.538970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.3968 | − | 15.0760i | −1.33888 | − | 0.554581i | −0.405703 | − | 0.914005i | \(-0.632973\pi\) |
−0.933174 | + | 0.359424i | \(0.882973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.1291 | + | 51.0103i | 0.776198 | + | 1.87391i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.45255 | − | 1.45255i | 0.0532888 | − | 0.0532888i | −0.679960 | − | 0.733249i | \(-0.738003\pi\) |
0.733249 | + | 0.679960i | \(0.238003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.6790 | − | 31.6790i | −1.16063 | − | 1.16063i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.7236 | + | 7.75555i | −0.685059 | + | 0.283761i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.01011 | − | 12.0955i | 0.183065 | − | 0.441959i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4254i | 0.635861i | 0.948114 | + | 0.317931i | \(0.102988\pi\) | ||||
−0.948114 | + | 0.317931i | \(0.897012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 49.9126i | − | 1.81892i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.1592 | + | 58.3255i | −0.879243 | + | 2.12268i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.2830 | + | 10.8868i | −0.955272 | + | 0.395686i | −0.805210 | − | 0.592990i | \(-0.797947\pi\) |
−0.150062 | + | 0.988677i | \(0.547947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.00551 | + | 6.00551i | 0.217986 | + | 0.217986i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.6001 | − | 13.6001i | 0.493003 | − | 0.493003i | −0.416248 | − | 0.909251i | \(-0.636655\pi\) |
0.909251 | + | 0.416248i | \(0.136655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.33420 | + | 12.8779i | 0.193111 | + | 0.466211i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.3102 | − | 13.3833i | −1.16818 | − | 0.483875i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.1121 | 0.906745 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.19053 | −0.295358 | −0.147679 | − | 0.989035i | \(-0.547180\pi\) | ||||
−0.147679 | + | 0.989035i | \(0.547180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.1999 | − | 14.1661i | −1.23168 | − | 0.510179i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.3176 | − | 29.7373i | −0.443033 | − | 1.06958i | −0.974879 | − | 0.222735i | \(-0.928502\pi\) |
0.531847 | − | 0.846841i | \(-0.321498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.45028 | + | 5.45028i | −0.195780 | + | 0.195780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.9870 | − | 15.9870i | −0.573531 | − | 0.573531i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.29097 | + | 3.43423i | −0.297055 | + | 0.123044i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.63015 | + | 8.76395i | −0.129897 | + | 0.313599i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 92.5100i | 3.30604i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.82817i | 0.350782i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.89741 | − | 9.40919i | 0.138928 | − | 0.335401i | −0.839068 | − | 0.544027i | \(-0.816899\pi\) |
0.977996 | + | 0.208626i | \(0.0668990\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 84.0504 | − | 34.8148i | 2.99227 | − | 1.23944i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.40004 | + | 2.40004i | 0.0853356 | + | 0.0853356i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7740 | − | 27.7740i | 0.986282 | − | 0.986282i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41.8871 | − | 101.124i | −1.48558 | − | 3.58651i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.2799 | + | 7.15756i | 0.612085 | + | 0.253534i | 0.667120 | − | 0.744951i | \(-0.267527\pi\) |
−0.0550349 | + | 0.998484i | \(0.517527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.79446 | 0.169616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −63.6162 | −2.24777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.52785 | + | 2.28971i | 0.195073 | + | 0.0808021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.80151 | − | 9.17765i | −0.133985 | − | 0.323470i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.1996 | − | 22.1996i | 0.781462 | − | 0.781462i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3548 | − | 28.3548i | −0.996902 | − | 0.996902i | 0.00309284 | − | 0.999995i | \(-0.499016\pi\) |
−0.999995 | + | 0.00309284i | \(0.999016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.90316 | + | 1.61674i | −0.137059 | + | 0.0567716i | −0.450159 | − | 0.892949i | \(-0.648633\pi\) |
0.313100 | + | 0.949720i | \(0.398633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.2760 | − | 73.0927i | 1.06183 | − | 2.56347i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 31.5756i | − | 1.10604i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4181i | 0.924254i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.93672 | + | 23.9894i | −0.347217 | + | 0.838256i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.8360 | − | 11.5300i | 0.971482 | − | 0.402401i | 0.160218 | − | 0.987082i | \(-0.448780\pi\) |
0.811264 | + | 0.584681i | \(0.198780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.7602 | − | 30.7602i | −1.07223 | − | 1.07223i | −0.997179 | − | 0.0750551i | \(-0.976087\pi\) |
−0.0750551 | − | 0.997179i | \(-0.523913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.7305 | + | 12.7305i | −0.443220 | + | 0.443220i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.60486 | − | 23.1882i | −0.333994 | − | 0.806332i | −0.998267 | − | 0.0588423i | \(-0.981259\pi\) |
0.664274 | − | 0.747489i | \(-0.268741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.5185 | − | 17.1975i | −1.44200 | − | 0.597295i | −0.481715 | − | 0.876328i | \(-0.659986\pi\) |
−0.960281 | + | 0.279033i | \(0.909986\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.3929 | −1.60935 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.46858 | 0.293419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.4952 | − | 10.5605i | −0.882297 | − | 0.365459i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.08573 | + | 17.1065i | 0.244919 | + | 0.591286i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.1198 | − | 31.1198i | 1.07437 | − | 1.07437i | 0.0773708 | − | 0.997002i | \(-0.475347\pi\) |
0.997002 | − | 0.0773708i | \(-0.0246525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8530 | + | 20.8530i | 0.719070 | + | 0.719070i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.2611 | − | 7.56398i | 0.628944 | − | 0.260517i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.77423 | − | 13.9402i | 0.198639 | − | 0.479558i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8086i | 0.440107i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 76.5009i | − | 2.62550i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.95969 | − | 11.9738i | 0.170016 | − | 0.410455i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.6797 | + | 9.80845i | −0.810777 | + | 0.335835i | −0.749264 | − | 0.662271i | \(-0.769593\pi\) |
−0.0615130 | + | 0.998106i | \(0.519593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94.0865 | − | 94.0865i | −3.21769 | − | 3.21769i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.7590 | − | 24.7590i | 0.845752 | − | 0.845752i | −0.143847 | − | 0.989600i | \(-0.545947\pi\) |
0.989600 | + | 0.143847i | \(0.0459475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.30545 | − | 7.98006i | −0.112780 | − | 0.272276i | 0.857404 | − | 0.514644i | \(-0.172076\pi\) |
−0.970184 | + | 0.242368i | \(0.922076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.60590 | − | 2.32204i | −0.191049 | − | 0.0791349i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.4394 | 1.20637 | 0.603185 | − | 0.797601i | \(-0.293898\pi\) | ||||
0.603185 | + | 0.797601i | \(0.293898\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.3012 | 1.13227 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.7764 | + | 17.3043i | 1.41880 | + | 0.587686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.53572 | + | 10.9502i | 0.153864 | + | 0.371460i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.0696 | − | 26.0696i | 0.883334 | − | 0.883334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.89638 | + | 4.89638i | 0.165717 | + | 0.165717i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.136788 | − | 0.0566593i | 0.00462427 | − | 0.00191543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9341 | + | 43.2968i | −0.605593 | + | 1.46203i | 0.262155 | + | 0.965026i | \(0.415567\pi\) |
−0.867748 | + | 0.497005i | \(0.834433\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.6591i | 0.764274i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.84917i | − | 0.163373i | −0.996658 | − | 0.0816863i | \(-0.973969\pi\) | ||
0.996658 | − | 0.0816863i | \(-0.0260306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9445 | − | 40.9077i | 0.570228 | − | 1.37665i | −0.331133 | − | 0.943584i | \(-0.607431\pi\) |
0.901361 | − | 0.433068i | \(-0.142569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −80.3855 | + | 33.2967i | −2.70213 | + | 1.11926i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.77550 | + | 7.77550i | 0.261076 | + | 0.261076i | 0.825491 | − | 0.564415i | \(-0.190898\pi\) |
−0.564415 | + | 0.825491i | \(0.690898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.75128 | + | 5.75128i | −0.192892 | + | 0.192892i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.58856 | + | 18.3204i | 0.254226 | + | 0.613757i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.8528 | + | 6.98067i | 0.563959 | + | 0.233599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.5379 | 1.75615 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4001 | −0.714527 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.8158 | + | 4.48005i | 0.360727 | + | 0.149418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.78525 | − | 16.3810i | −0.226049 | − | 0.545731i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.6307 | + | 12.6307i | −0.420323 | + | 0.420323i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0043 | − | 10.0043i | −0.332554 | − | 0.332554i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.75906 | − | 2.38548i | 0.191226 | − | 0.0792086i | −0.285015 | − | 0.958523i | \(-0.591999\pi\) |
0.476242 | + | 0.879314i | \(0.341999\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.5746 | + | 68.9853i | −0.947761 | + | 2.28810i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3924i | 0.509973i | 0.966945 | + | 0.254986i | \(0.0820710\pi\) | ||||
−0.966945 | + | 0.254986i | \(0.917929\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.36818i | 0.111470i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −52.0801 | + | 125.732i | −1.72171 | + | 4.15658i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.54001 | − | 1.05211i | 0.0838786 | − | 0.0347437i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0672 | + | 13.0672i | 0.431046 | + | 0.431046i | 0.888984 | − | 0.457938i | \(-0.151412\pi\) |
−0.457938 | + | 0.888984i | \(0.651412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.2394 | + | 39.2394i | −1.29298 | + | 1.29298i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.14692 | − | 22.0826i | −0.301075 | − | 0.726858i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.3821 | + | 10.5136i | 0.834557 | + | 0.345685i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −98.6690 | −3.24072 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.4450 | 0.473924 | 0.236962 | − | 0.971519i | \(-0.423848\pi\) | ||||
0.236962 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.7676 | + | 12.3301i | 0.975593 | + | 0.404104i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.1188 | − | 38.9142i | −0.527705 | − | 1.27399i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.10991 | + | 4.10991i | −0.134408 | + | 0.134408i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.56931 | + | 4.56931i | 0.149273 | + | 0.149273i | 0.777793 | − | 0.628520i | \(-0.216339\pi\) |
−0.628520 | + | 0.777793i | \(0.716339\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.4244 | − | 14.2591i | 1.12340 | − | 0.465327i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.29813 | + | 17.6192i | −0.237912 | + | 0.574371i | −0.997067 | − | 0.0765397i | \(-0.975613\pi\) |
0.759154 | + | 0.650911i | \(0.225613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.47827i | − | 0.113268i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 50.5852i | − | 1.64554i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.50198 | − | 10.8687i | 0.146295 | − | 0.353187i | −0.833698 | − | 0.552221i | \(-0.813780\pi\) |
0.979993 | + | 0.199034i | \(0.0637805\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.9286 | + | 5.76940i | −0.452140 | + | 0.187283i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 63.8843 | + | 63.8843i | 2.07159 | + | 2.07159i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.88290 | + | 9.88290i | −0.320138 | + | 0.320138i | −0.848820 | − | 0.528682i | \(-0.822687\pi\) |
0.528682 | + | 0.848820i | \(0.322687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.9394 | + | 43.3096i | 0.580506 | + | 1.40147i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.2630 | + | 10.4643i | 0.816637 | + | 0.338262i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.7816 | 0.671074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6569 | −0.924415 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 62.7946 | + | 26.0104i | 2.02353 | + | 0.838173i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.08262 | + | 19.5132i | 0.260189 | + | 0.628151i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.4467 | − | 27.4467i | 0.882626 | − | 0.882626i | −0.111175 | − | 0.993801i | \(-0.535461\pi\) |
0.993801 | + | 0.111175i | \(0.0354614\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.9125 | − | 21.9125i | −0.703931 | − | 0.703931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.2342 | − | 21.6361i | 1.67627 | − | 0.694335i | 0.677136 | − | 0.735858i | \(-0.263221\pi\) |
0.999138 | + | 0.0415225i | \(0.0132208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.44344 | + | 13.1416i | −0.174509 | + | 0.421301i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 45.3640i | − | 1.45281i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.1041i | − | 0.739165i | −0.929198 | − | 0.369582i | \(-0.879501\pi\) | ||
0.929198 | − | 0.369582i | \(-0.120499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.04603 | + | 9.76799i | −0.129312 | + | 0.312186i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66.8566 | + | 27.6929i | −2.13457 | + | 0.884167i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.7442 | − | 17.7442i | −0.565951 | − | 0.565951i | 0.365041 | − | 0.930991i | \(-0.381055\pi\) |
−0.930991 | + | 0.365041i | \(0.881055\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.5958 | + | 36.5958i | −1.16604 | + | 1.16604i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.71995 | + | 11.3950i | 0.150238 | + | 0.362706i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.45999 | − | 3.91846i | −0.300810 | − | 0.124600i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.68692 | −0.212417 | −0.106208 | − | 0.994344i | \(-0.533871\pi\) | ||||
−0.106208 | + | 0.994344i | \(0.533871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.0306 | −1.01646 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.82419 | − | 1.16982i | −0.0895328 | − | 0.0370857i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.39557 | + | 3.36920i | 0.0441981 | + | 0.106704i | 0.944437 | − | 0.328693i | \(-0.106608\pi\) |
−0.900239 | + | 0.435397i | \(0.856608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46.6668 | − | 46.6668i | 1.47647 | − | 1.47647i |
(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 | 1024.2.g.c.641.4 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.c.641.1 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.h.641.4 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.h.641.1 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.b.129.4 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.e.129.4 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.e.129.1 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.b.129.1 | ✓ | 16 | ||
32.3 | odd | 8 | 1024.2.g.e.897.1 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.h.385.1 | yes | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.c.385.1 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.b.897.1 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.b.897.4 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.c.385.4 | yes | 16 | |
32.27 | odd | 8 | 1024.2.g.h.385.4 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.e.897.4 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.n.1.2 | 8 | |||
64.21 | even | 16 | 4096.2.a.n.1.1 | 8 | |||
64.43 | odd | 16 | 4096.2.a.o.1.7 | 8 | |||
64.53 | even | 16 | 4096.2.a.o.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.129.1 | ✓ | 16 | 16.13 | even | 4 | ||
1024.2.g.b.129.4 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.b.897.1 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.b.897.4 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.c.385.1 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.c.385.4 | yes | 16 | 32.21 | even | 8 | inner | |
1024.2.g.c.641.1 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.c.641.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.e.129.1 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.e.129.4 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.e.897.1 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.e.897.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.h.385.1 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.h.385.4 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.h.641.1 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.h.641.4 | yes | 16 | 8.3 | odd | 2 | ||
4096.2.a.n.1.1 | 8 | 64.21 | even | 16 | |||
4096.2.a.n.1.2 | 8 | 64.11 | odd | 16 | |||
4096.2.a.o.1.7 | 8 | 64.43 | odd | 16 | |||
4096.2.a.o.1.8 | 8 | 64.53 | even | 16 |