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 | 129.4 | ||
Root | \(-1.66798 + 0.466730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.129 |
Dual form | 1024.2.g.e.897.4 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.20125 | − | 2.90008i | 0.693543 | − | 1.67436i | −0.0439740 | − | 0.999033i | \(-0.514002\pi\) |
0.737517 | − | 0.675328i | \(-0.235998\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.92673 | − | 1.21229i | 1.30887 | − | 0.542153i | 0.384318 | − | 0.923201i | \(-0.374437\pi\) |
0.924556 | + | 0.381047i | \(0.124437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.933460 | + | 0.933460i | −0.352815 | + | 0.352815i | −0.861156 | − | 0.508341i | \(-0.830259\pi\) |
0.508341 | + | 0.861156i | \(0.330259\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.84613 | − | 4.84613i | −1.61538 | − | 1.61538i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.435885 | + | 1.05232i | 0.131424 | + | 0.317286i | 0.975869 | − | 0.218356i | \(-0.0700695\pi\) |
−0.844445 | + | 0.535643i | \(0.820069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65154 | + | 1.09830i | 0.735405 | + | 0.304615i | 0.718771 | − | 0.695247i | \(-0.244705\pi\) |
0.0166339 | + | 0.999862i | \(0.494705\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | −5.66214 | − | 2.34533i | −1.29898 | − | 0.538056i | −0.377333 | − | 0.926078i | \(-0.623159\pi\) |
−0.921650 | + | 0.388021i | \(0.873159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58579 | + | 3.82843i | 0.346047 | + | 0.835431i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.67967 | − | 1.67967i | −0.350235 | − | 0.350235i | 0.509962 | − | 0.860197i | \(-0.329659\pi\) |
−0.860197 | + | 0.509962i | \(0.829659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.56057 | − | 3.56057i | 0.712114 | − | 0.712114i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.1753 | + | 4.62898i | −2.15070 | + | 0.890847i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.92673 | − | 7.06575i | 0.543480 | − | 1.31208i | −0.378772 | − | 0.925490i | \(-0.623654\pi\) |
0.922253 | − | 0.386588i | \(-0.126346\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −1.60036 | + | 3.86361i | −0.270510 | + | 0.653069i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.04072 | − | 2.08793i | 0.828689 | − | 0.343254i | 0.0723054 | − | 0.997383i | \(-0.476964\pi\) |
0.756384 | + | 0.654128i | \(0.226964\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.37033 | − | 6.37033i | 1.02007 | − | 1.02007i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03540 | + | 1.03540i | 0.161703 | + | 0.161703i | 0.783321 | − | 0.621618i | \(-0.213524\pi\) |
−0.621618 | + | 0.783321i | \(0.713524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.64959 | − | 3.98247i | −0.251561 | − | 0.607321i | 0.746770 | − | 0.665083i | \(-0.231604\pi\) |
−0.998330 | + | 0.0577615i | \(0.981604\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.0582 | − | 8.30839i | −2.99011 | − | 1.23854i | ||||
\(46\) | 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 | ||||||||
\(51\) | −4.67151 | − | 1.93500i | −0.654142 | − | 0.270954i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.21229 | + | 10.1694i | 0.578603 | + | 1.39687i | 0.894067 | + | 0.447933i | \(0.147840\pi\) |
−0.315464 | + | 0.948937i | \(0.602160\pi\) | |||||||
\(54\) | 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 | ||||||||
\(59\) | 8.08380 | − | 3.34842i | 1.05242 | − | 0.435927i | 0.211666 | − | 0.977342i | \(-0.432111\pi\) |
0.840756 | + | 0.541415i | \(0.182111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.23733 | + | 12.6440i | −0.670571 | + | 1.61890i | 0.110072 | + | 0.993924i | \(0.464892\pi\) |
−0.780643 | + | 0.624978i | \(0.785108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.04733 | 1.13986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.09181 | 1.12770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.91593 | + | 11.8681i | −0.600577 | + | 1.44992i | 0.272413 | + | 0.962180i | \(0.412178\pi\) |
−0.872989 | + | 0.487739i | \(0.837822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.88887 | + | 2.85346i | −0.829322 | + | 0.343516i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.88894 | − | 5.88894i | 0.698889 | − | 0.698889i | −0.265282 | − | 0.964171i | \(-0.585465\pi\) |
0.964171 | + | 0.265282i | \(0.0854650\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.71444 | − | 3.71444i | −0.434742 | − | 0.434742i | 0.455496 | − | 0.890238i | \(-0.349462\pi\) |
−0.890238 | + | 0.455496i | \(0.849462\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.04879 | − | 14.6031i | −0.698454 | − | 1.68622i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.38918 | − | 0.575417i | −0.158312 | − | 0.0655748i | ||||
\(78\) | 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 | ||||||||
\(83\) | 2.73199 | + | 1.13163i | 0.299874 | + | 0.124212i | 0.527547 | − | 0.849526i | \(-0.323112\pi\) |
−0.227673 | + | 0.973738i | \(0.573112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.95278 | − | 4.71444i | −0.211809 | − | 0.511353i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.9755 | − | 16.9755i | −1.81996 | − | 1.81996i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.56361 | − | 6.56361i | 0.695741 | − | 0.695741i | −0.267748 | − | 0.963489i | \(-0.586280\pi\) |
0.963489 | + | 0.267748i | \(0.0862795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50033 | + | 1.44988i | −0.366934 | + | 0.151989i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.83880 | − | 4.43925i | 0.190674 | − | 0.460329i | ||||
\(94\) | 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 | ||||||||
\(99\) | 2.98732 | − | 7.21203i | 0.300237 | − | 0.724836i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0658 | + | 4.16937i | −1.00158 | + | 0.414868i | −0.822376 | − | 0.568944i | \(-0.807352\pi\) |
−0.179204 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1802 | − | 10.1802i | 1.00308 | − | 1.00308i | 0.00308887 | − | 0.999995i | \(-0.499017\pi\) |
0.999995 | − | 0.00308887i | \(-0.000983218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.28234 | + | 9.28234i | 0.905864 | + | 0.905864i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.79522 | + | 9.16246i | 0.366897 | + | 0.885769i | 0.994255 | + | 0.107038i | \(0.0341365\pi\) |
−0.627357 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.75516 | + | 4.04072i | 0.934375 | + | 0.387031i | 0.797336 | − | 0.603535i | \(-0.206242\pi\) |
0.137038 | + | 0.990566i | \(0.456242\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −6.95218 | − | 2.87969i | −0.648294 | − | 0.268532i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.52718 | − | 18.1722i | −0.695888 | − | 1.68002i | ||||
\(118\) | 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 | ||||||||
\(123\) | 4.24653 | − | 1.75897i | 0.382897 | − | 0.158601i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.0429201 | − | 0.103618i | 0.00383889 | − | 0.00926790i | ||||
\(126\) | 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 | ||||||||
\(131\) | 0.796984 | − | 1.92409i | 0.0696328 | − | 0.168108i | −0.885232 | − | 0.465151i | \(-0.846000\pi\) |
0.954864 | + | 0.297042i | \(0.0960002\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.47465 | − | 3.09610i | 0.648135 | − | 0.268466i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.0955 | + | 27.0955i | −2.33201 | + | 2.33201i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1315 | − | 11.1315i | −0.951029 | − | 0.951029i | 0.0478269 | − | 0.998856i | \(-0.484770\pi\) |
−0.998856 | + | 0.0478269i | \(0.984770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.12347 | − | 9.95493i | −0.349748 | − | 0.844366i | −0.996649 | − | 0.0817925i | \(-0.973936\pi\) |
0.646902 | − | 0.762574i | \(-0.276064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.63182 | + | 3.57542i | 0.726930 | + | 0.301104i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.26900i | 0.273368i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 24.2276i | − | 2.01199i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.2466 | + | 6.31535i | 1.25752 | + | 0.520881i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.41201 | + | 13.0658i | 0.443369 | + | 1.07039i | 0.974759 | + | 0.223261i | \(0.0716701\pi\) |
−0.531389 | + | 0.847128i | \(0.678330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0916 | + | 14.0916i | 1.14676 | + | 1.14676i | 0.987186 | + | 0.159572i | \(0.0510115\pi\) |
0.159572 | + | 0.987186i | \(0.448988\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.80625 | + | 7.80625i | −0.631098 | + | 0.631098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.48005 | − | 1.85570i | 0.359846 | − | 0.149053i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.18726 | + | 2.86629i | −0.0947534 | + | 0.228755i | −0.964149 | − | 0.265362i | \(-0.914509\pi\) |
0.869395 | + | 0.494117i | \(0.164509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.5520 | 2.74015 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.13580 | 0.247136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.81438 | − | 9.20872i | 0.298765 | − | 0.721283i | −0.701200 | − | 0.712964i | \(-0.747352\pi\) |
0.999965 | − | 0.00831846i | \(-0.00264788\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.4643 | − | 4.33445i | 0.814643 | − | 0.337436i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.15971 | + | 6.15971i | −0.476653 | + | 0.476653i | −0.904059 | − | 0.427407i | \(-0.859427\pi\) |
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.36800 | − | 3.36800i | −0.259077 | − | 0.259077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.0737 | + | 38.8052i | 1.22918 | + | 2.96751i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.71198 | + | 4.02283i | 0.738388 | + | 0.305850i | 0.719994 | − | 0.693980i | \(-0.244145\pi\) |
0.0183942 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.64730i | 0.502488i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 27.4660i | − | 2.06447i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3222 | + | 6.34665i | 1.14523 | + | 0.474371i | 0.872932 | − | 0.487841i | \(-0.162215\pi\) |
0.272301 | + | 0.962212i | \(0.412215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70912 | + | 4.12619i | 0.127038 | + | 0.306697i | 0.974583 | − | 0.224026i | \(-0.0719202\pi\) |
−0.847545 | + | 0.530724i | \(0.821920\pi\) | |||||||
\(182\) | 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 | ||||||||
\(187\) | 1.69510 | − | 0.702133i | 0.123958 | − | 0.0513450i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.11077 | − | 14.7527i | 0.444493 | − | 1.07310i | ||||
\(190\) | 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 | ||||||||
\(195\) | 10.9216 | − | 26.3670i | 0.782108 | − | 1.88818i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0936 | − | 6.25199i | 1.07538 | − | 0.445436i | 0.226492 | − | 0.974013i | \(-0.427274\pi\) |
0.848885 | + | 0.528577i | \(0.177274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.682332 | + | 0.682332i | −0.0483693 | + | 0.0483693i | −0.730878 | − | 0.682508i | \(-0.760889\pi\) |
0.682508 | + | 0.730878i | \(0.260889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.5132 | + | 28.5132i | 2.01116 | + | 2.01116i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.86361 | + | 9.32758i | 0.271172 | + | 0.654668i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.28556 | + | 1.77514i | 0.299317 | + | 0.123981i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.2798i | 1.13152i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.98067i | − | 0.482863i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5403 | − | 6.43698i | −1.06984 | − | 0.443140i | −0.222903 | − | 0.974841i | \(-0.571553\pi\) |
−0.846933 | + | 0.531700i | \(0.821553\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0043 | − | 24.1525i | −0.685483 | − | 1.65490i | ||||
\(214\) | 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 | ||||||||
\(219\) | −15.2341 | + | 6.31019i | −1.02943 | + | 0.426403i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.76917 | − | 4.27116i | 0.119007 | − | 0.287309i | ||||
\(222\) | 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 | ||||||||
\(227\) | −10.8203 | + | 26.1225i | −0.718169 | + | 1.73381i | −0.0396690 | + | 0.999213i | \(0.512630\pi\) |
−0.678500 | + | 0.734600i | \(0.737370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.73012 | + | 3.61614i | −0.576903 | + | 0.238961i | −0.652005 | − | 0.758215i | \(-0.726072\pi\) |
0.0751019 | + | 0.997176i | \(0.476072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.33751 | + | 3.33751i | −0.219592 | + | 0.219592i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.99248 | − | 9.99248i | −0.654629 | − | 0.654629i | 0.299475 | − | 0.954104i | \(-0.403189\pi\) |
−0.954104 | + | 0.299475i | \(0.903189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.60828 | + | 8.71115i | 0.235378 | + | 0.568253i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 30.1775 | + | 12.4999i | 1.96024 | + | 0.811959i | ||||
\(238\) | 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 | ||||||||
\(243\) | 16.9630 | + | 7.02632i | 1.08818 | + | 0.450739i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.37339 | + | 15.3867i | 0.407181 | + | 0.983021i | ||||
\(246\) | 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 | ||||||||
\(251\) | 14.6903 | − | 6.08493i | 0.927244 | − | 0.384077i | 0.132612 | − | 0.991168i | \(-0.457664\pi\) |
0.794632 | + | 0.607091i | \(0.207664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03540 | − | 2.49969i | 0.0650953 | − | 0.157154i | ||||
\(254\) | 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 | ||||||||
\(259\) | −2.75631 | + | 6.65431i | −0.171269 | + | 0.413479i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.4249 | + | 20.0582i | −2.99742 | + | 1.24157i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4934 | + | 20.4934i | −1.26368 | + | 1.26368i | −0.314384 | + | 0.949296i | \(0.601798\pi\) |
−0.949296 | + | 0.314384i | \(0.898202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.6565 | + | 24.6565i | 1.51464 | + | 1.51464i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.1504 | − | 26.9195i | −0.682395 | − | 1.64745i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.24018 | − | 3.82741i | −0.563384 | − | 0.233361i | 0.0827697 | − | 0.996569i | \(-0.473623\pi\) |
−0.646153 | + | 0.763208i | \(0.723623\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 5.29885 | + | 2.19486i | 0.319533 | + | 0.132355i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.65583 | − | 13.6544i | −0.339826 | − | 0.820413i | −0.997732 | − | 0.0673127i | \(-0.978557\pi\) |
0.657906 | − | 0.753100i | \(-0.271443\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.41813 | − | 7.41813i | −0.444112 | − | 0.444112i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.45247 | + | 4.45247i | −0.265612 | + | 0.265612i | −0.827329 | − | 0.561717i | \(-0.810141\pi\) |
0.561717 | + | 0.827329i | \(0.310141\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.5158 | − | 9.32635i | 1.33843 | − | 0.554394i | 0.405379 | − | 0.914149i | \(-0.367140\pi\) |
0.933047 | + | 0.359755i | \(0.117140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.3220 | + | 56.3044i | −1.38148 | + | 3.33518i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.93302 | −0.114102 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4053 | 0.847368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.21371 | − | 2.93015i | 0.0711488 | − | 0.171769i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.66906 | + | 2.76241i | −0.389611 | + | 0.161382i | −0.568885 | − | 0.822417i | \(-0.692625\pi\) |
0.179274 | + | 0.983799i | \(0.442625\pi\) | |||||||
\(294\) | 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 | ||||||||
\(299\) | −2.60892 | − | 6.29848i | −0.150878 | − | 0.364251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.25731 | + | 2.17765i | 0.303026 | + | 0.125518i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.1999i | 1.96474i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.3548i | 2.48249i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3327 | + | 6.76523i | 0.932158 | + | 0.386112i | 0.796497 | − | 0.604643i | \(-0.206684\pi\) |
0.135661 | + | 0.990755i | \(0.456684\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.2944 | − | 41.7523i | −0.983843 | − | 2.37521i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.48818 | + | 9.48818i | 0.538025 | + | 0.538025i | 0.922949 | − | 0.384923i | \(-0.125772\pi\) |
−0.384923 | + | 0.922949i | \(0.625772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39347 | + | 8.39347i | −0.474427 | + | 0.474427i | −0.903344 | − | 0.428917i | \(-0.858895\pi\) |
0.428917 | + | 0.903344i | \(0.358895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.4791 | − | 10.9680i | 1.49193 | − | 0.617977i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0142 | − | 26.5907i | 0.618621 | − | 1.49348i | −0.234683 | − | 0.972072i | \(-0.575405\pi\) |
0.853305 | − | 0.521413i | \(-0.174595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.71115 | 0.487731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.1309 | 1.73756 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.77791 | + | 9.12069i | −0.210209 | + | 0.507489i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.3516 | − | 5.53040i | 0.740612 | − | 0.306772i | ||||
\(326\) | 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 | ||||||||
\(331\) | −3.90491 | − | 9.42728i | −0.214633 | − | 0.518170i | 0.779491 | − | 0.626413i | \(-0.215478\pi\) |
−0.994124 | + | 0.108243i | \(0.965478\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34.5464 | − | 14.3096i | −1.89313 | − | 0.784160i | ||||
\(334\) | 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 | ||||||||
\(339\) | 7.45645 | + | 3.08856i | 0.404979 | + | 0.167748i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.667224 | + | 1.61082i | 0.0361322 | + | 0.0872308i | ||||
\(342\) | 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 | ||||||||
\(347\) | 0.244423 | − | 0.101243i | 0.0131213 | − | 0.00543503i | −0.376113 | − | 0.926574i | \(-0.622740\pi\) |
0.389234 | + | 0.921139i | \(0.372740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.715459 | − | 1.72727i | 0.0382976 | − | 0.0924586i | −0.903573 | − | 0.428433i | \(-0.859066\pi\) |
0.941871 | + | 0.335975i | \(0.109066\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 10.0962 | − | 24.3745i | 0.535853 | − | 1.29366i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.16691 | − | 2.55442i | 0.326388 | − | 0.135194i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.40689 | + | 9.40689i | −0.496477 | + | 0.496477i | −0.910339 | − | 0.413863i | \(-0.864179\pi\) |
0.413863 | + | 0.910339i | \(0.364179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1242 | + | 13.1242i | 0.690746 | + | 0.690746i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.6553 | − | 28.1384i | −0.611745 | − | 1.47688i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.3741 | − | 6.36818i | −0.804720 | − | 0.333326i | ||||
\(366\) | 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 | ||||||||
\(371\) | −13.4247 | − | 5.56069i | −0.696976 | − | 0.288697i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.47997 | + | 13.2298i | 0.283742 | + | 0.685014i | 0.999917 | − | 0.0129074i | \(-0.00410866\pi\) |
−0.716175 | + | 0.697921i | \(0.754109\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | 8.57046 | − | 3.55000i | 0.440235 | − | 0.182351i | −0.151546 | − | 0.988450i | \(-0.548425\pi\) |
0.591781 | + | 0.806099i | \(0.298425\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.40122 | + | 17.8681i | −0.379176 | + | 0.915412i | ||||
\(382\) | 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 | ||||||||
\(387\) | −11.3054 | + | 27.2937i | −0.574687 | + | 1.38742i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.99494 | + | 3.31161i | −0.405360 | + | 0.167906i | −0.576041 | − | 0.817421i | \(-0.695403\pi\) |
0.170681 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | 12.6148 | + | 30.4549i | 0.634721 | + | 1.53235i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.97276 | + | 1.23136i | 0.149199 | + | 0.0618001i | 0.456033 | − | 0.889963i | \(-0.349270\pi\) |
−0.306834 | + | 0.951763i | \(0.599270\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 4.05880 | + | 1.68121i | 0.202183 | + | 0.0837471i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.1055 | + | 50.9531i | 1.04874 | + | 2.53188i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.39435 | + | 4.39435i | 0.217820 | + | 0.217820i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8932 | + | 17.8932i | −0.884760 | + | 0.884760i | −0.994014 | − | 0.109254i | \(-0.965154\pi\) |
0.109254 | + | 0.994014i | \(0.465154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.6540 | + | 18.9105i | −2.25195 | + | 0.932786i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.42029 | + | 10.6715i | −0.217508 | + | 0.525111i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.36765 | 0.459840 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.8234 | −1.65634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.62029 | + | 23.2254i | −0.469982 | + | 1.13464i | 0.494189 | + | 0.869354i | \(0.335465\pi\) |
−0.964171 | + | 0.265282i | \(0.914535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3467 | + | 8.42786i | −0.991635 | + | 0.410749i | −0.818723 | − | 0.574189i | \(-0.805318\pi\) |
−0.172912 | + | 0.984937i | \(0.555318\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −6.91385 | − | 16.6915i | −0.334585 | − | 0.807759i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.48036 | + | 3.92689i | 0.457716 | + | 0.189592i | ||||
\(430\) | 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 | ||||||||
\(435\) | −70.2620 | − | 29.1035i | −3.36880 | − | 1.39540i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.57112 | + | 13.4499i | 0.266503 | + | 0.643395i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2529 | − | 13.2529i | −0.632526 | − | 0.632526i | 0.316175 | − | 0.948701i | \(-0.397601\pi\) |
−0.948701 | + | 0.316175i | \(0.897601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.4776 | − | 25.4776i | 1.21322 | − | 1.21322i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.7407 | + | 13.1474i | −1.50805 | + | 0.624653i | −0.975154 | − | 0.221529i | \(-0.928895\pi\) |
−0.532893 | + | 0.846183i | \(0.678895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2529 | − | 27.1669i | 0.533439 | − | 1.28784i | ||||
\(446\) | 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 | ||||||||
\(451\) | −0.638259 | + | 1.54089i | −0.0300544 | + | 0.0725578i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.7943 | − | 23.9392i | 2.71541 | − | 1.12476i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.48684 | + | 8.48684i | −0.397869 | + | 0.397869i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.79873 | − | 9.79873i | −0.458365 | − | 0.458365i | 0.439753 | − | 0.898119i | \(-0.355066\pi\) |
−0.898119 | + | 0.439753i | \(0.855066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.45645 | + | 18.0015i | 0.348037 | + | 0.840237i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.43134 | − | 1.83552i | −0.206388 | − | 0.0854887i | 0.277095 | − | 0.960843i | \(-0.410628\pi\) |
−0.483483 | + | 0.875354i | \(0.660628\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 15.7099 | + | 6.50725i | 0.726967 | + | 0.301120i | 0.715305 | − | 0.698812i | \(-0.246288\pi\) |
0.0116621 | + | 0.999932i | \(0.496288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.48958 | − | 15.6672i | −0.299661 | − | 0.723445i | ||||
\(470\) | 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 | ||||||||
\(475\) | −28.5111 | + | 11.8097i | −1.30818 | + | 0.541866i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.8688 | − | 69.6954i | 1.32181 | − | 3.19113i | ||||
\(478\) | 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 | ||||||||
\(483\) | 3.76689 | − | 9.09407i | 0.171399 | − | 0.413795i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.95708 | − | 1.22486i | 0.134274 | − | 0.0556181i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.34809 | − | 5.34809i | 0.242345 | − | 0.242345i | −0.575475 | − | 0.817820i | \(-0.695183\pi\) |
0.817820 | + | 0.575475i | \(0.195183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.1240 | − | 22.1240i | −1.00048 | − | 1.00048i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8853 | + | 40.7647i | 0.762022 | + | 1.83968i | 0.467291 | + | 0.884104i | \(0.345230\pi\) |
0.294731 | + | 0.955580i | \(0.404770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3817 | − | 4.71444i | −0.512604 | − | 0.212328i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 24.7292i | − | 1.11149i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9942i | 0.493157i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.71852 | + | 1.95447i | 0.211230 | + | 0.0874943i | 0.485790 | − | 0.874076i | \(-0.338532\pi\) |
−0.274560 | + | 0.961570i | \(0.588532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4643 | + | 25.2630i | 0.467510 | + | 1.12867i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.81469 | + | 4.81469i | 0.214676 | + | 0.214676i | 0.806251 | − | 0.591574i | \(-0.201493\pi\) |
−0.591574 | + | 0.806251i | \(0.701493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.4053 | + | 24.4053i | −1.08602 | + | 1.08602i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.8133 | + | 5.72164i | −0.613469 | + | 0.254107i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.36909 | + | 5.71949i | −0.105008 | + | 0.253512i | −0.967647 | − | 0.252308i | \(-0.918810\pi\) |
0.862639 | + | 0.505821i | \(0.168810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.93456 | 0.306767 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 74.1328 | 3.27304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.4533 | − | 42.1360i | 0.769085 | − | 1.85674i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.13213 | + | 1.29737i | −0.137751 | + | 0.0570584i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.3331 | − | 23.3331i | 1.02421 | − | 1.02421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8240 | − | 13.8240i | −0.605642 | − | 0.605642i | 0.336162 | − | 0.941804i | \(-0.390871\pi\) |
−0.941804 | + | 0.336162i | \(0.890871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.11134 | + | 7.51144i | 0.136049 | + | 0.328452i | 0.977191 | − | 0.212363i | \(-0.0681159\pi\) |
−0.841141 | + | 0.540815i | \(0.818116\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.2777 | + | 7.98508i | 0.841347 | + | 0.348497i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.46574i | − | 0.107409i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.3574i | − | 0.754671i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −55.4020 | − | 22.9483i | −2.40424 | − | 0.995870i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.60823 | + | 3.88260i | 0.0696600 | + | 0.168174i | ||||
\(534\) | 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 | ||||||||
\(539\) | −5.53237 | + | 2.29158i | −0.238296 | + | 0.0987054i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.10142 | + | 21.9728i | −0.391300 | + | 0.944683i | 0.598357 | + | 0.801230i | \(0.295821\pi\) |
−0.989657 | + | 0.143453i | \(0.954179\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0194 | 0.601629 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.4493 | 1.43281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2561 | − | 39.2456i | 0.695060 | − | 1.67802i | −0.0392692 | − | 0.999229i | \(-0.512503\pi\) |
0.734329 | − | 0.678794i | \(-0.237497\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 86.6553 | − | 35.8938i | 3.69836 | − | 1.53191i | ||||
\(550\) | 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 | ||||||||
\(555\) | −20.7625 | − | 50.1250i | −0.881317 | − | 2.12769i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.8291 | − | 16.0835i | −1.64524 | − | 0.681481i | −0.648429 | − | 0.761275i | \(-0.724574\pi\) |
−0.996811 | + | 0.0797936i | \(0.974574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12.3714i | − | 0.523256i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 5.75936i | − | 0.243160i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.0331 | + | 15.3396i | 1.56076 | + | 0.646487i | 0.985221 | − | 0.171289i | \(-0.0547933\pi\) |
0.575536 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.11695 | + | 7.52498i | 0.131131 | + | 0.316578i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.2511 | − | 16.2511i | −0.682483 | − | 0.682483i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.5518 | + | 18.5518i | −0.777732 | + | 0.777732i | −0.979445 | − | 0.201713i | \(-0.935349\pi\) |
0.201713 | + | 0.979445i | \(0.435349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.69785 | + | 1.94591i | −0.196599 | + | 0.0814340i | −0.478811 | − | 0.877918i | \(-0.658932\pi\) |
0.282212 | + | 0.959352i | \(0.408932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.7761 | + | 42.9152i | −0.742606 | + | 1.79281i | ||||
\(574\) | 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 | ||||||||
\(579\) | −8.00902 | + | 19.3355i | −0.332843 | + | 0.803555i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.60653 | + | 1.49387i | −0.149624 | + | 0.0619762i | ||||
\(582\) | 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 | ||||||||
\(587\) | −10.8778 | − | 26.2613i | −0.448974 | − | 1.08392i | −0.972707 | − | 0.232037i | \(-0.925461\pi\) |
0.523733 | − | 0.851883i | \(-0.324539\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.66722 | − | 3.59008i | −0.357127 | − | 0.147927i | ||||
\(590\) | 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 | ||||||||
\(595\) | 6.22359 | + | 2.57789i | 0.255142 | + | 0.105683i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.15916 | + | 2.79847i | 0.0474414 | + | 0.114534i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.8797 | − | 10.8797i | −0.444531 | − | 0.444531i | 0.449001 | − | 0.893531i | \(-0.351780\pi\) |
−0.893531 | + | 0.449001i | \(0.851780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.9066 | − | 13.9066i | 0.567264 | − | 0.567264i | −0.364097 | − | 0.931361i | \(-0.618622\pi\) |
0.931361 | + | 0.364097i | \(0.118622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 81.3376 | − | 33.6911i | 3.31232 | − | 1.37201i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.7624 | − | 28.3970i | 0.478210 | − | 1.15450i | ||||
\(606\) | 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 | ||||||||
\(611\) | −3.26900 | + | 7.89207i | −0.132250 | + | 0.319279i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.2902 | + | 5.50500i | −0.536788 | + | 0.222345i | −0.634573 | − | 0.772863i | \(-0.718824\pi\) |
0.0977853 | + | 0.995208i | \(0.468824\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.2961 | − | 10.2961i | 0.415178 | − | 0.415178i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8105 | − | 17.8105i | −0.717025 | − | 0.717025i | 0.250970 | − | 0.967995i | \(-0.419251\pi\) |
−0.967995 | + | 0.250970i | \(0.919251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.80624 | − | 11.6033i | −0.193179 | − | 0.466376i | 0.797377 | − | 0.603481i | \(-0.206220\pi\) |
−0.990556 | + | 0.137105i | \(0.956220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.5460 | + | 10.9957i | 1.06525 | + | 0.441242i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2537i | 0.490935i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8217i | 0.992869i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.2445 | − | 8.38555i | −0.808487 | − | 0.334886i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.36329 | − | 8.11970i | −0.134103 | − | 0.323753i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8865 | − | 12.8865i | −0.513004 | − | 0.513004i | 0.402442 | − | 0.915446i | \(-0.368162\pi\) |
−0.915446 | + | 0.402442i | \(0.868162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.3355 | + | 37.3355i | −1.48395 | + | 1.48395i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.0323 | + | 7.46924i | −0.715592 | + | 0.296408i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.77412 | + | 13.9400i | −0.228779 | + | 0.552321i | ||||
\(638\) | 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 | ||||||||
\(643\) | 5.90799 | − | 14.2632i | 0.232988 | − | 0.562484i | −0.763538 | − | 0.645763i | \(-0.776539\pi\) |
0.996526 | + | 0.0832793i | \(0.0265394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −39.6018 | + | 16.4036i | −1.55932 | + | 0.645891i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4412 | − | 19.4412i | 0.764314 | − | 0.764314i | −0.212785 | − | 0.977099i | \(-0.568253\pi\) |
0.977099 | + | 0.212785i | \(0.0682534\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.04722 | + | 7.04722i | 0.276627 | + | 0.276627i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.42742 | + | 5.86030i | 0.0951380 | + | 0.229683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.38672 | + | 1.40282i | 0.132533 | + | 0.0548968i | 0.447964 | − | 0.894052i | \(-0.352149\pi\) |
−0.315432 | + | 0.948948i | \(0.602149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 6.59747i | − | 0.257784i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.0013i | 1.40454i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5711 | − | 6.44977i | −0.606565 | − | 0.251247i | 0.0581942 | − | 0.998305i | \(-0.481466\pi\) |
−0.664759 | + | 0.747058i | \(0.731466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.03928 | − | 14.5801i | −0.234901 | − | 0.567100i | 0.761841 | − | 0.647764i | \(-0.224296\pi\) |
−0.996741 | + | 0.0806641i | \(0.974296\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | −16.7840 | + | 6.95218i | −0.649880 | + | 0.269189i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.77370 | − | 4.28208i | 0.0685750 | − | 0.165555i | ||||
\(670\) | 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 | ||||||||
\(675\) | −23.3088 | + | 56.2724i | −0.897155 | + | 2.16592i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.5504 | + | 14.7255i | −1.36631 | + | 0.565945i | −0.940786 | − | 0.339000i | \(-0.889911\pi\) |
−0.425527 | + | 0.904946i | \(0.639911\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 2.35810 | + | 5.69296i | 0.0902303 | + | 0.217835i | 0.962552 | − | 0.271097i | \(-0.0873865\pi\) |
−0.872322 | + | 0.488932i | \(0.837386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.0736 | − | 19.0843i | −1.76038 | − | 0.729173i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.6619i | 1.13167i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.5909i | 1.20352i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.48765 | − | 2.68727i | −0.246802 | − | 0.102229i | 0.255854 | − | 0.966716i | \(-0.417644\pi\) |
−0.502655 | + | 0.864487i | \(0.667644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.94360 | + | 9.52069i | 0.149805 | + | 0.361661i | ||||
\(694\) | 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 | ||||||||
\(699\) | −40.9825 | + | 16.9755i | −1.55010 | + | 0.642072i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.81730 | − | 11.6300i | 0.181947 | − | 0.439258i | −0.806421 | − | 0.591342i | \(-0.798598\pi\) |
0.988368 | + | 0.152084i | \(0.0485983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.4381 | −1.26114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.5975 | 1.11470 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.50404 | − | 13.2879i | 0.207001 | − | 0.499744i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.06979 | + | 0.857335i | −0.0777326 | + | 0.0321979i | −0.421211 | − | 0.906963i | \(-0.638395\pi\) |
0.343478 | + | 0.939161i | \(0.388395\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | 3.96298 | + | 9.56749i | 0.148207 | + | 0.357804i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.6709 | + | 12.7043i | 1.14543 | + | 0.474451i | ||||
\(718\) | 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 | ||||||||
\(723\) | −2.00351 | − | 0.829880i | −0.0745113 | − | 0.0308636i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.7373 | − | 35.5789i | −0.547329 | − | 1.32137i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.75350 | + | 1.75350i | 0.0650337 | + | 0.0650337i | 0.738876 | − | 0.673842i | \(-0.235357\pi\) |
−0.673842 | + | 0.738876i | \(0.735357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.82254 | − | 3.82254i | 0.141575 | − | 0.141575i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.41505 | + | 2.65720i | −0.237269 | + | 0.0982801i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.447524 | + | 1.08042i | −0.0165297 | + | 0.0399062i | −0.931929 | − | 0.362641i | \(-0.881875\pi\) |
0.915399 | + | 0.402547i | \(0.131875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 52.2787 | 1.92833 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6318 | −0.538970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0760 | + | 36.3968i | −0.554581 | + | 1.33888i | 0.359424 | + | 0.933174i | \(0.382973\pi\) |
−0.914005 | + | 0.405703i | \(0.867027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.0103 | + | 21.1291i | −1.87391 | + | 0.776198i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.45255 | + | 1.45255i | −0.0532888 | + | 0.0532888i | −0.733249 | − | 0.679960i | \(-0.761997\pi\) |
0.679960 | + | 0.733249i | \(0.261997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.6790 | + | 31.6790i | 1.16063 | + | 1.16063i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.75555 | − | 18.7236i | −0.283761 | − | 0.685059i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0955 | − | 5.01011i | −0.441959 | − | 0.183065i | ||||
\(750\) | 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 | ||||||||
\(755\) | 58.3255 | + | 24.1592i | 2.12268 | + | 0.879243i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8868 | − | 26.2830i | −0.395686 | − | 0.955272i | −0.988677 | − | 0.150062i | \(-0.952053\pi\) |
0.592990 | − | 0.805210i | \(-0.297947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00551 | − | 6.00551i | −0.217986 | − | 0.217986i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.6001 | + | 13.6001i | −0.493003 | + | 0.493003i | −0.909251 | − | 0.416248i | \(-0.863345\pi\) |
0.416248 | + | 0.909251i | \(0.363345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8779 | + | 5.33420i | −0.466211 | + | 0.193111i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.3833 | + | 32.3102i | −0.483875 | + | 1.16818i | ||||
\(766\) | 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 | ||||||||
\(771\) | −14.1661 | + | 34.1999i | −0.510179 | + | 1.23168i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.7373 | − | 12.3176i | 1.06958 | − | 0.443033i | 0.222735 | − | 0.974879i | \(-0.428502\pi\) |
0.846841 | + | 0.531847i | \(0.178502\pi\) | |||||||
\(774\) | 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 | ||||||||
\(779\) | −3.43423 | − | 8.29097i | −0.123044 | − | 0.297055i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.76395 | + | 3.63015i | 0.313599 | + | 0.129897i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 92.5100i | 3.30604i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.82817i | 0.350782i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.40919 | − | 3.89741i | −0.335401 | − | 0.138928i | 0.208626 | − | 0.977996i | \(-0.433101\pi\) |
−0.544027 | + | 0.839068i | \(0.683101\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 34.8148 | + | 84.0504i | 1.23944 | + | 2.99227i | ||||
\(790\) | 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 | ||||||||
\(795\) | 101.124 | − | 41.8871i | 3.58651 | − | 1.48558i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.15756 | − | 17.2799i | 0.253534 | − | 0.612085i | −0.744951 | − | 0.667120i | \(-0.767527\pi\) |
0.998484 | + | 0.0550349i | \(0.0175270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.79446 | 0.169616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −63.6162 | −2.24777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.28971 | − | 5.52785i | 0.0808021 | − | 0.195073i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.17765 | − | 3.80151i | 0.323470 | − | 0.133985i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.1996 | + | 22.1996i | −0.781462 | + | 0.781462i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.3548 | + | 28.3548i | 0.996902 | + | 0.996902i | 0.999995 | − | 0.00309284i | \(-0.000984483\pi\) |
−0.00309284 | + | 0.999995i | \(0.500984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.61674 | − | 3.90316i | −0.0567716 | − | 0.137059i | 0.892949 | − | 0.450159i | \(-0.148633\pi\) |
−0.949720 | + | 0.313100i | \(0.898633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −73.0927 | − | 30.2760i | −2.56347 | − | 1.06183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 31.5756i | − | 1.10604i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4181i | 0.924254i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.9894 | + | 9.93672i | 0.838256 | + | 0.347217i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5300 | + | 27.8360i | 0.402401 | + | 0.971482i | 0.987082 | + | 0.160218i | \(0.0512199\pi\) |
−0.584681 | + | 0.811264i | \(0.698780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.7602 | + | 30.7602i | 1.07223 | + | 1.07223i | 0.997179 | + | 0.0750551i | \(0.0239133\pi\) |
0.0750551 | + | 0.997179i | \(0.476087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.7305 | − | 12.7305i | 0.443220 | − | 0.443220i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.1882 | − | 9.60486i | 0.806332 | − | 0.333994i | 0.0588423 | − | 0.998267i | \(-0.481259\pi\) |
0.747489 | + | 0.664274i | \(0.231259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.1975 | + | 41.5185i | −0.597295 | + | 1.44200i | 0.279033 | + | 0.960281i | \(0.409986\pi\) |
−0.876328 | + | 0.481715i | \(0.840014\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −46.3929 | −1.60935 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.46858 | 0.293419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5605 | + | 25.4952i | −0.365459 | + | 0.882297i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.1065 | + | 7.08573i | −0.591286 | + | 0.244919i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1198 | + | 31.1198i | −1.07437 | + | 1.07437i | −0.0773708 | + | 0.997002i | \(0.524653\pi\) |
−0.997002 | + | 0.0773708i | \(0.975347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8530 | − | 20.8530i | −0.719070 | − | 0.719070i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.56398 | + | 18.2611i | 0.260517 | + | 0.628944i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.9402 | − | 5.77423i | −0.479558 | − | 0.198639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8086i | 0.440107i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 76.5009i | − | 2.62550i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.9738 | − | 4.95969i | −0.410455 | − | 0.170016i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.80845 | − | 23.6797i | −0.335835 | − | 0.810777i | −0.998106 | − | 0.0615130i | \(-0.980407\pi\) |
0.662271 | − | 0.749264i | \(-0.269593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 94.0865 | + | 94.0865i | 3.21769 | + | 3.21769i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.7590 | + | 24.7590i | −0.845752 | + | 0.845752i | −0.989600 | − | 0.143847i | \(-0.954053\pi\) |
0.143847 | + | 0.989600i | \(0.454053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.98006 | − | 3.30545i | 0.272276 | − | 0.112780i | −0.242368 | − | 0.970184i | \(-0.577924\pi\) |
0.514644 | + | 0.857404i | \(0.327924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.32204 | + | 5.60590i | −0.0791349 | + | 0.191049i | ||||
\(862\) | 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 | ||||||||
\(867\) | 17.3043 | − | 41.7764i | 0.587686 | − | 1.41880i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9502 | + | 4.53572i | −0.371460 | + | 0.153864i | ||||
\(870\) | 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 | ||||||||
\(875\) | 0.0566593 | + | 0.136788i | 0.00191543 | + | 0.00462427i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.2968 | + | 17.9341i | 1.46203 | + | 0.605593i | 0.965026 | − | 0.262155i | \(-0.0844332\pi\) |
0.497005 | + | 0.867748i | \(0.334433\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −40.9077 | − | 16.9445i | −1.37665 | − | 0.570228i | −0.433068 | − | 0.901361i | \(-0.642569\pi\) |
−0.943584 | + | 0.331133i | \(0.892569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.2967 | − | 80.3855i | −1.11926 | − | 2.70213i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.77550 | − | 7.77550i | −0.261076 | − | 0.261076i | 0.564415 | − | 0.825491i | \(-0.309102\pi\) |
−0.825491 | + | 0.564415i | \(0.809102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.75128 | − | 5.75128i | 0.192892 | − | 0.192892i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.3204 | + | 7.58856i | −0.613757 | + | 0.254226i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.98067 | − | 16.8528i | 0.233599 | − | 0.563959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.5379 | 1.75615 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4001 | −0.714527 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.48005 | − | 10.8158i | 0.149418 | − | 0.360727i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3810 | − | 6.78525i | 0.545731 | − | 0.226049i | ||||
\(902\) | 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 | ||||||||
\(907\) | 2.38548 | + | 5.75906i | 0.0792086 | + | 0.191226i | 0.958523 | − | 0.285015i | \(-0.0919987\pi\) |
−0.879314 | + | 0.476242i | \(0.841999\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 68.9853 | + | 28.5746i | 2.28810 | + | 0.947761i | ||||
\(910\) | 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 | ||||||||
\(915\) | 125.732 | + | 52.0801i | 4.15658 | + | 1.72171i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.05211 | + | 2.54001i | 0.0347437 | + | 0.0838786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.0672 | − | 13.0672i | −0.431046 | − | 0.431046i | 0.457938 | − | 0.888984i | \(-0.348588\pi\) |
−0.888984 | + | 0.457938i | \(0.848588\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.2394 | − | 39.2394i | 1.29298 | − | 1.29298i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.0826 | − | 9.14692i | 0.726858 | − | 0.301075i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5136 | − | 25.3821i | 0.345685 | − | 0.834557i | ||||
\(926\) | 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 | ||||||||
\(931\) | 12.3301 | − | 29.7676i | 0.404104 | − | 0.975593i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.9142 | − | 16.1188i | 1.27399 | − | 0.527705i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.10991 | − | 4.10991i | 0.134408 | − | 0.134408i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.56931 | − | 4.56931i | −0.149273 | − | 0.149273i | 0.628520 | − | 0.777793i | \(-0.283661\pi\) |
−0.777793 | + | 0.628520i | \(0.783661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2591 | + | 34.4244i | 0.465327 | + | 1.12340i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6192 | + | 7.29813i | 0.574371 | + | 0.237912i | 0.650911 | − | 0.759154i | \(-0.274387\pi\) |
−0.0765397 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.47827i | − | 0.113268i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 50.5852i | − | 1.64554i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.8687 | − | 4.50198i | −0.353187 | − | 0.146295i | 0.199034 | − | 0.979993i | \(-0.436220\pi\) |
−0.552221 | + | 0.833698i | \(0.686220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.76940 | − | 13.9286i | −0.187283 | − | 0.452140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.8843 | − | 63.8843i | −2.07159 | − | 2.07159i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.88290 | − | 9.88290i | 0.320138 | − | 0.320138i | −0.528682 | − | 0.848820i | \(-0.677313\pi\) |
0.848820 | + | 0.528682i | \(0.177313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.3096 | + | 17.9394i | −1.40147 | + | 0.580506i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.4643 | − | 25.2630i | 0.338262 | − | 0.816637i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.7816 | 0.671074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6569 | −0.924415 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 26.0104 | − | 62.7946i | 0.838173 | − | 2.02353i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5132 | + | 8.08262i | −0.628151 | + | 0.260189i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.4467 | + | 27.4467i | −0.882626 | + | 0.882626i | −0.993801 | − | 0.111175i | \(-0.964539\pi\) |
0.111175 | + | 0.993801i | \(0.464539\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.9125 | + | 21.9125i | 0.703931 | + | 0.703931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6361 | + | 52.2342i | 0.694335 | + | 1.67627i | 0.735858 | + | 0.677136i | \(0.236779\pi\) |
−0.0415225 | + | 0.999138i | \(0.513221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1416 | + | 5.44344i | 0.421301 | + | 0.174509i | ||||
\(974\) | 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 | ||||||||
\(979\) | 9.76799 | + | 4.04603i | 0.312186 | + | 0.129312i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.6929 | − | 66.8566i | −0.884167 | − | 2.13457i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.7442 | + | 17.7442i | 0.565951 | + | 0.565951i | 0.930991 | − | 0.365041i | \(-0.118945\pi\) |
−0.365041 | + | 0.930991i | \(0.618945\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.5958 | − | 36.5958i | 1.16604 | − | 1.16604i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3950 | + | 4.71995i | −0.362706 | + | 0.150238i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.91846 | + | 9.45999i | −0.124600 | + | 0.300810i | ||||
\(990\) | 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 | ||||||||
\(995\) | −1.16982 | + | 2.82419i | −0.0370857 | + | 0.0895328i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.36920 | + | 1.39557i | −0.106704 | + | 0.0441981i | −0.435397 | − | 0.900239i | \(-0.643392\pi\) |
0.328693 | + | 0.944437i | \(0.393392\pi\) | |||||||
\(998\) | 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.e.129.4 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.e.129.1 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.b.129.4 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.b.129.1 | ✓ | 16 | ||
16.3 | odd | 4 | 1024.2.g.c.641.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.h.641.1 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.h.641.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.c.641.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.c.385.1 | yes | 16 | ||
32.5 | even | 8 | inner | 1024.2.g.e.897.4 | yes | 16 | |
32.11 | odd | 8 | 1024.2.g.b.897.4 | yes | 16 | ||
32.13 | even | 8 | 1024.2.g.h.385.1 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.h.385.4 | yes | 16 | ||
32.21 | even | 8 | 1024.2.g.b.897.1 | yes | 16 | ||
32.27 | odd | 8 | inner | 1024.2.g.e.897.1 | yes | 16 | |
32.29 | even | 8 | 1024.2.g.c.385.4 | yes | 16 | ||
64.5 | even | 16 | 4096.2.a.o.1.8 | 8 | |||
64.27 | odd | 16 | 4096.2.a.o.1.7 | 8 | |||
64.37 | even | 16 | 4096.2.a.n.1.1 | 8 | |||
64.59 | odd | 16 | 4096.2.a.n.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.129.1 | ✓ | 16 | 8.5 | even | 2 | ||
1024.2.g.b.129.4 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.b.897.1 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.b.897.4 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.c.385.1 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.c.385.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.c.641.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.c.641.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.e.129.1 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.e.129.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.e.897.1 | yes | 16 | 32.27 | odd | 8 | inner | |
1024.2.g.e.897.4 | yes | 16 | 32.5 | even | 8 | inner | |
1024.2.g.h.385.1 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.h.385.4 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.h.641.1 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.h.641.4 | yes | 16 | 16.11 | odd | 4 | ||
4096.2.a.n.1.1 | 8 | 64.37 | even | 16 | |||
4096.2.a.n.1.2 | 8 | 64.59 | odd | 16 | |||
4096.2.a.o.1.7 | 8 | 64.27 | odd | 16 | |||
4096.2.a.o.1.8 | 8 | 64.5 | even | 16 |