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 | 897.1 | ||
Root | \(1.66798 + 0.466730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.897 |
Dual form | 1024.2.g.e.129.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 | −0.737517 | − | 0.675328i | \(-0.764002\pi\) |
0.0439740 | − | 0.999033i | \(-0.485998\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.92673 | + | 1.21229i | 1.30887 | + | 0.542153i | 0.924556 | − | 0.381047i | \(-0.124437\pi\) |
0.384318 | + | 0.923201i | \(0.374437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.933460 | + | 0.933460i | 0.352815 | + | 0.352815i | 0.861156 | − | 0.508341i | \(-0.169741\pi\) |
−0.508341 | + | 0.861156i | \(0.669741\pi\) | |||||||
\(8\) | 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 | \(-0.929931\pi\) |
0.844445 | + | 0.535643i | \(0.179931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.65154 | − | 1.09830i | 0.735405 | − | 0.304615i | 0.0166339 | − | 0.999862i | \(-0.494705\pi\) |
0.718771 | + | 0.695247i | \(0.244705\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.94402i | − | 2.56753i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.61082i | 0.390681i | 0.980735 | + | 0.195341i | \(0.0625813\pi\) | ||||
−0.980735 | + | 0.195341i | \(0.937419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.66214 | − | 2.34533i | 1.29898 | − | 0.538056i | 0.377333 | − | 0.926078i | \(-0.376841\pi\) |
0.921650 | + | 0.388021i | \(0.126841\pi\) | |||||||
\(20\) | 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 | \(-0.670341\pi\) |
0.860197 | + | 0.509962i | \(0.170341\pi\) | |||||||
\(24\) | 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 | 0.922253 | + | 0.386588i | \(0.126346\pi\) |
−0.378772 | + | 0.925490i | \(0.623654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.53073 | −0.274928 | −0.137464 | − | 0.990507i | \(-0.543895\pi\) | ||||
−0.137464 | + | 0.990507i | \(0.543895\pi\) | |||||||
\(32\) | 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 | 0.756384 | − | 0.654128i | \(-0.226964\pi\) |
0.0723054 | + | 0.997383i | \(0.476964\pi\) | |||||||
\(38\) | 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 | \(-0.713524\pi\) |
0.783321 | + | 0.621618i | \(0.213524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.64959 | − | 3.98247i | 0.251561 | − | 0.607321i | −0.746770 | − | 0.665083i | \(-0.768396\pi\) |
0.998330 | + | 0.0577615i | \(0.0183963\pi\) | |||||||
\(44\) | 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 | −0.315464 | − | 0.948937i | \(-0.602160\pi\) |
0.894067 | − | 0.447933i | \(-0.147840\pi\) | |||||||
\(54\) | 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 | \(-0.567889\pi\) |
−0.840756 | + | 0.541415i | \(0.817889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.23733 | − | 12.6440i | −0.670571 | − | 1.61890i | −0.780643 | − | 0.624978i | \(-0.785108\pi\) |
0.110072 | − | 0.993924i | \(-0.464892\pi\) | |||||||
\(62\) | 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 | 0.872989 | + | 0.487739i | \(0.162178\pi\) |
−0.272413 | + | 0.962180i | \(0.587822\pi\) | |||||||
\(68\) | 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 | \(-0.414535\pi\) |
−0.964171 | + | 0.265282i | \(0.914535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.71444 | + | 3.71444i | −0.434742 | + | 0.434742i | −0.890238 | − | 0.455496i | \(-0.849462\pi\) |
0.455496 | + | 0.890238i | \(0.349462\pi\) | |||||||
\(74\) | 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 | \(-0.676888\pi\) |
0.227673 | + | 0.973738i | \(0.426888\pi\) | |||||||
\(84\) | 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 | 0.963489 | − | 0.267748i | \(-0.0862795\pi\) |
−0.267748 | + | 0.963489i | \(0.586280\pi\) | |||||||
\(90\) | 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 | −0.179204 | − | 0.983812i | \(-0.557352\pi\) |
−0.822376 | + | 0.568944i | \(0.807352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1802 | − | 10.1802i | −1.00308 | − | 1.00308i | −0.999995 | − | 0.00308887i | \(-0.999017\pi\) |
−0.00308887 | − | 0.999995i | \(-0.500983\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.28234 | − | 9.28234i | 0.905864 | − | 0.905864i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.79522 | + | 9.16246i | −0.366897 | + | 0.885769i | 0.627357 | + | 0.778731i | \(0.284136\pi\) |
−0.994255 | + | 0.107038i | \(0.965864\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.75516 | − | 4.04072i | 0.934375 | − | 0.387031i | 0.137038 | − | 0.990566i | \(-0.456242\pi\) |
0.797336 | + | 0.603535i | \(0.206242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 17.1266i | − | 1.62559i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.57112i | − | 0.241871i | −0.992660 | − | 0.120935i | \(-0.961411\pi\) | ||
0.992660 | − | 0.120935i | \(-0.0385894\pi\) | |||||||
\(114\) | 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 | \(-0.411864\pi\) | ||||
0.273362 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.5311 | −1.19134 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.796984 | − | 1.92409i | −0.0696328 | − | 0.168108i | 0.885232 | − | 0.465151i | \(-0.154000\pi\) |
−0.954864 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(132\) | 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 | −0.998856 | − | 0.0478269i | \(-0.984770\pi\) |
0.0478269 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.12347 | − | 9.95493i | 0.349748 | − | 0.844366i | −0.646902 | − | 0.762574i | \(-0.723936\pi\) |
0.996649 | − | 0.0817925i | \(-0.0260645\pi\) | |||||||
\(140\) | 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 | −0.531389 | − | 0.847128i | \(-0.678330\pi\) |
0.974759 | − | 0.223261i | \(-0.0716701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0916 | + | 14.0916i | −1.14676 | + | 1.14676i | −0.159572 | + | 0.987186i | \(0.551012\pi\) |
−0.987186 | + | 0.159572i | \(0.948988\pi\) | |||||||
\(152\) | 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 | 0.869395 | − | 0.494117i | \(-0.164509\pi\) |
−0.964149 | + | 0.265362i | \(0.914509\pi\) | |||||||
\(158\) | 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 | −0.999965 | − | 0.00831846i | \(-0.997352\pi\) |
0.701200 | − | 0.712964i | \(-0.252648\pi\) | |||||||
\(164\) | 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 | \(-0.140573\pi\) |
−0.427407 | + | 0.904059i | \(0.640573\pi\) | |||||||
\(168\) | 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 | 0.0183942 | − | 0.999831i | \(-0.494145\pi\) |
0.719994 | + | 0.693980i | \(0.244145\pi\) | |||||||
\(174\) | 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 | \(-0.837785\pi\) |
−0.272301 | + | 0.962212i | \(0.587785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70912 | − | 4.12619i | 0.127038 | − | 0.306697i | −0.847545 | − | 0.530724i | \(-0.821920\pi\) |
0.974583 | + | 0.224026i | \(0.0719202\pi\) | |||||||
\(182\) | 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 | \(-0.320172\pi\) | ||||
0.535371 | + | 0.844617i | \(0.320172\pi\) | |||||||
\(192\) | 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 | 0.848885 | − | 0.528577i | \(-0.177274\pi\) |
0.226492 | + | 0.974013i | \(0.427274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.682332 | + | 0.682332i | 0.0483693 | + | 0.0483693i | 0.730878 | − | 0.682508i | \(-0.239111\pi\) |
−0.682508 | + | 0.730878i | \(0.739111\pi\) | |||||||
\(200\) | 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 | \(-0.428447\pi\) |
0.846933 | + | 0.531700i | \(0.178447\pi\) | |||||||
\(212\) | 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 | \(-0.515743\pi\) | ||||
−0.0494382 | + | 0.998777i | \(0.515743\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −34.5099 | −2.30066 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8203 | + | 26.1225i | 0.718169 | + | 1.73381i | 0.678500 | + | 0.734600i | \(0.262630\pi\) |
0.0396690 | + | 0.999213i | \(0.487370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.73012 | − | 3.61614i | −0.576903 | − | 0.238961i | 0.0751019 | − | 0.997176i | \(-0.476072\pi\) |
−0.652005 | + | 0.758215i | \(0.726072\pi\) | |||||||
\(230\) | 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 | \(-0.903189\pi\) |
0.299475 | + | 0.954104i | \(0.403189\pi\) | |||||||
\(234\) | 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 | \(0.00708319\pi\) | ||||
−0.999752 | + | 0.0222507i | \(0.992917\pi\) | |||||||
\(242\) | 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 | \(-0.542336\pi\) |
−0.794632 | + | 0.607091i | \(0.792336\pi\) | |||||||
\(252\) | 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 | 0.949296 | + | 0.314384i | \(0.101798\pi\) |
0.314384 | + | 0.949296i | \(0.398202\pi\) | |||||||
\(264\) | 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 | −0.646153 | − | 0.763208i | \(-0.723623\pi\) |
0.0827697 | + | 0.996569i | \(0.473623\pi\) | |||||||
\(270\) | 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 | 0.657906 | + | 0.753100i | \(0.271443\pi\) |
−0.997732 | + | 0.0673127i | \(0.978557\pi\) | |||||||
\(278\) | 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 | \(-0.310141\pi\) |
−0.827329 | + | 0.561717i | \(0.810141\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.5158 | − | 9.32635i | −1.33843 | − | 0.554394i | −0.405379 | − | 0.914149i | \(-0.632860\pi\) |
−0.933047 | + | 0.359755i | \(0.882860\pi\) | |||||||
\(284\) | 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 | 0.179274 | − | 0.983799i | \(-0.442625\pi\) |
−0.568885 | + | 0.822417i | \(0.692625\pi\) | |||||||
\(294\) | 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 | \(-0.793316\pi\) |
−0.135661 | + | 0.990755i | \(0.543316\pi\) | |||||||
\(308\) | 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 | \(-0.874228\pi\) |
0.384923 | + | 0.922949i | \(0.374228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39347 | − | 8.39347i | −0.474427 | − | 0.474427i | 0.428917 | − | 0.903344i | \(-0.358895\pi\) |
−0.903344 | + | 0.428917i | \(0.858895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.4791 | − | 10.9680i | −1.49193 | − | 0.617977i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0142 | + | 26.5907i | 0.618621 | + | 1.49348i | 0.853305 | + | 0.521413i | \(0.174595\pi\) |
−0.234683 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(318\) | 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 | \(-0.784522\pi\) |
0.994124 | + | 0.108243i | \(0.0345224\pi\) | |||||||
\(332\) | 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 | \(0.0245460\pi\) | ||||
−0.997028 | + | 0.0770371i | \(0.975454\pi\) | |||||||
\(338\) | 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 | \(-0.377260\pi\) |
−0.389234 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.715459 | + | 1.72727i | 0.0382976 | + | 0.0924586i | 0.941871 | − | 0.335975i | \(-0.109066\pi\) |
−0.903573 | + | 0.428433i | \(0.859066\pi\) | |||||||
\(350\) | 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 | \(-0.135821\pi\) |
−0.413863 | + | 0.910339i | \(0.635821\pi\) | |||||||
\(360\) | 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 | −0.716175 | − | 0.697921i | \(-0.754109\pi\) |
0.999917 | + | 0.0129074i | \(0.00410866\pi\) | |||||||
\(374\) | 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 | \(-0.451575\pi\) |
−0.591781 | + | 0.806099i | \(0.701575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.40122 | − | 17.8681i | −0.379176 | − | 0.915412i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6316 | −1.10532 | −0.552661 | − | 0.833406i | \(-0.686388\pi\) | ||||
−0.552661 | + | 0.833406i | \(0.686388\pi\) | |||||||
\(384\) | 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 | 0.170681 | − | 0.985326i | \(-0.445403\pi\) |
−0.576041 | + | 0.817421i | \(0.695403\pi\) | |||||||
\(390\) | 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 | −0.306834 | − | 0.951763i | \(-0.599270\pi\) |
0.456033 | + | 0.889963i | \(0.349270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 25.3963i | − | 1.27140i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.2175i | − | 1.10949i | −0.832021 | − | 0.554744i | \(-0.812816\pi\) | ||
0.832021 | − | 0.554744i | \(-0.187184\pi\) | |||||||
\(402\) | 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 | 0.109254 | − | 0.994014i | \(-0.465154\pi\) |
−0.994014 | + | 0.109254i | \(0.965154\pi\) | |||||||
\(410\) | 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 | 0.964171 | + | 0.265282i | \(0.0854650\pi\) |
−0.494189 | + | 0.869354i | \(0.664535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3467 | − | 8.42786i | −0.991635 | − | 0.410749i | −0.172912 | − | 0.984937i | \(-0.555318\pi\) |
−0.818723 | + | 0.574189i | \(0.805318\pi\) | |||||||
\(422\) | 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 | \(0.250571\pi\) | ||||
−0.705837 | + | 0.708374i | \(0.749429\pi\) | |||||||
\(434\) | 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 | \(-0.602399\pi\) |
0.948701 | + | 0.316175i | \(0.102399\pi\) | |||||||
\(440\) | 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 | \(-0.0711049\pi\) |
0.532893 | + | 0.846183i | \(0.321105\pi\) | |||||||
\(444\) | 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 | −0.898119 | − | 0.439753i | \(-0.855066\pi\) |
0.439753 | + | 0.898119i | \(0.355066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.45645 | + | 18.0015i | −0.348037 | + | 0.840237i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.43134 | + | 1.83552i | −0.206388 | + | 0.0854887i | −0.483483 | − | 0.875354i | \(-0.660628\pi\) |
0.277095 | + | 0.960843i | \(0.410628\pi\) | |||||||
\(462\) | 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 | \(-0.753712\pi\) |
−0.0116621 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(468\) | 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 | \(-0.196095\pi\) | ||||
0.816168 | + | 0.577815i | \(0.196095\pi\) | |||||||
\(480\) | 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 | \(-0.304817\pi\) |
−0.817820 | + | 0.575475i | \(0.804817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22.1240 | + | 22.1240i | −1.00048 | + | 1.00048i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8853 | + | 40.7647i | −0.762022 | + | 1.83968i | −0.294731 | + | 0.955580i | \(0.595230\pi\) |
−0.467291 | + | 0.884104i | \(0.654770\pi\) | |||||||
\(492\) | 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 | \(-0.661468\pi\) |
0.274560 | + | 0.961570i | \(0.411468\pi\) | |||||||
\(500\) | 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 | \(-0.798507\pi\) |
0.591574 | + | 0.806251i | \(0.298507\pi\) | |||||||
\(504\) | 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 | 0.862639 | − | 0.505821i | \(-0.168810\pi\) |
−0.967647 | + | 0.252308i | \(0.918810\pi\) | |||||||
\(510\) | 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 | −0.941804 | − | 0.336162i | \(-0.890871\pi\) |
0.336162 | + | 0.941804i | \(0.390871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.11134 | + | 7.51144i | −0.136049 | + | 0.328452i | −0.977191 | − | 0.212363i | \(-0.931884\pi\) |
0.841141 | + | 0.540815i | \(0.181884\pi\) | |||||||
\(524\) | 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 | −0.989657 | − | 0.143453i | \(-0.954179\pi\) |
0.598357 | − | 0.801230i | \(-0.295821\pi\) | |||||||
\(542\) | 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 | −0.734329 | − | 0.678794i | \(-0.762503\pi\) |
0.0392692 | − | 0.999229i | \(-0.487497\pi\) | |||||||
\(548\) | 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 | −0.996811 | − | 0.0797936i | \(-0.974574\pi\) |
−0.648429 | + | 0.761275i | \(0.724574\pi\) | |||||||
\(558\) | 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 | \(-0.945207\pi\) |
−0.575536 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(564\) | 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 | 0.201713 | − | 0.979445i | \(-0.435349\pi\) |
−0.979445 | + | 0.201713i | \(0.935349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.69785 | + | 1.94591i | 0.196599 | + | 0.0814340i | 0.478811 | − | 0.877918i | \(-0.341068\pi\) |
−0.282212 | + | 0.959352i | \(0.591068\pi\) | |||||||
\(572\) | 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 | −0.523733 | − | 0.851883i | \(-0.675461\pi\) |
0.972707 | − | 0.232037i | \(-0.0745391\pi\) | |||||||
\(588\) | 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 | \(-0.945064\pi\) | ||
0.985144 | − | 0.171732i | \(-0.0549362\pi\) | |||||||
\(594\) | 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 | \(-0.648220\pi\) |
0.893531 | + | 0.449001i | \(0.148220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.9066 | + | 13.9066i | 0.567264 | + | 0.567264i | 0.931361 | − | 0.364097i | \(-0.118622\pi\) |
−0.364097 | + | 0.931361i | \(0.618622\pi\) | |||||||
\(602\) | 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 | \(-0.829412\pi\) | ||||
−0.859801 | + | 0.510629i | \(0.829412\pi\) | |||||||
\(608\) | 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 | 0.0977853 | − | 0.995208i | \(-0.468824\pi\) |
−0.634573 | + | 0.772863i | \(0.718824\pi\) | |||||||
\(614\) | 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 | \(-0.919251\pi\) |
0.250970 | + | 0.967995i | \(0.419251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.80624 | − | 11.6033i | 0.193179 | − | 0.466376i | −0.797377 | − | 0.603481i | \(-0.793780\pi\) |
0.990556 | + | 0.137105i | \(0.0437799\pi\) | |||||||
\(620\) | 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 | \(-0.631838\pi\) |
0.915446 | + | 0.402442i | \(0.131838\pi\) | |||||||
\(632\) | 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 | \(-0.223461\pi\) |
−0.996526 | + | 0.0832793i | \(0.973461\pi\) | |||||||
\(644\) | 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 | \(-0.431747\pi\) |
−0.977099 | + | 0.212785i | \(0.931747\pi\) | |||||||
\(648\) | 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 | −0.315432 | − | 0.948948i | \(-0.602149\pi\) |
0.447964 | + | 0.894052i | \(0.352149\pi\) | |||||||
\(654\) | 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 | \(-0.518534\pi\) |
0.664759 | + | 0.747058i | \(0.268534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.03928 | + | 14.5801i | −0.234901 | + | 0.567100i | −0.996741 | − | 0.0806641i | \(-0.974296\pi\) |
0.761841 | + | 0.647764i | \(0.224296\pi\) | |||||||
\(662\) | 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 | −0.425527 | − | 0.904946i | \(-0.639911\pi\) |
−0.940786 | + | 0.339000i | \(0.889911\pi\) | |||||||
\(678\) | 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 | \(-0.912614\pi\) |
0.872322 | + | 0.488932i | \(0.162614\pi\) | |||||||
\(684\) | 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 | \(-0.582356\pi\) |
0.502655 | + | 0.864487i | \(0.332356\pi\) | |||||||
\(692\) | 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 | 0.988368 | − | 0.152084i | \(-0.0485983\pi\) |
−0.806421 | + | 0.591342i | \(0.798598\pi\) | |||||||
\(702\) | 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 | 0.343478 | − | 0.939161i | \(-0.388395\pi\) |
−0.421211 | + | 0.906963i | \(0.638395\pi\) | |||||||
\(710\) | 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 | \(-0.764643\pi\) |
0.673842 | + | 0.738876i | \(0.264643\pi\) | |||||||
\(728\) | 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 | 0.915399 | − | 0.402547i | \(-0.131875\pi\) |
−0.931929 | + | 0.362641i | \(0.881875\pi\) | |||||||
\(734\) | 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 | 0.914005 | + | 0.405703i | \(0.132973\pi\) |
−0.359424 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(740\) | 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 | \(-0.238003\pi\) |
−0.679960 | + | 0.733249i | \(0.738003\pi\) | |||||||
\(744\) | 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 | 0.592990 | + | 0.805210i | \(0.297947\pi\) |
−0.988677 | + | 0.150062i | \(0.952053\pi\) | |||||||
\(758\) | 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 | \(-0.363345\pi\) |
−0.909251 | + | 0.416248i | \(0.863345\pi\) | |||||||
\(762\) | 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 | 0.846841 | − | 0.531847i | \(-0.178502\pi\) |
0.222735 | + | 0.974879i | \(0.428502\pi\) | |||||||
\(774\) | 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 | \(-0.566899\pi\) |
0.544027 | + | 0.839068i | \(0.316899\pi\) | |||||||
\(788\) | 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 | 0.998484 | − | 0.0550349i | \(-0.0175270\pi\) |
−0.744951 | + | 0.667120i | \(0.767527\pi\) | |||||||
\(798\) | 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 | −0.00309284 | − | 0.999995i | \(-0.500984\pi\) |
0.999995 | + | 0.00309284i | \(0.000984483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.61674 | − | 3.90316i | 0.0567716 | − | 0.137059i | −0.892949 | − | 0.450159i | \(-0.851367\pi\) |
0.949720 | + | 0.313100i | \(0.101367\pi\) | |||||||
\(812\) | 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 | −0.584681 | − | 0.811264i | \(-0.698780\pi\) |
0.987082 | − | 0.160218i | \(-0.0512199\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.7602 | + | 30.7602i | −1.07223 | + | 1.07223i | −0.0750551 | + | 0.997179i | \(0.523913\pi\) |
−0.997179 | + | 0.0750551i | \(0.976087\pi\) | |||||||
\(824\) | 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 | \(-0.518741\pi\) |
−0.747489 | + | 0.664274i | \(0.768741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.1975 | − | 41.5185i | −0.597295 | − | 1.44200i | −0.876328 | − | 0.481715i | \(-0.840014\pi\) |
0.279033 | − | 0.960281i | \(-0.409986\pi\) | |||||||
\(830\) | 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 | 0.997002 | + | 0.0773708i | \(0.0246525\pi\) |
0.0773708 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(840\) | 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 | 0.662271 | + | 0.749264i | \(0.269593\pi\) |
−0.998106 | + | 0.0615130i | \(0.980407\pi\) | |||||||
\(854\) | 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 | \(-0.454053\pi\) |
−0.989600 | + | 0.143847i | \(0.954053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.98006 | − | 3.30545i | −0.272276 | − | 0.112780i | 0.242368 | − | 0.970184i | \(-0.422076\pi\) |
−0.514644 | + | 0.857404i | \(0.672076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.32204 | − | 5.60590i | −0.0791349 | − | 0.191049i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.4394 | −1.20637 | −0.603185 | − | 0.797601i | \(-0.706102\pi\) | ||||
−0.603185 | + | 0.797601i | \(0.706102\pi\) | |||||||
\(864\) | 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 | 0.497005 | − | 0.867748i | \(-0.334433\pi\) |
0.965026 | + | 0.262155i | \(0.0844332\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.6591i | 0.764274i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.84917i | 0.163373i | 0.996658 | + | 0.0816863i | \(0.0260306\pi\) | ||||
−0.996658 | + | 0.0816863i | \(0.973969\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.9077 | − | 16.9445i | 1.37665 | − | 0.570228i | 0.433068 | − | 0.901361i | \(-0.357431\pi\) |
0.943584 | + | 0.331133i | \(0.107431\pi\) | |||||||
\(884\) | 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 | \(-0.690898\pi\) |
0.825491 | + | 0.564415i | \(0.190898\pi\) | |||||||
\(888\) | 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 | \(-0.908001\pi\) |
0.879314 | + | 0.476242i | \(0.158001\pi\) | |||||||
\(908\) | 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 | \(-0.651412\pi\) |
0.888984 | + | 0.457938i | \(0.151412\pi\) | |||||||
\(920\) | 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 | −0.777793 | − | 0.628520i | \(-0.783661\pi\) |
0.628520 | + | 0.777793i | \(0.283661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.2591 | + | 34.4244i | −0.465327 | + | 1.12340i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6192 | − | 7.29813i | 0.574371 | − | 0.237912i | −0.0765397 | − | 0.997067i | \(-0.524387\pi\) |
0.650911 | + | 0.759154i | \(0.274387\pi\) | |||||||
\(942\) | 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 | \(-0.563780\pi\) |
0.552221 | + | 0.833698i | \(0.313780\pi\) | |||||||
\(948\) | 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 | 0.848820 | − | 0.528682i | \(-0.177313\pi\) |
−0.528682 | + | 0.848820i | \(0.677313\pi\) | |||||||
\(954\) | 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 | \(-0.0354614\pi\) |
−0.111175 | + | 0.993801i | \(0.535461\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.9125 | − | 21.9125i | 0.703931 | − | 0.703931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.6361 | + | 52.2342i | −0.694335 | + | 1.67627i | 0.0415225 | + | 0.999138i | \(0.486779\pi\) |
−0.735858 | + | 0.677136i | \(0.763221\pi\) | |||||||
\(972\) | 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 | \(0.120499\pi\) | ||||
−0.929198 | + | 0.369582i | \(0.879501\pi\) | |||||||
\(978\) | 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 | \(-0.881055\pi\) |
0.365041 | + | 0.930991i | \(0.381055\pi\) | |||||||
\(984\) | 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 | \(-0.466129\pi\) | ||||
0.106208 | + | 0.994344i | \(0.466129\pi\) | |||||||
\(992\) | 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 | 0.328693 | − | 0.944437i | \(-0.393392\pi\) |
−0.435397 | + | 0.900239i | \(0.643392\pi\) | |||||||
\(998\) | 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.897.1 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.e.897.4 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.b.897.1 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.b.897.4 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.h.385.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.c.385.1 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.c.385.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.h.385.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.b.129.1 | ✓ | 16 | ||
32.5 | even | 8 | 1024.2.g.h.641.4 | yes | 16 | ||
32.11 | odd | 8 | 1024.2.g.c.641.4 | yes | 16 | ||
32.13 | even | 8 | inner | 1024.2.g.e.129.1 | yes | 16 | |
32.19 | odd | 8 | inner | 1024.2.g.e.129.4 | yes | 16 | |
32.21 | even | 8 | 1024.2.g.c.641.1 | yes | 16 | ||
32.27 | odd | 8 | 1024.2.g.h.641.1 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.b.129.4 | yes | 16 | ||
64.13 | even | 16 | 4096.2.a.n.1.2 | 8 | |||
64.19 | odd | 16 | 4096.2.a.n.1.1 | 8 | |||
64.45 | even | 16 | 4096.2.a.o.1.7 | 8 | |||
64.51 | odd | 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 | 32.3 | odd | 8 | ||
1024.2.g.b.129.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.b.897.1 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.b.897.4 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.c.385.1 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.c.385.4 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.c.641.1 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.c.641.4 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.e.129.1 | yes | 16 | 32.13 | even | 8 | inner | |
1024.2.g.e.129.4 | yes | 16 | 32.19 | odd | 8 | inner | |
1024.2.g.e.897.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.e.897.4 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.h.385.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.h.385.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.h.641.1 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.h.641.4 | yes | 16 | 32.5 | even | 8 | ||
4096.2.a.n.1.1 | 8 | 64.19 | odd | 16 | |||
4096.2.a.n.1.2 | 8 | 64.13 | even | 16 | |||
4096.2.a.o.1.7 | 8 | 64.45 | even | 16 | |||
4096.2.a.o.1.8 | 8 | 64.51 | odd | 16 |