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 | 129.3 | ||
Root | \(-1.50947 + 0.849413i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.129 |
Dual form | 1024.2.g.e.897.3 |
$q$-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 | ||||||||
\(3\) | 0.660056 | − | 1.59352i | 0.381083 | − | 0.920017i | −0.610673 | − | 0.791883i | \(-0.709101\pi\) |
0.991757 | − | 0.128134i | \(-0.0408988\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.512517 | + | 0.212292i | −0.229205 | + | 0.0949397i | −0.494330 | − | 0.869274i | \(-0.664587\pi\) |
0.265125 | + | 0.964214i | \(0.414587\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.69883 | + | 1.69883i | −0.642096 | + | 0.642096i | −0.951070 | − | 0.308974i | \(-0.900014\pi\) |
0.308974 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0177021 | + | 0.0177021i | 0.00590068 | + | 0.00590068i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.42542 | + | 3.44127i | 0.429781 | + | 1.03758i | 0.979357 | + | 0.202139i | \(0.0647894\pi\) |
−0.549576 | + | 0.835444i | \(0.685211\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.65154 | − | 2.34094i | −1.56746 | − | 0.649261i | −0.581091 | − | 0.813839i | \(-0.697374\pi\) |
−0.986364 | + | 0.164577i | \(0.947374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.956828i | 0.247052i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.26768i | 1.27760i | 0.769373 | + | 0.638799i | \(0.220569\pi\) | ||||
−0.769373 | + | 0.638799i | \(0.779431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80083 | + | 1.57436i | 0.871970 | + | 0.361182i | 0.773377 | − | 0.633946i | \(-0.218566\pi\) |
0.0985928 | + | 0.995128i | \(0.468566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.58579 | + | 3.82843i | 0.346047 | + | 0.835431i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.31195 | + | 4.31195i | 0.899104 | + | 0.899104i | 0.995357 | − | 0.0962527i | \(-0.0306857\pi\) |
−0.0962527 | + | 0.995357i | \(0.530686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.31793 | + | 3.31793i | −0.663586 | + | 0.663586i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.82044 | − | 1.99669i | 0.927694 | − | 0.384263i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.512517 | + | 1.23733i | −0.0951721 | + | 0.229766i | −0.964295 | − | 0.264830i | \(-0.914684\pi\) |
0.869123 | + | 0.494596i | \(0.164684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.53073 | −0.274928 | −0.137464 | − | 0.990507i | \(-0.543895\pi\) | ||||
−0.137464 | + | 0.990507i | \(0.543895\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.42458 | 1.11838 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.510031 | − | 1.23132i | 0.0862110 | − | 0.208132i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.61614 | − | 1.49785i | 0.594489 | − | 0.246245i | −0.0650915 | − | 0.997879i | \(-0.520734\pi\) |
0.659581 | + | 0.751634i | \(0.270734\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.46066 | + | 7.46066i | −1.19466 | + | 1.19466i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.69226 | − | 8.69226i | −1.35750 | − | 1.35750i | −0.876985 | − | 0.480518i | \(-0.840449\pi\) |
−0.480518 | − | 0.876985i | \(-0.659551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.211714 | − | 0.511123i | −0.0322861 | − | 0.0779456i | 0.906914 | − | 0.421316i | \(-0.138432\pi\) |
−0.939200 | + | 0.343370i | \(0.888432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0128306 | − | 0.00531461i | −0.00191267 | − | 0.000792255i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.73339i | 1.41976i | 0.704322 | + | 0.709881i | \(0.251251\pi\) | ||||
−0.704322 | + | 0.709881i | \(0.748749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.22798i | 0.175425i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.39412 | + | 3.47696i | 1.17541 | + | 0.486872i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.78771 | + | 6.73012i | 0.382921 | + | 0.924454i | 0.991398 | + | 0.130882i | \(0.0417809\pi\) |
−0.608477 | + | 0.793572i | \(0.708219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46111 | − | 1.46111i | −0.197016 | − | 0.197016i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.01752 | − | 5.01752i | 0.664587 | − | 0.664587i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.76469 | − | 1.14517i | 0.359933 | − | 0.149089i | −0.195387 | − | 0.980726i | \(-0.562596\pi\) |
0.555319 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.06575 | − | 7.40138i | 0.392529 | − | 0.947650i | −0.596858 | − | 0.802347i | \(-0.703584\pi\) |
0.989387 | − | 0.145303i | \(-0.0464157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0601454 | −0.00757761 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.39347 | 0.420909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.20995 | + | 5.33529i | −0.269988 | + | 0.651810i | −0.999482 | − | 0.0321778i | \(-0.989756\pi\) |
0.729494 | + | 0.683987i | \(0.239756\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.71729 | − | 4.02503i | 1.16982 | − | 0.484557i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.45315 | − | 9.45315i | 1.12188 | − | 1.12188i | 0.130424 | − | 0.991458i | \(-0.458366\pi\) |
0.991458 | − | 0.130424i | \(-0.0416338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.69977 | − | 1.69977i | −0.198944 | − | 0.198944i | 0.600603 | − | 0.799547i | \(-0.294927\pi\) |
−0.799547 | + | 0.600603i | \(0.794927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.09715 | + | 7.47719i | 0.357628 | + | 0.863391i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.26768 | − | 3.42458i | −0.942189 | − | 0.390267i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.8332i | 1.44385i | 0.691973 | + | 0.721923i | \(0.256742\pi\) | ||||
−0.691973 | + | 0.721923i | \(0.743258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.92427i | − | 0.991586i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.870678 | − | 0.360647i | −0.0955693 | − | 0.0395861i | 0.334387 | − | 0.942436i | \(-0.391471\pi\) |
−0.429956 | + | 0.902850i | \(0.641471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.11828 | − | 2.69977i | −0.121295 | − | 0.292832i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.63341 | + | 1.63341i | 0.175120 | + | 0.175120i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.14939 | + | 1.14939i | −0.121835 | + | 0.121835i | −0.765396 | − | 0.643560i | \(-0.777457\pi\) |
0.643560 | + | 0.765396i | \(0.277457\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5778 | − | 5.62413i | 1.42334 | − | 0.589569i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.01037 | + | 2.43925i | −0.104770 | + | 0.252938i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.28221 | −0.234150 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.83880 | −0.186702 | −0.0933508 | − | 0.995633i | \(-0.529758\pi\) | ||||
−0.0933508 | + | 0.995633i | \(0.529758\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0356847 | + | 0.0861505i | −0.00358645 | + | 0.00865845i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.76267 | + | 0.730123i | −0.175393 | + | 0.0726500i | −0.468652 | − | 0.883383i | \(-0.655260\pi\) |
0.293259 | + | 0.956033i | \(0.405260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.36725 | + | 5.36725i | −0.528851 | + | 0.528851i | −0.920230 | − | 0.391379i | \(-0.871998\pi\) |
0.391379 | + | 0.920230i | \(0.371998\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.62549 | − | 1.62549i | −0.158631 | − | 0.158631i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.19848 | − | 17.3787i | −0.695904 | − | 1.68006i | −0.732534 | − | 0.680731i | \(-0.761662\pi\) |
0.0366299 | − | 0.999329i | \(-0.488338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31591 | + | 2.61614i | 0.604954 | + | 0.250580i | 0.664070 | − | 0.747671i | \(-0.268828\pi\) |
−0.0591151 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6.75103i | − | 0.640780i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.60045i | 0.620918i | 0.950587 | + | 0.310459i | \(0.100483\pi\) | ||||
−0.950587 | + | 0.310459i | \(0.899517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.12534 | − | 1.29456i | −0.291440 | − | 0.120718i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0586043 | − | 0.141483i | −0.00541797 | − | 0.0130801i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.94887 | − | 8.94887i | −0.820341 | − | 0.820341i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.03237 | + | 2.03237i | −0.184761 | + | 0.184761i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.5886 | + | 8.11387i | −1.76625 | + | 0.731603i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.05758 | − | 4.96745i | 0.184036 | − | 0.444302i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.36789 | −0.387588 | −0.193794 | − | 0.981042i | \(-0.562079\pi\) | ||||
−0.193794 | + | 0.981042i | \(0.562079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.954226 | −0.0840149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.60628 | − | 6.29212i | 0.227712 | − | 0.549745i | −0.768186 | − | 0.640226i | \(-0.778841\pi\) |
0.995898 | + | 0.0904813i | \(0.0288405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.13151 | + | 3.78239i | −0.791802 | + | 0.327975i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.04668 | + | 2.04668i | −0.176150 | + | 0.176150i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.47465 | + | 5.47465i | 0.467731 | + | 0.467731i | 0.901179 | − | 0.433448i | \(-0.142703\pi\) |
−0.433448 | + | 0.901179i | \(0.642703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.44282 | + | 10.7259i | 0.376835 | + | 0.909760i | 0.992555 | + | 0.121795i | \(0.0388650\pi\) |
−0.615721 | + | 0.787965i | \(0.711135\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5103 | + | 6.42458i | 1.30620 | + | 0.541048i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 22.7853i | − | 1.90541i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.742954i | − | 0.0616990i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.95680 | + | 0.810533i | 0.161394 | + | 0.0668516i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.97276 | + | 4.76267i | 0.161615 | + | 0.390173i | 0.983855 | − | 0.178968i | \(-0.0572758\pi\) |
−0.822240 | + | 0.569141i | \(0.807276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9603 | + | 13.9603i | 1.13607 | + | 1.13607i | 0.989148 | + | 0.146924i | \(0.0469374\pi\) |
0.146924 | + | 0.989148i | \(0.453063\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0932487 | + | 0.0932487i | −0.00753871 | + | 0.00753871i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.784527 | − | 0.324962i | 0.0630148 | − | 0.0261016i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.64117 | + | 16.0332i | −0.530023 | + | 1.27959i | 0.401484 | + | 0.915866i | \(0.368494\pi\) |
−0.931507 | + | 0.363723i | \(0.881506\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.5646 | 0.996438 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.6505 | −1.15462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.95307 | + | 4.71513i | −0.152976 | + | 0.369317i | −0.981725 | − | 0.190303i | \(-0.939053\pi\) |
0.828749 | + | 0.559620i | \(0.189053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.29271 | + | 1.36388i | −0.256337 | + | 0.106178i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.52743 | − | 3.52743i | 0.272960 | − | 0.272960i | −0.557330 | − | 0.830291i | \(-0.688174\pi\) |
0.830291 | + | 0.557330i | \(0.188174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.2675 | + | 17.2675i | 1.32827 | + | 1.32827i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0394132 | + | 0.0951518i | 0.00301400 | + | 0.00727644i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1973 | − | 6.29491i | −1.15543 | − | 0.478593i | −0.279077 | − | 0.960269i | \(-0.590028\pi\) |
−0.876350 | + | 0.481676i | \(0.840028\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 11.2732i | − | 0.852171i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.16146i | − | 0.387959i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9061 | − | 8.65959i | −1.56260 | − | 0.647248i | −0.577057 | − | 0.816704i | \(-0.695799\pi\) |
−0.985538 | + | 0.169455i | \(0.945799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.60862 | − | 20.7830i | −0.639874 | − | 1.54479i | −0.826847 | − | 0.562427i | \(-0.809868\pi\) |
0.186974 | − | 0.982365i | \(-0.440132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.77065 | − | 9.77065i | −0.722267 | − | 0.722267i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.53535 | + | 1.53535i | −0.112881 | + | 0.112881i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.1275 | + | 7.50866i | −1.32562 | + | 0.549088i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.79706 | + | 11.5811i | −0.348935 | + | 0.842403i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4366 | 0.755168 | 0.377584 | − | 0.925975i | \(-0.376755\pi\) | ||||
0.377584 | + | 0.925975i | \(0.376755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.81806 | −0.274830 | −0.137415 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137415 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.23988 | − | 5.40755i | 0.160401 | − | 0.387243i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.6794 | + | 6.08042i | −1.04587 | + | 0.433212i | −0.838414 | − | 0.545033i | \(-0.816517\pi\) |
−0.207452 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0244 | − | 16.0244i | 1.13594 | − | 1.13594i | 0.146771 | − | 0.989171i | \(-0.453112\pi\) |
0.989171 | − | 0.146771i | \(-0.0468879\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.04318 | + | 7.04318i | 0.496788 | + | 0.496788i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.23132 | − | 2.97268i | −0.0864220 | − | 0.208641i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.30023 | + | 2.60964i | 0.440027 | + | 0.182265i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.152661i | 0.0106107i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.3238i | 1.05997i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2826 | − | 5.50184i | −0.914413 | − | 0.378762i | −0.124669 | − | 0.992198i | \(-0.539787\pi\) |
−0.789744 | + | 0.613436i | \(0.789787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.82413 | − | 21.3033i | −0.604620 | − | 1.45968i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.217014 | + | 0.217014i | 0.0148003 | + | 0.0148003i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.60045 | − | 2.60045i | 0.176530 | − | 0.176530i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.83056 | + | 1.58667i | −0.258845 | + | 0.107217i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3313 | − | 29.7705i | 0.829495 | − | 2.00258i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.3670 | −1.09602 | −0.548008 | − | 0.836473i | \(-0.684614\pi\) | ||||
−0.548008 | + | 0.836473i | \(0.684614\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.117468 | −0.00783122 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.15247 | − | 5.19652i | 0.142864 | − | 0.344905i | −0.836210 | − | 0.548410i | \(-0.815233\pi\) |
0.979074 | + | 0.203505i | \(0.0652333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1694 | + | 5.04072i | −0.804175 | + | 0.333100i | −0.746627 | − | 0.665243i | \(-0.768328\pi\) |
−0.0575475 | + | 0.998343i | \(0.518328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9143 | + | 10.9143i | −0.718105 | + | 0.718105i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.74984 | + | 1.74984i | 0.114636 | + | 0.114636i | 0.762098 | − | 0.647462i | \(-0.224169\pi\) |
−0.647462 | + | 0.762098i | \(0.724169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.06632 | − | 4.98853i | −0.134792 | − | 0.325416i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.4499 | + | 8.47062i | 1.32836 | + | 0.550226i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.7565i | − | 0.825152i | −0.910923 | − | 0.412576i | \(-0.864629\pi\) | ||
0.910923 | − | 0.412576i | \(-0.135371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.9660i | − | 1.22171i | −0.791743 | − | 0.610854i | \(-0.790826\pi\) | ||
0.791743 | − | 0.610854i | \(-0.209174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.240356 | + | 0.0995586i | 0.0154188 | + | 0.00638669i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.260689 | − | 0.629359i | −0.0166548 | − | 0.0402083i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.7951 | − | 17.7951i | −1.13227 | − | 1.13227i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.14939 | + | 1.14939i | −0.0728398 | + | 0.0728398i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.10639 | + | 3.77199i | −0.574790 | + | 0.238086i | −0.651092 | − | 0.758999i | \(-0.725689\pi\) |
0.0763018 | + | 0.997085i | \(0.475689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.69226 | + | 20.9850i | −0.546478 | + | 1.31931i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.04026 | −0.315633 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.06510 | −0.128817 | −0.0644087 | − | 0.997924i | \(-0.520516\pi\) | ||||
−0.0644087 | + | 0.997924i | \(0.520516\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.59860 | + | 8.68778i | −0.223606 | + | 0.539832i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0309758 | + | 0.0128306i | −0.00191736 | + | 0.000794194i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8612 | − | 17.8612i | 1.10137 | − | 1.10137i | 0.107120 | − | 0.994246i | \(-0.465837\pi\) |
0.994246 | − | 0.107120i | \(-0.0341629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.85750 | − | 2.85750i | −0.175535 | − | 0.175535i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.07291 | + | 2.59024i | 0.0656611 | + | 0.158520i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.6544 | + | 5.65583i | 0.832523 | + | 0.344842i | 0.757901 | − | 0.652370i | \(-0.226225\pi\) |
0.0746220 | + | 0.997212i | \(0.476225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.39655i | − | 0.145580i | −0.997347 | − | 0.0727901i | \(-0.976810\pi\) | ||
0.997347 | − | 0.0727901i | \(-0.0231903\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.3487i | − | 1.53418i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.1473 | − | 6.68845i | −0.973722 | − | 0.403329i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.82741 | + | 9.24018i | 0.229967 | + | 0.555189i | 0.996173 | − | 0.0874063i | \(-0.0278578\pi\) |
−0.766206 | + | 0.642595i | \(0.777858\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0270971 | − | 0.0270971i | −0.00162226 | − | 0.00162226i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8667 | − | 19.8667i | 1.18515 | − | 1.18515i | 0.206754 | − | 0.978393i | \(-0.433710\pi\) |
0.978393 | − | 0.206754i | \(-0.0662900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.76511 | − | 1.97378i | 0.283257 | − | 0.117329i | −0.236532 | − | 0.971624i | \(-0.576011\pi\) |
0.519788 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.50639 | + | 3.63674i | −0.0892307 | + | 0.215422i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.5333 | 1.74329 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7484 | −0.632259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.21371 | + | 2.93015i | −0.0711488 | + | 0.171769i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.2548 | − | 8.38983i | 1.18330 | − | 0.490139i | 0.297733 | − | 0.954649i | \(-0.403770\pi\) |
0.885568 | + | 0.464510i | \(0.153770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17384 | + | 1.17384i | −0.0683438 | + | 0.0683438i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.7423 | + | 13.7423i | 0.797411 | + | 0.797411i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.2751 | − | 34.4632i | −0.825552 | − | 1.99306i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.22798 | + | 0.508644i | 0.0707793 | + | 0.0293178i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.29077i | 0.189050i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.44417i | 0.254472i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9354 | + | 8.25751i | 1.13777 | + | 0.471281i | 0.870416 | − | 0.492317i | \(-0.163850\pi\) |
0.267356 | + | 0.963598i | \(0.413850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.01011 | + | 12.0955i | 0.285015 | + | 0.688088i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.4798 | + | 15.4798i | 0.877779 | + | 0.877779i | 0.993304 | − | 0.115526i | \(-0.0368553\pi\) |
−0.115526 | + | 0.993304i | \(0.536855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0918 | + | 14.0918i | −0.796516 | + | 0.796516i | −0.982544 | − | 0.186028i | \(-0.940438\pi\) |
0.186028 | + | 0.982544i | \(0.440438\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0308256 | − | 0.0127684i | 0.00173682 | − | 0.000719416i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.05683 | − | 7.37983i | 0.171688 | − | 0.414492i | −0.814490 | − | 0.580177i | \(-0.802983\pi\) |
0.986179 | + | 0.165685i | \(0.0529834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.98853 | −0.279304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −32.4446 | −1.81088 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.29319 | + | 20.0215i | −0.461445 | + | 1.11403i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.5185 | − | 10.9843i | 1.47098 | − | 0.609300i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.33771 | − | 8.33771i | 0.461076 | − | 0.461076i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5354 | − | 16.5354i | −0.911623 | − | 0.911623i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.68230 | + | 6.47564i | 0.147433 | + | 0.355934i | 0.980293 | − | 0.197550i | \(-0.0632983\pi\) |
−0.832860 | + | 0.553483i | \(0.813298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0905281 | + | 0.0374980i | 0.00496091 | + | 0.00205488i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.20358i | − | 0.175030i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.82843i | − | 0.154074i | −0.997028 | − | 0.0770371i | \(-0.975454\pi\) | ||
0.997028 | − | 0.0770371i | \(-0.0245460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.5179 | + | 4.35667i | 0.571255 | + | 0.236622i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.18194 | − | 5.26768i | −0.118159 | − | 0.285261i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9779 | − | 13.9779i | −0.754736 | − | 0.754736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.12580 | + | 4.12580i | −0.222126 | + | 0.222126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6041 | − | 4.39235i | 0.569256 | − | 0.235794i | −0.0794417 | − | 0.996840i | \(-0.525314\pi\) |
0.648698 | + | 0.761046i | \(0.275314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.18404 | − | 19.7580i | 0.438081 | − | 1.05762i | −0.538529 | − | 0.842607i | \(-0.681020\pi\) |
0.976611 | − | 0.215015i | \(-0.0689801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.9170 | −1.70361 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.0563 | 1.38684 | 0.693418 | − | 0.720535i | \(-0.256104\pi\) | ||||
0.693418 | + | 0.720535i | \(0.256104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.83808 | + | 6.85172i | −0.150629 | + | 0.363652i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.1669 | + | 8.35341i | −1.06735 | + | 0.442109i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.77460 | − | 6.77460i | 0.357550 | − | 0.357550i | −0.505359 | − | 0.862909i | \(-0.668640\pi\) |
0.862909 | + | 0.505359i | \(0.168640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.46732 | − | 1.46732i | −0.0772274 | − | 0.0772274i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.89713 | + | 4.58008i | 0.0995737 | + | 0.240392i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.23201 | + | 0.510316i | 0.0644864 | + | 0.0267112i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2892i | 1.00689i | 0.864028 | + | 0.503444i | \(0.167934\pi\) | ||||
−0.864028 | + | 0.503444i | \(0.832066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 0.307742i | − | 0.0160204i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.1691 | − | 6.69748i | −0.839460 | − | 0.347716i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.82311 | − | 6.81560i | −0.146175 | − | 0.352898i | 0.833786 | − | 0.552088i | \(-0.186169\pi\) |
−0.979961 | + | 0.199190i | \(0.936169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.55759 | − | 6.55759i | −0.338632 | − | 0.338632i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.79302 | − | 5.79302i | 0.298356 | − | 0.298356i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8072 | − | 5.30491i | 0.657861 | − | 0.272495i | −0.0286774 | − | 0.999589i | \(-0.509130\pi\) |
0.686538 | + | 0.727094i | \(0.259130\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.88305 | + | 6.96030i | −0.147703 | + | 0.356587i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.78803 | 0.193559 | 0.0967797 | − | 0.995306i | \(-0.469146\pi\) | ||||
0.0967797 | + | 0.995306i | \(0.469146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.96434 | 0.253006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.00530016 | − | 0.0127957i | 0.000269422 | − | 0.000650442i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.1472 | + | 7.93103i | −0.970801 | + | 0.402119i | −0.811010 | − | 0.585032i | \(-0.801082\pi\) |
−0.159791 | + | 0.987151i | \(0.551082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.7140 | + | 22.7140i | −1.14869 | + | 1.14869i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.30630 | − | 8.30630i | −0.418997 | − | 0.418997i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.72438 | − | 6.57723i | −0.137078 | − | 0.330936i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.41201 | + | 2.65594i | 0.321810 | + | 0.133298i | 0.537740 | − | 0.843111i | \(-0.319278\pi\) |
−0.215930 | + | 0.976409i | \(0.569278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.0478i | 0.853457i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0373i | 1.05055i | 0.850931 | + | 0.525277i | \(0.176038\pi\) | ||||
−0.850931 | + | 0.525277i | \(0.823962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.65100 | + | 3.58336i | 0.430937 | + | 0.178500i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.89455 | + | 4.57384i | 0.0941408 | + | 0.227276i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3090 | + | 10.3090i | 0.511000 | + | 0.511000i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.106839 | + | 0.106839i | −0.00528285 | + | 0.00528285i | −0.709743 | − | 0.704460i | \(-0.751189\pi\) |
0.704460 | + | 0.709743i | \(0.251189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3375 | − | 5.11037i | 0.608565 | − | 0.252076i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.75128 | + | 6.64219i | −0.135382 | + | 0.326841i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.522800 | 0.0256632 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0244 | 0.980599 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.75898 | − | 18.7318i | 0.379051 | − | 0.915110i | −0.613093 | − | 0.790011i | \(-0.710075\pi\) |
0.992144 | − | 0.125099i | \(-0.0399250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2756 | − | 5.08471i | 0.598275 | − | 0.247814i | −0.0629310 | − | 0.998018i | \(-0.520045\pi\) |
0.661206 | + | 0.750204i | \(0.270045\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.172301 | + | 0.172301i | −0.00837756 | + | 0.00837756i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.4778 | − | 17.4778i | −0.847796 | − | 0.847796i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.36548 | + | 17.7819i | 0.356441 | + | 0.860524i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36.3088 | − | 15.0396i | −1.75300 | − | 0.726118i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.96851i | 0.431998i | 0.976394 | + | 0.215999i | \(0.0693008\pi\) | ||||
−0.976394 | + | 0.215999i | \(0.930699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.14680i | − | 0.151225i | −0.997137 | − | 0.0756127i | \(-0.975909\pi\) | ||
0.997137 | − | 0.0756127i | \(-0.0240913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.18391 | − | 0.490391i | −0.0567641 | − | 0.0235125i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.60045 | + | 23.1775i | 0.459252 | + | 1.10873i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.35602 | + | 5.35602i | 0.255629 | + | 0.255629i | 0.823274 | − | 0.567645i | \(-0.192145\pi\) |
−0.567645 | + | 0.823274i | \(0.692145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0217377 | + | 0.0217377i | −0.00103513 | + | 0.00103513i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2372 | + | 7.13988i | −0.818964 | + | 0.339226i | −0.752524 | − | 0.658564i | \(-0.771164\pi\) |
−0.0664397 | + | 0.997790i | \(0.521164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.345077 | − | 0.833089i | 0.0163582 | − | 0.0394922i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.89153 | 0.420555 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.0511 | 1.65416 | 0.827082 | − | 0.562081i | \(-0.189999\pi\) | ||||
0.827082 | + | 0.562081i | \(0.189999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.5223 | − | 42.3026i | 0.825093 | − | 1.99195i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.4605 | − | 13.0314i | 1.47814 | − | 0.612267i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.76492 | + | 5.76492i | −0.270264 | + | 0.270264i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.65659 | + | 9.65659i | 0.451716 | + | 0.451716i | 0.895924 | − | 0.444207i | \(-0.146515\pi\) |
−0.444207 | + | 0.895924i | \(0.646515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.5179 | + | 25.3925i | 0.490935 | + | 1.18522i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2966 | − | 9.64976i | −1.08503 | − | 0.449434i | −0.232759 | − | 0.972534i | \(-0.574775\pi\) |
−0.852271 | + | 0.523100i | \(0.824775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.57747i | 0.0733113i | 0.999328 | + | 0.0366556i | \(0.0116705\pi\) | ||||
−0.999328 | + | 0.0366556i | \(0.988330\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 1.46465i | − | 0.0679215i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.6421 | + | 9.79289i | 1.09403 | + | 0.453161i | 0.855409 | − | 0.517953i | \(-0.173306\pi\) |
0.238618 | + | 0.971114i | \(0.423306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.30941 | − | 12.8181i | −0.245166 | − | 0.591883i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.1656 | + | 21.1656i | 0.975260 | + | 0.975260i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.45713 | − | 1.45713i | 0.0669991 | − | 0.0669991i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.8345 | + | 7.38728i | −0.818302 | + | 0.338952i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0697888 | + | 0.168485i | −0.00319541 | + | 0.00771441i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.1963 | 1.15125 | 0.575623 | − | 0.817715i | \(-0.304760\pi\) | ||||
0.575623 | + | 0.817715i | \(0.304760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.9431 | −1.09171 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.67016 | + | 23.3458i | −0.440008 | + | 1.06227i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.942415 | − | 0.390361i | 0.0427929 | − | 0.0177254i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4256 | + | 15.4256i | −0.699001 | + | 0.699001i | −0.964195 | − | 0.265194i | \(-0.914564\pi\) |
0.265194 | + | 0.964195i | \(0.414564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.22450 | + | 6.22450i | 0.281481 | + | 0.281481i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9376 | + | 28.8199i | 0.538736 | + | 1.30062i | 0.925606 | + | 0.378489i | \(0.123556\pi\) |
−0.386870 | + | 0.922134i | \(0.626444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.51783 | − | 2.69977i | −0.293548 | − | 0.121592i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 0.0517292i | − | 0.00232505i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.1185i | 1.44071i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.2722 | + | 14.6102i | 1.57900 | + | 0.654043i | 0.988255 | − | 0.152814i | \(-0.0488337\pi\) |
0.590746 | + | 0.806858i | \(0.298834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.29271 | − | 7.94930i | −0.147107 | − | 0.355149i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.18240 | − | 2.18240i | −0.0973084 | − | 0.0973084i | 0.656777 | − | 0.754085i | \(-0.271919\pi\) |
−0.754085 | + | 0.656777i | \(0.771919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.748402 | − | 0.748402i | 0.0333034 | − | 0.0333034i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.9135 | − | 16.1185i | 1.72821 | − | 0.715848i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.08482 | − | 7.44742i | 0.136732 | − | 0.330101i | −0.840651 | − | 0.541578i | \(-0.817827\pi\) |
0.977383 | + | 0.211477i | \(0.0678272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.77524 | 0.255482 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.4652 | 0.947710 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.61139 | − | 3.89023i | 0.0710061 | − | 0.171424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.4953 | + | 13.8742i | −1.47312 | + | 0.610187i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.0621 | + | 20.0621i | −0.880627 | + | 0.880627i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.94553 | − | 6.94553i | −0.304289 | − | 0.304289i | 0.538400 | − | 0.842689i | \(-0.319029\pi\) |
−0.842689 | + | 0.538400i | \(0.819029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.930625 | + | 2.24673i | 0.0406934 | + | 0.0982425i | 0.942919 | − | 0.333021i | \(-0.108068\pi\) |
−0.902226 | + | 0.431263i | \(0.858068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.9640 | − | 7.44092i | −0.784012 | − | 0.324748i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.06341i | − | 0.351248i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.1859i | 0.616777i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0692127 | + | 0.0286688i | 0.00300358 | + | 0.00124412i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.7765 | + | 69.4727i | 1.24645 | + | 3.00920i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.37869 | + | 7.37869i | 0.319009 | + | 0.319009i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.5984 | + | 27.5984i | −1.19096 | + | 1.19096i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.22580 | + | 1.75038i | −0.182018 | + | 0.0753944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5260 | + | 25.4120i | −0.452548 | + | 1.09255i | 0.518802 | + | 0.854894i | \(0.326378\pi\) |
−0.971350 | + | 0.237653i | \(0.923622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.8003 | −1.66508 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.79240 | −0.162448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.04627 | + | 2.52591i | −0.0447351 | + | 0.108000i | −0.944668 | − | 0.328029i | \(-0.893616\pi\) |
0.899932 | + | 0.436029i | \(0.143616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.185290 | − | 0.0767495i | 0.00790798 | − | 0.00327559i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.89598 | + | 3.89598i | −0.165974 | + | 0.165974i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.8014 | − | 21.8014i | −0.927088 | − | 0.927088i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.43319 | + | 3.46002i | 0.0608354 | + | 0.146870i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.7983 | − | 8.61495i | −0.881254 | − | 0.365027i | −0.104271 | − | 0.994549i | \(-0.533251\pi\) |
−0.776983 | + | 0.629522i | \(0.783251\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.38425i | 0.143138i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 33.8426i | 1.42884i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.9200 | − | 8.66534i | −0.881672 | − | 0.365201i | −0.104527 | − | 0.994522i | \(-0.533333\pi\) |
−0.777145 | + | 0.629321i | \(0.783333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.40122 | − | 3.38285i | −0.0589498 | − | 0.142317i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.1608 | + | 15.1608i | 0.636693 | + | 0.636693i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.276633 | + | 0.276633i | −0.0115970 | + | 0.0115970i | −0.712882 | − | 0.701284i | \(-0.752610\pi\) |
0.701284 | + | 0.712882i | \(0.252610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.9788 | − | 13.2460i | 1.33827 | − | 0.554329i | 0.405267 | − | 0.914198i | \(-0.367179\pi\) |
0.933003 | + | 0.359869i | \(0.117179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.88876 | − | 16.6309i | 0.287782 | − | 0.694767i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.6135 | −1.19327 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0407 | 1.25061 | 0.625306 | − | 0.780379i | \(-0.284974\pi\) | ||||
0.625306 | + | 0.780379i | \(0.284974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.52013 | + | 6.08413i | −0.104733 | + | 0.252848i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.09181 | − | 0.866455i | 0.0867828 | − | 0.0359466i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.1865 | + | 19.1865i | −0.794625 | + | 0.794625i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0600715 | + | 0.0600715i | 0.00248365 | + | 0.00248365i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5838 | − | 32.7941i | −0.560662 | − | 1.35356i | −0.909238 | − | 0.416277i | \(-0.863335\pi\) |
0.348575 | − | 0.937281i | \(-0.386665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.81806 | − | 2.40992i | −0.239729 | − | 0.0992990i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.4053i | 1.12730i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.66555i | 0.109461i | 0.998501 | + | 0.0547306i | \(0.0174300\pi\) | ||||
−0.998501 | + | 0.0547306i | \(0.982570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.48622 | + | 2.68668i | 0.265909 | + | 0.110143i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.9582 | − | 36.1122i | −0.612197 | − | 1.47797i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.9077 | − | 11.9077i | −0.486534 | − | 0.486534i | 0.420677 | − | 0.907211i | \(-0.361793\pi\) |
−0.907211 | + | 0.420677i | \(0.861793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.86501 | + | 1.86501i | −0.0760755 | + | 0.0760755i | −0.744121 | − | 0.668045i | \(-0.767131\pi\) |
0.668045 | + | 0.744121i | \(0.267131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.133566 | + | 0.0553250i | −0.00543924 | + | 0.00225301i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.610169 | − | 1.47308i | 0.0248069 | − | 0.0598891i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.47275 | 0.343898 | 0.171949 | − | 0.985106i | \(-0.444994\pi\) | ||||
0.171949 | + | 0.985106i | \(0.444994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.54976 | −0.224887 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.7853 | − | 55.0087i | 0.921796 | − | 2.22541i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3613 | − | 9.67657i | 0.943555 | − | 0.390833i | 0.142750 | − | 0.989759i | \(-0.454405\pi\) |
0.800805 | + | 0.598926i | \(0.204405\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.31700 | − | 8.31700i | 0.335374 | − | 0.335374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.91738 | − | 8.91738i | −0.359000 | − | 0.359000i | 0.504444 | − | 0.863444i | \(-0.331697\pi\) |
−0.863444 | + | 0.504444i | \(0.831697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.30623 | + | 5.56774i | 0.0926953 | + | 0.223786i | 0.963426 | − | 0.267973i | \(-0.0863539\pi\) |
−0.870731 | + | 0.491760i | \(0.836354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.3951 | + | 12.1759i | 1.17959 | + | 0.488601i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.90524i | − | 0.156460i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 20.4786i | − | 0.819143i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.4187 | + | 10.1146i | 0.975191 | + | 0.403937i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.89020 | + | 19.0486i | 0.314603 | + | 0.759519i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4932 | + | 33.4932i | 1.33334 | + | 1.33334i | 0.902361 | + | 0.430981i | \(0.141833\pi\) |
0.430981 | + | 0.902361i | \(0.358167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.5345 | + | 17.5345i | −0.696935 | + | 0.696935i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.23862 | − | 0.927266i | 0.0888369 | − | 0.0367974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.87462 | − | 6.93995i | 0.113897 | − | 0.274971i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.334680 | 0.0132397 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.8508 | −1.06054 | −0.530272 | − | 0.847827i | \(-0.677910\pi\) | ||||
−0.530272 | + | 0.847827i | \(0.677910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0339 | + | 31.4666i | −0.514006 | + | 1.24092i | 0.427528 | + | 0.904002i | \(0.359384\pi\) |
−0.941534 | + | 0.336918i | \(0.890616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.489057 | − | 0.202574i | 0.0192566 | − | 0.00797635i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.43000 | − | 6.43000i | 0.252789 | − | 0.252789i | −0.569324 | − | 0.822113i | \(-0.692795\pi\) |
0.822113 | + | 0.569324i | \(0.192795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.88172 | + | 7.88172i | 0.309384 | + | 0.309384i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.42742 | − | 5.86030i | −0.0951380 | − | 0.229683i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.6294 | − | 5.23125i | −0.494225 | − | 0.204715i | 0.121628 | − | 0.992576i | \(-0.461188\pi\) |
−0.615853 | + | 0.787861i | \(0.711188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.77811i | 0.147623i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.0601790i | − | 0.00234781i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.3485 | + | 5.94335i | 0.558939 | + | 0.231520i | 0.644224 | − | 0.764837i | \(-0.277180\pi\) |
−0.0852857 | + | 0.996357i | \(0.527180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.79664 | + | 21.2370i | 0.342150 | + | 0.826022i | 0.997498 | + | 0.0706953i | \(0.0225218\pi\) |
−0.655348 | + | 0.755327i | \(0.727478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.3003 | − | 39.3003i | −1.52630 | − | 1.52630i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.87708 | − | 3.87708i | 0.150347 | − | 0.150347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.54524 | + | 3.12534i | −0.292153 | + | 0.121014i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.8031 | + | 26.0811i | −0.417673 | + | 1.00835i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8402 | 1.15197 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6959 | 1.53017 | 0.765083 | − | 0.643932i | \(-0.222698\pi\) | ||||
0.765083 | + | 0.643932i | \(0.222698\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.36899 | + | 22.6187i | −0.360613 | + | 0.870596i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.7220 | − | 8.16911i | 0.757977 | − | 0.313964i | 0.0299855 | − | 0.999550i | \(-0.490454\pi\) |
0.727992 | + | 0.685586i | \(0.240454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.12380 | − | 3.12380i | 0.119880 | − | 0.119880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.85998 | − | 6.85998i | −0.262875 | − | 0.262875i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.39365 | + | 22.6783i | 0.359438 | + | 0.867760i | 0.995379 | + | 0.0960227i | \(0.0306121\pi\) |
−0.635941 | + | 0.771738i | \(0.719388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.96808 | − | 1.64363i | −0.151612 | − | 0.0627999i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.7192i | 0.866793i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 44.5614i | − | 1.69766i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.6135 | + | 5.63891i | 0.517883 | + | 0.214514i | 0.626287 | − | 0.779593i | \(-0.284574\pi\) |
−0.108404 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0857327 | − | 0.206977i | −0.00325671 | − | 0.00786241i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.55404 | − | 4.55404i | −0.172745 | − | 0.172745i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.7880 | − | 45.7880i | 1.73434 | − | 1.73434i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.94340 | − | 1.63341i | 0.149153 | − | 0.0617812i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6385 | − | 42.5832i | 0.666199 | − | 1.60835i | −0.121718 | − | 0.992565i | \(-0.538840\pi\) |
0.787917 | − | 0.615781i | \(-0.211160\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1025 | 0.607316 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.31319 | −0.350755 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.75412 | − | 4.23483i | 0.0659706 | − | 0.159267i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.8688 | − | 11.1294i | 1.00908 | − | 0.417974i | 0.183960 | − | 0.982934i | \(-0.441108\pi\) |
0.825118 | + | 0.564960i | \(0.191108\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.227174 | + | 0.227174i | −0.00851968 | + | 0.00851968i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.60045 | − | 6.60045i | −0.247189 | − | 0.247189i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.83714 | + | 11.6779i | 0.180899 | + | 0.436728i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.3277 | − | 8.42003i | −0.759154 | − | 0.314452i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.82423i | − | 0.0680323i | −0.999421 | − | 0.0340162i | \(-0.989170\pi\) | ||
0.999421 | − | 0.0340162i | \(-0.0108298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 18.2360i | − | 0.679146i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.2226 | − | 12.5186i | −1.12399 | − | 0.465573i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.40486 | − | 5.80585i | −0.0893144 | − | 0.215624i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1795 | − | 20.1795i | −0.748416 | − | 0.748416i | 0.225765 | − | 0.974182i | \(-0.427512\pi\) |
−0.974182 | + | 0.225765i | \(0.927512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.2485 | − | 19.2485i | 0.712909 | − | 0.712909i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.69243 | − | 1.11524i | 0.0995832 | − | 0.0412487i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.66073 | − | 11.2520i | 0.172148 | − | 0.415602i | −0.814133 | − | 0.580679i | \(-0.802787\pi\) |
0.986281 | + | 0.165077i | \(0.0527873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.17496 | −0.0433391 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.5103 | −0.792343 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.38552 | + | 22.6586i | −0.345252 | + | 0.833512i | 0.651915 | + | 0.758292i | \(0.273966\pi\) |
−0.997167 | + | 0.0752197i | \(0.976034\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −40.1024 | + | 16.6110i | −1.47320 | + | 0.610219i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.4077 | − | 30.4077i | 1.11555 | − | 1.11555i | 0.123164 | − | 0.992386i | \(-0.460696\pi\) |
0.992386 | − | 0.123164i | \(-0.0393041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.02215 | − | 2.02215i | −0.0740859 | − | 0.0740859i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.00902860 | − | 0.0217970i | −0.000330339 | − | 0.000797510i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.7523 | + | 17.2944i | 1.52560 | + | 0.631923i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.81357i | 0.212140i | 0.994359 | + | 0.106070i | \(0.0338268\pi\) | ||||
−0.994359 | + | 0.106070i | \(0.966173\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.0009i | 0.619547i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1185 | − | 4.19124i | −0.368251 | − | 0.152535i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.09998 | + | 2.65558i | 0.0399793 | + | 0.0965185i | 0.942608 | − | 0.333902i | \(-0.108365\pi\) |
−0.902629 | + | 0.430420i | \(0.858365\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.7025 | + | 27.7025i | 1.00554 | + | 1.00554i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.9432 | − | 17.9432i | 0.650442 | − | 0.650442i | −0.302658 | − | 0.953099i | \(-0.597874\pi\) |
0.953099 | + | 0.302658i | \(0.0978739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1740 | + | 6.28528i | −0.549336 | + | 0.227542i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0279956 | − | 0.0675875i | 0.00101218 | − | 0.00244363i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.3056 | −0.660976 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.98104 | −0.107499 | −0.0537495 | − | 0.998554i | \(-0.517117\pi\) | ||||
−0.0537495 | + | 0.998554i | \(0.517117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.36308 | + | 3.29077i | −0.0490902 | + | 0.118514i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4049 | − | 7.20933i | 0.626009 | − | 0.259302i | −0.0470471 | − | 0.998893i | \(-0.514981\pi\) |
0.673056 | + | 0.739591i | \(0.264981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.07886 | − | 5.07886i | 0.182438 | − | 0.182438i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4688 | + | 11.4688i | 0.411442 | + | 0.411442i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.3531 | − | 46.7225i | −0.693396 | − | 1.67401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.0056 | + | 19.0561i | 1.64621 | + | 0.681882i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.98779i | 0.249723i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.62716i | − | 0.343608i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1235 | − | 13.3060i | −1.14508 | − | 0.474307i | −0.272198 | − | 0.962241i | \(-0.587751\pi\) |
−0.872881 | + | 0.487934i | \(0.837751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.6727 | − | 40.2514i | −0.593563 | − | 1.43299i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2130 | − | 11.2130i | −0.398689 | − | 0.398689i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.6525 | + | 34.6525i | −1.23054 | + | 1.23054i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.43957 | + | 2.66736i | −0.228388 | + | 0.0946015i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.84385 | + | 16.5225i | −0.242422 | + | 0.585258i | −0.997522 | − | 0.0703512i | \(-0.977588\pi\) |
0.755101 | + | 0.655609i | \(0.227588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.2724 | −1.81389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0406932 | −0.00143782 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.42649 | − | 8.27229i | 0.120918 | − | 0.291923i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.50864 | − | 3.11018i | 0.264645 | − | 0.109620i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0253 | − | 18.0253i | 0.634521 | − | 0.634521i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.5558 | − | 10.5558i | −0.371123 | − | 0.371123i | 0.496763 | − | 0.867886i | \(-0.334522\pi\) |
−0.867886 | + | 0.496763i | \(0.834522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.78652 | − | 4.31304i | −0.0627333 | − | 0.151451i | 0.889404 | − | 0.457122i | \(-0.151120\pi\) |
−0.952138 | + | 0.305670i | \(0.901120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.81894 | − | 1.58186i | −0.133936 | − | 0.0554782i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.83121i | − | 0.0991728i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.27601i | − | 0.0796274i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.339914 | + | 0.140797i | 0.0118776 | + | 0.00491985i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.5300 | − | 25.4218i | −0.367501 | − | 0.887225i | −0.994158 | − | 0.107931i | \(-0.965578\pi\) |
0.626658 | − | 0.779295i | \(-0.284422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.1280 | − | 28.1280i | −0.980479 | − | 0.980479i | 0.0193343 | − | 0.999813i | \(-0.493845\pi\) |
−0.999813 | + | 0.0193343i | \(0.993845\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.3163 | + | 21.3163i | −0.742138 | + | 0.742138i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.6219 | − | 6.05658i | 0.508453 | − | 0.210608i | −0.113683 | − | 0.993517i | \(-0.536265\pi\) |
0.622136 | + | 0.782909i | \(0.286265\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7436 | + | 28.3516i | −0.407872 | + | 0.984691i | 0.577824 | + | 0.816161i | \(0.303902\pi\) |
−0.985697 | + | 0.168530i | \(0.946098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.2507 | 0.598419 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.46858 | −0.224123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.05902 | + | 2.55671i | −0.0366490 | + | 0.0884786i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.37881 | + | 3.05640i | −0.255049 | + | 0.105645i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2678 | + | 19.2678i | −0.665199 | + | 0.665199i | −0.956601 | − | 0.291401i | \(-0.905878\pi\) |
0.291401 | + | 0.956601i | \(0.405878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.2378 | + | 19.2378i | 0.663372 | + | 0.663372i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.5448 | − | 44.7710i | −0.638715 | − | 1.54199i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.5156 | − | 5.18414i | −0.430551 | − | 0.178340i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.90528i | − | 0.237268i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 8.89609i | − | 0.305313i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.0513 | + | 9.13394i | 0.755908 | + | 0.313107i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.53470 | − | 13.3619i | −0.189504 | − | 0.457504i | 0.800360 | − | 0.599520i | \(-0.204642\pi\) |
−0.989864 | + | 0.142016i | \(0.954642\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0403999 | − | 0.0403999i | −0.00138165 | − | 0.00138165i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.2115 | + | 16.2115i | −0.553775 | + | 0.553775i | −0.927528 | − | 0.373753i | \(-0.878071\pi\) |
0.373753 | + | 0.927528i | \(0.378071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.6351 | + | 10.6184i | −0.874658 | + | 0.362295i | −0.774423 | − | 0.632669i | \(-0.781960\pi\) |
−0.100235 | + | 0.994964i | \(0.531960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.4936 | − | 47.0617i | 0.664341 | − | 1.60386i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.8195 | 1.38951 | 0.694755 | − | 0.719246i | \(-0.255513\pi\) | ||||
0.694755 | + | 0.719246i | \(0.255513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.12521 | 0.310267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.09454 | + | 17.1277i | −0.240943 | + | 0.581689i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.1625 | + | 18.2927i | −1.49811 | + | 0.620538i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9792 | − | 24.9792i | 0.846389 | − | 0.846389i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0325505 | − | 0.0325505i | −0.00110167 | − | 0.00110167i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.94336 | + | 11.9343i | 0.167116 | + | 0.403454i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.8869 | + | 18.1786i | 1.48196 | + | 0.613846i | 0.969549 | − | 0.244896i | \(-0.0787540\pi\) |
0.512407 | + | 0.858743i | \(0.328754\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 37.8142i | − | 1.27544i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.849166i | 0.0286091i | 0.999898 | + | 0.0143046i | \(0.00455344\pi\) | ||||
−0.999898 | + | 0.0143046i | \(0.995447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.9223 | − | 20.6785i | −1.68002 | − | 0.695886i | −0.680692 | − | 0.732570i | \(-0.738321\pi\) |
−0.999327 | + | 0.0366838i | \(0.988321\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.09574 | + | 2.64534i | 0.0368327 | + | 0.0889221i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.8530 | + | 17.8530i | 0.599446 | + | 0.599446i | 0.940165 | − | 0.340719i | \(-0.110671\pi\) |
−0.340719 | + | 0.940165i | \(0.610671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.42029 | − | 7.42029i | 0.248868 | − | 0.248868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.7109 | − | 12.7209i | 1.02885 | − | 0.426165i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3238 | + | 36.9950i | −0.512792 | + | 1.23799i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5531 | 0.419604 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −64.3400 | −2.14825 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.784527 | − | 1.89402i | 0.0261655 | − | 0.0631690i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.4521 | + | 14.6847i | −1.18108 | + | 0.489220i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.62107 | − | 1.62107i | 0.0539457 | − | 0.0539457i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.82413 | + | 8.82413i | 0.293324 | + | 0.293324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.24679 | − | 10.2527i | −0.141012 | − | 0.340434i | 0.837558 | − | 0.546349i | \(-0.183983\pi\) |
−0.978570 | + | 0.205915i | \(0.933983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.0441276 | − | 0.0182783i | −0.00146362 | − | 0.000606252i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.1022i | − | 0.931067i | −0.885030 | − | 0.465534i | \(-0.845862\pi\) | ||
0.885030 | − | 0.465534i | \(-0.154138\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.51032i | − | 0.116174i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.08185 | + | 2.93340i | 0.234119 | + | 0.0969752i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.26160 | + | 15.1168i | 0.206776 | + | 0.499202i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.17031 | + | 5.17031i | 0.170553 | + | 0.170553i | 0.787222 | − | 0.616669i | \(-0.211518\pi\) |
−0.616669 | + | 0.787222i | \(0.711518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.3169 | − | 26.3169i | 0.867172 | − | 0.867172i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −75.5541 | + | 31.2955i | −2.48689 | + | 1.03011i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.02831 | + | 16.9678i | −0.231089 | + | 0.557899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.190023 | −0.00624116 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6165 | −0.709215 | −0.354608 | − | 0.935015i | \(-0.615386\pi\) | ||||
−0.354608 | + | 0.935015i | \(0.615386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93327 | + | 4.66733i | −0.0633604 | + | 0.152965i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.8848 | − | 14.4498i | 1.14208 | − | 0.473064i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.69664 | − | 7.69664i | 0.251707 | − | 0.251707i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3267 | + | 32.3267i | 1.05607 | + | 1.05607i | 0.998332 | + | 0.0577344i | \(0.0183876\pi\) |
0.0577344 | + | 0.998332i | \(0.481612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1541 | + | 31.7569i | 0.429269 | + | 1.03635i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.9077 | + | 9.90288i | 0.779368 | + | 0.322825i | 0.736660 | − | 0.676263i | \(-0.236402\pi\) |
0.0427073 | + | 0.999088i | \(0.486402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 74.9612i | − | 2.44107i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 6.95390i | − | 0.226210i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.6767 | − | 8.97880i | −0.704399 | − | 0.291772i | 0.00158544 | − | 0.999999i | \(-0.499495\pi\) |
−0.705985 | + | 0.708227i | \(0.749495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.62726 | + | 13.5854i | 0.182669 | + | 0.441001i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.74220 | − | 9.74220i | −0.315912 | − | 0.315912i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00440 | − | 3.00440i | 0.0973222 | − | 0.0973222i | −0.656769 | − | 0.754092i | \(-0.728077\pi\) |
0.754092 | + | 0.656769i | \(0.228077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.34895 | + | 2.21561i | −0.173088 | + | 0.0716954i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.29271 | + | 7.94930i | −0.106438 | + | 0.256965i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.6010 | −0.600657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6569 | −0.924415 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.180210 | − | 0.435066i | 0.00580720 | − | 0.0140198i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.95682 | − | 0.810542i | 0.0629923 | − | 0.0260923i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.1087 | + | 29.1087i | −0.936074 | + | 0.936074i | −0.998076 | − | 0.0620023i | \(-0.980251\pi\) |
0.0620023 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 26.4307 | + | 26.4307i | 0.849075 | + | 0.849075i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.258452 | − | 0.623957i | −0.00829411 | − | 0.0200237i | 0.919678 | − | 0.392673i | \(-0.128450\pi\) |
−0.927972 | + | 0.372649i | \(0.878450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.7690 | − | 10.6739i | −0.826117 | − | 0.342189i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 49.5079i | − | 1.58552i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.1041i | 1.05909i | 0.848281 | + | 0.529546i | \(0.177638\pi\) | ||||
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.59374 | − | 2.31700i | −0.178777 | − | 0.0740518i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0654936 | + | 0.158116i | 0.00209105 | + | 0.00504824i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.49880 | − | 1.49880i | −0.0478044 | − | 0.0478044i | 0.682800 | − | 0.730605i | \(-0.260762\pi\) |
−0.730605 | + | 0.682800i | \(0.760762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.23264 | − | 6.23264i | 0.198588 | − | 0.198588i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −37.2636 | + | 15.4351i | −1.18611 | + | 0.491304i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.29104 | − | 3.11684i | 0.0410526 | − | 0.0991098i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9387 | 0.823970 | 0.411985 | − | 0.911191i | \(-0.364836\pi\) | ||||
0.411985 | + | 0.911191i | \(0.364836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0895 | 0.383649 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.81094 | + | 11.6146i | −0.152517 | + | 0.368209i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.97395 | + | 2.47449i | −0.189197 | + | 0.0783679i | −0.475270 | − | 0.879840i | \(-0.657650\pi\) |
0.286074 | + | 0.958208i | \(0.407650\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4406 | − | 14.4406i | 0.456881 | − | 0.456881i |
(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.129.3 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.e.129.2 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.b.129.3 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.b.129.2 | ✓ | 16 | ||
16.3 | odd | 4 | 1024.2.g.c.641.2 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.h.641.2 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.h.641.3 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.c.641.3 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.c.385.2 | yes | 16 | ||
32.5 | even | 8 | inner | 1024.2.g.e.897.3 | yes | 16 | |
32.11 | odd | 8 | 1024.2.g.b.897.3 | yes | 16 | ||
32.13 | even | 8 | 1024.2.g.h.385.2 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.h.385.3 | yes | 16 | ||
32.21 | even | 8 | 1024.2.g.b.897.2 | yes | 16 | ||
32.27 | odd | 8 | inner | 1024.2.g.e.897.2 | yes | 16 | |
32.29 | even | 8 | 1024.2.g.c.385.3 | yes | 16 | ||
64.5 | even | 16 | 4096.2.a.n.1.5 | 8 | |||
64.27 | odd | 16 | 4096.2.a.n.1.6 | 8 | |||
64.37 | even | 16 | 4096.2.a.o.1.4 | 8 | |||
64.59 | odd | 16 | 4096.2.a.o.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.129.2 | ✓ | 16 | 8.5 | even | 2 | ||
1024.2.g.b.129.3 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.b.897.2 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.b.897.3 | yes | 16 | 32.11 | odd | 8 | ||
1024.2.g.c.385.2 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.c.385.3 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.c.641.2 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.c.641.3 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.e.129.2 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.e.129.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.e.897.2 | yes | 16 | 32.27 | odd | 8 | inner | |
1024.2.g.e.897.3 | yes | 16 | 32.5 | even | 8 | inner | |
1024.2.g.h.385.2 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.h.385.3 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.h.641.2 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.h.641.3 | yes | 16 | 16.11 | odd | 4 | ||
4096.2.a.n.1.5 | 8 | 64.5 | even | 16 | |||
4096.2.a.n.1.6 | 8 | 64.27 | odd | 16 | |||
4096.2.a.o.1.3 | 8 | 64.59 | odd | 16 | |||
4096.2.a.o.1.4 | 8 | 64.37 | even | 16 |